A Better Formulation of Objective Functions for History Matching Using Hausdorff Distances
Abstract
Abstract History matching aims at finding one or several reservoir models that closely reproduce the past behavior of the reservoir. Objective functions are often used to measure the quality of these models. Indeed when using assisted history matching techniques, a good formulation of the objective function is crucial since it increases the likelihood to get an acceptable history match. Moreover, for manual history matching, and in particular for large fields, objective functions can also be used in order to compare between runs and to help understanding the field. In this paper, we investigate an alternative new formulation of the objective function. The proposed formulation does not take into account only the difference between the production data (point by point) but also discrepancies in the shape. The proposed formulation is based on an appropriate Hausdorff distance. The proposed approach is applied on different data from different real history matching studies. Results are compared with the standard mean squared error formulation, and shown to satisfy more reservoir engineering principles when comparing between runs.