A Helmholtz free energy equation of state for the NH3–H2O fluid mixture: Correlation of the PVTx and vapor–liquid phase equilibrium properties

Accepted Manuscript Title: A Helmholtz free energy equation of state for the NH3 -H2 O fluid mixture: Correlation of the PVTx and vapor-liquid phase equilibrium properties Author: Shide Mao Jun Deng Mengxin L¨u PII: DOI: Reference:

S0378-3812(15)00092-8 http://dx.doi.org/doi:10.1016/j.fluid.2015.02.024 FLUID 10460

To appear in:

Fluid Phase Equilibria

Received date: Revised date: Accepted date:

17-11-2014 10-2-2015 16-2-2015

Please cite this article as: Shide Mao, Jun Deng, Mengxin L¨u, A Helmholtz free energy equation of state for the NH3-H2O fluid mixture: Correlation of the PVTx and vapor-liquid phase equilibrium properties, Fluid Phase Equilibria http://dx.doi.org/10.1016/j.fluid.2015.02.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A Helmholtz free energy equation of state for the NH3-H2O fluid mixture: Correlation of the PVTx and vapor-liquid phase equilibrium properties

Shide Mao*, Jun Deng, Mengxin Lü

State Key Laboratory of Geological Processes and Mineral Resources, and School of Earth Sciences and Resources, China University of Geosciences, Beijing, 100083, China

*

The corresponding author: ([email protected])

Highlights

► A Helmholtz free energy EOS is developed for the NH3-H2O fluid mixtures ► A

simple generalized departure function is used in the new EOS ► The EOS can predict both PVTx and VL phase equilibrium properties of NH3-H2O mixture ► Volume and phase equilibrium composition can be calculated by an iterative algorithm Abstract

An equation of state (EOS) explicit in Helmholtz free energy was developed to

calculate the PVTx and vapor-liquid phase equilibrium properties of the NH3-H2O fluid mixture. This EOS, where four mixing parameters are used, is based on highly accurate EOSs for the pure components (H2O and NH3) that NIST recommends and contains a simple generalized departure function presented by Lemmon and Jacobsen (1999). Comparison with thousands of reliable experimental data available indicates that the EOS can calculate both vapor-liquid phase equilibrium and volumetric properties of this binary fluid system, within or close to experimental uncertainties up to 706 K and 2000 bar over all composition range. The average absolute deviation is 0.68% in molar volume, and the average composition error of vapor phase and that of liquid phase except for those at the near-critical region are in general less than 0.03 and 0.07 in mole fraction, respectively.

Keywords: NH3-H2O, fluid mixture, equation of state, PVTx, phase equilibria

1. Introduction The NH3-H2O mixture is an important working fluid in the Kalina cycle [1] and the geothermal energy conversion processes [2]. Accurate knowledge of the thermodynamic properties, especially the PVTx and vapor-liquid equilibrium (VLE) properties, of this mixture over a wide temperature-pressure-composition range is needed. These properties are usually obtained from equations of state (EOSs) or thermodynamic models. During the past three decades, a large number of empirical, semi-empirical and theoretical equations or models have been published for modeling PVTx and VLE of

the NH3-H2O system. They can be classified into six groups: cubic EOSs [3-11], virial EOSs [12, 13], Gibbs excess energy models [14-16], Helmoltz free energy models [17-21], Leung-Griffiths model [22], and polynomial functions [23, 24]. Tillner-Roth and Friend [17] reviewed some EOSs and models before 1998, and Kherris et al. [14] reviewed in detail most of the EOSs and models up to 2013, where strength and weakness of each model was pointed out. In addition, Kherris et al. [14] presented a model in form of Gibbs free energy to calculate thermodynamic properties of the NH3-H2O system, which is valid up to 600 K and 110 bar. In 2014, Grandjean et al. [19] modeled the phase equilibria of the NH3-H2O system by the GC-PPC-SAFT EOS, but average absolute deviation of the saturated liquid volume of pure NH3 is about 2.7%. Among these equations or models, the widely used EOS is that of Tillner-Roth and Friend [17], which is in form of Helmoltz free energy based on the fundamental equations of the pure fluids [25, 26]. In the EOS of Tillner-Roth and Friend, additional terms are adopted to represent the property changes of mixing, where the mixing parameters were fitted from the experimental data to 1995 evaluated carefully by Tillner-Roth and Friend [27]. This EOS can calculate various thermodynamic properties of NH3-H2O fluid mixture of all compositions up to 623 K and 400 bar with or close to experimental accuracy. However, since 1995 more experimental PVTx data covering a larger temperature-pressure-composition (P-T-x) range have been published [28-37], and molar volumes calculated from the EOS of Tillner-Roth and Friend [17] deviate from the experimental data in some P-T-x regions, which leads to the motivation of this study.

