Prediction of thermodynamic properties of petroleum and refinery gases using PC-SAFT+FVT model
PETROVIETNAM
PETROVIETNAM JOURNAL
Volume 6/2020, pp. 45 - 53
ISSN 2615-9902
PREDICTION OF THERMODYNAMIC PROPERTIES OF PETROLEUM
AND REFINERY GASES USING PC-SAFT+FVT MODEL
Luu Tra My1, Nguyen Huynh Dong1, Nguyen Huynh Duong2
1Petrovietnam Manpower Training College (PVMTC)
2Petrovietnam Gas Joint Stock Corporation (PV GAS)
Email: dongnh@pvmtc.com.vn
Summary
The PC-SAFT equation of state (EoS) combined with the free-volume theory (FVT) recently proposed (DOI: 10.1016/j.fluid.2019.
112280) is extended in this work to simultaneously predict viscosity and some second-order derivative properties such as sound velocity
and isobaric heat capacity of some petroleum and refinery gases. The PC-SAFT pure component parameters are obtained by providing the
optimal description of its vapour pressure and saturated liquid density data. New FVT parameters were derived for various petroleum and
refinery gases and were validated with the National Institute of Standards and Technology’s data over a wide range of temperature and
pressure (up to 2,000 bars). The model is simple to incorporate into the design and simulation package such as Aspen Plus or Prosim, with
average absolute deviation obtained on viscosity within the experimental incertitude (< 3%), which is appropriate for most industrial
applications.
Key words: Viscosities, PC-SAFT, prediction, thermodynamic, petroleum gases.
1. Introduction
The importance of gases in oil recovery operations
still an important subject in the oil and gas industry.
So, the development of a thermodynamic model with
good accuracy in predicting the phase equilibria and
thermodynamic properties of fluids is a great importance.
In this paper, the applicability of the PC-SAFT+FVT model
is assessed on petroleum and refinery gases.
is increasing, as evidenced in the successful use of gases
such as carbon dioxide, nitrogen and their mixtures as
injection gases in enhanced oil recovery. The simulation
and modelling using the simulation package allow to
reduce capital, time and cost related to the operation of
oil and gas processing units and pipeline transportation.
In this, the viscosity model is an important component
of the package, ranging from the simulation of gas
production at reservoir condition to the design and
operation of pipeline transportation or petrochemical
plant. Although the experimental data are available
for numerous petroleum gases, there is still a need
for a generalised estimator that is able to predict the
thermodynamic properties of molecules over a wide
range of thermodynamic conditions, particularly at
extreme temperature and pressure condition.
2. PC-SAFT + FVT model
In previous works, the PC-SAFT + FVT model has been
proposed based on the assumption that the viscosity of
real fluids could be directly related to PC-SAFT molecular
parameters [1]. Our model has been successfully applied
to calculate the viscosity of several kinds of molecules
such as alkane, cycloalkane, alcohols, aromatics and
their mixtures [1, 2]. In this work, we apply, for the first
time, the PC-SAFT+FVT model to the calculation of the
thermodynamic second-order derivative properties and
the viscosity of several gases.
2.1. PC-SAFT EoS
Simultaneous prediction of transport properties
and fluid phase equilibria using equation of state is
The original PC-SAFT EoS is expressed as a sum of
different residual Helmholtz terms [3]:
Date of receipt: 7/9/2019. Date of review and editing: 7/9 - 9/10/2019.
Date of approval: 5/6/2020.
ares = ahc + adisp
(1)
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PETROLEUM PROCESSING
For all gases studied in this work, they are considered
In which T, M, and
are temperature (K), mass
as non-associative, non-polar molecules. PC-SAFT EoS
requires three parameters to describe these components
(dispersive energy - ε/k, segment diameter - σ and
segment number - m). The readers are referred directly
to the original papers for more details about the PC-
SAFT EoS [3]. All expressions used to calculate different
thermodynamic properties such as heat capacity or speed
of sound are explained in the references [4 - 6].
molecular (g/mol) and gas viscosity, respectively; σ and m
are PC-SAFT EoS hard-sphere diameter (Å) and segment
number. The reduced collision integral (Ω*) is calculated
using Equation (4) [7].
