Optimization of an enhanced oil recovery process with boundary controls—A large-scale non-linear maximization

Abstract

The problem of optimally determining the injected concentration histories for a micellar/polymer flooding enhanced oil recovery (EOR) system so as to maximize the net profitability of the project is considered. The state dynamics are described by a set of highly non-linear partial differential equations with boundary control inputs. The theoretical characterization of the optimal control policy is obtained using both a continuous and a discrete variational formulation. The numerical optimum-seeking algorithm is formulated based on generating a maximizing sequence which converges to the optimum control policy. This sequence is generated by employing gradient or conjugate directions of search on the performance measure. Numerical calculations are presented to illustrate optimal policies. Specific results depend on the physical chemistry as well as on reservoir parameters. The method has been tested on the realistic linear core experiments used to design the Sloss field test of Amoco. The optimization studies yield optimum injection strategies which improve the core flood performance by over 21%. The optimum value of the performance measure is about 81% of the greatest attainable economic value which corresponds to complete oil recovery at no chemical cost. This paper emphasizes the applicability of optimal control theory to a problem which is highly non-linear, mathematically complex and extensively large. The effectiveness of the approach has been established by numerical results.