The use of variable-metric (or quasi-Newton) methods with optimal
control theory is an attractive method for automatic history matching.
Optimal control theory provides for an efficient calculation of the
gradient of the performance index, and variable-metric methods are
the most efficient and accurate of the minimization methods that
require only the evaluation of the performance index and its gradient.
In addition, variable-metric methods can be used effectively with
parameter inequality constraints. Four variable-metric methods--
the BFGS method, Fletcher's switch algorithm, a self-scaling variable-metric
method, and an optimally conditioned self-scaling variable-metric
methodare tested with hypothetical single-phase reservoir history
matching problems. All four methods yield significantly more accurate
estimates with less computer effort than a previous history matching
algorithm which uses the steepest decent method. A constrained BFGS
algorithm is further tested with hypothetical waterfloods of one-
and two-dimensional reservoir models.
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