MARKOV-CHAIN MONTE-CARLO METHODS FOR CONDITIONING A PERMEABILITY FIELD TO PRESSURE DATA

Generating one realization of a random permeability field that is cons istent with observed pressure data and a known variogram model is nor a difficult problem. If however, one wants to investigate the uncertai nty of reservior behavior, one must generate a large number of realiza tions and ensure that the distribution of realizations properly reflec ts the uncertainty in reservoir properties. The most widely used metho d for conditioning permeability fields to production data has been the method of simulated annealing, in which practitioners attempt to mini mize 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 extremel y slow. In this paper, we present an alternative approach to generatin g realizations that are conditional to pressure data, focusing on the distribution of realizations and on the efficiency of the method. tind er certain conditions that can be verified easily, the Markov chain Mo nte Carlo method is known to produce stares whose frequencies of appea rance correspond to a given probability distribution, so we use this m ethod to generate the realizations. To make the method more efficient, we perturb the states in such a way that the variogram is satisfied a utomatically and the pressure data are approximately matched ar every step. These perturbations make use of sensitivity coefficients calcula ted from the reservoir simulator.