A power-law mixing rule has been developed to determine apparent diffusion coefficient of a binary gas mixture on the basis of molecular diffusion coefficients for pure gases in heavy oil. Diffusion coefficient of a pure gas under different pressures and different temperatures is predicted on the basis of the Hayduk and Cheng's equation incorporating the principle of corresponding states for one-dimensional gas diffusion in heavy oil such as the diffusion in a pressure–volume–temperature (PVT) cell. Meanwhile, a specific surface area term is added to the generated equation for three-dimensional gas diffusion in heavy oil such as the diffusion in a pendant drop. In this study, the newly developed correlations are used to reproduce the measured diffusion coefficients for pure gases diffusing in three different heavy oils, i.e., two Lloydminster heavy oils and a Cactus Lake heavy oil. Then, such predicted pure gas diffusion coefficients are adjusted based on reduced pressure, reduced temperature, and equilibrium ratio to determine apparent diffusion coefficient for a gas mixture in heavy oil, where the equilibrium ratios for hydrocarbon gases and CO2 are determined by using the equilibrium ratio charts and Standing's equations, respectively. It has been found for various gas mixtures in two different Lloydminster heavy oils that the newly developed empirical mixing rule is able to reproduce the apparent diffusion coefficient for binary gas mixtures in heavy oil with a good accuracy. For the pure gas diffusion in heavy oil, the absolute average relative deviations (AARDs) for diffusion systems with two different Lloydminster heavy oils and a Cactus Lake heavy oil are calculated to be 2.54%, 14.79%, and 6.36%, respectively. Meanwhile, for the binary gas mixture diffusion in heavy oil, the AARDs for diffusion systems with two different Lloydminster heavy oils are found to be 3.56% and 6.86%, respectively.

References

References
1.
Srivastava
,
R. K.
,
Huang
,
S.
, and
Dong
,
M.
,
1999
, “
Comparative Effectiveness of CO2 Produced Gas, and Flue Gas for Enhanced Heavy-Oil Recovery
,”
SPE Reservoir Eval. Eng.
,
2
(
3
), pp.
238
247
.
2.
Sahin
,
S.
,
Kalfa
,
U.
, and
Celebioglu
,
D.
,
2008
, “
Bati Raman Field Immiscible CO2 Application-Status Quo and Future Plans
,”
SPE Reservoir Eval. Eng.
,
11
(
4
), pp.
778
791
.
3.
Shi
,
J.
, and
Leung
,
J. Y.
,
2014
, “
Semi-Analytical Proxy for Vapex Process Modeling in Heterogeneous Reservoirs
,”
ASME J. Energy Resour. Technol.
,
136
(
3
), p.
032904
.
4.
Thomas
,
S.
,
2008
, “
Enhanced Oil Recovery—An Overview
,”
Oil Gas Sci. Technol.—Rev. IFP
,
63
(
1
), pp.
9
19
.
5.
Mullken
,
C. A.
, and
Sandler
,
S. I.
,
1980
, “
The Prediction of CO2 Solubility and Swelling Factors for Enhanced Oil Recovery
,”
Ind. Eng. Chem. Process Des. Dev.
,
19
(
4
), pp.
709
711
.
6.
Yadali Jamaloei
,
B.
,
Dong
,
M.
,
Yang
,
P.
,
Yang
,
D.
, and
Mahinpey
,
N.
,
2013
, “
Impact of Solvent Type and Injection Sequence on Enhanced Cyclic Solvent Process (ECSP) for Thin Heavy Oil Reservoirs
,”
J. Pet. Sci. Eng.
,
110
(
10
), pp.
169
183
.
7.
Li
,
H.
,
Zheng
,
S.
, and
Yang
,
D.
,
2013
, “
Enhanced Swelling Effect and Viscosity Reduction of Solvent(s)/CO2/Heavy-Oil Systems
,”
SPE J.
,
18
(
4
), pp.
695
707
.
8.
Li
,
H.
,
Yang
,
D.
, and
Tontiwachwuthikul
,
P.
,
2012
, “
Experimental and Theoretical Determination of Equilibrium Interfacial Tension for the Solvent(s)-CO2-Heavy Oil Systems
,”
Energy Fuels
,
26
(
3
), pp.
