Response Surface Methodology Approach for History Matching and Uncertainty Assessment of Reservoir Simulation Models

Abstract

Abstract We present theory and application of a new approach for assisted history matching and uncertainty assessment. In a Bayesian framework the a priori geological information is conditioned to the production history to give the posterior probability distribution function (pdf). The full posterior pdf is explored to assess the uncertainty through ensembles of reservoir models sampled by a Markov chain Monte Carlo algorithm. To achieve this we construct proxy functions for the output of the flow simulator for all measurements that enter a global objective function. The proxy functions are constructed using polynomials and multi dimensional kriging. An iterative loop, in which ensembles of reservoir models are sampled from the posterior pdf, is run to improve the quality of the proxy functions. The power of the application is demonstrated on two reservoir models. First we apply the method on a synthetic case. A modified reservoir simulation model from a small StatoilHydro operated oil field is investigated with a synthetic production history and 20 tuning parameters. Finally we apply the method to the StatoilHydro operated Heidrun field. A model which covers the upper formations of the field with 26 production wells, 11 injector wells, and 56 tuning parameters is conditioned to 11 years of production history. We show that it is possible to construct proxy functions accurate enough to describe the full posterior pdf and thereby assess the uncertainty associated with these reservoir models.