Spatial-Temporal ARX Modeling and Optimization for Polymer Flooding

A new polymer flooding model based on spatial-temporal decomposition and autoregressive model with external input (ARX) (STDARX model) is proposed. Karhunen-Loeve (K-L) decomposition is used to model the two-dimensional state parameters of reservoir (such as water saturation, pressure, and grid concentration). The polymer injection concentration and time coefficient got from the decomposition are taken as the input and output information. After being identified by least square method, the time iterative ARX models of all state variables are obtained, we build the ARX model among pressure, water saturation, grid concentration, and moisture content of production well, and identify it with recursive least-squares (RLS) method. After combining the above two models, we get the STDARX model of polymer flooding. The accuracy is proved by model with four injection wells and nine production wells through data which is obtained from mechanism model. In order to enhance the polymer flooding oil recovery when oil price is changing, iterative dynamic programming (IDP) is applied to optimize the STDARX model, to get the optimal injection of production scheme.