Accepted Manuscript
Evaluation of Prediction Models for the Physical Parameters in Natural Gas
Liquefaction Processes
Zongming Yuan, Mengmeng Cui, Rui Song, Ying Xie
PII:
S1875-5100(15)30175-X
DOI:
10.1016/j.jngse.2015.09.042
Reference:
JNGSE 1024
To appear in:
Journal of Natural Gas Science and Engineering
Received Date: 11 July 2015
Revised Date:
10 September 2015
Accepted Date: 17 September 2015
Please cite this article as: Yuan, Z., Cui, M., Song, R., Xie, Y., Evaluation of Prediction Models for
the Physical Parameters in Natural Gas Liquefaction Processes, Journal of Natural Gas Science &
Engineering (2015), doi: 10.1016/j.jngse.2015.09.042.
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.
ACCEPTED MANUSCRIPT
Evaluation of Prediction Models for the Physical Parameters in
Natural Gas Liquefaction Processes
Zongming Yuan1,
Mengmeng Cui1 †,
Rui Song2,
Ying Xie1
SC
RI
PT
1, School of Petroleum and Natural Gas Engineering, Southwest Petroleum University, Chengdu, 610500,
China
2, School of Geoscience and Technology, Southwest Petroleum University, Chengdu, 610500, China
†
Corresponding author.
Mengmeng Cui
Tel: 86-28-83033348; Fax: 86-28-83033248; Email: cuimm619@163.com
Address: School of Petroleum and Natural Gas Engineering, Southwest Petroleum University, 8# Xindu
Road, Xindu District, Chengdu City, Sichuan Province, PR China
AC
C
EP
TE
D
M
AN
U
Abstract:
The natural gas liquefaction process is a complicated and dynamic thermal system. Operation conditions
change during the process of compression, throttling and heat transfer, which inevitably leads to changes of
the thermodynamic property parameters and the phase state of the natural gas and refrigerants. Performing
a simulation of the liquefaction process is one of the main methods to improve the economic efficiency of
the process and to reduce the production cost; such a simulation can be conducted using a process
simulation software package, such as Aspen HYSYS, Aspen Plus, SIMSCI PRO-II and Honeywell UniSim
Design. Accurate prediction of the thermodynamic properties of natural gas and refrigerants with the
change of working conditions, such as density, specific heat capacity, enthalpy, and entropy, is of
significant importance for the simulation of natural gas liquefaction processes. There are many types of
property methods embedded in simulation software. Because each property method achieves good
performance in a certain range of working conditions, it is crucial to choose the proper method to conduct
the simulation. The Soave-Redlich-Kwong equation, the Peng-Robinson equation and the
Lee-Kesler-Plocker equation are the main calculation models for physical parameters in natural gas
liquefaction processes. According to a literature review, the GERG-2008 equation shows high precision in
calculating the thermodynamic properties and phase equilibrium of natural gas and similar mixtures in a
wide range of temperature and pressure. Based on accurate experimental data, a comprehensive comparison
and analysis among these equations is conducted in this paper. The GERG-2008 equation is recommended
as the basis for the calculation of the physical parameters in natural gas liquefaction processes.
Key words:
Liquefaction process; Equation of state; Thermodynamic properties; Phase equilibrium
Highlights:
The common prediction models for physical properties in natural gas liquefaction processes are
summarized.
A comprehensive comparison and analysis among the prediction models is conducted.
GERG-2008 shows better adaptability over a wide range of working conditions and feed gas
components.
1
ACCEPTED MANUSCRIPT
RI
PT
Abbreviations
LNG
Liquefied Natural Gas
SRK
Soave-Redlich-Kwong
PR
Peng-Robinson
LKP
Lee-Kesler-Plocker
RK
Redlich-Kwong
AD
absolute deviation
AAD
average absolute deviation
RD
relative deviation
ARD
average relative deviation
SC
1. Introduction
TE
D
M
AN
U
An expanding population and economic growth are the main causes for the growth of global energy
consumption (Kumar et al., 2011). According to the U.S. Energy Information Administration (2013), the
world total energy consumption demand will increase from 5.528×1017 kJ in 2010 to 6.646×1017 kJ in 2020
and to 8.651×1017 kJ in 2040, with a 30-year increase of 56 percent. With the increasing environmental
problems raised by the traditional petrochemical resources and the strong demand of alternative energy for
global economic developments, natural gas continues to be favored, with the characteristics of abundant
resources and robust production (Yuan et al., 2014). Although the energy market condition varies in
different areas of the world, natural gas will represent prosperity and development because of its flexibility
and environmental benefits.
AC
C
EP
Liquefied natural gas (LNG) is a safe and economic means of bringing natural gas to a potential market
(Khan et al., 2014) for marginal oil and gas recovery. Design and optimization of natural gas liquefaction
processes are target issues of academic research and engineering practice, in which process simulation
software is an important tool. With the development of computer technology, many types of software can
be used to simulate the liquefaction process, including Aspen HYSYS, Aspen Plus, SIMSCI PRO-II and
Honeywell UniSim Design. During the process of compression, throttling and heat transfer, the phase state
of natural gas and refrigerants varies, resulting in the change of the physical properties, an accurate
prediction of which is essential for process simulation and optimization. Extensive theoretical and
experimental research studies have been performed to determine the physical properties of natural gas,
among which the equations of state are preferred. There are many types of equation-of-state based property
methods embedded in simulation software, and different thermodynamic methods have been employed to
conduct the liquefaction processes. Because each property method achieves good performance over a
certain range of working conditions, it is crucial to choose the proper method to simulate the process, that is,
it is necessary to compare the prediction accuracy of different models for determining the physical
parameters.
In the simulation and optimization of natural gas liquefaction processes, the Soave-Redlich-Kwong
(SRK) equation, the Peng-Robinson (PR) equation and the Lee-Kesler-Plocker (LKP) equation are the
main models for predicting the physical parameters. To determine the refrigerant compositions and
operation conditions of a mixed refrigerant cascade cycle, a synthesis problem was posed by a nonconvex
2
ACCEPTED MANUSCRIPT
M
AN
U
SC
RI
PT
nonlinear program (Vaidyaraman & Maranas, 2002) in which the SRK equation of state was used for
calculations within the modules. Aspelund et al. (2007) described a new methodology for process synthesis,
combining the traditional pinch analysis with exergy calculations via Aspen HYSYS using the SRK
equation of state. Using the PR equation of state for physical properties calculations, Nogal et al. (2008)
presented a new approach for the optimal design of mixed refrigerant cycles. Shirazi and Mowla (2010)
conducted a research study on the selection and development of gas peak shaving processes for the lowest
energy consumption based on the use of the PR equation to calculate the thermodynamic properties. To
optimize the verified APCI LNG plant model, Alabdulkarem et al. (2011) explored the use of Aspen
HYSYS as the thermodynamic model and Matlab as the optimizer by selecting the PR equation of state to
model the property of substances. A comparison of the natural gas liquefaction processes with different
precooling cycles was performed by Castillo et al. (2013) using Aspen HYSYS with the Peng–Robinson
thermodynamic fluid package. Using the PR equation to calculate the thermodynamic properties, Khan and
Lee (2013) optimized a single mixed refrigerant natural gas liquefaction process using Honeywell UniSim
Design and the particle swarm paradigm. With the PR equation of state calculating the thermodynamic
properties, a typical single mixed refrigerant with low energy consumption was analyzed to determine the
optimum operating conditions (Moein et al., 2015). Cao et al. (2006) designed and simulated two typical
types of small-scale natural gas liquefaction processes using Aspen HYSYS, in which the PR equation and
the LKP equation were selected for the fluid package. Yuan et al. (2015) proposed a novel process to
condense the double-stage pre-cooled and compressed BOG at LNG Terminals, where the SRK equation
was used to calculate the phase equilibrium and the LKP equation was used to calculate the enthalpy and
entropy.
AC
C
EP
TE
D
Although these equations are widely used to simulate natural gas liquefaction processes, they still have
some defects in predicting the liquid density and phase equilibrium (Kunz & Wagner, 2012). Thus,
modifications of the liquid molar volume prediction have been made to improve the accuracy of the liquid
density prediction. Dauber and Span (2012) conducted a study of the comparison of the liquid density and
the isobaric heat capacity based on the standard SRK equation, the standard PR equation, the standard LKP
equation and the GERG-2008 equation, in which significant deviations at low temperature were observed.
