We propose a multiscale approach to data integration that accounts for the varying resolving power of different data types from the very outset. Starting with a coarse description, we match the production response at the wells by recursively refining the reservoir grid. A multiphase streamline simulator is used for modeling fluid flow in the reservoir. The well data are then integrated using conventional geostatistics, for example sequential simulation methods. There are several advantages to our proposed approach. First, we explicitly account for the resolution of the production response by refining the grid only up to a level sufficient to match the data, avoiding over-parameterization and incorporation of artificial regularization constraints. Second, production data are integrated at a coarse scale with fewer parameters, which makes the method significantly faster compared to direct fine-scale inversion of the production data. Third, decomposition of the inverse problem by scale greatly facilitates the convergence of iterative descent techniques to the global solution, particularly in the presence of multiple local minima. Finally, the streamline approach allows for parameter sensitivities to be computed analytically using a single simulation run, thus further enhancing the computational speed.
The proposed approach has been applied to synthetic as well as field examples. The synthetic examples illustrate the validity of the approach and also address several key issues, such as convergence of the algorithm, computational efficiency, and advantages of the multiscale approach compared to conventional methods. The field example is from the Goldsmith San Andres Unit (GSAU) in west Texas and includes multiple patterns consisting of 11 injectors and 31 producers. Using well-log data and water-cut history from producing wells, we characterize the permeability distribution, thus demonstrating the feasibility of the proposed approach for large-scale field applications.