Modeling the High-Pressure Ammonia−Water System with WATAM

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Ind. Eng. Chem. Res. 1998, 37, 1644-1650

Modeling the High-Pressure Ammonia-Water System with WATAM and the Peng-Robinson Equation of State for Kalina Cycle Studies Robert M. Enick,*,† Glenn P. Donahey, and Mike Holsinger Department of Chemical and Petroleum Engineering, 1249 Benedum Engineering Hall, University of Pittsburgh, Pittsburgh, Pennsylvania 15261

The Kalina power cycle uses an ammonia-water mixture as the working fluid in the 283-866 K temperature range and at pressures up to 22 MPa. Modeling of these cycles, typically accomplished with a process simulator, requires accurate descriptions of the phase behavior of this binary. Therefore 58 previously published Pxy isotherms in the 203-618 K temperature range were used to evaluate the predictive capabilities of the Peng-Robinson (PR) equation of state (EOS) and WATAM. WATAM provided a much better correlation of saturated liquid densities than the PR EOS. Although both models adequately correlated liquid phase compositions, WATAM provided a better fit of the near-critical vapor phase data. The PengRobinson EOS consistently overestimated the mixture critical pressures. Several correlations, based on different objective functions, for the temperature-dependent binary interaction parameter were developed. Slight improvements in the predictive capabilities of the PR EOS were realized using the Panagiotopolous and Reid composition-dependent mixing rule, which required two temperature-dependent parameters. Temperature-dependent correlations for each parameter were regressed from PTxy data. Guidelines for using the PR EOS in a process simulator to model Kalina cycles were developed. Introduction The most common power cycle found in the power industry is the Rankine cycle, which employs water as the working fluid. High-pressure water is vaporized as it absorbs heat from combustion products. The highpressure, high-temperature steam is then expanded in a turbine, generating useful work. The low-pressure steam turbine exhaust is then condensed and pumped back to the boiler, completing the cycle. In an attempt to attain a higher thermal efficiency than can be realized in the Rankine cycle, the Kalina cycle has been developed. The unique feature of the Kalina cycle is a working fluid composed of water and ammonia. The variable boiling point nature of this binary at a specified pressure (as opposed to the isothermal evaporation of water) enables more heat to be extracted from a hightemperature heat source, such as combustion gases, for a specified approach in a heat exchanger. A greater amount of recuperative heat transfer can also be accomplished using binary working fluids because heat can be transferred from low-pressure condensing streams to high-pressure boiling streams. This type of recuperative heat transfer cannot be accomplished in a Rankine cycle because the boiling point of water increases with pressure. A parametric analysis of a simplified Kalina cycle has been published (Marston, 1989), which illustrates the basic concepts of this power cycle. Process simulators are typically used to model Kalina cycles because of the interconnected nature of the plant, which consists of heat exchangers, turbines, pumps, mixers, splitters, and flash drums. The use of the simulator requires a selection of thermodynamic models provided in the simulator, such as the Peng-Robinson equation of state (PR EOS; Peng and Robinson, 1976). Alternately, the user can incorporate a thermodynamic †

E-mail address: [email protected].

model by developing a computer code and incorporating it into the simulator in the appropriate format. WATAM, a proprietary ammonia-water model developed by Exergy, is an example of an accurate user-added thermodynamic/transport property model. Ammonia-Water Vapor-Liquid Equilibrium Data Numerous literature sources were used to compile a vapor-liquid equilibrium (VLE) database for this study (Muller et al., 1988; Rizvi and Heidemann, 1987; Gillespie et al., 1985; Gullievic et al., 1985; Smolen et al., 1991; Sassen et al., 1990; Clifford and Hunter, 1933). The database consisted of 998 liquid phase compositions (x) and 1033 vapor phase compositions (y). The temperature range for these isotherms was 203 to 618 K. Pressures varied between 0.002 and 22.5 MPa. These literature sources were selected because most were relatively recent and have data in temperature and pressure ranges associated with the Kalina cycle. Several recent studies (Abovsky, 1996; Tillner-Roth and Friend 1997a; Friend and Haynes, 1996), including a very thorough document (Tillner-Roth and Friend, 1997a) that provides an assessment of the results of VLE data from 30 sources, have noted the disagreement between some of these sources, particularly in the critical region of the mixtures. Thermodynamic Models of the Ammonia-Water System Many thermodynamic models have been proposed for modeling the phase behavior of the ammonia-water mixture. Peng and Robinson (1980) presented a generalized method for modifying their equation of state (Peng and Robinson, 1976) for systems involving an aqueous phase. The expression for R was modified for

