This study presents a modified simultaneous perturbation stochastic approximation (SPSA) algorithm for automatic history matching. The new SPSA algorithm simultaneously perturbs the reservoir model by using unconditional realizations to generate a stochastic search direction. This search direction is always downhill and the expectation of the stochastic search direction is the Newton direction with CM as the approximate inverse Hessian matrix. As the unconditional realizations are used for perturbation, the changes made to the reservoir model during history matching and the final estimated reservoir models are more geological realistic than obtained with the original SPSA algorithm, which uses samples from a symmetric Bernoulli distribution as model perturbations. It is shown the new SPSA algorithm represent an approximation of the gradual deformation method but it has desirable properties that are lacking in all gradual deformation methods. The algorithm is successfully applied to the well known PUNQ-S3 test case to generate a maximum a posteriori (MAP) estimate and for uncertainty quantification of reservoir performance predictions using the RML method.
Recent publications:
- Li, G. and Reynolds, A.C.: Uncertainty Quantification of Reservoir Performance Predictions Using a Modification of SPSA Algorithm, Computational Geosciences, 2010.
- Gao, G.; Li, G. and Reynolds, A.C.: A Stochastic Optimization Algorithm for Automatic History Matching, SPE Journal, 2007.