Automatic History Matching With Variable-Metric Methods

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Abstract
Summary: Variable-metric minimization methods are introduced for use with optimal-control theory for automatic reservoir history matching. Variable-metric methods are more efficient and robust than the previously used minimization methods, such as steepest-descent and conjugate-gradient methods. in addition, variable-metric methods can be used effectively with parameter-inequality constraints. Two variable-metric methods — the Broyden/Fletcher/Goldfarb/Shanno (BFGS) method and a self-scaling variable-metric (SSVM) method — are tested with hypothetical two-phase reservoir history-matching problems. Estimated rock/fluid properties include permeability, porosity, and relative permeabilities. The SSVM method is more efficient than the BFGS method when the number of unknown parameters is large. Both methods perform better than the steepest-descent and Nazareth’s conjugate-gradient methods except when the performance index is nearly quadratic, where the conjugate-gradient methods may be more efficient than the BFGS method. A constrained BFGS algorithm is tested to be successful in problems where the unconstrained algorithms have failed