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
Petrovietnam Manpower Training College (PVMTC)
2
Petrovietnam Gas Joint Stock Corporation (PV GAS)
Email:

1

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
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.
Simultaneous prediction of transport properties
and fluid phase equilibria using equation of state is
Date of receipt: 7/9/2019. Date of review and editing: 7/9 - 9/10/2019.
Date of approval: 5/6/2020.

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.
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
The original PC-SAFT EoS is expressed as a sum of
different residual Helmholtz terms [3]:
ares = ahc + adisp
PETROVIETNAM - JOURNAL VOL 6/2020

(1)
45


PETROLEUM PROCESSING

For all gases studied in this work, they are considered
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 PCSAFT 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].

In which T, M, and
are temperature (K), mass
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].

2.2. Free-volume theory

The dimensionless temperature (T*) is a function
of temperature and PC-SAFT dispersive energy of pure
compound, small gases:


(4)

The fluids’ viscosity by FVT consists of two terms [1]:
(2)

T* =

The first term called dilute gas viscosity ( ) is
expressed as [1]:

The other contribution of viscosity in Equation (2) is
the residual viscosity (Δη), that could be estimated based

(3)
300

Methane
Methane
Methane

Methane

Methane
Methane
500

Methane
500
Methane

500 500

5

50

5

1,100 1,100
5 900
900
1,100 1,100
5 700 700
900 900

500
0.5 700
300
500
0.5 0.5

100
300
1000 1000 0.05 00.05 100
0
0.05
0.05
1000
0
1000
0
0.5

30
30

30

1
1

30

1
1

10

100
10
100

PressurePressure
(bar) (bar)
10 10
100 100
Pressure
Pressure
(bar) (bar)

500
700
300
500
100
300
0
150
300 300
450 450
600 600
0
150
100150 150
300 300
450 450
(g/l)
0150Density
150
300
450
Density

0
300
450(g/l)
600 600
150 150
300 300
450 450
Density
Density
(g/l) (g/l)

0.4

0.4 Methane
Methane

Viscosity
( mPa.s)
Viscosity
( mPa.s)

2000 2000
Methane
Methane

Viscosity
( mPa.s)
Viscosity
( mPa.s)

0.4 Methane
Methane

Sound
Spd. (m/s)
Sound
Spd. (m/s)

0.4

Spd. (m/s)
SoundSound
Spd. (m/s)

2000 2000
Methane
Methane

0.04

0.04

0.04 0.04

100 K 100 K
200 K 200 K
100 KK 100
300
300KK
200 KK 200

400
400KK
300 KK 300
500
500KK
400 KK 400
150
150KK
200
200
K 0.004 0.004
500 K 500
1
10
100
1000
1
10
100
1
10
100
1000
1
10
100
150
K
150
K

Pressure
(bar)
Pressure
(bar) (bar)
Pressure (bar)
Pressure
200
0.004
200
0.004
1
10
100
1000
1
10
1
10 (NIST
100
1000
1
100 100
Figure 1. Predicted
and experimental
Chemistry
Web Book) isobaric heat
capacity, liquid density, viscosity
and speed of10sound of methane.
Pressure
Pressure

Pressure
(bar) (bar)
Pressure
(bar) (bar)

46

PETROVIETNAM - JOURNAL VOL 6/2020

100 K100 K

50

50
Pressure
(bar) (bar)
Pressure

Pressure
Pressure
(bar) (bar)

50

100 K 100 K

Cp (J/mol*K)
Cp (J/mol*K)

Cp (J/mol*K)

Cp (J/mol*K)

300100 K 100 K
200 K 200 K
300 300 100 K 100 K
300 K 300 K
K
200 KK 200
400
400 K
300
300 KK 500KK
500
400 K 400 K
500 K 500 K

