Analysis of a novel combined thermal power and cooling cycle using ammonia-water mixture as working fluid

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Analysis of a novel combined thermal power and cooling cycle using ammonia-water mixture as working fluid
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x, 157 leaves : ill. ; 29 cm.
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Xu, Feng, 1967-
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Thesis:
Thesis (Ph. D.)--University of Florida, 1997.
Bibliography:
Includes bibliographical references (leaves 152-156).
Statement of Responsibility:
by Feng Xu.
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Typescript.
General Note:
Vita.

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ANALYSIS OF A NOVEL COMBINED THERMAL POWER AND COOLING CYCLE
USING AMMONIA-WATER MIXTURE AS A WORKING FLUID














By

FENG XU













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
1997













ACKNOWLEDGMENTS


I would like to sincerely thank my advisor Dr. D. Yogi Goswami for his constant

support, assistance and suggestions, which encouraged me throughout my work. The

encouragement and advice provided by Dr. S. A. Sherif are greatly appreciated. I owe a

great deal of thanks to Dr. J. E. Peterson, C. K. Hsieh and B. L. Capehart for their time

and effort devoted as part of the dissertation review committee. I would also like to thank

Ms. Barbara Walker, Mr. Charles Garretson and Mr. John West for all the help and

support they have rendered during my study at the Solar Energy and Energy Conversion

Laboratory.

Deep appreciation is extended to my family for the support and inspiration they have

always provided. Finally, I am grateful to my wife Hong and son Tom. This would not

have been possible solely by myself.














TABLE OF CONTENTS


page

ACKNOWLEDGMENTS ------------------------------------- ---- ii

NOMENCLATURE------------------------------------ ----------- vi

ABSTRACT ------------------------------------------------------- ix

CHAPTERS

1 INTRODUCTION-------------------------------- -------------------- 1

1.1 Power Cycle ------------------------------------------------- 2
1.2 Vapor Power Cycle----------------------------------- ----- 4
1.3 Multi-Component Working Fluid Research ---------------------------- 6
1.4 Combined Cycle ------------------------------------- ---------- 8
1.5 The Proposed Cycle ------------------------------------ -------- 9
1.5.1 Rankine Cycle Processes ------------------------------------- 10
1.5.2 Ammonia-Absorption Refrigeration Cycle Processes----------- 10
1.5.3 Combined Power and Cooling Cycle Processes------------- 10
1.6 Thermodynamic Properties of Ammonia-Water Mixtures ---------- 11

2 THERMODYNAMIC PROPERTIES OF AMMONIA-WATER
MIXTURES ---------------------------------------------- ---- 14

2.1 Introduction-------------------------------------- -- ------- 14
2.2 El-Sayed and Tribus Method------------------------------------- 16
2.2.1 Computational Procedure--------------------------------- 17
2.2.2 Ammonia-Water Mixture------------------------------ --- 24
2.2.3 Discussion -------------------------------------------- 26
2.3 Thermodynamic Properties of Ammonia-Water Mixtures by
Gibbs Free Energy Method---------------------------------- 26
2.3.1 Gibbs Free Energy for Pure Component ------------------------- 26
2.3.2 Thermodynamic Properties of a Pure Component ------------- 28








2.3.3 Ammonia-Water Liquid Mixtures------------------------ 29
2.3.4 Ammonia-Water Vapor Mixtures ----------------------------- 32
2.3.5 Vapor-Liquid Equilibrium----------------------------- 32
2.3.6 Discussion --------------- ----------------------- 33
2.4 Method by Park and Sonntag ----------------------------------- 33
2.5 An Alternative Method: Using Gibbs Free Energy Method for Pure
Components, and Bubble and Dew Point Temperature Equations
for Equilibrium Composition---------------------- ---- 36
2.6 Results and Comparision With Literature Data ------------------- 37
2.6.1 Comparison of Bubble and Dew Point Temperature ---------- 38
2.6.2 Comparison of Saturation Pressure at Constant Temperature- 39
2.6.3 Comparison of Saturated Liquid and Vapor Enthalpy--------- 39
2.6.4 Comparison of Saturated Liquid and Vapor Entropy------- 40
2.7 Conclusion--------------------------------------- 41

3 AMMONIA-BASED COMBINED POWER/COOLING CYCLE -------- 67

3.1 Introduction--------------------------------------- 67
3.2 Characteristics of the Novel Cycle as a Bottoming Cycle -------- 71
3.3 Thermodynamic Analysis of the Proposed Cycle------------------ 74
3.4 Thermodynamic Property Calculation-------------------------- 75
3.5 A New Improved Design Cycle -------------------------------- 79
3.6 Conclusion---------------------------------------- 84

4 THE SECOND LAW THERMODYNAMIC ANALYSIS------------- 85

4.1 Introduction-------------------------- 85
4.2 Work and Availability ------------------------------------- 85
4.3 Thermodynamic Processes and Cycles ---------- ------------------ 87
4.4 Exergy------------------------------------------ 87
4.5 Background of Dead State-------------------------------- 88
4.6 Exergy Analysis of the Proposed Cycle --------------------------- 92
4.7 Discussion -------------------------------------- 97
4.8 Conclusion--------------------------------------- 98

5 A THERORECTICAL COMPARISON OF THE PROPOSED CYCLE
AND THE RANKINE CYCLE--------------------------------- 99

5.1 Introduction-------------------------------------- 99
5.2 Cycle Description--------------------------------- 100
5.3 Thermal Boundary Condtions ------------------------------- 101
5.4 Temperature Limitation in the Heat Addition Exchanger -------- 101
5.5 Cycle Analysis -------------------------------------- 110
5.6 Conclusion--------------------------------------- 115








6 SYSTEM SIMULATION AND PARAMETRIC ANALYSIS --------------- 116

6.1 Introduction------------ -------------------------------- 116
6.2 Thermodanymic Analysis of the Proposed Cycle----------------- 116
6.3 Basic Equation ----------------------------------------- 118
6.4 Results and Discussion ------------------------------------------- 119
6.5 Conclusion---------------------------- --------------------124

7 CONCLUTIONS AND FUTURE WORK ------------------------------------148

REFERENCES----------------------------------------------------------- 152

BIOGRAPHICAL SKETCH------------------------------- ------ 157














NOMENCLATURE


A Helmholtz free energy

C, Specific heat

Ex Exergy

f Fugacity

G Gibbs free energy

H Enthalpy

h Enthalpy per unit mass

m Polarity factor

n Index

P Pressure

PB Reference pressure, PB= 10 bar

R Gas constant

S Entropy

s Entropy per unit mass

T Temperature

TB Reference temperature, TB = 100 K

V Volume

v Specific volume








w Eccentric factor

x Ammonia mass fraction

x' Ammonia mole fraction

y Ammonia vapor mass fraction

y' Ammonia vapor mole fraction

Z Compressiblity factor



Subscripts

0 Reference state

Ideal gas state

a Ammonia

b Bubble point

c Critical point

cw Critical point of water

cm Critical point of mixture

d Dew point

f Saturated liquid

g Saturated vapor

m Mixture

r Reduced property

v Vaporization

w Water








Supscript

E Excess property

g Vapor state

L Liquid state














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

ANALYSIS OF A NOVEL COMBINED THERMAL POWER AND COOLING CYCLE
USING AMMONIA-WATER MIXTURE AS A WORKING FLUID

By

Feng Xu

August 1997


Chairman: D. Yogi Goswami
Major Department: Mechanical Engineering

A combined thermal power and cooling cycle is proposed. Ammonia-water mixture

is used as a working fluid. The proposed cycle combines Rankine cycle and absorption

refrigeration cycle. It can provide power output as well as refrigeration with power

generation as a primary goal. The concept of this cycle is based on the varying

temperature boiling of a multi-component working fluid. The boiling temperature of the

ammonia-water mixture increases as the boiling process proceeds until all liquid is

vaporized, so that a better thermal match is obtained in the boiler. The proposed cycle

takes advantage of the low boiling temperature of ammonia vapor so that it can be

expanded to a low temperature while it is still in a vapor state or a high quality two phase

state. This cycle can be used as a bottoming cycle using waste heat from a topping cycle








and can be used as an independent cycle using low temperature sources such as

geothermal and solar energy.

Thermodynamic properties of the ammonia-water mixture are of technical

importance to predict the performance of the proposed cycle. A new method is developed

using Gibbs free energy equations to compute the pure component of ammonia and water

properties, using bubble and dew point temperature equations developed from the

experimental data in the literature for the mixture phase equilibrium calculations. Results

have shown very good agreement with the experimental data and other literature data.

This study has also conducted the first and second law thermodynamic analyses of

the proposed cycle. The mass composition of binary working fluid is considered in the

second law analysis while most of the studies in the literature treat a binary working fluid

as a simple fluid in the second law analysis. A comparison of the proposed cycle and the

conventional Rankine cycle under the same thermal boundary conditions shows the

advantage of the proposed cycle using ammonia-water mixture as a working fluid.

A completed cycle simulation program is developed and shows the performance of

the proposed cycle with different parameters.













CHAPTER 1
INTRODUCTION



Thermal power cycle efficiencies have been steadily improving over the past 100

years. A number of methods have been used to improve the thermal efficiency of a

power cycle. Raising the temperature of the heat source, using different working fluids,

improving the system design and lowering the temperature of heat rejection are the most

common ways.

The second law of thermodynamics sets an upper limit on the efficiencies of power

cycles operating between fixed temperatures. The main reason that the maximum

efficiency of a power cycle can not equal the efficiency of a Carot cycle is due to

irreversibilities in the system. Therefore, one way to increase the efficiency of a cycle

with a fixed temperature heat source and sink is to reduce the cycle irreversibilities.

Considering the limitation of the second law of thermodynamics, a new power cycle

combined with a cooling cycle has been proposed. Ammonia-water mixture is used as a

working fluid in this cycle. A new system design will exploit the unique thermodynamic

properties of ammonia-water mixtures to reduce the system irreversibilities. The

proposed cycle will produce power while providing cooling as well. This cycle will be

able to use low quality heat sources such as solar energy, geothermal heat and waste heat









while achieving high thermal efficiency. It may be used as an independent cycle or as a

bottoming cycle in a combined cycle system.






