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Heat and Mass Transfer for the Diffusion Driven Desalination Process

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HEAT AND MASS TRANSFER FOR THE DIFFUSION DRIVEN DES ALINATION PROCESS By YI LI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by YI LI

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This dissertation is dedicated with love and gratitude to my family. Without their love, support and faith in me, this accomplishment would not have been possible.

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iv ACKNOWLEDGMENTS My appreciation and respect go to my advisor, Professor J ames Klausner, for introducing me to the field of multiphase flow and for gi ving me the opportunity to study heat and mass transfer dynamics for my Ph.D. dissert ation. His continuous support and patience helped me to achieve this work. I would like to expre ss my special thanks to Professor Renwei Mei for his help and encouragement in m y study of turbulence and numerical analysis. I sincerely thank my committee m embers for their comments and help. I would like to thank all my colleagues, in particular Jess ica Knight and Jun Liao. I also extend my thanks to the individuals in the departmen t who have helped me in one way or another during my graduate studies. I would like to acknowledge the support of the U.S. Departme nt of Energy under Award No. DE-FG26-02NT41537 for this research. I also thank the University of Florida for the financial assistance through the UF Alumni Fell owship I was awarded for the academic years 2003-2006. Finally, I would like to thank my family for their contin uous support and encouragement through the years of my studies. To them, I dedicate this dissertation.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................... ................................................... .......iv LIST OF TABLES..................................... ................................................... ...............viii LIST OF FIGURES.................................... ................................................... .................ix NOMENCLATURE....................................... ................................................... ...........xiii ABSTRACT........................................... ................................................... ...................xvi CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW................ ..................................1 Description of Thermal Desalting and Membrane Separation. ..................................2 Description of HDH and MEH Process................... ..................................................4 Description of DDD Process.......................... ................................................... ........6 Comparison of the DDD Process with HDH and MEH....... ......................................8 Comparison of the DDD Process with MSF and RO...............................................10 Potential Applications for the DDD Process............ ...............................................12 Properties of Saline Water........................... ................................................... ........17 Objectives of the Study................................ ................................................... ........21 Scope of Work........................................ ................................................... .............21 2 THERMODYNAMIC ANALYSIS OF THE DDD PROCESS......... ......................23 Mathematic Model.................................... ................................................... ..........23 Computation Results and Analysis...................... ................................................... .26 3 EXPERIMENTAL STUDY................................ ................................................... .35 Experimental System Description...................... ................................................... ..35 Experimental Facility and Instrumentation.............. ................................................38 4 HEAT AND MASS TRANSFER FOR THE DIFFUSION TOWER.... ...................48 Heat and Mass Transfer Model for the Diffusion Tower. ........................................48 Model Comparison with Experiments for the Diffusion To wer...............................57 Pressure Drop through the Packing Material............. ..............................................60

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vi Optimization of the Packing Material................. ................................................... .61 5 HEAT AND MASS TRANSFER FOR THE DIRECT CONTACT COND ENSER73 Mathematical Model of the Packed Bed Direct Contact Conde nser.........................75 Model Comparison with Experiments for the Packed Bed Dire ct Contact Condenser........................................... ................................................... ............82 Wetting Phenomena within Packed Bed...................... ............................................87 Experimental Results of the Droplet Direct Contact Co ndenser..............................90 Condenser Effectiveness.............................. ................................................... ........95 6 DDD PROCESS OPTIMIZATION DESIGN AND ECONOMIC ANALY SIS.......98 Mathematical Model.................................. ................................................... ..........99 Computation Results and Analysis...................... ..................................................101 Economic Analysis.................................. ................................................... ..........111 7 CONCLUSIONS....................................... ................................................... ........119 APPENDIX A ONDAS CORRELATION............................... ................................................... 122 B EXPERIMENTAL DATA OF THE DIFFUSION TOWER......... .........................123 C EXPERIMENTAL DATA OF THE AIR SIDE PRESSURE DROP T HROUGH THE PACKING MATERIAL............................... ...............................................125 D EXPERIMENTAL DATA OF THE COUNTERCURRENT FLOW DIRE CT CONTACT CONDENSER STAGE WITH PACKED BED............ .....................126 E EXPERIMENTAL DATA OF THE CO-CURRENT FLOW DIRECT C ONTACT CONDENSER STAGE WITH PACKED BED.................... ................................128 F EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT CONDENSERS WITH CO-CURRENT AND COUNTERCURRENT FLOW. ....129 G EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT CONDENSER STAGE WITH COUNTERCURRENT FLOW........... ..................132 H UNCERTAINTY ANALYSIS OF THE FLUID PROPERTIES..... ......................133 Theory of Uncertainty.............................. ................................................... .........133 Uncertainty of the Calculated Fluid Properties........ ..............................................134 Uncertainty of the Mass and Heat Transfer Coefficien ts.......................................141 Results and Analysis................................. ................................................... .........144 LIST OF REFERENCES................................. ................................................... .........151

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vii BIOGRAPHICAL SKETCH................................ ................................................... ....155

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viii LIST OF TABLES Table page 1-1 Pumping and heating energy consumption of some desalinat ion processes.............4 1-2 Comparison of electricity consumption for DDD, MSF and RO desalination technologies....................................... ................................................... ...............10 1-3 Comparison of advantages and disadvantages of DDD, RO and MSF desalination technologies............................ ................................................... .......11 4-1 Packing material configurations...................... ................................................... ..63 6-1 Summary of direct costs......................... ................................................... .........114 6-2 Details of cost calculations.................... ................................................... ..........114

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ix LIST OF FIGURES Figure page 1-1 Schematic diagram of mechanical vapor compression proc ess ...... .........................2 1-2 Schematic diagram of thermal vapor compression combine d multi-effect destillation process ..... ............................................................................................3 1-3 Schematic diagram for diffusion driven desalination pro cess..................................7 1-4 Depth to saline ground water in the United States [18].... .....................................13 1-5 Flow diagram of DDD process driven by solar energy.... ......................................14 1-6 Flow diagram of DDD process driven by geothermal energ y................................15 2-1 Flow diagram for diffusion driven desalination process .......................................23 2-2 Rate of entropy generation for different exit brine temperature, T h =27 C.............27 2-3 Variation of exit brine temperature with exit air tem perature, T h =27 C................28 2-4 Fresh water production efficiency, T h =27 C................................................. .......28 2-5 Rate of entropy generation for different exit brine temperature: a) T h =50 C, b) T h =80 C................................................. ................................................... ..........29 2-6 Variation of exit brine temperature with exit air tem perature: a) T h =50 C, b) T h =80 C................................................. ................................................... ..........30 2-7 Fresh water production efficiency: a) T h =50 C, b) T h =80 C..............................32 2-8 Rate of energy consumption: a) T h =50 C, b) T h =80 C........................................33 2-9 Minimum rate of energy consumption for different T h ..........................................34 3-1 Pictorial view of the laboratory scale DDD experime nt........................................36 3-2 Schematic diagram of laboratory scale DDD facilit y............................................37 3-3 Schematic diagram of experimental diffusion tower. ............................................39

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x 3-4 Schematic diagram of experimental direct contact condenser...............................40 3-5 Pictorial view of spray nozzle..................... ................................................... .......41 3-6 Pictorial view of packing matrix..................... ................................................... ...42 3-7 Schematic diagram of the instrumentation system fo r the DDD experiment..........42 3-8 Example program of SoftWIRE...................... ................................................... ...44 3-9 Main panel of the DDD data acquisition program...... .......................................45 3-10 Schematic view panels of the DDD data acquisition program............................46 3-11 Histogram view panels of the DDD data acquisition pro gram..........................46 4-1 Diagram of diffusion tower........................ ................................................... .......49 4-2 Differential control volume for liquid/vapor heat a nd mass transfer within diffusion tower.................................... ................................................... ..............50 4-3 Comparison of predicted exit conditions with the data of Huang [33]: a) L = 2.0 kg/m 2 -s, b) L = 4.1 kg/m 2 -s................................................. .................................56 4-4 Comparison of predicted exit conditions with the expe rimental data for different liquid mass fluxes: a) L= 1.75 kg/m 2 -s, b) L= 1.3 kg/m 2 -s, c) L= 0.9 kg/m 2 -s.......58 4-5 Air specific pressure drop variation with air mass f lux for different water mass fluxes............................................. ................................................... ...................60 4-6 Energy consumption rate for fresh water production: Berl Saddle a) 0.5, b) 0.75, c) 1.0, d) 1.5; Raschig Ring e) 0.5, h) 1.0, g) 1.5 h) 2.0................64 4-7 Maximum possible exit humidity for feed water mass fl ux...................................67 4-8 Gas mass transfer coefficient for air mass flux.. ................................................... .68 4-9 Gas pressure drop for air mass flux................. ................................................... ...69 4-10 Required tower height for feed water mass flux..... ..............................................70 4-11 Energy consumption rate for feed water mass flux... .............................................71 4-12 Energy consumption rate for fresh water mass flow rate (cross section diameter of the packed bed is 15 m)............................... ................................................... ..71 5-1 Differential control volume for liquid/gas heat and mass transfer within a) countercurrent flow, b) co-current flow condensers..... .........................................77

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xi 5-2 Flow diagram for the countercurrent flow computation. .......................................82 5-3 Comparison of predicted exit temperatures and humidity with the experimental data for countercurrent flow: a) T a,in =36.9 C, b) T a,in =40.8 C, c) T a,in =42.8 C...83 5-4 Comparison of predicted exit temperatures and humidity with the experimental data for co-current flow: a) T a,in =35.5 C, b) T a,in =39.6 C, c) T a,in =42.9 C.........85 5-5 Droplet residence positions on the packing material: a ) on the top, b) in the corner, c) beneath the packing...................... ................................................... .....87 5-6 Observation of the liquid blockages within the packed bed: a ) side view, b) Top view................................................ ................................................... ..................89 5-7 Total temperature drop of the air/vapor mixture with v arying water to air mass flow ratios and different air inlet temperatures (witho ut packing).........................91 5-8 Total fresh water production rate with varying water to air mass flow ratios and different air inlet temperatures (without packing)........ .........................................91 5-9 Temperature drop of the air/vapor mixture with varying w ater to air mass flow ratios in the a) co-current, b) countercurrent stage (w ithout packing)....................92 5-10 Fresh water production rate with varying water to air m ass flow ratios and different air inlet temperatures in the a) co-current, b) countercurrent stage (without packing)..................................... ................................................... .........93 5-11 Comparison of the packed bed condenser effectiveness b etween co-current and countercurrent flow.................................. ................................................... .........96 5-12 Comparison of the countercurrent flow condensation e ffectiveness between droplet condenser and packed bed condenser................... .....................................97 6-1 Required diffusion tower height with variations in air to feed water mass flow ratio.............................................. ................................................... ..................101 6-2 Maximum exit humidity ratio variation with air to feed water mass flow ratio....102 6-3 Exit air temperature variation with air to feed water mass flow ratio...................103 6-4 Water side pressure drop variation with air to feed wa ter mass flow ratio...........103 6-5 Air/vapor side pressure drop variation with air to fee d water mass flow ratio.....104 6-6 Temperature and humidity ratio profiles through the co ndenser..........................105 6-7 Condenser temperature and humidity ratio variation w ith fresh water to air mass flow ratio......................................... ................................................... ...............106

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xii 6-8 Required direct contact condenser height with variat ions in air mass flux..........106 6-9 Condenser fresh water exit temperature variation wit h air mass flux...................107 6-10 Variation of the fresh water production efficiency w ith air mass flux.................108 6-11 Variation of the energy consumption with air to fe ed water mass flow ratio in diffusion tower.................................... ................................................... ............108 6-12 Variation of the energy consumption with air mass flux in condenser.................109 6-13 Variation of the total energy consumption rate with air mass flux.......................110 6-14 Net fresh water profit variation with electricit y retail price for different fresh water retail price.................................. ................................................... ...........115 6-15 Percent increase in profit with electricity profit for different fresh water profit...116 6-16 Water price in different countries for year 2001 & 2002.. ...................................117 H-1 Variation of the relative uncertainties of the ca lculated water properties with water temperature.................................... ................................................... ........145 H-2 Variation of the relative uncertainties of the ca lculated vapor properties with air temperature.......................................... ................................................... ...........145 H-3 Variation of the relative uncertainties of the ca lculated air properties with air temperature.......................................... ................................................... ...........146 H-4 Variation of the relative uncertainties of the ca lculated air/vapor mixture properties with air temperature........................ ................................................... 146 H-5 Variation of the relative uncertainties of the we tted area and mass transfer coefficients with temperature by using Ondas correlation. .................................148 H-6 Variation of the relative uncertainties of the he at transfer coefficients with temperature.......................................... ................................................... ...........149

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xiii NOMENCLATURE A control surface area (m 2 ) a specific area of packing material (m 2 /m 3 ) ai amortization factor (yr –1 ) Cp specific heat (kJ/kg) D molecular diffusion coefficient (m 2 /s) DC direct capital cost ($) d diameter (m) d p diameter of the packing material (m) f plant availability G air mass flux (kg/m 2 -s) g gravitational acceleration (m/s 2 ) H diffusion tower height (m) h enthalpy (kJ/kg) h fg latent heat of vaporization (kJ/kg) i interest rate k mass transfer coefficient (m/s) L water mass flux (kg/m 2 -s) l channel half width (m) M v vapor molecular weight (kg/kmol) m mass flow rate (kg/s)

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xiv n plant life (yr) P pressure (Pa or kPa) Pw electrical power consumption for pumps (W, kW or MW) Q retail price ($) R universal gas constant (kJ/kmol-K) s entropy generation rate in the diffusion tower (kW/ K) T temperature ( C or K) U heat transfer coefficient (W/m 2 -K) v air/vapor velocity (m/s) V control volume (m 3 ) V G air/vapor volumetric flow rate (m 3 /s) economic increase rate specific cost of operating labor ($/m 3 ) condensation effectiveness dynamic viscosity (kg/m-s) density (kg/m 3 ) L surface tension of liquid (N/m) C critical surface tension of the packing material (N/ m) w humidity ratio relative humidity profit ($) Subscripts a air

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xv c centerline elec electricity evap the portion of liquid evaporated f fresh water fixed fixed cost G air/vapor mixture GA gas side parameter based on the specific area of pac king h high i interface in inlet parameter L liquid phase LA liquid side parameter based on the specific area of packing Labor labor cost low low LW liquid side parameter based on the specific wet area of packing out exit parameter sat saturate state unit, p unit amount in terms of production v vapor phase sink sink temperature x local value of variable in transverse direction (all the temperatures are bulk temperatures unless denoted by subscript x) z fluid flow direction

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xvi Abstract of Dissertation Presented to the Graduate Schoo l of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy HEAT AND MASS TRANSFER FOR THE DIFFUSION DRIVEN DES ALINATION PROCESS By Yi Li May 2006 Chair: James F. Klausner Major Department: Mechanical and Aerospace Engineering This research concerns a diffusion driven desalination (DDD) process in which warm water is evaporated into a low humidity air stream, and the vapor is condensed out to produce distilled water. Although the process h as a low fresh water to feed water conversion efficiency, it has been demonstr ated that this process can potentially produce inexpensive distilled water when driven by low-grade energy such as waste heat. A dynamic analysis of heat and mass transf er demonstrates that the DDD process can yield a fresh water production of 1.14 million gal/day by utilizing waste heat from a 100 MW steam generating power plant based on a condens ing steam pressure of only 10.159 kPa in the main condenser. The optimal operatin g condition for the DDD process with a high temperature of 50 C and sink temperature of 25 C has an air mass flux of 1.5 kg/m 2 -s, air to feed water mass flow ratio of 1 in the diff usion tower, and a fresh water to air mass flow ratio of 2 in the direct contact condenser. Operating at these conditions yields a fresh water production efficiency (m f /m L ) of 0.035 and electric energy

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xvii consumption rate of 0.0022 kW-hr/kg fw This dissertation describes the research progress made in the development and analysis of the DDD process Throughout the past three years, the main focus of the desalination process has be en on the heat and mass transport phenomena in the diffusion tower and direct contact c ondenser within the packed bed. Detailed analyses required to size and analyze these hea t and mass transfer devices have been developed. A laboratory scale experimental DDD fac ility has been fabricated. Temperature and humidity data have been collected over a range of flow and thermal conditions for the diffusion tower and direct contac t condenser. The analyses agree quite well with the current data. The condensation effectivene ss of the direct contact condenser with and without packed bed has been compared. It has been experimentally observed that the fresh water production rate is significantly e nhanced when packing is added to the condenser. It has also been observed that the con densation effectiveness increases considerably when air and water flow configuration is coun tercurrent. Recently, it has been recognized that the heat and mass transfer within t he packed bed can be significantly diminished with water blockages. High-speed c inematography has been used to observe the liquid formation on the packing materi al. The cause of this phenomenon is addressed. Further experimental and analytica l analyses are required to evaluate its influence on the heat and mass transfer coe fficients for liquid and air flow within the packed bed.

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1 CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW Water is not only indispensable to life, industrial devel opment, economic growth, preservation of natural resources and social well-being, but sufficient drinking water resources are necessary for the development of humanit y. Adequate water supply has historically been the foundation for the growth of civil izations. Between 1900 and 1995, drinking water demand has grown twice as fast as the wor ld population. By 2025, this demand is expected to grow another 40% [1]. In fifty years, it is expected that without further technological developments, forty countries will lack adequate drinking water. In many parts of the world the discrepancy between freshwa ter needs and available supply has already limited further development, and has even j eopardized survival. Growing pollution in many regions is causing water shortages wher e such problems were inconceivable just a few decades ago. Due to economic and soc ial development, the growth of water demand never ceases. It is estimated th at fresh water shortages affect the lives of hundreds of millions of people on a daily basis w orldwide. Fresh water shortages limit food production and lead to destitution and poverty. When fresh water resources dry up, the affected populations have no choice but disappearance or exodus. One obvious solution to alleviate the fresh water shorta ges is seawater desalination. Desalination technologies are currently used throughout t he world and have been under development for the past century

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2 Description of Thermal Desalting and Membrane Separation The most common ways to desalt seawater involve some f orm of boiling or evaporation. In a simple still, seawater can be boil ed releasing steam which, when condensed, forms pure water. Many stills can be connected t ogether making the process more efficient. To achieve this, each still, or effec t, must be at different pressure. This is because in a vacuum, water can boil or flash at much lower temperatures. Multiple Effect Distillation (MED) and Multi-Stage Flash desalination ( MSF) makes use of this phenomenon. Other thermal processes include a variation of the simp le still such as vapor compression (VC). The vapor compression (VC) distillati on process is generally used for small and medium scale seawater desalting units. The he at for evaporating the water comes from the compression of vapor rather than the d irect exchange of heat from steam produced in a boiler. The two primary methods used to creat e a vacuum and compress the vapor are mechanical compression and steam jet. Fig. 1-1 s hows a schematic diagram of the mechanical vapor compression desalination process. Figure 1-1 Schematic diagram of mechanical vapor compression process [2]

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3 The mechanical compressor creates a vacuum in the liquid v essel and then compresses the evaporated vapor from the vessel. The c ompressed vapor condenses inside a tube bundle and gives up heat to the liquid side in the vessel. Seawater is sprayed on the outside of the heated tube bundle where it evapor ates completing the cycle. With a steam jet type VC unit, also called a thermocompressor, a venturi orifice on the steam jet eductor produces a vacuum and extracts evaporated water vapor from the main vessel. The extracted water vapor is compressed by the steam jet within the diverging portion of the eductor. This mixture is condensed in the tube bundle t o provide the thermal energy (heat of condensation) to evaporate the seawater spra yed over the outside of the tube bundle. A simplified schematic diagram of the thermal vapor compression combined multi-effect desalination process is shown in Fig. 1-2. Figure 1-2 Schematic diagram of thermal vapor compression co mbined multi-effect destillation process [2] Semi-permeable and ion specific membranes can also be us ed to desalt seawater. Membrane processes are based on separation rather than distillation. Reverse osmosis membranes basically let water pass through them but rejec t the passage of salt ions. In reality a small percentage, approximately 1%, of sea salt s pass through the membranes, or

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4 leak around the seals. For potable water this leakage is a cceptable, but for industrial purposes it may require further treatment. The operationa l pressure of reverse osmosis systems is a function of the salinity of the feed wat er. The salinity results in a colligative property known as osmotic pressure. The osmotic pressure o f brackish water is much lower than that of seawater. Typical 500 ppm potable water has an osmotic pressure of 0.2 MPa while normal seawater is close to 2.5 MPa. Another type of membrane separation process is ElectroDialysis Reversal (EDR). It makes use of ion specific membranes, which are arra yed between anodes and cathodes to drive salt ions in controlled migrations to the electr odes. While not as widespread as RO, it is still commonly used. RO is by far the most widely used separation process and has tremendous energy advantages over other thermal processes when 1% salt passa ge can be tolerated, and good quality seawater is available. Table 1-1 shows the pumping a nd heating energy consumption of some commonly used desalination processes [ 3]. Table 1-1 Pumping and heating energy consumption of some desa lination processes Energy Consumption (kW-hr/kg fw ) Technology Unit Capacity (10 6 kg/day) Electrical/Mechanical Thermal MSF 60 0.004 0.006 0.008-0.018 MEB 60 0.002 0.0025 0.0025-0.01 MED-VC 24 0.007 0.009 NA RO 24 0.005 0.007 NA Description of HDH and MEH Process A desalination technology that has drawn interest over the past two decades is referred to as Humidification Dehumidification (HDH). This process operates on the principle of mass diffusion and utilizes dry air to evapor ate saline water, thus humidifying the air. Fresh water is produced by condensing out the water vapor, which

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5 results in dehumidification of the air. A significant advantage of this type of technology is that it provides a means for low pressure, low temperat ure desalination and can operate off of waste heat, which is potentially very cost competi tive. Bourouni et al. [4], AlHallaj et al. [5], and Assouad and Lavan [6] respectively r eported on the operation of HDH units in Tunisia, Jordan, and Egypt. Muller-Holst et al [7] fabricated an experimental Multi-Effect Humidification (MEH) facil ity driven by solar energy and considered its performance over a wide range of operating conditions. The fresh water production varied on a seasonal basis since the process is driven by solar energy. The average fresh water production was about 52 gal/day with a maximum of 90 gal/day in May and a minimum of 14 gal/day in January. A computer simu lation of the operational performance of the process was developed, and the predicted behavior agreed well with the actual behavior. An excellent comprehensive review of the HDH process is provided by Al-Hallaj and Selman [8]. It was concluded that although the HDH process operates off of low-grade energy, it is not currently cost compe titive with reverse osmosis (RO) and mult-istage flash evaporation (MSF). There are thr ee primary reasons for the higher costs associated with the HDH process: 1. The HDH process is typically applied to low production r ates and economies of scale cannot be realized in construction. 2. Typically natural draft is relied upon, which results in low heat and mass transfer coefficients and a larger surface area humidifier. 3. Film condensation over tubes is typically used, which is extremely inefficient when non-condensable gases are present. Thus a much larger conde nser area is required for a given production rate, and the condenser accounts for the majority of the capital cost. Therefore, an economically feasible diffusion driven distillation process must overcome these shortcomings. Klausner et al. [9] have reported on a diffusion driven

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6 desalination (DDD) process that overcomes these shortc omings, resulting in an economically viable desalination process applied on a large scale (>1 million gal/day). Another type of desalination technology that makes use of water evaporating into an air stream is the Carrier-Gas Process (CGP) repor ted by Larson et al. [10]. This process has been further refined by Beckman [11, 12]. The CG P is designed to operate with a feed water temperature range of 55 – 88 C. Beckman demonstrates (based on 88 C feed water) that the CGP can produce fresh water with an operating cost of 3.35 $/10 3 gal using natural gas for heating and 1.52 $/10 3 gal when waste heat is used as the thermal source. The capital cost is apparently low, appr oximately $1397 for a 1000 gal/day facility. Description of DDD Process A simplified schematic diagram of the DDD process and sy stem, designed to be operated off of waste heat discharged from thermoelectri c power plants, is shown in Fig. 1-3. The process includes three main fluid circulation sy stems denoted as feed water, air/vapor, and freshwater. In the feed water system, a low pressure condensing steam from an adjacent power plant heats the feed water in the main feed water heater (a). The main feed water heater is typically a main condenser w hen used in conjunction with thermoelectric power plants. Because the required feed wat er exit temperature from the heater can be relatively low for the DDD process, the required heat input can be provided by a variety of sources such as low pressure condensing ste am in a power plant, exhaust from a combustion engine, waste heat from an oil ref inery, low grade geothermal energy, or other waste heat sources. The heated feed water then is sprayed into the top of the diffusion tower (b). A portion of feed water will eva porate and diffuse rapidly into the

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7 air. Evaporation in the tower is driven by a concentrat ion gradient at the liquid/vapor interface and bulk air, as dictated by Fick’s law. Via gravity, the water falls downward through a packed bed in the tower that is composed of very high surface area packing material. A thin film of feed water will form over th e packing material and contact the upward flowing air through the diffusion tower. The diffusio n tower should be designed so that the air/vapor mixture leaving it should be fully saturated. The purpose of heating the water prior to entering the diffusion tower is tha t the rate of evaporation and the exit humidity ratio increase with increasing temperature, thus yielding greater water vapor production. The water, not evaporated in the diffusion to wer will be collected at the bottom and discharged or re-circulated. Main Feed Water Heater (a) Main Feed Pump Seawater Reservoir Fresh Water Pump Water Cooler (d) Cooler Pump Diffusion Tower (b) Direct Contact Condenser (c) Exhaust Fresh Water Production Fresh Water Storage Tank Low Pressure Steam Seawater Air/Vapor Fresh Water Forced Draft Blower Power Plant Figure 1-3 Schematic diagram for diffusion driven desalinati on process

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8 In the air/vapor system, low humidity cold air is pumpe d into the bottom of the diffusion tower, and flows upward to be heated and humidif ied by the feed water. As mentioned before, the air/vapor mixture leaving the diffusi on tower is saturated and drawn into the direct contact condenser (c), where it is cooled and dehumidified by the fresh water in the condenser. The air could be directed back to the diffusion tower and used repeatedly. The condenser is another important compon ent of the DDD process because film condensation heat transfer is tremendousl y degraded in the presence of noncondensable gas. In order to overcome this problem Bharatha n et al. [13] describe the use of direct-contact heat exchangers. The direct contac t condenser approach is best suited for the DDD process. In the fresh water system, the cold fresh water will gain heat and mass due to air side vapor condensation in the condenser. After dischar ging from the direct contact condenser, it will be cooled in a conventional shell-an d-tube heat exchanger (d) by the incoming feed water. Here, the intake feed water flow is preheated by the heat removed from the fresh water, which helps to reduce the amount o f energy needed in the main feed water heater. Finally, a portion of the cooled fresh w ater will be directed back to the direct contact condenser to condense the water vapor fr om the air/vapor mixture discharging from the diffusion tower. The remaining f resh water is production. Comparison of the DDD Process with HDH and MEH The DDD process has following advantages compared with H DH and MEH: 1. The DDD process utilizes thermal stratification in t he seawater to provide improved performance. In fact, the DDD process can produce fresh water without any heating by utilizing the seawater thermal stratificat ion. 2. The thermal energy required for the DDD process may be entirely driven by waste heat, therefore eliminating the need for additional heat ing sources. This helps keep the DDD plant compact, which translates to reduced cost. The DDD process

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9 recommends using whatever heat source is best suited for t he region requiring fresh water production. The DDD process is very well suited to be integrated with steam power plants, and use the waste heat coming from these pl ants. Renewable resources such as solar heating, wind power and geothermal energy may be used as well. 3. In the DDD process the evaporation occurs in a forced dr aft packed bed diffusion tower as opposed to a natural draft humidifier. The dif fusion tower is packed with low pressure drop, high surface area packing material, which provides significantly greater surface area. This is very important because the rate of water evaporation is largely influenced by the liquid/vapor contact area availabl e. In addition, the forced draft provides for high heat and mass transfer coeffici ents. Thus, a diffusion tower is capable of high production rates in a very compact unit. Since the unit is compact, the capital cost will be minimized. The pric e paid in using forced draft is the pumping power required to pump the fluids through the system but the projected cost is low, thus providing potential for an econo mically competitive desalination technology. 4. The DDD process uses a direct contact condenser to extra ct fresh water from the air/vapor mixture. This type of condenser is significantl y more efficient than a conventional tube condenser, as is used with the HDH pro cess. Thus, the condenser will be considerably more compact for a given design produc tion rate. This also adds to cost reduction. 5. The diffusion tower and direct contact condenser can a ccommodate very large flow rates, and thus economies of scale can be taken advanta ge of to produce large production rates. 6. No exotic components are required to manufacture a DDD pla nt. All of the components required to fabricate a DDD plant are manufa ctured in bulk and are readily available from different suppliers. This facet of production also translates to reduced cost. The advantages of the DDD process compared with HDH and ME H are obvious. However, since the fraction of feed water converted t o fresh water using the DDD process is largely dependent on the difference in high and l ow temperatures in the system, when driving the process using waste heat, this tem perature difference will be moderate. Thus the fraction of feed water converted to f resh water will be low. A large amount of water and air must be pumped through the facility to accomplish a sizable fresh water production rate. This disadvantage is an inher ent characteristic of the DDD

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10 process. However, as long as the production cost of fresh water using the DDD process is cost competitive, it is a tolerable characteristic. Comparison of the DDD process with MSF and RO Table 1-2 below compares the energy consumption of the DD D process with reverse osmosis (RO) and multi-stage flash (MSF). It is readily observed that the thermal energy consumption for DDD is very high. This is to be expected because the DDD process is driven by low thermodynamic availability ene rgy. However, because the waste heat can be considered a free resource, the total energy required to drive the DDD process is quite competitive. Fresh water production using the DDD process has potential to be very inexpensive and comparative when driven by waste he at that would have otherwise been discarded. Therefore, to determine whether or not the technology is cost competitive, greater attention should be paid to the elect ric energy consumption. Table 1-2 Comparison of electricity consumption for DDD, MSF, and RO desalination technologies Energy Consumption (kW-hr/kg fw ) Technology Electrical/Mechanical Thermal Total DDD 0.002-0.0053 0.75 (free) 0.002 – 0.0053 MSF 0.004 0.006 0.008-0.018 0.012 – 0.024 RO 0.005 0.007 NA 0.005 – 0.007 A comparison of the advantages and disadvantages of the DDD, RO, and MSF processes is shown in Table 1-3. The DDD process is esse ntially a thermal distillation process that operates using waste heat. It therefore ha s all of the same operational advantages as MSF. In contrast to MSF, the DDD process has very low energy consumption and thus a low operating cost. The main disa dvantage of the DDD process is that the conversion efficiency is low, typically 5-10%. Despite the low conversion efficiency, the energy consumption is still low since pu mping occurs at low pressure.

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11 Table 1-3 Comparison of advantages and disadvantages of DDD RO, and MSF desalination technologies. Process Advantage Disadvantage DDD Low energy consumption and low cost of water production Waste heat utilized Low salinity concentration discharge, minimal environmental impact Low maintenance cost Lower conversion efficiency RO Feed water doesn’t require heating Lower energy requirements Removal of unwanted contaminants such as particles and bacteria High maintenance cost Performance degrades with time High salinity concentration discharge, environmental impact High cost of filer replacement MSF Large production rates and economies of scale Continuous operation without shutting down Large energy consumption High cost of water production However, the low conversion efficiency provides an enviro nmental advantage for the DDD process over RO and MSF. That is the salinity discharge concentration in the brine is comparatively very low. This environmental advant age is a very important issue within North America, Europe, and Japan. For example, th e city of Tampa, Florida recently constructed a 25 million gal/day RO desalination facility. But since its first days of construction there has been growing criticism from e nvironmental groups because of the high salinity discharge concentration into Tampa B ay [14]. Although nearly 5 billion gallons of drinking water has been produced since March 2003, t he plant has run sporadically, producing far short of its intended output, be cause the pretreatment process of the plant isn’t rigorous enough to filter out the sus pended particles from the intake seawater from Tampa Bay. Without significant modificat ion, the plant is too expensive to

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12 operate. Three of the companies involved in the project h ave filed for bankruptcy. The plant was taken off-line in June 2005 for repair, and it is scheduled to resume operations in the fall 2006 [15]. Potential Applications for the DDD Process The attractive feature of the DDD process is that it can operate at low temperatures so that it requires an energy input with low thermodynam ic availability. This is important because the process can be driven by waste heat that wo uld otherwise not be suitable for doing useful work or driving some other distillation process ( such as flash distillation). A very interesting application for the DDD process is to operate in conjunction with an existing process that produces large amounts of waste heat and is located in the vicinity of an ocean or sea. One such potential benefactor of th e DDD process is the electric utility industry. Conventional steam driven power plants dump a considerable amount of energy to the environment via cooling water that is used to c ondense low pressure steam within the main condenser. Typically this cooling water is either discharged back to its original source or it is sent to a cooling tower, where the thermal energy is discharged to the atmosphere. Instead of dumping the thermal energy to the environment, the DDD process provides a means for putting the discarded thermal energy to work to produce fresh water. Of course this application is limited to p ower producing facilities sited along the coastline. However, this should not be a significan t limitation. Bullard and Klausner [16] studied the geographical distribution of fossil fired powe r plants built in the United States from 1970 to 1984. In their study they found that the tw o most significant attributes for siting a new fossil fired plant in a gi ven geographical region are 1) proximity to a large body of water and 2) proximity to a la rge population base. The demographic make-up of the United States as well as other indu strialized nations is such

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13 that major population centers reside along the coastline. Thus, the DDD process appears to be well suited for the power generation infrastructure in the United States. Another potential application for the DDD process is f or fresh water production in the range of 1000-10000 gal/day. It is envisioned that the potential customers that can benefit from this application include single users such as small business entities, agricultural entities and small or middle size residency communities whose locations are such that they have access to saline ground water, seawat er or a geothermal reservoir. The extent of saline ground water resources in the United States are substantial, although little is known about the hydrogeology about most aquifers that contain saline ground water, since most efforts have focused on characterizing fresh water aquifers [17]. Fig. 14 below shows the depth of many saline ground water resour ces known in the U.S. This map illustrates the fact that there is a substantial po pulation that can benefit from the successful development of the DDD process. Depth to saline ground water (feet) Less than 500 500 1000 More than 1000 Inadequate information Figure 1-4 Depth to saline ground water in the United States [ 18]

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14 The fresh water conversion efficiency, defined as the ra tio of the fresh water output to the feed water input, is low for the DDD process. The refore, the process is best suited for applications using low-grade heat. One such resource is solar heating, which is abundantly available in the Southeast and Western Unite d States. Figure 1-5 shows a simple flow diagram for the DDD process coupled with so lar collectors. In this process the feed water will be drawn from saline ground water or seawater, and then heated by a solar thermal heating system. The electrical power re quired to drive the pumps and blowers can be driven by either a solar electric panel o r a wind turbine. In order to make efficient use of the thermal energy, the feed water i s preheated in the chiller using the discharge heat from the direct contact condenser. Diffusion Tower (b) Fresh Water Chiller (d) Sea Water Direct Contact Condenser (c) Solar Heating System (a) Fresh Water Out Warm Fresh Water Cool Fresh Water Wet Air Dry Air Feed Water (1) (2) (3) (4) (7) (5) (6) Warm Drain Feed Water Sea Water Preheater (e) Cool Drain Figure 1-5 Flow diagram of DDD process driven by solar energy Many investigations [19] show that solar heating is a matur e technology and is already being widely used in the United States. In 1897 30% of t he homes in Pasadena, just east of Los Angeles, were equipped with solar water heaters. As mechanical improvements were made, solar systems entered use in A rizona, Florida and many other sunny regions of the United States. By 1920, tens of thousands of solar water heaters had been sold. Today there are more than half a million s olar water heaters in California

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15 alone. They are used for heating water inside homes and businesses as well as for heating swimming pools. It is interesting to note that the commu nities that have a high rate of solar heater installations also have access to seawat er or saline ground water and suffer from fresh water shortages. Another interesting facet of renewable energy resources is that wind energy is abundantly available along the coastline of the United St ates. Therefore, it will be of interest to explore the combination of solar energy col lectors providing the thermal source and wind energy turbines providing the electrical sourc e for the DDD process. Some special geographic regions, such as islands, have ac cess to seawater or saline ground water, have substantial solar resources available, h ave sufficient wind power, and have middle sized residency communities that can benefi t from the solar/wind combined DDD system. Diffusion Tower (b) Air Cooling Tower (d) Geothermal Water Reservoir Direct Contact Condenser (c) Pre-treatment Equipment (a) Fresh Water Out Warm Fresh Water Cool Fresh Water Wet Air Dry Air Hot Feed Water (1) (2) (3) (4) (7) (5) (6) Cold Drain Heat Exchanger (e) Warm Drain Figure 1-6 Flow diagram of DDD process driven by geothermal energy Because the DDD process can operate off of low-grade the rmal energy, one interesting potential application is the demineralization of geothermal water in shallower reservoirs or the demineralization of the discharge wa ter from geothermal power plants.

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16 Geothermal resources are most abundant in the Western U nited States. The west coast boundary between the North American and Pacific plates is "sliding" along the San Andreas fault (many earthquakes but few volcanoes) from t he Gulf of California up to northern California and sub-ducting from the Cascade volc anoes north through the Aleutians. There are also volcanic hot spots under Yellows tone and Hawaii and intraplate extensions with hot springs in the Great Basin. T he history data of EIA [20] show that California generates the most geothermal electrici ty with about 824 MW at the Geysers (much less than its capacity, but still the wo rld's largest developed field and one of the most successful renewable energy projects in hist ory), 490 MW in the Imperial Valley, 260 MW at Coso, and 59 MW at smaller plants. Ther e are also power plants in Nevada (196 MW), Utah (31 MW), and Hawaii (25 MW). Due to environmental advantages and low capital and operating costs, direct use of geothermal energy has skyrocketed to 3858 GW-hr/yr, including 300,000 geothermal heat pumps. In the Western United States, hundreds of buildings are heated indi vidually and through district heating projects (Klamath Falls, Oregon; Boise, Idaho; S an Bernardino, California; and soon Mammoth Lakes and Bridgeport, California). Large greenh ouse and aquaculture facilities in Arizona, Idaho, New Mexico and Utah use lo w-temperature geothermal water, and onions and garlic are dried geothermally in Nevad a. However, geothermal water is usually highly mineralized containing many components such as silica, chloride, sulphate, bicarbonate, boron, sodium, potassium, lithium, calcium, rubidium, caesium, magnesium, ammonia, and hydrogen sulfide. The customers t ypically only use the high temperature geothermal water to produce electricity, after which the temperature of the water is lower than 60 C and is directly ejected. If t hese geothermal consumers want to

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17 sufficiently use the low temperature geothermal water, they could couple it with the DDD process to produce fresh water as a by-product. It could poten tially increase their economic profits. A simple schematic of a geothermal DD D process is shown in Fig. 1-6. The diffusion driven desalination process is very versat ile, in that it can be driven by many different energy resources. Here we have ident ified solar, wind, and geothermal energy resources that should be explored in conjunction with diffusion driven desalination. Properties of Saline Water There are two important factors that affect the physical properties of saline water: salt concentration rate and relative proportions of the components in the salt. These properties directly cause the scale formation, corrosio n and bacteria contamination problems in desalination facilities. The dominant chemica l and physical characteristics of seawater are as follows [21], 1. Abundant dissolved oxygen is the most important environmenta l factor for corrosion of steels, copper alloys, and stainless steel s. The oxygen content of seawater varies between 0-12 ppm depending on the temperature, salinity, and biological activity. The solubility of oxygen decreases w ith increasing water temperature or seawater concentration rate. 2. Seawater contains about 19,000 ppm chloride. The high chlorid e ion concentration will help seawater to penetrate the protective films of the facility and enhance corrosion reactions. 3. Seawater has excellent electrolytic conductivity. 4. Seawater contains a certain amount of heavy metal io ns such as Cu, Zn, Cd and Pb. 5. Abundant calcareous scale formers (cathodic inhibitors) such as calcium, strontium and magnesium ions, result in deposition of tight and a dherent films of lime salts (CaCO 3 SrCO 3 MgCO 3 and Mg(OH) 2 ). Normally, there are 4 type of scale that can form in t he desalination plants,

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18 1. Alkaline scale occurs when the heating of seawater causes the decomposition of bicarbonate content. 2. Calcium carbonate scale may be deposited even at low t emperature. 3. Calcium sulfate scale occurs when the concentration temperature path is not within its solubility. The deposition of calcium sulfate take s place because of its inverted solubility. 4. Magnesium hydroxide scale forms at higher temperature and/ or when seawater has been concentrated to a considerable level. In applying stability data for calcium sulfate, magnesium hydroxide, and calcium carbonate to seawater, Spiegler [22] made the following c onclusions about preventing scaling problems, 1. Discharge the brine when it reaches high concentratio n level. When seawater is concentrated to 2/3 of its volume, crystallization will occur if seeds, such as calcium sulfate scale, can be provided in the system. 2. Add acid to increase the solubility of calcium carbonate The solubility of calcium carbonate can be greatly increased even with weak acids such as carbonic. 3. Precipitation of magnesium hydroxide liberates acid that inhibits the precipitation of calcium carbonate. 4. Maintain a lower operation temperature of the system b ecause the scale will mainly consists of calcium carbonate when the water temper ature is less than 60 e C. To reduce the corrosion due to seawater, the following me thods are usually used, 1. To prevent the corrosion on the surface of the evapora tor and eliminate the carbonate scale problem, deaeration is used to remove th e dissolved gases in the seawater. 2. Control the pH level of seawater to minimize corrosio n, but it must be lower than the magnesium hydroxide scaling point. A pH level between 7 7.7 is desirable. 3. Select proper materials for the desalination plants such as stainless steel, copper alloys, aluminum alloys, titanium, and plastics. Since the DDD process is a low temperature and low fre sh water conversion process, bacterial contamination is considered as the most important problem for the system. Methods for disinfecting water include microfilt ration, chlorination, iodine,

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19 ozone, and ultraviolet light. Many of these methods are also effective at removing other contaminants from water. Extremely fine ceramic filters can be used to remove b acteria from water. Their pore size is normally 1 micron or less. To prevent clogg ing they can be brushed clean and reused many times. Silver compounds are used to prevent bacte ria growing through the filter medium. Although microfiltration is the simple st and cheapest disinfection method, it is only feasible for low flow rate units because of it high flow resistance. Iodine can also be used to disinfect water. Tablet form or solution form can be introduced manually to small batches of water, or automat ically mixed with pumped water. The effective contact time is fifteen minutes under most circumstances. Because it costs around twenty times more than chlorine, it is used primarily for emergencies and other special circumstances. Ozone, an activated form of oxygen, is a powerful oxidiz er. It is usually created with electricity and mixed with water. It kills microorga nisms and breaks down organic chemicals. Carbon filtration generally follows ozonat ion. However its energy consumption and cost are very high. Ultraviolet light is another method of killing microorga nisms in water. Water is circulated in a thin layer past an ultraviolet bulb enca sed in a quartz sleeve. The light energy kills microorganisms very quickly. Clear water i s needed for effective treatment because the particles in the water can shade the bacter ia from the light. Also the water flow has to be fully stopped when the light output is ineffective or during regular maintenance. Ultraviolet bulbs generally need replacing at least once a year.