T
ε
k

100 K 100 K
200 K 200 K
300
100 KK 100
300KK
400
200 KK 200
400KK
500
300 KK 300

500KK
150
400 KK 400
150KK
500 K
500 K 1000
1000
150 K 150 K
1000 1000


PETROVIETNAM

Table 1. PC-SAFT+FVT model parameters for gases [9, 10]
Compound
Iso-butane
Oxygen
Carbon monoxide
Carbon dioxide
Nitrogen
Methane
Ethane

ε/k (K)

σ (Å)

m

L x 103 (Å)

205.942
113.642
89.394
151.734
89.468
150.037
189.001

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

α x 103
(J m3/ mole kg)
3.9298
0.5549
0.5709
1.6735
0.9291
2.3798
2.4022

Fp

Fc x 102

1.0
1.35
0.15
2.8
1.85
1.0
1.35

2.2908
1.0599
1.2044
1.6207
1.1037

0.9832
1.2336

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]
Liquid density
Liquid viscosity
T (K)
AAD (%)
T (K)
AAD (%)
54 - 154
0.92
54 - 132
1.83
68 - 132
1.48
68 - 124
3.83
216 - 304
1.38
200 - 304
1.08
63 - 126
1.41
64 - 122
2.60
90 - 190
1.10
84 - 186
0.40

90 - 305
1.31
90 - 302
1.69
123 - 407
2.22
114 - 310
1.95
1000
1000
Ethane
Ethane

10 10
100100
Pressure
(bar)(bar)
Pressure
10 10
100100
Pressure
(bar)
Pressure
(bar)

1000
1000
1000
1000

Ethane
Ethane

Ethane
2000
2000Ethane

0.8 0.8
Viscosity
( mPa.s)
Viscosity
( mPa.s)
Viscosity
( mPa.s)
Viscosity
( mPa.s)

2000
2000

Sound
Spd. (m/s)
Sound
Spd. (m/s)
Sound
Spd.Spd.
(m/s)(m/s)
Sound

100 K100 K

10 10
Ethane
1 1
Ethane
700700
1 1
0.1 0.1 700
700
0.1 0.1
0.010.01
400400
0.010.01
0.001
0.001400400
0.001
0.001
0.0001
0.0001
100100
0 0 150150300300450450600600750750
0.0001
0.0001
0.00001
0.00001 100100
0 0
150150
300
600600
300 450450600

450
300
0 0 150150300
450(g/l)600 750750
Density
Density
(g/l)
0.00001
0.00001
0 0
150150
300300
450450
600600
Density
Density
(g/l)(g/l)

Ethane
Ethane

200200
1 1
200200 1
1

Ethane
Ethane

100 K 100 K

100100
10 10

600600
K K

50 50
1 1
50 50
1 1

1000
1000
100
100
200 K200 K

Ethane
Ethane

Vapour viscosity
T (K)
AAD (%)
54 - 600
0.81
68 - 600
1.17
270 - 610
1.83

64 - 600
0.56
84 - 600
0.31
90 - 600
1.29
150 - 600
1.95

200 K 200 K

Cp (J/mol*K)
Cp (J/mol*K)
Cp (J/mol*K)
Cp (J/mol*K)

Oxygen
Carbon monoxide
Carbon dioxide
Nitrogen
Methane
Ethane
Iso-butane
500500 100100
K K
200100
K
200
500500 100
K KK

320200
K
320
200 K KK
400320
K
400
320 K KK
500400
K
400500
K KK
600600
K
500500
K KK

Vapour pressure
T (K)
AAD (%)
54 - 154
0.67
68 - 132
0.38
216 - 304
0.28
63 - 126
0.24
90 - 190
0.51

90 - 305
0.67
123 - 407
3.28

Pressure
(bar) (bar)
Pressure
Pressure
(bar)(bar)
Pressure

Compound

Ethane
Ethane

0.8 0.8

0.080.08

100100
K K
200200
K K
100
K
320100
K KK
320

200
200
K
400400
K KK
320
K
500320
K KK
500
400
400
K
600600
K KK
500
K
500
K1000
1000
600600
K K
1000
1000

100100
K K
0.08
320
K K

320
0.08
100
K
100
K
500500
K K
320
320 K K
500500
K K

200200
K K
400400
K K
200
K
200
K
600600
K K
400
400 K K
600600
K K

0.008
0.008

10 10
100100
1 1
10 10
100100
Pressure
(bar)(bar)
Pressure
(bar)(bar)
Pressure
Pressure
0.008
0.008
10 10
100100
1 1
10 10
100100
Figure 2. Predicted and experimentalPressure
(NIST
Chemistry
Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound Pressure
of ethane.
Pressure
(bar)
Pressure
(bar)
(bar)
(bar)