1.1 Power Cycle




A thermal power cycle can be generally categorized by the working fluid as a vapor

power cycle or a gas power cycle. In a vapor power cycle, the working fluid usually

changes its phase from liquid to vapor and back to liquid in the cycle. In a gas power

cycle, the working fluid remains a gas.

A typical vapor power cycle using steam as a working fluid is the Rankine Cycle as

shown in figure 1-1:








to,




Cooling Wate
Pump

"P


Figure 1-1 Rankine cycle











2 3
Heat exchanger

Win Won
Conpres-sor Turbine

Heat xchanger 4







Figure 1-2 Brayton cycle




A typical gas power cycle using air as a working fluid is Brayton cycle as shown in

figure 1-2. Both cycles have similar working theories: heat is added to the working fluid

at the boiler or combustion chamber; the high temperature, high pressure working fluid

passes through a turbine and becomes low temperature and low pressure fluid; the result

is power output from the turbine. The fluid from the turbine goes through a heat

exchanger to further lower its temperature before going through a pump or compressor to

elevate its pressure.

It is well known that the higher the temperature of the working fluid at the turbine

inlet, the more efficiently the power cycle performs. There are limits of temperature and

pressure range for a vapor power cycle, which needs to operate between the ranges of two

phases. High temperature vapor causes high pressure which requires piping that can

withstand great stresses at elevated temperatures. For a gas power cycle, the high gas

temperature is also restricted by metallurgical limitations imposed by the materials used

to fabricate the turbine and other components.








Various modifications of the basic cycles are usually incorporated to improve the

overall performance under the allowable material conditions and other limitations.

Superheat, reheat and regeneration are the common modifications for vapor power cycles.

Reheat, regeneration and compression with intercooling are the common modifications

for gas power cycles.

An advantage of using a gas power system is that gas turbines tend to be lighter and

more compact than the vapor power systems. In addition, the favorable power output-to-

weight ratio and much higher turbine inlet temperatures make them well suited for certain

applications. But a high turbine inlet temperature also results in a high turbine outlet

temperature (i.e. a lot of heat has to be rejected). This is the main reason that makes a gas

power system function at a low second law efficiency. To solve this problem a combined

cycle is introduced. A combined cycle uses a gas power cycle as a topping cycle and a

vapor power cycle as the bottoming cycle to utilize the waste energy in the relatively

high temperature exhaust gas from the gas power cycle.

In this work, we are focusing on a vapor power cycle as an independent power cycle

or as a bottoming cycle.



1.2 Vapor Power Cycle



Since the first electric generating station in the United States, the Brush Electric

Light Company in Philadelphia, went into service in 1881, engineers have been working

to improve the efficiency of the Rankine Cycle for power production (Babcock & Wilcox,

1978). The additions of superheat, multiple reheat and supercritical cycles have helped








push the thermal efficiency from 7% to approximately 38% (Bejan, 1988). The

introduction and improvement of equipment such as air heaters, economizers and

regenerative feedwater heaters have also contributed to an increase in thermal efficiency.

Advances in metallurgy coupled with the previously mentioned improvements in cycle

and equipment have raised the steam generator outlet conditions from 10x106 Pa

(140psig) and 500 K (440 F) in the 1880s, to today's 2.4x 10 Pa (3500psig) and 865 K

(1100 F) range typical of units such as the Cleveland Electric Illuminating Company's

Avon Lake Station Unit #8 (Bannister and Silvestri., 1989; Duffy, 1964). However one

item has remained constant since the Hero of Alexandria's engine, the use of water as the

working fluid.

One of the methods of increasing the thermal efficiency of a vapor power cycle is the

binary cycle. In this system the heat exchanger with the higher boiling point fluid serves

as the boiler for the lower boiling point fluid. As early as the 1920s several binary cycles

were being explored. Some of the fluids being looked at were mercury, aluminum

bromide, zinc ammonium chloride and diphenyloxide (Gaffert, 1946). Mercury/water

binary cycles have the most operating experience. It should be noted that the New

Hampshire Public Service Shiller plant went on line in the early 1950s with a heat rate

commendable by today's standards, 9700 kJ/kWh (9200 Btu/kWh) (Zerban and Nye,

1957). It was decommissioned in the late 1970s. Metallurgical and safety concerns on

the mercury portion curtailed further development. A similar cycle receiving attention

lately is the patented Anderson Power Cycle(Patent No. 4,660,511, 1987; Patent No.

4,346,561, 1982). In the Anderson cycle the water condenser serves as boiler for the R-








22 refrigerant. It is important to remember that in these binary cycles the two

components are totally segregated.

The multi-component working fluid power cycle that this investigation is developing

is different from the previously mentioned binary cycles in that the working fluids

progress through the cycle; compression, vaporization, expansion and condensation;

together in the same flow stream. More than two fluids can be employed.



1.3 Multi-Component Working Fluid Research



A review of the literature shows that the studies of multi-component cycles are very

recent as compared to the conventional Rankine cycle. Kalina is recognized for

introducing the multi-component working fluid power cycle and for bringing it to it's

current state(Kalina, 1983, 1984; Kalina and Tribus, 1990; Kalina et al., 1986). However,

Back in 1953, Maloney and Robertson (1953) from Oak Ridge National Laboratory

studied an absorption-type power cycle using a mixture of ammonia and water as the

working fluid. Avery (1980) investigated ammonia-water mixtures as the heat exchange

media for power generation in the Ocean Thermal Energy Conversion (OTEC). Maloney

and Robertson, and Avery encountered difficulties in getting the thermodynamic

properties of ammonia-water mixtures in their systems analysis.

Kalina, Tribus and El-Sayed have collaborated on several publications. A

comparison of the multi-component cycle to the Rankine cycle by El-Sayed and Tribus

shows a 10% to 20% improvement in thermal efficiency (El-Sayed and Tribus, 1985b).






7

Marston (1990) conducted a detailed discussion of multi-component cycle behavior

to date. It includes the effect of turbine inlet NH3 mass fraction on cycle efficiency as

well as the associated change in mass fraction in separator flow. Also investigated was

the effect of varying the separator temperature on the cycle efficiency and separator inlet

flow. All work was done at one separator pressure. Turbine inlet conditions were 773.15

K and 1.0x 107 Pa. Marston found that the temperature at the separator and composition

at the turbine inlet are the key parameters for optimizing the Kalina cycle.

Ibrahim and Klein (1996), and Park and Sonntag (1990a) also analyzed the Kalina

cycle. Their studies show the advantages of Kalina cycle over the conventional Rankine

cycle under certain conditions. Park and Sonntag pointed out that since the Kalina cycle

uses many heat exchangers and separators for the distillation condensation process, the

parameters ( such as temperatures and pressures between heat exchangers) have small

differences. This makes the simulation of Kalina cycle very difficult. Ibrahim and Klein

(1996) concluded that Kalina cycle will have advantage over the conventional Rankine

cycle only when heat exchanger NTU is greater that 5.

Since Kalina cycle uses the conventional condensation process by exchanging heat

with the environment, it puts a constraint on the lowest temperature of the working fluid

exiting the turbine. This constraint can be relaxed if absorption condensation process is

employed.

Rogdakis and Antonopoulos (1991) proposed a triple stage power cycle which is

similar to the Kalina cycle. However, they replaced the distillation condensation of the

Kalina cycle with the absorption condensation process. Kouremenos el al. (1994) applied

this absorption type of power cycle as a bottoming cycle in connection with a gas turbine






8

topping cycle. The absorption condensation process in this power cycle removes the need

to use too many heat exchangers and simplifies the ammonia-water power cycle. Since

this cycle still uses ammonia-water vapor mixtures going through turbine, the exit

temperature must be relatively high in order to avoid condensation in the turbine. In their

cycle, Rogdakis and Antonopoulos (1991) used about 400 C heat source and triple stage

turbines to achieve high efficiency.

In this study a new cycle as proposed by Goswami (1995, 1996) is analyzed, that

retains the advantages of the Kalina cycle but removes the constraints of the Kalina cycle

and the Rogdakis and Antonopoulos cycle as identified above. The new cycle uses

ammonia-water mixtures as the working fluids but uses very high concentration ammonia

vapor in the turbine which allows it to expand the fluid in the turbine to a much lower

temperature without condensation. The new cycle also uses absorption condensation

process with its advantages as explained before.



1.4 Combined Cycle



A combined cycle is a synergistic combination of cycles operating at different

temperatures, in which each cycle could operate independently. The cycle which operates

at the higher temperature is called a topping cycle and the cycle which operates at the

lower temperature is called a bottoming cycle. The topping cycle rejects heat at a high

enough temperature to drive the bottoming cycle. The heat rejected from the topping

cycle is recovered and used by the bottoming cycle to produce additional power to

improve the overall efficiency of the combined cycle. Combined cycles which have been






9

proposed or commercialized include several combinations: diesel-steam, mercury-steam,

gas-steam, steam-organic fluid, gas-organic fluid, and MHD-steam.

Combined cycle systems have been recognized as efficient power systems. A typical

combined cycle system consists of a gas turbine cycle and a steam Rankine cycle which

uses the exhaust gas from the gas turbine as the high temperature source. The exhaust gas

provides the available energy for the bottoming cycle (the Rankine cycle) to improve the

efficiency of the combined cycle system over the gas turbine cycle alone.

The efficiency of the overall system is a function of the temperature and pressure of

the exhaust gas, the sink temperature of the bottoming cycle, and the type of the

bottoming cycle itself.



1.5 The Proposed Cycle

The proposed ammonia-based power/cooling cycle, first suggested by Dr. Yogi

Goswami(1995, 1996), combines two thermodynamic cycles, the Rankine cycle and the

ammonia-absorption refrigeration cycle. This novel cycle uses a mixed working fluid

(such as ammonia-water) with different compositions at different stages, therefore, it

cannot be shown on a single thermodynamic diagram (i.e. pressure-enthalpy chart).

