Semiautomatic Multiple Resolution Design for History Matching

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 objective function 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 SPE9 (Killough 1995) benchmark problem. We demonstrate the efficiency of this newly developed history-matching technique.

Introduction

History matching (Eide et al. 1994; Landa and Güyagüler 2003) is an inverse problem in which an engineer calibrates key geological/fluid flow parameters of reservoirs by fitting a reservoir simulator's output to the real reservoir production history. It has no unique solution because of insufficient constraints.

The traditional history matching is performed in a semi-empirical approach, which is based on the engineer's understanding of the field production behavior. Usually, the model parameters are adjusted using a one-factor-at-a-time approach. History matching can be very time consuming, because many simulation runs may be required for obtaining good fitting results.

Attempts have been made to automate the history-matching process by using optimal control theory (Chen et al. 1974) and gradient techniques (Gomez et al. 2001). Also, design of experiment (DOE) and response surface methodologies (Eide et al. 1994; Box and Wilson 1987; Montgomery 2001; Box and Hunter 1957; Box and Wilson 1951; Damsleth et al. 1992; Egeland et al. 1992; Friedmann et al. 2003) (RSM) were introduced in the late 1990s to guide automatic history matching. The goal of these automatic methods is to achieve reasonably faster history-matching techniques than the traditional method.

History matching is an optimization problem. The objective is to find the best of all possible sets of geological/fluid flow parameters to fit the production data of reservoirs. To assess the quality of the match, we define an OF (Atallah 1999). For history-matching problems, an objective function is usually defined as a distance (Landa and Güyagüler 2003) between a simulator's output and reservoir production data. History-matching solutions are obtained by searching for minima of the objective function. Experimental design and response surface methodologies provide an efficient approach to build up hypersurfaces (Kecman 2001) of objective functions (i.e., proxies of objective functions with a limited number of simulation runs for history matching). The search for minima can then be easily performed on these proxies as long as their accuracy is acceptable. The efficiency of this technique depends on constructing adequately accurate objective functions.