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Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1645

water at reduced temperatures less than 0.85, thereby improving the vapor pressure fit for pure water. Two different interaction parameters were used, a temperature-independent constant for the nonaqueous phase and a temperature-dependent parameter for the aqueous phase. For the limited set of ammonia-water VLE data studied (100-300 °F, 0-500 psia), however, a constant value of the aqueous phase interaction parameter was used. Although graphical representations of the results were provided, the actual values of the interaction parameters were not presented. The results of several other early investigations were limited to narrow ranges of temperature and pressure available at the time (Mathias and Copeman, 1983; Skogestad, 1983; Vidal, 1983). Heidemann and Rizvi (1986) used their own extensive database of higher temperature data to study various modifications of the PR EOS. They presented results for a temperature-dependent interaction parameter for the van der Waals mixing rule typically associated with the PR EOS. Typically, the bubble point locus was correlated more successfully than the dew point locus, and the ammonia relative volatility was too high. They then considered models involving additional parameters. These included the van der Waals-Evelain mixing rules, three dense fluid excess free energy models, a density dependent model, the Mathias-Copeman local composition model, and a chemical reaction model. These modifications, which involved additional parameters and some computational problems, yielded marginally improved results. A PengRobinson group contribution method referred to as PRASOG was recently presented by Tochigi et al. (1997) for ammonia-containing systems, including the ammonia-water binary. It is based upon 447 VLE data points from several references including the extensive work of Rizvi and Heidemann (1987). The optimized mixture parameters for the ammonia-water system yielded errors on P and y (for calculations in which T and x were input) of 3.7 and 2.6%, respectively. Numerous models unrelated to the PR EOS have also been employed in the modeling of the ammonia-water binary. Smolen et al. (1991) modeled ammonia-water VLE using a Redlich-Kwong equation of state modified to include Peneloux’s volume translation and a densitydependent mixing rule. Ziegler and Trepp (1984) presented correlations for the ammonia-water properties. These correlations were later incorporated into a computer code by Herold et al. (1988). Ibrahim and Klein (1992) correlated the thermodynamic properties for ammonia-water mixtures to the form of the equation of state given by Ziegler and Trepp. Their correlations covered VLE in the 0.2-110 bar pressure range and 230-600 K temperature range. El-Sayed and Tribus (1985) proposed a model for the ammonia-water system based on correlations for bubble point, dew point, Gibbs free energy of solution, pure component equations of state, and pure component ideal gas specific heat. Marston (1989) later provided a computer program for El-Sayed and Tribus correlation. Jarvis (1995) proposed a four-parameter equation of state that was incorporated into the Aspen process simulator for the design of Kalina power cycles. The parameters included Tc, Pc, ω, and Y. The Y parameter accounted for the strong polarity effects associated with this binary. The equation of state was a combination of the Lee-Kesler equation of state, which modeled the general behavior of the ammonia-water system, and the Keenan equa-

tion of state, which accounted for the polar nature of the system. Several recent thermodynamic models have been based on extensive amounts of recent high-pressure, high-temperature data. Tillner-Roth and Friend (1997a,b) presented a fundamental EOS for the ammonia-water binary. Their EOS was written in terms of the reduced Helmholtz free energy. This model was based on the pure water EOS of Pruss and Wagner (1995) and the EOS for pure ammonia developed by Tillner-Roth and Friend (1997b). WATAM is a proprietary code for the thermodynamic and transport properties of ammonia-water mixtures. WATAM was developed by Exergy, the company founded by its president Alexander Kalina, for use in designing Kalina cycles. One of three DOE contractor teams working on the LEBS (low emission boiler system) program to develop clean, efficient, and economic energy from coal considered a commercial-scale Kalina plant fueled by pulverized coal (Ruth, 1995; Enick et al., 1997). WATAM was used for thermodynamic and transport property predictions required for the design of this plant. In WATAM, the basic assumptions are the same as those used by El-Sayed and Tribus (1985). The mixture behaves as an ideal mixture of real gases. Chemical reactions are absent. A pressure-explicit equation of state is used for the pure components. Specific heat as constant volume for the pure components is a function of temperature alone. Dew and bubble point data of Rizvi and Heidemann (1987) are correlated to pressure and ammonia mass fraction. Pure component data for ammonia and water were extracted from the compilation prepared by Reynolds (1979). Tables of properties of saturated liquid and vapor ammonia-water mixtures based on extensive experimental data were developed at Exergy using the Law of Corresponding States. Compressed liquid enthalpies are calculated using the pure-component enthalpy change from saturation to the same reduced pressure to adjust the mixture bubble point enthalpy. Vapor enthalpies are calculated from the interpolated pure component ideal gas enthalpies plus the interpolated enthalpy departures at the same reduced pressure and temperature. Transport properties are determined using methods described by Reid et al. (1987). The WATAM program has been coded as a user-added package that runs in conjunction with AspenPlus process simulator. Objective of This Study The objective of this study was to evaluate the ability of the Peng-Robinson equation of state to correlate VLE data for the ammonia-water system over a wide range of temperature and pressure. These PR EOS results were then compared with the results obtained using WATAM. Guidelines were then developed for the use of the PR EOS in process simulators for modeling of Kalina cycles. Thermodynamic Models The following van der Waals mixing rule is commonly used with the PR EOS, with kij ) kji,

