Dynamic optimization of water flooding with multiple injectors and producers using optimal control theory

摘要

In this reservoir simulation study we optimized a water flood of an oil reservoir by dynamically changing the flow rates of the wells. The reservoir models to optimize were two-dimensional and horizontal, and contained a large scale, simple heterogeneity. The fluids present in the reservoir were oil and water. Along one edge of the reservoir a series of injectors were located, along the opposite edge a series of producers. The water flood was first simulated with equal rates per well during the entire water flood. After this simulation, the adjoint equation was calculated backwards in time, to obtain the gradients of the Hamiltonian with respect to the controls (i.e. injection and production rates). Based on these gradients the flow rates were changed over time and the simulation was re-run. This procedure was repeated until the results converged to an optimal dynamic flooding pattern. In all cases the total injection and production rates were held constant and equal. Results were compared to an earlier static water flood optimization study. In all cases, dynamic optimization resulted in an improvement in recovery relative to the base case. In a number of cases results can probably be improved even further if the stability of the adjoint equation can be improved, and/or if a more effective objective function is used.