Maximization of Water Sweep Efficiency by Controlling Production and Injection Rates

Abstract

SPE Member Abstract A method for computation of the best production scheme has been developed. It consists of a two dimensional, two phase reservoir simulator, search direction computation by implicit differentiation and a numerical search program. Applied to hypothetical cases of production by water drive, NPV improvements of 2–11% were achieved. Introduction The ultimate goal of reservoir simulation is to compute the best production scheme. With current simulators, this goal is pursued by trial and error: The reservoir engineer is left to decide how the operating parameters should be changed to improve the result, and when the search should be terminated. This obviously has strong elements of subjectivity. During the last decades, attempts have been made to develop simulators that compute of the best production scheme. Conceptually, this can be done by combining a reservoir simulator with a numerical search algorithm. However, finite difference simulators involve a multitude of variables and relationships that do not integrate easily with numerical optimization methods. By most reservoir optimization approaches, referenced below, the reservoir simulation model has been replaced by linearization of the pressure-production relationships. This may be an pressure-production relationships. This may be an acceptable approximation for single phase reservoirs, but not for reservoirs containing several mobile phases. By the method presented, the reservoir simulator is combined directly with a numerical search program. The key to the method is the total differentiation of the reservoir simulator, which enables efficient and precise computation of the gradient search direction. The method is equally applicable to muiti-phase and single-phase reservoir problems. In this work, it has been applied to maximize water sweep efficiency by control of well production and injection rates. Applied on some hypothetical cases, NPV (net present value) improvements of 2–11% were achieved compared to well rate allocation by the permeability-thickness product. Numerically, the permeability-thickness product. Numerically, the method performed beyond expectation, with fast convergence, stable solutions and apparently few problems with local maxima. Theory Problem definition. Problem definition. The problem considered is to maximize the net present value of production and injection streams, present value of production and injection streams, subject to reservoir and production constraints. (1) where: y: reservoir state variables such as pressures and saturations q: well rates subject to reservoir constraints, described by simulation equations (2) total flow capacity constraints (3) P. 273