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A Simple Method to Calculate the Viscosity of Heavy Oil Saturated with Supercritical CO2 using Correlations Yu Xiong, Chong Wang, Jun Jiang, and Hongwei Deng Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b00066 • Publication Date (Web): 21 Mar 2016 Downloaded from http://pubs.acs.org on March 29, 2016
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A Simple Method to Calculate the Viscosity of Heavy Oil Saturated with Supercritical CO2 using Correlations Yu Xiong†, Chong Wang＊†, Jun Jiang†, Hongwei Deng ‡ †
＊†
†
†
Petroleum Institute, Southwest Petroleum University, Chengdu 610500, P. R. China Research Institute of Exploration and Development of Shengli Oilfield, SINOPEC, Dongying 257015, P. R. China. ‡
ABSTRACT Supercritical carbon dioxide (sc CO2) could greatly reduce the viscosity of heavy oils and consequently increases their fluidity on account of its special properties, whose density close to that of the liquid while viscosity similar to that of the gas. No matter under reservoir conditions or in the pipelines, fluidity of heavy-oil/sc CO2 is of major concern, especially for the process of CO2 injection development in deep heavy oil reservoirs and the transportation of heavy oil diluted by sc CO2. In this paper, a method to calculate viscosities of heavy-oil/CO2 mixtures is introduced, which is based on Lederer equation. Contrary to earlier reports, this paper has calculated the parameters with empirical correlations especially for the viscosity of sc CO2, which was calculated with computing procedure using equation of state in previous references. In addition, the viscosity of dead-heavy-oil at high-pressure and high-temperature (HPHT) and the volume factor, Fo, are also calculated using correlations, which were not proposed in former papers with correlations. The method could calculate the viscosity of heavy oil saturated with sc CO2 by inputting the least parameters including the density (or the specific gravity) and the viscosity-temperature relationship of heavy oil as well as the pressure and temperature of heavy-oil/sc CO2 system. With the proposed method of the paper, the viscosity of heavy oil saturated with sc CO2 could be obtained with reasonable accuracy after setting the given temperature and pressure. Experimental data of heavy oil saturated with sc CO2 at 70℃, 80℃ and 90℃ were regenerated with AARDs equal to 12.98%, 6.22 % and 2.43%, respectively. In addition, the AARDs of 70℃ were reduced from 12.98% to 9.73% with the leveling data. Key words: heavy oil；viscosity；supercritical carbon dioxide；Lederer equation； 1. Introduction Viscosity is an important transport property for engineering design and simulation of bitumen/heavy-oil production and transportation. The reliability of reservoir simulation results is highly dependent on the estimation of the transport properties of reservoir fluids.1 As we know it, carbon dioxide could greatly reduce the viscosity of heavy oil and increases its fluidity by reducing oil viscosity, which is an important factor in recovery efficiency.2,3 Experimental results indicate that the dissolved CO2 in bitumen or heavy oil could lead to a significant oil-viscosity reduction, and the effect is greater at lower temperature and higher pressure.4 Therefore, prediction of mixture viscosities with reasonable accuracy is of importance in designing enhanced oil recovery operations as well as simulation of heavy-oil 1 ACS Paragon Plus Environment
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production and transportation.3 However, for mixtures of heavy oil and solvent (including CO2), accurate models are few.1 Several correlations have been developed for the calculation of mixture viscosities and several of them have been reviewed by Reid et al.5 Most of these correlations are generally empirical in nature and there are few accurate methods available for the prediction of mixture viscosities as a function of temperature, pressure and composition. This is due to the fact that the viscosity of heavy oil-CO2 mixture is complexly dependent on the composition of the mixture.3 However, it is impossible to obtain the detailed composition of heavy oil and the contribution of each component to the viscosity of the mixture.2 For correlation purposes, heavy oil-CO2 mixture is treated as a binary system: heavy oil and pure CO2, respectively. The viscosity ratio between the two components could be extremely high, 20 to 105 and 103 to 106.2,3 For such wide range of mixture viscosities, Shu,6 Chung et al.2 have shown that the Lederer7 equation