However, by evaluating the features of the individual Rankine and ammonia-absorption

refrigeration cycles, the features that apply to the overall cycle can be discussed.



1.5.1 Rankine Cycle Processes

An ideal Rankine cycle, shown in Figure 1-1, is a power generating cycle that has

been used in steam power plants. The process involves pumping a liquid to a high






10

pressure, heating it to a superheated vapor state in a boiler, expanding it through a turbine

to generate power while at the same time bringing the vapor to a saturated state,

condensing the fluid back to a saturated liquid, and finally pumping the liquid back to the

boiler.



1.5.2 Ammonia Absorption Refrigeration Cycle Processes

An ideal cycle for the vapor compression refrigeration is essentially a Rankine cycle

in reverse. The ammonia-absorption refrigeration cycle differs from the vapor-

compression cycle in the manner in which compression is achieved. In the ammonia-

absorption refrigeration cycle(Figure 1-3), low-pressure ammonia vapor from the

evaporator is absorbed in water and the liquid solution is pumped to a high pressure. The

liquid solution is then heated and ammonia vapor is separated from the water. The

ammonia vapor passes through a condenser where it is converted to a liquid and then

through an expansion valve to reduce its pressure. At this point the liquid enters an

evaporator, draws heat, and exits as a low pressure ammonia vapor.



1.5.3 Combined Power and Cooling Cycle Processes

The similarities in the Rankine and ammonia-absorption refrigeration cycle to the

proposed ammonia-based power and cooling cycle are evident as seen in Figure 1-4.

Within this one cycle, the Rankine cycle process of expanding a superheated vapor to

produce work is present, as are most of the absorption refrigeration cycle processes.










Boler Condenser



Heat Expanion
Exchanger al




Pump Absorber Evaporator










Figure 1-3 Ammonia-absorption refrigeration cycle




1.6 Thermodynamic Properties of Ammonia-Water Mixtures




Ammonia-water mixtures have been in use for several decades as working fluids of

absorption-refrigeration cycles where ammonia is the refrigerant and water is the

absorbent. Since 1980, ammonia-water mixtures have been investigated as potential

working fluids for power cycles.

Consistent and accurate thermodynamic properties data of ammonia-water mixtures

are very important for the power cycle analysis. In the past, properties of ammonia-water

mixtures were of interest in the operating range of the absorption refrigeration cycle. As

ammonia-water mixtures become attractive as power cycle working fluids, we need to

extend their properties data to a high pressure and temperature range. Computer






12

programs are also needed to generate these properties. The important properties required

are vapor pressure, equilibrium composition of the components, bubble and dew point

temperature, saturation enthalpy and entropy. Data over the region of compressed liquid

and superheated vapor are also required.

The literature survey shows that there are mainly three methods to compute the pure

ammonia and water properties: 1. free energy method(Gibbs or Helmholtz free energy);

2. a generalized equation method; and 3. use of basic thermodynamic relationships (El-

Sayed and Tribus method).

In chapter 2, these three methods are studied and evaluated. A method is developed

which combines the advantages of the available methods. This new method is faster than

the existing methods because it requires less iterations and it also provides a better match

with the available experimental data. The results from this study are compared with the

most recent experimental data.
















































A/V /XAl Supedwed Ammorna po,
V / // Song Aquamona Soton
S-Weak Aqa-amonia Solu-on


Figure 1-4 Ammonia-based combined power/cooling cycle













CHAPTER 2
THERMODYNAMIC PROPERTIES OF AMMONIA-WATER MIXTURES





2.1 Introduction



The thermodynamic properties of ammonia and water mixtures are of technical

importance since ammonia-water mixtures have been in use for several decades as

working fluids in absorption-refrigeration cycles. Use of multi-component working fluids

for power cycles has been investigated more recently over the last two decades.

Ammonia-water mixtures have been considered as potential working fluids for this

purpose because of relatively high expected coefficients of performance for this

combination.

For the power cycle analysis, the temperature and pressure range is much higher than

that of absorption-refrigeration cycles. So a consistent and extended set of

thermodynamic data for ammonia-water mixtures at higher temperatures and pressures is

required. The motive of this study is a lack of enthalpy and entropy data over the range of

variables needed. Also, it is necessary to use computer simulation to investigate

ammonia-water mixtures as potential working fluids for a power cycle.








Many studies of the vapor-liquid equilibrium and thermodynamic properties of

ammonia-water mixtures are cited in the literature. The temperature and pressure ranges

of thermodynamic properties of the majority of the data in the literature are suitable for

absorption-refrigeration cycle applications. Institute of Gas Technology (IGT) tables

(Macriss et al. 1964) cover the range up to a pressure of 34 bar and its corresponding

saturation temperature. Using the IGT data, Schultz (1972) developed equations of state

for a pressure range of 0.01 to 25 bar and a temperature range of 200 to 450 K. Ziegler

and Trepp (1984) presented a new correlation of equilibrium properties of ammonia-

water mixtures. They used an equation of state that is based on that developed by Schultz

and extended the range of applicability to 500 K and 50 bar. Ibrahim and Klein (1993)

used the form of the equation of state given by Ziegler and Trepp for pure ammonia and

pure water. They modified the correlation given by Ziegler and Trepp for the Gibbs

excess energy to include Gillespie et al. (1987) experimental data at higher temperatures

and pressures. The correlations by Ibrahim and Klein (1993) cover vapor-liquid

equilibrium pressures of 0.2 to 110 bar and temperatures of 230 to 600 K.

A study of power cycles using ammonia-water mixtures was recently initiated by

Kalina (1983). For power cycles, thermodynamic data of ammonia-water mixtures at

higher temperatures and pressures than those presented by IGT are required. Gillespie et

al. (1987) published vapor-liquid equilibrium measurements for five isotherms between

313 and 588 K. Corresponding pressures ranged from 0.1 to 210 bar. Herold et al.

(1988) developed a computer program for calculation of the thermodynamic properties of

ammonia-water mixtures using the Ziegler and Trepp correlation. El-Sayed and Tribus

(1985a) presented a method for computing the thermodynamic properties of mixtures








from the properties of pure components to extend the property correlation to higher

temperatures and pressures. Derived properties cover pressures of 0.1 to 110 bar and

temperatures between 300 and 770 K. Kalina et al. (1986) presented a similar method to

predict the thermodynamic properties of two miscible-component mixtures for the

purpose of power-cycle analysis. Park and Sonntag (1990b) published a set of

thermodynamic data of ammonia-water mixtures based on a generalized equation of state.

The pressure and temperature ranges are extended to 200 bar and 650 K respectively.

Based on the above discussion it is clear that methods developed by Ibrahim and

Klein (1993), Park and Sonntag (1990b) and El-Sayed and Tribus (1985a) cover all of the

modeling efforts reported in the literature. The following section gives detailed

discussions of these methods.



2.2 El-Saved and Tribus method



El-Sayed and Tribus method starts with the thermodynamic properties of pure

components, and mixes them according to certain assumptions. In the liquid region,

below the bubble point temperature, and in the vapor region, above the dew point

temperature, the enthalpy and entropy of the mixture are calculated by summing the

product of the thermodynamic properties and mass fractions of the pure components.

The bubble point temperature is defined as the temperature at which the first bubbles

of gas appear. The dew point temperature is the temperature at which condensate first

appears.






17

El-Sayed and Tribus use a group of equations developed exclusively for ammonia-

water mixtures based on vapor-liquid equilibrium data of Gillespie et al. (1987). The

advantage of these equations is that they allow us to determine the start and end of the

phase change of the mixture and compute the mass fractions of ammonia and water liquid

and vapor phase respectively. This avoids the complicated method of calculating fugacity

coefficient of a component in a mixture to determine the bubble and dew point

temperatures.



2.2.1 Computational Procedure



The basic equations are given below.

Bubble temperature Tb = T(P, x) 2-1

Dew temperature Td = T(P, x) 2-2

Equation of state P = P( T) 2-3


Tb = T, (C, + x)(ln( ))' 2-4
i=l j=l

where

4
T T_=T a.x 2-5
i=l


Pc = P exp(Ybix') 2-6


P in psia and T in F


Ta = T, (a, + A,,(in(1.0001 x))'(ln(-))' 2-7
i j-P








P in psia and T in OF.

Since El-sayed and Tribus used English units in their research, their equations are

kept in English units in this study. In the program, English units are converted to SI

units.



1. Pure ammonia liquid:


C,= A+BT+C(T T)-"2


h = [AT +0.5BT- 2C(T T)1"2]


where A =3.14894

B = -0.0006386

C = 16.66345

T, = ammonia critical temperature, 405.5 K

T = temperature, K

Ti = Reference temperature, 195.40 K

T2 = Final temperature, K

Coefficients A, B and C were found in Haar and Gallagher (1978).


ds
C ,p = T -
dT

1/2 ds
A+BT+C(T -T)-1/2 =T
c dT









AnT+BT+ CI (T T)"2 (TC)12 1 2-12
s =,T:2 (T T)'2 +(T)12 ,



2. Ammonia vaporization




H,2 = H, [ 2-13


where HvI = Known enthalpy of vaporization at a reference temperature TI,

cal/g mole

Hy2 = Enthalpy of vaporization, cal/g mole

T = Ammonia critical temperature, 405.5 K

Tr, = Reduced temperature, at temperature T1

Tr2 = Reduced temperature, at temperature T2

n =Constant

Equation 2-13 is transformed as follows:

H, = C(1-T,2)" 2-14

where


C, =
S (1- T,,)



The above equation can be set up in the form y = a + bx

InH2 =lnC + nln( -T,2) 2-15

where y = lnHv2








a= nCl

b=n

x = ln(1 Tr2)

Values of Hv2 and Tr2 from 0.1 bar to 112 bar were taken from published

literature(Haar and Gallagher, 1978) to find n as 0.38939. Ci is found by

InC = lnH2 -nln(1- Tr2) 2-16

The value of C used in this investigation was taken by averaging 11 values over the

previously mentioned range of pressures. It is

Ci = 7906.555

The enthalpy of vaporization equation used was found by using known values of C1

and n in equation 2-14.

