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New correlation equations for ammonia-water Vapor-Liquid Equilibrium (VLE) thermodynamic properties.

INTRODUCTION

An ammonia-water mixture is used as a refrigerant in absorption refrigeration cycles and as the working fluid in modern power generation cycles, such as the Kalina cycle. The mixture has no environmental impact; i.e., it does not contribute to ozone depletion. The knowledge of thermodynamic properties of ammonia-water mixtures is essential for design, simulation, and performance analysis of absorption refrigeration systems.

The thermodynamic properties of ammonia-water systems have been determined by a number of researchers. The vapor-liquid equilibrium (VLE) has been of primary interest due to the requirements of the absorption cycle. Park and Sonntag (1990) used a generalized equation of state, based on a four-parameter corresponding-states principle, to determine the thermodynamic properties of the ammonia-water mixtures with pressure and temperature ranges up to 200 bar (2910 psia) and 377[degrees]C (710[degrees]F), respectively. The extension in pressure and temperature ranges was made over that considered by the Institute of Gas Technology (IGT) (Macrisis et al. 1964) to cover the operating ranges of pressure and temperature of power cycles. Ibrahim and Klein (1993) used separate equations of state for liquid and gas phases for pure ammonia and pure water. They assumed the mixture to behave as an ideal solution in the liquid phase, while Gibbs excess energy was used to allow a shift from ideal solution behavior in the gas phase. Their correlation covers VLE pressures and temperatures up to 110 bar (1595 psia) and 327[degrees]C (620[degrees]F), respectively. Patek and Klomfar (1995) constructed correlations describing VLE properties of ammonia-water mixtures by fitting experimental data using simple functional forms. Tillner-Roth and Friend (1998) presented a thermodynamic model incorporating a fundamental equation of state for the Helmholtz free energy of the ammonia-water mixture, covering the thermodynamic space between the solid-liquid-vapor boundary and the critical locus. Their model presented the VLE properties for pressures up to 400 bar (5800 psia).

CORRELATIONS

Most of the reported correlations for ammonia-water mixture thermodynamic properties used formulations with complicated mathematical structures, such as the Helmholtz free energy formulation and the Gibbs excess energy formulation (Tillner-Roth and Friend 1998). Such formulations cannot be readily used for simulation in industrial applications. Therefore, the aim of this study is to present the ammonia-water VLE thermodynamic properties in a simple polynomial form that is easy to use in all applications. Hence, the experimental data (Gillespie et al. 1987), as well as data by Ibrahim and Klein (1993), have been used to develop simple, easy-to-use thermodynamic property correlations.

The first correlation pertains to the saturation temperature of an ammonia-water mixture in the liquid state. The saturation temperature is explicitly presented as a function of ammonia liquid mass concentration and saturation pressure of the mixture. The polynomial form of the correlation is given as:

[T.sub.l] = A + [n.summation over (i = 1)] ([B.sub.i][x.sup.i]) + [n.summation over (i = 1)] ([C.sub.i][P.sup.i]) + x * [(n - 1).summation over (i = 1)]([D.sub.i][P.sup.i]) + [x.sup.2] * [(n - 1).summation over (i = 1)]([E.sub.i][P.sup.i]) + [x.sub.3] * [(n - 1).summation over (i = 1)]([F.sub.i][P.sup.i]) (1)

The second correlation pertains to the saturation temperature of an ammonia-water mixture in the vapor state. The saturation temperature is explicitly presented as a function of ammonia vapor mass concentration and saturation pressure of the mixture. The polynomial form of the correlation is given as:

[T.sub.v] = A + [n.summation over (i = 1)] ([B.sub.i][y.sup.i]) + [n.summation over (i = 1)] ([C.sub.i][P.sup.i]) + y * [(n - 1).summation over (i = 1)]([D.sub.i][P.sup.i]) + [y.sup.2] * [(n - 1).summation over (i = 1)]([E.sub.i][P.sup.i]) + [y.sub.3] * [(n - 1).summation over (i = 1)] ([F.sub.i][P.sup.i]) + [y.sub.4] [(n - 1).summation over (i = 1)]([G.sub.i][P.sup.i]) (2)