1000
1000
1000
1000

PETROVIETNAM - JOURNAL VOL 6/2020

47


PETROLEUM PROCESSING

T
ε
k
T
T * = on the expression previously suggested [1]:
ε
k
T* =

(5)

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.
3. PC-SAFT+FVT parameters regression

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

55
55
55 55

Nitrogen
Nitrogen
Nitrogen
Nitrogen

100KK
100
200
100
100
KKK K
200
300
200
200
KKK K
300
400
300
300

400 KKK K
500
400
400
KKK K
500
600
500
500
600 KKK K
600600
K K

100
100
100100
10
10
10 10

40
40
40 40

11
1 1

25
25
25 2511

1 1

10
100
10
100
Pressure
(bar)
10 10
100
Pressure (bar) 100
Pressure
(bar)
Pressure
(bar)
100KK
100
100
100
KK K
300
300
K
300
300
500KKK K
500
500500
K K

1000
1000
1000
1000

0

150
150
150150

Nitrogen

0

300
600
900 Nitrogen
300
600
900
Nitrogen
Nitrogen
300
600
300
600
900900

300

450
600
300
450
600
Density
(g/l) 600600
Density
(g/l)
300300
450450
Density
Density
(g/l)(g/l)

900
900
900900

200KK
200
200
200
KKK K
400
400
400
400
KKK K
600

600
600600
K K

Viscosity
( mPa.s)
Viscosity
( (mPa.s)
Viscosity
mPa.s)
Viscosity ( mPa.s)

550
550
550550

10
100
10
100
Pressure(bar)
(bar)
10 10
100100
Pressure
Pressure
(bar)
Pressure
(bar)

Nitrogen
Nitrogen
Nitrogen
Nitrogen
1000
1000
1000
1000

0.01
0.01
0.010.0111
1 1

10
100
10
100
Pressure(bar)
(bar)
10 10Pressure
100100
Pressure
(bar)
Pressure
(bar)

Figure 3. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of nitrogen.

48

750
750
750750

0.1
0.1
0.1 0.1

850
850
850850

250
250
25025011
1 1

0.1
0.1
0.1 0.100
0 0

900
900
900
900
700
700
700

700
500
500
500
500
300
300
300
300
100
100
0
1001000

100KK
100
100
100
KKK K
300
300
300
300
KKK K
150
150
150150
K K

200KK

200
200
200
KK K
400
400
K
400
400
600KKK K
600
600600
K K

Sound
Spd.
(m/s)
Sound
Spd.
(m/s)
Sound
Spd.
(m/s)
Sound Spd. (m/s)

1150
1150
1150
1150

1000
1000
1000
1000

Pressure
(bar)
Pressure
(bar)
Pressure
(bar)
Pressure (bar)

CpCp
(J/mol*K)
Cp(J/mol*K)
(J/mol*K)
Cp (J/mol*K)

70
70
70 70

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)

PETROVIETNAM - JOURNAL VOL 6/2020

Nitrogen
Nitrogen
Nitrogen
Nitrogen
1000
1000
1000
1000


PETROVIETNAM

were next determined by minimising a quadratic residual
defined by relative viscosities.
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:

component is dictated by the availability of experimental
data from the Design Institute for Physical Property Data
(DIPPR) [8].

(6)

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.

