A mixed-integer nonlinear optimization approach for well placement and geometry

Optimizing well configuration within oil fields usually consists in maximizing profits from oil production in a long-term horizon. Such profits are typically predicted using CPU-time demanding fluid flow simulations. The variables of the optimization problem considered in this work are the number of wells, their locations and types, as well as the number and trajectories of the branches drilled from the given producers. We propose a methodology that reduces the complexity and the underlying simulation cost of this optimization problem. First, we introduce various physical constraints related to the distance between wells and oil bearing areas in order to select a suitable region for drilling. A direct search method is then coupled with surrogate models approximating the objective function to obtain a good estimation of the optimal number, location and type of wells while limiting the simulations' number. Given the solution determined in the previous step, we analyze the responses provided by the fluid flow simulator (e.g., oil saturation distribution) and apply a mixed-combinatorial method to define the geometry of the rectilinear well branches. This makes it possible to improve the current solution. The potential of the second step of the proposed methodology is evaluated with a synthetic two-dimensional reservoir model.