Abstract

Combining Data Assimilation with Markov Chain Monte Carlo for Uncertainty Quantification

Albert Reynolds
University of Tulsa

Multiple history-matched models conditional to dynamic data are obtained by a precursor of Randomized Maximum Likelihood (RML) where the forward model is a numerical model, a reservoir simulator in the computational examples presented here. In the RML-like procedure, the modes of the posterior probability density function (pdf) are obtained by data assimilation which is done either with a trust-region quasi-Newton method (BFGS) or a new (unpublished) version of the ensemble smoother with multiple data assimilations (ES-MDA) designed to approximate modes of the posterior pdf. Using the history-matching results, a Gaussian mixture probability distribution is constructed and used as the proposal distribution to construct a Markov chain using the Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm. Computational results indicate that the resulting MCMC procedure converges much faster to the stationary distribution (posterior pdf) than do standard MCMC implementations in use. The computational results illustrate that the uncertainty in model parameters and the predicted reservoir performance can be characterized very accurately with a large but fairly reasonable number of runs of the forward model.