Reservoir history matching using a stochastic method

In reservoir history matching the least square objective function is usually used to minimize the mismatch between the predicted production data and the observations. However, as history matching is an ill-posed inverse problem with non-unique solutions, the reservoir model after calibrating may be far from the real geology model by only matching the production data. In order to solve this problem, a regularization method for reservoir history matching is implemented, in which not only the production data is matched, but prior geological information is also used to correct and update the current reservoir model so that the updated model will be consistent with the geologic model. In this paper, the simultaneous perturbation stochastic approximation method (SPSA) coupled with fast streamline simulation provides an effective method (SLSPSA) to optimize the objective function. As a stochastic approximation algorithm, SLSPSA can guarantee the convergence of the algorithm. Compared to the gradient-based algorithms, it avoids the massive calculation and storage for adjoint or sensitivity matrix. In the calculation process of algorithm, parallel computing is implemented, which reduces the simulation time and improves the computational efficiency. The method was verified by matching an example test.