Markov chain Monte Carlo methods for conditioning a permeability field to pressure data |
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| Authors: | Dean S Oliver Luciane B Cunha and Albert C Reynolds |
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| Institution: | (1) Chevron Petrol. Tech. Co., P.O. Box 446, 90633-0446 La Habra, California;(2) Department of Petroleum Engineering, The University of Tulsa, 74104 Tulsa, Oklahoma;(3) Present address: Petróleo Brasileiro Research Center, Ilha de Fundao, Q7, 21949-900 Rio de Janiero, Brasil;(4) Department of Petroleum Engineering, The University of Tulsa, 74104 Tulsa, Oklahoma |
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| Abstract: | Generating one realization of a random permeability field that is consistent with observed pressure data and a known variogram
model is not 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 not 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. Under certain conditions that can
be verified easily, the Markov chain Monte Carlo method is known to produce states 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 at every step. These perturbations make use of sensitivity coefficients calculated from the reservoir simulator. |
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| Keywords: | conditional simulation Markov chain Monte Carlo sampling pressure data sensitivity well test |
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