Application of the Petrov-Galerkin method to chemical-flooding reservoir simulation in one dimension

Abstract A one-dimensional, chemical-flooding simulator is described. This program models the effect that polymers, surfactants and salts have on the enhanced recovery of oil. The flow equations are convection dominated and often shock-like profiles develop which traverse the domain. The simulator incorporates, with a few modifications, most of the physical and chemical package which is set forth by Pope and Nelson. The spacial discretization is performed via the Petrov-Galerkin, finite element method. This technique is mainly derived from the work of Hughes and Brooks and is modified for the case of chemical flooding. We compare this finite element method to the upstream, finite difference method and to Galerkin's method. Generally speaking, the Petrov-Galerkin results are significantly less sensitive to the number of grid points than are those of the upstream method. Its stability properties are nearly the same as those of the upstream techniques, which in turn, are superior to those of Galerkin's method.

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