Hv = 7906.555 x (1 T/Te)038939 2-17

The entropy of vaporization is

Sv = Hv / T 2-18



3. Ammonia vapor

Integrating the heat capacity equation 2-19 and comparing the results with published

enthalpy data did not yield good agreement.

C = A + BT + CT2 +DT3 2-19

As the pressure increased the agreement worsened. Therefore, a pressure

compensation term was added to obtain equation 2-20. In addition, the original

coefficients (A, B, C and D) were changed as reflected in equation 2-21. Coefficients

were taken from Haar and Gallagher (1978).








Cp= C, +EPT0

where C, = A + BT + CT2+ DT

A = 3.70315

B = 2.8074 x 10-"

C = 4.4199 x 10-6

D=-6.3441 x 10"9

E= 1.73447 x 1010

G= 4.3314

P = pressure, bar

T = temperature, K


S[ AT+ BT2 C DT EPT'-G+
h= AT+-C+-+--+--
2 3 4 (1-G) 1J

1 EPT-G T2
s= AlnT+ BT+ CT +DT' ---
L IT|


where Ti = Saturation temperature, K

T2 = Final temperature, K



4. Water liquid

The liquid enthalpy is found using the enthalpy of vaporization of H20 and the H20

vapor enthalpy. Figure 2-1 illustrates the use of these two values in finding the liquid

enthalpy.

Temperature Ti in figure 2-1 is the reference temperature, chosen for this work to be

273.15 K. The straight, horizontal segment, line 1-2, is the enthalpy of vaporization.








This now places the computations on the saturated vapor curve. Liquid enthalpies at

other temperatures are found by first "traveling" the H20 saturated vapor curve. Segment

2-3 is the H20 vapor enthalpy difference between the reference temperature and the

temperature of interest, T2. Point 3 is the H20 vapor enthalpy at temperature T2. The

liquid enthalpy is found by subtracting the enthalpy of vaporization from the saturated

vapor enthalpy. This is point 4 in figure 2-1. Point 5 is the critical temperature. Segment

5-6 is superheated vapor.

The liquid entropy of H20 was found in a manner similar to the enthalpy. In this

case the entropy of vaporization was used with the vapor entropy to find the liquid

entropy. Again use figure 2-1 as a reference.



5. Water vaporization

Enthalpy of vaporization Hv2 at temperature T2 is found from the following equation:


H2 = Tc T2 2-24
H,, T T,

In this equation, the known enthalpy of vaporization, H.i at temperature TI, and the

power coefficient, n, were found from Reid et al. 1987, resulting in the following

equation:


H2 C ( Tc 2-25


where C1 = 13468.42

C2 = 0.380

T, = H20 critical temperature, 647.3 K



























Ti 1
T1


Property


Figure 2-1 A generic diagram of water property (enthalpy or entropy) against temperature








6. Water vapor

C =A+BT+CT2 +DT3 2-26

where A = 32.24

B = 1.924 x 10-3

C =1.056 x 10-5

D = -3.596 x 10"9






[AT+ BT2 CT3 DT4]1V 2-27

= AT+-T+ + 2-28


2 3
TI

where TI = Saturation temperature, K

T2 = Final temperature, K



2.2.2 Ammonia-Water Mixtures



1. Liquid

The ammonia-water mixture is in the liquid phase when the temperature is below its

bubble point temperature.

hm = hNH3,f + (1 x)hH20,f 2-29

m = XSNH3f + (1 x)sH2o,f Rm(x'lnx' + (1 x')ln(l x') 2-30

where x = ammonia mass fraction








x' = ammonia mole fraction

Rm= gas constant of the mixture



2. Two phase region

The two phase region is the region between the bubble point and dew point.

hm = amv x XghNH3,g + amv(1 xg)hH2o,g

+ aml x XfhNH3,f + aml(1 Xf)hH2o,f 2-31




m = amv x XgSNH3.g + amv(l Xg)sH2o,g

+ aml xfSNH3,f + aml(1 xf)SH20,f

Rm(xg'ln x' + (1 xg')ln(1 Xg'))

R(xf'lnxi + (1 xf)ln(1 x/)) 2-32

where aml, amy = mass fractions of liquid and vapor in the mixture

x, and x,' = mass and mole fraction of ammonia of vapor

mixture

xf and xi = mass and mole fraction of ammonia of liquid

mixture



3. Vapor

The ammonia-water mixture is in the vapor phase when temperature is above its dew

point temperature.

hm = xhNH3,g + (1 X)hH2,g 2-33

Sm = XSNH3,g + (1 X)SH20,g Rm(x'lnx' + (1 x')ln(l x')) 2-34








2.2.3 Discussion



The advantage of using the El-Sayed and Tribus method is that it is very convenient

to calculate the bubble and dew temperatures, without having to compute the fugacity to

determine the two phase region. The disadvantage is that it needs to calculate the

saturation temperature to compute the enthalpy and entropy. And the saturation

temperatures of pure components are different from the saturation temperatures of the

mixtures, because the saturation temperature of a mixture changes even at the same

pressure. Also, the coefficients of heat capacity equations can not fit a wide range. In the

liquid region, the properties of two pure components cannot simply be mixed. Gibbs free

energy is still needed to calculate the difference from the ideal condition.





2.3 Thermodynamic Properties of Ammonia-Water Mixtures by
Gibbs Free Energy Method


2.3.1 Gibbs Free Energy for Pure Component



The fundamental equation of the Gibbs energy, G, of a pure component can be

derived from known relations for volume and heat capacity as a function of temperature

and pressure. The fundamental equation of the Gibbs energy is given in an integral form

as

T P TC
G = ho -Tso + JCdT+ vdP T dT 2-35
To Po To








where ho, so, To and Po are the enthalpy, entropy, temperature, and pressure at the

reference state. The volume, v, and the heat capacity at constant pressure, Cp, for liquid

phase are assumed to fit the following empirical relations proposed by Ziegler and

Trepp(1984);

v = al + a2P + a3T + a4T2 2-36

CpL = b + b2T + b3T2 2-37

For the gas phase, the corresponding empirical relations are




v = +c,+c2 + T c4p2 2-38
P T' T"

Cp,0 = d + d2T + d3T2 2-39

where the superscripts are L for liquid, g for gas, and o for the ideal gas state.

Integration leads to the following equations for the Gibbs energy for the pure

components.



Liquid phase:

G = h T,s, + B,(T, -T,,o)+ (T,2 T2) + -(T3 T3)- BT, In(
2 3 T".

-B2T,(T, -T,,) 3-(T2 T,) + (A, + A3T, + A4)(P, P,,o) + A(P, Po)
2 2

2-40


Gas phase:








D2 T D 3 DT(T2 T )+D(T T )-DT n(
G' = ho Ts, + D,(T, -T,,) + (T,2 + 3 roDT

-D2T,(T, -T,o))- (T, To)+T,n( r)
P P P, T, P P, PT
+C,(P,- P.) +C,( 4 +3 3( -12 + 11 )
o T I TI.o TT,

+o 12 +11
3 T," T;;, T,2,

2-41

where the reduced thermodynamic properties are defined as

T = T/TB

P, =P/PB

G, = G/RTB

hr = h/RT

s, =s/R

v,= vPs/RTB

The reference values for the reduced properties are R = 8.314 kJ/kmole-K, TB = 100

K and PB = 10 bar.


2.3.2 Thermodynamic Properties of a Pure Component


The molar specific enthalpy, entropy, and volume are related to Gibbs free energy by


h= -T2a (G/ T)


LT
J G
aT]









S= J 2-44


In terms of reduced variables


h =-RTBT,[ (G,/ T,) 2-45



s=-R G, 2-46



v -RT T, 2-47
P, OPr AT



2.3.3 Ammonia-Water Liquid Mixtures



The Gibbs excess energy for liquid mixtures allows for deviation from ideal solution

behavior. The Gibbs excess energy of the liquid mixture is expressed by the relation

proposed by Redlich and Kister(Reid et al. 1987; Ziegler and Trepp 1984), which is

limited to three terms and is given by

G = F, +F (2x -1)+ F(2x- 1)2(1 x) 2-48

where

FI = El + E2P, + (E3 + E4P,)Tr + Es/T4 + E/T,2

F2 = E4 + EP4 + (E9 + EioPr)Tr + EIl/Tr + E12/T,2

F3 E13 + E14Pr + E15/T, + E6/T,2








Table 2-1 Coefficients of equations 2-40 and 2-41

Coefficient Ammonia Water

A1 3.971423 102 2.748796 10-

A2 -1.790557 105 -1.016665 10-

A3 -1.308905 102 -4.452025 103

A4 3.752836 103 8.389246 104

B1 1.634519 10'1 1.214557 10+l

B2 -6.508119 -1.898065

B3 1.448937 2.911966 10"

C1 -1.049377 102 2.136131 10-2

C2 -8.288224 -3.169291 10+1

C3 -6.647257 10+ -4.634611 10O

C4 -3.045352 10+ 0.0

D1 3.673647 4.019170

D2 9.989629 102 -5.175550 10-

D3 3.617622 10-2 1.951939 10-2

hro 4.878573 21.821141

hr,o 26.468873 60.965058

Sro 1.644773 5.733498

Sro 8.339026 13.453430

Tro 3.2252 5.0705

P,o 2.000 3.000










Table 2-2 Coefficients of equation 2-48

El -41.733398 E9 0.387983

E2 0.02414 Elo 0.004772

E3 6.702285 El -4.648107

E4 -0.011475 E12 0.836376

Es 63.608967 E13 -3.553627

E6 -62.490768 E14 0.000904

E7 1.761064 E15 24.361723

Es 0.008626 E16 -20.736547


The excess enthalpy, entropy, and volume for the liquid mixtures are given as


hE = -RTBT2 -i (G" / T) 2-4
Tr ,x


r JP, ,


vE RTB GF
PB L JT,


The enthalpy, entropy, and volume of a liquid mixture are computed by

hm= xh +( -x,)h,+hE 2-


SL = xsL +(1 -xf)s +SE +smix








sm- = -R{xfln(x,)+(1-x,)ln(1-x,)} 2-54

v= Xf,v +(1- Xf)v+v 2-55



2.3.4 Ammonia-Water Vapor Mixture

Ammonia-water vapor mixtures are assumed to be ideal solutions. The enthalpy,

entropy, and volume of the vapor mixture are computed by

h, = x,h +(1-x- )h 2-56

s- = xgs + (1 Xg)sl + smx 2-57

v = xv + (1- x)v 2-58



2.3.5 Vapor-Liquid Equilibrium



At equilibrium, binary mixtures must have the same temperature and pressure.

