A Multiscale and Metamodel Simulation-Based Method for History Matching

This paper presents a novel framework for history matching using the concept of simulation-based optimization with guided search sampling, multiscale resolution and incremental metamodel (surrogate model) generation, aimed to mitigate the computational burden of large-scale history matching.<br><br>The initial stage of the framework consists of a multiscale treatment of the permeability field through successive wavelet transformations. The coarsest grid which represents a highly constrained parameter space, is sampled with the aid of a derivative-free stochastic optimization algorithm that detects the most promising search regions. Due to the size of the coarse grid, thousands of simulation runs are possible at a low computational cost. Next, a sequence of intermediate metamodels is built iteratively by gradually increasing the number of sampling points in the decision space and using these temporary models to guide an incremental sampling. This incremental sampling is dictated by the use of an optimization method that finds a local optimum solution in a few iteration steps. The iterative refinement process is terminated when the metamodel solution is capable of reproducing (within a predefined tolerance) the reservoir simulator response. These metamodels are constructed using a support vector machine approach that captures the causal relations embedded in reservoir simulation by discriminating the true signal from the noise without over-fitting the simulation results. Finally, the coarse grid optimal solution is used as an initial point for the next finer grid level with the use of the inverse wavelet transform. The procedure is repeated with a decreasing number of function evaluations as the grid resolution level is increased. The objective function includes well production data and sensor measurements. Numerical experiments on realistic data reveal that the proposed framework improves the history matching process, not only in terms of computing savings and the accuracy of the estimated permeability field.