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ANALYSIS OF A NOVEL COMBINED THERMAL POWER AND COOLING CYCLE USING AMMONIAWATER 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 MultiComponent 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 AmmoniaAbsorption Refrigeration Cycle Processes 10 1.5.3 Combined Power and Cooling Cycle Processes 10 1.6 Thermodynamic Properties of AmmoniaWater Mixtures  11 2 THERMODYNAMIC PROPERTIES OF AMMONIAWATER MIXTURES   14 2.1 Introduction   14 2.2 ElSayed and Tribus Method 16 2.2.1 Computational Procedure 17 2.2.2 AmmoniaWater Mixture  24 2.2.3 Discussion  26 2.3 Thermodynamic Properties of AmmoniaWater 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 AmmoniaWater Liquid Mixtures 29 2.3.4 AmmoniaWater Vapor Mixtures  32 2.3.5 VaporLiquid 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 AMMONIABASED 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 AMMONIAWATER 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. Ammoniawater 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 multicomponent working fluid. The boiling temperature of the ammoniawater 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 ammoniawater 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 ammoniawater 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. Ammoniawater mixture is used as a working fluid in this cycle. A new system design will exploit the unique thermodynamic properties of ammoniawater 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 11: to, Cooling Wate Pump "P Figure 11 Rankine cycle 2 3 Heat exchanger Win Won Conpressor Turbine Heat xchanger 4 Figure 12 Brayton cycle A typical gas power cycle using air as a working fluid is Brayton cycle as shown in figure 12. 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 outputto 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 multicomponent 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 MultiComponent Working Fluid Research A review of the literature shows that the studies of multicomponent cycles are very recent as compared to the conventional Rankine cycle. Kalina is recognized for introducing the multicomponent 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 absorptiontype power cycle using a mixture of ammonia and water as the working fluid. Avery (1980) investigated ammoniawater 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 ammoniawater mixtures in their systems analysis. Kalina, Tribus and ElSayed have collaborated on several publications. A comparison of the multicomponent cycle to the Rankine cycle by ElSayed and Tribus shows a 10% to 20% improvement in thermal efficiency (ElSayed and Tribus, 1985b). 7 Marston (1990) conducted a detailed discussion of multicomponent 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 ammoniawater power cycle. Since this cycle still uses ammoniawater 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 ammoniawater 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: dieselsteam, mercurysteam, gassteam, steamorganic fluid, gasorganic fluid, and MHDsteam. 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 ammoniabased power/cooling cycle, first suggested by Dr. Yogi Goswami(1995, 1996), combines two thermodynamic cycles, the Rankine cycle and the ammoniaabsorption refrigeration cycle. This novel cycle uses a mixed working fluid (such as ammoniawater) with different compositions at different stages, therefore, it cannot be shown on a single thermodynamic diagram (i.e. pressureenthalpy chart). However, by evaluating the features of the individual Rankine and ammoniaabsorption 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 11, 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 ammoniaabsorption refrigeration cycle differs from the vapor compression cycle in the manner in which compression is achieved. In the ammonia absorption refrigeration cycle(Figure 13), lowpressure 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 ammoniaabsorption refrigeration cycle to the proposed ammoniabased power and cooling cycle are evident as seen in Figure 14. 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 13 Ammoniaabsorption refrigeration cycle 1.6 Thermodynamic Properties of AmmoniaWater Mixtures Ammoniawater mixtures have been in use for several decades as working fluids of absorptionrefrigeration cycles where ammonia is the refrigerant and water is the absorbent. Since 1980, ammoniawater mixtures have been investigated as potential working fluids for power cycles. Consistent and accurate thermodynamic properties data of ammoniawater mixtures are very important for the power cycle analysis. In the past, properties of ammoniawater mixtures were of interest in the operating range of the absorption refrigeration cycle. As ammoniawater 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 SWeak Aqaamonia Soluon Figure 14 Ammoniabased combined power/cooling cycle CHAPTER 2 THERMODYNAMIC PROPERTIES OF AMMONIAWATER MIXTURES 2.1 Introduction The thermodynamic properties of ammonia and water mixtures are of technical importance since ammoniawater mixtures have been in use for several decades as working fluids in absorptionrefrigeration cycles. Use of multicomponent working fluids for power cycles has been investigated more recently over the last two decades. Ammoniawater 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 absorptionrefrigeration cycles. So a consistent and extended set of thermodynamic data for ammoniawater 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 ammoniawater mixtures as potential working fluids for a power cycle. Many studies of the vaporliquid equilibrium and thermodynamic properties of ammoniawater 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 absorptionrefrigeration 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 vaporliquid equilibrium pressures of 0.2 to 110 bar and temperatures of 230 to 600 K. A study of power cycles using ammoniawater mixtures was recently initiated by Kalina (1983). For power cycles, thermodynamic data of ammoniawater mixtures at higher temperatures and pressures than those presented by IGT are required. Gillespie et al. (1987) published vaporliquid 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 ammoniawater mixtures using the Ziegler and Trepp correlation. ElSayed 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 misciblecomponent mixtures for the purpose of powercycle analysis. Park and Sonntag (1990b) published a set of thermodynamic data of ammoniawater 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 ElSayed and Tribus (1985a) cover all of the modeling efforts reported in the literature. The following section gives detailed discussions of these methods. 