Moreover, the partial fugacity of each component in the liquid and gas mixtures must be

equal.

TL = T T 2-59

pL = p = 2-60

f.L = 2-61

i = f 2-62

where P and T are the equilibrium pressure and temperature of the mixture, and f is the

fugacity of each component in the mixture at equilibrium.

The fugacities of ammonia and water in liquid mixtures are given by Walas(1985)








f =yfxS. 2-63

f= yf(1-x)65 2-64

where y = activity coefficient

fo = standard state fugacity of pure liquid

component corrected to zero pressure

6 = Poynting correction factor from zero pressure to

saturation pressure of mixture

assuming an ideal mixture in the vapor phase, the fugacities of the pure components in

the vapor mixtures are given by

f. = aPy 2-65

f = wP(1-y) 2-66

where: 4 = fugacity coefficient



2.3.6 Discussion



The Gibbs free energy method is relatively simple for calculation of the pure

component thermodynamic properties. The reference temperature and pressure are fixed,

you only need to know the temperature and pressure of interest to determine the mixtures

properties.


2.4 Method by Park and Sonntag








The generalized equation of state approach is useful in predicting thermodynamic

and volumetric properties of substances for which experimental data are scarce and a

minimum number of data are available: critical temperature, critical pressure, critical

volume, and eccentric factor.

In this study, thermodynamic and volumetric properties of ammonia-water mixtures

are derived from three basic equations:

1. Helmholtz free energy equation for the ideal gas properties of water:


A'= R + 461n(T) -1011.249 T2-67
Li'= t -

where t= 1000/T

constants of ideal gas equation for water


Table 2-3


Coefficients of equation 2-67


a, 1857.065 a3 -419.465 as -20.5516

a2 3329.12 a4 36.6649 a6 4.85233


Similarly, for ammonia


A R= ai ln(T) + aT' +n(4.8180T)- 1 2-68




2. The generalized equation of state based on a four-parameter corresponding state

principle, which is expressed in terms of Zo, Z1, Z2; functions of T, and P,; eccentric

factor, w; and polarity factor, m, with appropriate correction term:








Z=Z +wZ +mZ2 2-

Z' =- -(Z' Z) 2-
ww
S= Z- Z + Z ZO)} 2-


where Z' and Z2 are the nonspherical and polar corrections, respectively.



Table 2-4 Coefficients of equation 2-68

a, -3.872727 a7 0.36893175 10-'0

a2 0.64463724 as -0.35034664 10"1

a3 3.2238759 as 0.2056303 10-16

a4 -0.00213769925 alo -0.6853420 10-20

a5 0.86890833 10- all 0.9939243 10-24

a6 -0.24085149 10-


3. The pseudocritical constants method:

Tm = Z ,TE, + eo,ot,


where subscript cm refers to critical property of mixture.

V. = CZev + e,o,v,


i iV
Sx i 2/3
O'- Ex,V ,3








p Z ZRTm 2-75
V.e

Zc = 02901 0.0879wm 0.0266m. 2-76

w = x,w, 2-77


mm = x,m 2-78




4. Discussion

Park and Sonntag claim that using the generalized equation method provides a

consistent way to calculate the thermodynamic properties of ammonia-water mixtures.

But in the high pressure range, they don't have experimental data to verify the reliability

of this method. This method needs to be further investigated.





2.5 An Alternative Method: Using Gibbs Free Energy Method for Pure Components,
and Bubble and Dew Point Temperature Equations for Equilibrium Composition



The Gibbs free energy of the mixture is a function of temperature, pressure and mixture

composition. The property data derived from such an equation of state are very

consistent and convenient. One can easily calculate the thermodynamic properties of

interest such as enthalpy, entropy, specific volume and vapor pressure without

considering the phase state. Most of the researchers tend to use equation of state model

in their properties calculation.








The criteria of phase equilibrium in a binary system is that the liquid fagucity (or

chemical potential) of a pure component equals the vapor fagucity (or chemical potential)

of that pure component. This requires several iterations to get the composition of each

component of phase equilibrium. The accuracy and convergent time vary at different

points. In a power cycle simulation, these iterations should be avoided for the accuracy

and the computation time of the simulations. El-Sayed and Tribus (1985) developed

bubble and dew point temperatures equations to calculate phase equilibrium. These

equations reduce iterations during phase equilibrium calculations and their temperature

ranges up to 770 K.

In the present study, a method that combines the advantages of Gibbs free energy

method and bubble and dew point temperatures equations is presented. The results show

a very good agreement with the available data based on experimental measurements and

the computation time is reduced.



2.6 Results and Comparisons with Literature Data



The properties of pure ammonia and water can be calculated very precisely by using the

Gibbs free energy equation. In order to calculate the properties of the mixtures it is very

important to predict equilibrium state of vapor-liquid mixture.

For the vapor-liquid equilibrium, experimental data are used. Most experiments

were done in the early 30s. IGT conducted their experiments in the 60s and combined

most of the data from the early experiments to produce vapor-liquid equilibrium data and

mixture properties data for temperature up to 500 K and pressure up to 34.45 bar. The






38

IGT data is accepted as a reliable source, and most computational data are compared with

it.

Wiltec Research Co. (Gillespie et al. 1987) conducted measurements of the

ammonia-water mixtures vapor-liquid equilibrium in the early 80s from 313 K and 589

K. Their data is used to extend the ammonia-water mixtures data to temperature up to

600 K and pressure up to 110 bar by Ibrahim and Klein (1993).

IGT and Wiltec data are used to make correlations to predict ammonia-water

mixtures equilibrium state. The accuracy of computation depends on the mathematical

models used to generate correlations, and computational methods used to compute the

thermodynamic properties of ammonia-water mixtures. It is not surprising that studies

reported in the literature have varying degrees of agreement with the IGT properties data.



2.6.1 Comparison of Bubble and Dew Point Temperatures



Figures 2-2 to 2-5 show that the bubble and dew point temperatures generated by

this study compares favorably with the IGT data.

For the bubble point temperature at constant pressure, IGT has a complete set of data

for pressures from 1 psia to 500 psia and ammonia mass concentration from 0 to 1

incremented by 0.1. The differences between our computed values and the IGT data are

less than 0.3%. Ziegler and Trepp, Ibrahim and Klein reported to have differences up to

2% with the IGT data.

IGT data has dew point temperatures with only four different ammonia mass

fractions of 0.9641, 0.9824, 0.9907 and 0.9953. The data for small moisture








concentrations are used primarily for the moisture effects of absorption refrigeration

cycle. Our results match equally well for the bubble temperatures. An advantage of this

comparison is that the working fluid used in the proposed power cycle also has a very

small percentage of moisture content.



2.6.2 Comparison of Saturation Pressure at Constant Temperature

Figures 2-6 to 2-10 show the saturation vapor and liquid pressures of ammonia-

water mixtures as compared with Gillespie et al. data.

For temperatures less than 406 K, the computation results fit the experimental data

well, except at saturated liquid pressure. At higher temperatures, our computed values

are within 5% of the Gillespie et al. (1987) data even at pressures higher than 110 bar,

while Ziegler and Trepp have reported more than 15% difference. Ibrahim and Klein

reported a less than 5% error under 110 bar and higher errors over 110 bar.



2.6.3 Comparison of Saturated Liquid and Vapor Enthalpy

1. Saturated liquid enthalpy

The enthalpy of saturated liquid of this work is compared with IGT data, as shown in

figures 2-11 to 2-14. The differences are less than 2% for all the data.

2. Saturated vapor enthalpy

The saturated vapor enthalpy at constant pressure is shown in figures 2-15 to 2-18.

The agreement with IGT data is within 3%. Ibrahim and Klein's model reported about a

5% maximum difference.








The ammonia mass fractions shown in these figures are not ammonia vapor

concentrations. In fact, these are ammonia liquid mass fractions when the mixtures reach

a saturated state. So in order to compute the saturated vapor enthalpy, the ammonia vapor

mass fraction has to be determined first. This means that the model has to be accurate in

predicting the ammonia compositions in saturated liquid and vapor.



2.6.4 Comparison of Saturated Liquid and Vapor Entropy

The value of entropy is very important in predicting the performance of a turbine in a

power cycle. Entropy data is also essential to the second law analysis of thermal systems.

Scatchard et al. (1947) published saturated liquid and vapor entropy data based on

experimental data from Zinner (1934), Wucherer (1932) and Perman (1901). Park and

Sonntag(1990b) published calculated entropy data based on their models and compared

with the Scatchard et al. data. In the present study, saturated liquid entropy data are

compared with Scatchard et al., and Park and Sonntag computational data. However,

saturated vapor data are compared with Scatchard et al. data only.



1. Saturated liquid entropy

Figures 2-19 to 2-22 show saturated liquid entropy data as compared with Scatchard

et al. data. Our data agree with the experimental data very well except in the region of

ammonia mass fraction from 0.3 to 0.6. In figures 2-19, 2-21 and 2-22, computed data

from Park and Sonntag (1990b) are also compared. It can be seen that the magnitude of

Park and Sonntag's data are very low as compared to Scatchard's data; it is more than

50% lower at ammonia mass fraction of 0.5.