At the end of last century, Lemmon and Jacobsen [38] established a generalized EOS explicit in Helmholtz free energy to represent the thermodynamic properties of mixtures containing CH4, C2H6, C3H8, n-C4H10, i-C4H10, C2H4, N2, Ar, O2 and CO2 within the uncertainty of experimental data. It contains a simple generalized departure function, and EOSs of pure fluids are from those NIST recommends. Although the generalized departure function in that model does not include H2O and NH3 in the optimization process, we found that it is also valid for the strong polar NH3-H2O mixture. Therefore, in this work, the generalized method of Lemmon and Jacobsen [38] is extended to calculate the PVTx and VLE properties of NH3-H2O mixture based on the highly accurate EOSs of pure H2O and NH3 [25, 26].

2. An equation of state explicit in Helmholtz free energy The EOS of NH3-H2O fluid mixture is in terms of dimensionless Helmholtz free energy α , defined as

α= where

A RT A

(1) is molar Helmholtz free energy,

R

is molar gas constant

( 8.314472 J ⋅ mol −1 ⋅ K −1 ), and T is temperature in K. The dimensionless Helmholtz free energy α of the mixture is represented by

α = α mid + α E

(2)

where α mid is the dimensionless Helmholtz free energy of an ideal mixture and α E is the excess dimensionless Helmholtz free energy. α mid comes directly from the fundamental equations of pure fluids and can be written as

2

α mid = α m0 (δ ,τ , x) + ∑ xiα ir (δ ,τ ) i =1

2

(3)

2

= ∑ xi α (δ ,τ ) + ln( xi )  + ∑ xiα (δ ,τ ) i =1

0 i

i =1

r i

where α m0 is the ideal-gas part of dimensionless Helmholtz free energy of the mixture, α i0 and α ir are the ideal-gas part and residual part of dimensionless Helmholtz free energy of component i, respectively, xi is the mole fraction of the component i. The superscripts “id”, “0” and “r” denote ideal mixing, the ideal-gas part and residual part of dimensionless Helmholtz free energy, respectively. The subscripts “i" and “m” denote the component and mixture, respectively. Here subscripts 1 and 2 refer to NH3 and H2O, respectively, so does the following equations. δ and τ are reduced parameters, which are defined by

δ=

ρ ρc

(4)

τ=

Tc T

(5)

where ρ is the density of mixture, and ρ c and Tc are defined as  2 x  ρ c =  ∑ i + x1 x2ζ 12   i =1 ρ ci 

−1

(6)

2

Tc = ∑ xiTci + x1β12 x2ς 12

(7)

i =1

where ρci and Tci are the critical density and critical temperature of the component i, respectively, x1 and x2 denote mole fraction of components 1 and 2, and ζ 12 ,

ς12 , and β12 are the mixture-dependent binary parameters associated with components 1 and 2 (NH3 and H2O). The α E in Eq. (2) is given by

10

α E = x1 x2 F12 ∑ N kδ d τ t k

k

(8)

k =1

where N k , d k and t k are general parameters independent of fluids, which can be found from the model of Lemmon and Jacobsen [38] (Table 1), F12 is a binary parameter of components 1 and 2.

The residual part of dimensionless Helmholtz free energy of NH3-H2O fluid mixture α r is defined by 2

α r = ∑ xiα ir (δ ,τ ) + α E (δ ,τ , x)

(9)

i =1

Values of the binary parameters ( ζ 12 , ς 12 , β12 and F12 ) in above equations for the NH3-H2O mixture are determined by a regression to experimental PVTx and VLE data. In this article, EOSs of pure NH3 and H2O fluids are from the references [25, 26]. These EOSs are all explicit in dimensionless Helmholtz energy and are considered to be the most accurate equations of the two pure fluids. Critical parameters of the pure NH3 and H2O are listed in Table 2.

