Semi-analytical solutions to one-dimensional advection-diffusion equations with variable diffusion coefficient and variable flow velocity

Applied Mathematics and Computation

Volumn 221, Issue , 2013, Pages 268-281

  Jia, Xinfeng ^a   Zeng, Fanhua ^a   Gu, Yongan ^a  

^a UNIVERSITY OF REGINA   (Canada)

Author keywords

Advection diffusion equation; Cyclic solvent injection; Flow velocity; Variable diffusion coefficient

Indexed keywords

ADVECTION-DIFFUSION EQUATION; CONCENTRATION DISTRIBUTIONS; INCOMPRESSIBLE FLUID FLOW; LAPLACE TRANSFORMATIONS; SEMI-ANALYTICAL SOLUTION; SOLVENT INJECTION; VARIABLE DIFFUSION COEFFICIENT; VARIABLE FLOW VELOCITY;

ADVECTION; CARBON DIOXIDE; CRUDE OIL; ENHANCED RECOVERY; FLOW VELOCITY; GRAVITATION; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; SOLVENTS;

DIFFUSION;

EID: 84880755028     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2013.06.052     Document Type: Article

References (25)

1. L.W. Holm, and V.A. Josendal Mechanisms of oil displacement by carbon dioxide J. Pet. Tecnol. 26 12 1974 1427 1436
2. J.J. Rathmell, F.I. Stalkup, R.C. Hassinger, A laboratory investigation of miscible displacement by carbon dioxide, in: Paper SPE 3483, presented at Fall Meeting of the Society of Petroleum Engineers of AIME, New Orleans, Louisiana, 1971
3. G.B. Lim, R.P. Kry, B.C. Harker, and K.N. Jha Three-dimensional scaled physical modelling of solvent vapour extraction of Cold Lake bitumen J. Can. Pet. Technol. 35 4 1996 32 40
4. J. Ivory, J. Chang, R. Coates, and K. Forshner Investigation of cyclic solvent injection process for heavy oil recovery J. Can. Pet. Technol. 49 9 2010 22 33
5. 2 huff-n-puff process for heavy oil reservoirs J. Can. Pet. Technol. 23 3 1984 29 36 (Pubitemid 14672862)
6. 2 huff-n-puff process in matrix-fracture experimental model Fuel 89 10 2010 2985 2990
7. I.J. Morkys, and R.M. Butler The rise of interfering solvent chambers: solvent analog model of steam-assisted gravity drainage Pet. Soc. Can. 32 3 1993 26 36
8. R.M. Butler, and I.J. Mokrys Solvent analogue model of steam-assisted gravity drainage AOSTRA J. Res. 5 1989 17 32
9. R.M. Butler, and I.J. Mokrys A new process (VAPEX) for recovering heavy oils using hot water and hydrocarbon vapour J. Can. Pet. Technol. 30 1 1991 97 106
10. S.R. Upreti, A. Lohi, A. Kapadia, and R. El-Haj Vapor extraction of heavy oil and bitumen: a review Energy Fuels 21 3 2007 1562 1574 (Pubitemid 46937845)
11. A. Boustani, and B.B. Maini The role of diffusion and convective dispersion in vapour extraction process J. Can. Pet. Technol. 40 4 2001 68 77 (Pubitemid 32486752)
12. A.S. Scott, G.H. Jirka, Environmental Fluid Mechanisms Part I: Mass Transfer and Diffusion, Karlsruhe, Germany, 2002.
13. G. Sposito, and S.W. Weeks Tracer advection by steady groundwater flow in a stratified aquifer Water Resour. Res. 34 5 1998 1051 1059 (Pubitemid 28219537)
14. M.A. Marino Numerical and analytical solutions of dispersion in a finite, adsorbing porous medium J. Am. Water Resour. Assoc. 10 1 1974 81 90
15. M.F. Wheeler, and C.N. Dawson An Operator-Splitting Method for Advection-Diffusion-Reaction Problems 1992 Academic Press London
16. A. Kumer, D.K. Jaiswal, and N. Kumer Analytical solutions of one dimensional advection-diffusion equation with variable coefficient in a finite domain J. Earth Syst. Sci. 118 5 2009 539 549
17. A.N.S. Al-niami, and K.R. Rushton Radial dispersion to an abstract well J. Hydrol. 39 3-4 1978 287 300
18. W. Hayduk, and S.C. Cheng Review of relation between diffusivity and solvent viscosity in dilute liquid solutions Chem. Eng. Sci. 26 5 1971 635 646
19. M. Abramowitz, and I.A. Stegun Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1970 Dover Publications New York
20. K.E. Muller Computing the confluent hypergeometric function, M(a, b, x) Numer. Math. 90 1 2001 179 196
21. H. Stehfest Numerical inversion of Laplace transformation Commun. ACM 13 1 1970 47 49
22. D.G. Zill A First Course in Differential Equations with Modeling Applications 2001 Brooks/Cole Pub Co. USA
23. E.L. Lederer Proceedings World Petroleum Congress, London 2 1933 526 528
24. W.R. Shu A viscosity correlation for mixtures of heavy oil, bitumen, and petroleum fractions SPE J. 24 3 1984 227 282
25. S.K. Das, and R.M. Butler Diffusion coefficients of propane and butane in Peace River bitumen Can. J. Chem. Eng. 74 6 1996 985 992 (Pubitemid 126451705)