The third correlation pertains to the ammonia vapor mass concentration of an ammonia-water mixture. The ammonia vapor mass concentration is explicitly presented as a function of ammonia liquid mass concentration and saturation pressure of the mixture. The polynomial form of the correlation is given as:

y = A + [n.summation over (i = 1)]([B.sub.i][x.sup.i]) + [n.summation over (i = 1)]([C.sub.i][P.sup.i]) + x * [(n - 1).summation over (i = 1)]([D.sub.i][P.sup.i]) + [x.sup.2] * [(n - 1).summation over (i = 1)]([E.sub.i][P.sup.i]) + [x.sub.3] * [(n - 1).summation over (i = 1)] ([F.sub.i][P.sup.i]) (3)

The fourth correlation pertains to the saturation enthalpy of an ammonia-water mixture in the liquid state. The saturation enthalpy is explicitly presented as a function of ammonia liquid mass concentration and saturation pressure of the mixture. The polynomial form of the correlation is given as:

[h.sub.l] = A + [n.summation over (i = 1)]([B.sub.i][x.sup.i]) + [n.summation over (i = 1)] ([C.sub.i][P.sup.i]) + x * [(n - 1).summation over (i=1)]([D.sub.i][P.sup.i]) + [x.sup.2] * [(n - 1).summation over (i=1)]([E.sub.i][P.sup.i]) + [x.sub.3] * [(n - 1).summation over (i=1)]([F.sub.i][P.sup.i]) (4)

The fifth correlation pertains to the saturation enthalpy of an ammonia-water mixture in the vapor state. The saturation enthalpy is explicitly presented as a function of ammonia vapor mass concentration and saturation pressure of the mixture. The polynomial form of the correlation is given as:

[h.sub.v] = A + [n.summation over (i = 1)]([B.sub.i][y.sup.i]) + [n.summation over (i = 1)]([C.sub.i][P.sup.i]) + y * [(n - 1).summation over (i=1)]([D.sub.i][P.sup.i]) + [y.sup.2] * [(n - 1).summation over (i=1)]([E.sub.i][P.sup.i]) + [y.sub.3] * [(n - 1).summation over (i=1)]([F.sub.i][P.sup.i]) (5)

The sixth correlation pertains to the saturation entropy of an ammonia-water mixture in the liquid state. The saturation entropy is explicitly presented as a function of ammonia liquid mass concentration and saturation pressure of the mixture. The polynomial form of the correlation is given as:

[s.sub.l] = A + [n.summation over (i = 1)]([B.sub.i][x.sup.i]) + [n.summation over (i = 1)] ([C.sub.i][P.sup.i]) + x * [(n - 1).summation over (i=1)]([D.sub.i][P.sup.i]) + [x.sup.2] * [(n - 1).summation over (i=1)]([E.sub.i][P.sup.i]) + [x.sub.3] * [(n - 1).summation over (i=1)]([F.sub.i][P.sup.i]) (6)

The seventh correlation pertains to the saturation entropy of an ammonia-water mixture in the vapor state. The saturation entropy is explicitly presented as a function of ammonia vapor mass concentration and saturation pressure of the mixture. The polynomial form of the correlation is given as:

[s.sub.v] = A + [n.summation over (i = 1)]([B.sub.i][y.sup.i]) + [n.summation over (i = 1)] ([C.sub.i][P.sup.i]) + y * [(n - 1).summation over (i=1)]([D.sub.i][P.sup.i]) + [y.sup.2] * [(n - 1).summation over (i=1)]([E.sub.i][P.sup.i]) + [y.sub.3] * [(n - 1).summation over (i=1)] ([F.sub.i][P.sup.i]) + [y.sub.4] [(n - 1).summation over (i=1)]([G.sub.i][P.sup.i]) (7)

The correlations cover the complete range of mass concentration and saturation pressure of up to 100 bar (1450 psia) with correlation coefficients of greater than 0.99.

The coefficients pertaining to the study correlations are listed in Table 1.