is excellent in representing such high-viscosity-ratio systems. Zirrahi et al. 1 has reviewed that Arrhenius8 used a logarithmic mixing rule to predict the viscosities of mixtures and the mixing rule is proportional to the mole fraction, volume fraction or mass fraction. A modified form of the Arrhenius mixing rule was applied by Lederer7 with the introduction of an adjusting parameter and the mixing rule has precedence for predicting the viscosity of binary mixtures compared to the previous mixing rules.1 More detailed introduction about the development history of Lederer equation and other viscosity model for predicting the viscosity of heavy oil saturated or diluted with CO2 could be found in other articles (Zirrahi et al.,1 Motahhari et al.,9 Zirrahi et al.,10 and Motahhari et al.11). In this paper, a method to calculate viscosities of heavy-oil/CO2 mixtures is introduced, which is based on Lederer equation. Contrary to earlier reports, this paper has calculated the parameters with empirical correlations especially for the viscosity of sc CO2, the viscosity of dead heavy oil at HPHT and the volume factor, Fo, which are not mentioned in the past references with correlations. The method could calculate the viscosity of heavy oil saturated with sc CO2 by inputting least parameters including the density (or the specific gravity), the viscosity-temperature relationship and the pressure and temperature of the heavy-oil/sc CO2 system. After setting the given temperature and pressure, the viscosity of heavy oil saturated with sc CO2 could be obtained with reasonable accuracy. 2. Theory and Calculation As aforementioned, the viscosity ratio between the pure CO2 and heavy oil could be very high in the range of 20 to 106. For such wide range of mixture viscosity ratio, Rahmes and Nelson, 12 Shu,6 Kokal and Sayegh3 and Chung et al.2 have shown that the Lederer7 equation is excellent in representing such high-viscosity-ratio systems. The Lederer equation is given by:
ln µ = m
X
o
ln( µ ) + X S ln( µ ) o
(1)
s
with
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X
s
=
V αV + V S
O
X
o
= 1− X
(2) S
(3)
S
where: V is the volume fraction, µ is viscosity, and the subscripts o, s, and m stand for the heavy oil, CO2, and mixture, namely, heavy-oil/CO2, respectively. Besides, α is an empirical parameter. Chung et al.2 have proposed that the volume fraction of CO2,Vs, in the mixture could be obtained from the CO2 solubility (or swelling factor) according to their definitions and the relationship among the CO2 solubility, Rs, the Xs and the swelling factor, Fs, can be written as the following formulation:
X
s
=
=
1
(4)
α F CO 2 / ( F o R s ) + 1
F F −1 α + F F −1 o
s
o
(5)
s
where: FCO2 is the ratio of CO2 gas volume at standard condition to the volume at system pressure and temperature. Fo is the ratio of oil volume at system temperature and 1 atm to the volume at system pressure and temperature. Swelling factor, Fs, is the ratio of the volume of the CO2-saturated oil at the temperature and pressure of the system to the volume of dead oil at the system temperature and 1atm. By using Eq. 4 and 5, we can determine the value of Xs from the information of CO2 solubility or swelling factor. In the following part, we will give the correlations of the parameters in Eq. 1 and 5. By using these correlations, one can use Eq. 1 to determine the viscosity of heavy oil saturated with sc CO2.
2.1 Correlation of α In Eq. 2, 4 and 5, α is an empirical parameter that has to be determined by fitting the data.2 Shu6 has proposed an empirical correlation for α based on the data of solvent mixed with heavy oil, however, Chung et al.2 put forward that Shu correlation cannot be applied for CO2/heavy-oil systems, for the reason that the density of CO2 may be greater than oil density at high pressures. Then, the parameter α was correlated as a function of temperature, pressure, and specific gravity, γ, of heavy oil by Chung et al.2 Kokal and Sayegh3 reported that no matter Shu correlation or Chung correlation, neither of them could yield acceptable values of α for heavy-oil-CO2 system studied by them and they obtained α by fitting their experimental data. However, Kokal and Sayegh3 did not give an empirical correlation of α for not enough data available to make a general correlation. Because some of the parameters used in our model are verified with the data from Chung et al. 2 and there was no better empirical correlation proposed by Kokal and Sayegh3, the correlation of Chung et al., namely, Chung-α correlation, will be used to determine the parameter α in this paper.