aij ) (aiaj)0.5[1 - kij]

(1)

A modification of the Peng-Robinson equation of state,

1646 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998

Figure 1. Correlations for the Peng-Robinson binary interaction parameter for ammonia-water.

which incorporates a two-parameter mixing rule, was also evaluated. This composition-dependent mixing rule

aij ) (aiaj)0.5[1 - kij + (kij - kji)xi]

(2)

was proposed by Panagiotopolous and Reid (1986) and was designed to provide improved correlation of mutual solubility in systems composed of highly polar, asymmetric mixtures. Note that if kij ) kji, the twoparameter rule reduces to the single-parameter form. Enick et al. (1987) successfully used this modified PR EOS to model carbon dioxide-water-crude oil systems exhibiting as many as four fluid phases. This mixing rule has several inconsistencies, however. The dilution of the mixture with multiple components reduces the two-parameter rule back to the one-parameter form because all of the x values approach zero. The mixing rule is also not invariant if a component is divided into identical pseudocomponents. Neither of these inconsistencies prevents the mixing rule from being used in the modeling of the ammonia-water binary. This modified PR EOS and the associated expression for the fugacity coefficient (Panagiotopolous and Reid, 1986; Enick et al., 1987) are incorporated in Simulation Science’s ProII simulator but would have to be modeled as a user-added thermodynamics package to simulators that do not include it. Although one may incorporate additional temperature-dependent parameters into the PR EOS to provide improved pure component matches of vapor pressure and/or saturated liquid density, as described by Heidemann and Rizvi (1986), Panagiotopolous and Reid (1986), and Enick et al. (1987), these modifications were not included in this analysis. The Peng-Robinson equation of state results were compared to results obtained using WATAM, which is currently being employed by the designers of Kalina cycle power plants. Our goal was to determine if the Peng-Robinson equation of state could yield results comparable to WATAM. If so, users of process simulators may be able to accurately model Kalina cycles using the PR EOS rather than being dependent upon models that are currently being developed, proprietary in nature, or difficult to integrate as a user-added package to a simulator.

Results AspenPlus Data Regression Results. A “data regression” run was performed using the AspenPlus process simulator to develop a correlation for the ammonia-water binary interaction parameter. The optimal binary interaction parameter was determined at each temperature. A third-order polynomial was then used to correlate the results to temperature in the 203-618 K range, as shown in Figure 1.

kij ) 3.8077 × 10-9T3 - 3.3959 × 10-6T2 + 1.1859 × 10-3T - 0.4131 (3) The average value of the interaction parameter for this correlation was -0.216 58. The correlation presented by Heidemann and Rizvi (1986), which was based upon their experimental work (Rizvi and Heidemann, 1987) between 305 and 618 K (with T in kelvin), is shown in Figure 1 for comparison purposes.

kij ) 0.5889Tr2 - 0.6341Tr - 0.07121

(4)

Tr ) T/647.29

(5)

This correlation had an average value of -0.212 47 over the 305-618 K temperature range. The AspenPlus process simulator has a default value of -0.2589 for the PR EOS interaction parameter, based on low-pressure data in the 273-420 K temperature range from Clifford and Hunter (1933), Polak and Lu (1975), and Wilson (1925). This is also indicated in Figure 1 for comparison with the other correlations. Minimization of AAPD. The 800 PTxy, 63 PTx, and 167 PTy values along 37 isotherms, representing the literature data with compositions recorded at five or more pressures at temperatures above 293 K, were selected. Experimental values of T and P were entered and phase compositions calculated. The optimal kij was determined by minimizing the average absolute percent deviation, AAPD, between n experimental and calculated ammonia molar concentrations in the water-rich phase and m experimental and calculated molar con-

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Figure 2. One-parameter PR kij and the PR Panagiotopolous-Reid two-parameter kij and kji values, PRP, i ) NH3, j ) H2O.

centrations in the ammonia-rich phase. The parameters were then correlated to temperature.