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20 Carbon, generally in the form of granular activated car bon, can be used to remove organic chemicals, including pesticides and chlorinated products as well as many tastes, odors and colors from water. It attracts and holds th e molecules of the organic chemicals. Carbon filters are available as cartridge filters for in-line use. However, for greatest effectiveness the water needs to flow slowly through th e carbon. A replacement is required when the carbon reaches its adsorption limit because it may begin releasing contaminant chemicals back into the water. The most popular water disinfection method used in this co untry is chlorination. This is because the chlorine is very effective in kill ing microorganisms if high enough concentration and sufficient time are provided. Simple c hlorination uses only 1 ppm (one gallon per 50,000 gallons of water) concentration, and a con tact time of at least 30 minutes is needed. Chlorine is generally added at the pump to e nsure adequate contact time to the water system. When 30 minutes of contact ti me is not possible, super chlorination can be used. The contact time can be reduced to around 5 minutes if the concentration is about 5 ppm (one gallon chlorine bleach per 10,000 gallons water). At this level, other methods may be needed to remove the st rong taste of water. Chlorination may be done manually or with automatic feed on-site sys tems. Shock chlorination at 50200 ppm (1-4 gallons chlorine bleach per 1,000 gallons water) conce ntration is only used for emergent treatment or the start of a new system. The entire system including pipes should be washed and allowed to sit overnight filled with this high concentration solution. One advantage of chlorination is that residual chlorine in the water can prevent recontamination. It will continue to kill microorganisms at low concentrations for a long time. However, there are problems with chlorination. Re actions with iron, sulfur,

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21 ammonia, slime, organic materials, and other chemicals can reduce the effective level of chlorine. In addition, some of the chemicals formed whe n chlorine reacts with organic chemicals are toxic or carcinogenic. Objectives of the Study There are four primary objectives for the research, an d provided these objectives are successfully met, this work will provide a basis for the design and fabrication of a diffusion driven desalination facility of any size. The se objectives are 1. Develop a thermodynamic model for the DDD process to eva luate the potential for fresh water production for a variety of operating condit ions. 2. Fabricate a laboratory scale DDD diffusion tower, e xperimentally measure the thermal and mass transport properties, the evaporation rate and the associated energy consumption required to heat the feed water and pu mp water and air through the facility. Measurements will be made over a w ide range of operating conditions in order to find an optimum condition wher e fresh water production is maximized with low energy consumption. 3. Fabricate a laboratory scale DDD direct contact conde nser, experimentally measure the thermal and mass transport properties, the condensati on rate and the associated energy consumption required to condense the vapor and pump w ater and air through the facility. Measurements will be made over a w ide range of operating conditions in order to find an optimum condition wher e fresh water production is maximized with low energy consumption. 4. Develop a computational modeling tool that reliably simulat es the heat and mass transfer processes within a DDD facility. The developm ent of a dynamic modeling tool for the diffusion tower and direct contact condense r is required. The successful completion of this objective will allow the fresh wate r production rate of a specified DDD configuration to be predicted as well as provide design recommendations for specific applications. Scope of Work In order to meet the research objectives outlined, the f ollowing major tasks have been undertaken: 1. Develop and implement a computational model for the count ercurrent flow diffusion tower and the co-current and countercurrent flo w direct contact condenser with a packed bed.

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22 2. Conduct experiments in the diffusion tower and direct co ntact condenser to validate or calibrate the computational model. 3. Conduct DDD experiments to compare the condensation effec tiveness of different condenser configurations. 4. Conduct a parametric investigation using the DDD computational model to investigate operating conditions that yield the minimum ener gy consumption and maximum fresh water production. 5. Conduct an economic analysis to assess the marketability of the DDD process. It is the ultimate goal of the research to assess the energy requirements and equipment specifications associated with fresh water pr oduction using the DDD process. Such an analysis will provide guidance as to the economic viability of the DDD process, and will provide guidance for the future design of large sca le plants. In order to accomplish this task, detailed and reliable modeling of th e heat and mass transport phenomena in the diffusion tower and direct contact c ondenser is required. Such modeling will provide detailed information on the size of th e required DDD facility components, energy requirements, flow rates and pumping r equirements. In what follows, the thermodynamic model of the diffusion tower, the lab-scale DDD experimental facility, the dynamic models for the diffusion tower and packed bed direct contact condensers, the parametric study and economic analysis of a DDD facility including one diffusion tower and one countercurrent flow direct co ntact condenser with packed bed will be presented.

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23 CHAPTER 2 THERMODYNAMIC ANALYSIS OF THE DDD PROCESS In order to explore the performance and parametric bounds of the Diffusion Driven Desalination process, a thermodynamic cycle analysis h as been performed. A simplified schematic diagram of the DDD process used for this anal ysis is shown in Figure 2-1. (i) Regenerative Heater (a) Main Feed Pump (b) Main Feed Water Heater (c) Diffusion Tower (g) Direct Contact Condenser (e) Brine Pump (d) Forced Draft Blower Salt Water Heat Input Waste Heat (f) Forced Draft Blower (h) Water Chiller Saturated Air Dry Air Chiller Pump (1) (2) (4) (3) (7) (5) (6) (4) Fresh Water Out ControlValve Figure 2-1 Flow diagram for diffusion driven desalination proce ss Mathematic Model In performing the thermodynamic analysis the following assumptions have been made, 1. The process operates at steady state conditions, 2. There are no energy losses to the environment from the heat and mass transfer equipment,

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24 3. Air and water vapor may be treated as perfect gas, 4. Changes in kinetic and potential energy are relatively sma ll, 5. The pumping power is neglected in the energy balance (es timating the required pumping power would require significant details regarding the construction of the diffusion tower, direct contact condenser and other hea t transfer equipment; these are beyond the scope of the current analysis). In the analysis, the temperature of the feed water dra wn into the main feed pump is fixed at 27 C. It is assumed that a large supply of cool water will be available at a sink temperature, T sink of 15 C. The condensate in the direct contact condenser will be chilled and a portion of it re-circulated. To avoid providi ng specifics on the heat transfer equipment, it is assumed that the heat transfer effec tiveness in the water chiller and direct contact condenser is unity, in which case T sink =T 5 =T 7 =15 C. The temperature of the feed water leaving the main feed water heater is the highest temperature in the DDD system, T h =T 1 and is a primary controlling variable for the process. D ifferent performance curves will be shown for a variable T h The air/vapor mixture leaving the diffusion tower is assu med to be fully saturated (relative humidity of unity), and due to heat transfer lim itations, its maximum temperature will be taken to be that of the feed water en tering the diffusion tower (T 4 T 1 ). The main purpose of this analysis is to explore the perfo rmance bounds of the DDD process. However, specification of the system oper ating variables is not arbitrary. Namely there are two constraints that must be satisfi ed, 1. The brine temperature leaving the diffusion tower must not be lower than the air inlet temperature (T 2 >15 C), so that the air can always absorb heat from the feed water during the humidification process through the diff usion tower, and 2. The net entropy generation in the diffusion tower must be positive.

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25 These constraints govern the parametric bounds for the d iffusion tower operation. While the first constraint is initially obvious, the sec ond constraint is simply a restatement of the second law of thermodynamics for t he present adiabatic system (diffusion tower). The control volume formulation of the second law of thermodynamics for an open system is expressed as, dA A Q T A d vs V sd t Dt Ds A A V + = 1r r (2.1) where V denotes the control volume, A is the control surface, and s is the entropy per unit mass. Assuming steady state processing of fresh water, the adiabatic diffusion tower assumption leads to, 0 = = A d vs Dt Ds s A r (2.2) and 3 3 3 1 1 4 4 4 2 2 v v a a L L v v a a L L s m s m s m s m s m s m s + + = (2.3) where m denotes the mass flow rate and the subscripts L a and v respectively refer to the liquid, air, and vapor phases. The numerical subscripts de note that the property is evaluated at the state corresponding to the position in t he process as shown schematically in Figure 2-1. Conservation of mass dictates that, ) ( 3 4 1 2w w= a L a L m m m m (2.4) The entropy generation rate in the diffusion tower per rate of air flow, which must be positive, is obtained from rearranging Eqn. (2.3 ) and combining with Eqn. (2.4) as, 1 1 3 3 4 4 3 4 3 4 2 3 4 1 ln ln ) ( L a L v v a a a L a L a s m m s s P P R T T Cp s m m m s + + n r =w w w w (2.5)

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26 where w is the humidity ratio, Cp is the specific heat, R is the engineering gas constant, and P a is the partial pressure of air. The control volume formulation of energy conservati on applied to the adiabatic diffusion tower leads to, 0 4 4 4 2 2 3 3 3 1 1 = + + v v a a L L v v a a L L h m h m h m h m h m h m (2.6) where h denotes the enthalpy. The enthalpy of the b rine exiting the diffusion tower is obtained from Eqs. (2.6) & (2.4) as, ) ( ) ( ) ( 3 4 1 4 4 3 3 3 4 1 1 2 2w w w w+ = a L v v a L a L L m m h h T T Cp h m m T h (2.7) and the brine temperature (T 2 ) is evaluated from the enthalpy. The air to feed w ater mass flow ratio through the diffusion tower, m a /m L 1 is another controlling variable in the analysis. For all computations the feed water mass flow rate is fixed at 100 kg/s while the air mass flow rate will be varied. The humidity ratio entering the diffusion tower, w 3 is determined by recognizing that it is the same as the humidity ratio exiting t he condenser, where T 7 is 15 C. Computation Results and Analysis The first case considered is where there is no heat ing in the main feed water heater. The desalination process is entirely driven by the difference in temperature of the feed water drawn at shallow depths and the cooling water drawn at more substantial depth. In this case, T h =27 C, T sink =15 C. Figure 2-2 shows the rate of entropy generation within the diffusion tower and the brine temperature exiti ng the diffusion tower for a locus of possible operating conditions. Here it is observed that the second law of thermodynamics

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27 is always satisfied for the entire parametric range considered, but there is a maximum entropy generation point for each air to feed water mass flow ratio. Exit Brine Temperature T 2 (C) 161820222426 Rate of Entropy Generation (kW/K) 0.0 0.1 0.2 0.3 0.4 0.5 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 T h = 27 Ch=m a /m L1 increase h Figure 2-2 Rate of entropy generation for different exit brine temperature, T h =27 C Figure 2-3 shows the brine temperature (T 2 ) exiting the diffusion tower as a function of the exit air temperature from the diffu sion tower (T 4 ) for the same locus of operating conditions as in Figure 2-2. It clearly s hows that the exit brine temperature decreases as the exit air temperature increases, an d the rate of brine temperature decrease increases with increasing the air to feed water mas s flow ratio. Since it is assumed that the exit air is saturated, it is advantageous to ha ve a high air temperature leaving the diffusion tower so that the humidity ratio and fres h water production rate are as high as possible. For this case the exit air temperature is constrained by the inlet feed water temperature (T 1 ) when the air to feed water mass flow ratio is low er than unity. When the air to feed water mass flow ratio exceeds unity, th e exit air temperature is limited by the fact that the brine exit temperature must be higher than the air inlet temperature.

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28 Exit Air Temperature T 4 (C) 20222426 Exit Brine Temperature T 2 (C) 15 17 19 21 23 25 27 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 T h = 27 Ch=m a /m L1 increase h Figure 2-3 Variation of exit brine temperature with exit air temperature, T h =27 C Exit Air Temperature T 4 (C) 20222426 Fresh Water to Feed water Ratio (m f /m L1 ) 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 increase hT h = 27 Ch=m a /m L1 Figure 2-4 Fresh water production efficiency, T h =27 C Figure 2-4 shows the fresh water to feed water mass flow ratio as a function of the exit air temperature for different air to feed wate r mass flow ratios. Clearly, the production rate increases with increasing exit air temperature under the same air to feed water mass flow ratio, meanwhile the production rat e grows with increasing air to feed water mass flow ratios under the same exit air temp erature. However, both of these

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29 parameters are constrained because the exit air tem perature must not exceed T h For the case of no heating of the feed water (T h =27 C, T low =15 C), the maximum fresh water production efficiency (m f /m L 1 ) is approximately 0.014. 20253035404550 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 increase h(a) T h = 50 Ch=m a /m L 1 Exit Brine Temperature T 2 (C)Rate of Entropy Generation (kW/K) 20304050607080 0 2 4 6 8 10 12 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 increase h(b) T h = 80 Ch=m a /m L 1 Exit Brine Temperature T 2 (C)Rate of Entropy Generation (kW/K) Figure 2-5 Rate of entropy generation for different exit brine temperature: a) T h =50 C, b) T h =80 C The next cases considered are where the diffusion t ower inlet water temperatures are 50 C and 80 C. Figures 2-5 a-b show the rate of entropy genera tion in the diffusion tower for T h =50 C and 80 C, respectively. Again the second law of thermodyn amics is

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30 satisfied for the entire parametric range considere d. The entropy generation tends to be lower for lower air to feed water flow ratios under the same exit brine temperature and has the maximum value with a certain exit brine tem perature under the same air to feed water mass flow ratio. At higher air to feed water flow ratios, the constraint is that the brine temperature must be higher than the air inlet temperature. 20253035404550 20 30 40 50 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 (a) T h = 50 Ch=m a /m L 1 increase h Exit Air Temperature T 4 (C)Exit Brine Temperature T 2 (C) 20304050607080 20 30 40 50 60 70 80 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 increase h (b) T h = 80 Ch=m a /m L 1 Exit Air Temperature T 4 (C)Exit Brine Temperature T 2 (C) Figure 2-6 Variation of exit brine temperature with exit air temperature: a) T h =50 C, b) T h =80 C

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31 Figure 2-6 a-b shows the range of possible exit bri ne temperatures and exit air temperatures for different air to feed water flow r atios when the diffusion tower inlet water temperature is 50 C and 80 C, respectively. The maximum fresh water productio n will occur with as high an exit air temperature as possible. For the energy balance on the diffusion tower, the exit brine temperature decreas es with increasing exit air temperature and the rate of brine temperature decrease increase s with increasing air to feed water mass flow ratio. In contrast to the case with no he ating, the exit air temperature is primarily constrained by the fact that the brine ca nnot be cooler than the inlet air, especially at higher air to feed water flow ratios. At very low air to feed water flow ratios, the exit air temperature is constrained by the inle t water temperature when T h is 50 C, meanwhile it is constrained by the fact that entrop y generation must be positive when T h is 80 C. For respective diffusion tower inlet water temperat ures of 50 C and 80 C, Figures 2-7 a-b show the ratio of fresh water production ef ficiency as a function of the exit air temperature for different air to feed water flow ra tios. It is observed that the fresh water production efficiency increases with increasing exi t air temperature and increasing air to feed water flow ratio. The maximum fresh water prod uction efficiency for T h =50 C is approximately 0.045 when air to feed water flow rat io is 1, while that for T h =80 C is approximately 0.1 when air to feed water flow ratio is 0.75. Therefore, one advantage of increasing the diffusion tower inlet water temperat ure is that the fresh water production efficiency increases.

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32 Exit Air Temperature T 4 (C) 20253035404550 Fresh Water to Feed Water Ratio (m f /m L1 ) 0.00 0.01 0.02 0.03 0.04 0.05 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 (a) T h = 50 Ch=m a / m L1 increase h Exit Air Temperature T 4 (C) 20304050607080 Fresh Water to Feed Water Ratio (m f /m L1 ) 0.00 0.02 0.04 0.06 0.08 0.10 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 (b) T h = 80 Ch=m a /m L 1 increase h Figure 2-7 Fresh water production efficiency: a) T h =50 C, b) T h =80 C For respective diffusion tower inlet water temperat ures of 50 C and 80 C, Figures 2-8 a-b show the thermal energy consumed per unit o f fresh water production as a function of exit air temperature for different air to feed water flow ratios over the entire parameter space considered. Although, details of th e low energy consumption regime are difficult to discern, it is interesting to observe that increasing both the exit air temperature and the air to feed water mass flow ratio results i n a reduced rate of energy consumption.

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33 20253035404550 0 5 10 15 20 25 30 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 increase h (a) T h = 50 Ch=m a /m L 1 Exit Air Temperature T 4 (C)Rate of Energy Consumption (kW-hr/kg fw ) 20304050607080 Rate of Energy Consumption (kW-hr/kg fw ) 0 10 20 30 40 50 60 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 (b) T h = 80 Ch=m a /m L 1 increase h Exit Air Temperature T 4 (C) Figure 2-8 Rate of energy consumption: a) T h =50 C, b) T h =80 C In order to explore the lower energy consumption re gime Figure 2-9 has been prepared for diffusion tower inlet water temperatur es of 50 C, 60 C, 70 C, and 80 C. It shows the lowest energy consumed per unit of fre sh water production as a function of different air to feed water flow ratios for differe nt T h Obviously there exists a minimum at a certain air to feed water mass flow ratio for every T h For T h =50 C the minimum rate of energy consumption is about 0.56 kW-h/kg fw when the air to water mass flow ratio is

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34 1, while that for T h =80 C is approximately 0.65 kWh/kg fw when the air to water mass flow ratio is 0.5. The results also indicate that t he minimum rate of energy consumption will occur with lower air to feed water mass flow r atio when T h is higher. Air to Feed Water Mass Flow Ratio h 0.51.01.52.02.5 0.6 0.8 1.0 1.2 1.4 50 60 70 80 Rate of Energy Consumption (kW-hr/kg fw ) T h (C) increase T h Figure 2-9 Minimum rate of energy consumption for d ifferent T h In this analysis the energy consumption due to pump ing is neglected, however, it is another important aspect of the energy consumption required for the system. It is especially important when the driving energy of the system is considered to be the waste heat where the electricity consumption of the pumps and blowers will be considered the only energy cost of the fresh water production. The refore, a dynamic simulation model must be developed to deduce the required pumping po wer for the DDD process.

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35 CHAPTER 3 EXPERIMENTAL STUDY A laboratory scale DDD facility will be used to (a) measure the thermal and mass transport properties within the diffusion tower and direct contact condenser, (b) measure the fresh water production rate for different inlet thermal and flow conditions, and (c) measure the associated energy consumption required to heat the feed water and pump water and air through the facility. These data will be used to validate the numerical model that will simulate the DDD process. Measurements wi ll be made over a wide range of operating conditions in order to find an optimum co ndition where fresh water production is maximized with low energy consumption. Experimental System Description Fig. 3-1 shows a pictorial view of the laboratory s cale DDD system. Fig. 3-2 shows a schematic diagram of the experimental facility. T he main feed water, which simulates the seawater, is drawn from one municipal water lin e. The feed water initially passes through a vane type flowmeter and then enters a pre heater that is capable of raising the feed water temperature to 50 C. The feed water then flows through the main heat er, which can raise its temperature to saturated condit ions. The feed water temperature is controlled with a PID feedback temperature controll er where the water temperature is measured at the outlet of the main heater. The feed water is then sent to the top of the diffusion tower, where it is sprayed over the top o f the packing material and gravitates downward. The portion of water that is not evapora ted is collected at the bottom of the diffusion tower in a sump and discharged through a drain. The temperature of the

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36 discharge water is measured with a thermocouple. St rain gauge type pressure transducers are mounted at the bottom and top of the diffusion tower to measure the static pressure. A magnetic reluctance differential pressure transduce r is used to measure the pressure drop across the length of the packing material. Air Heating Section Diffusion Tower Co-current Stage Countercurrent Stage Figure 3-1 Pictorial view of the laboratory scale D DD experiment Dry air is drawn into a centrifugal blower equipped with a 1.11 kW motor. The discharge air from the blower flows through a 10.2 cm inner diameter PVC duct in which a thermal air flowmeter is inserted. The air flow r ate is controlled by varying the speed of the blower. A three-phase autotransformer is used t o control the voltage to the motor and therefore regulate the speed. Downstream of the air flowmeter the inlet temperature and relative humidity of the air are measured with a th ermocouple and a resistance type humidity gauge. The air is forced through the packi ng material in the diffusion tower and discharges through an aluminum duct at the top of t he diffusion tower. At the top of the tower, the temperature and humidity of the discharg e air are measured in the same manner as at the inlet.

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37 Figure 3-2 Schematic diagram of laboratory scale DD D facility The condenser is designed to with two stages in a t win tower structure. The main feed water, which simulates the cold fresh water, i s drawn from another municipal water line. The feed fresh water is separated into two wa terlines and passes through two different turbine flowmeters. After the fresh water temperature is measured by a thermocouple at the inlet of the condenser tower, i t is sprayed from the top of each tower. The air drawn by the centrifugal blower flows out o f the top of the diffusion tower with an elevated temperature and absolute humidity. It then flows into the first stage of the direct contact condenser, which is also called the co-current flow stage. Here, the cold fresh water and hot saturated air will have heat an d mass exchange as they both flow to

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38 the bottom of this tower. The twin towers are conne cted by two PVC elbows where the temperature and relative humidity of air are measur ed by a thermocouple and a resistance type humidity gauge. The air is then drawn into the bottom of the second stage of the condenser. Because the fresh water is sprayed from the top and the wet air comes from the bottom, this stage of the condenser is denoted as the countercurrent flow stage. The air will continue being cooled down and dehumidifie d by the cold fresh water until it is discharged at the top of the second stage. At the o utlet, the temperature and humidity of the discharge air are measured in the same manner a s at the inlet. The water sprayed on top of the condenser gravitate s toward the bottom. The portion of the water condensate from the vapor is c ollected together with the initial inlet cold fresh water at the bottom of the twin towers a nd discharged through a drain. The temperature of the discharge water is measured with a thermocouple. There is one optional component of the condenser, t he packing materials. Whether or not it is required depends on the condensation e ffectiveness yielded by the direct contact condenser. Experimental Facility and Instrumentation A CAD design for the diffusion tower is shown in Fi g. 3-3. The diffusion tower consists of three main components: a top chamber co ntaining the air plenum and spray distributor, the main body containing the packing m aterial, and the bottom chamber containing the air distributor and water drain. The top and bottom chambers are constructed from 25.4 cm (10” nominal) ID PVC pipe and the main body is constructed from 24.1 cm ID acrylic tubing with wall thickness of 0.64 cm. The three sections are connected via PVC bolted flanges. The transparent m ain body accommodates up to 1 m of packing material along the length.

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39 Figure 3-3 Schematic diagram of experimental diffus ion tower A CAD design of the direct contact condenser is sho wn in Fig. 3-4. The condenser includes two towers. Each tower consists of two mai n components: a top chamber containing the air plenum, spray distributor and pa cking material, and a bottom chamber containing the packing material and water drain. Th e top chamber is constructed from 25.4 cm (10” nominal) ID acrylic tubing and the bot tom chamber is constructed from 25.1 cm ID PVC pipe. The two sections are connected via PVC bolted flanges. The transparent body accommodates up to 50 cm of packin g material along the length. The

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40 two towers are connected by two 25.4 cm (10” nomina l) ID PVC elbows which provide sufficient space for both holding drain water and p roviding an air flow channel. Figure 3-4 Schematic diagram of experimental direct contact condenser The water distributors for the entire experimental system consist of 3 full cone standard spray nozzles manufactured by Allspray. Ea ch nozzle maintains a uniform cone angle of 60 The nozzle is designed to allow a water capacity of about 14.7 lpm, and it is placed more than 30 cm away from the packing materi al in the diffusion tower and

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41 condenser to ensure that the spray covers the entir e desired area. The spray nozzle pictured in Fig. 3-5 is a one-piece construction ma chined from brass bar stock. Figure 3-5 Pictorial view of spray nozzle The pre-heater used for the present experiment is a 240 V point source water heater. It possesses a self-contained temperature c ontroller and can deliver water outlet temperatures ranging from 30 to 50 C. The main heater consists of two 3 kW electric coil heaters wrapped around a copper pipe through which the feed water flows. The power to the heaters is controlled with two PID feedback temperature controllers with a 240 V o utput. The feedback temperature to the controllers is supplied with a type-J thermocou ple inserted in the feed water flow at the discharge of the heater. The packing material used in the experiments is HD Q-PAC manufactured by Lantec and is shown pictorially in Fig. 3-6. The HD Q-PAC, constructed from polyethylene, was specially cut using a hotwire so that it fits tightly into the main body of the diffusion tower and condenser. The specific are a of the packing is 267 m 2 /m 3 and its effective diameter for modeling purposes is 17 mm.

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42 Figure 3-6 Pictorial view of packing matrix Figure 3-7 Schematic diagram of the instrumentation system for the DDD experiment

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43 The instrumentation system layout is shown in Fig. 3-7. The vane-type water mass flowmeter, constructed by Erdco Corporation, has a range of 1.5-15.14 lpm. It has been calibrated using the catch and weigh method. The fl owmeter has a 4-20 mA output that is proportional to the flow rate and has an uncertaint y of 2.2110 -2 kg/m 2 -s for the water inlet mass flux. The turbine water flowmeters, constructed by Proteu s Industries Inc., have a range of 1.5-12 gpm. They are also calibrated using the c atch and weigh method. These flowmeters have a 0-20 mA or 0-5 V output that is p roportional to the flow rate, and the measurement uncertainty is 3.4510 -2 kg/m 2 -s for the water inlet mass flux. The air flow rate is measured with a model 620S sma rt insertion thermal air flowmeter. The flowmeter has a response time of 200 ms with changes in air mass flow rate. The air flowmeter has a microprocessor-based transmitter that provides a 0-10 V output signal. The air flowmeter electronics are mo unted in a NEMA 4X housing. The meter range is 0-1125 SCFM of air. The measurement uncertainty is 5.9210 -3 kg/m 2 -s for the air inlet mass flux at 101.3 kPa, 20 C, an d 0% relative humidity. The relative humidity is measured with 4 duct-mount ed HMD70Y resistance-type humidity and temperature transmitters manufactured by Vaisala Corp. The humidity and temperature transmitters have a 0-10 V output signa l and have been factory calibrated. The measurement uncertainty is 1.18510 -3 for the absolute humidity. All temperature measurements used in the thermal an alysis are measured with typeE thermocouples with an estimated uncertainty of 0.2 C.. The pressures at the inlet and exit of the diffusio n tower are measured with two Validyne P2 static pressure transducers. All of the wetted parts are constructed with

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44 stainless steel. The transducers have an operating range of 0-0.34 atm (0-5 psi) and have a 0-5 V proportional output. The transducers have a n accuracy of 0.25% of full scale. They are shock resistant and operate in environment s ranging in temperature from –20 to 80 C. The pressure drop across the test section is measur ed with a DP15 magnetic reluctance differential pressure transducer. The pr essure transducer signal is conditioned with a Validyne carrier demodulator. The carrier de modulator produces a 0-10 VDC output signal that is proportional to the different ial pressure. The measurement uncertainty is 0.25% of full scale. Figure 3-8 Example program of SoftWIRE A digital data acquisition facility has been develo ped for measuring the output of the instrumentation on the experimental facility. T he data acquisition system consists of a 16-bit analog to digital converter and a multiplexe r card with programmable gain manufactured by Computer Boards calibrated for type E thermocouples and 0-10V input

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45 ranges. A software package, SoftWIRE, which operate s in conjunction with Microsoft Visual Basic, allows a user defined graphical inter face to be specified specifically for the experiment. SoftWIRE also allows the data to be imm ediately sent to an Excel spreadsheet. An example program layout using SoftWI RE is shown in Fig. 3-8. The experimental data acquisition system is designe d using the Virtual Instrumentation module. The control and observation panels are shown in Figs. 3-9 – 311. On the “Main” panel, shown in Fig. 3-9, there i s a switch button to begin or stop the data acquisition program. Once the program begins, the experimental data will be recorded in a database file. The file’s name, desti nation and recording frequency can be defined on this panel. Also, all of the experimenta l measurements are displayed here in real time. Figure 3-9 “Main” panel of the DDD data acquisition program

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46 This program also supplies the schematic view panel s for the diffusion tower and direct contact condenser, shown in Fig. 3-10. It sh ows the position and values of all the measurements from the experimental facility so that the operator can easily control the fresh water production. Figure 3-10 “Schematic view” panels of the DDD data acquisition program Because the current research investigation focuses on steady-state operation it is important to know when the physical processes have reached steady-state. The “Histogram View” panels, shown in Fig. 3-11, are us ed to display the measurement variations with time. The x-axis is the time coordi nate and y-axis displays the measurement value. The measurement range shown on t he y-axis can be changed manually at any time during the experiment to accur ately observe the parametric trend. Figure 3-11 “Histogram view” panels of the DDD data acquisition program

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47 Experimental measurements were taken at steady stat e conditions. Data were automatically recorded with a frequency of 1 Hz.

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48 CHAPTER 4 HEAT AND MASS TRANSFER FOR THE DIFFUSION TOWER The diffusion tower is one of the most important he at and mass transfer devices in the DDD process. An appropriately designed DDD fres h water production plant requires a detailed heat and mass transfer analysis of the d iffusion tower and direct contact condenser. This chapter will focus on the evaporati ve heat and mass transfer analyses required to design and analyze the diffusion tower. The evaporation of feed water in the diffusion towe r, shown in Fig. 4-1, is achieved by spraying heated feed water on top of a packed be d and blowing the dry air countercurrently through the bed. The falling liqui d will form a thin film over the packing material while in contact with the low humidity tur bulent air stream. Heat and mass transfer principles govern the evaporation of the w ater and the humidification of the air stream. When the system is operating at design cond itions, the exit air stream humidity ratio should be as high as possible. The ideal stat e of the exit air/vapor stream from the diffusion tower is saturated. Heat and Mass Transfer Model for the Diffusion Tower The most widely used model to estimate the heat and mass transfer associated with air/water evaporating systems is that due to Merkel [23], which is used to analyze cooling towers. However Merkel’s analysis contains two rest rictive assumptions, 1. On the water side, the mass loss by evaporation of water is negligible and 2. The Lewis number ( v v D Lea= which is a measure of the ratio between characteristic lengths for thermal and mass diffusi on) is unity.

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49 Heated feed water inlet Air/vapor plenum High surface area packing Dry air inlet Suction line to brine pump Figure 4-1 Diagram of diffusion tower Merkel’s analysis is known to under-predict the req uired cooling tower volume and is not useful for the current analysis since the pu rpose of the diffusion tower is to maximize the evaporation of water for desalination. Baker and Shryock [24] have presented a detailed analysis of Merkel’s original work and have elucidated the error contributed from each specific assumption in Merkel ’s model. Sutherland [25] developed an analysis that includes water loss by evaporation but ignores the interfacial temperature between the liquid and air. Osterle [26] assumed th at air is saturated throughout the whole process, Lewis number is unity, and air in co ntact with the liquid film is saturated

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50 at the water temperature. El-Dessouky et al. [27] h ave presented improved analyses for counter flow cooling towers, yet they assumed the a vailable interfacial area for heat transfer is the same as that for mass transfer, whi ch is only true when the packing is thoroughly wetted and is rare. An empirical enthalp y equation is used for the air/vapor mixture and is only valid for temperatures between 10-50 C. The present model does not require any of the assumptions used in prior works. The current model includes the evaporation of water, the interfacial heat resistan ce between water and air, and the different interfacial areas for heat transfer and m ass transfer. Packing material Liquid Gas/Vapor z z+dz ma+mv m L dmv evap dq Figure 4-2 Differential control volume for liquid/v apor heat and mass transfer within diffusion tower The current formulation is based on a two-fluid fil m model for a packed bed in which conservation equations for mass and energy ar e applied to a differential control volume shown in Figure 4-2. In this Figure, there i s a clear interface between liquid film and gas side. And because the gas is blown from bot tom to top of the packed bed, the zaxis denotes the axial direction through the packed bed. The conservation of mass applied to the liquid phase of the control volume in Fig. 4 -2 results in,

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51 ) ( ) ( , evap V z L m dz d m dz d = (4.1) where m is the mass flow rate, the subscript L v and evap denotes the liquid, vapor, and the portion of liquid evaporated respectively. Like wise, the conservation of mass applied to the gas (air/vapor mixture) side is expressed as ) ( ) ( , evap v z v m dz d m dz d = (4.2) For an air/vapor mixture the humidity ratio, w is related to the relative humidity, F through, ) ( ) ( 622 .0 a sat a sat a v T P P T P m m F F = =w (4.3) where P is the total system pressure and P sat (T a ) is the water saturation pressure corresponding to the air temperature T a It is assumed the total system pressure is constant. It is noted that the pressure drop is on the order of 100 Pa, which is a fraction of a percent of the absolute pressure. Using the defin ition of the mass transfer coefficient applied to the differential control volume and cons idering the interfacial area for mass transfer may differ from that of heat transfer, the n, A T T a k m dz d a v L sat v w G evap v )] ( ) ( [ ) ( , =r r (4.4) Applying the perfect gas law [28] to the vapor, the gradient of the evaporation rate is expressed as, A T T P T T P R M a k m dz d a a sat i i sat v w G evap v ) ) ( ) ( ( ) ( F = (4.5) where G k is the mass transfer coefficient on gas side, a is the specific area of packing, which is defined as the total surface area of the p acking per unit volume of space

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52 occupied, w a is the wetted specific area, v M is the vapor molecular weight, R is the universal gas constant, T i is the liquid/vapor interfacial temperature and A is the cross sectional area of the diffusion tower. Combining Eq s. (4.2), (4.3) & (4.5) the gradient of the humidity ratio in the diffusion tower is expres sed as, ) 622 .0 ) ( ( a i i sat v w G T P T T P R M G a k dz dw w w+ = (4.6) where G = A m a is the air mass flux. Equation (4.6) is a first or der ordinary differential equation with dependent variable, w and when solved yields the variation of humidity ratio along the height of the diffusion tower. In order to evaluate the liquid/vapor interfacial t emperature, it is recognized that the energy convected from the liquid is the same as tha t convected to the gas, ) ( ) ( a i G i L L T T U T T U = (4.7) where U L and U G are the respective liquid and gas heat transfer co efficients, and the interfacial temperature is evaluated from, L G a L G L i U U T U U T T + + = 1 (4.8) In general the liquid side heat transfer coefficien t is much greater than that on the gas side, thus the interfacial temperature is only slightly less than that of the liquid. The conservation of energy applied to the liquid phase of the control volume yields, A T T Ua h dz m d h m dz d a L Fg evap v L L ) ( ) ( ) ( + = (4.9)

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53 where U is the overall heat transfer coefficient, h is the enthalpy, and h Fg is the latent heat. Noting that L L L dT Cp dh = dz dh m dz dm h h m dz d L L L L L L + = ) ( and combining with Eqs. (4.9) & (4.1) results in an expression for the gradient of water temperature in the diffusion tower, L Cp T T Ua Cp h h dz d L G dz dT L a L L L Fg L ) ( ) ( + =w (4.10) where L= A m L is the water mass flux. Equation (4.10) is also a first order ordinary differential equation with T L being the dependent variable and when solved yield s the water temperature distribution through the diffusio n tower. The conservation of energy applied to the air/vapor mixture of the control volume yields, A T T Ua h dz m d h m h m dz d a L Fg evap v v v a a ) ( ) ( ) ( = + + (4.11) Noting that the specific heat of the air/vapor mixt ure is evaluated as, v v a v a v a a G Cp m m m Cp m m m Cp + + + = (4.12) and the latent heat of vaporization is evaluated as ) ( ) ( ) ( a L a v a Fg T h T h T h = (4.13) combining with Eqs. (4.11) & (4.2) yields the gradi ent of air temperature in the diffusion tower, ) 1( ) ( ) ( 1 1w w w+ + + = G Cp T T Ua Cp T h dz d dz dT G a L G a L a (4.14)

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54 Equation (4.14) is also a first order ordinary diff erential equation with T a being the dependent variable and when solved yields the air/v apor mixture temperature distribution along the height of the diffusion tower. Equations (4.6), (4.10), and (4.14) comprise a set of coupled ordinary differential equations that are used to solve for the humidity ratio, water temperature, and air/vapor mixture temperatur e distributions along the height of the diffusion tower. However, since a one-dimensional f ormulation is used, these equations require closure relationships. Specifically, the ov erall heat transfer coefficient and the gas side mass transfer coefficient are required. A sign ificant difficulty that has been encountered in this analysis is that correlations f or the water and air/vapor heat transfer coefficients for film flow though a packed bed, ava ilable in the open literature (McAdams et al. [29] and Huang and Fair [30]), are presented in dimensional form. Such correlations are not useful for the present analysis since a str uctured matrix type packing material is utilized, and the assumption employed to evaluate t hose heat transfer coefficients are questionable. In order to overcome this difficulty the mass transfer coefficients are evaluated for the liquid and gas flow using a widel y tested correlation and a heat and mass transfer analogy is used to evaluate the heat transfer coefficients. This overcomes the difficulty that gas and liquid heat transfer co efficients cannot be directly measured because the interfacial film temperature is not kno wn. The mass transfer coefficients associated with film flow in packed beds have been widely investigated. The most widely used and perha ps most reliable correlation is that proposed by Onda et al. [31]. Onda’s correlation, s hown in Appendix A, is used to calculate the mass transfer coefficients in the dif fusion tower, k G and k L However, it was

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55 found that Onda’s correlation under-predicted the w etted specific area of the packing material. Therefore, a correction was made as follo ws, n r = 5/1 05.0 2/1 4/3 Re 2.2 exp 1 L L LA L c w We Fr a as s (4.15) see Appendix A for details. As mentioned previously, the heat and mass transfer analogy [32] is used to compute the heat transfer coefficients for the liqu id side and the gas side. Therefore the heat transfer coefficients are computed as follows, Heat transfer coefficient on the liquid side 2 /1 2/1 Pr L L L L Sc Sh Nu = (4.16) 2/1 ) ( L L PL L L L D K C k Ur= (4.17) Heat transfer coefficient on the gas side 3/1 3/1 Pr G G G G Sc Sh Nu = (4.18) 3/2 3/1 ) ( ) ( G G PG G G G D K C k Ur= (4.19) Overall heat transfer coefficient 1 1 1 ) ( + = G L U U U (4.20) where K denotes thermal conductivity and D denotes the molecular diffusion coefficient. In order to test the proposed heat and mass transfe r model, consideration is first given to the cooling data of Huang [33]. Using the analysis presented above, the exit

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56 water temperature, exit air temperature and exit hu midity ratio are computed using the following procedure: 1. Specify the water mass flux, air mass flux, water i nlet temperature, air inlet temperature and inlet humidity ratio; 2. Guess the exit water temperature; 3. Compute the temperature and humidity distributions through the packed bed using Eqs. (4.6), (4.10), and (4.14) until z reaches the packed bed height used in the experiment; 4. Check whether the predicted inlet water temperature agrees with the specified inlet water temperature, and stop the computation if agre ement is found, otherwise repeat the procedure from step 2. A comparison between the measured exit water temper ature, exit air temperature and exit humidity ratio reported by Huang [33] with those computed using the current model are shown in Figs. 4-3 a-b for 2.54 cm pall r ing packing. As seen in the figures the comparison is generally good. The exit air temperat ure and exit water temperature are slightly over-predicted. The exit humidity ratio pr ediction is excellent. Air Mass Flux G (kg/m 2 -s) 0.60.81.01.2 Temperature T (C) 0 10 20 30 40 50 Humidity 0.00 0.05 0.10 0.15 0.20 0.25 L = 2.0 kg/m 2 -s Predicted Measured (a) T a,out T L,out w ww w out T a,out T L,out w ww w out Figure 4-3 Comparison of predicted exit conditions with the data of Huang [33]: a) L = 2.0 kg/m 2 -s, b) L = 4.1 kg/m 2 -s

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57 Air Mass Flux G (kg/m 2 -s) 0.60.81.01.21.41.6 Temperature T (C) 0 10 20 30 40 50 Humidity 0.00 0.05 0.10 0.15 0.20 0.25 L = 4.1 kg/m 2 -s Predicted Measured (b) T a,out T L,out w ww w out T a,out T L,out w ww w out Figure 4-3 Continued Model Comparison with Experiments for the Diffusion Tower Heat and mass transfer experiments were carried out in the diffusion tower with a packed bed height of 20 cm. The liquid mass flux wa s fixed at 1.75, 1.3 and 0.9 kg/m 2 -s and the air mass flux was varied from about 0.6-2.2 kg/m 2 -s. The inlet air temperature was about 23 C while the inlet water temperature was 60 C. The experiments were repeated to verify the repeatability of the results The measured exit humidity, exit air temperature, and exit water temperature are compare d with those predicted with the model for all three different liquid mass fluxes in Figs. 4-4 a-c. It is observed that the repeatability of the experiments is excellent. The exit water temperature, exit air temperature and exit humidity ratio all decrease wi th increasing air mass flux for a certain water mass flux. The comparison between the predict ed and measured exit water temperature and exit humidity ratio agreed very wel l, and the exit air temperature is

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58 slightly over predicted. Detailed experimental data associated with Figs. 4-4 a-c are tabulated in Appendix B. Air Mass Flux G (kg/m 2 -s) 0.60.81.01.21.41.61.82.02.22.4 Temperature T (C) 0 10 20 30 40 50 Humidity 0.00 0.05 0.10 0.15 0.20 0.25 L=1.75 kg/m 2 -s PredictedMeasuredSet 1Set 2 T a,out T L,out w ww w out (a) T a,out T L,out w ww w out Air Mass Flux G (kg/m 2 -s) 0.60.81.01.21.41.6 Temperature T (C) 0 10 20 30 40 50 Humidity 0.00 0.05 0.10 0.15 0.20 0.25 L=1.3 kg/m 2 -s PredictedMeasuredSet 1Set 2 T a,out T L,out w ww w out (b) T a,out T L,out w ww w out Figure 4-4 Comparison of predicted exit conditions with the experimental data for different liquid mass fluxes: a) L= 1.75 kg/m 2 -s, b) L= 1.3 kg/m 2 -s, c) L= 0.9 kg/m 2 -s

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59 Air Mass Flux G (kg/m 2 -s) 0.70.80.91.01.11.21.3 Temperature T (C) 0 10 20 30 40 50 Humidity 0.00 0.05 0.10 0.15 0.20 0.25 L=0.9 kg/m 2 -s PredictedMeasuredSet 1Set 2 T a,out T L,out w ww w out (c) T a,out T L,out w ww w out Figure 4-4 Continued In general, the analytical model proves to be quite satisfactory in predicting the evaporative heat and mass transfer of counter flow packed beds. The excellent agreement of the model with the measured exit water temperatu re and exit humidity ratio is most important for desalination and water-cooling applic ations. A rigorous set of conservation equations have been developed for a two-fluid model and mass transfer closure has been achieved using a widely tested empirical correlatio n, while heat transfer closure has been achieved by recognizing the analogous behavior betw een heat and mass transfer. The model does not require questionable assumptions tha t have plagued prior analyses. It is believed that the current model will be very useful to both designers of diffusion towers for desalination applications as well as designers of cooling towers for heat transfer applications.