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The empirical correlation of α proposed by Chung et al.2 is given by:
α = 0.255γ
−4.16
T
1.85 r
7.36 − 7.36(1− p r ) e e 7.36 −1 e
(6)
where: γ is specific gravity of heavy oil, Tr=T/547.57 and pr=p/1071 are reduced temperature and pressure, respectively, and T is in°R and p in psia.
2.2 CO2 solubility in heavy oil， ， Rs The solubility of CO2 in heavy oil, Rs, is defined as the maximum volume (in standard condition) of CO2, which could be dissolved in per unit dead-state heavy oil (in standard condition) at given temperature and pressure. A correlation for solubility of CO2 in heavy oil is proposed by Chung et al.,2 which is a function of temperature, pressure and specific gravity of heavy oil. The correlation for solubility of CO2 in heavy oil, namely, Chung-Rs correlation, is given:
R
s
=
0.1781073 −2
[0.4934 ×10
γ
(1.8T +32)
4.0928
−0.2499
(7)
+ 0.571×10−6 (1.8T +32)
1.6428
exp(−0.0981 p + 5.3871/ p)]
where: Rs is the solubility of CO2 in heavy oil, sm3/m3. γ is the specific gravity of heavy oil. T and p are in ℃ and MPa, respectively. The comparison results between the Chung-Rs correlation and the measurement data of the solubility of CO2 in heavy oil from the literature2,13,14 are shown in Table 1, which indicates a reasonable prediction for CO2 solubility in heavy oil with absolute average relative deviation (AARDs) of 2.275%, 8.636% and 2.687% at 60℃, 80℃, and 93.33℃, respectively. Table1 The comparison of experimental and calculated solubility data Temperature
Pressure
Experimental solubility
(℃ ℃)
(MPa)
3
(sm /m )
Chung-Rs correlation (sm /m )
60
**8.260
61.565
63.565
60
***11.580
70.000
72.074
60
**13.840
90.679
93.176
60
***17.880
90.000
91.816
60
***29.980
110.000
110.433
80
*7.600
56.173
47.021
80
***10.530
60.000
58.109
80
*12.200
88.965
73.918
80
***15.570
80.000
78.641
80
*18.000
117.893
102.224
80
***28.640
110.000
110.515
Calculated solubility with
3
3
AARDs(%)of Chung-Rs 3
correlation
2.275
8.636
93.33
**8.490
45.289
45.602
93.33
**13.810
73.108
74.369
93.33
**27.500
123.520 13
130.458 2
Data source： ：* ，γ=0.9500； ； ** ，16.8
。
API； ；***14，γ=1.0095； ；
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2.3 Swelling factor， ，Fs Following Welker and Dunlop15 and Chung et al.2, swelling factor, Fs, is defined as the ratio of the volume of the CO2-saturated oil at the temperature and pressure of system to the volume of dead oil at the system temperature and 1atm. As aforementioned, the volume of heavy oil has little change with the pressure and the magnitude of expansion for heavy oil is not as drastic as that for light oil, which can be swelled to more than twice its original volume.2 The swelling data were correlated as a linear function of solubility and the correlation presented by Welker and Dunlop15 gives a good fit to the experimental data measured by Chung et al.2 The swelling factor correlation presented by Welker and Dunlop,15 namely, Welker & Dunlop correlation, is given by:
F
s
= 1.0 +
0.35 R s
(8)
1000 × 0.1781073
where: Rs is CO2 solubility in heavy oil in sm3/m3 and 0.1781073 is the conversion constant. The comparison results of Welker & Dunlop correlation and the measurement data of the swelling factor of CO2-saturated-heavy-oil from the literature2,13,14 are shown in Table 2, which show a good fit with AARDs of 3.672%, 2.799% and 0.361% at 60 ℃ , 80 ℃ , and 93.33 ℃ , respectively. In addition, the swelling factor data calculated by simultaneous correlations of Chung-Rs correlation and Welker & Dunlop correlation is also presented in Table 2, which indicates a reasonable accuracy in prediction the swelling factor of CO2-saturated-heavy-oil with AARDs of 3.556%, 3.983% and 0.682% at 60℃, 80℃,and 93.33℃, respectively.