∑|xcalc - xexp|/nxexp Ey ) ∑|ycalc - yexp|/myexp Ex )

(6) (7)

The result for the 293-618 K temperature range, illustrated in Figure 1 along with the other correlations, was

kij ) 8.4828 × 10-9T3 - 9.9724 × 10-6T2 + -3

4.0923 × 10 T - 0.8334 (8) The R2 value of the correlation coefficient for the correlation was 0.847. The average value of the interaction parameter over the 293-618 K temperature range was -0.222 49. ProII Regress Results. All of the PTxy data from the database was used to generate a temperaturedependent correlation for kij using “Regress”, Simulation Science’s data regression utility for ProII. Both objective functions (one for Tx input, Py output and one for TP input, xy output) were used to develop the following correlation for the 293-618 K temperature range. This result is illustrated in Figures 1 and 2.

kij ) -1.9128 × 10-9T3 + 2.7243 × 10-6T2 1.0350 × 10-3T - 0.1354 (9) The average value of the interaction parameter over the 293-618 K temperature range was -0.221 41. These single-parameter correlations shown in Figure 1 were in good agreement up to 500 K. The divergence of the correlations at higher temperatures reflects the small amount of reliable data available in this range. Future VLE studies for this binary should concentrate on this region. Two-Parameter Results. Simulation Science’s “Regress” software was used to develop correlations for the composition-dependent two-parameter mixing rule (i ) NH3 and j ) H2O). The values of kij and kji were similar to each other, especially at higher temperatures. The

single-parameter result represents an average of the two-parameter correlations, Figure 2. Relative to the one-parameter results, the improvements in correlating VLE were not dramatic because the effect of the different parameters becomes less significant as the values converge (i.e., eq 2 reduces to eq 1 when kij approaches kji). Heidemann and Rizvi (1986) noted similar results in their study of modified versions of the PR EOS. Temperature-dependent correlations for both parameters in the 293-588 K temperature range are provided below, for i ) NH3 and j ) H2O.

kij ) 0.0151 ln T - 0.2833

(10)

kji ) 0.1543 ln T - 1.1875

(11)

The average values of kij and kji in the 293-588 K temperature range were -0.191 66 and -0.251 12, respectively. Values of the Interaction Parameter The PR EOS interaction parameters were negative values that increased in value (becoming smaller negative values) in all cases. The interaction parameter is typically a small, positive number for binary systems composed of small, nonpolar, nonreacting components. The ammonia water binary consists of two small, polar, H-bonding components. The negative value of the interaction parameter increases the a parameter, indicating an increase in attractive forces due to H-bonding. H-bonding forces become less significant at higher temperatures, resulting in the interaction parameter approaching values closer to zero, Figure 1. A reasonable correlation of the ammonia-water VLE can be accomplished using the PR EOS, which was not designed to model polar, H-bonding components, only by incorporating a temperature-dependent, negative value for the binary interaction parameter. This large, negative value of kij compensates for the intermolecular H-bonding forces that are associated with the ammonia-water system but are not explicitly accounted for in the development of the PR EOS. Comparison of WATAM and the PR EOS. A comparison of the errors associated with WATAM and

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Figure 3. Pxy diagram for ammonia-water at 526 K (data from Rizvi and Heidemann (1987)).

