Adjoint-Based Well-Placement Optimization Under Production Constraints

Determining the optimal location of wells with the aid of an automated search method can significantly increase it project's net present Value (NPV) as modeled in a reservoir simulator. This paper has two main contributions: first, to determine the effect of production constraints on optimal well locations and, second, to determine optimal well locations using a gradient-based optimization method. Our approach is based on the concept of surrounding the wells whose locations have to be optimized by so-called pseudowells. These pseudowells produce or inject at it very low rate and, thus, have a negligible influence on the overall flow throughout the reservoir. The gradients of NPV over the lifespan of the reservoir with respect to flow rates in the pseudowells tire Computed using an adjoint method. These gradients are used subsequently to approximate improving directions (i.e., directions to move the wells to achieve an increase in NPV), on the basis of which improving well locations can be determined. The main advantage over previous approaches such as finite-difference or stochastic-perturbation methods is that the method computes improving directions for all wells in only one forward (reservoir) and one backward (adjoint) simulation. The process is repeated until no further improvements are obtained. The method is applied to three waterflooding examples.