3. Data review The PVTx and VLE data of NH3-H2O fluid mixture have been reported by many studies. Tillner-Roth and Friend [27] surveyed and assessed the experimental thermodynamic data till 1995. Over fifty data sets have been found up to 1995, and details can be found in Table 1 of the reference [27]. Among these data, the reliable

PVTx and VLE data of NH3-H2O fluid mixture are from the references [8, 13, 39-42], with the experimental temperature and pressure up to 618 K and 380 bar. Since 1995, quite a few experimental studies have been done for the PVTx and VLE properties of NH3-H2O fluid mixture [28-37]. Polikhronidi et al. [37] measured the PVTx properties of NH3-H2O mixture (0.2607 mole fraction of NH3) in the nearand supercritical regions up to 634 K and 280 bar, but their data are inconsistent with other experimental data. If these data are added in the parameterization, big deviations will yield. Sakabe et al. [36] made experimental measurements of the critical parameters of NH3-H2O mixture with 0.9098, 0.7757 and 0.6808 mole fraction of NH3, and their data were used in the comparisons. The PVTx data of Magee and Kagawa [35] with high content of NH3 are inconsistent with other experimental data although data of low content of NH3 are of high quality. All their data are not used in the parameterization. The PVTx data [28-34] after 1995 are reliable. Therefore, these reliable PVTx and VLE data [8, 13, 28-34, 39-42] but those [35-37] were used to optimize binary parameters of the EOS, where the highest temperature and pressure of data are 706 K and 2000 bar.

4. Parameterization and calculation method As mentioned above, the values of ζ 12 , ς 12 , β12 and F12 for the NH3-H2O EOS are determined by a non-linear regression to experimental PVTx and VLE data, where objective function is defined as the sum of relative deviation of molar volume and fugacity difference of each component between vapor and liquid phases.

Regressed parameters are listed in Table 3. The molar volume or density of the NH3-H2O mixture can be calculated from Eq. (10) with the Newton iterative method. P = ρ RT 1 + δα δr 

(10)

where P is pressure, and α δr is the derivative of α r with respect to δ . If the mixture is in vapor or supercritical state, the initial density of mixture can be set equal to that of ideal gas. If the mixture is in liquid state, the initial density can be set as the saturated liquid density of pure water at temperature above 273.16 K, below which the saturated liquid density of pure NH3 can be set as the initial density.

Note: subscripts 1 and 2 refer to NH3 and H2O, respectively.

Fugacity and fugacity coefficient of the component i (NH3 or H2O) can be calculated from the following equations:

 ∂nα r  f i = xi ρ RT exp    ∂ni T ,V ,nj

(11)

 ∂nα r  ln ϕi =  − ln(1 + δαδr )   ∂ni T ,V ,nj

(12)

 ∂nα r   ∂α r  r = α + n     ∂ni T ,V ,nj  ∂ni T ,V , nj  ∂α r  n = δαδr  ∂ n  i T ,V , nj

 1 − 1  ρc 

+ τ ατr

1 Tc

 ∂ρ  2  ∂ρ     c  − ∑ xk  c     ∂xi  x j k =1  ∂xk  x j    

 ∂T  2  ∂T    c  − ∑ xk  c    ∂xi  xj k =1  ∂xk  x j    2

+ α − ∑ xkα xrk r xi

k =1

(13)

(14)

where f i is the fugacity of component NH3 or H2O, n is the total mole numbers,

V is the total volume, ni is the mole number of component i, n j is the mole number of component j and signifies that all mole numbers are held constant except ni , ϕi is the fugacity coefficient of component i, and ατr , α xri and α xrk are the derivatives of α r with respect to τ , xi and xk , respectively. VLE compositions at a given temperature ( T ) and pressure ( P ) can be calculated using the iterative algorithm of Michelsen [43]. Assume that the total mole number of NH3-H2O mixture is 1, bulk composition of component i is M i , mole number of vapor phase is N V , and vapor and liquid compositions of component i are xi and yi , then xi and yi at a given T and P can be calculated from the following steps: Step 1: Give a group of initial reasonable guess values (between 0 and 1) for M i , xi and yi . Step 2: First calculate the vapor and liquid densities form Eq. (10), then calculate the fugacity coefficient of component i in vapor phase ( ϕ iV ) and liquid phase ( ϕiL ) from Eq. (12). Step 3: Define an equilibrium factor ki =

yi ϕiL = , then calculate ki from ϕ iV and xi ϕiV

ϕiL . 2

Step 4: Calculate N V from the normalized equation

∑M i =1

Step

5:

Calculate

xi

and

yi

from

equations

i

ki − 1 = 0. 1 − N V + N V ki xi =

Mi 1 − N + N V ki V

and

yi =

ki M i , respectively. 1 − N V + N V ki

Step 6: Go to Step 2, and recalculate ϕ iV , ϕiL , ki , N V , xi and yi in turn until the calculated N V keeps unchangeable. Then xi and yi are the VLE compositions. It should be noted that when T and P approach the critical point, the initial values for xi and yi lie in a narrow range, which are frequently set by experience. Critical parameters (temperature, pressure and density) of the NH3-H2O fluid mixture of a certain composition can be obtained from this EOS. At the critical point, compositions in both vapor and liquid phases are identical for each component. Therefore, the aforementioned iterative algorithm of Michelsen [43] can also be used to calculate the critical parameters: At a given T , modify P to calculate compositions in vapor and liquid phases at the condition that T , P and fugacity of each component in vapor and liquid phases are the same. If the calculated phase compositions of each component approach to the same values, then the temperature, pressure and density can represent the critical temperature, critical pressure and critical density, respectively.

5. Results and discussions Once temperature, pressure and composition of the NH3-H2O fluid mixture are given, the corresponding volumetric properties can be calculated from Eq. (10) with the Newton iterative method. Table 4 gives the average and maximum absolute volume deviations of the EOS from each data set. Fig. 1 shows the deviations between experimental and calculated molar volumes of the NH3-H2O system. The average

absolute volume deviation of this EOS is about 0.68% over the whole P-T-x range, and maximal volume deviation is within 3%, which is close to experimental uncertainties. Fig. 2 compares the calculated molar volumes with experimental data of Muromachi et al. [29] measured at high pressures, and good agreement can be seen. Deviations of this EOS and that of Tillner-Roth and Friend [17] from the high-pressure PVTx data of Muromachi et al. [29] are shown in Fig. 3, where the average and maximal volume deviations calculated from the EOS of Tillner-Roth and Friend are 0.64% and 2.69%, respectively.

Nd: number of data points;

AAD = 100 (Vcal − Vexp ) / Vexp

, where

Vcal

and

Vexp

are the calculated

and experimental molar volumes, respectively; MAD: maximal absolute volume deviations between this EOS and experimental data.

4 Exp. Munakata et al. (2002) Number of data points = 633

100(Vcal-Vexp)/Vexp

2

0

-2

-4 300 a

330

360 T (K)

390

420

4 Exp. Holcomb and Outcalt (1999) Number of data points = 28

100(Vcal-Vexp)/Vexp

2

0

-2

-4 260

280

300

320

340

360

380

400

T (K)

b

4 Exp. Muromachi et al. (2008) Number of data points = 218

100(Vcal-Vexp)/Vexp

2

0

-2

-4 0

500

1000

1500

2000

P (bar)

c

4 Exp. Hnedkovsky et al. (1996) Number of data points = 135

100(Vcal-Vexp)/Vexp

2

0

-2

-4 300

400

d

500

600

700

T (K)

4

100(Vcal-Vexp)/Vexp

2

Exp. Ellerwald (1981) Number of data points = 228

0

-2

-4 300 e

350

400 T (K)

450

500

4 Exp. Harms-Watzenberg (1995) Number of data points = 1483

100(Vcal-Vexp)/Vexp

2

0

-2

-4 0.0

0.2

0.4

0.6

0.8

1.0

xNH

f

3

Fig. 1: Volume deviations of this EOS from experimental data of NH3-H2O fluid mixture: Vcal and Vexp denote the calculated molar volume and experimental volume, respectively. 30 Exp. Muromachi et al. (2008) This model

26

x

-1

Vm(cm ⋅ mol )

28

NH

3

= 0.1

3

24

048

0.204 6

22 0.3807

20 18

0.5565

T = 450 K

500

1000

a

1500

2000

P (bar)

50 Exp. Muromachi et al. (2008) This model

40

-1

Vm(cm ⋅ mol )

45

35

x

3

NH

3

= 0.7

008

30 0.8010 0.9102 1.0000

25 T = 450 K

20 400 b

800

1200 P (bar)

1600

2000

36 Exp. Muromachi et al. (2008) This model

-1

Vm(cm ⋅ mol )

32

28

x

NH

3

3

= 0.1 048 0.204

24

6

0.3807

20

0.5565

T = 500 K

500

1000

1500

2000

P (bar)

c

52 Exp. Muromachi et al. (2008) This model

48

3

-1

Vm(cm ⋅ mol )

44 40 36

x

NH

3

= 0.7

32

008

0.8010 0.9102 1.0000

28 T = 500 K

24 400

800

1200

1600

2000

P (bar)

d

Fig. 2: The calculated molar volumes and experimental data as a function of pressure: Vm is molar volume and P is pressure.

