Optimization of oil production under gas coning conditions

• The presence of gas coning in the production wells may reduce the oil production.
• There is an incentive to produce such wells in their subcritical phase.
• The model which describes the interaction between the well and the reservoir may be cast into a boundary control problem.
• A well rate controller for the boundary control problem is designed using the backstepping method.
• Simulation results show significant improvement of production profit of the proposed method compared to a conventional method.

Typically, a well is produced with a constant oil rate with constant gas–oil ratio (GOR) during the subcritical phase, i.e. before gas breakthrough. The presence of gas coning in production wells may reduce the oil production. The decline in the oil rate will be followed by an increase in the well head pressure. From an economical and operational point of view, this condition may be undesirable for several reasons; the gas price is much lower than the oil price, the afflicted well may be abandoned early, and the gas handling capacity often is a constraint. Therefore, there is an incentive to produce such wells in their subcritical phase for an extended period of time. 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 horizontal well 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 homogeneous Neumann's 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 backstepping method. The controller holds some formal performance guarantees and requires information on the gas–oil contact (GOC) at the well heel only. Furthermore, the controller has a tuning parameter which can be used to maximize a suitable performance measure, e.g. the net present value (NPV). 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 until gas breakthrough.