An efficient Bayesian approach to history matching and uncertainty assessment

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Title: An efficient Bayesian approach to history matching and uncertainty assessment
Author: Yuan, Chengwu
Abstract: Conditioning reservoir models to production data and assessment of uncertainty can be done by Bayesian theorem . This inverse problem can be computationally intensive , generally requiring orders of magnitude more computation time compared to the forward flow simulation . This makes it not practical to assess the uncertainty by multiple realizations of history matching for field applications . We propose a robust adaptation of the Bayesian formulation , which overcomes the current limitations and is suitable for large -scale applications . It is based on a generalized travel time inversion and utilizes a streamline -based analytic approach to compute the sensitivity of the travel time with respect to reservoir parameters . Streamlines are computed from the velocity field that is available from finite -difference simulators . We use an iterative minimization algorithm based on efficient SVD (singular value decomposition ) and a numerical ? ? ? ? ? ?stencil ? ? ? ? ? ? for calculation of the square root of the inverse of the prior covariance matrix . This approach is computationally efficient . And the linear scaling property of CPU time with increasing model size makes it suitable for large -scale applications . Then it is feasible to assess uncertainty by sampling from the posterior probability distribution using Randomized Maximum Likelihood method , an approximate Markov Chain Monte Carlo algorithms . We apply this approach in a field case from the Goldsmith San Andres Unit (GSAU ) in West Texas . In the application , we show the effect of prior modeling on posterior uncertainty by comparing the results from prior modeling by Cloud Transform and by generalized travel time inversion and utilizes a streamline -based analytic approach to compute the sensitivity of the travel time with respect to reservoir parameters . Streamlines are computed from the velocity field that is available from finite -difference simulators . We use an iterative minimization algorithm based on efficient SVD (singular value decomposition ) and a numerical Collocated Sequential Gaussian Simulation . Exhausting prior information will reduce the prior uncertainty and posterior uncertainty after dynamic data integration and thus improve the accuracy of prediction of future performance .
URI: http : / /hdl .handle .net /1969 .1 /4962
Date: 2007-04-25

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An efficient Bayesian approach to history matching and uncertainty assessment. Available electronically from http : / /hdl .handle .net /1969 .1 /4962 .

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