An approximate dynamic programming method for the optimal control of Alkai-Surfactant-Polymer flooding

Since the complexity, coupling, distributed parameter, etc. of alkali-surfactant-polymer (ASP) flooding, common optimization methods cannot acquire the optimal solutions well. This paper brings an optimal control method for ASP flooding based on approximate dynamic programming (ADP). At first, take the net present value (NPV) as the performance index. Then the Actor-Critic algorithm based on gradient descent method is adopted to get the optimal injection strategy, in which Actor and Critic are used to approximate the control and value function, respectively. To improve the approximation performance, the linear approximation basis function based on system characteristic is constructed. Furthermore, to train and predict the control and value function in next step, a temporal difference (TD) learning algorithm is introduced to update the weight coefficients. Then, the control in ADP is generated according to the Gauss function and its weight is updated according to the sigmoid function of TD error, so that the optimal control can be searched. At last, the enhanced oil recovery problem of ASP flooding with four injection wells and nine production wells is solved by the proposed method to test the effect of proposed method.