6533b82dfe1ef96bd1290839

RESEARCH PRODUCT

Solving a model for 1-D, three-phase flow vertical equilibrium processes in a homogeneous porous medium by means of a Weighted Essentially Non Oscillatory numerical scheme

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Mathematical models of multi-phase flow are useful in some engineering applications like enhanced oil recovery, filtration of pollutants into subsurface, etc. In this work, we derive a mathematical model for the motion of one-dimensional three-phase flow in a porous medium under the condition of vertical equilibrium, which can be viewed as an extension of some two-phase flow models described in the literature. Our model involves a system of two partial differential equations in the form of viscous conservation laws, whose solutions may contain very sharp transitions. We show that a high-order/high resolution Weighted Essentially Non Oscillatory scheme is an appropriate tool to discretize the buoyancy flux and obtain a well resolved representation of the solution of the model. In addition, we show that the efficiency of the scheme may be improved by using Implicit-Explicit (IMEX) strategies, where the parabolic terms are handled by an implicit discretization.