Joint Bayesian inversion for reservoir characterization and uncertainty quantification

Abstract

History matching of 4D seismic and well production data has been developed recently for reservoir characterization. This is a data driven optimization process to derive reservoir model parameters and constitutes a joint inverse problem. Considering the inherent non‐uniqueness in the inverse problem and the unique feature of Bayesian inference in data integration and uncertainty analysis, this joint inverse problem is formulated in a Bayesian framework and solved stochastically by reconstructing the posterior probability density (PPD) surface using a new multi‐scale Markov Chain Monte Carlo (MCMC) algorithm. In this new MCMC method, a technique of multi‐scaling is used to take advantage of the benefits from both the fine scale model and the coarse scale model. Although the coarse scale does not provide reliable information about the model, it helps speed up the convergence of the fine scale model to a good estimation, and, by exchanging information between the fine and coarse scales, works like a regularization operator to smooth the fine scale model and make it more realistic. The resulting PPD samples can also be used to quantify corresponding uncertainties in order to facilitate risk assessment associated with reservoir decision making and management. We use a numerical example to demonstrate how we derive reservoir's static and dynamic properties as well as quantify uncertainties in a Bayesian framework using the multi‐scale MCMC algorithm.