Multiple Markov Chains Monte Carlo Approach for Flow Forecasting in Porous Media*

Abstract

Predictions in subsurface formations consists of two steps: characterization and prediction using the characterization. In the characterization, we reconstruct the subsurface properties, such as distributions of permeability and porosity, with a set of limited data. A Bayesian approach using Markov Chain Monte Carlo (MCMC) methods is well suited for reconstructing permeability and porosity fields. This statistical approach aims at generating a Markov chain from which a stationary, posterior distribution of the characteristics of the subsurface may be constructed. A crucial step in this framework is the calculation of the likelihood information which can be computationally very demanding. This limitation hinders the application of the Bayesian framework for the flow predictions in porous media in a practical period of time. The parallel computation of multiple MCMCs can substantially reduce computation time and can make the framework more suitable to subsurface flows. In this paper, we consider multi–MCMC and compare the multi–MCMC with the MCMCs for the predictions of subsurface flows.