In Search of an Optimal Parameterization : An Innovative Approach to Reservoir Data Integration

Abstract

Abstract History matching, by nature, is an ill-posed inverse problem that can be computationaly intensive and practically infeasible for multi-million cells reservoir models. Therefore, the search of an optimal parameterization is of crucial interest to get a fast history matching procedure. One has to find the number of degrees of freedom of a given problem while avoiding the pitfall of overparameterization. Many techniques (such as singular value decomposition) allow to tackle this problem but the main limitation in reservoir engineering is coming from computational-speed issues. Using gradient-based optimization techniques, we propose here a complemetary approach which uses the power of adjoint state method to select the degrees of freedom which are significant for the objective function. Data integration may be performed by using the gradual deformation method (GDM) for the geological model parameterization : coefficients of a linear combination of geostatistical realizations are modified as the optimization process goes on. The parameterization is then reduced to the coefficients of the linear combination whatever the size of the geostatistical realizations. Working in a stochastic framework, there is initially an infinity of realizations to choose from. Following the new approach, we are able to compute a priori "refinement indicators" that indicate us which degrees of freedom (i.e. realizations) might improve the iterative reservoir model in a significant way. Using only those useful degrees of freedom, we are able to get a better and faster optimization problem resolution. The use of "refinement indicators" will allow us to reduce to one or even zero the number of randomly picked initial geostatistical realizations. We applied this methodology to integrate interference test data into 3D geostatistical models (both lognormal and facies-based permeability distributions) containing about two millions cells. This validation highlights the capability of the methodology to speed up the inverse problem resolution by selecting optimal geostatistical realizations from a given set.