2. Saturated vapor entropy

Excellent agreement of our computed values with the Scatchard et al. data of the

saturated vapor entropy is shown in figures 2-23 to 2-26. Data reported by Park and

Sonntag (1990b) are consistently lower than the Scatchard's data. Since it is very

difficult to identify Park and Sonntag's saturated vapor entropy data from the literature,

we didn't compare our results with them. Since the behavior of ammonia-water mixtures

in the vapor state is close to the ideal gas mixture, this results in a good match for our

mixture vapor model.



2.7 Conclusion

Different methods for calculating the ammonia-water mixture properties are studied.

A practical and accurate method is used in this study. This method uses Gibbs free

energy equations for pure ammonia and water properties, and bubble and dew point

temperature equations for vapor-liquid equilibrium. The iterations necessary for

calculating the bubble and dew point temperatures by the fugacity method are avoided.

This method is much faster than method of using fugacities or chemical potentials. The

computational results have been compared with the accepted experimental data and show

very good agreement.

With consistent and accurate thermodynamic properties data of ammonia-water

mixtures, we can perform the first and second law analyses of the proposed power cycle.
















400
This Work
380 0- IGT Data

360 P = 1.38 bar


340

2 320

0 300

280

260

240

220
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia Mass Fraction


Figure 2-2 Bubble and dew point temperatures at a pressure of 1.38 bar
















460
-- This Work
440 O IGT Data

420 P = 6.89 bar

400 -

380

S360 -

E
S340
I-

320

300

280

260
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia Mass Fraction


Figure 2-3 Bubble and dew point temperatures at a pressure of 6.89 bar
















480
-- This Work
460 0 IGT Data

440 P= 13.79 bar


420

T 400

S380 -
E

360 -

340 -

320

300
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia Mass Fraction


Figure 2-4 Bubble and dew point temperatures at a pressure of 13.79 bar
















540

52- This Work
5 0 IGT Data
500
500 P = 34.47 bar
480

460 -

S440

I 420
E
- 400

380

360

340

320
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia Mass Fraction


Figure 2-5 Bubble and dew point temperatures at a pressure of 34.47 bar


















30-


This work
25 0 Gillespie et al.



20







1a 10



5-








0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-6 Saturated pressures of ammonia-water mixtures at 333.15 K


















120

-- This work
100 0 Gillespie et al.



80 / 0






S40-



20-



0




0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-7 Saturated pressures of ammonia-water mixtures at 394.15 K

















140 -I


--This work
120 -
120 0 Gillespie et al.


100


80 -0


60 -
a-o


40


20


0



0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-8 Saturated pressures of ammonia-water mixtures at 405.95 K


















200

180 This work
0 Gillespie et al.
160

140


- 120-




a. 80 -

60 -

40

20 -
20



0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-9 Saturated pressures of ammonia-water mixtures at 449.85 K


















250 1 i i

SThis work
O Gillespie et al.
200 /




S150 -









50






0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Ammonia mass fraction


Figure 2-10 Saturated pressures of ammonia-water mixtures at 519.26 K


















500

SThis work
400 0 IGT data


300 -


200 -


100 -

0 -


-100 -


-200 -


-300


-400 I -
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-11 Saturated liquid enthalpy of ammonia-water mixtures at 1.38 bar


















800 I

This work
0 IGT data

600




i 400-


a-

ui 200




0-




-200 I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-12 Saturated liquid enthalpy of ammonia-water mixtures at 6.89 bar


















900

-- This work
800 \ 0 IGT data

700


600


500 -


400


300


200


100


0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-13 Saturated liquid enthalpy of ammonia-water mixtures at 13.79 bar


















1100 '
This work
1000 0 IGTdata


900 -


800 -


S700-


6 600 -


500 -


400-


300 -


200
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-14 Saturated liquid enthalpy of ammonia-water mixtures at 34.47 bar


















2800

SThis work
2600- 0 IGT data


2400


2200


3 2000 -


| 1800


1600


1400


1200


1000 -I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-15 Saturated vapor enthalpy of ammonia-water mixtures at 1.38 bar


















2800

-- This work
2600 0 IGT data


2400


2200


S2000
_Q- ~
, 1800-


1600


1400


1200


1000 -I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-16 Saturated vapor enthalpy of ammonia-water mixtures at 6.89 bar


















3000- I I

-- This work
2800 0 IGT data


2600


2400


2200


S2000


1800


1600


1400


1200
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-17 Saturated vapor enthalpy of ammonia-water mixture at 13.79 bar


















3000 I II

This work
2800 0 IGT data


2600


2400


| 2200


| 2000


1800


1600


1400


1200
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-18 Saturated vapor enthalpy of ammonia-water mixtures at 34.47 bar



















0.7
0 Scatchard et al.
-- This work
0.6 Park and Sonntag



0.5-








0.3 -


0.2 O




0.1 I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-19 Entropy of Saturated liquid at 310.9 K



















0.90 -I

o Scatchard et al.
0.85 This work



0.80



' 0.75



2 0.70-



0.65



0.60
0 0


0.55 I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-20 Entropy of Saturated liquid at 327.6 K





















1.1
SScatchard et al.
-- This work
1.0 0 Parketal.



0.9



| 0.8 :



o 0.7 -
w LJ


0.6 -


0 0
0.5 -



0.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-21 Entropy of Saturated liquid at 338.7 K




















1.6
D Scatchard et al.
This work
1.5 0 Park et al.


1.4


1.3-


S1.2
(D 0





1.0-




0.9
0.8 -------- i ----------- I------

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-22 Entropy of Saturated liquid at 366.5 K




















10.0

9.5-
o Scatchard et al.
9.0 --- This work

8.5

8.0

7.5 -

o, 7.0

6.5 -

2 6.0

5.5

5.0

4.5

4.0 -

3.5

3.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-23 Entropy of Saturated vapor at 310.9 K




















10.0-

9.5
Scatchard et al.
9.0 This work

8.5

8.0

7.5

0 7.0



j 6.0
5.5 -
6.0 -
C
W
5.5

5.0

4.5

4.0

3.5

3.0 -
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-24 Entropy of Saturated vapor at 327.6 K



















10.0

9.5
9.5 Scatchard et al.
9.0 -- This work

8.5

8.0

7.5

7.0 -

6.5

S6.0

5.5

5.0

4.5

4.0

3.5

3.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-25 Entropy of Saturated vapor at 338.7 K



















10.0

9.5
o Scatchard et al.
9.0 This work

8.5

8.0

7.5

' 7.0

S6.5

2 6.0

5.5 -

5.0

4.5

4.0

3.5

3.0 il -i
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-26 Entropy of Saturated vapor at 366.5 K













CHAPTER 3
AMMONIA-BASED COMBINED POWER/COOLING CYCLE





3.1 Introduction



Combined cycle systems have been recognized as efficient power systems. A typical

combined cycle system consists of the gas turbine cycle(the Brayton cycle), which

produces the base load, and the Rankine cycle, which uses the exhaust gas from the gas

turbine as the high temperature source. The exhaust gas provides the available energy to

the bottoming cycle (the Rankine cycle) to improve the efficiency of the combined cycle

system over the gas turbine cycle alone.

The efficiency of the overall system is a function of the temperature and pressure of

the exhaust gas, the sink temperature of the bottoming cycle, and the type of the

bottoming cycle itself.

Most heat sources available to the bottoming cycles, such as hot exhaust gases, are

sensible-heat sources because the temperature of the source is varying during the heat

transfer process. The amount of the cooling medium at the sink temperature in reality is

also limited so that the heat sink is sensible as well. This sensible heat does not satisfy








the isothermal process of the ideal cycle (the Carnot cycle). The ideal cycle to convert

sensible heat to mechanical or electrical energy is therefore not the Camot cycle.

The ideal cycle to convert sensible heat to mechanical or electrical energy is the

Lorenz cycle (Lorenz 1894). This cycle has a triangular shape on a temperature and

entropy diagram, generating the least entropy during the heat transfer process (Kalina

1984). The least production of entropy yields the highest thermodynamic efficiency. It is

interesting to note that with respect to the combined cycle efficiency, the Carot cycle is

still the ideal cycle to produce overall maximum work at a given source temperature since

the bottoming cycle of a triangular shape leads the overall combined cycle to the Camot

cycle, as seen in figure 3-1.

To increase the efficiency of the Rankine cycle working with sensible heat, two

conventional ways have been proposed:

(1) Incorporation of a multi-pressure boiler

(2) Implementation of the supercritical cycle

The multi-pressure boiler is widely used in industry, but results in only moderate

improvement in efficiency unless the number of boiler steps is very large. For the

exhaust gas temperature range from 900-1000 0F(755 811 K), the cycle efficiency is 20-

22% with a single pressure boiler and 23-25% with tri-pressure boiler (Foster-Pegg

1978). Since a significant increase in the number of boiler steps is technically and

economically not feasible, the number of such steps does not usually exceed three (Kalina

1984). The implementation of a supercritical cycle can theoretically achieve a triangular

shape cycle and thus high efficiency, but requires extremely high pressure in the boiler,








which in turn adversely affects the turbine performance (Kalina 1984). Milora and

Tester (1976) have given a detailed discussion of the supercritical cycle.











T













Ranklne Cycle



Q



S


Figure 3-1 Schematic diagram of the Rankine cycle
in connection with a combined cycle








An alternative way to increase the efficiency of the Rankine cycle working with a

sensible heat source is to use a multi-component working fluid. A multi-component

working fluid boils at a variable temperature with a change in the liquid composition of

the components. This variable temperature boiling process yields a better thermal match

with the sensible heat source than the constant temperature boiling process, and is close

to a triangular shape. The better thermal match contributes to the improvement of

thermodynamic efficiency in the boiler. Since the multi-component working fluid

condenses at a variable temperature as well, a part of the gain of the variable temperature

boiling is lost in the condenser. To reduce this loss, the simple condensation process is

complemented by an absorption distillation process (Babcock and Wilcox, 1978).

Our novel power cycle is proposed by Goswami(1995, 1996). The cycle uses a

multi-component working fluid and the condensing process of the Rankine cycle is

replaced by the absorption process. This cycle meets both conditions for higher

thermodynamic efficiency--a better thermal match in the boiler and a heat rejection

system complemented by the absorption system.