Figure 4. Pxy diagram for ammonia-water at 579 K (data from Rizvi and Heidemann (1987)).

the PR EOS when kij was made with the interaction parameter provided by the AAPD correlation, eq 8. A set of 37 isotherms between 293 and 618 K was selected. The average errors in ammonia concentration of the liquid and vapor phases were 8.82 and 8.53%, respectively, with the PR EOS. The errors in liquid and vapor phase ammonia concentrations were 10.9 and 7.05%, respectively, with WATAM. The PR EOS yielded a slighter better fit of the liquid phase (water-rich) compositions, but WATAM provided a superior fit of the vapor phase (ammonia-rich) compositions. When all 37 Pxy diagrams were viewed, it was evident that although both WATAM and the PR EOS provided an accurate description of near-critical bubble point data, the PR EOS overestimated vapor phase NH3 concentrations in the mixture near-critical region. As a result, the PR EOS consistently overestimated the mixture critical pressure. (This PR EOS overestimation was not reflected in average error calculation, which was based only on experimental xy values below the experimentally determined critical pressure.) Therefore, WATAM pro-

vided a slightly more accurate description of the ammonia-water binary than the PR EOS, especially in the near-critical region. Three Pxy diagrams, Figures 3-5 at 526, 579, and 610 K, provide a comparison of all of the models. The differences between the models become more marked as the temperature increases because the correlations for the interaction parameters become more dissimilar at higher temperatures, Figure 1. Liquid Density Computations. WATAM is a complete predictive tool for all of the thermodynamic and transport properties required for the design of a Kalina cycle power plant. It provides phase compositions, phase densities, liquid and vapor heat capacities, and enthalpy values for ammonia-water mixtures. The PR EOS can yield reasonable phase composition results and vapor phase densities. It would not be advisable to use the Peng-Robinson equation of state for liquid density calculations because of the significant underestimation of the saturated liquid values for pure water over most of the temperature range of interest. This leads to

Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1649

Figure 5. Pxy diagram for ammonia-water at 610 K (data from Rizvi and Heidemann (1987)). Table 1. Comparison of Saturated Liquid Density Results satd liquid density, AAPD temp, T (K)

data pts

WATAM

PR EOS

Rackett

288.2 313.2 333.2 353.2 394.3 405.9 449.8 519.3

5 4 4 4 4 4 3 2

0.49 0.61 0.50 0.59 1.02 8.26 1.22 2.39

13.35 12.75 13.79 14.50 16.57 18.33 14.81 13.82

2.38 2.28 4.21 4.48 6.57 13.56 15.92 21.22

30

1.89

15.80

7.76

underestimation of ammonia-water mixture liquid density. The PR EOS can be modified to reproduce the vapor pressure and saturated liquid density of each pure component, followed by the reoptimization of interaction parameter values to match mixture data, as done by Panagiotopolous and Reid (1986) and Enick et al. (1987). Alternately, the PR EOS can be used to calculate compositions, and another model found in most process simulators, such as the Rackett equation (1972) and its generalization by Spencer and Danner (1972), can be employed for liquid density calculations. Table 1 provides a comparison of the AAPD in saturated liquid density for 30 ammonia-water data points in the 288519 K temperature range from Gillespie et al. (1985). WATAM provided the best results. Although the PR EOS errors were high, the Rackett model provided more reasonable predictions, especially at lower temperatures. Both the PR EOS and Rackett equations consistently underestimated the liquid density. Guidelines for Designing the Kalina Cycle Using a Process Simulator All simulators provide the PR EOS as an option for the user. Some simulators, such as ProII, also provide the Panagiotopolous-Reid mixing rule. The simplest, but least accurate, method of incorporating these results into the process simulator is to use only the average interaction parameter value for a correlation over the temperature range of interest. If one desires to quickly incorporate the temperature dependence of these parameters, these guidelines should

be followed. The temperature-dependent correlation for the PR EOS binary interaction parameter cannot be incorporated directly into most simulators because they permit the user to enter a single value. One can, however, divide the Kalina plant flow diagram into sections containing as few as one unit operation. The average temperature of the ammonia-water mixture in each unit can be estimated and used to determine the appropriate interaction parameter to be used in that section. The PR EOS should not be used for liquid density calculations. Other options in the simulator, such as the Rackett equation, can be considered for these values. The most accurate, but most difficult, method for incorporating these results into a process simulator would be to incorporate a “user-defined” complete thermodynamic model into the simulator. The user would include the temperature dependence of the interaction parameter in the PR EOS. The user would also have to derive all of the associated thermodynamic functions (compressibility, fugacity coefficient, enthalpy, entropy) and include each in the user-defined model. Other options, such as the Rackett equation, should be selected for liquid phase density calculations. Conclusions The WATAM program developed by Exergy provided a very good fit of ammonia-water VLE over a wide range of temperature and pressure, including the PT region that is relevant to the design of Kalina cycles. The PR EOS provided a good fit of the same data only if a temperature-dependent mixing rule is employed. A correlation for this parameter was developed using an extensive database of ammonia-water data. A slightly better fit was obtained when a two-parameter, composition-dependent mixing rule was incorporated. Although the PR EOS provided a reasonable fit of the VLE, it tended to overestimate the ammonia concentration in the near-critical vapor phase. The PR EOS also overestimated mixture critical pressures. WATAM provided a slightly more accurate description of the VLE, especially in the near-critical region. WATAM also yielded a much better correlation of saturated liquid