Where NPsat and Nρliq are the number of the
experimental vapour pressures
and saturated liquid
exp
cal
AAD(%)
100.
density
data, respectively.
The choice of data for each

The PC-SAFT+FVT model parameters for different
gases considered in this work are reported in Table 1. Table
2 represents the experimental data sources and deviations
obtained with PC-SAFT+FVT model for pure gases. For all

Fobj

1
N P sat

N

P sat

Pcsaal t Pesxapt

Pesxapt

1

li q
cal

liq

li q
ex p
li q
ex p

1

Carbon monoxide
Carbon
monoxide
Carbon
monoxide

100 K
100
KK K
100
150
150
KK K
150

200
200
200
300 KK K
300
KK K
300
400
400
KK K
400
500
500
KK
500

1000
1000
1000

100
100
100
Pressure
(bar)
Pressure
(bar)
Pressure
(bar)
Pressure (bar)

CpCp
(J/mol*K)
Cp
(J/mol*K)
(J/mol*K)
Cp (J/mol*K)

N

exp

data

115
115
115

1
N l iq

10
1010

70
7070

1
11

25
2525 1
11

10
100
1010Pressure (bar) 100
100
Pressure
(bar)
Pressure
(bar)

1000
1000
1000

0.1
0.1
0.1 0
00

1500
Carbon monoxide
1500
1500 Carbon monoxide

900
900
900

700
700
700
500
500
500
300
300
300
100
100
100 0
00
150
150
150

Carbon
Carbon

Carbon
300
600
900 monoxide
300
monoxide
300 600
600 900
900monoxide
300

450
600
750
900
300
450
750
900
(g/l) 600
300Density
450
600
750
900
Density
(g/l)
Density
(g/l)

Carbon monoxide
Carbon
Carbonmonoxide
monoxide

Carbon monoxide

150
150
150 1
11

10
100
1010
100
Pressure (bar) 100
Pressure
(bar)
Pressure
(bar)

100 K
100
KK K
100
150
150
KK K
150
200
200
KK K
200
300
300
300
400 KK K
400
KK K
400

500
500
KK
500
1000
1000
1000

Viscosity
( mPa.s)
Viscosity
mPa.s)
Viscosity
(( mPa.s)
Viscosity ( mPa.s)

Sound
Spd.
(m/s)
Sound
Spd.
(m/s)
Sound
Spd.
(m/s)
Sound Spd. (m/s)

0.1
0.10.1

0.01
0.01
0.01 10
1010

100
100
100
Pressure
(bar)
Pressure
(bar)
Pressure
(bar)

100 K
100
KK K
100
300
300
KK K
300
500
500
KK
500

200 K
200

KK K
200
400
400
KK K
400
150
150
KK
150
1000
1000
1000

Figure 4. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of carbon monoxide.
PETROVIETNAM - JOURNAL VOL 6/2020

49


PETROLEUM PROCESSING

cases, the average absolute deviation obtained on vapour
N liq
N sat
sat
li q
li q
pressure, liquid density
is within

Psaturated
Pesxapt viscosities
1 Pand
1
cal
cal
ex p
Fobj
li q
the experimental N
accuracy
(lower
Pesxaptthan 2%)
N [2].
sat
l iq
1
1
ex p
P

The deviation is defined as:

AAD(%)

exp

100.
data

cal

(7)

exp

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

Carbondioxide
dioxide
Carbon
Carbon
Carbondioxide
dioxide

230KK
230
230
230KK
260KK
260
260
260KK
330KK
330
330

330KK
370KK
370
370
370KK
420KK
420
420
420KK
500KK
500
500
500KK
600KK
600
600
600KK

300
300
300
300

90
90
90
90

1,810
1,810

1,810
1,810

30
30
30
30

1,240
1,240
1,240
1,240

60
60
60
60
30
30
30
30

670
670
670
670
11
11

10

100
10
100
10
100
10
100
Pressure(bar)
(bar)
Pressure
Pressure
Pressure(bar)
(bar)

150
150
150
150

33
33
00
00

1000
1000
1000
1000

100

100
100
100 500
500
500
500

800 1,100
1,100 1,400
1,400
800
800
800 1,100
1,100 1,400
1,400
400
800
400
800
400
800
400 Density
800
Density(g/l)
(g/l)
Density
(g/l)
Density (g/l)