The purpose of this work is to conduct a study of the novel power cycle system in

connection with a combined cycle system as in Figure 3-2, comparing the novel cycle and

the Rankine cycle at the same thermal boundary conditions with different internal

conditions for the best performance of each cycle. This study is performed using the

thermodynamic properties of ammonia-water mixtures developed in Chapter 2 in this

study.








3.2 Characteristics of the Novel Cycle as a Bottoming Cycle



A bottoming cycle is a cycle which operates between the high temperature heat

rejected by a topping cycle and the ambient. The cycle utilizes the available heat of the

exhaust gas from the topping cycle. Most heat available to the bottoming cycle is

sensible; the temperature varies during the heat transfer process. This sensible heat can

not realize the isothermal heat supply process of the ideal cycle, the Carnot cycle.

Therefore, the Carot cycle is not the ideal bottoming cycle to convert sensible heat to

mechanical energy or electrical energy. Rather, the ideal cycle working with sensible heat

is the Lorenz cycle(Lorenz, 1894), which has a triangular shape in the temperature and

entropy coordinates.

The Lorenz cycle is composed of four processes, as shown in Figure 3-2

(1) Heat supply at a variable temperature(I-2)

(2) Isentropic expansion(2-3)

(3) Isothermal heat rejection(3-4)

(4) Isentropic compression(4-1)

The Lorenz cycle is exactly the same as the Camot cycle except for the process(l-2).

Possible ways to realize the Lorenz cycle are:

(1) Multi-pressure boiler

(2) Supercritical cycle

(3) The Kalina cycle

(4) The novel ammonia-based combined power/cooling cycle











T
2






1 Equivalnent
proposed cycle


4 QL 3







Figure 3-2 Schematic diagram of the novel cycle in connection with a combined cycle



The novel cycle combines two thermodynamic cycles, the Rankine cycle and the

ammonia-absorption refrigeration cycle, as seen in figure 1-4. In Rankine cycle,

ammonia-water mixture is pumped to a high pressure. The mixture is heated to boil off

ammonia, and ammonia is separated from water. After expanding through a turbine to

generate power, ammonia is brought to absorption refrigeration cycle. Low temperature

ammonia provides cooling in the evaporator and then it is absorbed by water in an








absorber and becomes ammonia-water mixture liquid. As seen in figure 3-3, the novel

cycle provides extra work (shade area) over Rankine cycle.

The novel cycle as a bottoming cycle is a creative way to realize the triangular shape

of the T-S diagram. The concept of this cycle is based on the varying temperature boiling

of a multi-component working fluid. The boiling temperature of the multi-component

working fluid increases as the boiling process proceeds until all liquid is vaporized, so

that a better thermal match is obtained in the boiler. This better thermal match yields a





T












Rankine Cycle



Q



S


Figure 3-3 T-S diagram showing advantage of the novel cycle
over a conventional Rankine cycle








better thermodynamic efficiency. The higher thermodynamic efficiency of the novel

cycle as the bottoming cycle results from

(1) The multi-component working fluid, having a variable boiling temperature, provides

significantly less available energy loss in the boiler, as the heat source has a variable

temperature in the boiler as well.

(2) The working fluid starts boiling almost immediately after entering the evaporator,

which increases the efficiency of the heat exchanger(boiler).

(3) The amount of heat rejected in the condenser is significantly smaller than that in the in

the Rankine cycle arrangement.





3.3 Thermodynamic Analysis of the Proposed Cycle



As seen in Figure 3-3 the proposed ammonia-based cycle is a combination of the

Rankine and the ammonia-absorption refrigeration cycles. Within this one cycle, the

Rankine cycle process of expanding a superheated vapor to produce work is present, as is

part of the ammonia-absorption refrigeration cycle. A difference between this cycle and

the ammonia-absorption refrigeration cycle is that ammonia vapor is not condensed and

then expanded to provide refrigeration, but the ammonia vapor is used as the working

fluid in a turbine.

This section gives a thermodynamic analysis of this novel cycle with assumed

thermal boundary conditions as








1. Power output: 2.5 kW

2. Turbine inlet temperature: 400 K 500 K

3. Turbine inlet pressure: 18 bar 32 bar

At this stage, the thermodynamic state conditions of the proposed combined cycle

are evaluated assuming a idealized cycle (that is irreversibilities associated with real

apparatus were neglected.) The idealized cycle does provide the analytical maximum

limits for real processes and is necessary in determining the efficiency limits of a real

system. The following list of assumptions was used in the initial analysis of the proposed

cycle.





3.4 Thermodynamic Property Calculation



The thermodynamic properties of the working fluids were evaluated using the

methods developed in Chapter 2. The following paragraphs explain the techniques used

to determine the thermodynamic properties at each state in the cycle.

Three working fluids were considered, ammonia vapor, strong ammonia/water

solution, and a weak ammonia water solution. Strong ammonia/water solution refers to

the condition where ammonia vapor and the weak ammonia/water solution have been

combined. Likewise, when the ammonia vapor is boiled off from the strong

ammonia/water solution, the remaining solution is considered the weak ammonia/water










Table 3-1 Assumptions and parameters of the proposed cycle

Assumptions State characteristics
a Strong ammonia/water mixture is pumped P2 = 27.6,
to 27.6 bar and heated to 466 K T4 = T7 = 466 K
b Superheated ammonia vapor is expanded P5 =2.1bar
through a turbine to 2.1 bar
c ammonia vapor exiting the turbine is used in T6 = 277 K
a refrigeration application which brings its
temperature to 277 K
d Neglect pressure drops in components and P2 = P3= P4 = P7 = P8 = 27.6 bar
pipelines. Ps = P6 = P9 = P1 = 2.1 bar

e Liquid solutions at states 1, 3, and 7 are
saturated liquids

f Pump process is assumed to be reversible h2 h = (P2- PI)VI
and adiabatic

g Steady state, steady flow.
h Pure ammonia vapor leaves boiler. xa = 1.0
i Turbine expansion is isentrophic (reversible, S4 = S5
adiabatic)

j The pressure reducing valve is an adiabatic h = h9
process
k Mass flow of weak aqua-ammonia solution
is assumed
1 Temperature of strong aqua-ammonia T3 = 373 K
solution is 373 K after leaving the heat
exchanger.








solution. Subscripts a, s, and w for the thermodynamic properties refer to the

ammonia vapor, strong ammonia/water solution, and weak ammonia/water solution,

respectively.

Since pressure drops in the components and pipelines are neglected, all pressures are

established from the given assumptions; States between the pump and the turbine, or the

pump and pressure relief valve are at 27.6 bar and the states between the turbine or

pressure relief valve and the pump are at 2.1 bar.

The concentrations of ammonia in the aqua-ammonia mixtures are determined using

the assumptions that the strong and weak liquids would be saturated at states 3 and 7,

respectively. The concentrations are assumed as x, = 0.54, xw = 0.125 and xa = 1.0.

Mass balance equations were used to determine the mass flow rates through the

cycle. With the following two equations:

ms = mw + ma,

msxs = mwxw + maxa

and assuming a value for one of the mass flow rates, the values of the other two flow rates

can be determined.

Table 3-2 shows the thermodynamic state including enthalpy at each point.

Table 3-3 shows the energy balance of each component.













Table 3-2 Example of operating conditions for the proposed cycle

State Description Fluid Phase Temp Pressure Enthalpy Concentration Flowrate
K bar kJ/kg kg NH3/kg mix kg/s
1 Absorber Exit / strong aqua- saturated 280 2.1 -209.16 0.540 0.01141
Pump Inlet ammonia liquid
solution
2 Pump Exit/ HEX strong aqua- liquid 280 27.6 -206.59 0.540 0.01141
Inlet ammonia
solution
3 HEX Exit / Boiler strong aqua- saturated 373 27.6 223.22 .540 0.01141
Inlet ammonia liquid
solution
4 Boiler Exit / Turbine ammonia superheated 466 27.6 1682.37 1.000 0.00541
Inlet vapor
5 Turbine Exit/ ammonia superheated 262 2.1 1256.28 1.000 0.00541
Cooler Inlet vapor
6 Cooler Exit / ammonia superheated 277 2.1 1290.98 1.000 0.00541
Absorber Inlet vapor
7 Boiler Exit / HEX weak aqua- saturated 466 27.6 760.95 0.125 0.006
inlet ammonia liquid
solution
8 HEX Exit /PRV weak aqua- subcooled 288 27.6 -15.5 0.125 0.006
Inlet ammonia liquid
solution
9 PRV Exit /Absorber weak aqua- subcooled 288 2.1 -15.5 0.125 0.006
Inlet ammonia liquid
solution








Table 3-3 Energy balance of each component

Component Energy equations Energy (kW)
Pump W= ms(h2 hi) 0.030
Boiler Qb = mah4 + mh7 msh3 11.120
Turbine Wt = m(hs h4) -2.305
Cooler Qc= m(h6 hs) 0.188
Absorber Qa = mah6 + mwh9 msh -9.278


Turbine power output:

Refrigeration:


First law efficiency:


W, = ma(h4 hs) = 2.305 kW

Qc= ma(he h5) 0.188 kW

W+Q 2.305+0.188
S+ Q, 2.305 + 0.188 x00% = 22.42%
Qb 11.12


3.5 A New Improved Design Cycle


The previous section has described the advantage of the conceptual proposed cycle

as shown in figure 1-4. In that section it was assumed that the boiler produced pure

ammonia vapor, however, the figure does not show how to generate highly concentrated

ammonia vapor. Usually, the boiler generates vapor with about 90% ammonia mass

fraction. At this ammonia mass fraction, vapor can not be expanded in a turbine to a very

low temperature because a certain amount of condensation will be generated in the

turbine. For an absorption refrigeration cycle, a condenser or rectifier is used to condense








part of the water vapor from the boiler. After the condenser, a highly concentrated

ammonia vapor is generated. The ammonia composition after the condenser can be over

99%.

Since water vapor is condensed in the condenser/rectifier, heat of condensation is

released. But this heat is not wasted, instead it is used to preheat the basic solution from

the absorber.

