A Revised Analytic Solution to the Linear Displacement Problem Including Capillary Pressure Effects

Transport in Porous Media

Volumn 86, Issue 3, 2011, Pages 881-894

  Ruth, D W ^a   Arthur, J K ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Analytical solution; Capillary pressure effects; Linear displacement; Porous media; Two phase; Waterflood

Indexed keywords

CAPILLARITY; CAPILLARY TUBES; POROUS MATERIALS;

ANALYTICAL RESULTS; CONTROLLING PARAMETERS; EXPLICIT SOLUTIONS; GOVERNING EQUATIONS; LINEAR DISPLACEMENTS; NUMERICAL SIMULATORS; TWO PHASE; WATER FLOOD;

PRESSURE EFFECTS;

CAPILLARY PRESSURE; COMPUTER SIMULATION; FLOOD; LINEARITY; MODEL VALIDATION; NUMERICAL MODEL; PARAMETERIZATION; POROUS MEDIUM; TWO PHASE FLOW; VISCOUS FLOW;

EID: 79251597425     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-010-9662-0     Document Type: Article

References (21)

1. Avraam D. G., Payatakes A. C.: Generalized relative permeability coefficients during steady-state two-phase flow in porous media, and correlation with the flow mechanisms. Transp. Porous Media 20, 135-168 (1995).
2. Buckley S. E., Leverett M. C.: Mechanism of displacement in sands. Trans. AIME 146, 107-116 (1942).
3. Chen Z.-X.: Some invariant solutions to two-phase fluid displacement problems including capillary effects. SPE Reserv. Eng. 3, 691-700 (1988).
4. Clarkson P. A., Fokas A. S., Ablowitz M. J.: Hodograph transformations of linearizable partial differential equations. SIAM J. Appl. Math. 49(4), 1188-1209 (1989).
5. Dong M., Dullien F. A. L.: A new model for immiscible displacement in porous media. Transp. Porous Media 27, 185-204 (1997).
6. Dong M., Dullien F. A. L., Zhou J.: Characterization of waterflood saturation profile histories by the 'complete' capillary number. Transp. Porous Media 31, 213-237 (1998).
7. Dong M., Dullien F. A. L., Dai L., Li D.: Immiscible displacement in the interacting capillary bundle model Part I. Development of interacting capillary bundle model. Transp. Porous Media 59, 1-18 (2005).
8. Douglas J. Jr, Blair P. M., Wagner R. J.: Calculation of linear waterflood behaviour including the effects of capillary pressure. Trans. AIME 213, 96-102 (1958).
9. Fokas A. S., Fuchssteiner B.: Backlünd transformations for hereditary symmetries. Nonlinear Theory Methods Appl. 5(4), 423-432 (1981).
10. Fokas A. S., Yortsos Y. C.: On the exactly solvable equation, occurring in two-phase flow in porous media. SlAM J. Appl. Math. 42(2), 318-332 (1982).
11. Hadad A., Bensabat J., Rubin H.: Simulation of immiscible multiphase flow in porous media: a focus on the capillary fringe of oil-contaminated aquifers. Transp. Porous Media 12, 245-269 (1996).
12. Kashchiev D., Firoozabadi A.: Analytical solutions for 1D countercurrent imbibitions in water-wet media. SPE J. 8, 401-408 (2003).
13. McWhorter D. B., Sunada D. K.: Exact solutions for two-phase flow. Water Resour. Res. 26, 399-413 (1990).
14. Mueller A. C., Carey G. F.: Continuously deforming finite elements. Int. J. Numer. Methods Eng. 21, 2099-2126 (1985).
15. Novy R. A., Davis H. T., Scriven L. E. L.: A comparison of synthetic boundary conditions for continuous-flow systems. Chem. Eng. Sci. 46(1), 57-68 (1991).
16. Pistiner A., Shapiro M., Rubin H.: Similarity solutions for immiscible phase migration in porous media: an analysis of free boundaries. Transp. Porous Media 5, 491-515 (1990).
17. Porcelli P. C., Bidner M. S.: Simulation and transport phenomena of a ternary two-phase flow. Transp. Porous Media 14, 101-122 (1994).
18. Riaz A., Tchelepi H. A.: Numerical simulation of immiscible two-phase flow in porous media. Phys. Fluids 18, 014104 (2006).
19. Ruth D. W., Li Y., Mason G., Morrow N. R.: An approximate analytical solution for counter-current spontaneous imbibition. Transp. Porous Media 66, 373-390 (2007).
20. Wu Y-S., Pruess K., Witherspoon P. A.: Displacement of a Newtonian fluid by a Non-Newtonian fluid in a porous Medium. Transp. Porous Media 6, 115-142 (1991).
21. Yortsos Y. C., Fokas A. S.: An analytical solution for linear waterflood including the effects of capillary pressure. SPE J. 23(1), 115-124 (1983).