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60 Pressure Drop through the Packing Material The pressure drop through the packing material on t he air side influences the energy consumption prediction of the DDD process. T herefore experiments considering the air pressure drop with water loading is another important objective in the research. This experiment is executed without heating the wat er. The comparison of the predicted pressure drop and the experimental data are shown b elow in Fig. 4-5 for different water mass flux loadings. Detailed experimental data asso ciated with Figs. 4-5 are tabulated in Appendix C. Air mass flux (kg/m 2 -s) 0.00.20.40.60.81.01.21.41.61.8 Specific air pressure drop (Pa/m) 0 20 40 60 80 100 DataModel 0.81.72.0 Water mass flux (kg/m 2 -s) Figure 4-5 Air specific pressure drop variation wit h air mass flux for different water mass fluxes The pressure drop is predicted using the empirical correlation specified by the manufacturer of the packing material. Figure 4-5 cl early shows that the pressure drop correlation is accurate for HD Q-Pac packing materi al. An interesting feature of the data is that the air specific pressure drop increases wi th increasing water mass flow rate under the same air mass flow rate.

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61 The air side dimensional pressure drop correlation specified by the manufacturer of the HD Q-Pac packing material is, ) 10 176 .1 654 .0 10 54.3( 4 2 4 4 2 5 2 G G L L G G v v v v z Pr r + + = D (4.21) where z is the height of the packing material (m), P D is the pressure drop through the packing (Pa), Gr is the gas density (kg/m 3 ), G v is the superficial gas velocity through the packing (m/s), and L v is the superficial liquid velocity through the pac king (m/s). Optimization of the Packing Material Optimization of the Diffusion Driven Desalination s ystem includes two major objectives, 1. For a specified packing material, find the optimal operating conditions to maximize the fresh water production rate with low energy con sumption rate. 2. For a specified operating condition, find the optim al packing material to maximize the fresh water production rate with low energy con sumption rate. The mathematic model developed in this chapter can be used for the diffusion tower analysis and design, as well as optimization of the packing material used for the diffusion tower. Energy consumption due to pumping power required for the pumps and blowers is considered in the analysis. Since the th ermal energy is assumed to be waste heat and free, it is not considered. The flow resis tance for packing material is an important feature for the packing selection. It is also well understood that large contact surface area between water and air can enhance the heat and mass transfer within packed beds. However, the packing materials with large sur face area usually have high flow resistance because of the narrow flow passages betw een the packing units. The optimal packing material will balance these two competitive factors for a specified operating

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62 condition to yield the best performance from the di ffusion tower. Two different types of optimal packing materials have been found in this a nalysis, 1. The packing material that can minimize the tower he ight for specified operating conditions. This kind of packing material will dire ctly reduce the facility construction cost. 2. The packing material that can minimize the energy c onsumption rate of fresh water production for specified operating conditions. This kind of packing material has a long-term cost advantage. The energy consumption rate on the water side is ca lculated as, L L L L P LA gz m Pw D = =r (4.22) where Pw (W) denotes the electrical power consumption, and the water side pressure drop is assumed to be equivalent to the gravitation al head loss which is given by, gz P L Lr= D (4.23) The energy consumption rate on the gas side is calc ulated as, G G G G in a G G G P GA P m P V Pw D = D + = D =r r w) 1( (4.24) where G V is the gas volume flow rate. The total energy consumption is calculated as, G L Pw Pw Pw + = (4.25) The energy consumption rate per unit of fresh water production is defined as, f f m Pw Pw = (4.26) where f m is the ideal fresh water production rate from the diffusion tower and is defined as, ) ( in out a f m mw w= (4.27)

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63 Combining above equations with the dynamic computat ional model of the diffusion tower, the performance characteristics of a specifi ed packing material can be explored, such as the exit water/air temperature, exit humidi ty, air to feed water mass flow ratio, packed bed height, fresh water production rate, pre ssure drop and energy consumption rate. The comparison of these parameters for differ ent packing materials will reveal the optimal packing material for the diffusion tower. A s an example, eight different types of packing material are investigated. They can be cate gorized into 2 geometric shapes and 8 nominal sizes. Detailed information is listed in Ta ble 4-1. The frictional pressure drop of air through the pac ked bed depends on the size and geometry of the packing material, and is calculated using Leva’s correlation [34] as, G L a G G a z P Lrr2 8 1 ) 10 )( 10( 2 = D (4.28) In this equation, a 1 and a 2 are the pressure drop constants for tower packing and are given by Treybal [35]. Table 4-1 Packing material configurations Packing Nominal size (inch) Specific area (m 2 /m 3 ) Specific packing diameter (m) 0.5 470 0.01 0.75 280 0.017 1.0 250 0.019 Berl Saddle 1.5 144 0.033 0.5 394 0.012 1.0 190 0.024 1.5 118 0.039 Raschig Ring 2.0 94 0.05 The procedure used to identify the optimum packing material is as follows: 1. Specify water inlet temperature, T L,in water mass flux, L, air to water mass flow ratio, m a /m L air inlet temperature, T a,in and inlet humidity in Find the thermodynamic states of the air and water entering the diffusion tower and their states discharging from the diffusion tower for eac h packing material using Eqs. (4.6), (4.10) & (4.14),

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64 2. Compute the required packed bed height in the diffu sion tower for the specified operating conditions for each packing material, 3. Compute the water and gas side pressure drop throug h the packing material for each packing material using Eqs. (4.23) & (4.28), 4. Compute the energy consumption rate for each packin g material using Eqs. (4.22), (4.24), (4.25) & (4.26), 5. Determine the optimal operating conditions for each packing material. Under these conditions, the energy consumption rate is minimize d for this packing material. 6. Find the best packing material by comparing the opt imum operating conditions for each packing. For all the computations, the water inlet temperatu re T L,in air inlet temperature T a,in and inlet humidity in diameter of the diffusion tower d are fixed at 50 C, 15 C, 0.0107 and 15 m respectively. The water inlet mass flux L will vary from 0.5 kg/m 2 -s to 5 kg/m 2 s, meanwhile the air to water mass flow ratio (m a /m L ) will vary from 0.3 to 1.5 for each fixed water inlet mass flux. For each type of packing material, Figures 4-6 a-h show the energy consumption rates for different air to water mass flow ratios w ith varying fresh water production level. Fresh water mass flow rate (kg/s) 10203040 Energy consumption rate (kW-hr/kg fw ) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.3 0.4 0.5 0.75 1.0 1.25 1.5 Berl Saddle 0.5"T L,in =50 C T a,in =15 C w in =0.0107 m a /m L Figure 4-6 Energy consumption rate for fresh water production: Berl Saddle – a) 0.5”, b) 0.75”, c) 1.0”, d) 1.5”; Raschig Ring – e) 0.5”, h) 1.0”, g) 1.5”, h) 2.0”

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65 Fresh water mass flow rate (kg/s) 10203040 Energy consumption rate (kW-hr/kg fw ) 0.00 0.02 0.04 0.06 0.08 0.10 0.3 0.4 0.5 0.75 1.0 1.25 1.5 Berl Saddle 0.75"T L,in =50 C T a,in =15 C w in =0.0107 m a /m L Fresh water mass flow rate (kg/s) 10203040 Energy consumption rate (kW-hr/kg fw ) 0.00 0.02 0.04 0.06 0.08 0.3 0.4 0.5 0.75 1.0 1.25 1.5 Berl Saddle 1"T L,in =50 C T a,in =15 C w in =0.0107 m a /m L Fresh water mass flow rate (kg/s) 10203040 Energy consumption rate (kW-hr/kg fw ) 0.00 0.02 0.04 0.06 0.08 0.3 0.4 0.5 0.75 1.0 1.25 1.5 Berl Saddle 1.5"T L,in =50 C T a,in =15 C w in =0.0107 m a /m L Figure 4-6 Continued

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66 Fresh water mass flow rate (kg/s) 10203040 Energy consumption rate (kW-hr/kg fw ) 0.0 0.2 0.4 0.6 0.3 0.4 0.5 0.75 1.0 1.25 1.5 Raschig Ring 0.5"T L,in =50 C T a,in =15 C w in =0.0107 m a /m L Fresh water mass flow rate (kg/s) 10203040 Energy consumption rate (kW-hr/kg fw ) 0.00 0.05 0.10 0.15 0.20 0.25 0.3 0.4 0.5 0.75 1.0 1.25 1.5 Raschig Ring 1"T L,in =50 C T a,in =15 C w in =0.0107 m a /m L Fresh water mass flow rate (kg/s) 10203040 Energy consumption rate (kW-hr/kg fw ) 0.00 0.05 0.10 0.15 0.20 0.3 0.4 0.5 0.75 1.0 1.25 1.5 Raschig Ring 1.5"T L,in =50 C T a,in =15 C w in =0.0107 m a /m L Figure 4-6 Continued

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67 Fresh water mass flow rate (kg/s) 10203040 Energy consumption rate (kW-hr/kg fw ) 0.00 0.05 0.10 0.15 0.20 0.3 0.4 0.5 0.75 1.0 1.25 1.5 Raschig Ring 2"T L,in =50 C T a,in =15 C w in =0.0107 m a /m L Figure 4-6 Continued Fig. 4-6 a-h clearly show that for each packing mat erial, the energy consumption rate is minimized for the same fresh water producti on rate when the air to water mass flow ratio is 0.75. The air to water mass flow rati o of 0.75 will be maintained when investigating the influence of other variables on t he diffusion tower performance. Feed water mass flux (kg/m 2 -s) 1234 5 Maximum possible exit humidity 0.00 0.02 0.04 0.06 0.08 0.10 Berl Saddle Raschig Ring T L,in =50 C T a,in =15 C w in =0.0107 m a /m L =0.75 0.5" 1.0" 1.5" 2.0" 0.5" 0.75" 1.0" 1.5" Figure 4-7 Maximum possible exit humidity for feed water mass flux

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68 Figure 4-7 shows the maximum possible exit humidity ratio for different packing materials and varying water inlet mass flux with ai r to water mass flow ratio of 0.75. The variation of the maximum possible exit humidity isn ’t dependent on the water mass flux or the packing material because the height of the p acked bed will change to insure the exit air is always saturated. Figure 4-8 shows the gas side mass transfer coeffic ient for different packing materials and varying air mass flux. For the same p acking material, the gas mass transfer coefficient increases with increasing the air mass flux. It also shows that the gas mass transfer coefficient increases with increasing the specific area of the packing material. Increasing the air mass flux will increase the shea r on the air water interface, and increasing the specific surface area of packing wil l increase the maximum possible contact area between water and air. This may explai n why large air mass flux and large specific surface area can enhance the mass transfer rate. Air mass flux (kg/m 2 -s) 0.51.01.52.02.53.03.5 Average air mass transfer coefficient (m/s) 0.00 0.05 0.10 0.15 0.20 Berl Saddle Raschig Ring T L,in =50 C T a,in =15 C w in =0.0107 m a /m L =0.75 Increasing specific surface area of packing 0.5" 0.75" 1.0" 1.5" 0.5" 1.0" 1.5" 2.0" Figure 4-8 Gas mass transfer coefficient for air ma ss flux

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69 Figure 4-9 shows the air side pressure drop through the packed bed for different packing materials and varying air mass flux. The ai r side pressure drop increases substantially with increasing the air mass flux for some packing materials. It also shows that the air pressure drop increases with the speci fic surface area of the packing materials with the same geometric shape. Air mass flux (kg/m 2 -s) 0.51.01.52.02.53.03.5 Air side pressure drop (Pa) 0 10000 20000 30000 40000 50000 60000 Berl Saddle Raschig Ring T L,in =50 C T a,in =15 C w in =0.0107 m a /m L =0.75 0.5" 0.75" 1.0" 1.5" 0.5" 1.0" 1.5" 2.0" Figure 4-9 Gas pressure drop for air mass flux Figure 4-10 shows the required packed bed height fo r different packing materials with varying water inlet mass flux. The tower heigh t is computed such that the maximum possible humidity ratio leaves the diffusion tower. For each type of the packing material, the required diffusion tower height increases with increasing the water inlet mass flux, and the rate of increase decreases after the water inlet mass flux exceed about 1.5 kg/m 2 s. It also shows that under the same water mass flu x, the required diffusion tower height decreases almost proportionally with increasing the specific surface area of the packing material. Considering Fig. 4-10 in conjunction with Fig. 4-7, it is obvious that Berl

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70 Saddle 0.5” can minimize the tower height without d ecreasing fresh water production rate, which implies that Berl Saddle 0.5” is the fi rst type of optimal packing material of the different packing materials considered. Feed water mass flux (kg/m 2 -s) 1234 5 Packed bed height (m) 0 1 2 3 4 5 6 Berl Saddle Raschig Ring T L,in =50 C T a,in =15 C w in =0.0107 m a /m L =0.75 Increasing specific surface area of packing 0.5" 0.75" 1.0" 1.5" 0.5" 1.0" 1.5" 2.0" Figure 4-10 Required tower height for feed water ma ss flux Figure 4-11 shows the energy consumption rate for e ach packing material with varying water mass flux. The energy consumption rat e increases with increasing the water mass flux for the same packing material. It a lso shows that under the same water inlet mass flux, the energy consumption rate increa ses with increasing air side pressure drop. Although the air side pressure drop is far le ss than the water side pressure drop through the packed bed, the volumetric flow rate of air is much higher than that of the water. This may explain why the air side pressure d rop has large influence on the total energy consumption rate in the diffusion tower.

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71 Feed water mass flux (kg/m 2 -s) 1234 5 Energy consumption rate (kW-hr/kg fw ) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Berl Saddle Raschig Ring T L,in =50 C T a,in =15 C w in =0.0107 m a /m L =0.75 Increasing air side pressure drop 0.5" 0.75" 1.0" 1.5" 0.5" 1.0" 1.5" 2.0" Figure 4-11 Energy consumption rate for feed water mass flux Fresh water mass flow rate (kg/s) 5101520253035 Energy consumption rate (kW-hr/kg fw ) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Berl Saddle Raschig Ring T L,in =50 C T a,in =15 C w in =0.0107 m a /m L =0.75 Increasing air side pressure drop 0.5" 1.0" 1.5" 2.0" 0.5" 0.75" 1.0" 1.5" Figure 4-12 Energy consumption rate for fresh water mass flow rate (cross section diameter of the packed bed is 15 m)

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72 Figure 4-12 shows the energy consumption rate for e ach packing material with varying fresh water production level. It clearly sh ows that under the same fresh water production level, the total energy consumption rate is always minimized for Berl Saddle 1.5” since it has the lowest air side pressure drop shown in Fig. 4-9, which means Berl Saddle 1.5” is the second type of optimal packing m aterial for the diffusion tower in the current analysis. Finally, it can be concluded that for a specified o perating condition and fresh water production rate, using the packing materials with l arge specific surface area can help reduce the tower height, and using the packing mate rials with low air side flow resistance can help reduce the total energy consumption rate. However, it is noticed that the current model cannot reveal the influence of the packing ma terial geometric shape on the diffusion tower performance since no parameter in t he current model explicitly describes the packing material shape.

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73 CHAPTER 5 HEAT AND MASS TRANSFER FOR THE DIRECT CONTACT CONDE NSER In order for the DDD process to be cost effective, an efficient and low cost method is required to condense water vapor out of the air stream. With a large fraction of the air/vapor mixture being non-condensable, direct con tact condensation is considerably more effective than film condensation. Another imp ortant heat and mass transfer device in the DDD process is the direct contact condenser. This chapter describes the performance of droplet direct contact condenser and packed bed condenser for both cocurrent and countercurrent flow. While a significant amount of literature is availab le on droplet direct contact condensation, considerably less information is avai lable for packed bed direct contact condensation. In analyzing direct contact condensat ion through packed beds, Jacobs et al. [36] and Kunesh [37] used a volumetric heat transfe r coefficient for the rate of convective heat transport and penetration theory [38] to relat e the heat and mass transfer coefficient. The volumetric approach does not account for local variations in heat and mass transfer. Penetration theory assumes the liquid behind the in terface is stagnant, infinitely deep, and the liquid phase resistance is controlling. As sugg ested by Jacobs et al. [36] these may or may not be reasonable assumptions, depending on the liquid film condensate resistance. Bharathan and Althof [39] and Bontozoglou and Karab elas [40] improved the analysis of packed bed direct contact condensation by consideri ng conservation of mass and energy applied to a differential control volume. Local hea t and mass transfer coefficients were

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74 used. Both analyses relied on penetration theory to relate heat and mass transfer coefficients. The motivation for this work is to explore the heat and mass transfer process within a direct contact condenser and develop a robust and reliable predictive model from conservation principles that is useful for design a nd analysis. A fresh approach is used that does not rely on penetration theory. One of th e difficulties encountered is that the interfacial temperature between the liquid and vapo r cannot be directly measured, and thus the liquid and vapor heat transfer coefficient s cannot be directly measured. Following the methodology used by Klausner et al. [ 41] for the evaporative heat and mass transfer analysis, the extensively tested Onda [31] correlation was used to evaluate the mass transfer coefficients on the liquid and ga s side. A heat and mass transfer analogy was applied to evaluate the liquid and gas heat tra nsfer coefficients. Excellent results were obtained, and a similar approach will be pursu ed here. A laboratory scale direct contact condenser has bee n fabricated. The condenser is constructed as a twin tower structure with two stag es, co-current and countercurrent. The performance of each stage has been evaluated over a range of flow and thermal conditions. As expected, the countercurrent stage is significantly more effective than the co-current stage. In addition, direct contact conde nsation within a packed bed is more effective than droplet direct contact condensation. It is also found that the manner in which the packing is wetted can significantly influ ence the heat and mass transfer performance. Visual observations of the wetted pac king have been made and a discussion relating the wetting characteristics to the different empirical constants suggested by Onda [31] is provided.

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75 Mathematical Model of the Packed Bed Direct Contact Condense r To explore the variation of temperature and humidit y within the countercurrent flow stage of the direct contact condenser, a physi cal model is developed for direct contact condensation by considering that cold water is sprayed on top of a packed bed while hot saturated air is blown through the bed fr om the bottom. The falling water is captured on the packing surface and forms a thin fi lm in contact with the saturated turbulent air stream. Energy transport during the condensation process is accomplished by a combination of convective heat transfer due to the temperature difference between water and air and the latent heat transport due to vapor condensation. Mass and energy conservation principles govern the condensation of the vapor and the dehumidification of the air stream. Noting that the relative humidity of the air is practically unity during the condensation process, the ideal state of the exit a ir/vapor temperature from the condenser is close to the water inlet temperature. A general approach for modeling the flow of water/a ir through a packed bed is to consider flow through an array of round channels wi th both transverse and longitudinal variations of temperature, pressure and humidity. This method was applied by Bemer and Kalis [42] in predicting the pressure drop and liquid hold-up of random packed beds consisting of ceramic Raschig rings and metal Pall rings. It was also used by Bravo et. al [43, 44] for structured packing. Because the air f low through the packing is highly turbulent, a 1/7 th law variation of air temperature in the transverse direction can be assumed [28] as, 7/1 , 1 = l x T T T T c a L x a L (5.1)

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76 where T a,c is the centerline air temperature, T L is the bulk liquid temperature, l is the half width of the hypothetical flow channel, and x is th e transverse axis. Although the 1/7 th law profile may not be exact, it has proven to be r obust in other channel and film flow applications. The centerline air temperature is in terms of the respective bulk air and liquid temperatures as, ( ) L a L c a T T T T + = 224 .1 (5.2) Eqn. (5.1) is used to evaluate the transverse distr ibution of air temperature. The local absolute humidity w x based on local transverse air temperature T a,x is related to the relative humidity F as, ) ( ) ( 622 .0 , x a sat x a sat a V x T P P T P m m F F = =w (5.3) where P (kPa) is the total system pressure, and P sat (kPa) is the water saturation pressure corresponding to the local air temperature T a,x The area-averaged humidity m at any cross section is expressed as, = l x m xdx l 0 2 2w w (5.4) and the bulk humidity at any cross section is calculated from Eqn. (5.3) based on the air bulk temperature T a which is a cross-sectional area-averaged value. A careful examination of the area-averaged humidity and the bulk humidity calculated at the same cross section shows that: fo r a given total system pressure P=101.3 kPa, the air bulk temperature T a 75 C, and the bulk temperature difference between the air and water |T a -T L | 20 C, the relative difference of the area-average d humidity and the bulk humidity m mw w w1.8%. It implies that replacing the area-averaged humidity

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77 m with the bulk humidity to account for the transverse variation of air tem perature will only cause minimal error in predicting the hea t and mass transfer within the packed bed. Therefore, the air temperature non-uniformity in the transverse direction is considered by using the bulk humidity in the curren t formulation. This observation allows a one-dimensional treatment of the conservat ion equations to be used along the zdirection with confidence. The current formulation is based on a two-fluid fil m model in which onedimensional conservation equations for mass and ene rgy are applied to a differential control volume shown in Fig. 5-1a. In this figure, the air/vapor mixture is blown from bottom to top (z-coordinate). Such an approach has been successfully used by Klausner et al. [41] to model film evaporation in the diffus ion tower. Liquid Air/Vapor G m a +m v L m L dz z z+dz dm v,cond dq (a) Countercurrent flow Liquid Gas/Vapor G m a +m v L m L z z+dz dm v,cond dq (b) Co-current flow Figure 5-1 Differential control volume for liquid/g as heat and mass transfer within a) countercurrent flow, b) co-current flow condensers

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78 The conservation of mass applied to the liquid and vapor phases of the control volume in Fig. 1a results in, ) ( ) ( ) ( , cond v z L z v m dz d m dz d m dz d = = (5.5) where m is the mass flow rate, the subscripts L, v, and cond denote the liquid, vapor, and condensate respectively. The conservation of energy applied to the liquid ph ase of the control volume yields, A T T Ua h dz m d h m dz d a L Fg cond v L L ) ( ) ( ) ( + = (5.6) where U is the overall heat transfer coefficient an d h is the enthalpy. Noting that L L p L dT C dh = and combining with Eqs. (5.5) & (5.6) results in a n expression for the gradient of water temperature in the condenser, L Cp T T Ua Cp h h dz d L G dz dT L a L L L Fg L ) ( ) ( + =w (5.7) where L is the water mass flux. Eqn. (7) is a firs t order ordinary differential equation with T L being the dependent variable and when solved yield s the water temperature distribution through the condenser. The conservation of energy applied to the air/vapor mixture of the control volume yields, A T T Ua T h dz m d h m h m dz d a L a Fg cond v v v a a ) ( ) ( ) ( ) ( = + (5.8) Noting that the specific heat of the air/vapor mixt ure is evaluated as, v p v a v Pa v a a G p C m m m C m m m C + + + = (5.9)

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79 and combining with Eqs. (5.5) & (5.8) yields the gr adient of air temperature in the condenser, ) 1( ) ( ) ( 1 1w w w+ + + = G Cp T T Ua Cp T h dz d dz dT G a L G a L a (5.10) Equation (5.10) is another first order ordinary dif ferential equation with T a being the dependent variable and when solved yields the a ir/vapor mixture temperature distribution along z direction. Thus Eqs. (5.7) & (5.10) are solved simultaneously to evaluate the temperature and humidity fields along the height of the condenser. Since a one-dimensional formulation is used, these equation s require closure relationships. Specifically, the humidity gradient and the overall heat transfer coefficient are required. The bulk humidity, w based on air temperature T a is related to the relative humidity F and calculated from Eqn. (5.3). An empirical repr esentation of the saturation curve is, ( ) 3 2 exp ) ( dT cT bT a T P sat + = (5.11) where empirical constants are a=0.611379, b=0.07236 69, c=2.7879310 -4 d=6.7613810 -7 and T ( C) is the temperature. Noting that the relative humidity of air remains ap proximately 100% during the condensation process, the absolute humidity is only a function of air temperature T a when the total system pressure P remains constant. Differentiating Eqn. (5.3) with respect to T a and combining with Eqn. (5.11), the gradient of hu midity can be expressed as, ) 3 2 ( ) ( 2 a a m a sat a dT cT b T P P P dz dT dz d + =w w (5.12)

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80 Eqn. (5.12) is used to compute the humidity distrib ution through the condenser. Eqs. (5.3) & (5.12) are used in the one-dimensional cond ensation model (Eqs. (5.7) & (5.10)) for closure. Following the methodology of Klausner et al. [41], the mass transfer coefficients are evaluated using a widely tested correlation and the heat transfer coefficients are evaluated using a heat and mass transfer analogy for the liqu id and gas. This approach overcomes the difficulty that gas and liquid heat transfer co efficients cannot be directly measured because the interfacial film temperature is not kno wn. The mass transfer coefficients associated with film flow in packed beds have been widely investigated. The most widely used and perhaps most reliable correlation is that proposed by Onda et al. [31] as listed in the Appendix.A. As mentioned previously, the heat a nd mass transfer analogy [32] is used to compute the heat transfer coefficients for the liquid and gas. Therefore the heat transfer coefficients are computed as described in Chapter 4. The overall heat transfer coefficient is also used in the one-dimensional con densation model (Eqs. (5.7) & (5.10)) for closure. A similar mass and energy balance analysis has been done for the co-current flow condenser stage. The one-dimensional conservation equations are applied to a differential control volume shown in Fig. 1b. The equations for evaluating the humidity gradient and air temperature gradient are the same as that for countercurrent flow. The gradient of water temperature in the co-current flo w condenser stage is, L C T T Ua C h h dz d L G dz dT L p a L L p L Fg L ) ( ) ( =w (5.20)

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81 Thus Eqs. (5.10) & (5.20) are used to evaluate the temperature fields in the co-current flow condenser stage. The humidity gradient, Onda’ s correlation and the heat and mass transfer analogy are used for closure. The condensation rate in the condenser is calculate d as, ) ( out in a cond m mw w= (5.21) The condenser effectiveness is defined as the ratio of the condensation rate in the condenser to the maximum possible condensation rate ) ( sin k in a cond m mw w e= (5.22) Here, k sinw is the minimum possible humidity exiting the conden ser, which is evaluated with Eqn. (5.3) assuming the air exits the condense r at the water inlet temperature. The condenser effectiveness is very useful in comparing the performance of the co-current and countercurrent flow condenser stages. For the countercurrent condensation analysis, the e xit water temperature, exit air temperature, and exit humidity are computed using t he following procedure: 1) specify the inlet water temperature, T L,in air temperature, T a,in and bulk humidity in ; 2) guess the exit water temperature T L,out ; 3) compute the temperatures and humidity at the n ext step change in height, starting from the bottom of the packed bed, using Eqs. (5.7), (5.10) & (5.12) until the computed packed bed height match es the experimental height; 4) check whether the computed inlet water temperature agrees with the specified inlet water temperature, and stop the computation if agreement is found, otherwise repeat the procedure from step 2. A detailed flow diagram of t he computation procedure is illustrated in Fig. 5-2.

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82 The computation is much simpler for the co-current flow condensation analysis. The exit water temperature, exit air temperature, a nd exit humidity are computed using the following procedure: 1) specify the inlet water temperature, T L,in air temperature, T a,in and bulk humidity in ; 2) compute the temperatures and bulk humidity, T a T L & at the next step change in z-direction, starting fr om the top of the packed bed, using Eqs. (5.10), (5.12) & (5.20) until the computed height m atches the experimental height. Output T L,,out T a,out , out Stop Start Calculate U by analogy method from Eqs. (5.16), (5.18) & (5.19) Calculate k G k L using Onda’s correlation from Eqs. (5.13) & (5.14) Calculate T a ,T L at next z using Eqs. (5.7), (5.10) & (5.12); use 4 th order Runge Kutta method If z < H Guess T L,out at z=0 Update T L T a & for the current z location Yes No Input T L,in at z = H, input T a,in and in at z = 0 If T L ? T L,in No Yes Figure 5-2 Flow diagram for the countercurrent flow computation Model Comparison with Experiments for the Packed Bed Dir ect Contact Condenser The effective packing diameter d p for the structured polyethylene packing is 17 mm. In Onda’s original work [31] he suggested that the coefficient in Eqn. (5.14) should

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83 be C=5.23 for d p >15 mm and C=2.0 for d p 15 mm. However, careful scrutiny of the data shows that the change in the coefficient is smooth, and the abrupt change represented by a bimodal coefficient is only an approximation. Th e 17 mm effective packing diameter used in this work is very close to the threshold su ggested by Onda. Good comparison between the measured data and the model is achieved for co-current and countercurrent flow by following Onda’s approximation for C=2.0. Onda did not attempt to explain the physical mechanism for reduced mass transfer rate w ith smaller packing diameter. We believe that the reduced gas mass transfer coeffici ent in condensers is due to increased liquid hold-up, which causes liquid bridging and re duced area for mass transfer. The wetting of the packing will be discussed in detail following presentation of the heat and mass transfer data. Water to air mass flow ratio (m L /m a ) 0.81.01.21.41.61.82.0 Exit temperature (C) 20 25 30 35 40 45 Exit humidity 0.000 0.005 0.010 0.015 0.020 0.025 0.030 Data Model T L,out T a,out w out G = 0.6 kg/m 2 -s T L,in = 19.8 C T a,in = 36.9 C (a) Figure 5-3 Comparison of predicted exit temperature s and humidity with the experimental data for countercurrent flow: a) T a,in =36.9 C, b) T a,in =40.8 C, c) T a,in =42.8 C

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84 Water to air mass flow ratio (m L /m a ) 0.81.01.21.41.61.82.0 Exit temperature (C) 25 30 35 40 45 50 Exit humidity 0.00 0.01 0.02 0.03 Data Model T L,out T a,out w out G = 0.6 kg/m 2 -s T L,in = 19.5 C T a,in = 40.8 C (b) Water to air mass flow ratio (m L /m a ) 0.81.01.21.41.61.82.0 Exit temperature (C) 20 30 40 50 60 Exit humidity 0.00 0.01 0.02 0.03 0.04 T L,out T a,out w out G = 0.6 kg/m 2 -s T L,in = 20.0 C T a,in = 42.8 C Data Model (c) Figure 5-3 Continued Heat and mass transfer experiments were carried out in the countercurrent flow stage. The air mass flux G was fixed at 0.6 kg/m 2 -s with the water to air mass flow ratio m L /m a varying from 0 to 2.5. The saturated air inlet te mperature T a,in was fixed at 36.9, 40.7, and 43.0 C respectively. The inlet water te mperature was about 20 C. The measured exit humidity out exit air temperature T a,out and exit water temperature T L,out

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85 are compared with those predicted with the model fo r all three different saturated air inlet temperatures in Figs. 5-3 a-c. It is observed that the exit water temperature, exi t air temperature and exit humidity all decrease with increasing water mass flux for a specified air mass flux. The comparison between the predicted and measured exit water temperature, exit air temperature and exit humidity agrees very well. Det ailed experimental data associated with Figs. 5-3 a-c are shown in Appendix D. Heat and mass transfer experiments were also carrie d out in the co-current stage. The saturated air inlet temperature was fixed at 35 .5, 39.6, and 43 C for each experiment set. The air mass flux was fixed at 0.6 kg/m 2 -s, and the water to air mass flow ratio was varied from 0 to 2.5. The inlet water temperature was about 22 C. Figs. 5-4 a-c show the measured exit humidity, exit air temperature, a nd exit water temperature compared with those predicted with the model for all three d ifferent saturated air inlet temperatures. Water to air mass flow ratio (m L /m a ) 1.01.21.41.61.82.02.2 Exit temperature (C) 26 28 30 32 34 Exit humidity 0.00 0.01 0.02 0.03 T L,out T a,out w out G = 0.6 kg/m 2 -s T L,in = 21.7 C T a,in = 35.5 C Data Model (a) Figure 5-4 Comparison of predicted exit temperature s and humidity with the experimental data for co-current flow: a) T a,in =35.5 C, b) T a,in =39.6 C, c) T a,in =42.9 C

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86 Water to air mass flow ratio (m L /m a ) 0.81.01.21.41.61.82.02.2 Exit temperature (C) 26 28 30 32 34 36 38 40 Exit humidity 0.00 0.01 0.02 0.03 0.04 T L,out T a,out w out G = 0.6 kg/m 2 -s T L,in = 22.4 C T a,in = 39.6 C Data Model (b) Water to air mass flow ratio (m L /m a ) 0.81.01.21.41.61.82.02.2 Exit temperature (C) 25 30 35 40 45 50 Exit humidity 0.01 0.02 0.03 0.04 0.05 T L,out T a,out w out G = 0.6 kg/m 2 -s T L,in = 22.3 C T a,in = 42.9 C Data Model (c) Figure 5-4 Continued It is observed that the exit water temperature, exi t air temperature and exit humidity all decrease with increasing water to air mass flow ratio. The predicted exit temperatures and exit humidity agree well with the experimental measurements. The exit water temperature has the largest deviation, although the error is acceptable for design and

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87 analysis applications. Detailed experimental data a ssociated with Figs. 5-4 a-c are tabulated in Appendix E. Wetting Phenomena within Packed Bed In order to explore the influence of the packing su rface wetting on the condensation heat and mass transfer rate, a high speed digital c amera was used to study the water film formation and shape on the packing. A static liqui d film formation has been observed when there is no water or air flow through the pack ed bed and only one droplet of water is on the packing surface. It is found that the wa ter droplet could have 3 possible residence locations as shown in Figs. 5-5 a-c. It is also found that the contact angle of water with the polypropylene packing is approximate ly 90, which is in agreement with Sellin et al [45]. (a) Figure 5-5 Droplet residence positions on the packi ng material: a) on the top, b) in the corner, c) beneath the packing

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88 (b) (c) Figure 5-5 Continued Observations of the dynamic water film formation on the packing surface have been made with water and air flowing countercurrent ly through the packed bed. Frames of the side view and top view are shown in Figs. 56 a-b respectively. These images show that some hemispherical water drops block the flow channels within the packed bed. It is observed that the water bridges are alw ays present even at high air to water mass flow ratio. The local heat and mass transfer rate decreases with increasing the water blockages since the active interfacial area between water and air is decreased. Also the air velocity in the vicinity of the blockages is la rgely reduced. It is well understood that the heat and mass transf er rate within the packed bed is directly related to the contact surface area betwee n the air and water. In order to achieve a high rate of heat and mass transfer, it is import ant to provide good surface wetting and liquid contact with air. The wettability of the pa cking surface with liquid depends on the contact angle between the liquid film and the packi ng surface. Water on polyethylene is poorly wetting. It is apparent that packing materi al with small packing diameter and poor wettability has a higher probability to form liquid bridges and block the air flow. Also,

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89 the condensation process will enhance liquid hold-u p and increase the probability of blocking flow passages. This may explain why the l ocal air side heat and mass transfer coefficients are lower for the condensation process than for the evaporation process. Despite its poor wetting characteristics, the polye thylene packing is used for the DDD process because it has a very low cost and is inexp ensive to replace. (a) (b) Figure 5-6 Observation of the liquid blockages with in the packed bed: a) side view, b) Top view The wide span of experimental data shown in Onda’s original work [31] reveal that there exist more factors important to packed bed he at and mass transfer than are accounted for in the correlation. For example, the water blockage problem on the

