Abstract
We study a model for simulating the flow of an immiscible displacement (waterflooding) of one incompressible fluid by another in a naturally fractured petroleum reservoir when the matrix blocks are quite small. This model is equivalent to a transformed one for immiscible flow in an unfractured reservoir with a reduced saturation and a saturation-dependent porosity. Existence and uniqueness of classical solutions are established. We present some numerical results and a comparison with a single porosity model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. N. Antoncev, On the solvability of boundary value problems for degenerate two-phase porous flow equations, (Russian), Dinamika 565–06 Sredy Vyp. 10 (1972), 28–53.
Todd Arbogast, Two—phase incompressible flow in a porous medium with various nonhomogeneous boundary conditions, (to appear).
Todd Arbogast, Jim Douglas Jr., and Ulrich Hornung, Modeling of naturally fractured reservoirs by formal homogenization techniques, (to appear).
Todd Arbogast, Jim Douglas Jr., and Juan E. Santos, Two-phase immiscible flow in naturally fractured reservoirs, in “Numerical Simulation in Oil Recovery,” Mary F. Wheeler, (ed.), The IMA Volumes in Mathematics and its Applications, Springer-Verlag, Berlin and New York, 1988, pp. 47–66.
Guy Chavent, A new formulation of diphasic incompressible flows in porous media, in “Applications of Methods of Functional Analysis to Problems in Mechanics,” Lecture Notes in Mathematics 503, P. Germain and B. Nayroles, eds., Springer-Verlag, Berlin and New York, 1976, pp. 258–270.
Jim Douglas Jr. and Todd Arbogast, Dual-porosity models for flow in naturally fractured reservoirs, in “Dynamics of Fluids in Hierarchial Porous Formations,” J. H. Cushman, ed., Academic Press, to appear.
Jim Douglas Jr., Todd Arbogast, and Paulo Jorge Paes Leme, Two models for the waterflooding of naturally fractured reservoirs, Paper SPE 18425, in “Proceedings, Tenth SPE Symposium on Reservoir Simulation,” Society of Petroleum Engineers, Dallas, Texas, 1989, pp. 219–225.
Jim Douglas, Jr., Todd Arbogast, and Jeffrey L. Hensley, A dual-porosity model for waterflooding in naturally fractured reservoirs, to appear.
S. N. Kružkov and S. M. 565–07, Boundary problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods, Math. USSR Sbornik 33 (1977), 62–80.
Mary F. Wheeler, A priori L 2 error estimates for Galerkin approximations to parabolic partial differential equations, SIAM J. Numer. Anal. 10 (1973), 723–759.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Douglas, J., Paes-Leme, P.J. & Hensley, J.L. A limit form of the equations for immiscible displacement in a fractured reservoir. Transp Porous Med 6, 549–565 (1991). https://doi.org/10.1007/BF00137849
Issue Date:
DOI: https://doi.org/10.1007/BF00137849