Field-scale rate optimization problems often involve highly complex reservoir models, production-and-facilities related constraints, and a large number of unknowns. These factors make optimal reservoir management through rate- and flood-front control difficult without efficient optimization tools. Some aspects of the optimization problem have been studied before mainly using an optimal control theory. However, the applications to date have been rather limited to small problems because of the computation time and the complexities associated with the formulation and solution of adjoint equations. Field-scale rate optimization for maximizing waterflood sweep efficiency under realistic field conditions has remained largely unexplored.
This paper proposes a practical and efficient approach for computing optimal injection and production rates, thereby managing the waterflood front to maximize sweep efficiency and delaying the arrival time to minimize water cycling. Our work relies on equalizing the arrival times of the waterflood front at all producers within selected subregions of a waterflood project. The arrival-time optimization has favorable quasilinear properties, and the optimization proceeds smoothly, even if our initial conditions are far from the solution. Furthermore, the sensitivity of the arrival time with respect to injection and production rates can be calculated analytically using a single-flow simulation. This makes our approach computationally efficient and suitable for large-scale field applications. The arrival time optimization ensures appropriate rate allocation and flood-front management by delaying the water breakthrough at the producing wells.
Several examples are presented to support the robustness and efficiency of the proposed optimization scheme. These include several 2D-synthetic examples for validation purposes and a 3D field application. In addition, we demonstrate the potential of the approach to optimize the flow profile along injection/production segments of horizontal-smart wells.