The author made a great improvement on applying the GERG-2008 equation to the simulation of the
liquefaction processes. However, the natural gas liquefaction process is a complicated thermal system that
is also affected by other important physical properties, such as the gas density, enthalpy, as well as phase
equilibrium parameters. Based on accurate experimental data and the Aspen Plus software (Aspen
Technology, 2013), a comprehensive comparison and analysis among the modified SRK equation, the
modified PR equation, the modified LKP equation and the GERG-2008 equation is conducted to predict the
gas and saturated liquid densities, specific heat capacities, enthalpies, dew points and phase equilibrium
parameters to provide a reference for the selection of property methods in the simulation of the liquefaction
processes.
2. Equations of state
The equation of state for real gas, which was proposed by van der Waals in 1873, acted as the basic form
of the cubic equations of state. Redlich and Kwong (RK) (1949) proposed a modified cubic equation of
state with two individual coefficients, which provided satisfactory results above the critical temperature for
any pressure. Reid introduced binary interaction parameters into the RK equation for calculating mixtures.
3
ACCEPTED MANUSCRIPT
To compensate for the defects of the RK equation in predicting the saturated pressure of pure substances
and multi-component phase equilibrium, Soave (1972) improved the RK equation by introducing a third
parameter with an acentric factor to obtain the Soave-Redlich-Kwong (SRK) equation. Peng and Robinson
(1976) developed a new two-constant equation of state, which showed great advantages in the prediction of
liquid phase densities.
M
AN
U
SC
RI
PT
The corresponding state principle is one of the methods for calculating the thermodynamic properties.
Taking the critical point as the reference point, van der Waals proposed the principle of corresponding
states in 1880, where a general form of the equation of state can be obtained by expressing the temperature,
pressure and volume as a monotonic function of the respective critical parameter. Pitzer et al. (1955)
introduced the acentric factor to improve the prediction accuracy of calculating the volume and the
thermodynamic parameters. Leach et al. (1968) introduced the molecular shape factors into the
pseudo-critical equations, which greatly improved the calculation of the vapor-liquid equilibrium for
nonpolar hydrocarbon mixtures. Based on the 3-parameter corresponding states principle, Lee and Kesler
(1975) developed an analytical correlation to facilitate processing using a computer, which was applied to
mixtures for thermodynamic properties calculation (Plocker et al. 1978) to obtain the Lee-Kesler-Plocker
equation.
TE
D
As the expanded version of the GERG-2004 equation, the GERG-2008 equation (Kunz & Wagner, 2012)
shows a good prediction performance over the gas phase, liquid phase, supercritical region, and
vapor-liquid equilibrium states for 21 mixtures, including methane, nitrogen, carbon dioxide, ethane,
propane, n-butane, isobutane, n-pentane, isopentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane,
hydrogen, oxygen, carbon monoxide, water, hydrogen sulfide, helium, and argon. The Aspen Plus software
provides a variety of thermodynamic calculation methods for phase equilibrium, enthalpy, entropy, density,
and other parameters, which is employed as the platform for accuracy analysis of the prediction models.
For the SRK equation, the PR equation and the LKP equation, the binary parameters of Knapp et al. (1982)
are used.
EP
2.1 Soave-Redlich-Kwong equation of state
AC
C
The Soave-Redlich-Kwong equation of state shows good performance in simulations of hydrocarbon
processing, including gas treatment and refinery and petrochemical processes; the equation of state is given
below:
p=
RT
a (T )
−
V − b V (V + b)
a (T ) = α (T )0.42747 R 2Tc2 / pc
b = 0.08664 RTc / pc
α (T ) = 1 + m (1 − Tr0.5 ) 
(1)
2
m = 0.480 + 1.5741ω − 0.1715ω 2
where p is the pressure, R is a gas constant, T is the temperature, V is the specific volume, a & b are the
constants relating to the gas compositions, subscript c represents the critical state, Tr is the reduced
temperature, Tr=T/Tc, Tc is the critical temperature, and ω is the acentric factor.
When the SRK equation is applied to mixtures, mixing rules are adopted to calculate a, b and the critical
4
ACCEPTED MANUSCRIPT
parameters in Equation 1. The SRK equation is expressed as:
Tcm = ∑ xiTci
i
pcm = ∑ xi pci
i
a = ∑∑ xi x j ( ai a j )
i
j
0.5
(2)
(1 − k )
ij
b = ∑ yi bi
RI
PT
i
where xi represents the molar fraction of component i, Tcm is the critical temperature of the mixture, pcm
is the critical pressure of the mixture, and kij is the binary parameters of the SRK equation.
Vmod = V − Vc
SC
In Aspen Plus, the SRK property method calculates all of the thermodynamic properties based on the
Soave-Redlich-Kwong equation of state, except the liquid molar volume of mixtures, which is calculated
using the Peneloux-Rauzy (1982) volume correction method, which is given below:
(3)
2.2 Peng-Robinson equation of state
M
AN
U
where V is the specific volume calculated from the equation of state without the correction, Vmod is the
modified molar volume, and Vc is the correction term.
TE
D
Peng-Robinson equation of state is often used as the basic property model of the natural gas and mixed
refrigerants in the liquefaction processes. The equation of state is given below:
RT
a(T )
−
(4)
p=
V − b V (V + b) − b(V − b)
where p is the pressure, R is the gas constant, T is the temperature, V is the specific volume, and a & b
are the constants related to the gas compositions.
AC
C
EP
At the critical point，
a (Tc ) = 0.45724 R 2Tc2 / pc
b(Tc ) = 0.07780 RTc / pc
(5)
Z c = 0.307
At temperatures other than the critical temperature,
a (T ) = a(Tc )α (T )
b(T ) = b(Tc )
α (T ) = 1 + k (1 − Tr0.5 ) 
2
(6)
k = 0.37464 + 1.54226ω − 0.26992ω 2
where p is the pressure, R is the gas constant, T is the temperature, V is the specific volume, a & b are the
constants relating to the gas compositions, subscript c represents the critical state, Tr is the reduced
temperature, and ω is the acentric factor.
When the PR equation of state is applied to mixtures, the same expression of the mixing rules as the
SRK equation in Equation 2 is employed with specified binary parameters for the PR equation. In Aspen
5
ACCEPTED MANUSCRIPT
Plus, the PENG-ROB property method calculates all of the thermodynamic properties based on the
Peng-Robinson equation of state, except for the liquid molar volume of mixtures, which is calculated using
the Rackett (1970) model, as given by:
2

1+ (1−Tr ) 7 

Vml =
RTc ( Z mRA )
(7)
pc
where Vml is the liquid specific volume and ZmRA is the compressibility term.
RI
PT
2.3 Lee-Kesler-Plocker equation of state
The Lee–Kesler–Plocker equation is a virial-type equation that shows good performance in the
calculation of the enthalpy and entropy of the mixed components. The equation is given below:
Z=
ω
(Z ( r ) − Z (0) )
ω (r )
SC
Z = Z (0) +
PV
B C D
r r
=1+ + 2 + 5
Tr
Vr Vr Vr
c4 
γ   γ 
β + 2  exp  − 2 
3 2 
Tr Vr 
Vr 
 Vr 
M
AN
U
+
B = b1 −
b2 b3 b4
−
−
Tr Tr2 Tr3
C = c1 −
c2 c3
+
Tr Tr3
d2
Tr
TE
D
D = d1 +
(8)
where Z is the compressibility factor; ω is the acentric factor; 0 and r signify the relevant parameters of
the simple and reference liquids, respectively; and b1~b4, c1~c4, d1, d2, β, and γ are constants.
AC
C
EP
When the LKP equation of state is applied to mixtures, the mixing rules are given in Equation 9.
TcmVcm0.25 = ∑∑ xi x jVcij0.25Tcij
i
j
Vcm = ∑∑ xi x jVcij
i
j
ωm = ∑ xiωi
(9)
i
Tcij = (TciTcj ) kij
0.5
Vcij =
(
1 13
1
Vci + Vcj 3
8
)
3
where xi represents the molar fraction of component i, Tcm is the critical temperature of the mixture, pcm
is the critical pressure of the mixture, and kij is the binary parameters of the LKP equation.
In Aspen Plus, the LK-PLOCK property method uses the Lee-Kesler-Plocker equation of state to
calculate all of the thermodynamic properties, with the Rackett (1970) model used to calculate the liquid
molar volume of mixtures.