2.2 ElSaved and Tribus method ElSayed 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 ElSayed and Tribus use a group of equations developed exclusively for ammonia water mixtures based on vaporliquid 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) 21 Dew temperature Td = T(P, x) 22 Equation of state P = P( T) 23 Tb = T, (C, + x)(ln( ))' 24 i=l j=l where 4 T T_=T a.x 25 i=l Pc = P exp(Ybix') 26 P in psia and T in F Ta = T, (a, + A,,(in(1.0001 x))'(ln())' 27 i jP P in psia and T in OF. Since Elsayed 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 1 212 s =,T:2 (T T)'2 +(T)12 , 2. Ammonia vaporization H,2 = H, [ 213 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 213 is transformed as follows: H, = C(1T,2)" 214 where C, = S (1 T,,) The above equation can be set up in the form y = a + bx InH2 =lnC + nln( T,2) 215 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) 216 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 214. Hv = 7906.555 x (1 T/Te)038939 217 The entropy of vaporization is Sv = Hv / T 218 3. Ammonia vapor Integrating the heat capacity equation 219 and comparing the results with published enthalpy data did not yield good agreement. C = A + BT + CT2 +DT3 219 As the pressure increased the agreement worsened. Therefore, a pressure compensation term was added to obtain equation 220. In addition, the original coefficients (A, B, C and D) were changed as reflected in equation 221. 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 106 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 (1G) 1J 1 EPTG 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 21 illustrates the use of these two values in finding the liquid enthalpy. Temperature Ti in figure 21 is the reference temperature, chosen for this work to be 273.15 K. The straight, horizontal segment, line 12, 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 23 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 21. Point 5 is the critical temperature. Segment 56 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 21 as a reference. 5. Water vaporization Enthalpy of vaporization Hv2 at temperature T2 is found from the following equation: H2 = Tc T2 224 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 225 where C1 = 13468.42 C2 = 0.380 T, = H20 critical temperature, 647.3 K Ti 1 T1 Property Figure 21 A generic diagram of water property (enthalpy or entropy) against temperature 6. Water vapor C =A+BT+CT2 +DT3 226 where A = 32.24 B = 1.924 x 103 C =1.056 x 105 D = 3.596 x 10"9 [AT+ BT2 CT3 DT4]1V 227 = AT+T+ + 228 2 3 TI where TI = Saturation temperature, K T2 = Final temperature, K 2.2.2 AmmoniaWater Mixtures 1. Liquid The ammoniawater mixture is in the liquid phase when the temperature is below its bubble point temperature. hm = hNH3,f + (1 x)hH20,f 229 m = XSNH3f + (1 x)sH2o,f Rm(x'lnx' + (1 x')ln(l x') 230 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 231 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/)) 232 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 ammoniawater mixture is in the vapor phase when temperature is above its dew point temperature. hm = xhNH3,g + (1 X)hH2,g 233 Sm = XSNH3,g + (1 X)SH20,g Rm(x'lnx' + (1 x')ln(l x')) 234 2.2.3 Discussion The advantage of using the ElSayed 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 AmmoniaWater 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 235 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 236 CpL = b + b2T + b3T2 237 For the gas phase, the corresponding empirical relations are v = +c,+c2 + T c4p2 238 P T' T" Cp,0 = d + d2T + d3T2 239 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 2 240 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, 241 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/kmoleK, 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 244 In terms of reduced variables h =RTBT,[ (G,/ T,) 245 s=R G, 246 v RT T, 247 P, OPr AT 2.3.3 AmmoniaWater 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) 248 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 21 Coefficients of equations 240 and 241 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 102 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 102 1.951939 102 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 22 Coefficients of equation 248 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) 24 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,)+(1x,)ln(1x,)} 254 v= Xf,v +(1 Xf)v+v 255 2.3.4 AmmoniaWater Vapor Mixture Ammoniawater vapor mixtures are assumed to be ideal solutions. The enthalpy, entropy, and volume of the vapor mixture are computed by h, = x,h +(1x )h 256 s = xgs + (1 Xg)sl + smx 257 v = xv + (1 x)v 258 2.3.5 VaporLiquid 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 259 pL = p = 260 f.L = 261 i = f 262 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. 263 f= yf(1x)65 264 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 265 f = wP(1y) 266 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 ammoniawater 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 T267 Li'= t  where t= 1000/T constants of ideal gas equation for water Table 23 Coefficients of equation 267 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) 1 268 2. The generalized equation of state based on a fourparameter 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 24 Coefficients of equation 268 a, 3.872727 a7 0.36893175 10'0 a2 0.64463724 as 0.35034664 10"1 a3 3.2238759 as 0.2056303 1016 a4 0.00213769925 alo 0.6853420 1020 a5 0.86890833 10 all 0.9939243 1024 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 275 V.e Zc = 02901 0.0879wm 0.0266m. 276 w = x,w, 277 mm = x,m 278 4. Discussion Park and Sonntag claim that using the generalized equation method provides a consistent way to calculate the thermodynamic properties of ammoniawater 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. ElSayed 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 vaporliquid mixture. For the vaporliquid 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 vaporliquid 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 ammoniawater mixtures vaporliquid equilibrium in the early 80s from 313 K and 589 K. Their data is used to extend the ammoniawater 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 ammoniawater 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 ammoniawater 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 22 to 25 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 26 to 210 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 211 to 214. 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 215 to 218. 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 219 to 222 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 219, 221 and 222, 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 223 to 226. 