Summary
History matching is an inverse problem in which an engineer calibrates key geological/fluid-flow parameters by fitting a simulator's output to the real reservoir production history. It has no unique solution because of insufficient constraints. History-match solutions are obtained by searching for minima of an objective function below a preselected threshold value. Experimental design and response surface methodologies provide an efficient approach to build proxies of objective functions (OF) for history matching. The search for minima can then be easily performed on the proxies of OF as long as its accuracy is acceptable.
In this paper, we first introduce a novel experimental design methodology for semi-automatically selecting the sampling points, which are used to improve the accuracy of constructed proxies of the nonlinear OF. This method is based on derivatives of constructed proxies.
We propose an iterative procedure for history matching, applying this new design methodology. To obtain the global optima, the proxies of an OF are initially constructed on the global parameter space. They are iteratively improved until adequate accuracy is achieved. We locate subspaces in the vicinity of the optima regions using a clustering technique to improve the accuracy of the reconstructed OF in these subspaces.
We test this novel methodology and history-matching procedure with two waterflooded reservoir models. One model is the Imperial College fault model (Tavassoli et al. 2004). It contains a large bank of simulation runs. The other is a modified version of the SPE9 (Killough 1995) benchmark problem. We demonstrate the efficiency of this newly developed history-matching technique.