2.4 GERG-2008 equation of state
6
ACCEPTED MANUSCRIPT
The GERG-2008 equation of state (Kunz & Wagner, 2012) is explicit in the Helmholtz free energy as a
function of density, temperature, and composition, which covers the gas phase, liquid phase, supercritical
region, and vapor-liquid equilibrium states for 21 mixtures. The equation of state is given below:
a ( ρ , T , x) = a o ( ρ , T , x ) + a r ( ρ , T , x )
(10)
where a is the Helmholtz free energy, ao is the ideal part, ar represents the residual mixture behavior, ρ is
RI
PT
the density, and x is the vector of the molar composition.
When the Helmholtz free energy a is expressed as the dimensionless form, the equation is expressed as,
α (δ ,τ , x) = α o ( ρ , T , x) + α r (δ ,τ , x)
(11)
SC
where α=a/RT, δ is the reduced density, δ=ρ/ρr, τ is the inverse reduced temperature, τ=Tr/T, with ρr and
Tr being the composition-dependent reducing functions for the mixture density and the temperature.
The ideal part of the Helmholtz free energy in the dimensionless form is given by,
N
M
AN
U
α o ( ρ , T , x) = ∑ xi α 0oi ( ρ , T ) + ln xi 
(12)
i =1
where N is the total number of components in the mixture and xi is the molar fraction of component i.
The residual part of the Helmholtz free energy is expressed as,
N
N −1
α r (δ ,τ , x) = ∑ xiα 0ri (δ ,τ ) + ∑
i =1 j = i +1
TE
D
i =1
N
∑ xx Fα
i
j
ij
r
ij
(δ ,τ )
(13)
where Fij is the composition dependent adjustable factor.
When the equation of state is applied to mixtures, the reduced density and temperature are calculated by,
1
()
AC
C
EP
ρr x
N
= ∑ xi2
i =1
1
ρ c ,i
N −1
+∑
N
∑ 2x x β
i =1 j = i +1
1 1
1 
 1/3 + 1/3 
8  ρc,i ρc , j 
N −1
i =1
i =1 j = i +1
Tr ( x ) = ∑ xi2Tc ,i + ∑
x + xj
β x + xj
j
c ,i
γ v,ij ⋅
x + xj
i
2
v ,ij i
β x + xj
⋅
(14)
N
∑ 2x x β
(T
v ,ij
3
N
i
2
T ,ij i
i
i
⋅ Tc , j )
j
γ
T ,ij T ,ij
⋅
0.5
where βv,ij, γv,ij, βT,ij, and γT,ij are the binary interaction parameters of GERG-2008 equation (Kunz &
Wagner, 2012).
In Aspen Plus, the GERG2008 property method uses the GERG-2008 equation of state to calculate all of
the thermodynamic properties.
3. Accuracy analysis of the prediction models for the thermodynamic parameters in
natural gas liquefaction processes
7
ACCEPTED MANUSCRIPT
To provide a quantitative analysis of the prediction accuracy of the equations of state, the absolute
deviation (AD), average absolute deviation (AAD), relative deviation (RD) and average relative deviation
(ARD) are defined as follows:
AD:
AD = xcal − xexp
(15)
AAD =
N
1
N
∑x
i =1
cal
− xexp
RD:
RD = xcal − xexp / xexp × 100%
ARD =
1
N
N
xcal − xexp
i =1
xexp
∑
SC
ARD:
RI
PT
AAD:
× 100%
(16)
(17)
(18)
M
AN
U
where the subscript cal represents the calculated result; the subscript exp represents the experimental
result; and N are the total numbers.
3.1 Accuracy analysis of the prediction models for the gas density
AC
C
EP
TE
D
Accurate prediction of the gas density is the basis for evaluating the accuracy of the equation of state.
The Gas Research Institute (Hwang et al., 1997; Magee et al., 1997) initiated a co-operative international
project to establish a set of standard reference p-V-T data for five natural gas mixtures, where a Burnett
apparatus was adopted to obtain the experimental results at 225-350 K for pressures to 11 MPa. A
combined effort (Atilhan et al., 2011a, 2011b; McLinden, 2011) between Qatar University, Texas A&M
University, and the National Institute of Standards and Technology on the pressure-density-temperature
behavior of natural gas was conducted in 2011, where an isochoric apparatus and a magnetic suspension
densimeter were used to measure the p-ρ-T data of four synthetic natural gas mixtures at 250-450 K for
pressures of up to 37 MPa. In consideration of the working conditions in the natural gas liquefaction
processes, we choose the precise experimental results at 225-325 K for pressures of up to 11 MPa as the
reference data for the evaluation of the SRK equation, the PR equation, the LKP equation and the
GERG-2008 equation. The components of the nine mixtures are shown in Table 1.
Table 1. The mixture components used in the gas density prediction
Composition
Mole Fraction
GU1
GU2
NIST1
NIST2
RG2
SNG1
SNG2
SNG3
SNG4
CH4
0.81299
0.81203
0.96580
0.90644
0.85898
0.89982
0.89990
0.89975
0.90001
C2H6
0.03294
0.04306
0.01815
0.04553
0.08499
0.03009
0.03150
0.02855
0.04565
C3H8
0.00637
0.00894
0.00405
0.00833
0.02296
0.01506
0.01583
0.01427
0.02243
i-C4H10
0.00101
0.00148
0.00099
0.00100
0.00351
0.00752
0.00781
0.00709
0.01140
n-C4H10
0.00100
0.00155
0.00102
0.00156
0.00347
0.00753
0.00790
0.00722
0.01151
i-C5H12
0.00000
0.00000
0.00047
0.00030
0.00051
0.00300
0.00150
0.00450
0.00450
n-C5H12
0.00000
0.00000
0.00032
0.00045
0.00053
0.00300
0.00150
0.00450
0.00450
n-C6H14
0.00000
0.00000
0.00063
0.00040
0.00000
0.00000
0.00000
0.00000
0.00000
8
ACCEPTED MANUSCRIPT
N2
0.13575
0.05703
0.00269
0.03134
0.01007
0.01697
0.01699
0.01713
0.00000
CO2
0.00994
0.07592
0.00589
0.00466
0.01498
0.01701
0.01707
0.01699
0.00000
Total numbers
24
25
23
23
18
20
11
22
9
Notes: GU1, GU2, NIST1, NIST2, RG2, SNG1, SNG2, SNG3, and SNG4 represent the names of different types of natural
gas, and the total numbers represent the total number of each of the data sets used in accuracy comparison for each type of
gas.
M
AN
U
SC
RI
PT
According to different experimental conditions, the mixture densities calculated using the SRK equation,
the PR equation, the LKP equation and the GERG-2008 equation are obtained based on the Aspen Plus
software. The experimental data and calculated results of “GU1” are presented in Table 2 as an example.
Through a comparison with the experimental data, the prediction accuracy of the equations of state is
illustrated in Table 3. The contrast results indicate that the GERG-2008 equation has the highest precision
in gas density prediction. Although the SRK equation and the PR equation are the most commonly used
models in the liquefaction processes, the accuracies are lower than that of the LKP equation and the
GERG-2008 equation. The GERG-2008 equation has achieved good prediction accuracy for different
components of natural gas over a wide range of working conditions. In consideration of the good
adaptability of GERG-2008 to different feed gas components, temperatures and pressures, this equation can
be used to predict the gas density of conventional gas, coal bed gas and other similar mixtures in
liquefaction processes.