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Table2 The comparison of experimental and calculated swelling factor data Calculated
Calculated swelling
swelling
factor with
AARD(%)of
factor with
simultaneous
Welker &
Welker &
correlations of
Dunlop
Dunlop
Chung-Rs and
correlation
correlation
Welker & Dunlop
AARDs(%) of simultaneous
Experimental Temperature
Pressure
(℃ ℃)
(MPa)
correlations of
swelling
Chung-Rs and
factor
Welker & Dunlop
60
**8.260
1.156
1.121
1.125
60
***11.580
1.185
1.138
1.142
60
**13.840
1.177
1.178
1.183
60
***17.880
1.248
1.177
1.180
60
***29.980
1.288
1.216
1.217
80
*7.600
1.116
1.110
1.092
80
***10.530
1.167
1.118
1.114
80
*12.200
1.176
1.175
1.145
80
***15.570
1.225
1.157
1.155
80
*18.000
1.236
1.232
1.201
80
***28.640
1.295
1.216
1.217
93.33
**8.490
1.082
1.089
1.090
93.33
**13.810
1.149
1.144
1.146
93.33
**27.500
1.243
1.243
1.256
Data source： ：*13，γ=0.9500； ； **2，16.8
3.672
3.556
2.799
3.983
0.361
0.682
。
API； ；***14，γ=1.0095； ；
2.4 Viscosity of sc Carbon dioxide， ，µs Heidaryan et al.16 has introduced a new correlation calculating the viscosity of CO2 at supercritical region based on Stephan and Lucas’s17 viscosity experimental data in pressure range of 7.5–101.4 MPa and temperature range of 310–900K. The new correlation for calculating viscosity of pure CO2 at supercritical region presented by Heidaryan et al.,16 namely, Heidaryan correlation, is given by: + A2 p + A3 p 2 + A4 ln(T ) + A5(ln(T )) 2 + A6(ln(T ))3 A 1 µs = (9) 1 + A7 p + A8ln(T ) + A (ln(T )) 2 9
where: µs is the viscosity of pure CO2 at supercritical region in mPa.s, T is in K and p in bar. A1-A9 are the tuned coefficients used in Eq.10, which is shown in Table 3.
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Table 3 Tuned coefficients used in Eq. 916 Coefficient
Tuned coefficients
A1
-1.146067E-01
A2
6.978380E-07
A3
3.976765E-10
A4
6.336120E-02
A5
-1.166119E-02
A6
7.142596E-04
A7
6.519333E-06
A8
-3.567559E-01
A9
3.180473E-02
The improved correlation has advantages of simplicity and with good accuracy. It is reported that Heidaryan correlation has resulted minimum values of AAE% among all other methods calculated for comparison. Heidaryan et al.16 had reported that the AAE% of Heidaryan correlation is less than 2.00 (1.71, 1.45 and 1.82 in comparison with the current experimental data, 16 Pensado et al.18 data and NIST web book data, 16 respectively), which indicates a reasonable accuracy in calculating the viscosity of pure CO2 at supercritical region.
2.5 Volume factor, Fo As mentioned before, volume factor, Fo, is defined as the ratio of oil volume at system temperature and 1 atm to the volume at system pressure and temperature. Based on the definition of Fo, the values of volume factor, Fo, could be determined by the density of dead oil at the same temperature and different pressures. In this paper, the values of Fo are calculated in the following two steps. First, the density of dead-heavy-oil, namely, ρsc in standard condition is adjusted to that of dead-heavy-oil at system temperature and 1 atm, namely, ρsc，T. Then, ρsc，T is adjusted to the density of dead-heavy-oil at system temperature and system pressure, namely, ρP,T. After that, the volume factor, Fo , could be determined by the ratio of ρP,T to ρsc，T. In order to calculate the volume factor, Fo, using correlation, it is essential to know the correlations of density of dead oil at HPHT. The volume factor, Fo, calculated by three different correlations, namely, Standing,19 Motahhari et al., 20 Han et al. 21 has been compared with reference values presented by Li22 and Li et al. 23,24, in which the values of Fo are independent with temperature. It is found that the Motahhari correlation presents the smallest deviation of the literature data among all of the three correlations. The comparison results of three correlations are shown in Table 4 and Figure 1. Consequently, Motahhari correlation is adopted to calculate the density of dead-heavy-oil at HPHT.
