Application of finite element methods to solving immiscible displacement problems with sharp fronts

Many reservoir engineering problems involve solving fluid flow equations, whose solutions are characterized by sharp fronts and low dispersion levels. This is particularly important in tracking small slugs which are characteristic of chemical floods, polymer floods, first and multiple contact hydrocarbon miscible displacements and most thermal processes. The use of finite difference approximations to solve these problems when low dispersion levels and small slugs need to be accurately modeled is prohibitively expensive. In two dimensions, as many as 500 grid blocks on a side would be required in order to obtain the necessary accuracy. However, the use of high order finite element schemes are shown to be a very effective means of economically solving this problem. This paper presents some numerical results of a research project recently completed which has demonstrated that high order finite element methods can be used to solve difficult reservoir engineering problems where finite difference approximations would be prohibitively expensive.