This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 143520, ’Modeling, Simulation, and Optimal Control of Oil Production Under Gas-Coning Conditions,’ by Agus Hasan, SPE, and Bjarne Foss, SPE, NTNU; and Svein Ivar Sagatun, Bjorn Peter Tjostheim, Atle Svandal, and Cato Hatland, Statoil ASA, prepared for the 2011 SPE Europec/EAGE Annual Conference and Exhibition, Vienna, Austria, 23-26 May. The paper has not been peer reviewed.

Gas coning is the tendency of gas to impel oil downward in an inverse-cone contour toward the well perforations. After gas reaches the well, gas production will dominate the flow stream and oil production will decrease significantly. In this paper, the gas-coning process in a gas/oil reservoir (completed with a single horizontal well) is modeled, simulated, and analyzed by applying a nonlinear-control approach. The model that describes the well/reservoir interaction can be a boundary-control problem of the porous media 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’s production rate.   


Optimizing the trade-off between oil and gas production is important in reservoir management. The use of secondary-recovery techniques (e.g., gas lift and waterflood) and enhanced-oil-recovery techniques (e.g., surfactant injection) has proved successful for increasing oil production significantly. These techniques are supported by the use of smart-well technologies. A smart well is one that is equipped with several valves that can be regulated during production. Operating these valves can be accomplished by use of optimal-control theory, particularly when combined with the adjoint method. Adjoint-based optimization can be used to determine optimal well placement and for history matching. Optimal-control theory combined with data assimilation forms a closed-loop reservoir management.

Although providing solutions in a relatively short time and in an efficient way, the adjoint method is difficult to implement because one needs access to the reservoir-simulator code to implement the algorithm. An alternative is creating a mathematical model that is simpler but can be used to explain the same physical process. This model is referred to as a proxy model and serves as a representative of a complex model that usually is contained in a reservoir simulator. A proxy model may be derived from a basic principle of physics, such as mass conservation or Darcy’s law. The proxy model is simpler and easier to work with than the high-fidelity model.

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