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Table 4 Volume factor values in literature 22,23,24 and calculated values using Motahhari, Standing, Han correlation Calculated volume Temperature
Pressure
(℃ ℃)
(MPa)
Calculated
Calculated
Volume factor
factor using
volume factor
volume factor
in literature
Motahhari
using Standing
using Han
Correlation
Correlation
Correlation 1.004163295
60
8
1.007
1.004410804
1.004056507
60
10
1.008
1.005530687
1.005045000
1.005175984
60
12
1.010
1.006651820
1.006023242
1.006177668
60
14
1.011
1.007774202
1.006991234
1.007168467
80
8
1.007
1.004852611
1.004102140
1.004229986
80
10
1.008
1.006085007
1.005101703
1.005257889
80
12
1.010
1.007318915
1.006090882
1.006274247
80
14
1.011
1.008554336
1.007069679
1.007279200
2.5.1 Standing correlation Fluid densities have been estimated using Standing method,19 which added some correction factors to predict the density of crude oil.25 The correction factors are pressure correction factor ∆ρP and temperature correction factor ∆ρT.25,26
ρ = ρ sc + ∆ρ p − ∆ ρ T
(10)
where: ρ is crude oil density (lb/ft3). T, p and ρsc are temperature, pressure and density in standard condition of crude oil, respectively. ∆ρP is density correction for compressibility of oil with pressure and ∆ρT is density correction for thermal expansion of oil. According to Standing19 relationships, density corrections for compressibility and thermal expansion could be estimated by the following correlations:
∆ρ
p
= [0.167 + (16.181)10
−0.0425
ρ p sc
] 1000
(11)
∆ ρ = [0.0133 + 152.4( ρ + ∆ρ )−2.45 ](T − 520) − T
sc
−6
[8.1× 10 − 90.0622 × 10
−0.764(
p
ρ ∆ρ sc
+
p
)
(12)
](T − 520)
2
where: ρsc, ∆ρp and ∆ρT are the density of heavy oil in standard condition, density correction for compressibility of oils and density correction for thermal expansion of oils, respectively. All of them are in lb/ft3.T is in °R and p is in psia.
2.5.2 Motahhari correlation The density of bitumen/heavy oil is increasing exponentially with pressure and the effect of temperature is considered as a second-order equation at a constant pressure.20,26,27 Kariznovi et al.27 reported that Motahhari correlation could predict the density of Athabasca bitumen with acceptable results and the correlated values show a 8 ACS Paragon Plus Environment
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maximum absolute deviation of ±0.7kg/m3 with measured values. For this reason, Motahhari correlation will be used to calculate the density of heavy oil at HPHT in this paper with the fitted coefficients from the literature,27 however, the coefficient concerning the density at standard condition should be adjusted according to the measured density data.