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densities for the ammonia-water binary than the PR EOS. More reasonable results for liquid density were attained when the PR EOS was used to determine the phase composition, and the Rackett model was then used to calculate liquid density. Guidelines for using these results in a process simulator to model Kalina cycles have been developed. The temperature dependency of kij can be indirectly incorporated by dividing the Kalina cycle into sections and using the average temperature of that section to determine the value of the interaction parameter. Acknowledgment The authors would like to thank ORISE for the support of Dr. Enick. Frank Qun Miao of ABB provided us with an AspenPlus user-added version of WATAM and a thorough description of its main features. Dr. Alexander Kalina provided useful insight into the Kalina cycle and WATAM. Mark Mirolli of Exergy permitted us to present the phase behavior results associated with the use of their model. Erika Hill and Nii-Kome Tettey provided invaluable assistance in evaluating the performance of the Peng-Robinson equation of state. Simulation Science’s ProII and Aspen Technology’s AspenPlus process simulators were used in this work. Literature Cited Abovsky, V. Thermodynamics of Ammonia-Water Mixture. Fluid Phase Equilib. 1996, 116, 170. Clifford, I.; Hunter, E. The System Ammonia-Water at Temperatures up to 150 °C and at Pressures up to Twenty Atmospheres. J. Phys. Chem. 1933, 37, 101. El-Sayed, Y.; Tribus, M. Thermodynamic Properties of WaterAmmonia Mixtures: Theoretical Implementation for Use in Power Cycle Analysis; ASME Paper AES-C; American Society of Mechanical Engineers: New York, 1985; Vol. 1. Enick, R. M.; Holder, G.; Mohamed, R. Four-Phase Flash Equilibrium Calculations Using the Peng-Robinson Equation of State and a Mixing Rule for Asymmetric Systems. SPE Reservoir Eng. 1987, 687. Enick, R.; Gale, T.; McIlvried, H.; Klara, J. The Modeling of LEBSKalina Power Cycles. Proceedings of the 22nd International Technical Conference on Coal Utilization and Fuel Systems, Clearwater, FL, Mar 16-19, 1997; Coal and Slurry Technology Association: Washington, DC, 1997. Friend, D.; Haynes, W. Report of the Workshop on Thermophysical Properties of Ammonia/Water Mixtures, June 26, 1996; Physical and Chemical Properties Division; National Institute of Standards and Technology: Boulder, CO, 1996. Gillespie, P.; Wilding, W.; Wilson, G. Vapor-Liquid Equilibrium Measurements on the Ammonia-Water System from 313 K to 589 K; GPA Research Report RR-90, Gas Processors Association: Tulsa, OK, 1985. Gullievic, J.; Richon, D.; Renon, H. Vapor-Liquid Equilibrium Data for the Binary System Water-Ammonia at 403.1, 453.1, and 503.1 K up to 7.0 MPa. J. Chem. Eng. Data 1985, 30, 332. Heidemann, R.; Rizvi, S. Correlation of Ammonia-Water Equilibrium Data with Various Modified Peng-Robinson Equations of State. Fluid Phase Equilib. 1986, 29, 439. Herold, K.; Han, K.; Moran, M. AMMWAT: A Computer Program for Calculating the Thermodynamic Properties of Ammonia and Water Mixtures Using A Gibbs Free Energy Formulation; ASME Proceedings AES; American Society of Mechanical Engineers: Vol. 4, p 65. Ibrahim, O.; Klein, S. Thermodynamic Properties of AmmoniaWater Mixtures; Solar Energy Laboratory, University of Wisconsin: Madison, WI, 1992. Jarvis, M. An Equation of State for Kalina Cycle Design and Evaluation. DOE Contract DE-AC21-90MC26328, Report No. 34BB-R95-001, Mar 29, 1995.