1776
1786
.
9.
Li
,
H.
,
Yang
,
D.
, and
Li
,
X.
,
2013
, “
Determination of Three-Phase Boundaries of Solvent(s)-CO2-Heavy Oil Systems Under Reservoir Conditions
,”
Energy Fuels
,
27
(
1
), pp.
145
153
.
10.
Okuno
,
R.
, and
Xu
,
Z.
,
2014
, “
Mass Transfer on Multiphase Transitions in Low-Temperature Carbon Dioxide Floods
,”
SPE J.
,
19
(
6
), pp.
1005
1023
.
11.
Yang
,
P.
,
Li
,
H.
, and
Yang
,
D.
,
2014
, “
Determination of Saturation Pressures and Swelling Factors of Solvent(s)-Heavy Oil Systems Under Reservoir Conditions
,”
Ind. Eng. Chem. Res.
,
53
(
5
), pp.
1965
1972
.
12.
Sayegh
,
S. G.
, and
Maini
,
B. B.
,
1984
, “
Laboratory Evaluation of the CO2 Huff-n-Puff Process for Heavy Oil Reservoirs
,”
J. Can. Pet. Technol.
,
23
(
3
), pp.
29
36
.
13.
Frauenfeld
,
T.
,
Jossy
,
C.
,
Rispler
,
K.
, and
Kissel
,
G.
,
2006
, “
Evaluation of the Bottom Water Reservoir VAPEX Process
,”
J. Can. Pet. Technol.
,
45
(
9
), pp.
29
35
.
14.
Fadaei
,
H.
,
Scarff
,
B.
, and
Sinton
,
D.
,
2011
, “
Rapid Microfluidics-Based Measurement of CO2 Diffusivity in Bitumen
,”
Energy Fuels
,
25
(
10
), pp.
4829
4835
.
15.
Shi
,
Y.
, and
Yang
,
D.
,
2016
, “
Quantification of a Single Gas Bubble Growth in Solvent(s)–CO2–Heavy Oil Systems With Consideration of Multicomponent Diffusion Under Nonequilibrium Conditions
,”
ASME J. Energy Resour. Technol.
,
139
(
2
), p.
022908
.
16.
Al Ghamdi
,
B. N.
, and
Ayala H
,
L. F.
,
2017
, “
Evaluation of Transport Properties Effect on the Performance of Gas-Condensate Reservoirs Using Compositional Simulation
,”
ASME J. Energy Resour. Technol.
,
139
(
3
), p.
032910
.
17.
Etminan
,
S. R.
,
Maini
,
B. B.
,
Chen
,
Z.
, and
Hassanzadeh
,
H.
,
2010
, “
Constant-Pressure Technique for Gas Diffusivity and Solubility Measurements in Heavy Oil and Bitumen
,”
Energy Fuels
,
24
(
1
), pp.
533
549
.
18.
Yang
,
C.
, and
Gu
,
Y.
,
2006
, “
Diffusion Coefficients and Oil Swelling Factors of Carbon Dioxide, Methane, Ethane, Propane, and Their Mixtures in Heavy Oil
,”
Fluid Phase Equilib.
,
243
(
1–2
), pp.
64
73
.
19.
Marufuzzaman
,
M.
,
2010
, “Solubility and Diffusivity of Carbon Dioxide, Ethane and Propane in Heavy Oil and Its SARA Fractions,” M.A.Sc. thesis, University of Regina, Regina, SK.
20.
Nadrei
,
K.
, and
Babadagli
,
T.
,
2015
, “
Solvent Selection Criteria and Optimal Application Conditions for Heavy-Oil/Bitumen Recovery at Elevated Temperatures: A Review and Comparative Analysis
,”
ASME J. Energy Resour. Technol.
,
138
(
1
), p.
012904
.
21.
Zheng
,
S.
,
Li
,
H.
,
Sun
,
H.
, and
Yang
,
D.
,
2016
, “
Determination of Diffusion Coefficient for Alkane Solvent-CO2 Mixtures in Heavy Oil With Consideration of Swelling Effect
,”
Ind. Eng. Chem. Res.