ρ = ρ 0 exp( β p)
(13)
β = a 4 exp(a 5T )
(14)
ρ =a +a T +a T 1
0
2
2
（15）
3
where: ρ and ρ0 are the density at HPHT and standard condition in kg/m3,respectively. T is in °C and p in MPa. The fitted coefficients could be found in the literature.27 In addition, the coefficient a1 should be corrected according to the density at standard condition, namely, ρ0. Table 5 The Fitting coefficients in Eq. 13-1527 Coefficient
Fitting coefficient
a1（Original） ）
1021.62
a1（Modified） ）
981.135881
a2
-5.8976E-01
a3
-1.0170E-04
a4
4.1870E-04
a5
4.7620E-03
2.5.3 Han correlation Han et al. 21 has proposed a new correlation to determine the density of heavy oil at HPHT with pressure and temperature correction factors based on the density at standard condition, whose idea is as same as that of Standing method.19
∆ρ
p
= ap exp(− bp
a
)
（16）
a = 0.00038794 + 0.0375885 × 10
( −2.653×
b = 1.00763 × 10 ( −6) + 0.00088631 × 10
ρ
sc
)
( − 3.7645×
ρ
（17） sc
)
（18）
∆ ρ T = c exp( − d ∆ ρ p )
（19）
c = c0 + c1 ⋅ (T − 15.56) + c 2 ⋅ (T − 15.56) 2
(20)
d = d 0 + d1 ⋅ (T − 15.56) + d 2 ⋅ (T − 15.56) 2
（21）
where: ρsc, ∆ρp and ∆ρT are the density of heavy oil in standard condition, density correction for compressibility of oils and density correction for thermal expansion of oils, respectively. All of them are in g/cm3. T is in °C and p is in MPa. 9 ACS Paragon Plus Environment
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Table 6 The Fitting Parameters used in Eq.16-2121 Parameter
Fitting Parameter
c0
1.697560E-04
c1
9.335380E-04
c2
-1.538320E-06
d0
1.296860E+01
d1
4.013680E-03
d2
-1.186300E-04
1.012
Volume factor values at 60℃ in literature
1.011
Volume factor values at 80℃ in literature
1.01
Volume factor
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Calculated volume factor at 60℃ using Motahhari correlation Calculated volume factor at 60℃ using Standing correlation Calculated volume factor at 60℃ using Han correlation
1.009 1.008 1.007
Calculated volume factor at 80℃ using Motahhari correlation Calculated volume factor at 80℃ using Standing correlation Calculated volume factor at 80℃ using Han correlation
1.006 1.005 1.004 1.003 6
8
10
12
14
16
Pressure (MPa) Figure 1 Volume factor in literature22,23,24 and calculated values using three different correlations
2.6 Viscosity of dead-heavy-oil at HPHT Yarrantonet al.28 has reported a new correlation to determine the viscosity of dead-heavy-oil at HPHT, which is based on the change of viscosity of Western Canadian Heavy oil with pressure and temperature. It is found that Yarranton correlation could give a reasonable prediction of the measured viscosity data by Li22 with AARDs of 1.21%, 0.88% and 2.90% at 60℃, 70℃ and 80℃, respectively. The data and the comparison of experimental and calculated data are shown in Table 7 and Figure 2, respectively. Furthermore, the molecular weight of heavy oil could be obtained using Edmister29 correlation in this paper if there is no measured data. The Yarranton correlation is given by:
µ ( p, T ) = µ (T ) 1 + σ o
o
(1 − σ 2T ) p
1
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σ
1
σ
2
= 0.008 + 0.00006MW
（23）
= 0.0033
（24）
Edmister (1958) correlation:
MW =
44.29γ 1.03 − γ
（25）
where: µo（p,T）and µo（T）are the viscosity of dead-heavy-oil at given temperature and given pressure and at given temperature and atmospheric pressure in mPa.s, respectively. T(℃), MW (kg/kmol) and γ are the given temperature, molecular weight of dead-heavy-oil and specific gravity of dead-heavy-oil. p(MPa) is the given pressure. σ1 and σ2 are fitting parameters. Table 7 Experimental viscosity22 and calculated viscosity using Yarranton28 correlation at
60℃ ℃, 70℃ ℃ and 80℃ ℃ Temperature (℃)
Viscosity at
Pressure
standard pressure (mPa.s)
（MPa） ）
Experimental viscosity
Calculated viscosity of
of dead-heavy-oil at
dead-heavy-oil at HPHT using
HPHT (mPa.s)
Yarranton correlation(mPa.s)
60
4896.5
8
6408.91
6460.96
60
4896.5
10
6860.94
6857.08
60
4896.5
12
7344.85
7253.19
60
4896.5
14
7862.9
7649.32
70
2332.15
8
2998.21
3046.63
70
2332.15
10
3195.12
3227.53
70
2332.15
12
3404.98
3408.43
70
2332.15
14
3618.61
3589.34
80
1274.15
8
1594.54
1647.75
80
1274.15
10
1687.73
1742.34
80
1274.15
12
1786.36
1836.93
80
1274.15
14
1890.75
1931.53 22
Experimental viscosity data at standard pressure and HPHT are from Li with the specific gravity value of heavy oil of 0.9693.