Table 2. The experimental data and calculated results of gas density for “GU1”
Calculated results
Experimental data
SRK
PR
3
GERG2008
p/MPa
ρ/kmol/m
ρ/kmol/m
ρ/kmol/m
ρ/kmol/m
ρ/kmol/m3
225.009
3.193
2.005
2.008
2.052
1.998
2.005
225.007
4.512
3.079
3.080
3.174
3.066
3.078
225.008
14.818
14.037
13.434
14.316
14.036
14.046
225.009
19.712
16.096
15.650
16.823
16.148
16.095
249.996
10.317
7.108
6.920
7.275
7.085
7.109
250.009
8.290
5.365
5.287
5.522
5.348
5.364
250.010
5.967
3.542
3.524
3.645
3.527
3.541
250.008
3.746
2.045
2.044
2.089
2.038
2.045
250.009
1.986
1.019
1.019
1.031
1.017
1.019
274.994
10.407
5.710
5.596
5.857
5.686
5.711
274.991
8.654
4.603
4.541
4.727
4.584
4.603
274.992
6.042
3.039
3.021
3.113
3.028
3.039
274.994
4.167
2.006
2.001
2.045
2.001
2.007
274.994
2.351
1.085
1.084
1.098
1.083
1.085
299.996
8.569
3.906
3.862
4.003
3.894
3.910
299.998
5.866
2.579
2.564
2.633
2.573
2.581
274.994
4.167
2.006
2.001
2.045
2.001
2.007
299.999
3.984
1.703
1.698
1.730
1.699
1.703
299.996
2.251
0.936
0.935
0.945
0.935
0.936
9
EP
AC
C
3
LKP
T/K
TE
D
3
3
ACCEPTED MANUSCRIPT
324.986
8.812
3.566
3.524
3.642
3.554
3.567
324.988
5.961
2.355
2.339
2.396
2.349
2.355
324.990
4.820
1.882
1.873
1.911
1.879
1.883
324.986
4.014
1.554
1.549
1.575
1.552
1.555
324.986
2.162
0.820
0.819
0.827
0.820
0.820
Table 3. The deviations of experimental and calculated results in gas density prediction
PR
LKP
GU1
0.89%
2.12%
0.27%
GU2
0.55%
2.29%
0.59%
NIST1
1.41%
2.01%
0.26%
NIST2
1.11%
2.02%
0.27%
RG2
0.64%
2.41%
0.42%
SNG1
3.65%
3.50%
SNG2
2.38%
2.74%
SNG3
3.05%
3.12%
SNG4
3.55%
Overall ADD
1.73%
GERG-2008
RI
PT
SRK
0.02%
0.04%
0.03%
0.05%
0.02%
SC
AAD
0.23%
0.19%
0.10%
0.22%
0.24%
M
AN
U
0.11%
3.80%
0.50%
0.37%
2.55%
0.31%
0.10%
3.2 Accuracy analysis of the prediction models for saturated liquid density
TE
D
The experimental data regarding the saturated liquid density of natural gas are scare. Through a grant
administered by the American Gas Association, an experimental program (Hiza & Haynes, 1980; Haynes,
1982) to obtain orthobaric liquid densities for the major components of LNG and their mixtures was
performed in the temperature range from 105 to 140 K, where a magnetic suspension densimeter was used.
The components of the mixtures used for the accuracy analysis of saturated liquid densities are shown in
Table 4.
Composition
EP
Table 4. The mixture components used in saturated liquid density prediction
Mole Fraction
B
C
D
E
F
N2
0.00000
0.04250
0.00000
0.00000
0.00601
0.00973
CH4
0.85443
0.81300
0.85892
0.84558
0.90613
0.88225
C2H6
0.05042
0.04750
0.11532
0.08153
0.06026
0.07259
C3H8
0.04038
0.04870
0.01341
0.04778
0.02154
0.02561
i-C4H10
0.02577
0.02410
0.00530
0.01259
0.00300
0.00490
n-C4H10
0.02901
0.02420
0.00705
0.01252
0.00306
0.00492
Total numbers
4
4
4
4
4
3
AC
C
A
Mole Fraction
Composition
G
H
I
J
K
L
N2
0.01383
0.00000
0.00000
0.00859
0.00801
0.00599
CH4
0.85934
0.85341
0.75442
0.75713
0.74275
0.90068
C2H6
0.08477
0.07898
0.15401
0.13585
0.16505
0.06537
C3H8
0.02980
0.04729
0.06950
0.06742
0.06547
0.02200
10
ACCEPTED MANUSCRIPT
i-C4H10
0.00519
0.00854
0.00978
0.01336
0.00843
0.00291
n-C4H10
0.00707
0.00992
0.01057
0.01326
0.00893
0.00284
i-C5H12
0.00000
0.00097
0.00089
0.00223
0.00069
0.00010
n-C5H12
0.00000
0.00089
0.00083
0.00216
0.00067
0.00011
Total numbers
4
5
4
5
4
4
Notes: A, B, C, D, E, F, G, H, I, J, K, L represents the name of different LNG, total numbers represent the total number of data
RI
PT
sets used in accuracy comparison for each kind of gas.
M
AN
U
SC
According to different experimental conditions, the saturated liquid densities calculated using the SRK
equation, the PR equation, the LKP equation and the GERG-2008 equation are obtained based on Aspen
Plus software. Taking “A” as an example, the experimental data and the calculated results of the liquid
density are presented in Table 5. Through a comparison with the experimental data, the prediction accuracy
of the equations of state is illustrated in Table 6. The prediction accuracy of the GERG-2008 equation is the
highest, and the average relative deviation is 0.19%. There are 12 types of natural gas used for accuracy
analysis of the saturated liquid densities covering the commercial components of LNG, and the good
prediction accuracy of the GERG-2008 equation indicates that this equation can be used for the prediction
of saturated liquid densities in liquefaction processes. The use of the modified PR equation with the Rackett
model to calculate the saturated liquid densities shows better performance than the SRK equation with
volume correction. Large deviations are observed for the LKP equation, which proves that it is not suitable
for the prediction in regions near the critical point.
Table 5. The experimental data and calculated results of saturated liquid density for “A”
Calculated results
Experimental data
TE
D
SRK
3
PR
LKP
3
GERG2008
T/K
p/MPa
ρ/mol/dm
ρ/mol/dm
ρ/mol/dm
ρ/mol/dm
ρ/mol/dm3
105
0.052
24.878
25.230
24.719
15.125
24.797
110
0.082
24.538
24.895
24.419
15.056
24.475
115
0.119
24.208
24.548
24.115
14.975
24.148
120
0.170
23.886
24.187
23.782
14.935
23.793
EP
3
3
Table 6. The deviations of experimental and calculated results in saturated liquid density prediction
SRK
PR
LKP
GERG-2008
A
1.38%
0.49%
38.37%
0.30%
B
1.69%
0.12%
35.50%
0.20%
C
1.41%
0.10%
0.10%
0.09%
D
1.32%
0.22%
15.45%
0.16%
E
1.26%
0.07%
6.93%
0.13%
F
1.45%
0.08%
0.08%
0.13%
G
1.31%
0.13%
0.13%
0.22%
H
1.42%
0.21%
18.72%
0.23%
I
1.50%
0.42%
12.72%
0.14%
J
1.39%
0.41%
10.75%
0.36%
K
1.59%
0.33%
6.07%
0.08%
AC
C
AAD
11
ACCEPTED MANUSCRIPT
L
1.28%
0.07%
0.07%
0.14%
Overall ADD
1.42%
0.23%
12.43%
0.19%
3.3 Accuracy analysis of the prediction models for enthalpy
Table 7. The mixture components used in enthalpy prediction
SC
RI
PT
The experimental enthalpy-temperature relationships of natural gas not only have an important
significance for the evaluation of equations of state but also provide benefits for the economic design of
natural gas liquefaction stations and LNG terminals. Scholars in the University of Leeds and the Air
Products (Ashton & Haselden, 1980) adopted a flow calorimeter to obtain the enthalpy-temperature
relationships of natural gas over the range of temperatures from 373 K to 200 K. To improve the
predictions of a computer program based on a modified Redlich-Kwong equation of state, the
enthalpy-temperature relationships of binary mixtures of methane and ethane, propane, and nitrogen were
determined in Shell Laboratorium (Van Kasteren & Zeldenrust, 1979). The above data are the basis for the
accuracy analysis of the equations of state in enthalpy prediction, where the components of the mixtures are
shown in Table 7.