,
55
(
6
), pp.
1533
1549
.
22.
Sun
,
H.
,
Li
,
H.
, and
Yang
,
D.
,
2014
, “
Coupling Heat and Mass Transfer for a Gas Mixture-Heavy Oil System at High Pressures and Elevated Temperatures
,”
Int. J. Heat Mass Transfer
,
74
, pp.
173
184
.
23.
Zheng
,
S.
, and
Yang
,
D.
,
2017
, “
Determination of Individual Diffusion Coefficients of C3H8/n-C4H10/CO2/Heavy Oil Systems at High Pressures and Elevated Temperatures by Dynamic Volume Analysis
,”
SPE J.
,
22
(
3
), pp.
799
816
.
24.
Zheng
,
S.
, and
Yang
,
D.
,
2016
, “
Experimental and Theoretical Determination of Diffusion Coefficients of CO2-Heavy Oil Systems by Coupling Heat and Mass Transfer
,”
ASME J. Energy Resour. Technol.
,
139
(
2
), p.
022901
.
25.
Zheng
,
S.
,
Sun
,
H.
, and
Yang
,
D.
,
2016
, “
Coupling Heat and Mass Transfer for Determining Individual Diffusion Coefficient of a Hot C3H8-CO2 Mixture in Heavy Oil Under Reservoir Conditions
,”
Int. J. Heat Mass Transfer
,
102
, pp.
251
263
.
26.
Hayduk
,
W.
, and
Cheng
,
S. C.
,
1971
, “
Review of Relation Between Diffusivity and Solvent Viscosity in Dilute Liquid Solutions
,”
Chem. Eng. Sci.
,
26
(5), pp.
635
646
.
27.
Yarranton
,
H. W.
,
Dorp
,
J. J.
,
Verlaan
,
M. L.
, and
Lastovka
,
V.
,
2013
, “
Wanted Dead or Live: Crude-Cocktail Viscosity—A Pseudocomponent Method to Predict the Viscosity of Dead Oils, Live Oils, and Mixtures
,”
J. Can. Pet. Technol.
,
52
(
3
), pp.
176
191
.
28.
McCain
,
W. D.
, Jr.
,
1990
,
The Properties of Petroleum Fluids
,
2nd ed.
,
PennWell Publishing Company
,
Tulsa, OK
.
29.
Hildebrand
,
J. H.
,
1936
,
Solubility of Non-Electrolytes
,
2nd ed.
,
Reinhold Publishing Corporation
,
New York
.
30.
Lide
,
D. R.
,
2009
,
CRC Handbook of Chemistry and Physics
,
90th ed.
,
CRC Press
,
Boca Raton, FL
.
31.
Chen
,
Z.
, and
Yang
,
D.
,
2017
, “
Optimization of the Reduced Temperature Associated With Peng–Robinson Equation of State and Soave–Redlich–Kwong Equation of State to Improve Vapor Pressure Prediction for Heavy Hydrocarbon Compounds
,”
J. Chem. Eng. Data
,
62
(
10
), pp.
3488
3500
.
32.
Computer Modelling Group Ltd.
, 2014, “WINPROP Manual, Version 2014.10,” Computer Modelling Group Ltd., Calgary, AB, Canada.
33.
Li
,
H.
, and
Yang
,
D.
,
2011
, “
Modified α Function for the Peng–Robinson Equation of State to Improve the Vapor Pressure Prediction of Non-Hydrocarbon and Hydrocarbon Compounds
,”
Energy Fuels
,
25
(
1
), pp.
215
223
.
34.
Lindeloff
,
N.
,
Pedersen
,
K. S.
,
Ronningsen
,
H. P.
, and
Milter
,
J.
,
2004
, “
The Corresponding States Viscosity Model Applied to Heavy Oil Systems
,”
J. Can. Pet. Technol.
,
43
(
9
), pp.
47
53
.
35.
Luo
,
P.
,
Yang
,
C.
, and
Gu
,
Y.
,
2007
, “
Enhanced Solvent Dissolution Into In-Situ Upgraded Heavy Oil Under Different Pressures
,”
Fluid Phase Equilib.