Table 1. Coefficients for Present Study Correlations (Equations 1-7)

Correlation        n             A      [B.sub.1]    [B.sub.2]

1                       4       370.8        -272.3         93.74
2                       5       365.7        -127.3          1045
3                       4      0.1435         5.694        -12.33
4                       4       405.1         -1758        -166.9
5                       4        2651    -538.53167         -3617
6                       4       1.261         -2.21        -5.845
7                       5        7.48        -1.056         9.391

Correlation     [C.sub.1]   [C.sub.2]     [C.sub.3]     [C.sub.4]

1                   10.11     -0.2768   0.003686299   -0.00001785
2                   13.25     -0.5531       0.01268    -0.0001395
3            -0.001178057   0.0002992   -3.0203E-06    0.00000001
4                   44.06      -1.195   0.015999011    -0.0000779
5                   13.58     -0.4555   0.006558325   -0.00003351
6                  0.1162   -0.003638    0.00005275  -0.000000273
7                 -0.1369    0.006572    -0.0001601   0.000001833

Correlation     [D.sub.1]   [D.sub.2]     [D.sub.3]     [D.sub.4]

1                 -0.7369     0.05012    -0.0004538             -
2                  -3.711  0.07897612      0.001022   0.000005033
3                -0.01574  -0.0001743    0.00000197             -
4                      -4      0.3508     -0.002959             -
5                  -1.766    -0.01591   -0.00002691             -
6                 0.04415   -0.000176  -0.000000865             -
7                -0.01428   0.0006243  -0.000008639      4.38E-08

Correlation     [F.sub.1]   [F.sub.2]     [F.sub.3]     [F.sub.4]

1                   4.564    -0.06016      0.000141             -
2                  -17.53      0.2862   -0.00322449    0.00001503
3                -0.07766   0.0008663  -0.000004077             -
4                   12.76     0.04592     -0.001865             -
5                  -14.77      0.1091    -0.0009271             -
6                0.008434    0.000355  -0.000005891             -
7                 -0.1461    0.006177    -0.0000834   0.000000421

Correlation   [B.sub.3]   [B.sub.4]   [B.sub.5]

1                  99.21     -54.83            -
2                  -3733       5228        -2530
3                  10.53     -2.988            -
4                   2598      -1245            -
5                   6302      -3539            -
6                  10.58      -4.37            -
7                 -39.19      55.02        -26.3

Correlation    [C.sub.5]

1                      -
2            0.000000583
3                      -
4                      -
5                      -
6                      -
7              -7.89E-09

Correlation    [E.sub.1]  [E.sub.2]    [E.sub.3]     [E.sub.4]

1                 -5.851  0.0470549   0.00007047             -
2                  9.538    -0.1524     0.001717  -0.000007935
3                  0.101  -0.000863  0.000003258             -
4                 -15.94     -0.251     0.003846             -
5                   13.7   -0.06589    0.0007111             -
6               -0.03866  -0.000358   7.6646E-06             -
7             0.07947493  -0.003291   0.00004413  -0.000000221

Correlation    [G.sub.1]  [G.sub.2]    [G.sub.3]     [G.sub.4]

1                      -          -            -             -
2                    8.4    -0.1174     0.001222  -0.000005517
3                      -          -            -             -
4                      -          -            -             -
5                      -          -            -             -
6                      -          -            -             -
7                0.07477  -0.003363  0.000045612


RESULTS AND DISCUSSIONS

A comparison is carried out between the ammonia-water VLE thermodynamic properties determined using the developed correlations and the ones reported in the literature. A number of these properties have been determined for different ammonia mass concentrations. The properties determined include bubble-and dew-point temperatures, vapor pressure, equilibrium composition of the components, enthalpy, and entropy of the mixtures at saturation pressures.

Engineering Equation Solver (EES) is used to perform calculations and generate the comparison curves (Klein 2009). EES has an internal function to determine the properties of ammonia-water mixtures. This internal function is based on the correlations developed by Ibrahim and Klein (1993). Hence, EES implicitly uses the Ibrahim and Klein correlations in order to determine the thermodynamic properties of ammonia-water mixtures. The following equations reported by Patek and Klomfar (1995) are similarly used to determine the thermodynamic properties:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The data reported by Park and Sonntag (1990) and the data reported by Tillner-Roth and Friend (1998) have been entered into the look-up tables of EES to determine the required properties. Finally, after all the data were entered into EES, parametric tables were generated to compare the thermodynamic properties determined by different approaches. The final results are presented in graphical form in Figures 1-6.