M
AN
U
Composition (mole fraction)
Item
CH4
C2H6
C3H8
i-C4H10
n-C4H10
1
0.04450
0.92770
0.02310
0.00400
0.00030
0.00040
2
0.04590
0.92630
0.02310
0.00400
0.00030
0.00040
3
0.04700
0.92520
0.02310
0.00400
0.00030
0.00040
4
0.04830
0.92380
0.02330
0.00400
0.00030
0.00030
5
0.04980
0.92230
0.02330
0.00400
0.00030
0.00030
6
0.05100
0.92100
0.02330
0.00400
0.00030
0.00040
7
0.05220
0.91980
0.02330
0.00400
0.00030
0.00040
8
0.05300
0.91910
0.02330
0.00390
0.00030
0.00040
9
0.05500
0.91720
0.02320
0.00390
0.00030
0.00040
10
0.05620
0.91610
0.02320
0.00380
0.00030
0.00040
11
0.05750
0.91480
0.02320
0.00380
0.00030
0.00040
12
0.05840
0.91390
0.02320
0.00380
0.00030
0.00040
13
0.05940
0.91300
0.02310
0.00380
0.00030
0.00040
14
0.06020
0.91220
0.02310
0.00380
0.00030
0.00040
0.07390
0.89720
0.02320
0.00480
0.00040
0.00050
0.07520
0.89590
0.02320
0.00480
0.00040
0.00050
0.07560
0.89550
0.02320
0.00480
0.00040
0.00050
0.07720
0.89390
0.02320
0.00480
0.00040
0.00050
19
0.07850
0.89270
0.02330
0.00470
0.00040
0.00040
20
0.07900
0.89210
0.02330
0.00470
0.00040
0.00040
21
0.15760
0.80300
0.03020
0.00720
0.00090
0.00110
22
0.15800
0.80260
0.03020
0.00720
0.00090
0.00110
23
0.15800
0.80250
0.03020
0.00730
0.00090
0.00110
24
0.15820
0.80220
0.03020
0.00740
0.00090
0.00110
25
0.15830
0.80210
0.03020
0.00740
0.00090
0.00110
16
17
18
EP
AC
C
15
TE
D
N2
12
Notes
Natural
gas
ACCEPTED MANUSCRIPT
0.15850
0.80170
0.03040
0.00740
0.00100
0.00110
27
0.15870
0.80160
0.03040
0.00720
0.00100
0.00110
28
0.15870
0.80150
0.03050
0.00720
0.00100
0.00110
29
0.15210
0.80810
0.03070
0.00690
0.00110
0.00110
30
0.15210
0.80810
0.03080
0.00680
0.00110
0.00110
31
0.15230
0.80790
0.03060
0.00700
0.00110
0.00110
32
0.15270
0.80760
0.03050
0.00700
0.00110
0.00110
33
0.15320
0.80730
0.03050
0.00680
0.00110
0.00110
34
0.15320
0.80740
0.03050
0.00670
0.00110
0.00110
35
0.15300
0.80760
0.03050
0.00670
0.00110
0.00110
36
0.46700
0.53300
0.00000
0.00000
0.00000
0.00000
37
0.00000
0.71400
0.28600
0.00000
0.00000
0.00000
38
0.00000
0.91000
0.00000
0.09000
0.00000
0.00000
RI
PT
26
Binary
SC
mixtures
TE
D
M
AN
U
According to different experimental conditions, the enthalpies calculated using the SRK equation, the PR
equation, the LKP equation and the GERG-2008 equation are obtained based on Aspen Plus software.
There is 1 set of experimental data for each group of natural gas (item “1”-“35” in Table 7), 39 sets of
experimental data for item “36” in Table 7, 32 sets of experimental data for item “37” in Table 7, and 26
sets of experimental data for item “38” in Table 7. The experimental data and calculated results of gas “1”
for enthalpy differences are presented in Table 8 as an example. Through a comparison with the
experimental data, the prediction accuracy of the equations of state is illustrated in Table 9. Although the
LKP equation is considered to be an exact equation for calculating enthalpies, the GERG-2008 performs
better than the LKP equation, indicating that the GERG-2008 equation can be used for the prediction of
enthalpies in liquefaction processes.
Table 8. The experimental data and calculated results of enthalpy difference for “1”
Experimental data
Calculated results
SRK
PR
LKP
GERG
Tout/K
p/MPa
∆H/J/mol
∆H/J/mol
∆H/J/mol
∆H/J/mol
∆H/J/mol
366.91
200.32
1.389
6184.5
6287
6279
6303
6293
EP
Tin/K
AC
C
Notes: Tin is the inlet temperature, Tout is the outlet temperature, ∆H is the enthalpy difference with the change of condition.
Table 9. The deviations of experimental and calculated results in enthalpy prediction
AAD
SRK
PR
LKP
GERG-2008
1
1.66%
1.53%
1.92%
1.75%
2
0.62%
0.19%
1.65%
1.31%
3
0.51%
0.01%
1.87%
1.34%
4
1.57%
0.37%
4.90%
2.48%
5
2.25%
1.99%
2.50%
2.39%
6
2.19%
1.98%
2.13%
1.98%
7
1.62%
1.32%
2.04%
1.85%
8
1.16%
0.15%
2.03%
1.47%
9
3.39%
2.86%
4.09%
4.01%
13
ACCEPTED MANUSCRIPT
4.14%
3.89%
3.85%
3.63%
11
1.63%
1.28%
1.70%
1.41%
12
2.58%
1.51%
4.09%
3.80%
13
2.57%
0.79%
1.73%
1.18%
14
1.97%
0.75%
2.67%
2.10%
15
2.36%
2.25%
2.25%
2.21%
16
0.37%
0.24%
0.55%
0.42%
17
3.78%
3.43%
3.93%
3.90%
18
0.70%
1.14%
0.68%
19
1.24%
0.67%
1.50%
20
3.17%
1.69%
5.96%
21
3.26%
3.14%
3.18%
22
1.80%
1.65%
1.87%
23
1.38%
0.90%
24
1.97%
1.40%
25
5.47%
4.39%
26
3.33%
27
1.08%
28
4.32%
29
6.53%
30
4.18%
31
6.21%
32
2.52%
35
36
37
38
Overall ADD
SC
1.45%
4.59%
3.14%
1.77%
1.32%
1.67%
1.84%
6.18%
5.45%
M
AN
U
1.24%
3.04%
3.27%
3.18%
0.43%
0.96%
1.00%
3.42%
4.85%
4.59%
5.31%
7.08%
6.79%
2.81%
0.79%
4.62%
3.82%
7.24%
6.48%
2.02%
2.47%
2.33%
TE
D
34
0.56%
4.81%
2.56%
4.21%
4.31%
0.79%
1.53%
0.31%
0.93%
2.42%
1.51%
2.56%
2.25%
6.19%
3.41%
2.89%
2.08%
5.88%
1.73%
4.87%
0.90%
EP
33
RI
PT
10
7.18%
2.33%
6.15%
1.17%
5.15%
2.30%
3.85%
1.71%
AC
C
3.4 Accuracy analysis of the prediction models for specific heat capacity
It is difficult to obtain the experimental data of isobaric specific heat capacities for natural gas. Relative
data comes from the binary mixtures of methane, ethane, propane, and nitrogen determined in Shell
Laboratorium (Van Kasteren & Zeldenrust, 1979). The Aspen Plus software is employed to calculate the
specific heat capacities using the SRK equation, the PR equation, the LKP equation and the GERG-2008
equation. The components of the binary mixtures are shown in Table 10. There are 35 set of experimental
data for item “a” in Table 10, 17 sets of experimental data for item “b” in Table 10, and 18 sets of
experimental data for item “c” in Table 10. Through a comparison with the experimental data, the
experimental and calculated results for gas “a” are presented in Table 11, and the overall deviations of the
equations are illustrated in Table 12. The results show that the GERG-2008 equation is superior to other
equations regarding specific heat capacity prediction.
