Optimal well placement using dynamic mathematical programming

Abstract

As oil resources are being depleted and energy demand is rising, optimal well placement is becoming a more and more critical decision for reservoir management team with huge techno-economical impacts. This study focuses on modeling this problem and proposing a potential rigorous solution approach for that. We use mathematical programming approach, which previously has been largely ignored in this field, and model the problem using big-M formulation and dynamic model of multiphase flow. Moreover, to solve this model, we modify the "Outer Approximation with Equality Relaxation and Augmented Penalty" approach. It decomposes the well placement problem into a "fixed well location-production optimization" which is "integer free but nonlinear" and "linearized-well dependent optimization" which is "linear but integer dependent" models. We solve the production optimization part sequentially. The results show that the algorithm can efficiently find an improving direction to locate the new sites for drilling new wells. Since, well placement is a non-convex problem new sites are potentially local optimums. To our best knowledge, this is the first contribution that captures the dynamic feature of hydrocarbon production while locating the drilling sites for new wells using "mathematical programming approach".