Modeling, Simulation, and Optimal Control of Oil Production under Gas

Gas coning is a tendency of the gas to impel the oil downward in an inverse cone contour toward the well perforations. Once the gas reaches the well, gas production will dominate the well flow and the oil production will hence significantly decrease. From an economical and operational standpoint this condition is undesirable since the gas price is much lower than the oil price, and the gas handling capacity often is a constraint. Therefore, there is an incentive to maximize oil production up until gas breakthrough. In this paper, the gas coning process in a gas oil reservoir completed with a single horizontal well is analytically modeled, simulated, and analyzed applying a nonlinear control approach. The model which describes the interaction between the well and the reservoir may be cast into a boundary control problem of the porous media equation with two boundary conditions; a Neumann boundary condition describing no flow at the outer boundary of the reservoir, and a nonlinear boundary condition describing the well production rate. A well rate controller for the boundary control problem is designed using the Lyapunov method. The controller holds some formal performance guarantees and requires information on the gas oil contact at the well heel only. Further, the controller has a tuning parameter which can be used to maximize a suitable performance measure. The controller is evaluated using a detailed ECLIPSE simulator of a gas coning reservoir. Simulation results show significant improvement of production profit of the proposed method compared to a conventional method which usually uses a constant rate up until gas breakthrough.