(4)
2.2. Free-volume theory
The dimensionless temperature (T*) is a function
of temperature and PC-SAFT dispersive energy of pure
compound, small gases:
The fluids’viscosity by FVT consists of two terms [1]:
(2)
T
*
T =
The first term called dilute gas viscosity ( ) is
expressed as [1]:
ε
k
The other contribution of viscosity in Equation (2) is
the residual viscosity (Δη), that could be estimated based
(3)
300
Methane
100 K
200 K
300 K
400 K
500 K
Methane
500
50
1,100
5
900
700
500
0.5
300
100
0
150
150
300
450
300
600
30
0.05
1
10
100
Pressure (bar)
1000
0
450
Density (g/l)
2000
0.4
Methane
Methane
0.04
100 K
200 K
300 K
400 K
500 K
150 K
100 K
200 K
300 K
400 K
500 K
150 K
1000
200
0.004
1
10
100
1000
1
10
100
Pressure (bar)
Pressure (bar)
Figure 1. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of methane.
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Table 1. PC-SAFT+FVT model parameters for gases [9, 10]
α x 10ꢀ3
(J m3/ mole kg)
3.9298
Compound
Iso-butane
ε/k (K)
σ (Å)
m
L x 103 (Å)
Fp
Fc x 10ꢀ2
205.942
113.642
89.394
151.734
89.468
3.6584
3.1759
3.1964
2.5608
3.2945
3.7042
3.5098
2.4587
1.1481
1.3699
2.5807
1.2376
1.0003
1.6364
3.4260
2.5913
5.5051
1.9059
1.6560
2.1652
3.7890
1.0
1.35
0.15
2.8
1.85
1.0
2.2908
1.0599
1.2044
1.6207
1.1037
0.9832
1.2336
Oxygen
0.5549
0.5709
1.6735
0.9291
2.3798
2.4022
Carbon monoxide
Carbon dioxide
Nitrogen
Methane
Ethane
150.037
189.001
1.35
Table 2. The average absolute deviation (AAD) for the PC-SAFT+FVT for all of the investigated molecules. Experimental data are taken from DIPPR [8]
ꢂaꢁour ꢁreꢃꢃure ꢄiꢅuid denꢃitꢆ ꢄiꢅuid ꢇiꢃcoꢃitꢆ ꢂaꢁour ꢇiꢃcoꢃitꢆ
ꢀomꢁound
T ꢈꢉꢊ
ꢋꢋꢌ ꢈꢍꢊ
T ꢈꢉꢊ
ꢋꢋꢌ ꢈꢍꢊ
0.92
1.48
1.38
1.41
1.10
1.31
2.22
T ꢈꢉꢊ
ꢋꢋꢌ ꢈꢍꢊ
T ꢈꢉꢊ
ꢋꢋꢌ ꢈꢍꢊ
0.81
1.17
1.83
0.56
0.31
1.29
1.95
Oxygen
54 - 154
68 - 132
216 - 304
63 - 126
90 - 190
90 - 305
123 - 407
0.67
0.38
0.28
0.24
0.51
0.67
3.28
54 - 154
68 - 132
216 - 304
63 - 126
90 - 190
90 - 305
123 - 407
54 - 132
68 - 124
200 - 304
64 - 122
84 - 186
90 - 302
114 - 310
1.83
3.83
1.08
2.60
0.40
1.69
1.95
54 - 600
68 - 600
270 - 610
64 - 600
84 - 600
90 - 600
150 - 600
Carbon monoxide
Carbon dioxide
Nitrogen
Methane
Ethane
Iso-butane
500
1000
100 K
Ethane
200 K
320 K
400 K
500 K
600 K
100
10
Ethane
1
700
400
100
0.1
0.01
0.001
0.0001
0
150 300 450 600 750
50
1
0.00001
0
150
300
450
600
10
Pressure (bar)
100
1000
Density (g/l)
Ethane
2000
Ethane
0.8
0.08
100 K
320 K
500 K
200 K
400 K
600 K
100 K
200 K
320 K
400 K
500 K
600 K
1000
200
1
0.008
1
10
100
Pressure (bar)
10
100
1000
Pressure (bar)
Figure 2. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of ethane.
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PETROLEUM PROCESSING
on the expression previously suggested [1]:
characteristic parameters of fluid according to FVT theory.
The FVT parameter triplet set and the Fc can be obtained
by regressing to the experimental viscosity data.
(5)
3. PC-SAFT+FVT parameters regression
Six petroleum and refinery gases and oxygen have
been studied. These gases have been selected to test
the model due to the availability of experimental data.
