A Hybrid Markov Chain Monte Carlo Method for Generating Permeability Fields Conditioned to Multiwell Pressure Data and Prior Information

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Abstract
Summary: It is necessary to construct and sample the a posteriori probability density functions (pdf's) for the rock property fields to properly evaluate the uncertainty in reservoir performance predictions. In this work, the a posteriori pdf is constructed based on prior means and variograms (covariance function) for log-permeability and multiwell pressure data. Within the context of sampling the probability density function, we argue that the notion of equally probable realizations is the wrong paradigm for reservoir characterization. If the simulation of Gaussian random fields with a known variogram is the objective, it is shown that the variogram should not be incorporated directly into the objective function if simulated annealing (SA) is applied either to sample the a posteriori pdf or to estimate a global minimum of the associated objective function. It is shown that the hybrid Markov chain Monte Carlo (MCMC) method provides a way to explore more fully the set of plausible log-permeability fields and does not suffer from the high rejection rates of more standard MCMC methods.