1999 Xu and Goswami

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Energy 24 (1999) 525536 www.elsevier.com/locate/energy

Thermodynamic properties of ammoniawater mixtures forpower-cycle applications

Feng Xua, D. Yogi Goswamib,*

aDonlee Technologies, Inc., 693 North Hills Road, York, PA 17402, USA

bDepartment of Mechanical Engineering, University of Florida, Gainesville, FL 32611, USA

Received 28 July 1997

Abstract

Ammoniawater mixtures have been used as working fluids in absorptionrefrigeration cycles for severaldecades. Their use as multi-component working fluids for power cycles has been investigated recently.The thermodynamic properties required are known or may be calculated at elevated temperatures andpressures. We present a new method for these computations using Gibbs free energies and empirical equa-tions for bubble and dew point temperature to calculate phase equilibria. Comparisons of calculated and

experimental data show excellent agreement. 1999 Published by Elsevier Science Ltd. All rights reserved.

1. Background

Many studies have been published on vaporliquid equilibrium (VLE) and the thermodynamicproperties of ammoniawater mixtures, including ptxy data and caloric properties. For enthalpydata, see Refs. [13]. Ref. [4] published new values of enthalpy and entropy from 70 to 370F

and pressure up to 300 psia using experimental data from [2,3,5]. Ref. [6] created tables of VLEand caloric properties that were used by other researchers to propose computational models [79]. In Ref. [10], measured data from [11] were used to give correlations for pressures of 0.2 to110 bar and temperatures of 230 to 600 K. Refs. [1216] also presented models for calculatingthe thermodynamic data at elevated temperatures and pressures.

In the present study, a method that combines the Gibbs free energy method for mixture proper-ties and bubble and dew point temperature equations for phase equilibrium is used. This method

* Corresponding author. Fax: 1-352-392-1701; e-mail: [email protected]

0360-5442/99/$ - see front matter 1999 Published by Elsevier Science Ltd. All rights reserved.PII: S 0 3 6 0 - 5 4 4 2 ( 9 9 ) 0 0 0 0 7 - 9


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526 F. Xu, D.Y. Goswami/Energy 24 (1999) 525536

combines the advantages of the two and avoids the need for iterations for phase equilibrium bythe fugacity method.

2. Gibbs free energy equation for a pure component

The Gibbs free energy of a pure component is given by

G h0 Ts0 T

T0

Cp dT P

P0

v dP T

T

T0

(Cp/T) dT, (1)

where h0, s0, T0 and P0 are the specific enthalpy, specific entropy, temperature and pressure at

the reference state. Use of empirical relations for v and Cp [9] leads to the following equations.For the liquid phase:

GLr hLr,o Trs

Lr,o B1(Tr Tr,o) (B2/2)(T

2r T

2r,o) (B3/3)(T

3r T

3r,o)

B1Tr ln(Tr/Tr,o) B2Tr(Tr Tr,o) (B3/2)(T2r T

2r,o) (A1 A3Tr A4T

2r )(Pr (2)

Pr,o) (A2/2)(P2r P

2r,o).

For the gas phase:

Ggr hgr,o Trs

gr,o D1(Tr Tr,o) (D2/2)(T

2r T

2r,o) (D3/3)(T

3r T

3r,o)

D1Tr ln(Tr/Tr,o) D2Tr(Tr Tr,o) (D3/2)(T2r T

2r,o) Tr ln(Pr/Pr,o) C1(Pr (3)

Pr,o) C2(Pr/T3r 4Pr,o/T

3r,o 3Pr,oTr/T

4r,o) C3(Pr/T

11r 12Pr,o/T

11r,o

11Pr,oTr/T12r,o) (C4/3)(P

3r/T

11r 12P

3r,o/T

11r,o 11P

3r,oTr/T

12r,o).

