A Geostatistical Approach to Streamline-Based History Matching

Summary History matching large reservoir models under a realistic geological continuity constraint remains an outstanding problem. We propose a new combined geostatistical and streamline-based method potentially capable of history matching large reservoir models, while accounting consistently for geological continuity as provided by a permeability histogram and variogram and by production data. While most existing history-matching techniques somehow rely on the calculation of single-gridblock sensitivity coefficients, the proposed method avoids such calculation entirely by perturbing jointly effective permeabilities along a set of streamlines. Such perturbation results in large changes of the permeability field that reduce significantly error in each iteration of the history-matching procedure. The problem of mapping streamline effective permeability perturbations to single gridblocks is performed under a Gauss-Markov random function constraint. This novel stochastic mapping procedure accounts for the target histogram and variogram while honoring the streamline effective permeability perturbations. Forward flow simulation is achieved by a streamline simulator. The methodology is presented on synthetic cases; it appears to be computationally efficient and robust.