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90 packing is similar to a local flooding situation, a nd it could happen at any operating condition depending on the contact angle, packing s urface conditions/geometry and heat/mass transfer rate. Predictive models for wat er blockage are not currently available. Further understanding of liquid flow blockage withi n packed beds is required to improve existing heat and mass transfer correlations. Experimental Results of the Droplet Direct Contact Conde nser The steady state heat and mass transfer experiments were carried out in the droplet direct contact condenser. The hot saturated air mas s flux was fixed at 0.875 kg/m 2 -s and its inlet temperature was varied from 37 C to 42 C. The inlet cold fresh water temperature was about 25 C. For a fixed air inlet temperature, a full range of cold water flow rates varying from zero to maximum was explore d where steady state conditions were maintained for several distinct flow rates. Th us data of the condenser’s performance for several different steady states is obtained. Th e data are shown in the figures to follow. Fig. 5-7 shows the total temperature drop of the ai r/vapor mixture as it passes through both the co-current and countercurrent cond enser stages. The air temperature drop increases with water to air mass flow ratio fo r a specified air inlet temperature. And it also increases with increasing air inlet tempera ture when the water to air mass flow ratio is fixed. With no water flow, there is a fini te temperature drop of the air/vapor mixture, which implies there is a degree of cooling due to heat loss to the environment from the condenser walls. Indeed, for a practical c ondenser design the heat loss is good since it enhances condensation. The U-shape design of the condenser not only reduces the construction area, but also increases the wall area of the condenser that increases the heat loss of the air. This is demonstrated clearly in th e experiments. However, the figure also

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91 shows that for a certain air inlet temperature ther e exists a threshold water to air mass flow ratio that yields a maximum temperature drop. Once this threshold is exceeded, the air temperature drop hardly changes with increasing water to air mass flow ratio. Water to air mass flow ratio (m L /m a ) 01234567 Total temperature drop of air/vapor mixture (C) 2 4 6 8 10 12 36.9 40.0 41.9 T a,in (C) Increasing T a,in Figure 5-7 Total temperature drop of the air/vapor mixture with varying water to air mass flow ratios and different air inlet temperatures (w ithout packing) Water to air mass flow ratio (m L /m a ) 01234567 Total fresh water production rate (lpm) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 36.9 40.0 41.9 T a,in (C) Increasing T a,in Figure 5-8 Total fresh water production rate with v arying water to air mass flow ratios and different air inlet temperatures (without packi ng)

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92 Fig. 5-8 shows the total fresh water production rat e by both condenser stages. It shows that for a fixed feed water inlet temperature and air inlet mass flux, the fresh water production rate is strongly dependent on both the w ater to air mass flow ratio and the air inlet temperature. Trends show that the fresh water production decreases significantly with a small drop in the air inlet temperature. Thi s trend suggests that there will be little to no fresh water production when the air inlet tem perature is lower than 30 C. The peak in temperature drop observed in Fig. 5-7 results in a peak in fresh water production as shown in Fig. 5-8. Therefore increasing the water t o air mass flow ratio past the threshold does not result in increasing the fresh water produ ction rate. Water to air mass flow ratio (m L /m a ) 0.00.51.01.52.02.53.03.5 Temperature drop of the air/vapor mixture (C) 2 3 4 5 6 7 8 9 36.9 40.0 41.9 T a,in (C) Increasing T a,in (a) co-current Figure 5-9 Temperature drop of the air/vapor mixtur e with varying water to air mass flow ratios in the a) co-current, b) countercurrent stag e (without packing) Figs. 5-9 a-b show the temperature drop of the air/ vapor mixture through the cocurrent and the countercurrent condenser stages, re spectively. The air/vapor mixture’s temperature drop shows the same trend in these figu res as in Fig. 5-7. The main difference is that the heat loss in the countercurr ent condenser stage is very small because

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93 the air/vapor mixture already loses a lot of energy in the co-current stage before it enters the countercurrent condenser stage. The heat transf er driving potential is not large enough to overcome the heat resistance of the condenser wa ll. Water to air mass flow ratio (m L /m a ) 0.00.51.01.52.02.53.03.5 Temperature drop of the air/vapor mixture (C) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 36.9 40.0 41.9 T a,in (C) Increasing T a,in (b) Countercurrent Figure 5-9 Continued Water to air mass flow ratio (m L /m a ) 0.00.51.01.52.02.53.03.5 Fresh water production rate (lpm) 0.01 0.02 0.03 0.04 0.05 0.06 36.9 40.0 41.9 T a,in (C) Increasing T a,in (a) Co-current Figure 5-10 Fresh water production rate with varyin g water to air mass flow ratios and different air inlet temperatures in the a) co-curre nt, b) countercurrent stage (without packing)

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94 Water to air mass flow ratio (m L /m a ) 0.00.51.01.52.02.53.0 Fresh water production rate (lpm) 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 36.9 40.0 41.9 T a,in (C) Increasing T a,in (b) Countercurrent Figure 5-10 Continued Figs. 5-10 a-b show the fresh water production rate through the co-current and the countercurrent condenser stages, respectively. By c omparing Figs. 5-10 a & b for the same air inlet temperature, the maximum fresh water production rate in the countercurrent condenser stage is about 25% of that in the co-current stage, which means the countercurrent stage is very important to the t otal production of the system. Detailed experimental data associated with Figs. 57 – 5-10 are tabulated in Appendix F. All figures show that there exists a th reshold water to air mass flow ratio where the air temperature drop and fresh water prod uction rate reach a maximum. When the water to air mass flow ratio increases beyond t his threshold, neither the air temperature drop nor the fresh water production rat e shows much increase. This interesting phenomenon can be explained by consider ing the droplet heat transfer process in the condenser. High-speed cinematography has bee n used to observe the droplet size and velocity for different water flow rate. It is f ound that increasing the cold water flow rate will result in increased droplet velocity and decreased droplet size. High droplet

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95 velocity will reduce the droplet residence time in the condenser, which results in reduced heat transfer. Meanwhile, the smaller droplet size increases the heat transfer surface area between the water and air for a given amount of wat er. Therefore, as the water flow rate is initially increased, an increase in heat transfe r is initially observed because the overall surface area for heat transfer is increased. Also t he heat capacity is larger and a larger driving potential for heat transfer can be maintain ed. However, after the threshold is reached, no further increase in heat transfer is ob served because the deleterious effect from the droplet velocity becomes severe. Another r esult shown in the above figures is that the threshold cold water flow rate increases w ith increasing condenser air inlet temperature. For a fixed water to air mass flow rat io, hotter saturated air provides a larger driving potential for heat transfer. This larger dr iving potential overcomes the negative effects of increasing droplet velocity as described earlier. Condenser Effectiveness In order to compare the packed bed direct contact c ondensation effectiveness between co-current and countercurrent flow, several sets of experiments have been compiled where the air flow rate, air inlet tempera ture/humidity, and water inlet temperature are almost the same for each condenser stage. The condensation effectiveness is shown in Fig. 5-11 with varying th e water to air mass flow ratio and different saturated air inlet temperatures. Detaile d experimental data associated with Fig. 5-11 are tabulated in Appendix D & E. These data elucidate the fact that the countercurre nt flow condenser stage is evidently more effective than the co-current stage for the same water to air mass flow ratio, air inlet temperature/humidity and water inl et temperature. The condensation effectiveness is strongly dependent on the water to air mass flow ratio and not very

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96 sensitive to the air inlet temperature/humidity. Th e condenser effectiveness, for both cocurrent and countercurrent flow, appears to reach a threshold when the water to air mass flow ratio exceeds 2.0. Operating with this thresho ld water to air mass flow ratio appears to be an optimal operating condition. In general, t he difference between the condenser effectiveness of the co-current and countercurrent stages is approximately 15% for the same water to air mass flow ratio. Water to air mass flow ratio (m L /m a ) 0.60.81.01.21.41.61.82.02.22.4 Condensation effectiveness 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 35.5 39.6 42.8 36.9 40.7 43.0 Co-current Countercurrent T a,in Figure 5-11 Comparison of the packed bed condenser effectiveness between co-current and countercurrent flow Similarly, a comparison of the countercurrent flow condensation effectiveness between the droplet condenser and packed bed conden ser has been done. Several experiment sets of countercurrent flow droplet cond ensation have been taken when the water to air mass flow ratio, air inlet temperature /humidity, and water inlet temperature are almost the same as that for the packed bed cond ensation experiments. The condensation effectiveness is shown in Fig. 5-12 wi th varying the water to air mass flow

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97 ratio and different saturated air inlet temperature s. Detailed experimental data associated with Fig. 5-12 are tabulated in Appendix D & G. Water to air mass flow ratio (m L /m a ) 0.60.81.01.21.41.61.82.02.22.4 Condensation effectiveness 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 35.5 39.6 42.8 36.9 40.7 43.0 Droplet Packed bed T a,in Figure 5-12 Comparison of the countercurrent flow c ondensation effectiveness between droplet condenser and packed bed condenser These data clearly show that the direct contact con densation is generally 15% more effective when the packed bed is applied in the con denser for the same water to air mass flow ratio, air inlet temperature/humidity and wate r inlet temperature.

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98 CHAPTER 6 DDD PROCESS OPTIMIZATION DESIGN AND ECONOMIC ANALYS IS The three main parameters that dominate direct cont act heat and mass transfer performance include the retention time, the interfa cial area and the heat/mass transfer rate of water and air in the tower. In lieu of droplet d irect contact, the current investigation focuses on packed bed direct contact evaporation an d condensation due to the increased residence time and contact surface of the air and w ater. The increase in capital cost of the diffusion tower and condenser with packing is small because it is normally 10 20% of the total cost depending on the type and size of th e tower (Skold [46]). The maintenance of such a tower is routine since fouled packing can be easily and inexpensively replaced. The disadvantage of the packed bed direct contact h eat and mass transfer is that increased pumping energy is required to drive the air/vapor m ixture through the tower. In designing direct contact heat exchangers, it is prudent to use mathematical models that reliably capture the dominant physics g overning the heat and mass transfer. Burger [47] reported that the size and capital cost of a cooling tower can be reduced by 10% by lowering the cold water temperature by 1r C using an appropriately designed packed tower. In order to reduce the capital cost o f the DDD process and operate at the optimal flow and thermal conditions, it is necessar y to size the diffusion tower and condenser. Once the size is determined, its perform ance requires determination of the temperature/humidity distribution, energy consumpti on and fresh water production rate. Therefore mathematical models that simulate the dif fusion tower described in Chapter 4

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99 and the direct contact condenser with packed bed de scribed in Chapter 5 are combined in order to evaluate the DDD performance over a range of operating conditions. The objective of this computational analysis is to explore the influence of the operating parameters on the overall DDD process per formance. These parameters include the water/air/vapor temperatures, humidity ratio, w ater mass flux, air to feed water mass flow ratio, and tower size. The water mass flux and the air to feed water mass flow ratio through the tower are two primary controlling varia bles in the analysis. A DDD facility, including a diffusion tower and a countercurrent fl ow direct contact condenser with packed bed, is considered in this analysis. Mathematical Model In performing the analyses, the following assumptio ns have been made: 1. The process operates at steady-state conditions; 2. There are no energy losses to the environment from the heat and mass transfer apparatus. 3. Both the air and water vapor may be treated as perf ect gases, 4. Changes in kinetic and potential energy are relativ ely small. 5. The pumping power for water is that which is necess ary to overcome gravity (estimating the exact required pumping power would require significant details regarding the construction of the diffusion tower, heat transfer equipment, and the plumbing; these are beyond the scope of the current analysis). The current formulation for the diffusion tower is based on a two-fluid film model (Eqs. (4.6), (4.10) & (4.14)) described in Chapter 4. When solving, it yields the humidity ratio, water temperature, and air/vapor mixture tem perature distributions along the height of the diffusion tower. For the countercurrent flow direct contact condense r with packed bed, the current formulation is based on the analytical model descri bed in Chapter 5. The water

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100 temperature, air temperature and the humidity distr ibution in the condenser are found by solving Eqs. (5.7) (5.10) & (5.12) simultaneously. Onda’s correlation is used to calculate the mass tr ansfer coefficients in the diffusion tower and condenser, k G and k L The heat transfer coefficients for the air and wa ter are evaluated using the mass transfer analogy as descri bed by Klausner et al. [41]. The fresh water production rate equals to the conde nsation rate in the condenser, which is calculated from Eqn. (5.21). It is assumed that the inlet humidity to the diffusion tower equals to the exit humidity from the condense r. An empirical relation provided by the manufacturer of the packing material, which has been validated with experiments and expressed a s Eqn. (4.21), is used to compute the pressure drop for air/vapor passing through the pac king material. It is noted that estimating the exact required pump ing power would require significant details regarding the construction of t he diffusion tower, condenser and other equipments. However, the majority of pumping power is consumed pumping the fluids through the diffusion tower and the direct contact condenser. Therefore, the pumping power for water is that which is necessary to overc ome gravity in raising water to the top of the diffusion tower and condenser and is calcula ted from Eqn. (4.22). The pumping power for air/vapor through the diffusion tower and direct contact condenser is calculated from Eqn. (4.24). The total pumping energy consumpt ion rate for the DDD process includes the pumping power consumed by the diffusio n tower and condenser for both the water side and air/vapor side and is calculated fro m Eqn. (4.25). So the energy consumption rate per unit of fresh water production is defined as Eqn. (4.26).

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101 Computation Results and Analysis For all computations considered in the diffusion to wer, the water inlet temperature T L,in gas inlet temperature T a,in inlet humidity w in specific area a and diameter of the packing material d p are fixed as 50 C, 26 C, 0.023, 267 m 2 /m 3 and 0.017m. The inlet feed water mass flux is varied from 0.5 kg/m 2 -s to 3 kg/m 2 -s, meanwhile the air to feed water mass flow ratio (m a /m L ) is varied from 0.5 to 1.5 for every fixed inlet f eed water mass flux. All the cases analyzed in this report ar e below the flooding curve of the packing material. The reason that the inlet feed wa ter temperature is fixed at 50 C is that this is typically the highest water temperature tha t can be expected to exit the main condenser of a thermoelectric power plant. Air to Feed Water Mass Flow Ratio 0.40.60.81.01.21.4 Diffusion Tower Height (m) 0 1 2 3 4 5 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Figure 6-1 Required diffusion tower height with var iations in air to feed water mass flow ratio Figure 6-1 shows the required diffusion tower heigh t for different inlet water mass flux and varying air to feed water mass flow ratio. The tower height is computed such that the maximum possible humidity ratio leaves the diffusion tower. For every fixed air to feed water mass flow ratio, the required diffusi on tower height decreases with

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102 increasing inlet water mass flux and decreases with increasing air to feed water mass flow ratio. It also shows that for a fixed inlet water t emperature and the maximum possible exit humidity ratio, the required diffusion tower height is strongly influenced by both the inlet water mass flux and the air to feed water mass flow ratio. It is particularly noteworthy that the typically required diffusion tower height does not exceed 2 m for an air to feed water mass flow ratio above unity. This is an impor tant consideration in evaluating the cost of fabricating a desalination system. Due to t he small size of the diffusion tower, it is feasible to manufacture the tower off site and deli ver it to the plant site following fabrication and thus lower the overall cost. Air to Feed Water Mass Flow Ratio 0.40.60.81.01.21.4 Maximum Exit Humidity Ratio 0.04 0.05 0.06 0.07 0.08 0.09 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Figure 6-2 Maximum exit humidity ratio variation wi th air to feed water mass flow ratio Figure 6-2 shows the maximum possible exit humidity ratio for different inlet water mass flux and varying air to feed water mass flow r atios. For fixed inlet water and air temperatures, the maximum possible exit humidity ra tio is strongly dependent on the air to feed water mass flow ratio and is largely indepe ndent of the inlet water mass flux. These results indicate that increasing the air to w ater mass flow ratio will not necessarily

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103 assist in increasing the fresh water production sin ce the exit humidity ratio decreases with increasing air to water mass flow ratio. Air to Feed Water Mass Flow Ratio 0.40.60.81.01.21.4 Exit Air Temperature (C) 38 40 42 44 46 48 50 52 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Figure 6-3 Exit air temperature variation with air to feed water mass flow ratio Figure 6-3 shows the exit air temperature for diffe rent inlet water mass flux and varying air to feed water mass flow ratios. The exi t air temperature is sensitive to variations in both the inlet water mass flux and th e air to feed water mass flow ratio. Air to Feed Water Mass Flow Ratio 0.40.60.81.01.21.4 Water Pressure Drop (kPa) 0 10 20 30 40 50 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Figure 6-4 Water side pressure drop variation with air to feed water mass flow ratio

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104 Figure 6-4 shows the variation of the water side pr essure drop across the diffusion tower with varying air to feed water mass flow rati o. The water pressure drop decreases with increasing inlet water mass flux and decreases rapidly with increasing air to feed water mass flow ratio. Figures 6-4 illustrates that the water side pressure drop follows the same trend as the diffusion tower height, which is to be expected since the water side pressure drop is due to the gravitational head whic h must be overcome to pump the water to the top of the diffusion tower. Air to Feed Water Mass Flow Ratio 0.40.60.81.01.21.4 Air/Vapor Pressure Drop (kPa) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Figure 6-5 Air/vapor side pressure drop variation w ith air to feed water mass flow ratio Figure 6-5 shows the variation of the air side pres sure drop with the air to feed water mass flow ratio. For high water mass flux, th e air side pressure drop increases rapidly when the air to feed water mass flow ratio exceeds 0.5. The main energy consumption for the DDD process is due to the press ure loss through the diffusion tower and condenser. Although the air side pressure drop is much lower than that for water, the volumetric flow rate of air is much larger than tha t of water. Thus, both the air and water pumping power contribute significantly to the total energy consumption.

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105 The flow conditions used to investigate temperature and humidity variations in the countercurrent flow packed bed direct contact conde nser are the exit flow conditions from the diffusion tower. A typical set of flow con ditions are as follows, inlet air temperature of 42.5 C, air mass flux of 2.0 kg/m 2 -s, and fresh water inlet temperature of 25 C. When the fresh water to air mass flow ratio is 2, the required condenser tower height is 1.37 m, and Figure 6-6 shows the water te mperature, air temperature and humidity ratio distributions through the condenser. With a fresh water mass flux of 4.0 kg/m 2 -s, the exit humidity ratio is approximately 0.021, which corresponds to a fresh water production rate of about 0.069 kg/m 2 -s. Condenser Tower Height (m) 0.00.20.40.60.81.01.21.4 Temperatures (C) 25 30 35 40 45 50 Humidity Ratio 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Water Air/Vapor Humidity Ratio Condenserm a = 2.0 kg/m 2 -s T a,in = 42.442 C w in = 0.0553 T L,in = 25 C Figure 6-6 Temperature and humidity ratio profiles through the condenser Figure 6-7 shows the condenser exit water temperatu re, minimum air temperature and exit humidity ratio variation with varying fres h water to air mass flow ratio with the same inlet air temperature and mass flux. Although not shown, all the values decrease with increasing inlet water mass flux. However, the results in Figure 6-7 show that there is no further decreases in exit humidity ratio when the fresh water to air mass flow ratio

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106 exceeds 2. Thus the optimum fresh water to air mass flow ratio that yields the maximum fresh water production is 2. Fresh Water to Air Mass Flow Ratio 246810 Temperatures (C) 0 10 20 30 40 50 60 Humidity Ratio 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 Water Air/Vapor Humidity Ratio Condenserm a = 0.5 kg/m 2 -s T a,in = 48.611 C w in = 0.078 T L,in = 25 C Figure 6-7 Condenser temperature and humidity ratio variation with fresh water to air mass flow ratio Air Mass Flux (kg/m 2 -s) 0.00.51.01.52.02.53.0 Condenser Height (m) 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Condenser m fw /m a = 2 Figure 6-8 Required direct contact condenser height with variations in air mass flux

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107 Figure 6-8 shows the required condenser height for different air mass flux with a constant fresh water to air mass flow ratio of 2 in the condenser. The tower height is computed such that the minimum humidity ratio leave s the condenser. For a fixed feed water mass flux at the inlet of the diffusion tower the required condenser height decreases with increasing air mass flux, and it als o decreases with decreasing the feed water mass flux with the same air mass flux. Figure s 6-8 indicates that the condenser height follows the same trend as the diffusion towe r exit air temperature, which is to be expected since the required condenser height strong ly depends on the air inlet humidity ratio. Air Mass Flux (kg/m 2 -s) 0.00.51.01.52.02.53.0 Exit Fresh Water Temperature (C) 32 34 36 38 40 42 44 46 48 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Condenser m fw /m a = 2 Figure 6-9 Condenser fresh water exit temperature v ariation with air mass flux Because the sink temperature is 25 C, the minimum condenser exit air temperature is taken as 26 C. Figure 6-9 shows the condenser f resh water exit temperature for different inlet feed water mass flux in the diffusi on tower and varying air mass flux. The fresh water exit temperature is sensitive to variat ions in both the feed water inlet mass flux and air mass flux.

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108 Air Mass Flux (kg/m 2 -s) 0.00.51.01.52.02.53.0 Fresh Water Product Efficiency (m fw /m L ) 0.024 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040 0.042 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Condenser m fw /m a = 2 Figure 6-10 Variation of the fresh water production efficiency with air mass flux Air to Feed Water Mass Flow Ratio 0.40.60.81.01.21.4 Energy Consumption Rate (kW-hr/kg fw ) 0.000 0.002 0.004 0.006 0.008 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Figure 6-11 Variation of the energy consumption wit h air to feed water mass flow ratio in diffusion tower Figure 6-10 shows the fresh water production effici ency of the system with varying air mass flux. It is clear that the fresh water pro duction efficiency increases rapidly with the air to feed water mass flow ratio. But the rate of increase diminishes when the air to feed water mass flow ratio exceeds unity. It is als o interesting to note that the maximum fresh water production efficiency tends to approach a value of 0.04 when the feed water

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109 mass flux is 0.5 kg/m 2 -s. The maximum production efficiency is largely co ntrolled by the ratio of the diffusion tower inlet water temperatur e to the sink temperature. In this case, it is 1.12. Perhaps the most important consideration in this an alysis is the rate of energy consumption due to pumping because the operating co st of the DDD process is largely dependent on the cost of electricity to drive the p umps and blowers. Figure 6-11 shows the energy consumption rate for the diffusion tower for different inlet feed water mass flux and varying air to feed water mass flow ratios The energy consumption increases with increasing inlet water mass flux for a fixed a ir to feed water mass flow ratio. It is particularly interesting that a minimum energy cons umption occurs when the air to feed water mass flow ratio is approximately 0.5. As the inlet water mass flux decreases, the energy consumption becomes relatively insensitive t o variations in the air to feed water mass flow ratio. Air Mass Flux (kg/m 2 -s) 0.00.51.01.52.02.53.0 Energy Consumption Rate (kW-hr/kg fw ) 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Condenser m fw /m a = 2 Figure 6-12 Variation of the energy consumption wit h air mass flux in condenser

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110 Figure 6-12 shows the energy consumption rate for t he direct contact condenser with fixed fresh water to air mass flow ratio of 2. It shows clearly that there exists a critical point for every feed water mass flux. When the air mass flux is higher than the critical condition, the energy consumption rate in the condenser will increase very rapidly with increasing air mass flux. An interesting resul t is that the energy consumption rate in the condenser will remain low for all feed water in let mass flux considered provided the air mass flux remains below 1.5 kg/m 2 -s. Air Mass Flux (kg/m 2 -s) 0.00.51.01.52.02.53.0 Energy Consumption Rate (kW-hr/kg fw ) 0.000 0.005 0.010 0.015 0.020 0.025 0.5 1 1.5 2 2.5 3 Diffusion Tower m L (kg/m 2 -s) Condenser m fw /m a = 2 Figure 6-13 Variation of the total energy consumpti on rate with air mass flux Figure 6-13 shows the variation of the total energy consumption rate for the system with air mass flux. There exists a minimum energy c onsumption rate for every feed water mass flux, and it increases with increasing feed wa ter inlet mass flux. However, when the air mass flux is less than 1.5 kg/m 2 -s the total energy consumption rate for the system is below 0.0039 kW-hr /kg fw for all feed water inlet mass flux. The minimum sh own in this Figure, 0.0004 kW-hr/kg fw occurs when the air mass flux is 0.5 kg/m 2 -s, air to feed water mass flow ratio is 1, and fresh water to air mass f low ratio is 2. At these conditions a fresh water production rate of 0.018 kg/m 2 -s is realized. This minimum is about an order

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111 of magnitude less energy consumption than reverse o smosis. However, operating at these low mass fluxes requires a sizable land footprint, and is not likely to be practical for a large production rate facility. Finally, the optimum operating conditions of the sy stem should satisfy competing requirements: high fresh water production efficienc y and low energy consumption rate. Based on data presented in Fig. 6-10 and Fig. 6-13, a reasonable optimum operating condition has an air mass flux of 1.5 kg/m 2 -s, air to feed water mass flow ratio of 1, and fresh water to air mass flow ratio of 2. These cond itions can yield a fresh water production efficiency of 0.035 and energy consumpti on rate of 0.0022 kW-hr/kg fw Economic Analysis As an example, consider a 100 MW power plant where the thermal efficiency is 40%. The total input energy is then 250 MW. If the power plant operates with 10.159 kPa pressure in the main condenser, there would be appr oximately 150 MW of energy at 50 C available from low pressure condensing steam. If retrofitted with a diffusion driven desalination (DDD) plant, there is a potential to p roduce as much as 1.14 million gallons/day of fresh water assuming the feed water temperature enters the diffusion tower at 50 C. The energy consumption from the feed water, air and cold fresh water pumps in the DDD process is about 0.0022 kW-hr per kilogram of fresh water. This requires a land footprint of approximately 0.47 acres. The total el ectrical power requirement is 391 kW in total. The thermal energy consumed in the DDD pr ocess is waste heat, and is not of concern for the economic analysis. The fresh water production cost strongly depends on the process capacity, site characteristics and design features. The system cap acity defines the required sizes for

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112 various process equipment, pumping units, and requi red heat exchanger surface area. Site characteristics have a strong influence on the type of pretreatment and post-treatment equipment, and consumption rate of chemicals. Proce ss design features affect consumption of electric power and chemicals (Wangni ck et al [48] and Hisham et al [49]). Production cost is divided into direct and i ndirect capital costs and annual operating costs. Direct capital costs include the p urchase cost of major equipment, auxiliary equipment, land and construction. Indirec t capital costs include labor, maintenance, and amortization. They are usually exp ressed as percentages of the total direct capital cost. Land – The cost of land may vary considerably, from zer o to a sum that depends on site characteristics. Government-owned plants normally h ave zero charges. Plants constructed under build-own-operate-transfer (BOOT) contracts w ith governments or municipalities can have near zero or greatly reduced charges. The price of the land near the coast of Florida varies significantly from 1k 1000k $/acre Building construction – Construction costs vary from 100 1000 $/m 2 This cost is sitespecific and depends on the building type. Building s could include a control room, laboratory, offices and workshops. Process equipment – This category includes processing equipment, as wel l as instrumentation and controls, pipes and valves, ele ctric wiring, pumps, process cleaning systems, and preand post-treatment equipment. The se are some of the most expensive items, and their cost depends on the type of proces s and capacity. Equipment costs may be less than $1000 ( e.g., a laboratory scale RO unit used to treat low-salini ty water). On the other hand, the equipment cost for a 100000 m 3 /day RO system could approach $50

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113 million. MSF and MEE equipment are generally more expensive than tha t of RO systems — current estimates for a plant capacity of 27000 m 3 /day are $40 million. Because the increase in salinity concentration of the DDD disch arge water is small, there is no need for post-treatment. Also the feed water flow is sup plied by the main pumps used in the power plant’s cooling system. So the capital cost o f the pre-treatment, post-treatment and main feed water pumps will not be included in this analysis. The other process equipment costs among different manufacturers range from $200 k-$1700k. Auxiliary equipment – The following are considered auxiliary equipment: o pen intakes or wells, transmission piping, storage tanks, generato rs and transformers, pumps, pipes and valves. The current analysis will not include these items. As an example, consider the DDD system coupled with a 100 MW power plant. Table 6summarizes the variation in direct costs w hile Table 6-2 shows calculation details for the unit fresh water production cost. T he capital cost calculations are based on the following assumptions: 1. interest rate i = 5%; 2. plant life n = 30 yr; 3. amortization factor ai = 1 ) 1( ) 1( + + n n i i i = 0.0651 /yr; 4. plant availability f = 0.9; 5. chemical costs are not considered; 6. electricity is considered as operating cost; 7. the specific cost of operating labor is typically ranges from 0.025 to 0.05 $/m 3 since DDD is a low temperature and pressure process ( is typically $0.1/m 3 for the thermal processes and $0.05/m 3 for RO).

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114 Table 6-1 Summary of direct costs Name Land Building construction Major equipment Cost ($) 470-470000 190202-1902023 200000-1700000 Total Direct Cost DC ($) 390672-4072023 Table 6-2 Details of cost calculations Name Formula Result Annual fixed charges AC fixed ($) DC ai AC fixed = 25433 – 265089 Annual labor cost AC labor ($) 365 = f labor m f ACg 35389 – 70779 Total annual cost AC total ($) labor fixed total AC AC AC + = 60822 – 335868 Unit product cost AC unit, p ($/m 3 ) 1 ) 365 ( = f total p unit m f AC AC 0.043 – 0.237 The computation reveals that the production cost, n ot including electricity costs, ranges from 0.163 – 0.895 $/10 3 gal. For illustrative purposes, we take the product ion cost to be 0.525 $/10 3 gal. Here two cases are considered: First, the DDD utility is economically independent from the power plant, which means although the DDD process utilize the waste he at from the power plant, it needs to pay the electricity cost in additional to basic pro duction cost. So the fresh water profit in this situation can be calculated as, elec f p unit f f Q Pw AC Q = P , (6.1) where f ($/10 3 gal) is the net fresh water profit, Q f ($/10 3 gal) is the retail price of fresh water, and Q elec ($/kW-hr) is the retail price of electricity. Here AC unit,p is 0.525 $/10 3 gal. Figure 6-14 shows the net fresh water profit variat ion with the electricity retail price for different fresh water retail price. The fresh water profit decreases with increasing electricity cost, and increases with increasing the fresh water price. As seen in Fig. 6-14, profit is only realized when the fresh water retail price is greater than 1 $/10 3 gal.

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115 Electricity Retail Price ($/kW-hr) 0.040.060.080.100.120.140.160.180.20 Net Fresh Water Profit ($/10 3 gal) 0 1 2 3 4 5 6 1 2 3 4 5 6 Water Retail Price ($/10 3 gallon) Figure 6-14 Net fresh water profit variation with e lectricity retail price for different fresh water retail price Second, the DDD utility is combined with a power pl ant, which means this combined system has a fresh water production capaci ty of 1.14 million gallons/day besides the electricity production. But the total e lectrical power requirement of the DDD process will be subtracted from the total electrici ty production of the power plant as the operating cost. The daily profit of the combined sy stem is calculated from, elec f f elec f f total Pw m E m P + P = P ) ( 24 (6.2) where total ($/day) is the daily profit of the combined system E elec (MW) is the electricity production capacity of the power plant before combining with the DDD system, and elec ($/kWhr) is the electricity profit. The percent inc rease in profit of the combined power plant is calculated as, elec elec elec elec total E E P P P =b (6.3) The percent increase in profit for the power plant combined with the DDD process for different fresh water profits is shown in Fig. 6-15. This Figure shows that the profit

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116 increase decreases with increasing electricity prof it. It is also important to note that the profit increase of the combined power and DDD plant tends to be zero when the electricity profit is higher than 0.2 $/kW-hr, whic h is not likely in the near future. The profit increase grows almost proportionally with th e fresh water price that can be commanded on the open market. It clearly shows that the combined power and DDD plants yield a profit increase when the fresh water is sold at a rate higher than 1 $/10 3 gal. This is strongly competitive in most regions of the world. Electricity Profit ($/kW-hr) 0.0010.010.1 Profit Increase (%) 1 10 100 1000 1 2 3 4 5 6 Water Profit ($/10 3 gallon) 0.2 Figure 6-15 Percent increase in profit with electri city profit for different fresh water profit A recent survey [50] by the NUS Consulting Group st udying water rates across the world found that rates increased from 2001 to 2002 in 12 of 14 countries surveyed. The result is shown in Figure 6-16. The survey was base d on prices as of July 1, 2002 for an organization with an annual usage of at least 10000 cubic meters. Where there was more than a single supplier, an unweighted average of av ailable prices was used. The percentage change for each country was calculated u sing the local currency in order to eliminate currency exchange distortion. Water rates in the United States were among the

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117 lowest in the countries surveyed and were one half to one third the rates charged in most European countries. And it is also important to rec ognize that most countries investigated show a positive increase in water price, which refl ects the increased demand for fresh water. $XVWUDOLD %HOJLXP &DQDGD 'HQPDUN )LQODQG )UDQFH *HUPDQ\ ,WDO\ 6RXWK$IULFD 6SDLQ 6ZHGHQ 7KH1HWKHUODQGV 8QLWHG.LQJGRP 8QLWHG6WDWHV )UHVK:DWHU&RVWJDOORQ Figure 6-16 Water price in different countries for year 2001 & 2002 Finally, an investigation of the electricity market in the United States is conclueded to explore the economic advantage of the DDD proces s within different geographical markets. The average revenue in the United States f or electricity generation [51] is $0.0693/kW-hr. The average cost to produce electric ity in 2001 [52] is $0.06/kWhr for gas and oil and $0.02/kW-hr for coal. Since electri city profits are low, the DDD process

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118 provides an opportunity for electric utilities to r ealize additional revenues through fresh water production. The above considerations suggest that there exists economic benefit for the DDD process to electric utilities. It is anticipated th at this benefit will grow as the world fresh water supply continues to diminish.

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119 CHAPTER 7 CONCLUSIONS An innovative Diffusion Driven Desalination (DDD) p rocess has been studied theoretically and experimentally. Although the proc ess has a low fresh water to feed water conversion efficiency, it has been demonstrat ed that this process can potentially produce inexpensive distilled water when driven by low-grade energy such as waste heat. A detailed parametric analysis shows that the waste heat from a 100 MW steam generating power plant can be used to produce 1.14 million gallons of fresh water per day using the DDD process. Since the energy used to dri ve the process is low thermodynamic availability energy, the only energy cost is that u sed to power the pumps and blowers. An economic simulation of the DDD system shows that th e fresh water production cost of the DDD combined power plant is very competitive co mpared with the costs required for reverse osmosis or flash evaporation technologies. A laboratory scale DDD facility, which includes the diffusion tower and direct contact condenser has been fabricated. The whole sy stem has been fully instrumented for detailed heat and mass transfer measurements. Exten sive measurements of the diffusion tower and direct contact condenser were taken to va lidate their numerical simulation models. It has been experimentally proved that in t he current operating condition range, the condensation effectiveness is much higher for c ountercurrent flow than for co-current flow within the packed bed, and it is also higher f or packed bed condenser than for droplet condenser. The models of the diffusion towe r and packed bed direct contact condenser prove to be quite satisfactory in predict ing the thermal performance of packed

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120 beds evaporation and condensation. Nevertheless, du e to the empiricism involved in the correlations, they must be used with caution. Highspeed cinematography is used to explore the mechanism for the decrease in the gas s ide mass transfer coefficient for packing material with a small effective packing dia meter. The local heat and mass transfer rate decreases with an increasing number o f local water blockages. This is due to a reduction in the active interfacial area between water and air, and the air velocity near the vicinity of the blockages is reduced. It is bel ieved that there exists a higher probability to form liquid blockages within packing material wh ich has a small packing diameter and poor wettability. The analysis and observations pre sented in this work should be useful to the designers of direct contact heat exchangers. Although the current analysis shows that the Diffus ion Driven Desalination process appears to be an economically attractive distillati on process, the precise values presented in the dissertation need to be viewed with caution since losses other than pressure losses have not been considered, and the assumed feed wate r temperature into the diffusion tower may be optimistic. Nevertheless, the trends p resented demonstrate the potential that can be gained from the DDD process, and it provides useful and practical guidance for choosing the operating conditions to achieve near o ptimum performance. Furthermore, although the Diffusion Driven Desalina tion is a promising technology for fresh water production using waste heat from el ectric power plants, current industry practice will limit its implementation until the va lue of fresh water sharply increases. The current practice of electric power plants is to pum p a very large rate of cooling water through the main condenser so that the temperature rise of the water across the condenser is only about 6 C. The DDD requires the discharge water from the main condenser to be

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121 approximately 45 C. This could be accomplished by lowering the flow rate through the main condenser and providing more heat transfer sur face area to compensate for the reduced heat transfer rate. This would require a po wer plant installing a DDD facility to also replace or modify the main condenser. This is not a likely scenario. The best prospect for incorporating the DDD facility into an electric power plant for fresh water production is with the fabrication of new plants wh ere the main condenser could be sized appropriately for the specified flow conditions. Recently it has been recognized that the fresh wate r production efficiency can be significantly enhanced with air heating. Air heatin g can be accomplished with air-cooled condensers used in power plant applications. The he ated air discharging the condenser could be directly ducted to the diffusion tower. Th e laboratory experimental DDD facility has been modified with an air heating section, and temperature and humidity data have been collected over a range of flow and thermal con ditions. It has been experimentally observed that the fresh water production rate is en hanced when air is heated prior to entering the diffusion tower. While a significant a mount of literature is available on evaporative heat and mass transfer between hot wate r and cold air within the packed bed for cooling tower applications, considerably less i nformation is available for the air heating configuration. Therefore, more experiments need to be conducted to fully understand the benefits of the heated air input. Fu rther analytical analysis is required to predict the thermal and mass transport with this co nfiguration. In addition, a cost analysis should be performed to analyze the additional costs of the heated air.

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122 APPENDIX A ONDA’S CORRELATION 3/1 4.0 5.0 3/2 ) ( Re 0051 .0 n r = L L p L Lw L g ad Sc kr m G p G GA G aD ad Sc C k 2 3/1 7.0 ) ( Re = (C=5.23 if dp > 15 mm; C=2 if dp 15 mm) n r = 5/1 05.0 2/1 4/3 # Re 2.2 exp 1 L L LA L c w We Fr a as s L w LW a Lm= Re G GA a Gm= Re L LA a Lm= Re L L L L D Scr m= G G G G D Scr m= g a L Fr L Lr2 = a L We L L Ls r2 = # This equation has been modified from Onda’s origi nal correlation.

