Markov chain Monte Carlo methods for conditioning a permeability field to pressure data

Generating one realization of a random permeability field that is consistent with observed pressure data and a known variogram model is nor a difficult problem. If however, one wants to investigate the uncertainty of reservior behavior, one must generate a large number of realizations and ensure that the distribution of realizations properly reflects the uncertainty in reservoir properties. The most widely used method for conditioning permeability fields to production data has been the method of simulated annealing, in which practitioners attempt to minimize the difference between the ''true'' and simulated production data, and ''true'' and simulated variograms. Unfortunately, the meaning of the resulting realization is nor clear and the method can be extremely slow. In this paper, we present an alternative approach to generating realizations that are conditional to pressure data, focusing on the distribution of realizations and on the efficiency of the method. tinder certain conditions that can be verified easily, the Markov chain Monte Carlo method is known to produce stares whose frequencies of appearance correspond to a given probability distribution, so we use this method to generate the realizations. To make the method more efficient, we perturb the states in such a way that the variogram is satisfied automatically and the pressure data are approximately matched ar every step. These perturbations make use of sensitivity coefficients calculated from the reservoir simulator.