Figure 3-4 shows a more detailed design of the proposed cycle. In this system, the

boiler generates ammonia rich vapor (state 5). Before the vapor is superheated in a

superheater (state 7), it passes through a condenser or rectifier (state 6) to get a higher

concentration ammonia vapor. After expansion in the turbine, the ammonia vapor drops

to a very low temperature. The cold ammonia vapor provides cooling by passing through

the cooler (state 9). The ammonia vapor is then reunited with the weak solution from the

boiler in the absorber to regenerate the basic solution (state 1). The basic solution is then

pumped to a high pressure (state 2) to complete the loop. The basic solution coming out

of the absorber is used as the cooling fluid for the condenser. At state 2, part of the

solution goes through a solution heat exchanger, and another part goes to the condenser.

These two streams mix before the boiler. So no heat is wasted while a highly

concentrated ammonia vapor is obtained as a working fluid.

Table 3-4 shows typical operating conditions of the proposed cycle. Table 3-5

shows the performance of each component based on a unit mass of the basic solution at

the conditions of table 3-4.

















































Figure 3-4 A modified ammonia-based combined power/cooling cycle



















Table 3-4 Typical operating conditions

State T p h s x Flow rate
(K) (bar) (kJ/kg) (kJ/kg K) m/ml
1 280.0 2.0 -214.1 -0.1060 0.5300 1.0000
2 280.0 30.0 -211.4 -0.1083 0.5300 1.0000
3 378.1 30.0 246.3 1.2907 0.5300 1.0000
4 400.0 30.0 1547.2 4.6102 0.9432 0.2363
5 360.0 30.0 205.8 1.1185 0.6763 0.0366
6 360.0 30.0 1373.2 4.1520 0.9921 0.1997
7 410.0 30.0 1529.7 4.5556 0.9921 0.1997
8 257.0 2.0 1148.9 4.5558 0.9921 0.1997
9 280.0 2.0 1278.7 5.0461 0.9921 0.1997
10 400.0 30.0 348.2 1.5544 0.4147 0.8003
11 300.0 30.0 -119.0 0.2125 0.4147 0.8003
12 300.0 2.0 -104.5 0.2718 0.4147 0.8003



















Table 3-5 Results from the table 3-4 state conditions

cycle high temperature and pressure are 410.0 K and 30.0 bar
cycle low temperature and pressure are 257.0 K and 2.0 bar
boiler heat input = 390.4
super heat input = 31.3
condenser heat reject = -83.8
absorber heat reject = -358.8
cooler cooling load = 25.9
turbine work output = 76.0
turbine liquid fraction = 0.0692
turbine vapor fraction = 0.9308
pump work input = 2.7

total heat input = 421.6
total work output = 73.33
cycle efficiency = 23.54%
All energy units are kW/kg basic solution








3.6 Conclusion



The initial thermodynamic analysis has shown that the ammonia-based combined

power/cooling cycle has a promising application. In the case study of turbine inlet

condition of 466 K and 27.6 bar, we obtain a pretty good first law system efficiency of

20.7%. At this condition, the steam is still a condensed liquid which means that the

steam Rankine cycle can't even be used for such low temperature application. Further

study with different turbine inlet temperature will also show that the proposed cycle will

have better first law efficiency. The proposed cycle can be applied to many low

temperature heat sources such as geothermal and solar energy heat sources.

An improved design of the proposed cycle is also presented in this chapter with

detailed information. A second law analysis and system simulation based on this design

are discussed in the following chapter.














CHAPTER 4
THE SECOND LAW THERMODYNAMIC ANALYSIS




4.1 Introduction



With the increasing cost of our most widely used fuels and the potential decrease in

their availability in the future, the importance of effective use of our available energy

resources is now receiving more and more attention. The location and degree of

inefficient use of energy in our energy systems should be a primary factor in the design

and performance analysis of the system. The second law analysis is directed to providing

this information by a systematic approach.

To evaluate the effectiveness of energy use in different systems, a realistic measure

of energy utilization must be applied. The exergy method of analysis will provide this

true measure of effective energy use through its application of principles of both the first

and second laws of thermodynamics.



4.2 Work and Availability



The final product of interest from the expenditure of energy resources is work which

is used to perform tasks such as generating electricity, pumping water and moving






86

objects. Work is made available from the energy resources in many forms. For example,

the combustion of oil or gas in a power plant provides high-pressure, high-temperature

steam that is available to do work through a turbine and generator system. When the

temperature and pressure of the steam are near the conditions of the surrounding

environment(condensed liquid near ambient temperature), the work available in the steam

has essentially disappeared. Another example is that, the water behind a dam on a river

is available to do work by driving a hydraulic turbine and an electric generator. The

available work in the water behind the dam reverts to zero when the water level falls to

the level in front of the dam. So when the mass comes into equilibrium with the

environment, no more changes of state will occur and the mass will not be capable of

doing any work. Therefore, the steady-state condition of our surrounding environment is

a reference state which a mass at a given state(such as high temperature and high pressure

steam, water held in a dam) can achieve after a process to perform maximum available

work. This concept of available work referenced to the surrounding environment is the

basis of the exergy method of energy-systems analysis.

It is also a realistic method of comparing the efficient use of our energy resources. It

should be noted that a fluid or gas that is not in equilibrium with the ambient

surroundings has the potential to perform work as its condition reverts to the ambient

surrounding conditions, as everything will do naturally. This means that a fluid that is

colder than the ambient surroundings will be available to perform work as it warms up to

the ambient surroundings just as a warm fluid is available to perform work in its passage

to the ambient surrounding conditions.








4.3 Thermodynamic Processes and Cycles



Energy systems are made up of a series of individual processes that form closed or

open cycles. Each process in a system or cycle can be analyzed separately from the

system by performing a first-law energy balance around the component involved in the

process.

As the available work in a system working fluid decreases through energy-related

processes, there are losses in the available work since no transfer of heat or conversion

between mechanical work and heat can be performed without some irreversibility in the

process. In a system in which many processes are involved, the loss of work in the

system will be distributed throughout the individual processes. It is important to establish

the relative losses in each process if we are to effectively improve the system efficiency.

It should be noted that the conventional heat-balance method of evaluating system

losses and system efficiency is misleading and not a true representation of system

effectiveness. Only through an evaluation of the available work throughout the system

can we have a true measure of the losses in the system processes, which is necessary for

effective energy conservation in system design and operation.



4.4 Exergy



Exergy is defined as the work that is available in a mass as a result of conditions

nonequilibrium relative to some reference condition. As we have described in the








previous paragraph, atmospheric condition generally is a reference condition. Useful

work can be recovered during the cooling and expansion processes of steam through a

steam engine or turbine and heat exchangers. The exergy that is not recovered as useful

work is lost.

Exergy is an explicit property at steady-state conditions. Its value can be calculated

at any point in an energy system from the other properties that are determined from an

energy balance on each process in the system. Exergy is calculated at a point in the

system relative to the reference condition by the following general equation:



Exergy = (u uo) To(s so) + Po(v vo) + V2/2g + g(z zo) + Z(ti pio)x, 4-1

Internal Entropy Work Momentum Gravity Chemical
Energy Potential

Where the subscript 0 denotes the reference condition and i denotes as i-th

composition. There are variations of this general exergy equation, and in most systems

analyses some, but not all, of the terms shown in equation 4-1 would be used. Since

exergy is the work available from any source, terms can also be developed using electrical

current flow, magnetic fields, and diffusion flow of materials.



4.5 Background of Dead State



The exergy method of analysis is a particular approach to application of the second

law of thermodynamics to engineering systems. Another frequently used term is








availability analysis, which is often found in classical thermodynamic text books

(Sonntag et al, 1994; Moran and Shapiro, 1992).

"Exergy is the maximum theoretical work that can be extracted from a combined

system or system and environment as the system passes from a given state to equilibrium

with the environment-that is, passes to the dead state." (Moran and Sciubba, 1994).

Environment or surroundings are often used as a reference state for availability

analysis. When the mass comes into equilibrium with the environment, no change of

state will occur. So the mass is incapable of doing any work or is in a dead state.

One standard atmospheric pressure is normally used as a reference pressure.

Different reference environment temperature have been used by researchers such as 293

K (Aphorratana and Eames, 1995), 298 K (Egrican, 1988) and 300 K (Waked, 1991).

Krakow(1991) proposed a dead-state definition. He indicated that the reservoir of a

system that is not the environment is defined as the system reservoir. The system

reservoir serves as the source for engines and coolers and as the sink for heat pumps. The

environment serves as the sink for engines and coolers and as the source for heat pumps.

So instead of using universal ambient condition as a dead state, he proposed that one of

the high-temperature and low-temperature reservoirs of the system to be considered as a

reference state.

Since reservoirs of real systems are finite, their temperatures change during any heat

transfer process. Therefore, the dead state temperature in a real process changes during

the process. To account for the change in the dead state temperature in real processes,








Krakow defined an effective reservoir temperature for heat sources and sinks which is

essentially the same as the entropic average temperature used by Herold (1989).

The effective reservoir temperature, which is used as the dead state for the reservoir,

is defined as the temperature that will make its initial exergy equal to the final exergy.

Neglecting the momentum, gravity and chemical exergies, the initial and final exergies of

a reservoir are

Ex, = (hi hef) Te(sI sef) 4-2

Ex2 = (h2 hf) Tf(2 Sef) 4-3

where subscripts 1 and 2 stand for the initial and final conditions of the reservoir, and ef

stands for the effective temperature condition.

Tef is defined such that Exl = EX2.

The entropic average temperature of a reservoir is defined as


T, =Q = Q 4-4

IT

where QI-2 is the heat exchanged with the reservoir.

Above methods and definitions can be used easily for single working fluids such as

steam. However, it is difficult to define the dead state for mixtures such as LiBr/water

and ammonia/water. Since a dead state composition must also be defined. In other

words, it is important to know what work will be done by changing mixture composition

at the same temperature and pressure, or will the composition change at all under the

same temperature and pressure.




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