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 ammoniawater 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 ammoniawater 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 vaporliquid 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 ammoniawater 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 22 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 23 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 24 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 25 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 26 Saturated pressures of ammoniawater 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 27 Saturated pressures of ammoniawater mixtures at 394.15 K 140 I This work 120  120 0 Gillespie et al. 100 80 0 60  ao 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 28 Saturated pressures of ammoniawater 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 29 Saturated pressures of ammoniawater 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 210 Saturated pressures of ammoniawater 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 211 Saturated liquid enthalpy of ammoniawater 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 212 Saturated liquid enthalpy of ammoniawater 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 213 Saturated liquid enthalpy of ammoniawater 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 214 Saturated liquid enthalpy of ammoniawater 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 215 Saturated vapor enthalpy of ammoniawater 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 216 Saturated vapor enthalpy of ammoniawater 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 217 Saturated vapor enthalpy of ammoniawater 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 218 Saturated vapor enthalpy of ammoniawater 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 219 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 220 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 221 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 222 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 223 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 224 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 225 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 226 Entropy of Saturated vapor at 366.5 K CHAPTER 3 AMMONIABASED 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 sensibleheat 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 31. To increase the efficiency of the Rankine cycle working with sensible heat, two conventional ways have been proposed: (1) Incorporation of a multipressure boiler (2) Implementation of the supercritical cycle The multipressure 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 9001000 0F(755 811 K), the cycle efficiency is 20 22% with a single pressure boiler and 2325% with tripressure boiler (FosterPegg 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 31 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 multicomponent working fluid. A multicomponent 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 multicomponent 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 multicomponent working fluid and the condensing process of the Rankine cycle is replaced by the absorption process. This cycle meets both conditions for higher thermodynamic efficiencya 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 32, 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 ammoniawater 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 32 (1) Heat supply at a variable temperature(I2) (2) Isentropic expansion(23) (3) Isothermal heat rejection(34) (4) Isentropic compression(41) The Lorenz cycle is exactly the same as the Camot cycle except for the process(l2). Possible ways to realize the Lorenz cycle are: (1) Multipressure boiler (2) Supercritical cycle (3) The Kalina cycle (4) The novel ammoniabased combined power/cooling cycle T 2 1 Equivalnent proposed cycle 4 QL 3 Figure 32 Schematic diagram of the novel cycle in connection with a combined cycle The novel cycle combines two thermodynamic cycles, the Rankine cycle and the ammoniaabsorption refrigeration cycle, as seen in figure 14. In Rankine cycle, ammoniawater 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 ammoniawater mixture liquid. As seen in figure 33, 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 TS diagram. The concept of this cycle is based on the varying temperature boiling of a multicomponent working fluid. The boiling temperature of the multicomponent 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 33 TS 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 multicomponent 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 33 the proposed ammoniabased cycle is a combination of the Rankine and the ammoniaabsorption 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 ammoniaabsorption refrigeration cycle. A difference between this cycle and the ammoniaabsorption 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 31 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 aquaammonia solution is assumed 1 Temperature of strong aquaammonia 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 aquaammonia 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 32 shows the thermodynamic state including enthalpy at each point. Table 33 shows the energy balance of each component. Table 32 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 33 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 14. 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 34 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 34 shows typical operating conditions of the proposed cycle. Table 35 shows the performance of each component based on a unit mass of the basic solution at the conditions of table 34. Figure 34 A modified ammoniabased combined power/cooling cycle Table 34 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 35 Results from the table 34 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 ammoniabased 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 highpressure, hightemperature 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 steadystate 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 energysystems 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 firstlaw energy balance around the component involved in the process. As the available work in a system working fluid decreases through energyrelated 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 heatbalance 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 steadystate 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, 41 Internal Entropy Work Momentum Gravity Chemical Energy Potential Where the subscript 0 denotes the reference condition and i denotes as ith composition. There are variations of this general exergy equation, and in most systems analyses some, but not all, of the terms shown in equation 41 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 environmentthat 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 deadstate 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 hightemperature and lowtemperature 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) 42 Ex2 = (h2 hf) Tf(2 Sef) 43 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 44 IT where QI2 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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