11

11

10
10
10
10

100
100
100
100
Pressure(bar)
(bar)
Pressure
Pressure
Pressure(bar)
(bar)

230KK
230
230
230KKKK
260
260
260
260KKKK
330
330
330
330KKKK

370
370
370
370KKKK
420
420
420
420KKKK
500
500
500
500KKKK
600
600
600
600KK
1000
1000
1000
1000

Viscosity
mPa.s)
Viscosity
(( mPa.s)
Viscosity
mPa.s)
Viscosity
(( mPa.s)

0.12
0.12
0.12
0.12

0.012
0.012
0.012
0.012

11
11

10
10
10
10

100
100
100
100
Pressure(bar)
(bar)
Pressure
Pressure
Pressure(bar)
(bar)

Figure 5. Predicted and experimental (NIST Chemistry Web Book) isobaric heat capacity, liquid density, viscosity and speed of sound of carbon dioxide.

50

1,200
1,200
1,200
1,200

Carbondioxide
dioxide
Carbon
Carbon
Carbondioxide
dioxide

Carbondioxide
dioxide
Carbon
Carbon
Carbondioxide
dioxide

Sound
Spd.
(m/s)
Sound
Spd.
(m/s)
Sound
Spd.

(m/s)
Sound
Spd.
(m/s)

1500
1500
1500
1500

230
230
230
230
KK KK

120
120
120
120

3000
3000
3000
3000 Carbon
Carbondioxide
dioxide
Carbon
Carbondioxide
dioxide

260
260
260
260
KK KK

Cp
(J/mol*K)
Cp
(J/mol*K)
Cp
(J/mol*K)
Cp
(J/mol*K)

150
150
150
150

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 suband super critical regions. The experimental data are taken
from the NIST chemistry web book (t.
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

Pressure
(bar)
Pressure
(bar)
Pressure
(bar)
Pressure
(bar)

180
180
180
180

stringent than their correlation accuracy. This prediction
also allows to validate the prediction potential of the
model over a wide range of thermodynamic conditions.

PETROVIETNAM - JOURNAL VOL 6/2020

230KK
260KK
230
260
230
260
230KK
260KK
310KK

330KK
310
330
310
K
330
310 K
330KK
370KK
420KK
370
420
370
420
370KK
420KK
500KK
600KK
500
600
500
600
500KK
600KK
1000
1000
1000
1000

PETROVIETNAM

1000
1000
1000
1000

7575
75 Oxygen
Oxygen
75
Oxygen
Oxygen

100100
K K
100
100KK

Cp Cp
(J/mol*K)
(J/mol*K)
Cp
Cp(J/mol*K)
(J/mol*K)

100
100
100
100

5050
50
50

100100
K K
100 K
100
KK K
300300
300 K
300
KK K
500500
500 K
500 K

Pressure
(bar)
Pressure
(bar)
Pressure
Pressure(bar)
(bar)

1010
10
10

200200
K K
200 K
200
KK K
400400
400 K
400
KK K
600600
600 K
600 K

700
700
700
700

1 1
1
1

0.10.1
0.1
0.1

400
400
400
400

0.01
0.01
0.01
0.01

2525
25
25 1 1
1
1

1000
1000
1000
1000

Oxygen
Oxygen
Oxygen
Oxygen

Oxygen
Oxygen
Oxygen
Oxygen

120120
120
120 1 1

1
1

1010
100100
10
100
10 Pressure
(bar)
Pressure
(bar)100
Pressure (bar)
Pressure (bar)

100100
K K
100 K
200200
100
KK K
200 K
200
KK K
300300
300 K
300
KK K
400400
400 K
500500

400
KK K
500 K
500
KK K
600600
600 K
600 K
1000
1000
1000
1000

Viscosity
( mPa.s)
Viscosity
( mPa.s)
Viscosity
Viscosity( mPa.s)
( mPa.s)