3.0

3.0

100(Vcal-Vexp)/Vexp

Exp. Muromachi et al. (2008)

1.5

1.5

0.0

0.0

-1.5

-1.5 Tillner-Roth and Friend (1998)

This model

-3.0 0.0

-3.0 0.2

0.4

0.6

0.8

1.0 0.0

XNH

3

0.2

0.4

0.6

0.8

1.0

XNH

3

Fig.3: Volume deviations from experimental high-pressure data (Muromachi et al., 2008) of NH3-H2O fluid mixture: Vcal and Vexp denote the calculated molar volume and experimental volume, respectively.

VLE compositions can also be obtained from the EOS following calculation steps described in Section 4. Fig. 4 compares the phase equilibrium compositions calculated from this EOS with the experimental data [13, 33, 40, 42]. The average deviation of vapor and liquid phase compositions from Polak and Lu [40], Holcomb and Outcalt [33], Harms-Watzenberg [13] and Sassen et al. [42] is about 0.01, 0.03, 0.05 and 0.04, respectively. The average composition error of vapor phase and that of liquid phase except for those at the near-critical region are in general less than 0.03 and 0.07 in mole fraction, which are close to experimental uncertainties. Rizvi and Heldemann [41] reported the extensive VLE data for the NH3-H2O system, and their data are compared with calculations of this EOS and that of Tillner-Roth and Friend [17] (Fig. 5). From Fig. 5a, it can be seen that the VLE compositions at middle to high temperatures calculated from the two EOSs are of about the same precisions. Fig. 5b shows that the liquid-phase compositions at low temperatures calculated from the EOS of Tillner-Roth and Friend are more accurate than those of this EOS, but the vapor-phase compositions calculated from this EOS are better than those of the EOS of Tillner-Roth and Friend.

0.2 Polak and Lu (1975)

3

xNH ,cal-xNH ,exp

0.1

3

0.0

-0.1

-0.2 360 a

380

400 T (K)

420

440

0.2

Holcomb and Outcalt (1999)

3

xNH ,cal-xNH ,exp

0.1

3

0.0

-0.1

-0.2 300

320

340

360

380

T (K)

b

0.2 Harms-Watzenberg (1995)

3

xNH ,cal-xNH ,exp

0.1

3

0.0

-0.1

-0.2 300

350

400

450

500

T (K)

c

0.2 Sassen et al. (1990)

3

xNH ,cal-xNH ,exp

0.1

3

0.0

-0.1

-0.2 350 d

400

450

500

550

600

T (K)

Fig. 4: Deviations between calculated mole fractions of NH3 and experimental values: T is temperature, P is pressure, X NH3 is mole fraction of NH3, and X NH3cal and X NH3 exp are the calculated and experimental mole fraction of NH3, respectively.

250

This model Tillner-Roth and Friend (1998) Rizvi and Heidemann (1987) 610.2 K 579.7 K 526.2 K

200 P (bar)

451.5 K

150 100 50 0 0.0

0.2

0.4

0.6

0.8

xNH

a

3

120 100

1.0

411.9 K Rizvi and Heidemann (1987) This model Tillner-Roth and Friend (1998)

P (bar)

80 60 359.7K

40 20 0 0.0

305.6 K

0.2

b

0.4

0.6

0.8

1.0

xNH

3

Fig. 5: Vapor-liquid phase equilibria of NH3-H2O fluid mixture: P is pressure and X NH3 is mole fraction of NH3.

Critical parameters (temperature, pressure and density) of the NH3-H2O fluid mixture can be obtained from this EOS. The critical temperature, pressure and density calculated from this EOS as a function of mole fraction of NH3 are shown in Fig. 6, where calculations of the EOS of Tillner-Roth and Friend are also added for comparison. It can be seen that both the critical temperatures calculated from this EOS and that of Tillner-Roth and Friend are in good agreement with the experimental data [36, 41, 42]. The critical pressures calculated from this EOS are in agreement with the data of Rizvi and Heldemann [41] but deviate largely from the data of Sakabe et al. [36] and Sassen et al. [42], whereas calculations of the EOS of Tillner-Roth and Friend are on the contrary. The critical densities calculated from this EOS decrease with increasing composition at the beginning then increase slowly with increasing composition, and decrease rapidly with increasing composition at last. So does the EOS of Tillner-Roth and Friend. The critical densities calculated from this EOS show more than 10% deviations from three experimental data points of Sakabe et al. [36].