Here, the superscripts are L for liquid and g for gas, while subscript o is for the ideal gas state.The reduced (subscript r) thermodynamic properties are Tr T/TB, Pr P/PB, Gr G/RTB, hr h/RTB, sr s/R and vr vPB/RTB. The reference values for the reduced properties are R 8.314 kJ/kmol K, TB 100 K and PB 10 bar. The constants in Eqs. (2) and (3) are given inTable 1.

3. Thermodynamic properties of a pure component

The molar specific enthalpy, entropy and volume are related to Gibbs free energy, in terms ofreduced variables, by

h RTBT2r

Tr(Gr/Tr)

Pr

, (4)


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527F. Xu, D.Y. Goswami/Energy 24 (1999) 525536

Table 1Coefficients of Eqs. (2) and (3)

Coefficient Ammonia Water

A1 3.971423 102 2.748796 102

A2 1.790557 105

1.016665 105

A3 1.308905 102

4.452025 103

A4 3.752836 103 8.389246 104

B1 1.634519 10+1 1.214557 10+1

B2 6.508119 1.898065

B3 1.448937 2.911966 102

C1 1.049377 102 2.136131 102

C2 8.288224 3.169291 10+1

C3 6.647257 10+2

4.634611 10+4

C4 3.045352 10+3 0.0

D1 3.673647 4.019170D2 9.989629 10

2 5.175550 102

D3 3.617622 102 1.951939 102

hLr,o 4.878573 21.821141hgr,o 26.468873 60.965058sLr,o 1.644773 5.733498

sgr,o 8.339026 13.453430Tr,o 3.2252 5.0705Pr,o 2.000 3.000

s RGr

Tr Pr(5)

and

v RTB

PB GrPr Tr

. (6)

4. Ammoniawater liquid mixtures

The Gibbs excess energy for liquid mixtures allows for deviation from ideal solution behavior.The Gibbs excess energy of a liquid mixture is expressed by the relationship proposed in [9],which is limited to three terms and is given by:

GEr [F1 F2(2x 1) F3(2x 1)2](1 x), (7)

where x is the ammonia mass fraction

F1 E1 E2Pr (E3 E4Pr)Tr E5/T4 E6/T2r ,


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F2 E4 E8P4 (E9 E10Pr)Tr E11/Tr E12/T2r

and

F3 E13 E14Pr E15/Tr E16/T2r

The constants for Eq. (7) are given in Table 2.The excess enthalpy, entropy and volume for the liquid mixtures are given as:

hE RTBT2r

Tr(GEr/Tr)

Pr, x

, (8)

sE R GEr

Tr Pr, x(9)

and

vE RTB

PB GEr

Pr Tr, x. (10)

In addition, the enthalpy, entropy and volume of a liquid mixture are given by:

hLm xfhLa (1 xf)h

Lw h

E, (11)

sLm xfsLa (1 xf)s

Lw s

E smix, (12)

smix R[xf ln(xf) (1 xf) ln(1 xf)] (13)

and

vLm xfvLa (1 xf)v

Lw v

E, (14)

Table 2Coefficients of Eq. (7)

E1 41.733398 E9 0.387983E2 0.02414 E10 0.004772E3 6.702285 E11 4.648107

E4 0.011475 E12 0.836376E5 63.608967 E13 3.553627E6 62.490768 E14 0.000904

E7 1.761064 E15 24.361723

E8 0.008626 E16 20.736547


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where subscripts a and w refer to ammonia and water, respectively and subscript f refers to thesaturated liquid condition.

