Original Paper

Computational Geosciences

, Volume 15, Issue 4, pp 691-707

Application of the two-stage Markov chain Monte Carlo method for characterization of fractured reservoirs using a surrogate flow model

  • Victor GintingAffiliated withDepartment of Mathematics, University of Wyoming
  • , Felipe PereiraAffiliated withDepartment of Mathematics and School of Energy Resources, University of Wyoming
  • , Michael PreshoAffiliated withDepartment of Mathematics, Colorado State University Email author 
  • , Shaochang WoAffiliated withEnhanced Oil Recovery Institute, University of Wyoming

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Abstract

In this paper, we develop a procedure for subsurface characterization of a fractured porous medium. The characterization involves sampling from a representation of a fracture’s permeability that has been suitably adjusted to the dynamic tracer cut measurement data. We propose to use a type of dual-porosity, dual-permeability model for tracer flow. This model is built into the Markov chain Monte Carlo (MCMC) method in which the permeability is sampled. The Bayesian statistical framework is used to set the acceptance criteria of these samples and is enforced through sampling from the posterior distribution of the permeability fields conditioned to dynamic tracer cut data. In order to get a sample from the distribution, we must solve a series of problems which requires a fine-scale solution of the dual model. As direct MCMC is a costly method with the possibility of a low acceptance rate, we introduce a two-stage MCMC alternative which requires a suitable coarse-scale solution method of the dual model. With this filtering process, we are able to decrease our computational time as well as increase the proposal acceptance rate. A number of numerical examples are presented to illustrate the performance of the method.

Keywords

Dual porosity Dual permeability Markov chain Monte Carlo method