Accepted Manuscript

Title: A Helmholtz free energy equation of state for theNH3-H2O fluid mixture: Correlation of the PVTx andvapor-liquid phase equilibrium properties

Author: Shide Mao Jun Deng Mengxin Lu

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

To appear in: Fluid Phase Equilibria

Received date: 17-11-2014Revised date: 10-2-2015Accepted date: 16-2-2015

Please cite this article as: Shide Mao, Jun Deng, Mengxin Lu, A Helmholtzfree energy equation of state for the NH3-H2O fluid mixture: Correlation ofthe PVTx and vapor-liquid phase equilibrium properties, Fluid Phase Equilibriahttp://dx.doi.org/10.1016/j.fluid.2015.02.024

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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: (maoshide@163.com)

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

A

RTα = (1)

where A is molar Helmholtz free energy, R is molar gas constant

( 1 18.314472 J mol K− −⋅ ⋅ ), and T is temperature in K.

The dimensionless Helmholtz free energy α of the mixture is represented by

id Emα α α= + (2)

where idmα is the dimensionless Helmholtz free energy of an ideal mixture and Eα

is the excess dimensionless Helmholtz free energy. idmα comes directly from the

fundamental equations of pure fluids and can be written as

2id 0 rm m i i

1

2 20 r

i i i i ii 1 i 1

( , , ) ( , )

( , ) ln( ) ( , )

i

x x

x x x

α α δ τ α δ τ

α δ τ α δ τ

=

= =

= +

= + +

∑

∑ ∑ (3)

where 0mα is the ideal-gas part of dimensionless Helmholtz free energy of the

mixture, 0iα and r

iα are the ideal-gas part and residual part of dimensionless

Helmholtz free energy of component i, respectively, ix 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

c

ρδρ

= (4)

cT

Tτ = (5)

where ρ is the density of mixture, and cρ and cT are defined as

12

ic 1 2 12

i 1 ci

xx xρ ζ

ρ

−

=

= + ∑ (6)

12

2

c i ci 1 2 12i 1

T xT x xβ ς=

= +∑ (7)

where ciρ and ciT are the critical density and critical temperature of the component

i, respectively, 1x and 2x denote mole fraction of components 1 and 2, and 12ζ ,

12ς , and 12β are the mixture-dependent binary parameters associated with

components 1 and 2 (NH3 and H2O).

The Eα in Eq. (2) is given by

k k

10E

1 2 12 kk 1

d tx x F Nα δ τ=

= ∑ (8)

where kN , kd and kt are general parameters independent of fluids, which can be

found from the model of Lemmon and Jacobsen [38] (Table 1), 12F is a binary

parameter of components 1 and 2.

The residual part of dimensionless Helmholtz free energy of NH3-H2O fluid

mixture rα is defined by

2

r r Ei i

i 1

( , ) ( , , )x xα α δ τ α δ τ=

= +∑ (9)

Values of the binary parameters (12ζ , 12ς , 12β and 12F ) 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 near-

and 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 12ζ , 12ς , 12β and 12F 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.

r1P RT δρ δα = + (10)

where P is pressure, and rδα is the derivative of rα 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:

j

r

i ii , ,

expT V n

nf x RT

n

αρ ∂= ∂

(11)

j

r

ii , ,

ln ln(1 )r

T V n

n

n δαϕ δα

∂= − + ∂ (12)

j j

r rr

i i, , , ,T V n T V n

nn

n n

α αα ∂ ∂= + ∂ ∂

(13)

j j j

j j

i k

r 2r

kk 1i i k, ,

2r

kk 1i k

2r r

kk 1

11

1

c c

cT V n x x

c c

c x x

x x

n xn x x

T Tx

T x x

x

δ

τ

ρ ρα δαρ

τ α

α α

=

=

=

∂ ∂∂ = − − ∂ ∂ ∂

∂ ∂ + − ∂ ∂

+ −

∑

∑

∑

(14)

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

V is the total volume, in is the mole number of component i, jn is the mole

number of component j and signifies that all mole numbers are held constant except

in , iϕ is the fugacity coefficient of component i, and rτα , i

rxα and

k

rxα

are the

derivatives of rα with respect to τ , ix and kx , 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 iM , mole

number of vapor phase is VN , and vapor and liquid compositions of component i are

ix and iy , then ix and iy 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 iM , ix

and iy .

