Abstract
In determining the optimal well controls by maximizing net-present-value (NPV) for the remaining life of a reservoir, one typically defines the length of the control steps a priori. Moreover, these control steps are often the same for all wells. We provide a scale splitting/merging method for adaptively selecting the lengths of control steps as the overall optimization proceeds. We start with reasonably small number of control steps and find the associated optimal controls by maximizing NPV. Then, using the control values of the current best estimate for the optimum solution and at most two gradient calculations, we decide which set of control steps will potentially yield the greatest improvement in NPV without unnecessarily increasing the number of control variables. Once new control steps have been defined by refining and/or coarsening the control steps at the previous stage, we again maximize NPV. This process of adaptively selecting control steps and optimizing is continued until no further improvement in NPV is achieved. Both adjoint-gradient-based and derivative- free optimization algorithms are considered. The adaptive approach is applied to two example problems and the results are compared with those obtained using a pre-determined number of control steps.