The regression of PC-SAFT+FVT model parameters has
been carried out in a sequential manner, with alternate
optimisation of the PC-SAFT EoS parameters and then the
correction factor (Fc) and the FVT triplet set in Equation (5)
Where the viscosity is given in mPas; R is universal
gas constant (8.314 J/mol.K) and P is pressure (in bar). The
liquid density (ρ, in kg/m3) is the only property yielded
by the PC-SAFT. L is the length parameter (in Å) which
is related to the molecular size, α is the barrier energy
required for self-diffusion (in J m3/(mol.Kg), and Fp is the
free-volume overlap. These last three parameters are
70
Nitrogen
1000
100
100 K
200 K
300 K
400 K
500 K
600 K
55
40
25
10
900
700
500
1
300
100
Nitrogen
0
300
600
900
0.1
0
150
300
450
Density (g/l)
600
750
900
1
10
100
1000
Pressure (bar)
100 K
200 K
100 K
300 K
500 K
200 K
400 K
600 K
1150
300 K
150 K
400 K
600 K
0.1
850
550
250
Nitrogen
1000
Nitrogen
1000
0.01
1
10
100
Pressure (bar)
1
10
100
Pressure (bar)
Figure 3. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of nitrogen.
PETROVIETNAM - JOURNAL VOL 6/2020
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were next determined by minimising a quadratic residual
defined by relative viscosities.
component is dictated by the availability of experimental
data from the Design Institute for Physical Property Data
(DIPPR) [8].
Step 1: The PC-SAFT EoS parameters of petroleum and
refinery gases were determined by simultaneously fitting
on its vapour pressure and saturated liquid density. The
regression function that was used is written as:
N
Step 2: Having three PC-SAFT parameters, the
correction factor (Fc) of gases is fitted using their dilute
gas viscosity data. Three adjustable parameters (L, α, Fp)
in Equation (5) were obtained by fitting the model to the
saturated liquid viscosity.
NPsat
sat
liq
liq
cal
liq
exp
Psat
P
exp
1
NPsat
1
cal
Fobj
(6)
liq
exp
Psat
N
liq
1
1
exp
The PC-SAFT+FVT model parameters for different
gases considered in this work are reported inTable 1. Table
2 represents the experimental data sources and deviations
obtained with PC-SAFT+FVT model for pure gases. For all
Where NPsat and Nρliq are the number of the
experimental vapour pressures and saturated liquid
density data, respectively. The choice of data for each
100 K
150 K
200 K
300 K
400 K
500 K
Carbon monoxide
1000
100
115
70
10
900
700
500
1
300
Carbon
100
monoxide
0
300
300
600
450
900
600
25
0.1
1
10
100
1000
0
150
750
900
Pressure (bar)
Density (g/l)
1500
Carbon monoxide
Carbon monoxide
0.1
100 K
150 K
200 K
300 K
400 K
500 K
100 K
300 K
500 K
200 K
400 K
150 K
150
0.01
1
10
100
1000
10
100
Pressure (bar)
1000
Pressure (bar)
Figure 4. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of carbon monoxide.
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PETROLEUM PROCESSING
cases, the average absolute deviation obtained on vapour
pressure, liquid density and saturated viscosities is within
the experimental accuracy (lower than 2%) [2].
stringent than their correlation accuracy. This prediction
also allows to validate the prediction potential of the
model over a wide range of thermodynamic conditions.
The deviation is defined as:
Figures 1 to 7 show the comparison between the
predicted values obtained with the current model and the
experimental data of several petroleum gases in both sub-
and super critical regions. The experimental data are taken
gov/chemistry/fluid). An excellent match between the
predicted and experimental liquid density and viscosity
was obtained for all considered gases. Considering the
results of these figures, it is evident that the PC-SAFT+FVT
model provides a very good result for heat capacity. The
exp
cal
AAD(%) 100.
(7)
exp
data
4. Results and discussion
The liquid density, isobaric heat capacity, speed of
sound and viscosity of seven gases were predicted in
the temperature range of 100K to 600K and pressure up
to 2,000 bars. This extrapolation test seems to be more
3000
Carbon dioxide
Carbon dioxide
230 K
260 K
330 K
370 K
420 K
500 K
600 K
180
150
120
90
300
1,810
30
1,240
670
60
100
30
500
800 1,100 1,400
400 800
3
1
10
100
1000
0
1,200
Density (g/l)
Pressure (bar)
1500
Carbon dioxide
Carbon dioxide
0.12
230 K
260 K
330 K
370 K
420 K
500 K
600 K
230 K
310 K
370 K
500 K
260 K
330 K
420 K
600 K
150
0.012
1
10
100
Pressure (bar)
1000
1
10
100
Pressure (bar)
1000
Figure 5. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of carbon dioxide.