Step 2: First calculate the vapor and liquid densities form Eq. (10), then calculate the

fugacity coefficient of component i in vapor phase ( Viϕ ) and liquid phase (L

iϕ ) from

Eq. (12).

Step 3: Define an equilibrium factor L

i ii V

i i

yk

x

ϕϕ

= = , then calculate ik from Viϕ and

Liϕ .

Step 4: Calculate VN from the normalized equation 2

ii V V

i 1 i

10

1

kM

N N k=

− =− +∑ .

Step 5: Calculate ix and iy from equations ii V V

i1

Mx

N N k=

− + and

i ii V V

i1

k My

N N k=

− +, respectively.

Step 6: Go to Step 2, and recalculate Viϕ , L

iϕ , ik , VN , ix and iy in turn until the

calculated VN keeps unchangeable. Then ix and iy are the VLE compositions. It

should be noted that when T and P approach the critical point, the initial values

for ix and iy 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; cal exp expAAD 100 ( ) /V V V= − , where calV and expV are the calculated

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

experimental data.

300 330 360 390 420-4

-2

0

2

4

100(

Vca

l-Vex

p)/V

exp

T (K)

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

a

260 280 300 320 340 360 380 400-4

-2

0

2

4

100(

Vca

l-Vex

p)/

Vex

p

T (K)

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

b

0 500 1000 1500 2000-4

-2

0

2

4

100(

Vca

l-Vex

p)/V

exp

P (bar)

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

c

300 400 500 600 700-4

-2

0

2

4

100(

Vca

l-Vex

p)/

Vex

p

T (K)

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

d

300 350 400 450 500-4

-2

0

2

4

100(

Vca

l-Vex

p)/

Vex

p

T (K)

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

e

0.0 0.2 0.4 0.6 0.8 1.0-4

-2

0

2

4

100(

Vca

l-Vex

p)/

Vex

p

xNH

3

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

f

Fig. 1: Volume deviations of this EOS from experimental data of NH3-H2O fluid

mixture : calV and expV denote the calculated molar volume and experimental

volume, respectively.

500 1000 1500 200018

20

22

24

26

28

30

0.5565

0.3807

Vm(c

m3 ⋅⋅ ⋅⋅m

ol-1

)

P (bar)

Exp. Muromachi et al. (2008) This model

T = 450 K

xNH

3

= 0.1048

0.2046

a

400 800 1200 1600 200020

25

30

35

40

45

50

1.00000.9102

xNH

3

= 0.7008

T = 450 K

Exp. Muromachi et al. (2008) This model

Vm(c

m3 ⋅⋅ ⋅⋅m

ol-1

)

P (bar)

0.8010

b

500 1000 1500 2000

20

24

28

32

36

0.5565

0.3807

0.2046

xNH

3

= 0.1048

T = 500 K

Exp. Muromachi et al. (2008) This model

Vm(c

m3 ⋅⋅ ⋅⋅m

ol-1

)

P (bar)c

400 800 1200 1600 200024

28

32

36

40

44

48

52

1.00000.91020.8010

xNH

3

= 0.7008

T = 500 K

Exp. Muromachi et al. (2008) This model

Vm(c

m3 ⋅⋅ ⋅⋅m

ol-1

)

P (bar)d

Fig. 2: The calculated molar volumes and experimental data as a function of

pressure: mV is molar volume and P is pressure.

0.0 0.2 0.4 0.6 0.8 1.0-3.0

-1.5

0.0

1.5

3.0

0.0 0.2 0.4 0.6 0.8 1.0-3.0

-1.5

0.0

1.5

3.0

XNH

3

100(

Vca

l-Vex

p)/

Vex

p

XNH

3

This model

Exp. Muromachi et al. (2008)

Tillner-Roth and Friend (1998)

Fig.3: Volume deviations from experimental high-pressure data (Muromachi et

al., 2008) of NH3-H2O fluid mixture : calV and expV 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.