The first comparative result pertains to the bubble-point (incipient boiling) temperature. Figure 1 shows a comparison of bubble-point temperatures of ammonia-water mixtures, determined using different correlations, plotted against ammonia liquid mass concentration at a pressure of 50 bar (725 psia). The figure indicates that the results obtained using different correlations are in good agreement with each other and with those from this study. The bubble-point temperatures, obtained using the correlation developed by Ibrahim and Klein (1993) and Tillner-Roth and Friend (1998), exhibit very close agreement with those obtained using the correlations developed by Park and Sonntag (1990) and Patek and Klomfar (1995). The maximum deviation observed between the values of bubble-point (incipient boiling) temperatures, obtained using the present correlation and those developed by Park and Sonntag (1990), are less than 3% in the range of 0.3 to 0.5 ammonia liquid mass concentrations.

The second comparative property is the dew-point temperature. Figure 2 shows a comparison of dew-point temperatures of ammonia-water mixtures plotted against ammonia vapor mass concentration at a pressure of 50 bar (725 psia). It is clear from the plot that all the results, with the exception of those by Tillner-Roth and Friend (1998), are in good agreement with each other. In other words, the dew-point temperatures of Ibrahim and Klein (1993), Park and Sonntag (1990), and Patek and Klomfar (1995) are in good agreement with those determined by the present correlation. However, the values by Tillner-Roth and Friend (1998) are slightly different from the others at low ammonia vapor mass concentrations. The average deviation between the dew-point temperatures of Tillner-Roth and Friend (1998) and others can be more than 3% for ammonia vapor mass concentration values less than 0.6.

The third comparative property is the liquid enthalpy. In thermodynamic analyses, usually the enthalpy difference is used rather than the absolute value of the enthalpy. Thus, one should be aware that values of enthalpies given in property tables and/or charts in different references might refer to different data (for zero enthalpy). Therefore, comparisons for enthalpies from different sources should be based on enthalpy changes rather than individual enthalpy values. Figure 3 shows a comparison of saturated liquid enthalpy change of ammonia-water mixtures with respect to the enthalpy at zero ammonia mass concentration and plotted against ammonia liquid mass concentration at a pressure of 50 bar (725 psia). The figure indicates that the results determined using the correlation from Park and Sonntag (1990) show the highest enthalpy change, whereas the results determined using correlations by Patek and Klomfar (1995) show the lowest enthalpy change. The result obtained using different correlations exhibits the same trend; i.e., an increase in the enthalpy change until the point of inflection and then a decrease in the enthalpy change afterwards. The negative values in the enthalpy change signify the fact that the enthalpy at zero ammonia mass concentration is higher than the data under consideration. The enthalpy change by Ibrahim and Klein (1993) is in good agreement with the results of the present study, with a deviation of less than 0.7%. Other enthalpy change results show greater deviations from both Ibrahim and Klein (1993) and those of the present work.

Figure 4 shows a comparison of saturated vapor enthalpy change of ammonia-water mixtures with respect to the enthalpy at zero ammonia mass concentration and plotted against ammonia vapor mass concentration at a pressure of 50 bar (725 psia). The figure indicates that the results by Ibrahim and Klein (1993), Park and Sonntag (1990), and Patek and Klomfar (1995) shows good agreement with the results of the present study. However, the values of enthalpy change determined using the Tillner-Roth and Friend (1998) correlation are less compared to the others' values. The average deviation between the enthalpy change values for saturated vapor mixtures determined by the present study, Ibrahim and Klein (1993), Park and Sonntag (1990), and Patek and Klomfar (1995) is less than 2%.

The fifth comparative property pertains to the saturated liquid entropy. It is similar to enthalpy in thermodynamic analysis in that usually the entropy difference is used rather than the absolute value of the entropy. Figure 5 shows a comparison of entropy change of saturated liquid ammonia-water mixtures with respect to the entropy at zero ammonia mass concentration and plotted against ammonia liquid mass concentration at a pressure of 50 bar (725 psia). The figure indicates that the results obtained using the Park and Sonntag (1990) correlation show the highest entropy change values, whereas the results obtained using the Tillner-Roth and Friend (1998) correlation show the lowest value of entropy change. The point of inflection occurs at around 0.75 ammonia liquid mass concentration for the properties, using the correlations from Ibrahim and Klein (1993) and Park and Sonntag (1990). However, it occurs at around 0.6 ammonia liquid mass concentration for the value obtained using the Tillner-Roth and Friend (1998) correlations. The negative values in the entropy change signify that the entropy at zero ammonia mass concentration is higher than the data under consideration. In general, the entropy change obtained using that of Ibrahim and Klein's data (1993) is lower than that of Park and Sonntag (1990). However, at the saturation lines (i.e., at pure water and pure ammonia), the values of entropy change are identical for both.