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123 APPENDIX B EXPERIMENTAL DATA OF THE DIFFUSION TOWER m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,out ( C) T a, in ( C) out in 0.042 0.030 60.8 32.6 42.3 22.2 0.059 0.009 0.042 0.040 60.6 30.8 39.6 22.5 0.051 0.009 0.042 0.051 60.7 27.9 37.2 22.7 0.044 0.010 0.042 0.059 60.5 26.7 35.7 22.8 0.041 0.010 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,out ( C) T a, in ( C) out in 0.042 0.031 59.1 32.8 41.5 22.2 0.057 0.009 0.042 0.039 60.2 31.3 39.1 22.4 0.049 0.009 0.042 0.051 60.2 30.5 36.3 22.7 0.042 0.010 0.042 0.061 60.1 27.4 34.8 23.0 0.038 0.010 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,out ( C) T a, in ( C) out in 0.059 0.021 60.5 37.3 50.4 22.6 0.091 0.005 0.059 0.031 59.5 33.3 46.3 22.5 0.072 0.005 0.059 0.041 60.0 31.3 43.4 22.1 0.061 0.005 0.059 0.050 60.6 29.3 42.0 22.3 0.056 0.005 0.059 0.061 60.1 28.2 39.2 22.5 0.048 0.005 0.059 0.070 59.8 28.8 37.2 22.6 0.043 0.005 0.059 0.080 60.3 26.4 36.0 22.7 0.040 0.005 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,out ( C) T a, in ( C) out in 0.059 0.021 59.8 38.8 50.0 22.7 0.090 0.005 0.059 0.032 59.9 36.7 45.7 22.9 0.069 0.005 0.059 0.041 59.6 33.7 44.2 22.6 0.067 0.005 0.059 0.050 59.7 31.3 41.8 22.7 0.058 0.005 0.059 0.061 60.0 29.3 39.3 22.9 0.047 0.005 0.059 0.071 59.8 25.9 37.5 23.2 0.045 0.005 0.059 0.080 59.5 26.1 36.4 23.4 0.040 0.005

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124 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,out ( C) T a, in ( C) out in 0.080 0.029 60.7 35.3 49.5 23.1 0.087 0.010 0.080 0.039 60.7 33.7 46.1 23.0 0.071 0.010 0.080 0.049 60.5 33.6 44.3 22.7 0.063 0.010 0.080 0.060 60.5 30.7 42.6 22.9 0.058 0.010 0.080 0.069 60.8 29.4 40.5 23.1 0.051 0.010 0.080 0.078 60.3 28.2 39.2 23.2 0.047 0.010 0.080 0.089 61.3 27.9 37.6 23.5 0.043 0.010 0.080 0.101 60.9 26.6 34.9 23.8 0.037 0.010 0.080 0.109 60.3 26.4 33.1 24.1 0.034 0.010 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,out ( C) T a, in ( C) out in 0.080 0.031 60.8 36.9 48.7 23.1 0.083 0.010 0.080 0.039 60.6 34.3 46.7 23.2 0.074 0.010 0.080 0.051 60.3 33.3 43.9 22.8 0.062 0.010 0.080 0.060 60.4 29.3 41.8 22.9 0.054 0.010 0.080 0.070 60.7 29.0 40.1 23.2 0.049 0.010 0.080 0.079 60.6 27.9 38.8 23.6 0.046 0.010 0.080 0.092 60.7 27.4 36.9 23.9 0.041 0.010 0.080 0.101 60.7 26.6 34.3 24.2 0.035 0.010 0.080 0.108 60.4 25.8 33.9 24.6 0.035 0.010

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125 APPENDIX C EXPERIMENTAL DATA OF THE AIR SIDE PRESSURE DROP THR OUGH THE PACKING MATERIAL L (kg/m 2 -s) G (kg/m 2 -s) n P/z (Pa/m) 0 0 0.258384 2.511111 0.524775 7.8 0.810332 20.44444 1.054124 28.28889 1.346835 56.8 1.544484 75.26667 0.803389 1.941271 77.97778 0 0 0.148759 0.955556 0.405831 9.133333 0.951576 34.42222 1.543965 66.13333 1.868464 88.4 1.373636 2.047198 83.8 0 0 0.292747 7 0.512864 11.25 0.887309 25.15 1.150059 37 1.470995 69.1 1.661633 88.75 1.733611 2.03956 84.8 0 0 0.280726 2.977778 0.550711 11.13333 0.754084 17.04444 1.020072 32.71111 1.332571 65.35556 1.631835 92.06667 2.000957 1.717701 76.42222

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126 APPENDIX D EXPERIMENTAL DATA OF THE COUNTERCURRENT FLOW DIRECT CONTACT CONDENSER STAGE WITH PACKED BED m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.024 0.031 19.0 33.2 36.5 30.0 0.041 0.029 0.033 0.030 19.3 32.2 36.8 28.0 0.041 0.026 0.048 0.030 19.4 30.4 36.8 25.8 0.041 0.023 0.062 0.030 19.5 28.6 37.0 24.4 0.042 0.021 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.054 0.030 19.4 29.5 37.0 24.7 0.042 0.021 0.044 0.030 19.3 30.2 37.0 26.2 0.042 0.023 0.038 0.031 19.2 31.4 37.1 27.1 0.042 0.025 0.031 0.031 19.7 32.0 37.1 28.6 0.042 0.027 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.024 0.029 19.5 36.1 40.8 31.6 0.052 0.032 0.035 0.031 19.3 34.6 40.6 29.4 0.052 0.028 0.048 0.030 19.4 32.9 40.9 27.4 0.053 0.025 0.058 0.031 19.0 31.3 40.7 26.2 0.053 0.023 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.053 0.031 18.9 31.9 40.7 26.5 0.053 0.024 0.044 0.030 19.1 32.7 40.7 27.5 0.053 0.025 0.038 0.031 19.3 33.1 40.7 28.3 0.053 0.026 0.031 0.030 19.3 34.5 40.8 29.6 0.053 0.029 0.023 0.030 19.4 35.4 40.8 31.4 0.053 0.032

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127 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.024 0.029 19.8 40.3 42.7 34.9 0.059 0.039 0.033 0.030 19.9 38.5 42.7 32.1 0.059 0.033 0.041 0.031 19.8 37.2 42.7 30.4 0.059 0.030 0.051 0.031 19.7 34.8 42.8 28.4 0.060 0.026 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.061 0.030 19.5 33.3 42.8 27.1 0.060 0.024 0.054 0.030 19.7 34.0 42.9 28.0 0.061 0.026 0.045 0.030 19.8 34.8 42.9 29.1 0.061 0.028 0.034 0.030 19.8 37.0 42.9 32.0 0.061 0.033 0.030 0.030 19.6 37.8 42.9 33.2 0.061 0.035

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128 APPENDIX E EXPERIMENTAL DATA OF THE CO-CURRENT FLOW DIRECT CON TACT CONDENSER STAGE WITH PACKED BED m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.032 0.031 22.5 29.0 35.6 31.2 0.038 0.029 0.042 0.031 21.6 27.7 35.5 29.4 0.038 0.026 0.053 0.031 21.5 26.7 35.5 28.6 0.038 0.025 0.058 0.031 21.4 25.7 35.4 28.0 0.038 0.024 0.066 0.031 21.4 25.5 35.2 27.4 0.037 0.023 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.025 0.031 23.6 34.0 39.7 35.1 0.048 0.037 0.042 0.031 22.2 31.9 39.7 32.4 0.048 0.031 0.052 0.031 22.2 30.7 39.7 31.6 0.048 0.030 0.059 0.031 22.0 30.3 39.6 30.7 0.048 0.028 0.069 0.031 22.1 28.6 39.2 29.5 0.047 0.026 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.024 0.032 23.5 38.5 42.8 38.3 0.058 0.044 0.044 0.031 22.2 34.6 43.1 34.3 0.059 0.035 0.055 0.031 22.0 33.5 42.9 33.2 0.058 0.033 0.060 0.031 22.1 32.0 43.0 32.5 0.058 0.032 0.067 0.031 22.2 31.6 42.9 31.8 0.058 0.030

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129 APPENDIX F EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT CON DENSERS WITH CO-CURRENT AND COUNTERCURRENT FLOW m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) in Diffusion tower 0.062 0.040 60.0 37.7 26.9 0.010 m L (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.005 22.9 23.2 42.4 38.5 0.056 0.045 0.070 22.3 27.8 42.3 35.9 0.056 0.039 0.081 23.6 27.9 42.2 35.2 0.056 0.037 0.098 24.2 28.1 41.6 34.3 0.054 0.035 0.110 24.2 28.1 41.4 33.8 0.053 0.034 0.123 24.3 28.1 41.7 33.5 0.054 0.034 0.119 24.4 28.1 41.9 33.5 0.055 0.034 0.109 24.7 28.2 42.1 33.8 0.055 0.034 0.092 24.9 28.0 41.6 34.4 0.054 0.035 0.075 25.0 28.0 42.1 35.6 0.055 0.038 Co-current condenser stage 0.006 25.1 27.9 42.3 38.8 0.056 0.046 0.001 22.9 23.2 38.5 38.8 0.045 0.046 0.063 22.3 27.8 36.0 34.1 0.039 0.035 0.075 23.6 27.9 35.2 32.9 0.037 0.032 0.089 24.2 28.1 34.3 31.6 0.035 0.030 0.101 24.2 28.1 33.8 30.9 0.034 0.029 0.115 24.3 28.1 33.5 30.4 0.034 0.028 0.111 24.4 28.1 33.5 30.6 0.034 0.028 0.100 24.7 28.2 33.8 31.0 0.034 0.029 0.084 24.9 28.0 34.4 31.9 0.035 0.031 0.067 25.0 28.0 35.6 33.5 0.038 0.034 Countercurrent condenser stage 0.001 25.1 27.9 38.8 39.0 0.046 0.046

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130 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) in Diffusion tower 0.047 0.040 60.7 39.1 26.9 0.010 m L (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.006 23.0 23.8 40.5 37.3 0.050 0.042 0.069 25.1 27.6 40.4 35.0 0.050 0.037 0.073 26.0 28.0 40.0 34.5 0.049 0.036 0.086 26.2 28.0 40.1 33.8 0.049 0.034 0.100 26.3 28.3 40.2 33.2 0.049 0.033 0.118 26.2 28.0 40.0 32.7 0.049 0.032 0.123 26.2 28.0 39.8 32.5 0.049 0.032 0.107 26.0 28.0 39.8 32.9 0.049 0.032 0.090 26.0 28.1 39.7 33.4 0.048 0.033 0.074 26.1 28.0 40.0 34.2 0.049 0.035 Co-current condenser stage 0.006 26.2 28.0 40.2 36.9 0.050 0.041 0.001 23.0 23.8 37.3 37.6 0.045 0.046 0.061 25.1 27.6 35.0 33.4 0.039 0.035 0.066 26.0 28.0 34.5 32.8 0.037 0.032 0.079 26.2 28.0 33.8 31.8 0.035 0.030 0.092 26.3 28.3 33.2 30.9 0.034 0.029 0.110 26.2 28.0 32.7 30.2 0.034 0.028 0.113 26.2 28.0 32.5 30.0 0.034 0.028 0.097 26.0 28.0 32.9 30.5 0.034 0.029 0.080 26.0 28.1 33.4 31.4 0.035 0.031 0.066 26.1 28.0 34.2 32.6 0.038 0.034 Countercurrent condenser stage 0.001 26.2 28.0 36.9 37.0 0.046 0.046

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131 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) in Diffusion tower 0.065 0.041 51.4 36.4 26.8 0.010 m L (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.006 21.9 23.3 37.0 34.0 0.041 0.034 0.071 24.2 27.9 36.9 32.3 0.041 0.031 0.088 24.9 27.8 36.5 31.6 0.040 0.030 0.097 25.4 27.9 36.5 31.5 0.040 0.030 0.110 25.6 28.0 36.8 31.2 0.041 0.029 0.123 25.7 28.1 37.2 31.0 0.042 0.029 0.117 25.6 28.1 37.3 31.0 0.042 0.029 0.098 25.6 28.1 37.0 31.5 0.041 0.030 0.079 25.6 28.0 37.1 32.1 0.042 0.031 Co-current condenser stage 0.006 25.5 27.4 37.2 34.5 0.042 0.036 0.001 21.9 23.3 34.0 34.2 0.034 0.035 0.062 24.2 27.9 32.3 31.3 0.031 0.029 0.079 24.9 27.8 31.6 30.2 0.030 0.027 0.088 25.4 27.9 31.5 30.0 0.030 0.027 0.100 25.6 28.0 31.2 29.5 0.029 0.026 0.116 25.7 28.1 31.0 29.2 0.029 0.026 0.108 25.6 28.1 31.0 29.3 0.029 0.026 0.089 25.6 28.1 31.5 29.9 0.030 0.027 0.071 25.6 28.0 32.1 30.8 0.031 0.029 Countercurrent condenser stage 0.001 25.5 27.4 34.5 34.7 0.036 0.036

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132 APPENDIX G EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT CON DENSER STAGE WITH COUNTERCURRENT FLOW m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.072 0.037 24.6 29.7 36.1 29.6 0.039 0.027 0.060 0.037 24.6 30.6 36.3 30.1 0.040 0.027 0.048 0.037 24.7 30.8 36.4 31.5 0.040 0.030 0.039 0.038 24.6 31.0 36.6 32.3 0.040 0.031 0.031 0.038 24.6 31.1 36.6 33.0 0.040 0.033 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.070 0.034 25.3 30.9 39.9 31.6 0.049 0.030 0.064 0.034 25.1 31.5 40.0 32.0 0.049 0.031 0.058 0.035 25.2 31.5 40.1 32.8 0.049 0.032 0.046 0.035 24.9 31.7 40.2 34.5 0.050 0.036 0.042 0.035 25.3 32.2 40.3 35.1 0.050 0.037 0.038 0.035 25.1 32.6 40.3 35.6 0.050 0.038 0.028 0.035 25.1 33.3 40.3 36.5 0.050 0.040 m L (kg/s) m a (kg/s) T L, in ( C) T L,out ( C) T a,in ( C) T a, out ( C) in out 0.069 0.033 24.9 33.0 42.8 32.2 0.058 0.031 0.061 0.033 24.8 34.1 42.8 33.1 0.057 0.033 0.049 0.033 24.7 34.5 42.8 34.7 0.058 0.036 0.042 0.033 25.0 34.4 42.8 36.1 0.058 0.039 0.035 0.033 24.9 34.6 42.9 37.0 0.058 0.041 0.029 0.034 24.9 35.8 42.9 37.7 0.058 0.043

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133 APPENDIX H UNCERTAINTY ANALYSIS OF THE FLUID PROPERTIES Experimental data will have errors and uncertaintie s. These uncertainties will be introduced into the computational model when using the experimental data to calibrate a numerical model. The performance of the DDD process is affected by this problem. Therefore, understanding the possible errors is an important issue for the experiments and computations. The conclusions drawn from the analyt ical model will depend on how well the uncertainties are controlled in both the experi ment and computation. This work analyzes the uncertainties in predicting the fluid properties by using the current empirical correlations. The uncertainties of the calculated v alues introduced by the current experimental measurements are presented. Theory of Uncertainty There are two ways to record uncertainties: the abs olute value of the uncertainty or the uncertainty relative to the mean value. The abs olute uncertainty has the same units as the mean value. The relative uncertainty has no uni ts since it is the ratio of the absolute uncertainty to the mean value. If a result is calculated based on a number of meas ured quantities, the total uncertainty is the combination of the uncertainties of the individual components, where each component will have a certain influence on the final result. For example, in the DDD formulations, temperature, relative humidity, a nd volumetric flow rate are measured to calculate the mass transfer coefficient s using Onda’s correlation. Each measured quantity has an associated uncertainty and will affect the computation result.

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134 Assuming N is the computed quantity, it is a functi on of several directly measured quantities X 1 X 2 X 3 . The relation of N with X i can be expressed as [53], ) , ( 3 2 1 X X X f N = (H.1) The absolute uncertainty of N, N D is calculated by, D = = = D ) ( ) ( i i i i X X f dX X f Df N (H.2) and the relative uncertainty of N, N N D is calculated by, n r D = n r = = = D i i i i X X f dX X f f D f Df N N ) (ln ) (ln ) (ln (H.3) Uncertainty of the Calculated Fluid Properties The current experiment system can only measure the water temperature, air temperature, relative humidity, gas side pressure, water volumetric flow rate and air volumetric flow rate. Many other fluid properties s uch as viscosity, surface tension and heat conductivity have to be calculated by empirica l formulations based on the measured values. The following analysis will elucidate the i nfluence of the measurement uncertainties on the calculated values. However, si nce this analysis only focuses on the influence from the measurement uncertainties, it is assumed that all the empirical formulations of the fluid properties will not intro duce additional numerical error to the calculated result. Water Viscosity Water viscosity is expressed as, 1 2 10 178811 .0 N L e =m (H.4) where 3 6 2 3 1 1 10 935912 .0 10 237304 .0 10 332283 .0 ) ( L L L L T T T T N + = (H.5)

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135 The relative uncertainty of water viscosity is expr essed as, L L L L T T F D = D 1m m and 3 6 2 3 1 1 10 935912 .0 2 10 237304 .0 ) ( L L L T T T N F + = (H.6) Water Density Water density is expressed as, 1 2 8 7 3 ) 10 655823 .0 10 329673 .0 10 999968 .0( ) ( + = L L L L T T Tr (H.7) The relative uncertainty of water density is expres sed as, L L L L T T F D = D 2r r and ) ( ) 10 655823 .0 10 999968 .0( 1 2 8 3 2 L L L T T Fr = (H.8) Water Surface Tension Water surface tension is expressed as, 2 6 3 10 233607 .0 10 146149 .0 0757742 .0 ) ( L L L L T T T =s (H.9) The relative uncertainty of water surface tension i s expressed as, L L L L T T F D = D 3s s and ) ( 10 233607 .0 0757742 .0 1 2 6 3 L L L T T Fs + = (H.10) Water Diffusivity Water diffusivity is expressed as, 298 15. 273 10 16.2 ) ( 9 + = L L L T T D (H.11) The relative uncertainty of water diffusivity is ex pressed as, L L L L T T F D D D = D 4 and 15. 273 15. 273 1 4 + = L T F (H.12) Water Specific Heat Water specific heat is expressed as,

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136 2 4 2 10 88714 .0 10 316356 .0 21662 .4 ) ( L L L L T T T Cp + = (H.13) The relative uncertainty of water specific heat is expressed as, L L L L T T F Cp Cp D = D 5 and ) ( 10 88714 .0 21662 .4 1 2 4 5 L L L T Cp T F = (H.14) Water Heat Conductivity Water heat conductivity is expressed as, 2 5 2 10 892407 .0 10 201072 .0 562574 .0 ) ( L L L L T T T K + = (H.15) The relative uncertainty of water heat conductivity is expressed as, L L L L T T F K K D = D 6 and ) ( 10 892407 .0 562574 .0 1 2 5 6 L L L T K T F + = (H.16) Vapor Viscosity Vapor viscosity is expressed as, 2 12 7 6 10 815994 .0 10 39911 .0 10 01801 .8 ) ( a a a v T T T + + =m (H.17) The relative uncertainty of vapor viscosity is expr essed as, a a v v T T F D = D 7m m and ) ( 10 815994 .0 10 01801 .8 1 2 12 6 7 a v a T T Fm = (H.18) Vapor Density Vapor density is expressed as, 2 108 206 N V e =r (H.19) where 3 6 2 3 1 2 10 672679 .0 10 271791 .0 10 687293 .0 ) ( a a a a T T T T N + = (H.20) The relative uncertainty of vapor density is expres sed as, a a v v T T F D = D 8r r and 3 6 2 3 2 8 10 672679 .0 2 10 271791 .0 ) ( a a a T T T N F + = (H.21)

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137 Vapor Saturation Pressure Vapor saturation pressure is expressed as, 3 611379 .0 N sat e P = (H.22) where 3 6 2 3 1 3 10 676138 .0 10 278793 .0 10 723669 .0 ) ( a a a a T T T T N + = (H.23) The relative uncertainty of vapor saturation pressu re is expressed as, a a sat sat T T F P P D = D 9 and 3 6 2 3 3 9 10 676138 .0 2 10 278793 .0 ) ( a a a T T T N F + = (H.24) Vapor Specific Heat Vapor specific heat is expressed as, 2 5 3 10 326009 .0 10 518644 .0 85406 .1 ) ( a a a v T T T Cp + + = (H.25) The relative uncertainty of vapor specific heat is expressed as, a a v v T T F Cp Cp D = D 10 and ) ( 10 326009 .0 85406 .1 1 2 5 10 a v a T Cp T F = (H.26) Vapor Heat Conductivity Vapor heat conductivity is expressed as, 2 7 4 10 943145 .0 10 549804 .0 0182188 .0 ) ( a a a v T T T K + + = (H.27) The relative uncertainty of vapor heat conductivity is expressed as, a a v v T T F K K D = D 11 and ) ( 10 943145 .0 0182188 .0 1 2 7 11 a v a T K T F = (H.28) Air Viscosity Air viscosity is expressed as, 2 10 7 4 10 335868 .0 10 490401 .0 10 172011 .0 ) ( a a a a T T T + =m (H.29) The relative uncertainty of air viscosity is expres sed as,

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138 a a a a T T F D = D 12m m and ) ( 10 335868 .0 10 172011 .0 1 2 10 4 12 a a a T T Fm + = (H.30) Air Density Air density is expressed as, 2 4 2 10 11752 .0 10 458748 .0 29238 .1 ) ( a a a a T T T + =r (H.31) The relative uncertainty of air density is expresse d as, a a a a T T F D = D 13r r and ) ( 10 11752 .0 29238 .1 1 2 4 13 a a a T T Fr = (H.32) Air Specific Heat Air specific heat is expressed as, 2 6 4 10 486923 .0 10 193781 .0 00379 .1 ) ( a a a a T T T Cp + + = (H.33) The relative uncertainty of air specific heat is ex pressed as, a a a a T T F Cp Cp D = D 14 and ) ( 10 486923 .0 00379 .1 1 2 6 14 a a a T Cp T F = (H.34) Air Heat Conductivity Air heat conductivity is expressed as, a a a T T K 4 10 72538 .0 0241462 .0 ) ( + = (H.35) The relative uncertainty of Air heat conductivity i s expressed as, a a a a T T F K K D = D 15 and ) ( 0241462 .0 1 15 a a T K F = (H.36) Gas Diffusivity Gas diffusivity is expressed as,

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139 5.1 5 298 15. 273 10 6.2 ) ( + = a a G T T D (H.37) The relative uncertainty of gas diffusivity is expr essed as, a a G G T T F D D D = D 16 and 15. 273 15. 273 1 5.1 16 + = a T F (H.38) Gas Mass Flow rate The measurement output value from the air flowmeter in the experiment is a standard air flow rate, m std which is an air flow rate when P=P std =14 psi and T a =T std =20C. The actual air flow rate, m a is calculated from, = std a sat std std a T T P P P m mf (H.39) The relative uncertainty of gas mass flux is expres sed as, D + D + D + D = Df f f fsat sat sat sat a a std std a a P P P P P T T m m m m (H.40) Absolute Humidity Absolute humidity is calculated from, f f wsat sat P P P = 622 .0 (H.41) The relative uncertainty of the absolute humidity i s expressed as, D + D = Df f f w wsat sat sat P P P P P (H.42) Gas Viscosity Gas viscosity is calculated from, a v Gm w m w w m+ + + = 1 1 1 (H.43)

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140 The relative uncertainty of gas viscosity is expres sed as, a a a v v v v a v a G Gm m m m w m m m m w w w w m m w m mD + + D + + D + + + = D 1 1 1 1 1 1 1 1 1 1 1 (H.44) Gas Density Gas density is expressed as, a v Gr w r w w r+ + + = 1 1 1 (H.45) The relative uncertainty of gas density is expresse d as, a a a v v v v a v a G Gr r r r w r r r r w w w w r r w r rD + + D + + D + + + = D 1 1 1 1 1 1 1 1 1 1 1 (H.46) Gas Specific Heat Gas specific heat is expressed as, a v G Cp Cp Cpw w w + + + = 1 1 1 (H.47) The relative uncertainty of gas specific heat is ex pressed as, a a a v v v v a v a G G Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp D + + D + + D + + + = Dw w w w w w1 1 1 1 1 1 1 1 1 1 1 (H.48) Gas Heat Conductivity Gas heat conductivity is expressed as, a v G K K Kw w w + + + = 1 1 1 (H.49) The relative uncertainty of gas heat conductivity i s expressed as,

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141 a a a v v v v a v a G G K K K K K K K K K K K K D + + D + + D + + + = Dw w w w w w1 1 1 1 1 1 1 1 1 1 1 (H.50) Uncertainty of the Mass and Heat Transfer Coefficients In the current evaporation and condensation computa tional models, the mass transfer coefficients are evaluated for the liquid and gas flow using Onda’s correlation and a heat and mass transfer analogy is used to eva luate the heat transfer coefficients. The temperature and humidity profiles through the packe d bed can be calculated using the energy and mass conservation equations. It is appar ent that Onda’s correlation and the heat/mass transfer analogy formulations are the cor e of the current analytical models. However, the calculated fluid properties will be us ed in Onda’s correlation and the heat and mass transfer analogy formulations to get the m ass and heat transfer coefficients of liquid and gas. This use of fluid properties will p ass the measurement uncertainties to the calculated heat and mass transfer coefficients and eventually affect the accuracy of the model predictions. Wetted Area of Packing Onda’s correlation is shown in Appendix A, and the wetted area of packing can be expressed as, 0 aN a w = (H.51) where 1 1 0 X e N = 5/1 05.0 2/1 4/3 1 Re 2.2 L L LA L c We Fr X =s s (H.52)

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142 Assuming the uncertainties of the gravitational acc eleration and the critical surface tension are negligible, where 0 = D = D c gs the relative uncertainty of the wetted area can be expressed as, D + D + D + D + D + D = D L L L L L L L L X w w a a m m e X a a a ar r m m s s25.0 5.0 75.0 95.0 1 1 1 (H.53) Recall Taylor’s series of e x as, + + + = = 2 1 2 0 x x n x e n x (H.54) Using the first order Taylor series expansion of 1 X e and combining with Eqn. (H.53), the relative uncertainty of the wetted area of packing can be expressed as, L L L L L L L L w w m m a a a ar r m m s sD + D + D + D + D = D 25.0 5.0 95.0 75.1 (H.55) Mass Transfer Coefficient on the Liquid Side The liquid side mass transfer coefficient is calcul ated by, 3/1 4.0 5.0 3/2 ) ( Re 0051 .0 n r = L L g ad Sc k p L Lw Lr m (H.56) The relative uncertainty of the liquid side mass tr ansfer coefficient can be expressed as, p p L L L L L L L L L L L L d d D D m m a a k k D + D + D + D + D + D + D = D 4.0 5.0 633 .0 333 .1 567 .1 833 .1s s r r m m (H.57) Mass Transfer Coefficient on the Gas Side The gas side mass transfer coefficient is expressed as, G p G GA G aD ad Sc k 2 3/1 7.0 ) ( Re 23.5 = (H.58)

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143 The relative uncertainty of the gas side mass trans fer coefficient can be expressed as, G G a a G G G G p p G G m m D D a a d d k kr r m mD + D + D + D + D + D = D 333 .0 7.0 033 .1 333 .1 7.1 2 (H.59) Finally, the uncertainties of the liquid and gas ma ss transfer coefficients can be calculated by Eqs (H.57) and (H.59). They clearly show the inf luence of the uncertainty from each individual fluid property to the total uncertainty of the liquid/gas mass transfer coefficient by using Onda’s correlation. For example, Eqn. (H.5 7) shows that when all the fluid properties have the same amount of relative uncerta inties, the uncertainty of liquid viscosity has the largest influence on the predicti on accuracy of the liquid mass transfer coefficient. Heat Transfer Coefficient on the Liquid Side Using the heat and mass transfer analogy method, th e liquid side heat transfer coefficient can be expressed as, 2/1 ) ( L L PL L L L D K C k Ur= (H.60) The relative uncertainty of the liquid side heat tr ansfer coefficient can be expressed as, L L L L L L L L L L L L K K D D Cp Cp k k U U D + D + D + D + D = D 5.0 5.0 5.0 5.0r r (H.61) Heat Transfer Coefficient on the Gas Side The gas side heat transfer coefficient is calculate d from, 3/2 3/1 ) ( ) ( G G PG G G G D K C k Ur= (H.62) The relative uncertainty of the gas side heat trans fer coefficient can be expressed as, G G G G G G G G G G G G Cp Cp D D K K k k U U D + D + D + D + D = D 333 .0 333 .0 667 .0 667 .0r r (H.63)

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144 Results and Analysis To calculate the uncertainties of the heat and mass transfer coefficients in the current model, following assumptions are made, 1. The uncertainties of the specific area of the packi ng and the diameter of the packing are negligible, 0 = D = D p d a 2. Water temperature, T L varies from 20-70 C. 3. Air temperature, T a varies from 20-70 C. 4. Relative humidity, is unity. The experimental measurements have different uncert ainties and are shown below as, 1. Absolute uncertainty of water temperature: C T L = D 5.0 ; 2. Absolute uncertainty of water temperature: C T a = D 5.0 ; 3. Relative uncertainty of water mass flux: % 5.1 = D L L m m ; 4. Relative uncertainty of water mass flux: % 1 = D std std m m ; 5. Relative uncertainty of relative humidity: % 5.2 = D f f Figure H-1 shows that the relative uncertainty of w ater property predictions varies with water temperature measurement. It clearly show s that among all the calculated water properties, water viscosity prediction has the larg est relative uncertainty of about 1%, whereas the other properties only have a relative u ncertainty of approximately 0.1%. Noting that the water mass flow rate has a 1.5% rel ative uncertainty, and considering the result of this figure together with Eqn. (H.57), it is obvious that the prediction uncertainty of the liquid mass transfer coefficient is mainly i nfluenced by the uncertainties of the water mass flow rate and the water viscosity.

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145 Water temperature (C) 203040506070 Relative Uncertainty (%) 0.01 0.1 1 m L D L K L s L r L Cp L Figure H-1 Variation of the relative uncertainties of the calculated water properties with water temperature Air temperature (C) 203040506070 Relative Uncertainty (%) 0.01 0.1 1 10 P sat r v m v Cp v K v Figure H-2 Variation of the relative uncertainties of the calculated vapor properties with air temperature Figure H-2 shows the relative uncertainty of calcul ated vapor property influenced by the air temperature. It shows that the vapor sat uration pressure and density have very high uncertainty of 6%, the vapor viscosity and hea t conductivity have 0.5% relative

PAGE 163

146 uncertainty, and vapor specific heat prediction has the smallest relative uncertainty of about 0.05%. Air temperature (C) 203040506070 Relative Uncertainty (%) 0.001 0.01 0.1 1 r a m a K a Cp a Figure H-3 Variation of the relative uncertainties of the calculated air properties with air temperature Air temperature (C) 203040506070 Relative Uncertainty (%) 1 10 wm a D G K G r G m G Cp G Figure H-4 Variation of the relative uncertainties of the calculated air/vapor mixture properties with air temperature Figure H-3 shows the relative uncertainty of the co mputed air property influenced by the air temperature. It clearly shows that the r elative uncertainty of the air specific heat

PAGE 164

147 calculation is only 0.01% when T a < 70 C, which means that the current air temperat ure measurement has the least influence on the air spec ific heat calculation. The other property calculations have a much higher relative u ncertainty of 0.3% comparing to the air specific heat. The gas side of the DDD process is an air and vapor mixture. During the computation, the mixture properties are used to cal culate the mass and heat transfer coefficients. Figure H-4 shows the relative uncerta inty of the calculated air/vapor mixture property influenced by air temperature. It clearly shows that there are mainly two types of uncertainties varying with air temperature measurem ent. The first type, which includes the absolute humidity, mixture mass flow rate, and viscosity, is barely varying with the air temperature. The other type, which includes the diffusivity, heat conductivity, density, and specific heat of the mixture, is increasing alm ost exponentially with the air temperature. Obviously, the second type of variatio n is undesirable for a numerical calculation because it will limit the applicable te mperature range of the model. Fig. H-5 shows that the wetted area prediction has approximately 2% uncertainty caused by the measurement error. However, Onda [31] analyzed the relative uncertainty of the wetted area prediction to be approximately 2 0% based on his collection of experiment data including the column packed with ra chig rings, berl saddles, spheres and rods made of ceramic, glass, and polyvinylchloride. Therefore, it is clear to see that the major uncertainty in predicting the wetted area is still from the original Onda’s experimental data and the manner that he correlated them. The current experiment measurement method only introduces minimal uncertai nty on the prediction.

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148 Water temperature (C) 203040506070 203040506070Relative Uncertainty (%) 1 10 Air temperature (C) a w k L k G Figure H-5 Variation of the relative uncertainties of the wetted area and mass transfer coefficients with temperature by using Onda’s corre lation Fig. H-5 also shows that the liquid side mass trans fer coefficient prediction has a 4.5% relative uncertainty caused by the measurement error. It is interesting to note that there exists a minimum prediction uncertainty of th e gas mass transfer coefficient of 5% when the gas is about 35 C, and the uncertainty wi ll increase quickly when the air temperature exceeds 50 C. This result indicates th at the current analytical models are relatively more accurate and reliable when the high est air temperature is less than 50 C. Although this indication may limit the applicable t emperature range of the current model, the air side temperature of 50 C seems to be the m ost practical operating temperature for the DDD applications. The uncertainty will also be introduced into the he at transfer coefficients using the heat and mass transfer analogy method. Figure H-6 s hows the relative uncertainty of the heat transfer coefficient varying with the temperat ure measurement. It is clear to see that the liquid side heat transfer prediction has a 4% r elative uncertainty. The gas side heat

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149 transfer coefficient relative uncertainty maintains at 8% when the operating air temperature is lower than 50 C, then it increases very fast with the air temperature. Water temperature (C) 203040506070 203040506070Relative Uncertainty (%) 0 5 10 15 20 Air temperature (C) U L U G Figure H-6 Variation of the relative uncertainties of the heat transfer coefficients with temperature In conclusion, the influence of the experimental da ta uncertainties on the calculated fluid properties has been explored. When the measur ed temperature is less than 60 C, the current measurement method will only introduce a re lative uncertainty of 2% to the wetted area prediction, 10% to the mass transfer co efficient prediction, and 8% to the heat transfer coefficient prediction. Onda et. al [ 31] announced that the relative uncertainty to be approximately 20% to the wetted a rea prediction, and 30% to the mass transfer coefficient prediction based on his experi mental database. It indicates that the major error of the current model is caused by the e mpiricism involved in the correlations. Using the current experimental system to calibrate Onda’s correlation should be acceptable and reliable. The results shown in this analysis indicates that the accuracy of the current model can be improved by using better f ormulations of the air saturation

PAGE 167

150 pressure and absolute humidity, and by using more a ccurate measurement methods of air flow rate and air temperature. And the largest impr ovement on the accuracy of the predictions could be achieved by the experimental c alibration of Onda’s correlation based on only one specified packing material.

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151 LIST OF REFERENCES 1. World Resources Institute, United Nations Developme nt Programme, the United Nations Environment Programme, and the World Bank, World Resources 2000 – 2001 People and Ecosystems, Ch 2, pp. 104-105, Sep 2000. 2. Ettouney H., Visual Basic Computer Package for Ther mal and Membrane Desalination Processes, Vol. 165, pp. 393-408, 2004 3. International Atomic Energy Agency, Technical and E conomic Evaluation of Potable Water Production through Desalination of Se awater by Using Nuclear Energy and Other Means, IAEA-TECDOC-666, Vienna, 19 92. 4. Bourouni, K., M. Chaibi, M.T., and Tadrist, L., Wat er Desalination by Humidification and Dehumidification of Air: State o f the Art, Desalination, Vol. 137, Issues 1-3, pp. 167-176, 2001. 5. Al-Hallaj, S., Farid, M.M., and Tamimi, A.R., Solar Desalination with A Humidification-Dehumidification Cycle: Performance of the Unit, Desalination, Vol. 120-3, pp. 273-280, 1998. 6. Assouad, Y., and Lavan, Z., Solar Desalination with Latent Heat Recovery, Journal of Solar Energy Engineering, Vol. 110-1, pp. 14-16, 1988. 7. Muller-Holst, H., Engelhardt, M., Scholkopf, W., Sm all-Scale Thermal Seawater Desalination Simulation and Optimization of System Design, Desalination Vol. 122-3, pp. 255-262, Jul 1999. 8. Al-Hallaj, S. and Selman, J.R., A Comprehensive Stu dy of Solar Desalination with a Humidification – Dehumidification Cycle, A Report by the Middle East Desalination Research Center, Muscat, Sultanate of Oman, 2002. 9. Klausner J.F., Li Y., Darwish M., and Mei R. Innova tive Diffusion Driven Desalination Process, Journal of Energy Resources T echnology, Vol. 126-3, pp. 219-225, 2004. 10. Larson, R.L., Albers, W., Beckman, J., and Freeman, S., The Carrier-Gas Process – A New Desalination and Concentration Technology, De salination, Vol. 73, pp. 119-137, 1989.

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152 11. Beckman, J.R., Innovative Atmospheric Pressure Desa lination, Desalination Research and Development Program Final report No. 5 2 for Department of Interior Agreement No. 98-FC-81-0049, Sep 1999. 12. Beckman, J.R., Carrier-Gas Enhanced Atmospheric Pre ssure Desalination, Desalination Research and Development Program Final report No. 92 for Department of Interior Agreement No. 99-FC-81-0186, Oct 2002. 13. Bharathan, D., Parsons, B.K., and Althof, J.A., Dir ect-Contact Condensers for Open-Cycle OTEC Applications, National Renewable En ergy Laboratory Report SERI/TP-252-3108 for DOE Contract No. DE-AC02-83CH1 0093, 1988. 14. WWW.CNN.COM, Thirsty Tampa Bay Ponders Huge Desalin ation Plant, from CNN Correspondent Sean Callebs, April 20, 2000. 15. WWW.tampabaywater.org, Tampa Bay Seawater Desalinat ion Uses Seawater to Provide A Drought-proof Supply of Drinking Water, O ctober, 28, 2005. 16. Bullard, C.W. and Klausner, J.F., Empirical Analysi s of Power Plant Siting, Energy Systems and Policy, Vol. 11, pp. 103-120, 1987. 17. Alley, W.M., Desalination of Ground Water: Earth Sc ience Perspectives, U.S. Geological Survey Fact Sheet 075-03, Oct 2003. 18. Feth, J.H., and others, Preliminary Map of the Cont erminous United States Showing Depth to and Quality of Shallowest Ground W ater Containing More Than 1000 Parts per Million Dissolved Solids, U.S. Geolo gical Survey Hydrologic Investigations Atlas HA-199, 1965. 19. Energy Information Administration, Annual Solar The rmal and Photovoltaic Manufacturing Activities, form number EIA-63A and f orm number EIA-63B, U.S. Department of Energy, 2001. 20. Energy Information Administration, State Electricit y Profile, publication number DOE/EIA-0629, U.S. Department of Energy, released N ov 2001. 21. Schrieber, C.F., Measurements and Control Related t o Corrosion and Scale in Water Desalination Installations, in Desalination a nd Water Purification 2, Measurements and Control in Water Desalination, Lio r, N. (Ed), Elsevier, New York, 1986. 22. Spiegler, K.S., Salt-Water Purification, second edi tion, Plenum Press, New York, 1977. 23. Merkel F. Verdunstungskuhlung, VDI Forschungsarbeit en, 275, Berlin, 1925. 24. Baker D.R. and Shryock, H.A., A Comprehensive Appro ach to the Analysis of Cooling Tower Performance, J. Heat Transfer, pp. 33 9-350, 1961.

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153 25. Sutherland J.W., Analysis of Mechanical-Draught Cou nterflow Air/Water Cooling Towers, J. Heat Transfer, Vol. 105, pp. 576-583, 19 83. 26. Osterle F., On the Analysis of Counter-Flow Cooling Towers, Int. J. Heat Mass Transfer, Vol. 34-4/5, pp. 1316-1318, 1991. 27. El-Dessouky, H.T.A., Ai-Haddad A., and Ai-Juwayhel F., A Modified Analysis of Counter Flow Wet Cooling Towers, J. Heat Transfer, Vol. 119, pp. 617-626, 1997. 28. Kays W. M., Crawford M. E. & Weigand B., Convective Heat and Mass Transfer, 34, New York, 2005. 29. McAdams W.H., Pohlenz J.B., and St. John R.C., Tran sfer of Heat and Mass Between Air and Water in A Packed Tower, Chem. Eng. Prog., Vol. 45, pp. 241252, 1949. 30. Huang C.C., Fair J.R., Direct-Contact Gas-Liquid He at Transfer In A Packed Column, Heat Transfer Engineering, Vol. 10-2, pp. 1 9-28, 1989. 31. Onda K., Takechi H., and Okumoto Y., Mass Transfer Coefficients Between Gas and Liquid Phases In Packed Columns, J. Chem. Eng. Jpn., Vol. 1, pp. 56-62, 1968. 32. Eckert, E. R. G., Analogies to Heat Transfer Proces ses, in Measurements in Heat Transfer, ed. Eckert, E. R. G. and Goldstein, R. J. pp. 397-423, Hemisphere Pub., New York, 1976. 33. Huang C. C. Heat Transfer by Direct Gas-Liquid Cont acting, M.S. thesis, University of Texas, Austin, 1982. 34. Perry, R.H. and C.H. Chilton, Eds., Chemical Engine ers Handbook (Sixth edition), McGraw-Hill Book Company, New York, 1984. 35. Treybal, R, Mass Transfer Operations. McGraw-Hill B ook Company, Inc. New York, 1955. 36. Jacobs, H. R., Thomas, K. D. and Boehm, R. F. (1979 ) Direct Contact Condensation of Immiscible Fluids in Packed Beds, P resented at Natl Heat Transfer Conf, 18th San Diego, CA, USA, ASME 103 – 110. 37. Kunesh, J. G., Direct-contact Heat Transfer From A Liquid Spray Into A Condensing Vapor, Industrial & Engineering Chemistr y Research vol. 32 no. 10 pp. 2387-2389, 1993. 38. Higbie, R., The Rate of Absorption of A Pure Gas In to a Still Liquid During Short Periods of Exposure, Transactions of AIChE, vol. 31 pp. 365 – 389, 1935.