,
252
(
1–2
), pp.
143
151
.
36.
Luo
,
P.
, and
Gu
,
Y.
,
2009
, “
Characterization of a Heavy Oil-Propane System in the Presence or Absence of Asphaltene Precipitation
,”
Fluid Phase Equilib.
,
277
(
1
), pp.
1
8
.
37.
Yang
,
C.
,
2005
, “A New Method for Measuring Solvent Diffusion Coefficients and Oil Swelling Factors of Heavy Oil-Solvent Systems,” Ph.D. dissertation, University of Regina, Regina, SK.
38.
Tharanivasan
,
A. K.
,
Yang
,
C.
, and
Gu
,
Y.
,
2006
, “
Measurements of Molecular Diffusion Coefficients of Carbon Dioxide, Methane, and Propane in Heavy Oil Under Reservoir Conditions
,”
Energy Fuels
,
20
(6), pp.
2509
2517
.
39.
Welty
,
J.
,
Wicks
,
C.
,
Wilson
,
R.
, and
Rorrer
,
G.
,
2008
,
Fundamentals of Momentum, Heat, and Mass Transfer
,
5th ed.
,
Wiley
,
New York
.
40.
Gas Processors Suppliers Association Editorial Review Board
,
1991
, “
Convergence Pressure and Vapor-Liquid Ratios: GPA Technical Publication TP-22
,”
Gas Processors Association
,
Tulsa, OK
.
41.
Standing
,
M. B.
,
1979
, “
A Set of Equations for Computing Equilibrium Ratios of a Crude Oil/Natural Gas System at Pressures Below 1,000 Psia
,”
J. Pet. Technol.
,
31
(
9
), pp.
1193
1195
.
42.
Standing
,
M. B.
,
1952
,
Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems
,
Reinhold Publishing Corporation
,
New York
.
43.
Ahmed
,
T. H.
,
2010
,
Reservoir Engineering Handbook
,
2nd ed.
, Gulf Professional Publishing, Burlington, MA.
44.
Li
,
H.
, and
Yang
,
D.
,
2016
, “
Determination of Individual Diffusion Coefficients of Solvent/CO2 Mixture in Heavy Oil With Pressure-Decay Method
,”
SPE J.
,
21
(
1
), pp.
131
143
.
45.
Li
,
H.
,
Sun
,
H.
, and
Yang
,
D.
,
2017
, “
Effective Diffusion Coefficients of Gas Mixture in Heavy Oil Under Constant-Pressure Conditions
,”
Heat Mass Transfer
,
53
(
5
), pp.
1527
1540
.
46.
Nguyen
,
T. A.
, and
Farouq Ali
,
S. M.
,
1998
, “
Effect of Nitrogen on the Solubility and Diffusivity of Carbon Dioxide Into Oil and Oil Recovery by the Immiscible WAG Process
,”
J. Can. Pet. Technol.
,
37
(
2
), pp.
24
31
.
47.
Talbi
,
K.
, and
Maini
,
B. B.
,
2008
, “
Experimental Investigation of CO2-Based VAPEX for Recovery of Heavy Oils and Bitumen
,”
J. Can. Pet. Technol.
,
47
(
4
), pp.
1
8
.
48.
Luo
,
P.
,
Zhang
,
Y.
,
Wang
,
X.
, and
Huang
,
S.
,
2012
, “
Propane-Enriched CO2 Immiscible Flooding for Improved Heavy Oil Recovery
,”
Energy Fuels
,
26
(
4
), pp.
2124
2135
.
49.
Upreti
,
S. R.
,
Lohi
,
A.
,
Kapadia
,
R. A.
, and
El-haj
,
R.
,
2007
, “
Vapor Extraction of Heavy Oil and Bitumen: A Review
,”
Energy Fuels
,
21
(
3
), pp.
1562
1574
.
50.
Qi
,
J.
, and
Polikar
,
M.
,
2005
, “
Optimal Solvent and Well Geometry for Production of Heavy Oil by Cyclic Solvent Injection
,”
Canadian International Petroleum Conference (CIPC)
, Calgary, AB, Canada, June 7–9, Paper No.
PETSOC-2005-194
.
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