Abstract
Given the substantial costs and potential rewards associated with petroleum field development and reservoir management, it is essential that these operations be performed as close to optimally as possible. This paper addresses problems where the goal is to simultaneously determine the optimal number and type of new wells, the sequence in which they should be drilled, as well as their corresponding locations and time-varying controls. The optimization is posed as a mixed-integer nonlinear programming (MINLP) problem involving categorical, integer and real-valued variables. The formulation handles bound, linear, and nonlinear constraints, with the latter treated using filter-based techniques. Noninvasive derivative-free approaches are applied for the optimizations. Methods considered include Mesh Adaptive Direct Search (MADS, a local pattern search method), Particle Swarm Optimization (PSO, a global search technique), a PSO-MADS hybrid and Branch and Bound (B&B, a rigorous search procedure that requires relaxation of the categorical variables). Two example cases involving channelized reservoir models are presented. The PSO-MADS hybrid is shown to outperform the standalone MADS and PSO procedures. In the example case in which B&B is applied, the PSO-MADS approach is shown to give comparable solutions but at much lower computational cost. This is significant since B&B provides near-exhaustive search capabilities. It is concluded that the methodology presented here appears to be applicable for realistic petroleum field development and reservoir management.
