Pseudospectral Method for Optimal Control Analysis in Porous Media

In the process of extracting oil, it is common that there is still a large amount of oil remaining in the crust because of the tension force and resistance caused by the capillary in the porous media. To eliminate the trapped oil in the porous media, a excitation frequency is applied and causes oil blobs resonance. Because of the resonance, oil blobs can easily cancel out the resistance of capillarity and tension force. In this research, an optimal control problem is constructed in order to minimize the energy consumption by adjusting the excitation frequency and extracting force. Pseudospectral method, which is a numerical method specializing in solving partial differential equation, is applied to simplify the origin function and transforms the origin optimal control problem into a nonlinear program. Therefore, this problem can eventually be solved by GAMS.