5. Ammoniawater vapor mixture

Ammoniawater vapor mixtures are often assumed to be ideal solutions. The enthalpy, entropyand volume of the vapor mixture are computed by:

hgm xghga (1 xg)h

gw, (15)

sgm xgsga (1 xg)s

gw s

mix (16)

and

vgm xgvga (1 xg)v

gw. (17)

6. Vaporliquid equilibrium

At equilibrium, binary mixtures must have the same temperature and pressure. Moreover, thepartial fugacity of each component in the liquid and gas mixtures must be equal:

fLa fga, (18)

fLw fgw, (19)

where f is the fugacity of each component in the mixture at equilibrium. The fugacities ofammonia and water in liquid mixtures are given by [17]:

fLa af0axa (20)

and

fLw wf0w(1 x)w, (21)

where is the activity coefficient, f0 is the standard-state fugacity of the pure liquid componentcorrected to zero pressure, is the Poynting correction factor from zero pressure to saturationpressure of the mixture and x is the ammonia mass fraction in liquid phase.

Assuming an ideal mixture in the vapor phase, the fugacities of the pure components in thevapor mixtures are given by

fga aPy (22)

and


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fgw wP(1 y), (23)

where is the fugacity coefficient and y is the ammonia mass fraction in vapour phase.

Eqs. (18) and (19) are used to calculate the boiling and dew point temperatures given thepressure and ammonia concentration in the liquid mixture. However, these two equations mustbe solved iteratively to produce the VLE properties of ammoniawater mixtures. Alternatively,the bubble and dew point temperatures can be calculated using the explicit equations developedin Ref. [14].

7. Bubble point and dew point temperature equations

Eqs. (24) and (25), developed in [14], determine the start and end of the mixture phase change

and compute the mass fractions of ammonia and water in the liquid and vapor phases, respectively.This avoids the complicated method of calculating the fugacity coefficient of a component in amixture to determine the bubble (Tb) and dew point (Td) temperatures.

Tb Tc 7

i 1

(Ci 10

j 1

Cijxj)[ln(Pc/P)]

i (24)

and

Td Tc 6

i 1

(ai 4

j 1

Aij[ln(1.0001 x)]j[ln(Pc/P)])

i, (25)

where

Tc Tcw 4

i 1

aixi, (26)

Pc Pcw exp(8

i 1

bixj), (27)

P in psia and T in

F.

8. Results

In this study, the Gibbs free energy method is used to calculate the properties of pure ammoniaand water [Eqs. (2)(6)]. The properties of the ammoniawater mixture are also calculated fromthe Gibbs free energy method using Eqs. (7)(17). In order to determine the phase quilibrium,bubble and dew points are calculated using the alternative method of Eqs. (24)(27) instead ofthe conventional method of equating the fugacities [Eqs. (18)(23)]. Using the alternative method


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avoids the iterative solution necessary to solve Eqs. (18)(23), thereby reducing the compu-tational time.

The property data generated in this study have been compared with available experimental andtheoretical data in the literature.

9. Comparison of bubble and dew point temperatures

Fig. 1 shows that the bubble and dew point temperatures generated by this study comparefavorably with the data from Ref. [6]. The differences between our computed values and the dataare less than 0.3%. Refs. [9,10] are reported to have differences of up to 2% from these data.

10. Comparison of saturation pressure at constant temperature

Figs. 2 and 3 show the saturation pressures of ammoniawater mixtures as compared with thedata from Ref. [11].

For temperatures less than 406 K, the computational results fit the experimental data well,except at saturated liquid pressures. At higher temperatures, our computed values are within 5%of the data even at pressures higher than 110 bar, while Ref. [9] has reported a difference of morethan 15%. Ref. [10] reported an error of less than 5% under 110 bar and higher errors over 110 bar.

Fig. 1. Bubble and dew point temperatures at a pressure of 34.47 bar.


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Fig. 2. Saturation pressures of ammoniawater mixtures at 333.15 K.

Fig. 3. Saturation pressures of ammoniawater mixtures at 405.95 K.


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11. Comparison of saturated liquid and vapor enthalpy

1. Saturated liquid enthalpy. The saturated liquid enthalpy of this work is compared with thedata from Ref. [6], as shown in Fig. 4. The differences are less than 2% for all the data.

