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The relevant physicochemical algebraic equations are shown as below: A. Alkali consumptionMany kinds of conditions can influence the alkali consumption, while only the adsorption consumption, acid consumption and heavy metal ion consumption are considered in this paper to describe the mechanism well and simply. The alkali consumption is given through the chemical reaction term 𝑟 𝑖 , which is defined as follows:

Because of the mechanism complexity, coupling, and time-space characteristic of alkali-surfactant-polymer (ASP) flooding, common methods are very hard to be implemented directly. In this paper, an iterative dynamic programming (IDP) based on a biorthogonal spatial-temporal Wiener modeling method is developed to solve the enhanced oil recovery for ASP flooding. At first, a comprehensive mechanism model for the enhanced oil recovery of ASP flooding is introduced. Then the biorthogonal spatial-temporal Wiener model is presented to build the relation between inputs and states, in which the Wiener model is expanded on a set of spatial basis functions and temporal basis functions. After inferring the necessary condition of solutions, these basis functions are determined by the snapshot method. Furthermore, a theorem is proved to identify parameters in the Wiener model. Combined with the least square estimation (LSE), all unknown parameters are determined. In addition, the ARMA model is applied to build the model between states and outputs, whose parameters are identified by recursive least squares (RLS). Thus, the whole modeling process for ASP flooding is finished. At last, the IDP algorithm is applied to solve the enhanced oil recovery problem for ASP flooding based on the identification model to obtain the optimal injection strategy. Simulations on the ASP flooding with four injection wells and nine production wells show the accuracy and effectiveness of the proposed method.

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