A particularly efficient flow solver can be obtained by combining a recent mixed multiscale finite-element method for computing pressure and velocity fields with a streamline method for computing fluid transport. This multiscale- streamline method has shown to be a promising approach for fast flow simulations on high-resolution geologic models with multimillion grid cells. The multiscale method solves the pressure equation on a coarse grid while preserving important fine-scale details. Fine-scale heterogeneity is accounted for through a set of generalized, heterogeneous basis functions that are computed numerically by solving local flow problems. When included in the coarse-grid equations, the basis functions ensure that the global equations are consistent with the local properties of the underlying differential operators. The multiscale method offers a substantial gain in computation speed, without significant loss of accuracy, when the multiscale basis functions are updated infrequently throughout a dynamics simulation. In this paper we propose to combine the multiscale- streamline method with a recent ‘generalized travel-time inversion’ method to derive a fast and robust method for history matching high-resolution geologic models. A key point in the new method is the use of sensitivities that are calculated analytically along streamlines with little computational overhead. The sensitivities are used in the travel-time inversion formulation to give a robust quasilinear method that typically converges in a few iterations and generally avoids much of the subjective judgments and time-consuming trial- and-errors in manual history matching. Moreover, the sensitivities are used to control a procedure for adaptive updating of the basis functions only in areas with relatively large sensitivity to the production response. The sensitivity- based adaptive approach allows us to selectively update only a fraction of the total number of basis functions, which gives a substantial savings in computation time for the forward flow simulations. We demonstrate the power and utility of our approach using a simple 2D model and a highly detailed 3D geomodel. The 3D simulation model consists of more than one million cells with 69 producing wells. Using our proposed approach, history matching over a period of 7 years is accomplished in less than forty minutes on an ordinary workstation PC.
展开▼
