Optimization of Displacements in Porous Media Using Rate Control

Abstract

Abstract In many applications involving the injection of a fluid in a porous medium to displace another, a main objective is the maximization of the displacement efficiency. For a fixed arrangement of injection and production wells, such optimization is possible by controlling the injection rate policy. This paper is an abbreviated version of Ref. [1], where we described a fundamental approach based on optimal control theory, for the simplified case when the fluids are miscible, of equal viscosity and in the absence of dispersion and gravity effects. Both homogeneous and heterogeneous porous media are considered. The optimal injection policy that maximizes the displacement efficiency at the time of arrival of the injected fluid, is of the "bang-bang" type, namely where the rates take their extreme values in the range allowed. This result applies to both homogeneous and heterogeneous media. Examples in simple geometries and for various constraints are shown. In the heterogeneous case, the effect of the permeability heterogeneity, particularly its spatial correlation structure, on diverting the flow paths, is analysed. "Bang-bang" injection remains the optimal approach, compared to constant rate, if they were both designed under the assumption that the medium was homogeneous.