SPE 143520 Modeling, Simulation, and Optimal Control of Oil Production under Gas Coning Conditions

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. Introduction Optimization of the trade-off between oil and gas production is an important issue in reservoir management. The use of secondary recovery techniques such as gas lift and waterflooding, and EOR techniques such as surfactant injection has been proven successful to increase the oil production significantly. Those techniques are now supported by the growing application of smart well technologies. A smart well is usually equipped with several valves that can be regulated over the time of production. Questions regarding how to operate these valves can be partially answered using optimal control theory, in particular when it is combined with the adjoint method; see [1], [2], and [3]. Adjoint based optimization can also be used to determine optimal well placement [4] and for history matching [5]. Optimal control theory combined with data assimilation form a closed-loop reservoir management. A comprehensive summary of the closed loop reservoir management concept may be found in [6]. Although providing solutions in a relatively short time in an efficient way, the adjoint method is difficult to implement. This is because one needs access to reservoir simulator code and implements the algorithm there. An alternative way which can be done is by creating a mathematical model which is simpler but can be used to explain the same physical process. This model will then be referred to as a proxy model and serves as a representative of a complex model which is usually contained in a reservoir simulator. A proxy model may be derived from the basic principle of physics such as mass conservation and Darcy law. Since the proxy model is simpler than the high-fidelity model, a proxy model is certainly easier than working with the actual one. Therefore, instead of using the full model, in this paper a proxy model will be used for design and analysis purposes. Further, the results will be tested using a complex reservoir dynamics which is usually contained in a tested and well known reservoir