360 380 400 420 440-0.2

-0.1

0.0

0.1

0.2

x NH

3,cal-x

NH

3,exp

T (K)

Polak and Lu (1975)

a

300 320 340 360 380-0.2

-0.1

0.0

0.1

0.2

x NH

3,ca

l-xN

H3,

exp

T (K)

Holcomb and Outcalt (1999)

b

300 350 400 450 500-0.2

-0.1

0.0

0.1

0.2

x NH

3,cal-x

NH

3,exp

T (K)

Harms-Watzenberg (1995)

c

350 400 450 500 550 600-0.2

-0.1

0.0

0.1

0.2

x NH

3,ca

l-xN

H3,

exp

T (K)

Sassen et al. (1990)

d

Fig. 4: Deviations between calculated mole fractions of NH3 and experimental

values: T is temperature, P is pressure, 3NHX is mole fraction of NH3, and

3NH calX

and 3NH expX are the calculated and experimental mole fraction of NH3, respectively.

0.0 0.2 0.4 0.6 0.8 1.00

50

100

150

200

250

610.2 K 579.7 K 526.2 KP

(b

ar)

xNH

3

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

451.5 K

a

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

120

b

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

411.9 K

359.7K

305.6 K

P (

bar

)

xNH

3

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

3NHX 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].

0.0 0.2 0.4 0.6 0.8 1.0400

450

500

550

600

650

700

T c (K)

xNH

3

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

a

0.0 0.2 0.4 0.6 0.8 1.0100

120

140

160

180

200

220

240

260

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

P c (bar

)

xNH

3b

0.0 0.2 0.4 0.6 0.8 1.00.22

0.24

0.26

0.28

0.30

0.32

0.34

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

ρρ ρρ c(g⋅⋅ ⋅⋅cm

-3)

xNH

3c

Fig. 6: Calculated critical parameters (temperature, pressure, and density) of

NH3-H2O fluid mixture: Tc is critical temperature, Pc is critical pressure, cρ is

critical density, and 3NHX 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 kN kd kt

1 -2.45476271425D-2 1 2

2 -2.41206117483D-1 1 4

3 -5.13801950309D-3 1 -2

4 -2.39824834123D-2 2 1

5 2.59772344008D-1 3 4

6 -1.72014123104D-1 4 4

7 4.29490028551D-2 5 4

8 -2.02108593862D-4 6 0

9 -3.82984234857D-3 6 4

10 2.69923313540 D -6 8 -2

Table 2: Critical parameters of pure fluids

i ci (K)T -3ci (mol dm )ρ ⋅

NH3 405.40 13.21177715

H2O 647.096 17.87371609

Table 3: Parameters of the NH3-H2O fluid mixture

Mixture 12F 3 112(dm mol )ζ −⋅ 12(K)ς 12β

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

References

T (K) P (bar) 3NHx Nd

AAD

(%)

MAD

(%)

Ellerwald (1981) 323.15-523.15 0.476-83.486 0.0884-0.9725 228 0.18 1.66

Harms-Watzenberg

(1995) 243.18-498.15 0.221-375.77 0.1-0.9 1483 0.61 2.83

Hnedkovsky et al.

(1996) 298.15-705.65 1-370 0.0033-0.0530 135 0.20 1.15

Holcomb and

Outcalt (1999) 280.04-378.51 10.1-76.51 0.836-0.9057 28 0.13 0.54

Kondo et al. (2002) 310-400 2-170 0.2973-0.8374 342 1.48 2.96

Munakata et al.

(2002) 310-400 1-170 0.1016-0.8952 633 0.75 1.51

Oguchi and Ibusuki

(2004) 297.75-309.151 5.21-156.551 0.5133-0.5357 15 0.80 0.87

Oguchi and Ibusuki

(2005) 253.18-309.15 2.98-169.26 0-0.1436 277 0.96 2.54

Muromachi et al.

(2008) 450-500 100-2000 0.1048-1 218 0.26 1.47