0.10.1
0.1
0.1

Sound
Spd.Spd.
(m/s)
Sound
(m/s)

Sound
SoundSpd.
Spd.(m/s)
(m/s)

1200
1200
1200
1200

1010
100100
10
100
10 Pressure
(bar)
Pressure
(bar)100
Pressure (bar)
Pressure (bar)

100
Oxygen
100
Oxygen
100100
100 400
400 700
7001,000
1,0001,300

1,300Oxygen
0.001
0.001 100 100 400 700 1,000 1,300Oxygen
0.001
100 400 700 1,000 1,300
400
800
1,200
0.001 0 0
400
800
1,200
0
400Density
800
1,200
(g/l)
Density
(g/l)
0
400 Density
800
1,200
(g/l)
Density (g/l)

100100
K K 200200
K K
100 K

200 K
100
KK
200
KK
300300
400
K
400 K
300 K
400 K
300
KK
400 KK
500500
K 600600
K
500 K
600 K
500 K
600 K

0.01
0.01
0.01
0.01 1 1
1
1

1010

100100
10
100
10 Pressure
(bar)
Pressure
(bar)100
Pressure (bar)
Pressure (bar)

1000
1000
1000
1000

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
PETROVIETNAM - JOURNAL VOL 6/2020

51


PETROLEUM PROCESSING

1000
1000
1000
1000

1010
1010
1 11
1
Pressure(bar)
(bar)

Pressure
Pressure(bar)
(bar)
Pressure

Cp(J/mol*K)
(J/mol*K)
Cp
Cp(J/mol*K)
(J/mol*K)
Cp

220
220
220
220

180
180
180
180

Iso
Iso
-butane
Iso-butane
-butane
Iso
-butane

100
100
100
100

400
400
400
400

0.1
0.1
0.1
0.1

350
350
350
350

0.01
0.01
0.01
0.01

300
300
300
300

0.001
0.001
0.001
0.001

250
250
250
250

0.0001
0.0001
0.0001
0.0001

140
140
140
140

200
200
200
200

0.00001
0.00001
0.00001
0.00001

150
150
150
150

0.000001
0.000001
0.000001
0.000001
100
100
100
100

1 11
1

1010
100
100
100
1010
100
Pressure
Pressure
(bar)
(bar)
Pressure(bar)
(bar)
Pressure

1000
1000
1000
1000

0.0000001
0.0000001
0.0000001
0.0000001

150K K
150
150KK
150

150
150
K KK
150
150
K
250
250
KK
250
250 K K
350
350
K KK

350
350
K
450
450
KK
450
450 K K
550
550
K KK
550
550
K

Iso -butane

250K K
250
250KK
250

260
260
260
260
Iso
Iso
-butane
Iso-butane

-butane

100
100
100
100
200
200
200
200

500
500
800
800
500
800
500
800
300
300
600
600
300Density
600
300
600
Density
(g/l)
(g/l)

Density
(g/l)
Density
(g/l)

0 00
0

4 44
4 Iso
Iso
-butane
Iso-butane
-butane

Iso
Iso
-butane
Iso-butane
-butane
Iso
-butane

Iso -butane

1500
1500
1500
1500
Viscosity( mPa.s)

( mPa.s)
Viscosity
Viscosity( (mPa.s)
mPa.s)
Viscosity

150
150
K KK
150
150
K

250
250
K KK
250
250
K

350
350
K KK
350
350
K

450
450
K KK

450
450
K

550
550
K KK
550
550
K

SoundSpd.
Spd.(m/s)
(m/s)
Sound
SoundSpd.
Spd.(m/s)
(m/s)
Sound

0.4
0.4
0.4
0.4

150
150
150
150

150
150
K KK
150
150
K
250
250
KK
250
250 K K
350
350
K KK
350
350
K
450
450
KK
450
450 K K
550
550
K KK
550
550
K
1 11
1

1010
1010

100
100
100
100
Pressure
Pressure
(bar)
(bar)
Pressure
(bar)
Pressure (bar)