14
ACCEPTED MANUSCRIPT
Table 10. The mixture components used in specific heat capacity prediction
Composition (mole fraction)
Item
N2
CH4
C2H6
C3H8
a
0.46700
0.53300
--
--
b
--
0.71400
0.28600
0.00000
c
--
0.91000
--
0.09000
RI
PT
Table 11. The experimental data and calculated results of specific heat capacity for “a”
Calculated results
Experimental data
SRK
PR
LKP
GERG2008
p/MPa
110
5.07
2560
2758.5
2627.3
2693.1
2607.4
120
5.07
2680
2896.1
2782.1
2737.4
2714.1
130
5.07
2830
3110.5
3022.1
135
5.07
2960
3266.3
3197.5
140
5.07
3150
3476.2
3436.4
145
5.07
3400
3774.5
3782.8
3349.0
3482.9
150
5.07
3860
4234.6
4336.1
3784.0
3960.5
152
5.07
4180
4498.6
4665.5
4065.4
4261.8
154
5.07
4600
4838.7
5103.7
4465.8
4681.9
180
5.07
3300
3313.7
3098.9
3336.3
3327.7
185
5.07
2830
2863.8
2731.4
2897.4
2876.9
190
5.07
2570
2589.3
2497.6
2621.0
2596.4
195
5.07
2380
2403.7
2335.5
2430.2
2405.1
205
5.07
2100
2168.1
2124.9
2183.4
2161.0
215
5.07
1960
2024.7
1994.2
2030.9
2012.6
225
5.07
1850
1928.8
1905.9
1928.2
1913.9
235
5.07
1790
1860.9
1843.1
1855.4
1844.5
245
5.07
1730
1811.1
1796.8
1802.0
1794.0
255
5.07
1680
1773.9
1762.2
1762.1
1756.6
265
5.07
1650
1745.8
1736.1
1732.2
1728.6
2849.7
2886.4
2950.5
3017.4
3103.8
3202.4
M
AN
U
TE
D
EP
AC
C
115
Specific heat capacity/J/(kg*K)
SC
T/K
3.04
2680
2889.4
2765.6
2746.6
2705.4
3.04
2820
3115.1
3015.4
2854.4
2882.4
3.04
3180
3529.1
3481.4
3113.5
3229.9
3.04
2350
2272.8
2215.7
2334.0
2355.1
3.04
2050
2040.7
2006.7
2080.4
2077.8
190
3.04
1890
1909.2
1885.9
1933.7
1925.2
195
3.04
1830
1862.7
1842.8
1881.3
1872.1
205
3.04
1750
1792.6
1777.5
1802.2
1793.5
215
3.04
1690
1742.8
1730.9
1746.1
1738.7
225
3.04
1650
1706.3
1696.7
1705.0
1699.2
235
3.04
1610
1679.0
1671.1
1674.4
1670.1
245
3.04
1580
1658.6
1652.0
1651.7
1648.7
125
135
170
180
15
ACCEPTED MANUSCRIPT
255
3.04
1560
1643.5
1637.9
1634.9
1633.0
265
3.04
1540
1632.5
1627.8
1622.9
1621.9
275
3.04
1530
1625.1
1621.1
1614.6
1614.4
Table 12. The deviations of experimental and calculated results in specific heat capacity prediction
SRK
PR
LKP
GERG-2008
a
5.31%
4.97%
2.94%
2.56%
b
7.10%
1.91%
5.47%
0.59%
c
9.45%
4.26%
5.78%
Overall ADD
6.81%
4.04%
4.29%
RI
PT
AAD
1.09%
1.70%
SC
4. Accuracy analysis of the prediction models for phase equilibrium in natural gas
liquefaction processes
TE
D
M
AN
U
The evaluation of the phase equilibrium properties at various working conditions is important for the
simulation and optimization of natural gas liquefaction processes. The phase equilibrium data of a
methane-ethane-propane system at low temperatures and high pressures (Mukhopadhyay & Awasthi, 1981);
a four-component mixture (Kunz & Wagner, 2012) of ethane, propane, n-butane, and isobutane; and a
five-component mixture (Kunz & Wagner, 2012) of propane, n-butane, isobutane, n-pentane, and n-hexane
comprise the reference state. The experimental data for the selected six types of mixtures are shown in
Table 13. Based on Aspen Plus software, the predicted results using the SRK equation, the PR equation, the
LKP equation and the GERG-2008 equation are illustrated in Table 13 as well. The prediction accuracies
are summarized in Table 14, where GERG-2008 still shows the highest precision.
Table 14. The deviations of experimental and calculated results in phase equilibrium prediction
SRK
PR
LKP
GERG-2008
1
10.53%
7.86%
7.98%
7.49%
2
2.90%
2.42%
6.36%
1.47%
3
0.90%
1.71%
1.76%
0.71%
1.88%
0.94%
3.67%
0.36%
21.12%
14.36%
2.19%
8.06%
2.90%
0.81%
4.04%
0.35%
Overall ADD
6.52%
4.62%
4.70%
3.13%
1
10.71%
8.03%
100.00%
7.55%
2
1.55%
2.97%
6.11%
3.45%
3
2.81%
2.68%
10.73%
2.22%
4
2.80%
2.22%
7.14%
2.96%
5
1.32%
1.44%
10.60%
1.47%
6
10.67%
11.71%
8.94%
9.36%
Overall ADD
4.92%
4.81%
25.85%
4.55%
4
5
AC
C
6
EP
AAD
Notes
xi'
xi''
In addition, the prediction accuracy for the dew point is an important index of the phase equilibrium
calculation results. The dew point prediction is related to the calculation of multiple parameters of the gas
phase and the liquid phase, such as the compression factor, fugacity, and density, the accuracy of which
16
ACCEPTED MANUSCRIPT
RI
PT
reflects the physical parameter prediction accuracy of the equations of state. A custom chilled mirror
apparatus (Mørch et al., 2006) was adopted to measure the dew points of five natural gas mixtures, the
components of which are shown in Table 11. According to different experimental conditions, the dew
points calculated using the SRK equation, the PR equation, the LKP equation and the GERG-2008 equation
are obtained based on Aspen Plus software, as shown in Figures 1-5. Through a comparison with the
experimental data, the prediction accuracy of the equations of state is illustrated in Table 12. In the
prediction of the dew points, the GERG-2008 equation has the highest accuracy, and the average relative
deviation is 0.32%. Although the dew point prediction accuracies of the SRK equation for NG2 and NG4
are higher than that of GERG-2008, the data stability of GERG-2008 is the best, which shows that this
equation can be used for the prediction of dew points in liquefaction processes.
Table 15. The mixture components used in dew point prediction
Mole fraction
NG2
NG3
NG4
NG5
N2
0.00000
0.00000
0.00000
0.00000
0.00000
CO2
0.00000
0.00000
0.00000
0.00000
0.00000
CH4
0.93505
0.84280
0.96611
0.94085
0.93600
C2H6
0.02972
0.10067
0.00000
0.04468
0.02630
C3H8
0.01008
0.04028
0.00000
0.00000
0.00000
i-C4H10
0.01050
0.00597
0.01527
0.00000
0.01490
n-C4H10
0.01465
0.01028
0.01475
0.00000
0.01490
n-C5H12
0.00000
0.00000
0.00385
0.01447
0.00795
Total numbers
14
14
16
19
20
M
AN
U
NG1
SC
Composition
TE
D
Notes: NG1, NG2, NG3, NG4, NG5 represents the name of different natural gas, total numbers represent the total number of
data sets used in accuracy comparison for each kind of gas
Table 16. The deviations of experimental and calculated results in dew point prediction
SRK
PR
LKP
GERG-2008
0.38%
0.97%
0.28%
0.24%
0.18%
0.62%
0.14%
0.20%
0.25%
1.18%
0.19%
0.17%
0.51%
1.09%
0.55%
0.64%
NG5
0.42%
1.41%
0.37%
0.27%
Overall ADD
0.36%
1.09%
0.32%
0.32%
NG1
NG2
NG3
AC
C
NG4
EP
AAD
17
ACCEPTED MANUSCRIPT
Table 13. The experimental and predicted data on vapor-liquid equilibrium
Mole fraction
p/MPa
Experimental data
SRK
PR
xi
xi'
xi''
xi'
xi''
xi'
C2H6
0.02
0.0197
0.0467
0.014265
0.033784
0.017628
C3H8
0.96
0.9567
0.9423
0.962039
0.9551
0.961243
n-C4H10
0.01
0.0112
0.00461
0.012068
0.005029
0.010603
i-C4H10
0.01
0.0124
0.00639
0.011628
0.006087
0.010525
Composition
Mole fraction
366.48
Experimental data
SRK
xi'
xi''
C3H8
0.01
0.0089
0.0229
0.008598
n-C4H10
0.5
0.5008
0.6032
i-C4H10
0.15
0.1436
n-C5H12
0.2
n-C6H14
0.14
xi''
xi'
xi''
0.041582
0.02
0
0.019344
0.046003
0.948688
0.96
0
0.960387
0.944668
0.00451
0.01
0
0.010146
0.004229
0.01
0
0.010124
0.005101
0.00522
1.039
LKP
GERG-2008
xi''
xi'
xi''
xi'
xi''
0.022959
0.008672
0.023488
0.008003
0.021391
0.008894
0.023994
0.48928
0.599094
0.490206
0.599491
0.484317
0.589448
0.492723
0.592101
0.2169
0.142931
0.215347
0.143939
0.211567
0.138162
0.217521
0.144423
0.220589
0.2061
0.1159
0.208578
0.120703
0.20739
0.124929
0.213158
0.124954
0.206321
0.119998
0.1406
0.0411
0.150613
0.149793
0.040523
0.156361
0.046684
0.147639
0.043318
T/K
213.9
Experimental data
xi''
xi'
p/MPa
CH4
0.845
0.784
0.9061
C2H6
0.1476
0.2037
0.0914
C3H8
0.0074
0.0123
0.0025
5.51208
PR
LKP
GERG-2008
xi''
xi'
xi''
xi'
xi''
xi'
xi''
0.784127
0.908157
0.786382
0.908159
0.776822
0.917951
0.78297
0.907861
0.20389
0.089198
0.201796
0.089205
0.210768
0.080009
0.204904
0.089528
0.002645
0.011822
0.002635
0.012409
0.00204
0.012126
0.002611
AC
C
EP
xi'
T/K
0.041895
SRK
xi
Mole fraction
xi'
xi'
TE
D
xi''
Composition
xi''
PR
xi'
Mole fraction
GERG-2008
p/MPa
xi
Composition
LKP
M
AN
U
T/K
1.713
RI
PT
Composition
322.04
SC
T/K
0.011983
213.9
Experimental data
p/MPa
SRK
2.75604
PR
LKP
GERG-2008
xi
xi'
xi''
xi'
xi''
xi'
xi''
xi'
xi''
xi'
xi''
CH4
0.6199
0.3725
0.8673
0.363954
0.867456
0.377668
0.867221
0.389992
0.874311
0.371569
0.866502
C2H6
0.3231
0.5193
0.127
0.525527
0.127309
0.514735
0.127438
0.505835
0.120889
0.519323
0.128243
C3H8
0.057
0.1082
0.0057
0.110519
0.005235
0.107596
0.005341
0.104173
0.004799
0.109108
0.005255
18
ACCEPTED MANUSCRIPT
Composition
Mole fraction
172.2
p/MPa
Experimental data
SRK
PR
xi
xi'
xi''
xi'
xi''
xi'
CH4
0.926
0.8565
0.9955
0.814097
0.995433
0.827729
C2H6
0.0249
0.0462
0.0035
0.059256
0.003583
0.055129
C3H8
0.0491
0.0973
0.001
0.126647
0.000984
0.117142
Composition
Mole fraction
LKP
xi''
xi'
172.2
GERG-2008
xi''
xi'
xi''
0.995527
0.852335
0.996094
0.840391
0.995437
0.003513
0.047797
0.003113
0.051251
0.003527
0.000961
0.099868
0.000793
0.108358
0.001036
p/MPa
Experimental data
SRK
SC
T/K
2.06703
RI
PT
T/K
PR
xi'
xi''
xi'
xi''
xi'
CH4
0.7619
0.5487
0.9751
0.534409
0.976454
C2H6
0.2036
0.3826
0.0246
0.394912
C3H8
0.0345
0.0687
0.0003
0.070679
LKP
GERG-2008
xi''
xi'
xi''
xi'
xi''
0.552062
0.976091
0.567153
0.977114
0.546882
0.975108
0.023168
0.380023
0.023517
0.367449
0.022531
0.384212
0.024509
0.000378
0.067915
0.000392
0.065398
0.000355
0.068907
0.000383
AC
C
EP
TE
D
Notes: the subscript ' represents the liquid phase, the subscript '' represents the gas phase.
