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Computer-aided history matching of oil production data requires the solution of a challenging minimization problem. Usually, gradient based techniques have been applied to this aim: starting from an initial guess of the solution, these methods converge to the closest local minimum, along specified descend directions. Typically, however, the parameter space is populated by many, local minima, each giving a different response in terms of forecasted production profiles. Theoretically, it is thus important to identify the lowest possible minimum among all candidates.