2. Saturated vapor enthalpy. The saturated vapor enthalpy at constant pressure is shown in Fig.5. The agreement with the data is within 3%. Ref. [10] reported a 5% maximum difference.

The mass fraction of ammonia vapor shown in this figure is the ammonia liquid mass fractionwhen the mixture reaches a saturated state. So, in order to compute the saturated vapor enthalpy,the ammonia vapor mass fraction must be determined first.

12. Comparison of saturated liquid and vapor entropy

The value of entropy is very important in predicting the performance of a turbine in a powercycle. Entropy data are also essential to the second-law analysis of thermal systems. Ref. [4]published saturated liquid and vapor entropy data based on experimental data from [2,3,5]. Ref.[16] published calculated entropy. The entropy data from the present study are compared withthe experimental data in Ref. [4] and the computational data of Ref. [16].

1. Saturated liquid entropy. Fig. 6 shows saturated liquid entropy data compared with those of

Fig. 4. Saturated liquid enthalpy of ammoniawater mixtures at 34.47 bar.


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Fig. 5. Saturated vapor enthalpy of ammoniawater mixtures at 34.47 bar.

Fig. 6. Entropy of saturated liquid at 310.9 K.


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Fig. 7. Entropy of saturated vapor at 310.9 K.

Ref. [4]. Our data agree with the experimental data of [4] much better than the data generatedby the method of Ref. [16].

2. Saturated vapor entropy. Fig. 7 shows an excellent agreement of our computed values ofsaturated vapor entropy with the data of Ref. [4]. Data computed by Ref. [16] are consistentlylower. Since it was very difficult to identify saturated vapor entropy data from Ref. [16], wedid not compare our results with them.

13. Conclusion

Different methods for calculating the properties of ammoniawater mixtures are studied. Apractical and accurate method is used in this study. This method uses Gibbs free energy equations

for pure ammonia and water properties, and empirical bubble and dew point temperature equationsfor vaporliquid equilibrium. The iterations necessary for calculating the bubble and dew pointtemperatures by the fugacity method are avoided. Therefore, this method is much faster thanusing the fugacity method. The computational results have been compared with accepted experi-mental data in the literature and show very good agreement.

References

[1] Jennings BH, Shannon FP. Refrig Eng 1938;44:333.[2] Zinner KZ, Gesamt Z. Kalte-Ind 1934;41:21.


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[3] Wucherer J, Gesamt Z. Kalte-Ind 1932;39:97.[4] Scatchard G, Epstein LF, Warburton J, Cody PJ. Refrig Eng 1947;53:413.[5] Perman EP. J Chem Soc 1901;79:718.

[6] Macriss RA, Eakine BE, Ellington RT, Huebler J. Research bulletin no 34. Chicago (IL): Chicago Institute ofGas Technology, 1964.

[7] Gupta CP, Sharma CP. ASME paper 75-WA/PID-2. New York (NY): ASME, 1975.[8] Schulz SCG. Proc XIIth Int Cong Refrig 1972;2:431.[9] Ziegler B, Trepp C. Int J Refrig 1984;7:101.

[10] Ibrahim OM, Klein SA. ASHRAE Trans 1993;99:1495.[11] Gillespie PC, Wilding WV, Wilson GM. AIChE Symp Ser 1987;83:97.[12] Kalina AI. ASME paper 83-JPGC-GT-3. New York (NY): ASME, 1983.[13] Herold KE, Han K, Moran MJ. ASME Proc 1988;4:65.[14] El-Sayed YM, Tribus M. ASME special publication AES 1. New York (NY): ASME, 1985:89.[15] Kalina AI, Tribus M, El-Sayed YM. ASME paper 86-WA/HT-54. New York (NY): ASME, 1986.[16] Park YM, Sonntag RE. ASHRAE Trans 1992;97:150.[17] Walas SM. Phase equilibria in chemical engineering. Stoneham (MD): Butterworths, 1985.

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1999 Xu and Goswami