A Finite Element Formulation of the Two-Phase Flow Equations for Oil Reservoirs

Abstract In the present paper, the differential equations governing two phase, immiscible flow in porous media is solved by the finite element method. The saturation of the wetting phase (water) and the non wetting phase (oil) have been used as independent variables. In this finite element formulation the saturation and pressure equations are solved simultaneously and the formulation is entirely implicit. The time derivatives are approximated by backward Euler differences. The Newton Raphson method is applied to solve the non linear equations. The differential equations are solved in the original form without simplifications. The simulations are performed in a two dimensional model, but the algorithms will have equal advantages in three dimensional simulations. The results of the simulations are presented as saturation and pressure isocurves, and velocity vector field.