Figure 6 shows a comparison of entropy change of saturated vapor ammonia-water mixtures with respect to the entropy at zero ammonia mass concentration and plotted against ammonia vapor mass concentration at a pressure of 50 bar (725 psia). The figure indicates that the results by Ibrahim and Klein (1993) and Park and Sonntag (1990) show good agreement with the present study's correlation. However, the results of entropy change obtained using the correlation developed by Tillner-Roth and Friend (1998) are less compared to the other values. The average deviation between the entropy change data for saturated vapor mixtures obtained by the present study, Ibrahim and Klein (1993), and Park and Sonntag (1990) is less than 5%.

CONCLUSIONS

A set of seven polynomial forms of correlations that are simple, easy to use, and explicitly defined and that best describe the thermodynamic VLE properties of ammonia-water mixture has been developed based on experimental data. These correlations give results that are in excellent agreement with the results obtained using the correlations from Ibrahim and Klein (1993).

NOMENCLATURE

[h.sub.i] = saturation enthalpy of ammonia-water solution in liquid state, KJ/kg

[h.sub.v] = saturation enthalpy of ammonia-water solution in vapor state, KJ/kg

P = saturation pressure of ammonia-water solution, bar (psia)

[S.sub.l] = saturation entropy of ammonia-water solution in liquid state, KJ/kg * K

[S.sub.v] = saturation entropy of ammonia-water solution in vapor state, KJ/kg * K

[T.sub.l] = saturation temperature of ammonia-water solution in liquid state, K

[T.sub.v] = saturation temperature of ammonia-water solution in vapor state, K

x = mass concentration of ammonia in liquid state

y = mass concentration of ammonia in vapor state

ACKNOWLEDGEMENT

The authors would like to acknowledge the support of both King Abdulaziz City for Science and Technology (KACST) through NSTIP project number 08-ENE56-4 and King Fahd University of Petroleum and Minerals in conducting this study.

REFERENCES

Klein, S.A. 2009. Engineering Equation Solver. Academic Professional version 8.427-3D. Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI.

Gillespie, P.C., W.V. Wilding, and G.M. Wilson. 1987. Vapor-liquid equilibrium measurements on the ammonia-water system from 313K to 589K. AIChE Symposium Series 83:256.

Ibrahim, O.M., and S.A. Klein. 1993. Thermodynamic properties of ammonia-water mixtures. ASHRAE Transactions 99(1):1495.

Macrisis, R.A., B.E. Eakin, R.T. Ellington, and J. Huebler. 1964. Physical and thermodynamic properties of ammonia-water mixtures. Research Bulletin 34, Institute of Gas Technology-Chicago, IL.

Park, Y.M., and R.E. Sonntag. 1990. Thermodynamic properties of ammonia-water mixtures: A generalized equation-of-state approach. ASHRAE Transactions 97(1):150.

Patek, J., and J. Klomfar. 1995. Simple functions for fast calculations of selected thermodynamic properties of the ammonia-water system. International Journal of Refrigeration 18(4):228.

Tillner-Roth, R., and D.G. Friend. 1998. Survey and assessment of available measurements on thermodynamic properties of the mixture (water-ammonia). J.Phys.Chem. Ref Data 27(1):45.

M.A.I. El-Shaarawi, PhD

S.A.M. Said, PhD

M.U. Siddiqui

M.A.I. El-Shaarawi and S.A.M. Said are professors and M.U. Siddiqui is a master's student in the Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.
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Title Annotation:DA-13-025
Author:El-Shaarawi, M.A.I.; Said, S.A.M.; Siddiqui, M.U.
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:7SAUD
Date:Jan 1, 2013
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