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Determining the optimal location of wells with the aid of an automated search algorithm can significantly increase a 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 pseudo-wells. These pseudo-wells produce or inject at a 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 pseudo-wells are computed using an adjoint model. These are subsequently used to approximate ‘improving directions’, i.e. directions in which to move the wells to achieve an increased NPV, based on which improving well positions 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 and one backward (adjoint) simulation. The process is repeated until no further improvements are obtained. The method is illustrated by two waterflooding examples. In the first the location of a single injector is optimized to maximize NPV. Starting from four different initial injector locations the algorithm converges to four similar local optima. The second example involves optimization of the locations of 9 producers and 4 injectors. Starting from two different initial well configurations we obtain nearly the same (local) optimum. |
