The optimal control theory of distributed-parameter systems has been applied to the problem of determining the best injection policy of a surfactant slug for a tertiary oil recovery chemical flood. The optimization criterion is to maximize the amount of oil recovered while minimizing the chemical cost. A steepest-descent gradient method was used as the computational approach to the solution of this dynamic optimization problem.The performance of the algorithm was examined for the surfactant injection in a one-dimensional flooding problem. Two types of interfacial tension (1FT) behavior were considered. These are a Type A system where the 1FT is a monotonically decreasing function with solute concentration and a Type B system where a minimum 1FT occurs at a nominal surfactant concentration. For a Type A system, the shape of the optimal injection strategy was not unique; however, there is a unique optimum for the amount of surfactant needed. For a Type B system, the shape of the optimal injection as well as the ·amount injected was unique.

The theory of optimal control of distributed-parameter systems is presented for determining the best possible injection policies for EOR processes. The optimization criterion is to maximize the amount of oil recovered at minimum injection costs. Necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin's weak minimum principle. A gradient method is proposed for the computation of optimal injection policies.

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