In the process of reservoir development, we always wish to drill wells at optimal locations so that more hydrocarbons can be extracted at a lower cost. Because well locations in a reservoir simulator are commonly treated as discrete variables, standard implementations of gradient based optimization is difficult so the optimization for this problem is normally done with a non-gradient based method such as the genetic algorithm. Here, we present a novel idea to convert the problem of optimizing on discrete variables into an optimization problem on continuous variables for the optimal well placement. The idea is to initialize the problem by putting a well in every grid-block and then optimize NPV. As the cost of "drilling a well" detracts from the NPV, when NPV is optimized some wells will be shutin (eliminated). For two very simple cases where the problem is to determine the optimal location of a water injection well, we show this problem formulation yields good results with a single injection well remaining after the optimization process.

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