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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: ([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
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