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9000
Experimental viscosty at 60℃
8000
Vviscosity(mPa.s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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Calculated viscosity at 60℃ using Yarranton Correlation
7000 6000
Experimental viscosty at 70℃
5000
Calculated viscosity at 70℃ using Yarranton Correlation
4000 3000
Experimental viscosty at 80℃
2000 1000 7
8
9
10
11
12
13
14
Pressure（ （MPa） ）
Calculated viscosity at 80℃ using Yarranton Correlation
Figure 2 Experimental viscosity data22 and calculated viscosity using Yarranton28 correlation at 60℃ ℃and 80℃ ℃
3. Results As mentioned before, the correlations could determine the parameters of Lederer equation with reasonable accuracy. The flow diagram of the simple method to calculate the viscosity of heavy oil saturated with sc CO2 using correlations is shown in Figure 3. The results of the new method have been compared with the experimental data of CO2/Zheng-32-heavy-oil in literature (Li, 2011;22 Li et al.,242013b). The new method has generally resulted AARDs of 6.22% and 2.43% for isotherms of 80℃ and 90℃, respectively. However, the AARDs of 70℃ is 12.98%, which may be due to the fact that the data of 70℃ in the literature may be of not all accuracy and with some measurement error. As we can see in Figure 4, the sequence of experimental data at 70℃ is different from the other two sequences of 80℃ and 90℃, however, the sequences of different isotherms for heavy oil should have similar trend. Then, the second and third points of 70℃ is regulated according to the sequences of 80℃ and 90℃. With the leveling points of 70℃, the AARDs of 70℃is decreased from 12.98% to 9.73% and the AARDs of all the three isotherms is also reduced from 7.21% to 6.13%. It should be noted that the prediction of 70℃ and 80℃ is higher than the experimental data in the literature. It may be due to the fact that Motahhari correlation tends to under-predict the volume factor, Fo. According to Eq. 1-5, the following Eq. 26 could be derived:
ln µ = m
α α + F oF s −1
ln( µ ) + o
F F − 1 ln(µ ) α + F F −1 o
s
s
o
(26)
s
From the Eq. 26, it is seen that the viscosity of heavy oil/CO2 mixture increases with the decreasing Fo. The under-prediction of Fo may be one reason for the 12 ACS Paragon Plus Environment
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over-prediction of 70℃ and 80℃. With regard to the third and fourth calculated points of 90℃, it is seen that the two points are of under-prediction compared to the experimental data. It may due to the minor experimental error (and the minor measured error could lead to a big increase of the deviation) or the fact that the Heidaryan correlation for the viscosity of sc CO2 is of a little under-prediction compared to the experimental data.
