Abstract. One of the most difficult tasks in reservoir simulations is reliable characterization of fractured subsurfaces. A typical situation in petroleum engineering employs dynamic data integrations such as the oil production history to be matched with simulated responses associated with a set of porosity and/or permeability fields. Among the challenges found in practice are proper mathematical modelings of the flow in the presence of fractured systems, persisting heterogeneity in the porosity and permeability, and the uncertainties inherent in them. In this paper we propose a Bayesian framework Monte Carlo Markov Chain simulation (MCMC) to sample a set of subsurface's characteristics from the posterior distribution that are conditioned to the production data. This process requires obtaining the simulated responses over many realizations. The flow for this simulated response is governed by a dual porosity, dual permeability model. As this can be a prohibitively expensive endeavor, we address the possibility of using the Multiscale Finite Volume Element (MsFVEM) combined with a sparse stochastic collocation technique to provide a venue for an efficient computation. A set numerical examples illustrating the procedure will be presented.