History matching, by nature, is an ill-posed inverse problemthat can be computationaly intensive and practically infeasiblefor multi-million cells reservoir models. Therefore, the searchof an optimal parameterization is of crucial interest to get afast history matching procedure. One has to find the number ofdegrees of freedom of a given problem while avoiding thepitfall of overparameterization. Many techniques (such assingular value decomposition) allow to tackle this problem butthe main limitation in reservoir engineering is coming fromcomputational-speed issues.Using gradient-based optimization techniques, we proposehere a complemetary approach which uses the power ofadjoint state method to select the degrees of freedom whichare significant for the objective function. Data integration maybe performed by using the gradual deformation method(GDM) for the geological model parameterization :coefficients of a linear combination of geostatisticalrealizations are modified as the optimization process goes on.The parameterization is then reduced to the coefficients of thelinear combination whatever the size of the geostatisticalrealizations. Working in a stochastic framework, there isinitially an infinity of realizations to choose from. Followingthe new approach, we are able to compute a priori “refinementindicators” that indicate us which degrees of freedom (i.e.realizations) might improve the iterative reservoir model in asignificant way. Using only those useful degrees of freedom,we are able to get a better and faster optimization problemresolution. The use of “refinement indicators” will allow us toreduce to one or even zero the number of randomly pickedinitial geostatistical realizations.We applied this methodology to integrate interference testdata into 3D geostatistical models (both lognormal and faciesbasedpermeability distributions) containing about two millions cells. This validation highlights the capability of themethodology to speed up the inverse problem resolution byselecting optimal geostatistical realizations from a given set.
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