Figure 3 The flow diagram of the simple method to calculate the viscosity of heavy oil saturated with sc CO2 using correlations
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Table 8 Experimental viscosity data by Li, 22 Li et al.24and calculated viscosity of heavy oil saturated with sc CO2 using correlations Temperature
Pressure
Experimental viscosity
Calculated viscosity
(℃ ℃)
（MPa） ）
(Li,2011)(mPa.s)
(mPa.s)
70
8
112.78
120.04
70
10
73.24（ （leveling with 78.80） ）
85.27
70
12
56.35（ （leveling with 58.79） ）
65.01
70
14
45.89
52.17
80
8
97.12
104.84
80
10
70.03
73.60
80
12
53.44
55.21
80
14
40.09
43.51
90
8
84.32
85.09
90
10
59.88
59.98
90
12
47.37
44.81
90
14
36.15
34.98
Experimental viscosity at 70℃ ℃ Calculated viscosity at 70℃ ℃ Experimental viscosity at 80℃ ℃ Calculated viscosity at 80℃ ℃ Experimental viscosity at 90℃ ℃ Calculated viscosity at 90℃ ℃ Experimental viscosity at 70℃ ℃(leveling)
120
Viscosity(mPa.s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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110 100 90 80 70 60 50 40 30 6
8
10
12
14
16
Pressure (MPa) Figure 4 Experimental viscosity by Li,22 Li et al.24 and calculated viscosity of heavy oil saturated with sc CO2 using correlations
4. Conclusion We applied correlations to calculate the parameters of Lederer equation, which could determine the viscosity of heavy oil saturated with sc CO2. Comparisons with 14 ACS Paragon Plus Environment
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experimental viscosity data of CO2/Zheng-32-heavy-oil mixture showed acceptable accuracy. As mentioned before, Kokal and Sayegh3 reported that Shu correlation or Chung correlation could not yield acceptable values of α for heavy oil diluted with CO2 for their experimental data. However, they did not give an empirical correlation for α for not enough data available to make a general correlation. Some of the parameters used in our proposed model are verified with the data from Chung et al. 2 and there was no better empirical correlation proposed by Kokal and Sayegh3. For the above reasons, Chung-α correlation was used in this paper. Chung-Rs correlation could give good prediction for the solubility of pure CO2 in heavy oil with AARDs of 2.275%, 8.636% and 2.687% at 60℃, 80℃, and 93.33℃, respectively. In addition, the comparison results of Welker & Dunlop correlation and the measured data of the swelling factor of CO2-saturated-heavy-oil show a good fit with AARDs of 3.672%, 2.799% and 0.361% at 60℃, 80℃, and 93.33℃, respectively. Furthermore, the swelling factor data calculated by simultaneous correlations of Chung-Rs correlation and Welker &Dunlop correlation indicates a reasonable accuracy in prediction the swelling factor of CO2-saturated-heavy-oil with AARDs of 3.556%, 3.983% and 0.682% at 60℃, 80℃,and 93.33℃, respectively. The developed correlation calculating the viscosity of pure CO2 at supercritical region, namely, Heidaryan correlation, has advantages of simplicity and low prediction error with AAE of less than 2.00%. Among three different correlations for the density of dead-oil at HPHT, namely, Standing, Motahhari, Han correlation, compared with experimental data published in literature, Motahhari correlation shows the smallest deviation of the literature data. For this reason, the volume factor will be determined using Motahhari correlation and the AARDs are equal to 0.71% and 3.13% at 60℃ and 80℃, respectively. When it comes to the viscosity of dead-heavy-oil at HPHT, it was found that Yarranton correlation could give a reasonable prediction with AARDs of 1.21%, 0.88% and 2.90% at 60℃, 70℃ and 80℃, respectively. With the flow diagram of the new method to calculate the viscosity of heavy oil saturated with sc CO2 using correlations shown in Figure 3, the new method has generally resulted AARDs of 12.98%, 6.22% and 2.43% of 70℃, 80℃ and 90℃, respectively. With the leveling data of 70℃, the AARDs of 70℃ could be reduced to 9.73% and the AARDs of all the three different temperatures could be also decreased from 7.21% to 6.13%. The over-prediction calculation of 70℃and 80℃ may be due to the fact that Motahhari correlation tends to under-predict the volume factor, Fo. Although the proposed method of this paper could obtain reasonable accuracy for the viscosity of heavy oil saturated with sc CO2, it should be noted that there are still some limitations of this method. First, the prediction of volume factor, Fo, calculated with Motahhari correlation is still of under-prediction to the values of the literature. Secondly, the deviation of the viscosity of dead-heavy-oil at HPHT with Yarranton correlation may be a little bit big for the temperature under 70℃. All of the two problems should be solved with more accurate correlation for further research.
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Acknowledgements The authors are grateful to Zhangxing Chen, Ruihe Wang, Fanhua Zeng and Guanghuan Wu for their feedback and great advice for the improvement of our paper.
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