1000
1000
1000
1000

0.04
0.04
0.04
0.04

0.004
0.004
0.004
0.004

1 11
1

1010
1010
Pressure
Pressure
(bar)
(bar)
Pressure
(bar)
Pressure
(bar)

100
100
100
100

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].
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.
52

PETROVIETNAM - JOURNAL VOL 6/2020

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.
[2] Nguyen Huynh Dong, Luu Tra My, Xuan Thi Thanh
Nguyen, Chau Thi Quynh Mai, and Siem Thi Kim Tran, "Freevolume theory coupled with modified group-contribution
PC-SAFT for predicting the viscosities. II. Alcohols and


PETROVIETNAM

their mixtures", Fluid Phase Equilibria, Vol. 502, 2019. DOI:
10.1016/j.fluid.2019.112298.
[3] Joachim Gross and Gabriele Sadowski, "PerturbedChain SAFT: An equation of state based on a perturbation
theory for chain molecules", Industrial & Engineering
Chemistry Research, Vol. 40, No. 4, pp. 1244 - 1260, 2001.
[4] Helena Lubarsky, Ilya Polishuk, and Nguyen
Huynh Dong, "The group contribution method (GC)
versus the critical point-based approach (CP): Predicting

thermodynamic properties of weakly- and non-associated
oxygenated compounds by GC-PPC-SAFT and CP-PCSAFT", The Journal of Supercritical Fluids, Vol. 110, pp. 11 21, 2016.
[5] Helena Lubarsky, Ilya Polishuk, and Nguyen Huynh
Dong, "Implementation of GC-PPC-SAFT and CP-PC-SAFT
for predicting thermodynamic properties of mixtures of
weakly- and non-associated oxygenated compounds", The
Journal of Supercritical Fluids, Vol. 115, pp. 65 - 78, 2016.
[6] Nguyen Huynh Dong, "A modified groupcontribution PC-SAFT equation of state for prediction of
phase equilibria", Fluid Phase Equilibria, Vol. 430, pp. 33 46, 2016.
[7] Philip.D.Neufeld, A.R.Janzen, and R.A.Aziz,
"Empirical equations to calculate 16 of the transport
collision integrals Ω(l, s)* for the Lennard‐Jones (12-6)
potential", The Journal of Chemical Physics, Vol. 57, No. 3,
pp. 1100 - 1102, 1972.

[8] R. Rowley, W.Wilding, J.Oscarson, and N.Giles,
"DIPPR® data compilation of pure chemical properties,
Design Institute for Physical Properties", AIChE Journal,
2010.
[9] Siem Thi Kim Tran, Nguyen Huynh Dong, Nicolas
Ferrando, J.P.Passarello, Jean-Charles de Hemptinne,
and Tobaly Pascal, "Modeling VLE of H2 + Hydrocarbon
mixtures using a group contribution SAFT with a kij
correlation method based on London's theory", Energy
and Fuels, Vol. 23, No. 5, pp. 2658 - 2665, 2009.
[10] Nguyen
Huynh
Dong,
Modélisation
thermodynamique de mélanges symétriques et asymétriques

de composés polaires oxygénés et/ou aromatiques par GCSAFT, PhD thesis in Institut Galileé, Universite Paris Nord,
Villetaneuse, France, 2008, pp. 59 - 105.
[11] Ilya Polishuk, Helena Lubarsky, and Nguyen
Huynh Dong, "Predicting phase behavior in aqueous
systems without fitting binary parameters II: Gases and
non-aromatic hydrocarbons", AIChE Journal, Vol. 63, No.
11, pp. 5064 - 5075, 2017. DOI: 10.1002/aic.15815.
[12] Nguyen Huynh Duong and Nguyen Huynh
Dong, "Application of the modified group-contribution
perturbed-chain SAFT to branched alkanes, n-olefins and
their mixtures", Fluid Phase Equilibria, Vol. 434, pp. 176 192, 2017.

PETROVIETNAM - JOURNAL VOL 6/2020

53