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154 39. Bharathan, D. and Althof, J., An Experimental Stud y of Steam Condensation on Water in Countercurrent Flow in Presence of Inert G as, Proc. Of ASME, paper 84WA/Sol-25, New Orleans, 1984. 40. Bontozoglou, V. and Karabelas, A. J., Direct-contac t Steam Condensation with Simultaneous Noncondensable Gas Absorption, AIChE J ournal vol. 41 no. 2 pp. 241-250, 1995. 41. Klausner, J.F., Li, Y., Mei, R., Evaporative Heat a nd Mass Transfer for the Diffusion Driven Desalination Process, J. Heat and Mass Transfer, Vol. 42-6, pp. 528-536, 2005. 42. Bemer, G. G. and Kalis. G. A. J., A New Method to P redict Hold-up and Pressure Drop in Packed Columns, Trans Inst. Chem. Eng. Vol. 56, pp. 200-204, 1978. 43. Bravo, J. L., Rocha, J. A., and Fair, J. R., Mass T ransfer in Gauze Packings, Hydrocarbon Process, Vol. 64-1, pp. 91, 1985. 44. Bravo, J. L., Rocha, J. A., and Fair, J. R., Pressu re Drop in Structured Packings, Hydrocarbon Process, Vol. 56-3, pp. 45, 1986. 45. Sellin, N., Sinezio, J. and Campos, C., Surface Com position Analysis of PP Films Treated by Corona Discharge, Materials Research, Vo l. 6-2, pp. 163-166, 2003. 46. Skold, J. O., Energy Savings in Cooling Tower Packi ngs, Chem. Eng. Prog, 77 (10), 48-53, 1981. 47. Burger, R., Modernize Your Cooling Tower, Chem. Eng Prog. 86(9) 37-40, 1990. 48. Wangnick, K., 2002 IDA Worldwide Desalting Plants I nventory Report No. 17, produced by Wangnick Consulting for IDA, Gnarrenbur g, Germany, 2002. 49. Hisham M. Ettouney and Hisham T. El-Dessouky, Kuwai t Univ.; Ron S. Faibish and Peter J. Gowin, International Atomic Energy Age ncy, Evaluating the Economics of Desalination, Chem. Eng. Prog., 32-39, Dec 2002. 50. Survey by the NUS Consulting Group, based on the mu nicipal water price as of July 1, 2002 in U.S. 51. U.S. DOE Energy Information Administration, Elect ric Power Monthly Annual, U.S, August, 2001. 52. Nuclear Energy Institute, The Economic Benefits Of Oyster Creek Generating Station, Prepared for AmerGen Energy Co. LLC, Ocean County, New Jersey, March 2004. 53. Wilson, E.B., Jr., An Introduction to Scientific Re search, McGraw-Hill Book Company, Inc., New York, 1952.

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155 BIOGRAPHICAL SKETCH Yi Li obtained a bachelor’s degree in engineering m echanics in September 2000 and a master’s degree in nuclear engineering in Jan uary 2003 at Tsinghua University in P.R. China. He started his Ph.D. research in the De partment of Mechanical and Aerospace Engineering at the University of Florida in May 2003.


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Title: Heat and Mass Transfer for the Diffusion Driven Desalination Process
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Copyright Date: 2008

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Holding Location: University of Florida
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Permanent Link: http://ufdc.ufl.edu/UFE0013737/00001

Material Information

Title: Heat and Mass Transfer for the Diffusion Driven Desalination Process
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0013737:00001


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HEAT AND MASS TRANSFER FOR THE DIFFUSION DRIVEN DESALINATION
PROCESS

















By

YI LI













A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA


2006


































Copyright 2006

by

YI LI
































This dissertation is dedicated with love and gratitude to my family. Without their love,
support and faith in me, this accomplishment would not have been possible.















ACKNOWLEDGMENTS

My appreciation and respect go to my advisor, Professor James Klausner, for

introducing me to the field of multiphase flow and for giving me the opportunity to study

heat and mass transfer dynamics for my Ph.D. dissertation. His continuous support and

patience helped me to achieve this work. I would like to express my special thanks to

Professor Renwei Mei for his help and encouragement in my study of turbulence and

numerical analysis. I sincerely thank my committee members for their comments and

help.

I would like to thank all my colleagues, in particular Jessica Knight and Jun Liao. I

also extend my thanks to the individuals in the department who have helped me in one

way or another during my graduate studies.

I would like to acknowledge the support of the U.S. Department of Energy under

Award No. DE-FG26-02NT41537 for this research. I also thank the University of Florida

for the financial assistance through the UF Alumni Fellowship I was awarded for the

academic years 2003-2006.

Finally, I would like to thank my family for their continuous support and

encouragement through the years of my studies. To them, I dedicate this dissertation.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ...................... .. .. ............. ...............................................iv

L IST O F T A B L E S .........................................................................viii

L IS T O F F IG U R E S ...................... .. ............. .. .. ....................................... ix

N O M E N C L A T U R E ...................... .. .. ......... .. ............................ ..........................xiii

A B STR A C T ............. ......... ........................................................... xvi

CHAPTER

1 INTRODUCTION AND LITERATURE REVIEW................................................ 1

Description of Thermal Desalting and Membrane Separation .................................. 2
Description of HDH and MEH Process....................................... 4
Description of DDD Process.............................. .............. ............. 6
Comparison of the DDD Process with HDH and MEH.......... ...................... 8
Comparison of the DDD Process with MSF and RO ....................................... 10
Potential Applications for the DDD Process .......... ............................. 12
Properties of Saline Water .............. ............... ... .............. 17
O objectives of the Study.......................................................................... 21
Scope of W ork...................................................................... ....... ........ 21

2 THERMODYNAMIC ANALYSIS OF THE DDD PROCESS...............................23

M ath em atic M o d el ................................................................................................. 2 3
Computation Results and Analysis.............................. ................26

3 EXPERIM ENTAL STUDY .. ..... ............................................. ...................... 35

Experimental System Description..... ..................... ................ 35
Experimental Facility and Instrumentation.... ........... ....................................38

4 HEAT AND MASS TRANSFER FOR THE DIFFUSION TOWER .......................48

Heat and Mass Transfer Model for the Diffusion Tower........................................48
Model Comparison with Experiments for the Diffusion Tower.............................57
Pressure Drop through the Packing Material................................. ................. 60









Optimization of the Packing Material ............ ................................. ........... 61

5 HEAT AND MASS TRANSFER FOR THE DIRECT CONTACT CONDENSER 73

Mathematical Model of the Packed Bed Direct Contact Condenser ......................... 75
Model Comparison with Experiments for the Packed Bed Direct Contact
C ondenser ................................................................. ................... 82
Wetting Phenomena within Packed Bed........................... ............ 87
Experimental Results of the Droplet Direct Contact Condenser ............................ 90
Condenser Effectiveness.......................................................... ........... ..... 95

6 DDD PROCESS OPTIMIZATION DESIGN AND ECONOMIC ANALYSIS....... 98

M them atical M odel .................................................................. ............... 99
Computation Results and Analysis................................. .............. 101
Econom ic A analysis ............................................................. .... .. ......... 111

7 CONCLUSIONS .................................... ............................ ........... 119

APPENDIX

A O N D A 'S C O R R E LA TIO N .......... ............................................................... 122

B EXPERIMENTAL DATA OF THE DIFFUSION TOWER................................. 123

C EXPERIMENTAL DATA OF THE AIR SIDE PRESSURE DROP THROUGH
TH E PA CK IN G M A TERIAL ................................................................ ....... 125

D EXPERIMENTAL DATA OF THE COUNTERCURRENT FLOW DIRECT
CONTACT CONDENSER STAGE WITH PACKED BED ................................ 126

E EXPERIMENTAL DATA OF THE CO-CURRENT FLOW DIRECT CONTACT
CONDENSER STAGE WITH PACKED BED ................................................... 128

F EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT
CONDENSERS WITH CO-CURRENT AND COUNTERCURRENT FLOW..... 129

G EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT
CONDENSER STAGE WITH COUNTERCURRENT FLOW........................... 132

H UNCERTAINTY ANALYSIS OF THE FLUID PROPERTIES ........................... 133

T theory of U uncertainty ......................................................................................... 133
Uncertainty of the Calculated Fluid Properties ..................................................... 134
Uncertainty of the Mass and Heat Transfer Coefficients ............. ... ............... 141
Results and Analysis..... ................................................................. 144

LIST OF REFERENCES ................................. ............................ ........ 151









BIO GR APH ICAL SK ETCH ....................................................................................... 155
















LIST OF TABLES


Table p

1-1 Pumping and heating energy consumption of some desalination processes ............4

1-2 Comparison of electricity consumption for DDD, MSF, and RO desalination
technologies ............. ........ ............... ............ .................. 10

1-3 Comparison of advantages and disadvantages of DDD, RO, and MSF
desalination technologies ........... .............. ...... ........... ... 11

4-1 Packing m material configurations ....................................................... .............. 63

6-1 Summary of direct costs ............. .. ................................. 114

6-2 Details of cost calculations ........... ............. ..................... .. 114
















LIST OF FIGURES


Figure page

1-1 Schematic diagram of mechanical vapor compression process ............................2

1-2 Schematic diagram of thermal vapor compression combined multi-effect
destillation process ............................................. ....................... 3

1-3 Schematic diagram for diffusion driven desalination process............................ 7

1-4 Depth to saline ground water in the United States [18] .............. .............. 13

1-5 Flow diagram of DDD process driven by solar energy....................................... 14

1-6 Flow diagram of DDD process driven by geothermal energy .......... .............. 15

2-1 Flow diagram for diffusion driven desalination process....................................23

2-2 Rate of entropy generation for different exit brine temperature, Th=270C .............27

2-3 Variation of exit brine temperature with exit air temperature, Th=270C ................28

2-4 Fresh water production efficiency, Th=27 C................................ .... .............. 28

2-5 Rate of entropy generation for different exit brine temperature: a) Th=500 C, b)
Th= 800 C ......................... ............ ............... ............ .............. 29

2-6 Variation of exit brine temperature with exit air temperature: a) Th=500 C, b)
T h= 800 C ............................................ ............................ 30

2-7 Fresh water production efficiency: a) Th=500 C, b) Th=800 C............................32

2-8 Rate of energy consumption: a) Th=500 C, b) Th=800 C ............... ............... 33

2-9 Minimum rate of energy consumption for different Th............... ............... 34

3-1 Pictorial view of the laboratory scale DDD experiment ..................................36

3-2 Schematic diagram of laboratory scale DDD facility .................. ............. 37

3-3 Schematic diagram of experimental diffusion tower .......................... .......... 39









3-4 Schematic diagram of experimental direct contact condenser ............................ 40

3-5 P ictorial view of spray nozzle..................................................... .................... 4 1

3-6 Pictorial view of packing m atrix .............. ......... ...................... ...................42

3-7 Schematic diagram of the instrumentation system for the DDD experiment.......... 42

3-8 Exam ple program of SoftW IRE ......... ................. ................... .................... 44

3-9 "Main" panel of the DDD data acquisition program ........................ ... .......... 45

3-10 "Schematic view" panels of the DDD data acquisition program........................... 46

3-11 "Histogram view" panels of the DDD data acquisition program .......................46

4-1 Diagram of diffusion tower ............ ............ .... .............. 49

4-2 Differential control volume for liquid/vapor heat and mass transfer within
diffusion tow er ................. ........ ............................ 50

4-3 Comparison of predicted exit conditions with the data of Huang [33]: a) L = 2.0
kg/m 2-s, b) L = 4.1 kg/m 2-s ....... .... ......... .. .................................. .............. 56

4-4 Comparison of predicted exit conditions with the experimental data for different
liquid mass fluxes: a) L= 1.75 kg/m2-s, b) L= 1.3 kg/m2-s, c) L= 0.9 kg/m2-s.......58

4-5 Air specific pressure drop variation with air mass flux for different water mass
fluxes ......... .................. ................................. ...........................60

4-6 Energy consumption rate for fresh water production: Berl Saddle a) 0.5", b)
0.75", c) 1.0", d) 1.5"; Raschig Ring e) 0.5", h) 1.0", g) 1.5", h) 2.0"................64

4-7 Maximum possible exit humidity for feed water mass flux ............................. 67

4-8 Gas mass transfer coefficient for air mass flux.................................. ...............68

4-9 Gas pressure drop for air mass flux.............................................. 69

4-10 Required tower height for feed water mass flux.............. .... ................70

4-11 Energy consumption rate for feed water mass flux ..........................................71

4-12 Energy consumption rate for fresh water mass flow rate (cross section diameter
of the packed bed is 15 m ).......................................................... .............. 71

5-1 Differential control volume for liquid/gas heat and mass transfer within a)
countercurrent flow, b) co-current flow condensers ...................................77









5-2 Flow diagram for the countercurrent flow computation .............. .................. 82

5-3 Comparison of predicted exit temperatures and humidity with the experimental
data for countercurrent flow: a) Ta,n=36.90 C, b) Ta,n=40.80 C, c) T,,,=42.8 C... 83

5-4 Comparison of predicted exit temperatures and humidity with the experimental
data for co-current flow: a) T,,,=35.50 C, b) T,,3=39.60 C, c) T,,,=42.90 C ......... 85

5-5 Droplet residence positions on the packing material: a) on the top, b) in the
corner, c) beneath the packing .................................... ............................ ........ 87

5-6 Observation of the liquid blockages within the packed bed: a) side view, b) Top
view .................................... .................................. .......... 89

5-7 Total temperature drop of the air/vapor mixture with varying water to air mass
flow ratios and different air inlet temperatures (without packing) ....................91

5-8 Total fresh water production rate with varying water to air mass flow ratios and
different air inlet temperatures (without packing) ............................................91

5-9 Temperature drop of the air/vapor mixture with varying water to air mass flow
ratios in the a) co-current, b) countercurrent stage (without packing) ..................92

5-10 Fresh water production rate with varying water to air mass flow ratios and
different air inlet temperatures in the a) co-current, b) countercurrent stage
(w without packing) ................................ .......... .. ............... .... .......... 93

5-11 Comparison of the packed bed condenser effectiveness between co-current and
countercurrent flow ............................................................... ............... 96

5-12 Comparison of the countercurrent flow condensation effectiveness between
droplet condenser and packed bed condenser ...................................................97

6-1 Required diffusion tower height with variations in air to feed water mass flow
ratio ................................................................ ........ .......... 101

6-2 Maximum exit humidity ratio variation with air to feed water mass flow ratio.... 102

6-3 Exit air temperature variation with air to feed water mass flow ratio................. 103

6-4 Water side pressure drop variation with air to feed water mass flow ratio........... 103

6-5 Air/vapor side pressure drop variation with air to feed water mass flow ratio ..... 104

6-6 Temperature and humidity ratio profiles through the condenser........................ 105

6-7 Condenser temperature and humidity ratio variation with fresh water to air mass
flow ratio ...................................................................... ......... 106









6-8 Required direct contact condenser height with variations in air mass flux......... 106

6-9 Condenser fresh water exit temperature variation with air mass flux................. 107

6-10 Variation of the fresh water production efficiency with air mass flux ............... 108

6-11 Variation of the energy consumption with air to feed water mass flow ratio in
diffusion tow er ................................................................. ... ........ 108

6-12 Variation of the energy consumption with air mass flux in condenser............... 109

6-13 Variation of the total energy consumption rate with air mass flux ....................... 110

6-14 Net fresh water profit variation with electricity retail price for different fresh
w after retail price ..................................................................... ..... 115

6-15 Percent increase in profit with electricity profit for different fresh water profit... 116

6-16 Water price in different countries for year 2001 & 2002.................................... 117

H-1 Variation of the relative uncertainties of the calculated water properties with
water temperature............... ... .............................. ... .............. 145

H-2 Variation of the relative uncertainties of the calculated vapor properties with air
tem perature .............. .................................................................... 145

H-3 Variation of the relative uncertainties of the calculated air properties with air
tem perature .................................................................. ......... ....... 146

H-4 Variation of the relative uncertainties of the calculated air/vapor mixture
properties with air temperature....................................... .............. 146

H-5 Variation of the relative uncertainties of the wetted area and mass transfer
coefficients with temperature by using Onda's correlation.............. .............. 148

H-6 Variation of the relative uncertainties of the heat transfer coefficients with
tem p eratu re ............ .......... .. .......... ............................... ............................ 14 9















NOMENCLATURE

A control surface area (m2)

a specific area of packing material (m2/m3)

ai amortization factor (yr1)

Cp specific heat (kJ/kg)

D molecular diffusion coefficient (m2/s)

DC direct capital cost ($)

d diameter (m)

dp diameter of the packing material (m)

f plant availability

G air mass flux (kg/m2-s)

g gravitational acceleration (m/s2)

H diffusion tower height (m)

h enthalpy (kJ/kg)

hfg latent heat of vaporization (kJ/kg)

i interest rate

k mass transfer coefficient (m/s)

L water mass flux (kg/m2-s)

/ channel half width (m)

My vapor molecular weight (kg/kmol)

m mass flow rate (kg/s)









n

P

Pw

Q

R

s

T

U

v

V

VG

P








p










H
5L



COC
0






Subscripts

a


plant life (yr)

pressure (Pa or kPa)

electrical power consumption for pumps (W, kW or MW)

retail price ($)

universal gas constant (kJ/kmol-K)

entropy generation rate in the diffusion tower (kW/K)

temperature (C or K)

heat transfer coefficient (W/m2-K)

air/vapor velocity (m/s)

control volume (m3)

air/vapor volumetric flow rate (m3/s)

economic increase rate

specific cost of operating labor ($/m3)

condensation effectiveness

dynamic viscosity (kg/m-s)

density (kg/m3)

surface tension of liquid (N/m)

critical surface tension of the packing material (N/m)

humidity ratio

relative humidity

profit ($)



air









c centerline

elec electricity

evap the portion of liquid evaporated

f fresh water

fixed fixed cost

G air/vapor mixture

GA gas side parameter based on the specific area of packing

h high

i interface

in inlet parameter

L liquid phase

LA liquid side parameter based on the specific area of packing

Labor labor cost

low low

LW liquid side parameter based on the specific wet area of packing

out exit parameter

sat saturate state

unit, p unit amount in terms of production

v vapor phase

sink sink temperature

x local value of variable in transverse direction (all the temperatures

are bulk temperatures unless denoted by subscript x)

z fluid flow direction















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

HEAT AND MASS TRANSFER FOR THE DIFFUSION DRIVEN DESALINATION
PROCESS

By

Yi Li

May 2006

Chair: James F. Klausner
Major Department: Mechanical and Aerospace Engineering

This research concerns a diffusion driven desalination (DDD) process in

which warm water is evaporated into a low humidity air stream, and the vapor is

condensed out to produce distilled water. Although the process has a low fresh water to

feed water conversion efficiency, it has been demonstrated that this process can

potentially produce inexpensive distilled water when driven by low-grade energy such as

waste heat. A dynamic analysis of heat and mass transfer demonstrates that the DDD

process can yield a fresh water production of 1.14 million gal/day by utilizing waste heat

from a 100 MW steam generating power plant based on a condensing steam pressure of

only 10.159 kPa in the main condenser. The optimal operating condition for the DDD

process with a high temperature of 50 C and sink temperature of 25 C has an air mass

flux of 1.5 kg/m2-s, air to feed water mass flow ratio of 1 in the diffusion tower, and a

fresh water to air mass flow ratio of 2 in the direct contact condenser. Operating at these

conditions yields a fresh water production efficiency (m/mL) of 0.035 and electric energy









consumption rate of 0.0022 kW-hr/kgfw. This dissertation describes the research progress

made in the development and analysis of the DDD process. Throughout the past three

years, the main focus of the desalination process has been on the heat and mass transport

phenomena in the diffusion tower and direct contact condenser within the packed bed.

Detailed analyses required to size and analyze these heat and mass transfer devices have

been developed. A laboratory scale experimental DDD facility has been fabricated.

Temperature and humidity data have been collected over a range of flow and thermal

conditions for the diffusion tower and direct contact condenser. The analyses agree quite

well with the current data. The condensation effectiveness of the direct contact condenser

with and without packed bed has been compared. It has been experimentally observed

that the fresh water production rate is significantly enhanced when packing is added to

the condenser. It has also been observed that the condensation effectiveness increases

considerably when air and water flow configuration is countercurrent. Recently, it has

been recognized that the heat and mass transfer within the packed bed can be

significantly diminished with water blockages. High-speed cinematography has been

used to observe the liquid formation on the packing material. The cause of this

phenomenon is addressed. Further experimental and analytical analyses are required to

evaluate its influence on the heat and mass transfer coefficients for liquid and air flow

within the packed bed.














CHAPTER 1
INTRODUCTION AND LITERATURE REVIEW

Water is not only indispensable to life, industrial development, economic growth,

preservation of natural resources and social well-being, but sufficient drinking water

resources are necessary for the development of humanity. Adequate water supply has

historically been the foundation for the growth of civilizations. Between 1900 and 1995,

drinking water demand has grown twice as fast as the world population. By 2025, this

demand is expected to grow another 40% [1]. In fifty years, it is expected that without

further technological developments, forty countries will lack adequate drinking water. In

many parts of the world the discrepancy between freshwater needs and available supply

has already limited further development, and has even jeopardized survival. Growing

pollution in many regions is causing water shortages where such problems were

inconceivable just a few decades ago. Due to economic and social development, the

growth of water demand never ceases. It is estimated that fresh water shortages affect the

lives of hundreds of millions of people on a daily basis worldwide. Fresh water shortages

limit food production and lead to destitution and poverty. When fresh water resources dry

up, the affected populations have no choice but disappearance or exodus.

One obvious solution to alleviate the fresh water shortages is seawater desalination.

Desalination technologies are currently used throughout the world and have been under

development for the past century.









Description of Thermal Desalting and Membrane Separation

The most common ways to desalt seawater involve some form of boiling or

evaporation. In a simple still, seawater can be boiled releasing steam which, when

condensed, forms pure water. Many stills can be connected together making the process

more efficient. To achieve this, each still, or effect, must be at different pressure. This is

because in a vacuum, water can boil or flash at much lower temperatures. Multiple Effect

Distillation (MED) and Multi-Stage Flash desalination (MSF) makes use of this

phenomenon.

Other thermal processes include a variation of the simple still such as vapor

compression (VC). The vapor compression (VC) distillation process is generally used for

small and medium scale seawater desalting units. The heat for evaporating the water

comes from the compression of vapor rather than the direct exchange of heat from steam

produced in a boiler. The two primary methods used to create a vacuum and compress the

vapor are mechanical compression and steam jet. Fig. 1-1 shows a schematic diagram of

the mechanical vapor compression desalination process.


Evaporator
Eaporato Feed Seawater


SVapor Suction Tube
--- Mist Eliminator


Pro duct
Distillate Feed Preheater


Brine
Compressor 7

Rejected Brine Intake Seawater
Brine Feed Preheater

Figure 1-1 Schematic diagram of mechanical vapor compression process [2]









The mechanical compressor creates a vacuum in the liquid vessel and then

compresses the evaporated vapor from the vessel. The compressed vapor condenses

inside a tube bundle and gives up heat to the liquid side in the vessel. Seawater is sprayed

on the outside of the heated tube bundle where it evaporates completing the cycle. With a

steam jet type VC unit, also called a thermocompressor, a venturi orifice on the steam jet

eductor produces a vacuum and extracts evaporated water vapor from the main vessel.

The extracted water vapor is compressed by the steam jet within the diverging portion of

the eductor. This mixture is condensed in the tube bundle to provide the thermal energy

(heat of condensation) to evaporate the seawater sprayed over the outside of the tube

bundle. A simplified schematic diagram of the thermal vapor compression combined

multi-effect desalination process is shown in Fig. 1-2.

Steam Jet Ejector

Low Pressure Steam High Pressure Steam
Feed Seawater ------ ---- -----
Seawater


Intake
Heating Seawter
Steam ..:. Rejected Brine

Condensate Distillate

Figure 1-2 Schematic diagram of thermal vapor compression combined multi-effect
destillation process [2]

Semi-permeable and ion specific membranes can also be used to desalt seawater.

Membrane processes are based on separation rather than distillation. Reverse osmosis

membranes basically let water pass through them but reject the passage of salt ions. In

reality a small percentage, approximately 1%, of sea salts pass through the membranes, or









leak around the seals. For potable water this leakage is acceptable, but for industrial

purposes it may require further treatment. The operational pressure of reverse osmosis

systems is a function of the salinity of the feed water. The salinity results in a colligative

property known as osmotic pressure. The osmotic pressure of brackish water is much

lower than that of seawater. Typical 500 ppm potable water has an osmotic pressure of

0.2 MPa while normal seawater is close to 2.5 MPa.

Another type of membrane separation process is Electro-Dialysis Reversal (EDR).

It makes use of ion specific membranes, which are arrayed between anodes and cathodes

to drive salt ions in controlled migrations to the electrodes. While not as widespread as

RO, it is still commonly used.

RO is by far the most widely used separation process and has tremendous energy

advantages over other thermal processes when 1% salt passage can be tolerated, and good

quality seawater is available. Table 1-1 shows the pumping and heating energy

consumption of some commonly used desalination processes [3].

Table 1-1 Pumping and heating energy consumption of some desalination processes
Tec y Unit Capacity Energy Consumption (kW-hr/kgw)
technology (x 106 kg/day) Electrical/Mechanical Thermal
MSF 60 0.004 0.006 0.008-0.018
MEB 60 0.002 0.0025 0.0025-0.01
MED-VC 24 0.007 0.009 NA
RO 24 0.005 0.007 NA

Description of HDH and MEH Process

A desalination technology that has drawn interest over the past two decades is

referred to as Humidification Dehumidification (HDH). This process operates on the

principle of mass diffusion and utilizes dry air to evaporate saline water, thus

humidifying the air. Fresh water is produced by condensing out the water vapor, which









results in dehumidification of the air. A significant advantage of this type of technology

is that it provides a means for low pressure, low temperature desalination and can operate

off of waste heat, which is potentially very cost competitive. Bourouni et al. [4], Al-

Hallaj et al. [5], and Assouad and Lavan [6] respectively reported on the operation of

HDH units in Tunisia, Jordan, and Egypt. Muller-Holst et al. [7] fabricated an

experimental Multi-Effect Humidification (MEH) facility driven by solar energy and

considered its performance over a wide range of operating conditions. The fresh water

production varied on a seasonal basis since the process is driven by solar energy. The

average fresh water production was about 52 gal/day with a maximum of 90 gal/day in

May and a minimum of 14 gal/day in January. A computer simulation of the operational

performance of the process was developed, and the predicted behavior agreed well with

the actual behavior. An excellent comprehensive review of the HDH process is provided

by Al-Hallaj and Selman [8]. It was concluded that although the HDH process operates

off of low-grade energy, it is not currently cost competitive with reverse osmosis (RO)

and mult-istage flash evaporation (MSF). There are three primary reasons for the higher

costs associated with the HDH process:

1. The HDH process is typically applied to low production rates and economies of
scale cannot be realized in construction.

2. Typically natural draft is relied upon, which results in low heat and mass transfer
coefficients and a larger surface area humidifier.

3. Film condensation over tubes is typically used, which is extremely inefficient when
non-condensable gases are present. Thus a much larger condenser area is required
for a given production rate, and the condenser accounts for the majority of the
capital cost.

Therefore, an economically feasible diffusion driven distillation process must

overcome these shortcomings. Klausner et al. [9] have reported on a diffusion driven









desalination (DDD) process that overcomes these shortcomings, resulting in an

economically viable desalination process applied on a large scale (>1 million gal/day).

Another type of desalination technology that makes use of water evaporating into

an air stream is the Carrier-Gas Process (CGP) reported by Larson et al. [10]. This

process has been further refined by Beckman [11, 12]. The CGP is designed to operate

with a feed water temperature range of 55 880 C. Beckman demonstrates (based on 880

C feed water) that the CGP can produce fresh water with an operating cost of 3.35

$/103gal using natural gas for heating and 1.52 $/103gal when waste heat is used as the

thermal source. The capital cost is apparently low, approximately $1397 for a 1000

gal/day facility.

Description of DDD Process

A simplified schematic diagram of the DDD process and system, designed to be

operated off of waste heat discharged from thermoelectric power plants, is shown in Fig.

1-3. The process includes three main fluid circulation systems denoted as feed water,

air/vapor, and freshwater. In the feed water system, a low pressure condensing steam

from an adjacent power plant heats the feed water in the main feed water heater (a). The

main feed water heater is typically a main condenser when used in conjunction with

thermoelectric power plants. Because the required feed water exit temperature from the

heater can be relatively low for the DDD process, the required heat input can be provided

by a variety of sources such as low pressure condensing steam in a power plant, exhaust

from a combustion engine, waste heat from an oil refinery, low grade geothermal energy,

or other waste heat sources. The heated feed water then is sprayed into the top of the

diffusion tower (b). A portion of feed water will evaporate and diffuse rapidly into the










air. Evaporation in the tower is driven by a concentration gradient at the liquid/vapor

interface and bulk air, as dictated by Fick's law. Via gravity, the water falls downward

through a packed bed in the tower that is composed of very high surface area packing

material. A thin film of feed water will form over the packing material and contact the

upward flowing air through the diffusion tower. The diffusion tower should be designed

so that the air/vapor mixture leaving it should be fully saturated. The purpose of heating

the water prior to entering the diffusion tower is that the rate of evaporation and the exit

humidity ratio increase with increasing temperature, thus yielding greater water vapor

production. The water, not evaporated in the diffusion tower will be collected at the

bottom and discharged or re-circulated.


- Low Pressure Steam Air/Vapor
Seawater ---------- Fresh Water


Figure 1-3 Schematic diagram for diffusion driven desalination process









In the air/vapor system, low humidity cold air is pumped into the bottom of the

diffusion tower, and flows upward to be heated and humidified by the feed water. As

mentioned before, the air/vapor mixture leaving the diffusion tower is saturated and

drawn into the direct contact condenser (c), where it is cooled and dehumidified by the

fresh water in the condenser. The air could be directed back to the diffusion tower and

used repeatedly. The condenser is another important component of the DDD process

because film condensation heat transfer is tremendously degraded in the presence of non-

condensable gas. In order to overcome this problem Bharathan et al. [13] describe the use

of direct-contact heat exchangers. The direct contact condenser approach is best suited

for the DDD process.

In the fresh water system, the cold fresh water will gain heat and mass due to air

side vapor condensation in the condenser. After discharging from the direct contact

condenser, it will be cooled in a conventional shell-and-tube heat exchanger (d) by the

incoming feed water. Here, the intake feed water flow is preheated by the heat removed

from the fresh water, which helps to reduce the amount of energy needed in the main feed

water heater. Finally, a portion of the cooled fresh water will be directed back to the

direct contact condenser to condense the water vapor from the air/vapor mixture

discharging from the diffusion tower. The remaining fresh water is production.

Comparison of the DDD Process with HDH and MEH

The DDD process has following advantages compared with HDH and MEH:

1. The DDD process utilizes thermal stratification in the seawater to provide
improved performance. In fact, the DDD process can produce fresh water without
any heating by utilizing the seawater thermal stratification.

2. The thermal energy required for the DDD process may be entirely driven by waste
heat, therefore eliminating the need for additional heating sources. This helps keep
the DDD plant compact, which translates to reduced cost. The DDD process









recommends using whatever heat source is best suited for the region requiring fresh
water production. The DDD process is very well suited to be integrated with steam
power plants, and use the waste heat coming from these plants. Renewable
resources such as solar heating, wind power and geothermal energy may be used as
well.

3. In the DDD process the evaporation occurs in a forced draft packed bed diffusion
tower as opposed to a natural draft humidifier. The diffusion tower is packed with
low pressure drop, high surface area packing material, which provides significantly
greater surface area. This is very important because the rate of water evaporation is
largely influenced by the liquid/vapor contact area available. In addition, the forced
draft provides for high heat and mass transfer coefficients. Thus, a diffusion tower
is capable of high production rates in a very compact unit. Since the unit is
compact, the capital cost will be minimized. The price paid in using forced draft is
the pumping power required to pump the fluids through the system, but the
projected cost is low, thus providing potential for an economically competitive
desalination technology.

4. The DDD process uses a direct contact condenser to extract fresh water from the
air/vapor mixture. This type of condenser is significantly more efficient than a
conventional tube condenser, as is used with the HDH process. Thus, the condenser
will be considerably more compact for a given design production rate. This also
adds to cost reduction.

5. The diffusion tower and direct contact condenser can accommodate very large flow
rates, and thus economies of scale can be taken advantage of to produce large
production rates.

6. No exotic components are required to manufacture a DDD plant. All of the
components required to fabricate a DDD plant are manufactured in bulk and are
readily available from different suppliers. This facet of production also translates to
reduced cost.

The advantages of the DDD process compared with HDH and MEH are obvious.

However, since the fraction of feed water converted to fresh water using the DDD

process is largely dependent on the difference in high and low temperatures in the

system, when driving the process using waste heat, this temperature difference will be

moderate. Thus the fraction of feed water converted to fresh water will be low. A large

amount of water and air must be pumped through the facility to accomplish a sizable

fresh water production rate. This disadvantage is an inherent characteristic of the DDD









process. However, as long as the production cost of fresh water using the DDD process is

cost competitive, it is a tolerable characteristic.

Comparison of the DDD process with MSF and RO

Table 1-2 below compares the energy consumption of the DDD process with

reverse osmosis (RO) and multi-stage flash (MSF). It is readily observed that the thermal

energy consumption for DDD is very high. This is to be expected because the DDD

process is driven by low thermodynamic availability energy. However, because the waste

heat can be considered a free resource, the total energy required to drive the DDD process

is quite competitive. Fresh water production using the DDD process has potential to be

very inexpensive and comparative when driven by waste heat that would have otherwise

been discarded. Therefore, to determine whether or not the technology is cost

competitive, greater attention should be paid to the electric energy consumption.

Table 1-2 Comparison of electricity consumption for DDD, MSF, and RO desalination
technologies
Energy Consumption (kW-hr/kgw)
Technology
Techn y Electrical/Mechanical Thermal Total
DDD 0.002-0.0053 0.75 (free) 0.002 0.0053
MSF 0.004 0.006 0.008-0.018 0.012 0.024
RO 0.005 0.007 NA 0.005 0.007

A comparison of the advantages and disadvantages of the DDD, RO, and MSF

processes is shown in Table 1-3. The DDD process is essentially a thermal distillation

process that operates using waste heat. It therefore has all of the same operational

advantages as MSF. In contrast to MSF, the DDD process has very low energy

consumption and thus a low operating cost. The main disadvantage of the DDD process

is that the conversion efficiency is low, typically 5-10%. Despite the low conversion

efficiency, the energy consumption is still low since pumping occurs at low pressure.









Table 1-3 Comparison of advantages and disadvantages of DDD, RO, and MSF
desalination technologies.
Process Advantage Disadvantage
Low energy consumption and Lower conversion efficiency
low cost of water production
Waste heat utilized
DDD Low salinity concentration
discharge, minimal
environmental impact
Low maintenance cost

Feed water doesn't require High maintenance cost
heating Performance degrades with time
Lower energy requirements High salinity concentration
RO Removal of unwanted discharge, environmental impact
contaminants such as particles High cost of filer replacement
and bacteria


Large production rates and Large energy consumption
MSF economies of scale High cost of water production
Continuous operation without
shutting down

However, the low conversion efficiency provides an environmental advantage for

the DDD process over RO and MSF. That is the salinity discharge concentration in the

brine is comparatively very low. This environmental advantage is a very important issue

within North America, Europe, and Japan. For example, the city of Tampa, Florida

recently constructed a 25 million gal/day RO desalination facility. But since its first days

of construction there has been growing criticism from environmental groups because of

the high salinity discharge concentration into Tampa Bay [14]. Although nearly 5 billion

gallons of drinking water has been produced since March 2003, the plant has run

sporadically, producing far short of its intended output, because the pretreatment process

of the plant isn't rigorous enough to filter out the suspended particles from the intake

seawater from Tampa Bay. Without significant modification, the plant is too expensive to









operate. Three of the companies involved in the project have filed for bankruptcy. The

plant was taken off-line in June 2005 for repair, and it is scheduled to resume operations

in the fall 2006 [15].

Potential Applications for the DDD Process

The attractive feature of the DDD process is that it can operate at low temperatures

so that it requires an energy input with low thermodynamic availability. This is important

because the process can be driven by waste heat that would otherwise not be suitable for

doing useful work or driving some other distillation process (such as flash distillation). A

very interesting application for the DDD process is to operate in conjunction with an

existing process that produces large amounts of waste heat and is located in the vicinity

of an ocean or sea. One such potential benefactor of the DDD process is the electric

utility industry. Conventional steam driven power plants dump a considerable amount of

energy to the environment via cooling water that is used to condense low pressure steam

within the main condenser. Typically this cooling water is either discharged back to its

original source or it is sent to a cooling tower, where the thermal energy is discharged to

the atmosphere. Instead of dumping the thermal energy to the environment, the DDD

process provides a means for putting the discarded thermal energy to work to produce

fresh water. Of course this application is limited to power producing facilities sited along

the coastline. However, this should not be a significant limitation. Bullard and Klausner

[16] studied the geographical distribution of fossil fired power plants built in the United

States from 1970 to 1984. In their study they found that the two most significant

attributes for siting a new fossil fired plant in a given geographical region are 1)

proximity to a large body of water and 2) proximity to a large population base. The

demographic make-up of the United States as well as other industrialized nations is such










that major population centers reside along the coastline. Thus, the DDD process appears

to be well suited for the power generation infrastructure in the United States.

Another potential application for the DDD process is for fresh water production in

the range of 1000-10000 gal/day. It is envisioned that the potential customers that can

benefit from this application include single users such as small business entities,

agricultural entities and small or middle size residency communities whose locations are

such that they have access to saline ground water, seawater or a geothermal reservoir.

The extent of saline ground water resources in the United States are substantial, although

little is known about the hydrogeology about most aquifers that contain saline ground

water, since most efforts have focused on characterizing fresh water aquifers [17]. Fig. 1-

4 below shows the depth of many saline ground water resources known in the U.S. This

map illustrates the fact that there is a substantial population that can benefit from the

successful development of the DDD process.


Depth to saline ground water (feet)
I Less than 500
500-1000
More than 1000
| Inadequate mformation


Figure 1-4 Depth to saline ground water in the United States [18]










The fresh water conversion efficiency, defined as the ratio of the fresh water output

to the feed water input, is low for the DDD process. Therefore, the process is best suited

for applications using low-grade heat. One such resource is solar heating, which is

abundantly available in the Southeast and Western United States. Figure 1-5 shows a

simple flow diagram for the DDD process coupled with solar collectors. In this process

the feed water will be drawn from saline ground water or seawater, and then heated by a

solar thermal heating system. The electrical power required to drive the pumps and

blowers can be driven by either a solar electric panel or a wind turbine. In order to make

efficient use of the thermal energy, the feed water is preheated in the chiller using the

discharge heat from the direct contact condenser.

Feed Warm Fresh
SWater Water .(2)
Wet Air r- -
Fresh Direct Contact I- Diffusion
(6) Condenser (4)
Sea Water ( Condenser Tower
Water Chiller (c) (b)
(d) (5) (7) (3)
Cool Dry Air
u -Fresh
Cool Water (1)
S Drain Fresh Water Out
Feed Water
Sea Water P ter (e) I Solar Heating System (a)


Warm Drain


Figure 1-5 Flow diagram of DDD process driven by solar energy

Many investigations [19] show that solar heating is a mature technology and is

already being widely used in the United States. In 1897 30% of the homes in Pasadena,

just east of Los Angeles, were equipped with solar water heaters. As mechanical

improvements were made, solar systems entered use in Arizona, Florida and many other

sunny regions of the United States. By 1920, tens of thousands of solar water heaters had

been sold. Today there are more than half a million solar water heaters in California










alone. They are used for heating water inside homes and businesses as well as for heating

swimming pools. It is interesting to note that the communities that have a high rate of

solar heater installations also have access to seawater or saline ground water and suffer

from fresh water shortages.

Another interesting facet of renewable energy resources is that wind energy is

abundantly available along the coastline of the United States. Therefore, it will be of

interest to explore the combination of solar energy collectors providing the thermal

source and wind energy turbines providing the electrical source for the DDD process.

Some special geographic regions, such as islands, have access to seawater or saline

ground water, have substantial solar resources available, have sufficient wind power, and

have middle sized residency communities that can benefit from the solar/wind combined

DDD system.


Warm Drain Heat Exchanger (e) Cold Drain

/ Warm (6) (2)
Fresh
Wet Air
Water
Geothermal Water Air Direct Contact Diffusion
Reservoir Cooling Condenser (4) Tower
Tower (c) (b)
(d) (5) (7) (3)
Cool Dry Air
Fresh
Water (1)
) Fresh Water Out


Pre-treatment Equipment (a) Hot Feed Water



Figure 1-6 Flow diagram of DDD process driven by geothermal energy

Because the DDD process can operate off of low-grade thermal energy, one

interesting potential application is the demineralization of geothermal water in shallower

reservoirs or the demineralization of the discharge water from geothermal power plants.