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75
50
25
1000
100
10
Oxygen
700
400
100
1
100 K
300 K
500 K
200 K
400 K
600 K
0.1
0.01
0.001
Oxygen
100 400 700 1,000 1,300
400 800
1
10
100
1000
0
1,200
Pressure (bar)
Density (g/l)
1200
Oxygen
Oxygen
0.1
100 K
300 K
500 K
200 K
400 K
600 K
100 K
200 K
300 K
400 K
500 K
600 K
0.01
120
1
10
100
1000
1
10
100
1000
Pressure (bar)
Pressure (bar)
Figure 6. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of oxygen.
average absolute deviation results from experimental data
is around 1 - 3% for most of cases, except for iso-butane,
at temperature lower than 200K, the predicted values
deviate largely from the measured data. In fact, the speed
of sound is generally represented as a severe consistency
test for any EoS, since it involves the temperature and
density partial derivatives of pressure, and PC-SAFT is not
able to describe with great accuracy the p(ρ, T) [4 - 6]. The
model was also not able to reproduce the transaction
regions, e.g. for iso-butane, the model could not match
the 350K isotherm data ranging from 1 bar to 10 bars, for
both speed of sound and viscosity [11].
5. Conclusion
In this work, the PC-SAFT+FVT model has been
applied to some petroleum and refinery gases. The pure
component parameters for several gases have been
reported. Single phase liquid density, isobaric heat
capacity, sound velocity and viscosity of these molecules
have been predicted and compared with experimental
data. Results have indicated that with the exception
of the speed of sound at condition lower than 200K,
PC-SAFT+FVT accurately predicts the thermodynamic
properties of petroleum and refinery gases. PC-SAFT is
not adequate for predicting the isobaric heat capacity
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260
1000
100
150 K
250 K
350 K
450 K
550 K
Iso -butane
Iso -butane
10
220
180
140
100
1
400
350
300
250
200
150
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
100
200
500
300
800
600
1
10
100
1000
0
Pressure (bar)
Density (g/l)
4
Iso -butane
150 K
Iso -butane
1500
250 K
350 K
450 K
550 K
0.4
0.04
150 K
250 K
350 K
450 K
550 K
0.004
150
1
10
Pressure (bar)
100
1
10
100
Pressure (bar)
1000
Figure 7. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of iso-butane.
of iso-butane at temperature lower than 450K. These
deviations were already observed in the prediction of
other similar pure fluids such as alkanes or non-polar
molecules [6, 12].
References
[1] Nguyen Huynh Dong, Chau Thi Quynh Mai, and
Siem Thi Kim Tran, "Free-volume theory coupled with
modified group-contribution PC-SAFT for predicting
the viscosities. I. Non-associated compounds and their
mixtures", Fluid Phase Equilibria, Vol. 501, 2019. DOI:
10.1016/j.fluid.2019.112280.
For conclusion, the PC-SAFT+FVT model could be used
as a robust estimator for the thermodynamic properties of
petroleum gases with good accuracy, particularly in the
temperature and pressure conditions of interest in the oil
and gas industry. The model is simple to incorporate into
the design and simulation package such as Aspen Plus or
Prosim, with the average absolute deviation obtained by
the model being within the experimental incertitude.
[2] Nguyen Huynh Dong, Luu Tra My, Xuan Thi Thanh
Nguyen, ChauThi Quynh Mai, and SiemThi KimTran, "Free-
volume theory coupled with modified group-contribution
PC-SAFT for predicting the viscosities. II. Alcohols and
PETROVIETNAM - JOURNAL VOL 6/2020
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their mixtures", Fluid Phase Equilibria, Vol. 502, 2019. DOI:
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[3] Joachim Gross and Gabriele Sadowski, "Perturbed-
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[10] Nguyen
Huynh
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[11] Ilya Polishuk, Helena Lubarsky, and Nguyen
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systems without fitting binary parameters II: Gases and
non-aromatic hydrocarbons", AIChE Journal, Vol. 63, No.
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[12] Nguyen Huynh Duong and Nguyen Huynh
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[7] Philip.D.Neufeld, A.R.Janzen, and R.A.Aziz,
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