Solution Of Optimal Control For Polymer Flooding Based On SWIFT And Its Parallelization

Polymer flooding is an important technique for enhancing oil recovery. Because the polymer is expensive and the risk of polymer flooding is high, it is of great significance to study the optimal control problem (OCP) in order to make the optimal plan. The polymer flooding model mainly contains some partial differential equations. When solving the OCP, we should achieve huge computation work. So it is necessary to study the parallelization of optimization methods. In this thesis, the optimal injection strategies are obtained by using sequential weight increasing factor technique (SWIFT). Also, the parallelization of solving the OCPs of polymer flooding based on SWIFT is implemented. The main works of this thesis are described as follows.In this thesis, the finite difference method which is applied to solve partial differential equations is introduced. Besides, the basic knowledge of parallel computing is demonstrated. A small-scale parallel computing platform is built based on PCs cluster and tested by using an example of parallel solving linear algebraic equations.The solution of OCPs based on SWIFT is researched in this thesis. SWIFT is a direct search method in nonlinear programming (NLP), which is used to solve the constrained optimization problem. It is based on simplex method and penalty function method. SWIFT uses penalty function method to transform a constrained optimization problem to an unconstrained optimization problem which is solved by using simplex method. When using SWIFT to solve an OCP, it is necessary to transform the OCP into a NLP. The transformation can be achieved by parameterized optimization method. This method divides the time range into several intervals by some time nodes. The values of control variables at these nodes are chosen as parameters of the control vector. The rest values of control variables can be decided by interpolation. Once the optimal control vector is determined, the optimal control can be gained. So the NLP which is required to get the optimal control vector is established. The results of the OCPs for heat conduction show the effectivity of SWIFT.Based on the core experiment model, the solution of OCP for polymer flooding based on SWIFT is researched. In the optimal control model, the profit of polymer flooding is chosen as the performance index. The governing equations are the flow equations which describe the mechanism of polymer flooding. The injection concentration and the injection time are selected as the control variables, which are always limited in some certain ranges. The optimal injection strategies for simple slug, double slugs and three slugs are obtained by using SWIFT. The results validate that SWIFT is an effective method to solve the OCPs for polymer flooding.The parallel computing of the OCPs for polymer flooding based on SWIFT is studied. The parallelization is implemented by partial parallel for algorithm structure of SWIFT and parallelization of numerical simulation of polymer flooding model. In the latter, the parallel difference schemes based on interface correction and moving interface are applied to solve partial differential equation of second order. The comparisons between the serial computing results and the parallel computing results prove the validity of parallelization.