Geothermal resources are most abundant in the Western United States. The west coast

boundary between the North American and Pacific plates is "sliding" along the San

Andreas fault (many earthquakes but few volcanoes) from the Gulf of California up to

northern California and sub-ducting from the Cascade volcanoes north through the

Aleutians. There are also volcanic hot spots under Yellowstone and Hawaii and intra-

plate extensions with hot springs in the Great Basin. The history data of EIA [20] show

that California generates the most geothermal electricity with about 824 MW at the

Geysers (much less than its capacity, but still the world's largest developed field and one

of the most successful renewable energy projects in history), 490 MW in the Imperial

Valley, 260 MW at Coso, and 59 MW at smaller plants. There are also power plants in

Nevada (196 MW), Utah (31 MW), and Hawaii (25 MW). Due to environmental

advantages and low capital and operating costs, direct use of geothermal energy has

skyrocketed to 3858 GW-hr/yr, including 300,000 geothermal heat pumps. In the

Western United States, hundreds of buildings are heated individually and through district

heating projects (Klamath Falls, Oregon; Boise, Idaho; San Bernardino, California; and

soon Mammoth Lakes and Bridgeport, California). Large greenhouse and aquaculture

facilities in Arizona, Idaho, New Mexico and Utah use low-temperature geothermal

water, and onions and garlic are dried geothermally in Nevada. However, geothermal

water is usually highly mineralized containing many components such as silica, chloride,

sulphate, bicarbonate, boron, sodium, potassium, lithium, calcium, rubidium, caesium,

magnesium, ammonia, and hydrogen sulfide. The customers typically only use the high

temperature geothermal water to produce electricity, after which the temperature of the

water is lower than 600 C and is directly ejected. If these geothermal consumers want to









sufficiently use the low temperature geothermal water, they could couple it with the DDD

process to produce fresh water as a by-product. It could potentially increase their

economic profits. A simple schematic of a geothermal DDD process is shown in Fig. 1-6.

The diffusion driven desalination process is very versatile, in that it can be driven

by many different energy resources. Here we have identified solar, wind, and geothermal

energy resources that should be explored in conjunction with diffusion driven

desalination.

Properties of Saline Water

There are two important factors that affect the physical properties of saline water:

salt concentration rate and relative proportions of the components in the salt. These

properties directly cause the scale formation, corrosion and bacteria contamination

problems in desalination facilities. The dominant chemical and physical characteristics of

seawater are as follows [21],

1. Abundant dissolved oxygen is the most important environmental factor for
corrosion of steels, copper alloys, and stainless steels. The oxygen content of
seawater varies between 0-12 ppm depending on the temperature, salinity, and
biological activity. The solubility of oxygen decreases with increasing water
temperature or seawater concentration rate.

2. Seawater contains about 19,000 ppm chloride. The high chloride ion concentration
will help seawater to penetrate the protective films of the facility and enhance
corrosion reactions.

3. Seawater has excellent electrolytic conductivity.

4. Seawater contains a certain amount of heavy metal ions such as Cu, Zn, Cd and Pb.

5. Abundant calcareous scale former cathodicc inhibitors), such as calcium, strontium
and magnesium ions, result in deposition of tight and adherent films of lime salts
(CaCO3, SrCO3, MgCO3, and Mg(OH)2).

Normally, there are 4 type of scale that can form in the desalination plants,









1. Alkaline scale occurs when the heating of seawater causes the decomposition of
bicarbonate content.

2. Calcium carbonate scale may be deposited even at low temperature.

3. Calcium sulfate scale occurs when the concentration temperature path is not within
its solubility. The deposition of calcium sulfate takes place because of its inverted
solubility.

4. Magnesium hydroxide scale forms at higher temperature and/or when seawater has
been concentrated to a considerable level.

In applying stability data for calcium sulfate, magnesium hydroxide, and calcium

carbonate to seawater, Spiegler [22] made the following conclusions about preventing

scaling problems,

1. Discharge the brine when it reaches high concentration level. When seawater is
concentrated to 2/3 of its volume, crystallization will occur if seeds, such as
calcium sulfate scale, can be provided in the system.

2. Add acid to increase the solubility of calcium carbonate. The solubility of calcium
carbonate can be greatly increased even with weak acids such as carbonic.

3. Precipitation of magnesium hydroxide liberates acid that inhibits the precipitation
of calcium carbonate.

4. Maintain a lower operation temperature of the system because the scale will mainly
consists of calcium carbonate when the water temperature is less than 60 C.

To reduce the corrosion due to seawater, the following methods are usually used,

1. To prevent the corrosion on the surface of the evaporator and eliminate the
carbonate scale problem, deaeration is used to remove the dissolved gases in the
seawater.

2. Control the pH level of seawater to minimize corrosion, but it must be lower than
the magnesium hydroxide scaling point. A pH level between 7 7.7 is desirable.

3. Select proper materials for the desalination plants such as stainless steel, copper
alloys, aluminum alloys, titanium, and plastics.

Since the DDD process is a low temperature and low fresh water conversion

process, bacterial contamination is considered as the most important problem for the

system. Methods for disinfecting water include microfiltration, chlorination, iodine,









ozone, and ultraviolet light. Many of these methods are also effective at removing other

contaminants from water.

Extremely fine ceramic filters can be used to remove bacteria from water. Their

pore size is normally 1 micron or less. To prevent clogging they can be brushed clean and

reused many times. Silver compounds are used to prevent bacteria growing through the

filter medium. Although microfiltration is the simplest and cheapest disinfection method,

it is only feasible for low flow rate units because of it high flow resistance.

Iodine can also be used to disinfect water. Tablet form or solution form can be

introduced manually to small batches of water, or automatically mixed with pumped

water. The effective contact time is fifteen minutes under most circumstances. Because it

costs around twenty times more than chlorine, it is used primarily for emergencies and

other special circumstances.

Ozone, an activated form of oxygen, is a powerful oxidizer. It is usually created

with electricity and mixed with water. It kills microorganisms and breaks down organic

chemicals. Carbon filtration generally follows ozonation. However its energy

consumption and cost are very high.

Ultraviolet light is another method of killing microorganisms in water. Water is

circulated in a thin layer past an ultraviolet bulb encased in a quartz sleeve. The light

energy kills microorganisms very quickly. Clear water is needed for effective treatment

because the particles in the water can shade the bacteria from the light. Also the water

flow has to be fully stopped when the light output is ineffective or during regular

maintenance. Ultraviolet bulbs generally need replacing at least once a year.









Carbon, generally in the form of granular activated carbon, can be used to remove

organic chemicals, including pesticides and chlorinated products as well as many tastes,

odors and colors from water. It attracts and holds the molecules of the organic chemicals.

Carbon filters are available as cartridge filters for in-line use. However, for greatest

effectiveness the water needs to flow slowly through the carbon. A replacement is

required when the carbon reaches its adsorption limit because it may begin releasing

contaminant chemicals back into the water.

The most popular water disinfection method used in this country is chlorination.

This is because the chlorine is very effective in killing microorganisms if high enough

concentration and sufficient time are provided. Simple chlorination uses only 1 ppm (one

gallon per 50,000 gallons of water) concentration, and a contact time of at least 30

minutes is needed. Chlorine is generally added at the pump to ensure adequate contact

time to the water system. When 30 minutes of contact time is not possible, super

chlorination can be used. The contact time can be reduced to around 5 minutes if the

concentration is about 5 ppm (one gallon chlorine bleach per 10,000 gallons water). At

this level, other methods may be needed to remove the strong taste of water. Chlorination

may be done manually or with automatic feed on-site systems. Shock chlorination at 50-

200 ppm (1-4 gallons chlorine bleach per 1,000 gallons water) concentration is only used

for emergent treatment or the start of a new system. The entire system including pipes

should be washed and allowed to sit overnight filled with this high concentration

solution. One advantage of chlorination is that residual chlorine in the water can prevent

recontamination. It will continue to kill microorganisms at low concentrations for a long

time. However, there are problems with chlorination. Reactions with iron, sulfur,









ammonia, slime, organic materials, and other chemicals can reduce the effective level of

chlorine. In addition, some of the chemicals formed when chlorine reacts with organic

chemicals are toxic or carcinogenic.

Objectives of the Study

There are four primary objectives for the research, and provided these objectives

are successfully met, this work will provide a basis for the design and fabrication of a

diffusion driven desalination facility of any size. These objectives are

1. Develop a thermodynamic model for the DDD process to evaluate the potential for
fresh water production for a variety of operating conditions.

2. Fabricate a laboratory scale DDD diffusion tower, experimentally measure the
thermal and mass transport properties, the evaporation rate and the associated
energy consumption required to heat the feed water and pump water and air
through the facility. Measurements will be made over a wide range of operating
conditions in order to find an optimum condition where fresh water production is
maximized with low energy consumption.

3. Fabricate a laboratory scale DDD direct contact condenser, experimentally measure
the thermal and mass transport properties, the condensation rate and the associated
energy consumption required to condense the vapor and pump water and air
through the facility. Measurements will be made over a wide range of operating
conditions in order to find an optimum condition where fresh water production is
maximized with low energy consumption.

4. Develop a computational modeling tool that reliably simulates the heat and mass
transfer processes within a DDD facility. The development of a dynamic modeling
tool for the diffusion tower and direct contact condenser is required. The successful
completion of this objective will allow the fresh water production rate of a
specified DDD configuration to be predicted as well as provide design
recommendations for specific applications.

Scope of Work

In order to meet the research objectives outlined, the following major tasks have

been undertaken:

1. Develop and implement a computational model for the countercurrent flow
diffusion tower and the co-current and countercurrent flow direct contact condenser
with a packed bed.









2. Conduct experiments in the diffusion tower and direct contact condenser to validate
or calibrate the computational model.

3. Conduct DDD experiments to compare the condensation effectiveness of different
condenser configurations.

4. Conduct a parametric investigation using the DDD computational model to
investigate operating conditions that yield the minimum energy consumption and
maximum fresh water production.

5. Conduct an economic analysis to assess the marketability of the DDD process.

It is the ultimate goal of the research to assess the energy requirements and

equipment specifications associated with fresh water production using the DDD process.

Such an analysis will provide guidance as to the economic viability of the DDD process,

and will provide guidance for the future design of large scale plants. In order to

accomplish this task, detailed and reliable modeling of the heat and mass transport

phenomena in the diffusion tower and direct contact condenser is required. Such

modeling will provide detailed information on the size of the required DDD facility

components, energy requirements, flow rates and pumping requirements. In what follows,

the thermodynamic model of the diffusion tower, the lab-scale DDD experimental

facility, the dynamic models for the diffusion tower and packed bed direct contact

condensers, the parametric study and economic analysis of a DDD facility including one

diffusion tower and one countercurrent flow direct contact condenser with packed bed

will be presented.

















CHAPTER 2
THERMODYNAMIC ANALYSIS OF THE DDD PROCESS

In order to explore the performance and parametric bounds of the Diffusion Driven

Desalination process, a thermodynamic cycle analysis has been performed. A simplified

schematic diagram of the DDD process used for this analysis is shown in Figure 2-1.


(b) Main Feed Water Heater Heatlnput (f) Forced
*Waste Heat Draft Blower

SSaturated
(1) Air Dry Air
(g) Direct
(i) Regenerative (5) Contact (7)
Heater (c) Diffusion F Condenser Fc
Tower



(a) Main
Feed Pump ( (4)
Chiller Pump Fresh
Water Out
Control (2) (3)
V 've W
(d) Forced -I
Draft Blower (6)

(e) Brine
PumSalt Water
(h) Water Chiller




Figure 2-1 Flow diagram for diffusion driven desalination process

Mathematic Model

In performing the thermodynamic analysis the following assumptions have been

made,

1. The process operates at steady state conditions,

2. There are no energy losses to the environment from the heat and mass transfer
equipment,









3. Air and water vapor may be treated as perfect gas,

4. Changes in kinetic and potential energy are relatively small,

5. The pumping power is neglected in the energy balance (estimating the required
pumping power would require significant details regarding the construction of the
diffusion tower, direct contact condenser and other heat transfer equipment; these
are beyond the scope of the current analysis).

In the analysis, the temperature of the feed water drawn into the main feed pump is

fixed at 270 C. It is assumed that a large supply of cool water will be available at a sink

temperature, Tsink, of 150 C. The condensate in the direct contact condenser will be

chilled and a portion of it re-circulated. To avoid providing specifics on the heat transfer

equipment, it is assumed that the heat transfer effectiveness in the water chiller and direct

contact condenser is unity, in which case Tsink=T5=T7=15 C. The temperature of the feed

water leaving the main feed water heater is the highest temperature in the DDD system,

Th=T1, and is a primary controlling variable for the process. Different performance curves

will be shown for a variable Th.

The air/vapor mixture leaving the diffusion tower is assumed to be fully saturated

(relative humidity of unity), and due to heat transfer limitations, its maximum

temperature will be taken to be that of the feed water entering the diffusion tower

(T4
The main purpose of this analysis is to explore the performance bounds of the

DDD process. However, specification of the system operating variables is not arbitrary.

Namely there are two constraints that must be satisfied,

1. The brine temperature leaving the diffusion tower must not be lower than the air
inlet temperature (T2>150 C), so that the air can always absorb heat from the feed
water during the humidification process through the diffusion tower, and

2. The net entropy generation in the diffusion tower must be positive.








These constraints govern the parametric bounds for the diffusion tower operation.

While the first constraint is initially obvious, the second constraint is simply a

restatement of the second law of thermodynamics for the present adiabatic system

(diffusion tower). The control volume formulation of the second law of thermodynamics

for an open system is expressed as,

Ds a1
-=-f p sdV + p sv dAdA, (2.1)
Dt At V A TA

where V denotes the control volume, A is the control surface, and s is the entropy per unit

mass. Assuming steady state processing of fresh water, the adiabatic diffusion tower

assumption leads to,

Ds
Ds= p- sv dA 0 (2.2)
Dt

and

s = mL2SL2 + maSa+4 v4Sv4 mL1SL1 maSa3 mv3S3 (2.3)

where m denotes the mass flow rate and the subscripts L, a, and v respectively refer to the

liquid, air, and vapor phases. The numerical subscripts denote that the property is

evaluated at the state corresponding to the position in the process as shown schematically

in Figure 2-1. Conservation of mass dictates that,

mL2 M (4 ). (2.4)
ma ma

The entropy generation rate in the diffusion tower per rate of air flow, which must

be positive, is obtained from rearranging Eqn. (2.3) and combining with Eqn. (2.4) as,
-=I ) roLI (2.5)
-((403) SL2+Cpln 1-Rln 41+- (04sv4 33 SL1, (2.5)
m m T3) -P3 ma









where co is the humidity ratio, Cp is the specific heat, R is the engineering gas constant,

and Pa is the partial pressure of air.

The control volume formulation of energy conservation applied to the adiabatic

diffusion tower leads to,

mLlhL1 + maha3 + m3h3 mL2hL2 maha4 m4h4 = 0. (2.6)

where h denotes the enthalpy. The enthalpy of the brine exiting the diffusion tower is

obtained from Eqs. (2.6) & (2.4) as,

ShLL -hCp, -T,) + h,,3 94h4
hL2 (T2)=L 4 (2.7)

ma

and the brine temperature (T2) is evaluated from the enthalpy. The air to feed water mass

flow ratio through the diffusion tower, ma/mL1, is another controlling variable in the

analysis. For all computations the feed water mass flow rate is fixed at 100 kg/s while the

air mass flow rate will be varied.

The humidity ratio entering the diffusion tower, cou, is determined by recognizing

that it is the same as the humidity ratio exiting the condenser, where T7 is 150 C.

Computation Results and Analysis

The first case considered is where there is no heating in the main feed water heater.

The desalination process is entirely driven by the difference in temperature of the feed

water drawn at shallow depths and the cooling water drawn at more substantial depth. In

this case, Th=270C, Tsink=150 C. Figure 2-2 shows the rate of entropy generation within

the diffusion tower and the brine temperature exiting the diffusion tower for a locus of

possible operating conditions. Here it is observed that the second law of thermodynamics










is always satisfied for the entire parametric range considered, but there is a maximum

entropy generation point for each air to feed water mass flow ratio.


0.5 i


S- Th = 27 C
0 .4 R.n I- ~ h

0.25
S3 a/m-------------- 0.5
C0 z -< ~- ------ -0.75
/ ..1.25
C 0.2 -" ------- 1.5
>, / / ---- 1.25

2.25
O ----- 2.5
S0.1

increase 7
0.0
16 18 20 22 24 26
Exit Brine Temperature T2 (C)


Figure 2-2 Rate of entropy generation for different exit brine temperature, Th=27C

Figure 2-3 shows the brine temperature (T2) exiting the diffusion tower as a

function of the exit air temperature from the diffusion tower (T4) for the same locus of

operating conditions as in Figure 2-2. It clearly shows that the exit brine temperature

decreases as the exit air temperature increases, and the rate of brine temperature decrease

increases with increasing the air to feed water mass flow ratio. Since it is assumed that

the exit air is saturated, it is advantageous to have a high air temperature leaving the

diffusion tower so that the humidity ratio and fresh water production rate are as high as

possible. For this case the exit air temperature is constrained by the inlet feed water

temperature (Ti) when the air to feed water mass flow ratio is lower than unity. When the

air to feed water mass flow ratio exceeds unity, the exit air temperature is limited by the

fact that the brine exit temperature must be higher than the air inlet temperature.










27
increase q
25 ..- ..... .... -- Th = 27 C
23 *~ "- -" .... .............. 0.
=Ma/mLI

S23 0.25
C.U "-0.5
I 21 0.75
E 1
I- '- --- 1.25
H 1.25
S19 ---- 1.5
S -- 1.75
m ,2

15 --------- 2.5

15
20 22 24 26
Exit Air Temperature T4 (C)


Figure 2-3 Variation of exit brine temperature with exit air temperature, Th=270C


E 0.014 -
.7 .- *Th = 27C
0.012- m f/mL1

n 0.010 0.25
S, 0.5
U 0.5
S0.008 ----- 0.75
-o Y J ,^ \ ./" ^-^^ --........- 1
-D _1
a 0.006 --- 1.25
o -. -. .....- 1.5
1.75
S0.004 -
2.25
S0.002- 2.5
U- increase )7
LL 0.000
20 22 24 26
Exit Air Temperature T4 (C)


Figure 2-4 Fresh water production efficiency, Th=270 C

Figure 2-4 shows the fresh water to feed water mass flow ratio as a function of the

exit air temperature for different air to feed water mass flow ratios. Clearly, the

production rate increases with increasing exit air temperature under the same air to feed

water mass flow ratio, meanwhile the production rate grows with increasing air to feed

water mass flow ratios under the same exit air temperature. However, both of these











parameters are constrained because the exit air temperature must not exceed Th. For the


case of no heating of the feed water (Th=270C, T1ow=150 C), the maximum fresh water


production efficiency (mf/mL1) is approximately 0.014.

3.5

3.0 ,,,, -- -
(a)

S2.5 "a/nmL1
D 0.25
S 2.0 0.5
S................... 0.5
-. / 0.75
1.5 1.25
1.5
5 -- 1.75
1.0 -2
S................... 2 .2 5
0.5 / ------- 2.5
/ 2' \ 25
Increase 75

0.0
20 25 30 35 40 45 50
Exit Brine Temperature T2 (C)

12
12n---------------------------------------

S10 ,.A... .(b)
STh 80 C
S8---, 17a/mL1
a / .--' \ -- - --- 0
S' ----0.25

-9 6- -.------ 0.75
S......... .. 1
S--- 1.25
1.5
4 1.75
2
2.25
2------ 2.5
increase 7


20 30 40 50 60 70 80
Exit Brine Temperature T2 (C)


Figure 2-5 Rate of entropy generation for different exit brine temperature: a) Th=500 C,
b) Th=800 C

The next cases considered are where the diffusion tower inlet water temperatures


are 500 C and 800 C. Figures 2-5 a-b show the rate of entropy generation in the diffusion


tower for Th=500 C and 800 C, respectively. Again the second law of thermodynamics is











satisfied for the entire parametric range considered. The entropy generation tends to be

lower for lower air to feed water flow ratios under the same exit brine temperature and

has the maximum value with a certain exit brine temperature under the same air to feed

water mass flow ratio. At higher air to feed water flow ratios, the constraint is that the

brine temperature must be higher than the air inlet temperature.


50
~~ -___ increase yr
.......... -^ T 5(a)
O Th 50 C
1- '.. I/ lma/mL1
40-\ \
O 0.25
0.5
E \----- 0.75
*i \X\ \ \ \ ,
0 30 1
-C, 1.25
S\\ ---- 1.5
\ \ 1.75
^20- \ \\\\ \ X- -
x\ 2
W 20 2.25
2.5


20 25 30 35 40 45 50
Exit Air Temperature T4 (C)


80 .
(b)
0o 70 .. T = 80 C
Increase rh
I- -ma/mL1
| 60-
I O\ 0.25
0- 50 \- 0.5
E -\ \ 0.75
I- \\ -.. -....- 1
a 40 \ 1.25
S1.5
S3 1.75
i 30 "\ \ \
2.25
20- \ 2.5

20 30 40 50 60 70 80
Exit Air Temperature T4 (C)


Figure 2-6 Variation of exit brine temperature with exit air temperature: a) Th=500 C, b)
Th=800 C









Figure 2-6 a-b shows the range of possible exit brine temperatures and exit air

temperatures for different air to feed water flow ratios when the diffusion tower inlet

water temperature is 500 C and 800 C, respectively. The maximum fresh water production

will occur with as high an exit air temperature as possible. For the energy balance on the

diffusion tower, the exit brine temperature decreases with increasing exit air temperature

and the rate of brine temperature decrease increases with increasing air to feed water

mass flow ratio. In contrast to the case with no heating, the exit air temperature is

primarily constrained by the fact that the brine cannot be cooler than the inlet air,

especially at higher air to feed water flow ratios. At very low air to feed water flow ratios,

the exit air temperature is constrained by the inlet water temperature when Th is 500 C,

meanwhile it is constrained by the fact that entropy generation must be positive when Th

is 800 C.

For respective diffusion tower inlet water temperatures of 500 C and 800 C, Figures

2-7 a-b show the ratio of fresh water production efficiency as a function of the exit air

temperature for different air to feed water flow ratios. It is observed that the fresh water

production efficiency increases with increasing exit air temperature and increasing air to

feed water flow ratio. The maximum fresh water production efficiency for Th=500 C is

approximately 0.045 when air to feed water flow ratio is 1, while that for Th=800 C is

approximately 0.1 when air to feed water flow ratio is 0.75. Therefore, one advantage of

increasing the diffusion tower inlet water temperature is that the fresh water production

efficiency increases.











0.05
-1
E / / (a)
E / Th= 50 C
0.04 / / / / /
/o / / / / ,amL1

S / .0.25
2 0.03-
0.5
S /.^// .- -- 0.75
/ 0.75
1
S0.02 1.25
S/ \ 1.5
/ // 1.75
ro 0 .0 1 2 .. .... \ 2
2.25
.c ... 2.5
increase q
u 0.00 ..
20 25 30 35 40 45 50
Exit Air Temperature T4 (C)


: 0.10
E / (b)
E / Th = 80 C
S0.08- / / /mL1

0.25
J 0.06 0.5
S/ / / 0.75
/ / / / 1

S0.04- // 1.25
0/ / 1.5
1.75
S0.02 2
increase 7 -- -- 2.5

lL 0.00
20 30 40 50 60 70 80
Exit Air Temperature T4 (C)


Figure 2-7 Fresh water production efficiency: a) Th=500 C, b) Th=800 C

For respective diffusion tower inlet water temperatures of 500 C and 800 C, Figures


2-8 a-b show the thermal energy consumed per unit of fresh water production as a

function of exit air temperature for different air to feed water flow ratios over the entire

parameter space considered. Although, details of the low energy consumption regime are

difficult to discern, it is interesting to observe that increasing both the exit air temperature

and the air to feed water mass flow ratio results in a reduced rate of energy consumption.











)30

2 \(a)
25 Th 50 C

q =m/mLL1
o. 20 -
.220 0.25
E 0........ .5
=15- increase ---- 0.75
0 / ... .. 1
/ 1.25
10 -- --.- 1.5
S---- 1.75
2
LU. I./ 2
0 5 ..2.25
2.5
S.... ............

20 25 30 35 40 45 50
Exit Air Temperature T4 (C)


6 60
(b)
0 T= 80 C
S50 -
1r=ma/mL1

S40 -
.0 0.25
CE 0.5
3 30 increase 0.75
1
0 1.25
> 20 /1.5
S1.75
S\ 2
S10\\ ./ \ .... 2.25
o 2.5

W 0
20 30 40 50 60 70 80
Exit Air Temperature T4 (C)


Figure 2-8 Rate of energy consumption: a) Th=500 C, b) Th=800 C

In order to explore the lower energy consumption regime Figure 2-9 has been


prepared for diffusion tower inlet water temperatures of 500 C, 600 C, 700 C, and 800 C.


It shows the lowest energy consumed per unit of fresh water production as a function of


different air to feed water flow ratios for different Th. Obviously there exists a minimum


at a certain air to feed water mass flow ratio for every Th. For Th=500C the minimum rate


of energy consumption is about 0.56 kW-h/kgfw when the air to water mass flow ratio is










1, while that for Th=800 C is approximately 0.65 kWh/kgfwwhen the air to water mass

flow ratio is 0.5. The results also indicate that the minimum rate of energy consumption

will occur with lower air to feed water mass flow ratio when Th is higher.




1.4 -


i1.2 -
S. Th (C)
increase Th
S1.0 50
0. 60
060
S- 70
a 0.8 \ 80


-0.6

0.5 1.0 1.5 2.0 2.5
Air to Feed Water Mass Flow Ratio r7

Figure 2-9 Minimum rate of energy consumption for different Th

In this analysis the energy consumption due to pumping is neglected, however, it is

another important aspect of the energy consumption required for the system. It is

especially important when the driving energy of the system is considered to be the waste

heat where the electricity consumption of the pumps and blowers will be considered the

only energy cost of the fresh water production. Therefore, a dynamic simulation model

must be developed to deduce the required pumping power for the DDD process.














CHAPTER 3
EXPERIMENTAL STUDY

A laboratory scale DDD facility will be used to (a) measure the thermal and mass

transport properties within the diffusion tower and direct contact condenser, (b) measure

the fresh water production rate for different inlet thermal and flow conditions, and (c)

measure the associated energy consumption required to heat the feed water and pump

water and air through the facility. These data will be used to validate the numerical model

that will simulate the DDD process. Measurements will be made over a wide range of

operating conditions in order to find an optimum condition where fresh water production

is maximized with low energy consumption.

Experimental System Description

Fig. 3-1 shows a pictorial view of the laboratory scale DDD system. Fig. 3-2 shows

a schematic diagram of the experimental facility. The main feed water, which simulates

the seawater, is drawn from one municipal water line. The feed water initially passes

through a vane type flowmeter and then enters a preheater that is capable of raising the

feed water temperature to 500 C. The feed water then flows through the main heater,

which can raise its temperature to saturated conditions. The feed water temperature is

controlled with a PID feedback temperature controller where the water temperature is

measured at the outlet of the main heater. The feed water is then sent to the top of the

diffusion tower, where it is sprayed over the top of the packing material and gravitates

downward. The portion of water that is not evaporated is collected at the bottom of the

diffusion tower in a sump and discharged through a drain. The temperature of the









discharge water is measured with a thermocouple. Strain gauge type pressure transducers

are mounted at the bottom and top of the diffusion tower to measure the static pressure. A

magnetic reluctance differential pressure transducer is used to measure the pressure drop

across the length of the packing material.



Countercurrent
Stage


Co-current
Stage

Diffusion
Tower

Air Heating
Section





Figure 3-1 Pictorial view of the laboratory scale DDD experiment

Dry air is drawn into a centrifugal blower equipped with a 1.11 kW motor. The

discharge air from the blower flows through a 10.2 cm inner diameter PVC duct in which

a thermal air flowmeter is inserted. The air flow rate is controlled by varying the speed of

the blower. A three-phase autotransformer is used to control the voltage to the motor and

therefore regulate the speed. Downstream of the air flowmeter the inlet temperature and

relative humidity of the air are measured with a thermocouple and a resistance type

humidity gauge. The air is forced through the packing material in the diffusion tower and

discharges through an aluminum duct at the top of the diffusion tower. At the top of the

tower, the temperature and humidity of the discharge air are measured in the same

manner as at the inlet.









V-3 L3
00
V-2 L2
0C
Water Line 2 Exhaust
Exhaust
V-1 L1 Water Heater N

Water Line 1



Transformer 2

G C Air Heater F'ac I ng C.:. urreri C:uriler,:urrerI
[ lalerial SaIe SaIe

Air Distributor
Blower


SDiffusion Direct Contact
Tower Condenser

Transformer 1
r 1 G Air flowmeter I
V-4 V-5
L Water flowmeter IDr/inI
V Valve

Figure 3-2 Schematic diagram of laboratory scale DDD facility

The condenser is designed to with two stages in a twin tower structure. The main

feed water, which simulates the cold fresh water, is drawn from another municipal water

line. The feed fresh water is separated into two waterlines and passes through two

different turbine flowmeters. After the fresh water temperature is measured by a

thermocouple at the inlet of the condenser tower, it is sprayed from the top of each tower.

The air drawn by the centrifugal blower flows out of the top of the diffusion tower

with an elevated temperature and absolute humidity. It then flows into the first stage of

the direct contact condenser, which is also called the co-current flow stage. Here, the cold

fresh water and hot saturated air will have heat and mass exchange as they both flow to









the bottom of this tower. The twin towers are connected by two PVC elbows where the

temperature and relative humidity of air are measured by a thermocouple and a resistance

type humidity gauge. The air is then drawn into the bottom of the second stage of the

condenser. Because the fresh water is sprayed from the top and the wet air comes from

the bottom, this stage of the condenser is denoted as the countercurrent flow stage. The

air will continue being cooled down and dehumidified by the cold fresh water until it is

discharged at the top of the second stage. At the outlet, the temperature and humidity of

the discharge air are measured in the same manner as at the inlet.

The water sprayed on top of the condenser gravitates toward the bottom. The

portion of the water condensate from the vapor is collected together with the initial inlet

cold fresh water at the bottom of the twin towers and discharged through a drain. The

temperature of the discharge water is measured with a thermocouple.

There is one optional component of the condenser, the packing materials. Whether

or not it is required depends on the condensation effectiveness yielded by the direct

contact condenser.

Experimental Facility and Instrumentation

A CAD design for the diffusion tower is shown in Fig. 3-3. The diffusion tower

consists of three main components: a top chamber containing the air plenum and spray

distributor, the main body containing the packing material, and the bottom chamber

containing the air distributor and water drain. The top and bottom chambers are

constructed from 25.4 cm (10" nominal) ID PVC pipe and the main body is constructed

from 24.1 cm ID acrylic tubing with wall thickness of 0.64 cm. The three sections are

connected via PVC bolted flanges. The transparent main body accommodates up to 1 m

of packing material along the length.












15


I I


I 1


17 PVC connection
16 Humidity test port
15 Air exhaust port
14 Top hatch
S7 13 Water inlet port
12 Top flanges
11 Pressure testport
10 Acrylic Wall
S 09 Packing material
08 Pressure testport
07 Bottom flanges
06 Air inlet pipe hatch
05 Water level test port
04 Water level test port
03 Bottom hatch
02 Drain port
01 Air inlet pipe
No. Device
Diffusion tower design


Figure 3-3 Schematic diagram of experimental diffusion tower


A CAD design of the direct contact condenser is shown in Fig. 3-4. The condenser


includes two towers. Each tower consists of two main components: a top chamber


containing the air plenum, spray distributor and packing material, and a bottom chamber


containing the packing material and water drain. The top chamber is constructed from


25.4 cm (10" nominal) ID acrylic tubing and the bottom chamber is constructed from


25.1 cm ID PVC pipe. The two sections are connected via PVC bolted flanges. The


transparent body accommodates up to 50 cm of packing material along the length. The







40



two towers are connected by two 25.4 cm (10" nominal) ID PVC elbows which provide


sufficient space for both holding drain water and providing an air flow channel.

17 6



7


4
Air inlet port 11
SC water exit port 10
Water inlet port 09
Humidity test port 08
PVC elbow 07
Bottom flanges 06


Packing material 05 Humidity test port
Acrylic Wall 04 Drain port
PVC connection 03 Water level test port
Water inlet port 02 Water level test port
Top hatch 01 SC water inlet port
Air exhaust port No. Device
Direct contact condenser design


Figure 3-4 Schematic diagram of experimental direct contact condenser

The water distributors for the entire experimental system consist of 3 full cone


standard spray nozzles manufactured by Allspray. Each nozzle maintains a uniform cone


angle of 600. The nozzle is designed to allow a water capacity of about 14.7 1pm, and it is


placed more than 30 cm away from the packing material in the diffusion tower and


2-


3









condenser to ensure that the spray covers the entire desired area. The spray nozzle

pictured in Fig. 3-5 is a one-piece construction machined from brass bar stock.








AL R








Figure 3-5 Pictorial view of spray nozzle

The pre-heater used for the present experiment is a 240 V point source water

heater. It possesses a self-contained temperature controller and can deliver water outlet

temperatures ranging from 30 to 500 C.

The main heater consists of two 3 kW electric coil heaters wrapped around a copper

pipe through which the feed water flows. The power to the heaters is controlled with two

PID feedback temperature controllers with a 240 V output. The feedback temperature to

the controllers is supplied with a type-J thermocouple inserted in the feed water flow at

the discharge of the heater.

The packing material used in the experiments is HD Q-PAC manufactured by

Lantec and is shown pictorially in Fig. 3-6. The HD Q-PAC, constructed from

polyethylene, was specially cut using a hotwire so that it fits tightly into the main body of

the diffusion tower and condenser. The specific area of the packing is 267 m2/m3 and its

effective diameter for modeling purposes is 17 mm.







42






























Figure 3-6 Pictorial view of packing matrix


Water Heater


Figure 3-7 Schematic diagram of the instrumentation system for the DDD experiment


Water Lire 2









The instrumentation system layout is shown in Fig. 3-7. The vane-type water mass

flowmeter, constructed by Erdco Corporation, has a range of 1.5-15.14 1pm. It has been

calibrated using the catch and weigh method. The flowmeter has a 4-20 mA output that is

proportional to the flow rate and has an uncertainty of 2.21 x 10-2 kg/m2-s for the water

inlet mass flux.

The turbine water flowmeters, constructed by Proteus Industries Inc., have a range

of 1.5-12 gpm. They are also calibrated using the catch and weigh method. These

flowmeters have a 0-20 mA or 0-5 V output that is proportional to the flow rate, and the

measurement uncertainty is 3.45x 10-2 kg/m2-s for the water inlet mass flux.

The air flow rate is measured with a model 620S smart insertion thermal air

flowmeter. The flowmeter has a response time of 200 ms with changes in air mass flow

rate. The air flowmeter has a microprocessor-based transmitter that provides a 0-10 V

output signal. The air flowmeter electronics are mounted in a NEMA 4X housing. The

meter range is 0-1125 SCFM of air. The measurement uncertainty is 5.92x 10- kg/m2-s

for the air inlet mass flux at 101.3 kPa, 200 C, and 0% relative humidity.

The relative humidity is measured with 4 duct-mounted HMD70Y resistance-type

humidity and temperature transmitters manufactured by Vaisala Corp. The humidity and

temperature transmitters have a 0-10 V output signal and have been factory calibrated.

The measurement uncertainty is 1.185 x 10-3 for the absolute humidity.

All temperature measurements used in the thermal analysis are measured with type-

E thermocouples with an estimated uncertainty of 0.20 C..

The pressures at the inlet and exit of the diffusion tower are measured with two

Validyne P2 static pressure transducers. All of the wetted parts are constructed with






44


stainless steel. The transducers have an operating range of 0-0.34 atm (0-5 psi) and have

a 0-5 V proportional output. The transducers have an accuracy of 0.25% of full scale.

They are shock resistant and operate in environments ranging in temperature from -200

to 800 C.

The pressure drop across the test section is measured with a DP 15 magnetic

reluctance differential pressure transducer. The pressure transducer signal is conditioned

with a Validyne carrier demodulator. The carrier demodulator produces a 0-10 VDC

output signal that is proportional to the differential pressure. The measurement

uncertainty is + 0.25% of full scale.

t .S.' ftIll i [f ilI
Function I ray I Business I Control Data Acquisition I Database I Excel I GPIB I COM I I
SPrint... Export... Update Symbols...
How to Register... Help ( Known Issues

0 1 2 3 1 4




CC:


SSubject: Ib Message: ab




Figure 3-8 Example program of SoftWIRE

A digital data acquisition facility has been developed for measuring the output of

the instrumentation on the experimental facility. The data acquisition system consists of a

16-bit analog to digital converter and a multiplexer card with programmable gain

manufactured by Computer Boards calibrated for type E thermocouples and 0-10V input










ranges. A software package, SoftWIRE, which operates in conjunction with Microsoft

Visual Basic, allows a user defined graphical interface to be specified specifically for the

experiment. SoftWIRE also allows the data to be immediately sent to an Excel

spreadsheet. An example program layout using SoftWIRE is shown in Fig. 3-8.

The experimental data acquisition system is designed using the Virtual

Instrumentation module. The control and observation panels are shown in Figs. 3-9 3-

11. On the "Main" panel, shown in Fig. 3-9, there is a switch button to begin or stop the

data acquisition program. Once the program begins, the experimental data will be

recorded in a database file. The file's name, destination and recording frequency can be

defined on this panel. Also, all of the experimental measurements are displayed here in

real time.









-Dffuin T-i -DTif rect GfntatCo denr or
Mechanica & Aerpa eEng
sir-inWtetr-- rFrestWanter o r









-WWI Irmpltn



F r -9ed


IP ---pi. AhB llu.r [

Figure 3-9 "Main" panel of the DDD data acquisition program










This program also supplies the schematic view panels for the diffusion tower and

direct contact condenser, shown in Fig. 3-10. It shows the position and values of all the

measurements from the experimental facility so that the operator can easily control the

fresh water production.








P- Pkg -EB






Figure 3-10 "Schematic view" panels of the DDD data acquisition program

Because the current research investigation focuses on steady-state operation it is

important to know when the physical processes have reached steady-state. The

"Histogram View" panels, shown in Fig. 3-11, are used to display the measurement

variations with time. The x-axis is the time coordinate and y-axis displays the

measurement value. The measurement range shown on the y-axis can be changed

manually at any time during the experiment to accurately observe the parametric trend.






Figre3-1."is.grm .vew p o the,,,DD .d ...

7 IF-
7F F
F- F-




Figure 3-11 "Histogram view" panels of the DDD data acquisition program






47


Experimental measurements were taken at steady state conditions. Data were

automatically recorded with a frequency of 1 Hz.














CHAPTER 4
HEAT AND MASS TRANSFER FOR THE DIFFUSION TOWER

The diffusion tower is one of the most important heat and mass transfer devices in

the DDD process. An appropriately designed DDD fresh water production plant requires

a detailed heat and mass transfer analysis of the diffusion tower and direct contact

condenser. This chapter will focus on the evaporative heat and mass transfer analyses

required to design and analyze the diffusion tower.

The evaporation of feed water in the diffusion tower, shown in Fig. 4-1, is achieved

by spraying heated feed water on top of a packed bed and blowing the dry air

countercurrently through the bed. The falling liquid will form a thin film over the packing

material while in contact with the low humidity turbulent air stream. Heat and mass

transfer principles govern the evaporation of the water and the humidification of the air

stream. When the system is operating at design conditions, the exit air stream humidity

ratio should be as high as possible. The ideal state of the exit air/vapor stream from the

diffusion tower is saturated.

Heat and Mass Transfer Model for the Diffusion Tower

The most widely used model to estimate the heat and mass transfer associated with

air/water evaporating systems is that due to Merkel [23], which is used to analyze cooling

towers. However Merkel's analysis contains two restrictive assumptions,

1. On the water side, the mass loss by evaporation of water is negligible and

2. The Lewis number (Le = a,/D, which is a measure of the ratio between
characteristic lengths for thermal and mass diffusion) is unity.













