Note: Special Date and Location
Abstract: In immiscible three-phase (oil, gas and water) flow in petroleum reservoirs generated by the injection of a mixture of water and gas, the leading oil front can split into a classical Buckley-Leverett shock followed by a new type of shock wave which is related to the existence of an elliptic region or an umbilical point for the system of nonlinear conservation laws describing the convective transport of the fluid phases. Unlike classical shock waves (e.g., Buckley-Leverett fronts), this non-classical ``transitional'' shock wave is very sensitive to the form of the parabolic terms in the equations that arise from diffusive effects; thus, it is imperative that capillary pressure effects be modeled accurately in order to obtain physically correct transitional waves.
We present an accurate numerical procedure for the simulation of these flows which properly includes capillary pressure effects. We focus on two-dimensional, heterogeneous problems, where we verify that transitional waves, which had been identified theoretically for one-dimensional problems, are present in two-dimensional heterogeneous reservoirs.
Our operator-splitting procedure combines mixed finite element methods for the approximation of parabolic (diffusive transport) and elliptic (pressure-velocity) subproblems with a non-oscillatory, second-order, conservative central difference scheme to handle a system of conservation laws (advective transport) to treat the three-phase flow problem in heterogeneous porous media.
Future talks in Scientific Computing Seminar
Nov. 11: Jiwen He, Department of Mathematics, University of Houston.
Nov. 18: E.W. Sachs, Department of Mathematics, Virginia Tech.
Nov. 22: P. Bochev: Sandia National Laboratories.
Nov. 23: O. Pironneau, Universite Pierre-et-Marie-Curie, France.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.