M
AN
U
xi
1.37802
19
SC
RI
PT
ACCEPTED MANUSCRIPT
Figure 2. The experimental and predicted
data on dew points of NG2
TE
D
M
AN
U
Figure 1. The experimental and predicted
data on dew points of NG1
EP
Figure 3. The experimental and predicted
data on dew points of NG3
AC
C
Figure 4. The experimental and predicted
data on dew points of NG4
Figure 5. The experimental and predicted data on dew points of NG5
20
ACCEPTED MANUSCRIPT
5. Evaluation of the equations of state in natural gas liquefaction processes
The predicted results in terms of the gas density, saturated liquid density, enthalpy, heat capacity and
phase equilibrium of the SRK equation, the PR equation, the LKP equation and the GERG-2008 equation
are summarized in Table 17.
Table 17. Summary of the deviations of experimental and calculated results
SRK
PR
LKP
GERG-2008
Gas density
1.73%
2.55%
0.31%
0.10%
Saturated liquid density
1.42%
0.23%
12.43%
0.19%
Enthalpy
5.15%
2.30%
3.85%
1.71%
Isobaric specific heat capacity
6.81%
4.04%
4.29%
1.70%
xi' in vapor-liquid equilibrium
6.52%
4.62%
4.70%
3.13%
xi'' in vapor-liquid equilibrium
4.92%
4.81%
25.85%
4.55%
Dew point
0.36%
1.09%
0.32%
0.32%
M
AN
U
SC
RI
PT
AAD
AC
C
EP
TE
D
The SRK equation has a good performance in predicting the dew point. With the volume correction
method, the accuracy of the equation is greatly improved in terms of saturated liquid density. Large
deviations are observed in the calculation of enthalpy and heat capacity. Regarding the prediction of the gas
density and phase equilibrium, good matching results with the experimental data are obtained to some
extent.
The PR equation shows good accuracy in terms of the enthalpy and isobaric specific heat capacity
prediction. Significant improvements are observed in predicting the saturated liquid density with the
Rackett model. The equation also shows good prediction accuracy in the calculation of the vapor-liquid
equilibrium. However, the deviations of the two basic parameters of gas density and dew point are
relatively large in comparison with the experimental results.
The LKP equation has good precision in predicting the gas density and dew point. Good agreements are
also obtained in the predictions of the enthalpy and the isobaric specific heat capacity. Large deviations are
observed in regions near the critical point. The equation is not suitable for the calculation of saturated
liquid density and vapor-liquid equilibrium.
Although the SRK equation, the PR equation and the LKP equation are the popular basic models for
calculating the physical properties of natural gas liquefaction processes, large deviations are observed from
the accurate experimental data for some parameters or under certain conditions, which may lead to
inaccurate results for the simulation and optimization of liquefaction processes. GERG-2008 achieves good
accuracy in predicting all of the thermodynamic properties and phase equilibria over a wide range of
temperatures, pressures and feed gas components. On account of the remarkable adaptability of working
conditions and gas compositions, GERG-2008 is recommended as the basis for predicting the physical
parameters in natural gas liquefaction processes.
The standard form of the cubic equations of state, such as the SRK equation and the PR equation, has
obvious defects in predicting liquid densities, which have been modified by the volume correction method
and the Rackett model. The binary parameters of Knapp et al. (1982) are used in this paper for the SRK
equation, the PR equation and the LKP equation. However, the prediction accuracy can be improved
through the regression of binary parameters using phase equilibrium data. To simplify the analysis, studies
on the pretreatment and liquefaction of natural gas are usually performed separately; thus, this paper is not
21
ACCEPTED MANUSCRIPT
related to prediction accuracy for natural gas containing water. Because the SRK equation and the PR
equation are also widely used in the pretreatment processes, a further study should be performed regarding
the prediction accuracy of cubic equations of state and GERG-2008 for natural gas containing water, heavy
hydrocarbons, and other impurities.
6. Conclusions
M
AN
U
SC
RI
PT
The natural gas liquefaction process is a complicated and dynamic thermal system. Accurate prediction
of the thermodynamic properties and the phase equilibrium parameters with the change of working
conditions is of significant importance for the design and simulation of liquefaction processes. Combined
with the accurate experimental data, Aspen Plus was employed to conduct a comprehensive comparison
and analysis among the SRK equation, the PR equation, the LKP equation and the GERG-2008 equation in
predicting the gas and saturated liquid density, specific heat capacity, enthalpy, dew point and vapor-liquid
equilibrium. Although the SRK equation, the PR equation and the LKP equation are popular basic models
for calculating the physical properties of natural gas liquefaction processes, large deviations are observed
from the accurate experimental data for some parameters or under certain conditions, which may lead to
inaccurate results for the simulation and optimization of liquefaction processes. GERG-2008 achieves good
accuracy in predicting all of the thermodynamic properties and phase equilibrium over a wide range of
temperatures, pressures and feed gas components. As a result, GERG-2008 is recommended as the basis for
predicting physical parameters in natural gas liquefaction processes.
TE
D
Acknowledgements
This work is supported by the oil and gas storage and transportation engineering department in Southwest
Petroleum University, China.
EP
References
AC
C
Alabdulkarem, A., Mortazavi, A., Hwang, Y., Radermacher, R., & Rogers, P., 2011. Optimization of
propane pre-cooled mixed refrigerant LNG plant. Applied Thermal Engineering, 31(6), 1091-1098. Castillo,
L.,
Ashton, G. J., & Haselden, G. G., 1980. Measurements of enthalpy and phase equilibrium for simulated
natural gas mixtures and correlation of the results by a modified Starling equation. Cryogenics, 20(1),
41-47.
Aspelund, A., Berstad, D. O., & Gundersen, T., 2007 An Extended Pinch Analysis and Design procedure
utilizing pressure based exergy for subambient cooling. Applied Thermal Engineering, 27(16), 2633-2649.
Aspen Technology, Inc., 2013. Aspen Plus Help. Aspen Technology, Inc, US.