Heated feed
water inlet








High surface
area packing









Suction line to
brine pump


Air/vapor
plenum


Dry air
inlet


Figure 4-1 Diagram of diffusion tower

Merkel's analysis is known to under-predict the required cooling tower volume and

is not useful for the current analysis since the purpose of the diffusion tower is to

maximize the evaporation of water for desalination. Baker and Shryock [24] have

presented a detailed analysis of Merkel's original work and have elucidated the error

contributed from each specific assumption in Merkel's model. Sutherland [25] developed

an analysis that includes water loss by evaporation but ignores the interfacial temperature

between the liquid and air. Osterle [26] assumed that air is saturated throughout the

whole process, Lewis number is unity, and air in contact with the liquid film is saturated









at the water temperature. El-Dessouky et al. [27] have presented improved analyses for

counter flow cooling towers, yet they assumed the available interfacial area for heat

transfer is the same as that for mass transfer, which is only true when the packing is

thoroughly wetted and is rare. An empirical enthalpy equation is used for the air/vapor

mixture and is only valid for temperatures between 10-50 C. The present model does not

require any of the assumptions used in prior works. The current model includes the

evaporation of water, the interfacial heat resistance between water and air, and the

different interfacial areas for heat transfer and mass transfer.

mL Gas/Vapor
z+dz



dmV evap

dq

z

.ima+mv
Packing Liquid
material

Figure 4-2 Differential control volume for liquid/vapor heat and mass transfer within
diffusion tower

The current formulation is based on a two-fluid film model for a packed bed in

which conservation equations for mass and energy are applied to a differential control

volume shown in Figure 4-2. In this Figure, there is a clear interface between liquid film

and gas side. And because the gas is blown from bottom to top of the packed bed, the z-

axis denotes the axial direction through the packed bed. The conservation of mass applied

to the liquid phase of the control volume in Fig. 4-2 results in,










(m,)= d (m,evap). (4.1)
dz dz

where m is the mass flow rate, the subscript L, v, and evap denotes the liquid, vapor, and

the portion of liquid evaporated respectively. Likewise, the conservation of mass applied

to the gas (air/vapor mixture) side is expressed as,

d d
(mM ) = (m)evap (4.2)
dz dz

For an air/vapor mixture the humidity ratio, co, is related to the relative humidity,

D, through,

m 0.6220Pa, (Ta)
S,= (4.3)
m. P Psa(Ta)

where P is the total system pressure and Psat(Ta) is the water saturation pressure

corresponding to the air temperature Ta. It is assumed the total system pressure is

constant. It is noted that the pressure drop is on the order of 100 Pa, which is a fraction of

a percent of the absolute pressure. Using the definition of the mass transfer coefficient

applied to the differential control volume and considering the interfacial area for mass

transfer may differ from that of heat transfer, then,


d (mevap) = kGaw[pvt TL)- p (Ta )]A. (4.4)

Applying the perfect gas law [28] to the vapor, the gradient of the evaporation rate

is expressed as,

kd M, Ps, (T ) OPsa, (Ta)
d (m ,evap) = kGaw- ( -i l w( T )A, (4.5)
dz R T, T1

where kG is the mass transfer coefficient on gas side, a is the specific area of packing,

which is defined as the total surface area of the packing per unit volume of space









occupied, aw is the wetted specific area, M, is the vapor molecular weight, R is the

universal gas constant, Ti is the liquid/vapor interfacial temperature and A is the cross

sectional area of the diffusion tower. Combining Eqs. (4.2), (4.3) & (4.5) the gradient of

the humidity ratio in the diffusion tower is expressed as,

do) k M P (T) co P
=- ( I) (4.6)
dz G R T, 0.622 + o T


where G = m/A is the air mass flux. Equation (4.6) is a first order ordinary differential

equation with dependent variable, co, and when solved yields the variation of humidity

ratio along the height of the diffusion tower.

In order to evaluate the liquid/vapor interfacial temperature, it is recognized that the

energy convected from the liquid is the same as that convected to the gas,

UL -T) = UG T), (4.7)

where UL and UG are the respective liquid and gas heat transfer coefficients, and the

interfacial temperature is evaluated from,

TL+ UU Ta
U

1+ G


In general the liquid side heat transfer coefficient is much greater than that on the

gas side, thus the interfacial temperature is only slightly less than that of the liquid. The

conservation of energy applied to the liquid phase of the control volume yields,

d d(m vevap)
S(mLh) = d e hFg + Ua(T T)A, (4.9)
dz dz






53


where U is the overall heat transfer coefficient, h is the enthalpy, and hFg is the latent

d dm+ dh,
heat. Noting that dhL = CpLdTL (mh,) = h, + m L and combining with
dz dz dz

Eqs. (4.9) & (4.1) results in an expression for the gradient of water temperature in the

diffusion tower,

dT G dC (hFg -h,) Ua(T -T) 0)
+ (4.10)
dz L dz CpL CpL


where L= mL is the water mass flux. Equation (4.10) is also a first order ordinary

differential equation with TL being the dependent variable and when solved yields the

water temperature distribution through the diffusion tower.

The conservation of energy applied to the air/vapor mixture of the control volume

yields,

d d(m ....p)
(maha +mvh,)+ ev hFg = -Ua(TL -T)A. (4.11)
dz dz

Noting that the specific heat of the air/vapor mixture is evaluated as,

m m
CpG = a Cpa + Cp, (4.12)
ma + mv ma + mv

and the latent heat of vaporization is evaluated as,

hFg (Ta) = h(T) h (T), (4.13)

combining with Eqs. (4.11) & (4.2) yields the gradient of air temperature in the diffusion

tower,

dT 1 do h,(T) Ua(TL T )
dz +) dz CG CpG(+(4.14)
dz 1+o dz CpG CpGG(1+ o)









Equation (4.14) is also a first order ordinary differential equation with Ta being the

dependent variable and when solved yields the air/vapor mixture temperature distribution

along the height of the diffusion tower. Equations (4.6), (4.10), and (4.14) comprise a set

of coupled ordinary differential equations that are used to solve for the humidity ratio,

water temperature, and air/vapor mixture temperature distributions along the height of the

diffusion tower. However, since a one-dimensional formulation is used, these equations

require closure relationships. Specifically, the overall heat transfer coefficient and the gas

side mass transfer coefficient are required. A significant difficulty that has been

encountered in this analysis is that correlations for the water and air/vapor heat transfer

coefficients for film flow though a packed bed, available in the open literature (McAdams

et al. [29] and Huang and Fair [30]), are presented in dimensional form. Such correlations

are not useful for the present analysis since a structured matrix type packing material is

utilized, and the assumption employed to evaluate those heat transfer coefficients are

questionable. In order to overcome this difficulty the mass transfer coefficients are

evaluated for the liquid and gas flow using a widely tested correlation and a heat and

mass transfer analogy is used to evaluate the heat transfer coefficients. This overcomes

the difficulty that gas and liquid heat transfer coefficients cannot be directly measured

because the interfacial film temperature is not known.

The mass transfer coefficients associated with film flow in packed beds have been

widely investigated. The most widely used and perhaps most reliable correlation is that

proposed by Onda et al. [31]. Onda's correlation, shown in Appendix A, is used to

calculate the mass transfer coefficients in the diffusion tower, kG and kL. However, it was









found that Onda's correlation under-predicted the wetted specific area of the packing

material. Therefore, a correction was made as follows,

[ ( 3/4 1
a= a exp- Re FrL eL1 (4.15)


see Appendix A for details.

As mentioned previously, the heat and mass transfer analogy [32] is used to

compute the heat transfer coefficients for the liquid side and the gas side. Therefore the

heat transfer coefficients are computed as follows,

Heat transfer coefficient on the liquid side

NuL = ShL (4.16)
p kL/2 LC (4.6)


U ( = k (p1C)2 (4.17)
DL

Heat transfer coefficient on the gas side

NuG ShG
Nu G =ShG (4.18)
PrG 13 c 13 '


UG = kG (pC )1 3(KG)2 3, (4.19)
DG

Overall heat transfer coefficient

U = (UL + UG)-', (4.20)

where K denotes thermal conductivity and D denotes the molecular diffusion coefficient.

In order to test the proposed heat and mass transfer model, consideration is first

given to the cooling data of Huang [33]. Using the analysis presented above, the exit







56


water temperature, exit air temperature and exit humidity ratio are computed using the

following procedure:

1. Specify the water mass flux, air mass flux, water inlet temperature, air inlet
temperature and inlet humidity ratio;

2. Guess the exit water temperature;

3. Compute the temperature and humidity distributions through the packed bed using
Eqs. (4.6), (4.10), and (4.14) until z reaches the packed bed height used in the
experiment;

4. Check whether the predicted inlet water temperature agrees with the specified inlet
water temperature, and stop the computation if agreement is found, otherwise
repeat the procedure from step 2.

A comparison between the measured exit water temperature, exit air temperature

and exit humidity ratio reported by Huang [33] with those computed using the current

model are shown in Figs. 4-3 a-b for 2.54 cm pall ring packing. As seen in the figures the

comparison is generally good. The exit air temperature and exit water temperature are

slightly over-predicted. The exit humidity ratio prediction is excellent.

L = 2.0 kg/m2-s (a)
Predicted Measured
Taout o Taout
*** TLout A TL,out
--*--- (Wout O('out
50 025


40 0-20
o ****A.. ... ......
A
S30 015 3
I I
0 20 010
E
10 *~- *-*-3..._._ 005


0- 000
06 08 10 12
Air Mass Flux G (kg/m2-s)

Figure 4-3 Comparison of predicted exit conditions with the data of Huang [33]: a) L =
2.0 kg/m2-s, b) L = 4.1 kg/m2-s







57


L = 4.1 kg/m2-s (b)
Predicted Measured
T ,out o Ta,out
""" L,out A TL,out
------- )ut 0 out
out 0 0ut
50 -0 25


40 020


30 015


0 20 010
O.
E
I-
10 .- ....... 005


0 000
06 08 10 12 14 16

Air Mass Flux G (kg/m2-s)


Figure 4-3 Continued

Model Comparison with Experiments for the Diffusion Tower

Heat and mass transfer experiments were carried out in the diffusion tower with a

packed bed height of 20 cm. The liquid mass flux was fixed at 1.75, 1.3 and 0.9 kg/m2-s

and the air mass flux was varied from about 0.6-2.2 kg/m2-s. The inlet air temperature

was about 230 C while the inlet water temperature was 600 C. The experiments were

repeated to verify the repeatability of the results. The measured exit humidity, exit air

temperature, and exit water temperature are compared with those predicted with the

model for all three different liquid mass fluxes in Figs. 4-4 a-c. It is observed that the

repeatability of the experiments is excellent. The exit water temperature, exit air

temperature and exit humidity ratio all decrease with increasing air mass flux for a certain

water mass flux. The comparison between the predicted and measured exit water

temperature and exit humidity ratio agreed very well, and the exit air temperature is








58



slightly over predicted. Detailed experimental data associated with Figs. 4-4 a-c are


tabulated in Appendix B.


S 40

I-
30
1-


E

10 -


0
06 08 10 12 14 16 18 20

Air Mass Flux G (kg/m2-s)


50 4


040-
I-
30-

20
C- 20
E


L=1.75 kg/m2-s (a)
Predicted Measured Set 1 Set 2
-- Ta,out Ta,out o
......... TL,out TL,out A A
o
- mout mout




--------
;'" ".... ... -..**Oo
A"-.'... ......

I -. .... ... ..-- i --

^-^.


0 05


I 000
22 24


0 25


- 020


-015

E
-010


- 005


- 00


06 08 10 12 14 16

Air Mass Flux G (kg/m2-s)


Figure 4-4 Comparison of predicted exit conditions with the experimental data for
different liquid mass fluxes: a) L= 1.75 kg/m2-s, b) L= 1.3 kg/m2-s, c) L= 0.9
kg/m2-s


)015

E
010


L=1.3 kg/m2-s (b)
Predicted Measured Set 1 Set 2
--- Ta,out Ta,out o
......... TL,out TL,out
--- mout 0out



1- ----


"... ..... oo

S... ..


L







59


L=0.9 kg/m2-s (C)
Predicted Measured Set 1 Set 2
--- Ta,out Ta,out 0 o
......... TL,out TL,out A A
--- -fout fout
50 0.25


40- 0.20

S .... ..... .... ^
w 30- 000000**.. A -0.15 >1
S0..A.......... .......... A


E
S20- -0.10
I-I
10 ---------0.05


0 0.00
0 .......i--- i --- i --- i --- i --- i 0.00
0.7 0.8 0.9 1.0 1.1 1.2 1.3

Air Mass Flux G (kg/m2-s)

Figure 4-4 Continued

In general, the analytical model proves to be quite satisfactory in predicting the

evaporative heat and mass transfer of counter flow packed beds. The excellent agreement

of the model with the measured exit water temperature and exit humidity ratio is most

important for desalination and water-cooling applications. A rigorous set of conservation

equations have been developed for a two-fluid model and mass transfer closure has been

achieved using a widely tested empirical correlation, while heat transfer closure has been

achieved by recognizing the analogous behavior between heat and mass transfer. The

model does not require questionable assumptions that have plagued prior analyses. It is

believed that the current model will be very useful to both designers of diffusion towers

for desalination applications as well as designers of cooling towers for heat transfer

applications.







60


Pressure Drop through the Packing Material

The pressure drop through the packing material on the air side influences the


energy consumption prediction of the DDD process. Therefore experiments considering


the air pressure drop with water loading is another important objective in the research.


This experiment is executed without heating the water. The comparison of the predicted


pressure drop and the experimental data are shown below in Fig. 4-5 for different water


mass flux loadings. Detailed experimental data associated with Figs. 4-5 are tabulated in


Appendix C.


Water mass flux (kg/m2-s) Data Model
08 O
17 V
20
100

V
80 /

0 / /
60 /


40
.--.

S_ 20
CU).



00 02 04 06 08 10 12 14 16 18
Air mass flux (kg/m2-s)


Figure 4-5 Air specific pressure drop variation with air mass flux for different water mass
fluxes

The pressure drop is predicted using the empirical correlation specified by the


manufacturer of the packing material. Figure 4-5 clearly shows that the pressure drop


correlation is accurate for HD Q-Pac packing material. An interesting feature of the data


is that the air specific pressure drop increases with increasing water mass flow rate under


the same air mass flow rate.









The air side dimensional pressure drop correlation specified by the manufacturer of

the HD Q-Pac packing material is,

AP
-= pG (3.5410- +0.654v+ 1.176x104v p2v7), (4.21)
z

where z is the height of the packing material (m), AP is the pressure drop through the

packing (Pa), pG is the gas density (kg/m3), VG is the superficial gas velocity through the

packing (m/s), and v, is the superficial liquid velocity through the packing (m/s).

Optimization of the Packing Material

Optimization of the Diffusion Driven Desalination system includes two major

objectives,

1. For a specified packing material, find the optimal operating conditions to maximize
the fresh water production rate with low energy consumption rate.

2. For a specified operating condition, find the optimal packing material to maximize
the fresh water production rate with low energy consumption rate.

The mathematic model developed in this chapter can be used for the diffusion

tower analysis and design, as well as optimization of the packing material used for the

diffusion tower. Energy consumption due to pumping power required for the pumps and

blowers is considered in the analysis. Since the thermal energy is assumed to be waste

heat and free, it is not considered. The flow resistance for packing material is an

important feature for the packing selection. It is also well understood that large contact

surface area between water and air can enhance the heat and mass transfer within packed

beds. However, the packing materials with large surface area usually have high flow

resistance because of the narrow flow passages between the packing units. The optimal

packing material will balance these two competitive factors for a specified operating






62


condition to yield the best performance from the diffusion tower. Two different types of

optimal packing materials have been found in this analysis,

1. The packing material that can minimize the tower height for specified operating
conditions. This kind of packing material will directly reduce the facility
construction cost.

2. The packing material that can minimize the energy consumption rate of fresh water
production for specified operating conditions. This kind of packing material has a
long-term cost advantage.

The energy consumption rate on the water side is calculated as,


(4.22)


PWL = mLgz = AP,,
PL


where Pw (W) denotes the electrical power consumption, and the water side pressure

drop is assumed to be equivalent to the gravitational head loss which is given by,


AP, = pgz.


(4.23)


The energy consumption rate on the gas side is calculated as,


PWG = VGPG al n ) PG
PG


GA AP,
PG


(4.24)


where VG is the gas volume flow rate.

The total energy consumption is calculated as,


Pw = Pw, +PwG,


(4.25)


The energy consumption rate per unit of fresh water production is defined as,


(4.26)


Pwf =m
mf


where mf is the ideal fresh water production rate from the diffusion tower and is defined

as,


m f = ma (ot on).


(4.27)









Combining above equations with the dynamic computational model of the diffusion

tower, the performance characteristics of a specified packing material can be explored,

such as the exit water/air temperature, exit humidity, air to feed water mass flow ratio,

packed bed height, fresh water production rate, pressure drop and energy consumption

rate. The comparison of these parameters for different packing materials will reveal the

optimal packing material for the diffusion tower. As an example, eight different types of

packing material are investigated. They can be categorized into 2 geometric shapes and 8

nominal sizes. Detailed information is listed in Table 4-1.

The frictional pressure drop of air through the packed bed depends on the size and

geometry of the packing material, and is calculated using Leva's correlation [34] as,

aAL G2
= a1 (10-8)(10 P ) (4.28)
z PG

In this equation, ai and a2 are the pressure drop constants for tower packing and are given

by Treybal [35].

Table 4-1 Packing material configurations
S. Nominal size 3 Specific packing
Packing .inl s Specific area (m/m3) Specific packing
(inch) diameter (m)
0.5 470 0.01
Bl S e 0.75 280 0.017
Berl Saddle
1.0 250 0.019
1.5 144 0.033
0.5 394 0.012
S1.0 190 0.024
RaschRng 1.5 118 0.039
2.0 94 0.05
The procedure used to identify the optimum packing material is as follows:

1. Specify water inlet temperature, TL,.n, water mass flux, L, air to water mass flow
ratio, ma/mL, air inlet temperature, Ta., and inlet humidity co,. Find the
thermodynamic states of the air and water entering the diffusion tower and their
states discharging from the diffusion tower for each packing material using Eqs.
(4.6), (4.10) & (4.14),










2. Compute the required packed bed height in the diffusion tower for the specified
operating conditions for each packing material,

3. Compute the water and gas side pressure drop through the packing material for
each packing material using Eqs. (4.23) & (4.28),

4. Compute the energy consumption rate for each packing material using Eqs. (4.22),
(4.24), (4.25) & (4.26),

5. Determine the optimal operating conditions for each packing material. Under these
conditions, the energy consumption rate is minimized for this packing material.

6. Find the best packing material by comparing the optimum operating conditions for
each packing.

For all the computations, the water inlet temperature TL,,n, air inlet temperature Ta,,,

and inlet humidity co,n, diameter of the diffusion tower d are fixed at 500 C, 150 C, 0.0107

and 15 m respectively. The water inlet mass flux L will vary from 0.5 kg/m2-s to 5 kg/m2-

s, meanwhile the air to water mass flow ratio (ma/mL) will vary from 0.3 to 1.5 for each

fixed water inlet mass flux.

For each type of packing material, Figures 4-6 a-h show the energy consumption

rates for different air to water mass flow ratios with varying fresh water production level.


014- Berl Saddle 0 5"
TL, =50 C
012 I T= 50C



03
S 008 I ................ 04
012
-0-0/ / -=- 05




0 020
E 0062 / y -..... 075



0 00 ""_____ 15


10 20 30 40
Fresh water mass flow rate (kg/s)

Figure 4-6 Energy consumption rate for fresh water production: Berl Saddle a) 0.5", b)
0.75", c) 1.0", d) 1.5"; Raschig Ring e) 0.5", h) 1.0", g) 1.5", h) 2.0"














010



S008
-c


0
006



E 004









10 20 30

Fresh water mass flow rate (kg/s)
008 -
0 002

0)

0 002















0 00
10 20 30

Fresh water mass flow rate (kg/s)




























0 0 8 -]------------------
006 -





o 004 -

E /















0 ..' ^







10 20 30

Fresh water mass flow rate (kg/s)
0 08
0 002
c0




0 004




U Ub










o 004














Fresh water mass flow rate (kg/s)

Figure 4-6 Continued


40


40


40








66






S06-

-F



04


E

I 02

21-


00

10 20 30

Fresh water mass flow rate (kg/s)
0 25



- 020
-,


| 015
C
o /

E 010 -
0
o

S005
w e


00 00
10 20 30

Fresh water mass flow rate (kg/s)
0 20



0r
- 015 -




S010

E



0 0/



0 00 ,
10 20 30

Fresh water mass flow rate (kg/s)


40


40


Figure 4-6 Continued


40












0 20


10 20 30 40
Fresh water mass flow rate (kg/s)


Figure 4-6 Continued


Fig. 4-6 a-h clearly show that for each packing material, the energy consumption


rate is minimized for the same fresh water production rate when the air to water mass


flow ratio is 0.75. The air to water mass flow ratio of 0.75 will be maintained when


investigating the influence of other variables on the diffusion tower performance.


TL,=5 Berl Saddle Raschig Ring
=15C 0.5" -- 0.5"
................ 0.75" -.-.- .- 1.0"
co,,=0.0107 _____ 1.0" ---- 1.5"
mJmL=0.75 _.._.._. 1.5" 2.0"
0.10



S0.08 -
E
:3

a 0.06
a)
0)

S0.04 -
E
E
S0.02



0.00
1 2 3 4 E

Feed water mass flux (kg/m2-s)


Figure 4-7 Maximum possible exit humidity for feed water mass flux











Figure 4-7 shows the maximum possible exit humidity ratio for different packing

materials and varying water inlet mass flux with air to water mass flow ratio of 0.75. The

variation of the maximum possible exit humidity isn't dependent on the water mass flux

or the packing material because the height of the packed bed will change to insure the

exit air is always saturated.

Figure 4-8 shows the gas side mass transfer coefficient for different packing

materials and varying air mass flux. For the same packing material, the gas mass transfer

coefficient increases with increasing the air mass flux. It also shows that the gas mass

transfer coefficient increases with increasing the specific area of the packing material.

Increasing the air mass flux will increase the shear on the air water interface, and

increasing the specific surface area of packing will increase the maximum possible

contact area between water and air. This may explain why large air mass flux and large

specific surface area can enhance the mass transfer rate.


TLr,=50 C Berl Saddle Raschig Ring
T =15 C 0.5" -- 0.5"
15................ 0.75" ---- -- 1.0"
co,,=0.0107 _____ 1.0" ---- 1.5"
mJmL=0.75 -..-..-. 1.5" -- 2.0"
0.20
Increasing specific surface area of packing


0.15-



C 0.10 -
CU

E
S0.05



0.00
0.5 1.0 1.5 2.0 2.5 3.0 3.5
Air mass flux (kg/m2-s)

Figure 4-8 Gas mass transfer coefficient for air mass flux







69


Figure 4-9 shows the air side pressure drop through the packed bed for different

packing materials and varying air mass flux. The air side pressure drop increases

substantially with increasing the air mass flux for some packing materials. It also shows

that the air pressure drop increases with the specific surface area of the packing materials

with the same geometric shape.


TL=5 C Berl Saddle Raschig Ring
TI ,.=50 C
T =15C 0.5" --- 0.5"
................ 0.75" --- 1.0"
c,=0.0107 ______ 1.0" ---- 1.5"
mm,=0.75 _.._.... 1.5" -- 2.0"
60000
/
50000 -
/
Q 40000 -
2 /

S30000 -
/
0)

0 20000 -

10000 ..


0.5 1.0 1.5 2.0 2.5 3.0 3.5
Air mass flux (kg/m2-s)

Figure 4-9 Gas pressure drop for air mass flux

Figure 4-10 shows the required packed bed height for different packing materials

with varying water inlet mass flux. The tower height is computed such that the maximum

possible humidity ratio leaves the diffusion tower. For each type of the packing material,

the required diffusion tower height increases with increasing the water inlet mass flux,

and the rate of increase decreases after the water inlet mass flux exceed about 1.5 kg/m2-

s. It also shows that under the same water mass flux, the required diffusion tower height

decreases almost proportionally with increasing the specific surface area of the packing

material. Considering Fig. 4-10 in conjunction with Fig. 4-7, it is obvious that Berl







70


Saddle 0.5" can minimize the tower height without decreasing fresh water production

rate, which implies that Berl Saddle 0.5" is the first type of optimal packing material of

the different packing materials considered.


TL, 0 Berl Saddle Raschig Ring
TL,in=50 C
T =15 C 0.5" --- 0.5"
................ 0.75" ------ 1.0"
o,,=0.0107 ______ 1.0" ---- 1.5"
malmL=0.75 -. 1.5" -- -- 2.0"


Increasing specific surface area of packing
5-



4-











1 2 3 4 .
2---






Feed water mass flux (kg/m2-s)

Figure 4-10 Required tower height for feed water mass flux

Figure 4-11 shows the energy consumption rate for each packing material with

varying water mass flux. The energy consumption rate increases with increasing the

water mass flux for the same packing material. It also shows that under the same water

inlet mass flux, the energy consumption rate increases with increasing air side pressure

drop. Although the air side pressure drop is far less than the water side pressure drop

through the packed bed, the volumetric flow rate of air is much higher than that of the

water. This may explain why the air side pressure drop has large influence on the total

energy consumption rate in the diffusion tower.

















0.35


S0.30

L Increasing air side pressure drop /
0.25 /
0) /

P 0.20 /


S0.15 /


O 0.10 -


S0.05 .
W-
........ .... ." "
0.00 -
1 2 3 4

Feed water mass flux (kg/m2-s)


Figure 4-11 Energy consumption rate for feed water mass flux


5 10 15 20 25 30 35


Fresh water mass flow rate (kg/s)


Figure 4-12 Energy consumption rate for fresh water mass flow rate (cross section
diameter of the packed bed is 15 m)









Figure 4-12 shows the energy consumption rate for each packing material with

varying fresh water production level. It clearly shows that under the same fresh water

production level, the total energy consumption rate is always minimized for Berl Saddle

1.5" since it has the lowest air side pressure drop shown in Fig. 4-9, which means Berl

Saddle 1.5" is the second type of optimal packing material for the diffusion tower in the

current analysis.

Finally, it can be concluded that for a specified operating condition and fresh water

production rate, using the packing materials with large specific surface area can help

reduce the tower height, and using the packing materials with low air side flow resistance

can help reduce the total energy consumption rate. However, it is noticed that the current

model cannot reveal the influence of the packing material geometric shape on the

diffusion tower performance since no parameter in the current model explicitly describes

the packing material shape.














CHAPTER 5
HEAT AND MASS TRANSFER FOR THE DIRECT CONTACT CONDENSER

In order for the DDD process to be cost effective, an efficient and low cost method

is required to condense water vapor out of the air stream. With a large fraction of the

air/vapor mixture being non-condensable, direct contact condensation is considerably

more effective than film condensation. Another important heat and mass transfer device

in the DDD process is the direct contact condenser. This chapter describes the

performance of droplet direct contact condenser and packed bed condenser for both co-

current and countercurrent flow.

While a significant amount of literature is available on droplet direct contact

condensation, considerably less information is available for packed bed direct contact

condensation. In analyzing direct contact condensation through packed beds, Jacobs et al.

[36] and Kunesh [37] used a volumetric heat transfer coefficient for the rate of convective

heat transport and penetration theory [38] to relate the heat and mass transfer coefficient.

The volumetric approach does not account for local variations in heat and mass transfer.

Penetration theory assumes the liquid behind the interface is stagnant, infinitely deep, and

the liquid phase resistance is controlling. As suggested by Jacobs et al. [36] these may or

may not be reasonable assumptions, depending on the liquid film condensate resistance.

Bharathan and Althof [39] and Bontozoglou and Karabelas [40] improved the analysis of

packed bed direct contact condensation by considering conservation of mass and energy

applied to a differential control volume. Local heat and mass transfer coefficients were









used. Both analyses relied on penetration theory to relate heat and mass transfer

coefficients.

The motivation for this work is to explore the heat and mass transfer process within

a direct contact condenser and develop a robust and reliable predictive model from

conservation principles that is useful for design and analysis. A fresh approach is used

that does not rely on penetration theory. One of the difficulties encountered is that the

interfacial temperature between the liquid and vapor cannot be directly measured, and

thus the liquid and vapor heat transfer coefficients cannot be directly measured.

Following the methodology used by Klausner et al. [41] for the evaporative heat and

mass transfer analysis, the extensively tested Onda [31] correlation was used to evaluate

the mass transfer coefficients on the liquid and gas side. A heat and mass transfer analogy

was applied to evaluate the liquid and gas heat transfer coefficients. Excellent results

were obtained, and a similar approach will be pursued here.

A laboratory scale direct contact condenser has been fabricated. The condenser is

constructed as a twin tower structure with two stages, co-current and countercurrent. The

performance of each stage has been evaluated over a range of flow and thermal

conditions. As expected, the countercurrent stage is significantly more effective than the

co-current stage. In addition, direct contact condensation within a packed bed is more

effective than droplet direct contact condensation. It is also found that the manner in

which the packing is wetted can significantly influence the heat and mass transfer

performance. Visual observations of the wetted packing have been made and a

discussion relating the wetting characteristics to the different empirical constants

suggested by Onda [31] is provided.









Mathematical Model of the Packed Bed Direct Contact Condenser

To explore the variation of temperature and humidity within the countercurrent

flow stage of the direct contact condenser, a physical model is developed for direct

contact condensation by considering that cold water is sprayed on top of a packed bed

while hot saturated air is blown through the bed from the bottom. The falling water is

captured on the packing surface and forms a thin film in contact with the saturated

turbulent air stream. Energy transport during the condensation process is accomplished

by a combination of convective heat transfer due to the temperature difference between

water and air and the latent heat transport due to vapor condensation. Mass and energy

conservation principles govern the condensation of the vapor and the dehumidification of

the air stream. Noting that the relative humidity of the air is practically unity during the

condensation process, the ideal state of the exit air/vapor temperature from the condenser

is close to the water inlet temperature.

A general approach for modeling the flow of water/air through a packed bed is to

consider flow through an array of round channels with both transverse and longitudinal

variations of temperature, pressure and humidity. This method was applied by Bemer

and Kalis [42] in predicting the pressure drop and liquid hold-up of random packed beds

consisting of ceramic Raschig rings and metal Pall rings. It was also used by Bravo et. al

[43, 44] for structured packing. Because the air flow through the packing is highly

turbulent, a 1/7h law variation of air temperature in the transverse direction can be

assumed [28] as,

T -T x'
L l _X 117. (5.1)
TL To I I









where Ta, is the centerline air temperature, TL is the bulk liquid temperature, / is the half

width of the hypothetical flow channel, and x is the transverse axis. Although the 1/7th

law profile may not be exact, it has proven to be robust in other channel and film flow

applications. The centerline air temperature is in terms of the respective bulk air and

liquid temperatures as,

T,c = TL +1.224(T TL). (5.2)

Eqn. (5.1) is used to evaluate the transverse distribution of air temperature. The local

absolute humidity co, based on local transverse air temperature T,x, is related to the

relative humidity $ as,

m, 0.6220Pet (T,x)
= 0622) (5.3)
mo P- @P^ (T(,x)

where P (kPa) is the total system pressure, and Psat (kPa) is the water saturation pressure

corresponding to the local air temperature Ta,x.

The area-averaged humidity onm at any cross section is expressed as,

2 1
) = 2 x xdx, (5.4)
0

and the bulk humidity co at any cross section is calculated from Eqn. (5.3) based on the

air bulk temperature Ta, which is a cross-sectional area-averaged value.

A careful examination of the area-averaged humidity and the bulk humidity

calculated at the same cross section shows that: for a given total system pressure P=101.3

kPa, the air bulk temperature Ta < 750 C, and the bulk temperature difference between the

air and water Ta-TLI < 200 C, the relative difference of the area-averaged humidity and


the bulk humidity --'m 1.8%. It implies that replacing the area-averaged humidity
O)m











or with the bulk humidity co to account for the transverse variation of air temperature


will only cause minimal error in predicting the heat and mass transfer within the packed


bed. Therefore, the air temperature non-uniformity in the transverse direction is


considered by using the bulk humidity in the current formulation. This observation


allows a one-dimensional treatment of the conservation equations to be used along the z-


direction with confidence.


The current formulation is based on a two-fluid film model in which one-


dimensional conservation equations for mass and energy are applied to a differential


control volume shown in Fig. 5-la. In this figure, the air/vapor mixture is blown from


bottom to top (z-coordinate). Such an approach has been successfully used by Klausner


et al. [41] to model film evaporation in the diffusion tower.


(a) Countercurrent flow
L

mL

Sz+dz
-- -dmyv,cond
Liquid Air/Vapor dz
--- dq


i ma+mv

G

(b) Co-current flow
L G

mL ma+mv


-- -dmv,cond
Liquid Gas/Vapor

-dq
z+dz
Figure 5-1 Differential control volume for liquid/gas heat and mass transfer within a)
countercurrent flow, b) co-current flow condensers









The conservation of mass applied to the liquid and vapor phases of the control

volume in Fig. la results in,

d d d
dz (mz) = (m ) (mv,cond), (5.5)
dz dz dz

where m is the mass flow rate, the subscripts L, v, and cond denote the liquid, vapor, and

condensate respectively.

The conservation of energy applied to the liquid phase of the control volume yields,


d(mh) = nd hFg + Ua(T Ta)A, (5.6)
dz dz

where U is the overall heat transfer coefficient and h is the enthalpy. Noting that

dhL = CpLdTL and combining with Eqs. (5.5) & (5.6) results in an expression for the

gradient of water temperature in the condenser,

dTL G do) (hFg -h,) Ua(TL --T)
dz L dz CpL CpL

where L is the water mass flux. Eqn. (7) is a first order ordinary differential equation

with TL being the dependent variable and when solved yields the water temperature

distribution through the condenser.

The conservation of energy applied to the air/vapor mixture of the control volume

yields,

d d(mvcofd)
d (mh, + mh,) d vcond hFg T) = -Ua(T T0)A. (5.8)
dz dz

Noting that the specific heat of the air/vapor mixture is evaluated as,

m m
C PG m Cp + m Cp (5.9)
PG + a Pv'
m0 +m, m +m, (9









and combining with Eqs. (5.5) & (5.8) yields the gradient of air temperature in the

condenser,

dT_ 1 d) hL (T Ua(TL-To (5
-= -+ (5.10)
dz 1+o dz CPG CpGG(1+ g)

Equation (5.10) is another first order ordinary differential equation with To being

the dependent variable and when solved yields the air/vapor mixture temperature

distribution along z direction. Thus Eqs. (5.7) & (5.10) are solved simultaneously to

evaluate the temperature and humidity fields along the height of the condenser. Since a

one-dimensional formulation is used, these equations require closure relationships.

Specifically, the humidity gradient and the overall heat transfer coefficient are required.

The bulk humidity, co, based on air temperature Ta, is related to the relative

humidity ( and calculated from Eqn. (5.3). An empirical representation of the saturation

curve is,

P (T) =aexp(bT-cT2 +dT3), (5.11)

where empirical constants are a=0.611379, b=0.0723669, c=2.78793 x10-4,

d=6.76138x10-7, and T (0 C) is the temperature.

Noting that the relative humidity of air remains approximately 100% during the

condensation process, the absolute humidity co is only a function of air temperature T,

when the total system pressure P remains constant. Differentiating Eqn. (5.3) with

respect to T, and combining with Eqn. (5.11), the gradient of humidity can be expressed

as,

dc dT P
d- (b 2cT + 3dT2). (5.12)
dz dz P-P P,, (T, )









Eqn. (5.12) is used to compute the humidity distribution through the condenser. Eqs.

(5.3) & (5.12) are used in the one-dimensional condensation model (Eqs. (5.7) & (5.10))

for closure.

Following the methodology ofKlausner et al. [41], the mass transfer coefficients are

evaluated using a widely tested correlation and the heat transfer coefficients are evaluated

using a heat and mass transfer analogy for the liquid and gas. This approach overcomes

the difficulty that gas and liquid heat transfer coefficients cannot be directly measured

because the interfacial film temperature is not known. The mass transfer coefficients

associated with film flow in packed beds have been widely investigated. The most widely

used and perhaps most reliable correlation is that proposed by Onda et al. [31] as listed in

the Appendix.A. As mentioned previously, the heat and mass transfer analogy [32] is

used to compute the heat transfer coefficients for the liquid and gas. Therefore the heat

transfer coefficients are computed as described in Chapter 4. The overall heat transfer

coefficient is also used in the one-dimensional condensation model (Eqs. (5.7) & (5.10))

for closure.

A similar mass and energy balance analysis has been done for the co-current flow

condenser stage. The one-dimensional conservation equations are applied to a

differential control volume shown in Fig. lb. The equations for evaluating the humidity

gradient and air temperature gradient are the same as that for countercurrent flow. The

gradient of water temperature in the co-current flow condenser stage is,

dTL Gd( (h hL) Ua(TL -T)
d L C CL (5.20)
dz L dz CpL C LL









Thus Eqs. (5.10) & (5.20) are used to evaluate the temperature fields in the co-current

flow condenser stage. The humidity gradient, Onda's correlation and the heat and mass

transfer analogy are used for closure.

The condensation rate in the condenser is calculated as,

mcond = ma( )out) (5.21)

The condenser effectiveness is defined as the ratio of the condensation rate in the

condenser to the maximum possible condensation rate.

M= cond (5.22)
ma ()n )sink)

Here, sink is the minimum possible humidity exiting the condenser, which is evaluated

with Eqn. (5.3) assuming the air exits the condenser at the water inlet temperature. The

condenser effectiveness is very useful in comparing the performance of the co-current

and countercurrent flow condenser stages.

For the countercurrent condensation analysis, the exit water temperature, exit air

temperature, and exit humidity are computed using the following procedure: 1) specify

the inlet water temperature, TL,,n, air temperature, Ta,,,, and bulk humidity co,,; 2) guess

the exit water temperature TL,out; 3) compute the temperatures and humidity at the next

step change in height, starting from the bottom of the packed bed, using Eqs. (5.7), (5.10)

& (5.12) until the computed packed bed height matches the experimental height; 4) check

whether the computed inlet water temperature agrees with the specified inlet water

temperature, and stop the computation if agreement is found, otherwise repeat the

procedure from step 2. A detailed flow diagram of the computation procedure is

illustrated in Fig. 5-2.









The computation is much simpler for the co-current flow condensation analysis.

The exit water temperature, exit air temperature, and exit humidity are computed using

the following procedure: 1) specify the inlet water temperature, TL,,n, air temperature,

Ta,,n, and bulk humidity co,; 2) compute the temperatures and bulk humidity, Ta, TL, & co,

at the next step change in z-direction, starting from the top of the packed bed, using Eqs.

(5.10), (5.12) & (5.20) until the computed height matches the experimental height.


Figure 5-2 Flow diagram for the countercurrent flow computation

Model Comparison with Experiments for the Packed Bed Direct Contact Condenser

The effective packing diameter dp for the structured polyethylene packing is 17

mm. In Onda's original work [31] he suggested that the coefficient in Eqn. (5.14) should







83


be C=5.23 for dp>15 mm and C=2.0 for dp,15 mm. However, careful scrutiny of the data

shows that the change in the coefficient is smooth, and the abrupt change represented by

a bimodal coefficient is only an approximation. The 17 mm effective packing diameter

used in this work is very close to the threshold suggested by Onda. Good comparison

between the measured data and the model is achieved for co-current and countercurrent


flow by following Onda's approximation for C=2.0. Onda did not attempt to explain the

physical mechanism for reduced mass transfer rate with smaller packing diameter. We

believe that the reduced gas mass transfer coefficient in condensers is due to increased

liquid hold-up, which causes liquid bridging and reduced area for mass transfer. The

wetting of the packing will be discussed in detail following presentation of the heat and

mass transfer data.


G = 0.6 kg/m2-s (a) Data Model
TL,out -
TL,, = 19.8 C Ta,out 0
T = 36.9 C mout a .....
45 0.030

A
.... A 0.025
40 ""**... ..........

". ** ..****. 0.020
35 -

a 0.015 =

S30 -OLU
S,,,,O 0.010
25 *O
L-c


25 0.005



20 0.000
0.8 1.0 1.2 1.4 1.6 1.8 2.0
Water to air mass flow ratio (mL/ma)


Figure 5-3 Comparison of predicted exit temperatures and humidity with the
experimental data for countercurrent flow: a) Ta,,=36.90 C, b) Ta,,=40.80 C,
c) T,,n=42.8 C