Marston, C. Parametric Analysis of the Kalina Cycle; ASME 89GT-218; American Society of Mechanical Engineers: New York, 1989. Mathias, P.; Copeman, T. Extension of the Peng-Robinson Equation of State to Complex Mixtures: Evaluation of Various Forms of the Local Composition Concept. Fluid Phase Equilib. 1983, 13, 91. Muller, G.; Bender, E.; Maurer, G. Das Dampf-Flussigkeitsgleichgewicht des ternaren Systems Ammoniak-KohlendioxideWasser bei hohen Wassergehalten im Bereich zwischen 373 un 473 Kelvin. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 148. Panagiotopolous, A.; Reid, R. In New Mixing Rule for Cubic Equations of State for Highly Polar Asymmetric Systems; Chao, K., Robinson, R., Eds.; ACS Symposium Series 300; American Chemical Society: Washington, D.C., 1986; p 571. Peng, D.; Robinson, D. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 59. Peng, D.; Robinson, D. Two- and Three-Phase Equilibrium Calculations for Coal Gasification and Related Processes; Newman, S. A., Ed.; ACS Symposium Series 133; American Chemical Society: Washington, D.C., 1980; p 393. Polak, J.; Lu, B. C.-Y. Vapor-Liquid Equilibria in System Ammonia-Water at 14.69 and 65 psia. J. Chem. Eng. Data 1975, 20, 182. Pruss, A.; Wagner, W. Eine neue Fundamentalgleichung fur das Zustandsgebeit von Wasser fur Temperaturen von der Schmelzlinie bis zu 1273 K bei Drucken bis zu 1000 MPa, FortschritteBerichte No. 320; VDI Verlag: Dusseldorf, Germany, 1995. Rackett, H. G. Equation of State for Saturated Liquids. J. Chem. Eng. Data 1972, 17, 514. Reid, R.; Prausnitz, J.; Poling, B. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. Reynolds, W. Thermodynamic Properties in SI; Graphs, Tables and Computational Equations for 40 Substances; Department of Mechanical Engineering, Stanford University: Palo Alto, CA, 1979. Rizvi, S.; Heidemann, R. Vapor-Liquid Equilibria in the Ammonia-Water System. J. Chem. Eng. Data 1987, 32, 183. Ruth, L. The U.S. Department of Energy’s Combustion 2000 Program: Clean, Efficient Electricity from Coal. International Symposium on Advanced Energy Conversion Systems and Related Technologies, Nagoya, Japan, 1995; Pergamon-Elsevier Science, Ltd.: Amsterdam, The Netherlands, 1995. Sassen, C.; van Kwartel, R.; van der Kool, H.; de Swaan Arons, J. Vapor-Liquid Equilibria for the System Ammonia + Water up to the Critical Region. J. Chem. Eng. Data 1990, 35, 140. Skogestad, S. Experience in Norsk Hydro with Cubic Equations of State. Fluid Phase Equilib. 1983, 13, 179. Smolen, T.; Manley, D.; Poling, B. Vapor-Liquid Equilibrium Data for the NH3-H2O System and Its Description with a Modified Cubic Equation of State. J. Chem. Eng. Data 1991, 36, 202. Spencer, C.; Danner, R. Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data 1972, 17, 236. Tillner-Roth, R.; Friend, D. Survey and Assessment of Available Measurements on Thermodynamic Properties of the Mixture {Water + Ammonia}. Preprint; Institut fut Thermodynamik, Universitat Hannover, Hannover, Germany, 1997a. Tillner-Roth, R.; Friend, D. G. A Helmholtz Free Energy Formulation of the Thermodynamic Properties of the Mixture (Water + Ammonia). J. Phys. Chem. Ref. Data 1997b, submitted for publication. Tochigi, K.; Kurihara, K.; Satou, T.; Kojimi, K. Prediction of Phase Behavior for the Systems Containing Ammonia Using PRASOG. Proceedings of the 4th International Symposium on Supercritical Fluids, May 11-14, 1997, Sendai, Japan; 1997. Vidal, J. Equations of State-Reworking the Old Forms. Fluid Phase Equilib. 1983, 13, 15. Wilson, T. A. The Total and Partial Vapor Pressure of Aqueous Ammonia. Bull.sIll., Univ., Eng. Exp. Stn. 1925, 146. Ziegler, B.; Trepp, C. Equation of State for Ammonia-Water Mixtures. Int. J. Refrig. 1984, 7, 101.

Received for review September 10, 1997 Revised manuscript received December 30, 1997 Accepted January 5, 1998 IE970638S