Atilhan, M., Aparicio, S., Ejaz, S., Cristancho, D., & Hall, K. R., 2011a. P ρ T Behavior of a Lean Synthetic
Natural Gas Mixture Using Magnetic Suspension Densimeters and an Isochoric Apparatus: Part I. Journal
of Chemical & Engineering Data, 56(2), 212-221.
Atilhan, M., Aparicio, S., Ejaz, S., Cristancho, D., Mantilla, I., & Hall, K. R., 2011b. p–ρ–T Behavior of
Three Lean Synthetic Natural Gas Mixtures Using a Magnetic Suspension Densimeter and Isochoric
Apparatus from (250 to 450) K with Pressures up to 150 MPa: Part II. Journal of Chemical & Engineering
22
ACCEPTED MANUSCRIPT
TE
D
M
AN
U
SC
RI
PT
Data, 56(10), 3766-3774.
Cao, W. S., Lu, X. S., Lin, W. S., & Gu, A. Z., 2006. Parameter comparison of two small-scale natural gas
liquefaction processes in skid-mounted packages. Applied Thermal Engineering, 26(8), 898-904.
Castillo, L., Dahouk, M. M., Di Scipio, S., & Dorao, C. A., 2013. Conceptual analysis of the precooling
stage for LNG processes. Energy conversion and management, 66, 41-47.
Dauber, F., & Span, R., 2012. Modelling liquefied-natural-gas processes using highly accurate property
models. Applied Energy, 97, 822-827.
Haynes, W. M., 1982. Measurements of orthobaric-liquid densities of multicomponent mixtures of lng
components (N2, CH4, C2H6, C3H8, CH3CH(CH3)CH3, C4H10, CH3CH(CH3)C2H5 and C5H12) between 110
and 130 K. The Journal of Chemical Thermodynamics, 14(7), 603-612.
Hiza, M. J., & Haynes, W. M., 1980. Orthobaric liquid densities and excess volumes for multicomponent
mixtures of low molar-mass alkanes and nitrogen between 105 and 125 K. The Journal of Chemical
Thermodynamics, 12(1), 1-10.
Hwang, C. A., Simon, P. P., Hou, H., Hall, K. R., Holste, J. C., & Marsh, K. N., 1997. Burnett and
pycnometric (p, Vm, T) measurements for natural gas mixtures. The Journal of Chemical Thermodynamics,
29(12), 1455-1472.
Khan, M. S., & Lee, M., 2013. Design optimization of single mixed refrigerant natural gas liquefaction
process using the particle swarm paradigm with nonlinear constraints. Energy, 49, 146-155.
Khan, M. S., Lee, S., Hasan, M., & Lee, M., 2014. Process knowledge based opportunistic optimization of
the N2–CO2 expander cycle for the economic development of stranded offshore fields. Journal of Natural
Gas Science and Engineering, 18, 263-273.
Knapp, H., Döring R., Oellrich L., Plöcker U., & Prausnitz. J. M., 1982. Vapor-liquid equilibria for
mixtures of low-boiling substances. Dechema Chemistry Data, Vol. VI.
Kumar, S., Kwon, H. T., Choi, K. H., Cho, J. H., Lim, W., & Moon, I., 2011. Current status and future
projections of LNG demand and supplies: A global prospective. Energy Policy, 39(7), 4097-4104.
Kunz, O., & Wagner, W., 2012. The GERG-2008 wide-range equation of state for natural gases and other
mixtures: an expansion of GERG-2004. Journal of chemical & engineering data, 57(11), 3032-3091.
EP
Leach, J. W., Chappelear, P. S., & Leland, T. W., 1968. Use of molecular shape factors in vapor‐liquid
equilibrium calculations with the corresponding states principle. AIChE Journal, 14(4), 568-576.
AC
C
Lee, B. I., & Kesler, M. G., 1975. A generalized thermodynamic correlation based on three‐parameter
corresponding states. AIChE Journal, 21(3), 510-527.
Magee, J. W., Haynes, W. M., & Hiza, M. J., 1997. Isochoric (p, ρ, T) measurements for five natural gas
mixtures from T = (225 to 350) K at pressures to 35 MPa. The Journal of Chemical Thermodynamics,
29(12), 1439-1454.
McLinden, M. O., 2011. p−ρ−T Behavior of Four Lean Synthetic Natural-Gas-Like Mixtures from 250 K
to 450 K with Pressures to 37 MPa. Journal of Chemical & Engineering Data, 56(3), 606-613.
Moein, P., Sarmad, M., Ebrahimi, H., Zare, M., Pakseresht, S., & Vakili, S. Z., 2015. APCI-LNG single
mixed refrigerant process for natural gas liquefaction cycle: Analysis and optimization. Journal of Natural
Gas Science and Engineering, 26, 470-479.
Mørch, Ø., Nasrifar, K., Bolland, O., Solbraa, E., Fredheim, A. O., & Gjertsen, L. H., 2006. Measurement
and modeling of hydrocarbon dew points for five synthetic natural gas mixtures. Fluid phase equilibria,
239(2), 138-145.
23
ACCEPTED MANUSCRIPT
AC
C
EP
TE
D
M
AN
U
SC
RI
PT
Mukhopadhyay, M., & Awasthi, R., 1981. K-value predictions for the Methane-Ethane-Propane System.
Cryogenics, 21(6), 345-348.
Nogal, F. D., Kim, J. K., Perry, S., & Smith, R., 2008. Optimal design of mixed refrigerant cycles.
Industrial & Engineering Chemistry Research, 47(22), 8724-8740.
Péneloux, A., Rauzy, E., & Fréze, R., 1982. A consistent correction for Redlich-Kwong-Soave volumes.
Fluid Phase Equilibria, 8(1), 7-23.
Peng, D. Y., & Robinson, D. B., 1976. A new two-constant equation of state. Industrial & Engineering
Chemistry Fundamentals, 15(1), 59-64.
Plocker, U., Knapp, H., & Prausnitz, J., 1978. Calculation of high-pressure vapor-liquid equilibria from a
corresponding-states correlation with emphasis on asymmetric mixtures. Industrial & Engineering
Chemistry Process Design and Development, 17(3), 324-332.
Pitzer, K. S., Lippmann, D. Z., Curl Jr, R. F., Huggins, C. M., & Petersen, D. E., 1955. The Volumetric and
Thermodynamic Properties of Fluids. II. Compressibility Factor, Vapor Pressure and Entropy of
Vaporization1. Journal of the American Chemical Society, 77(13), 3433-3440.
Rackett, H. G., 1970. Equation of state for saturated liquids. Journal of Chemical and Engineering Data,
15(4), 514-517.
Redlich, O., & Kwong, J. N., 1949. On the thermodynamics of solutions. V. An equation of state. Fugacities
of gaseous solutions. Chemical reviews, 44(1), 233-244.
Shirazi, M. M. H., & Mowla, D., 2010. Energy optimization for liquefaction process of natural gas in peak
shaving plant. Energy, 35(7), 2878-2885.
Soave, G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical
Engineering Science, 27(6), 1197-1203.
U.S.
Energy
Information
Administration.
International
energy
outlook
2013,
<
http://www.eia.gov/forecasts/ieo/ >
Vaidyaraman, S., & Maranas, C. D., 2002. Synthesis of mixed refrigerant cascade cycles. Chemical
Engineering Communications, 189(8), 1057-1078.
Van Kasteren, P. H., & Zeldenrust, H., 1979. A flow calorimeter for condensable gases at low temperatures
and high pressures. 2. Compilation of experimental results and comparison with predictions based on a
modified Redlich-Kwong Equation of state. Industrial & Engineering Chemistry Fundamentals, 18(4),
339-345.
Yuan, Z., Cui, M., Xie, Y., & Li, C., 2014. Design and analysis of a small-scale natural gas liquefaction
process adopting single nitrogen expansion with carbon dioxide pre-cooling. Applied Thermal Engineering,
64(1-2), 139-146.
Yuan Z. M., Cui M. M., Song R., Xie Y., & Han L., 2015. Performance Improvement of a Boil-off Gas
Re-condensation Process with Precooling at LNG Terminals. International Journal of Thermodynamics,
18(2), 74-80.
24
ACCEPTED MANUSCRIPT
AC
C
EP
TE
D
M
AN
U
SC
RI
PT
Highlights:
The common prediction models for physical properties in natural gas liquefaction processes are
summarized.
A comprehensive comparison and analysis among the prediction models is conducted.
GERG-2008 shows better adaptability over a wide range of working conditions and feed gas
components.