700

This model Tillner-Roth and Friend (1998) Rizvi and Heidemann (1987) Sassen et al. (1990) Sakabe et al. (2008)

650

Tc (K)

600 550 500 450 400 0.0 a

0.2

0.4

0.6 xNH

3

0.8

1.0

260 240

Pc (bar)

220 200 180 160 140 120 100 0.0

This model Tillner-Roth and Friend (1998) Rizvi and Heidemann (1987) Sassen et al. (1990) Sakabe et al. (2008)

0.2

0.4

0.6

0.8

1.0

0.8

1.0

xNH

b

3

0.34

0.30

-3

ρc(g⋅ cm )

0.32

0.28 0.26 0.24 0.22 0.0 c

This model Tillner-Roth and Friend (1998) Sakabe et al. (2008)

0.2

0.4

0.6 xNH

3

Fig. 6: Calculated critical parameters (temperature, pressure, and density) of NH3-H2O fluid mixture: Tc is critical temperature, Pc is critical pressure, ρ c is critical density, and X NH3 is mole fraction of NH3.

6. Conclusions A fundamental EOS for the Helmholtz free energy of NH3-H2O fluid mixture has been established, from which the PVTx and VLE properties can be obtained by thermodynamic relations. The EOS can reproduce the volume and phase equilibrium compositions from 273 to 706 K and from 0 to 2000 bar, with or close to experimental

accuracy. This work validates that the simple generalized departure function developed by Lemmon and Jacobsen [38] can be extended to the strong polar fluid mixtures. Experimental volumetric data at high temperatures and pressures (e.g., above 706 K and 2000 bar) are still lacking for the NH3-H2O fluid system, and future experimental studies of this system can be focused on this temperature-pressure region.

Acknowledgements: We thank the two anonymous reviewers for their detailed and helpful comments, which improved greatly the quality of the manuscript. Dr. Junfeng Qin is thanked for providing part experimental data. This work is supported by the National Natural Science Foundation of China (41173072) and the Fundamental Research Funds for the Central Universities (2652013032).

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Table 1: Coefficients and exponents of Eq. (8) k

Nk

dk

tk

1 2 3 4 5

-2.45476271425D-2 -2.41206117483D-1 -5.13801950309D-3 -2.39824834123D-2 2.59772344008D-1

1 1 1 2 3

2 4 -2 1 4

6 7 8 9 10

-1.72014123104D-1 4.29490028551D-2 -2.02108593862D-4 -3.82984234857D-3 2.69923313540 D -6

4 5 6 6 8

4 4 0 4 -2

Table 2: Critical parameters of pure fluids i

Tci (K)

ρ ci (mol ⋅ dm -3 )

NH3 H 2O

405.40 647.096

13.21177715 17.87371609

Table 3: Parameters of the NH3-H2O fluid mixture Mixture

F12

ζ 12 (dm 3 ⋅ mol −1 )

ς 12 (K)

β12

NH3-H2O

0.87211862D+00

0.42332477D-02

0.25115705D+02

1.25

Table 4: Calculated volume deviations from experimental data of NH3-H2O fluid mixture T (K)

P (bar)

xNH3

Nd

AAD (%)

MAD (%)

323.15-523.15

0.476-83.486

0.0884-0.9725

228

0.18

1.66

243.18-498.15

0.221-375.77

0.1-0.9

1483

0.61

2.83

298.15-705.65

1-370

0.0033-0.0530

135

0.20

1.15

280.04-378.51

10.1-76.51

0.836-0.9057

28

0.13

0.54

310-400

2-170

0.2973-0.8374

342

1.48

2.96

310-400

1-170

0.1016-0.8952

633

0.75

1.51

297.75-309.151

5.21-156.551

0.5133-0.5357

15

0.80

0.87

253.18-309.15

2.98-169.26

0-0.1436

277

0.96

2.54

References Ellerwald (1981) Harms-Watzenberg (1995) Hnedkovsky et al. (1996) Holcomb and Outcalt (1999) Kondo et al. (2002) Munakata et al. (2002) Oguchi and Ibusuki (2004) Oguchi and Ibusuki (2005)

Muromachi (2008)

et

al.

450-500

100-2000

0.1048-1

218

0.26

1.47