Classic and Hybrid MCMC Methods to Approximate Pore Size Distributions of Carbonate Reservoirs Using Pore-network Models
J.E Juri, M.I.J. van Dijke, K.S. Sorbie and S.K. Masalmeh
Event name: ECMOR XII - 12th European Conference on the Mathematics of Oil Recovery
Session: Capillary and Surface Effects
Publication date: 06 September 2010
Info: Extended abstract, PDF ( 625.08Kb )
Price: € 20
Carbonate reservoirs contain a large fraction of the remaining oil reserves, but their highly heterogeneous structures, at the pore scale, make them difficult to characterize and this is one of the main reasons for their low recovery factors. Pore space imaging and reconstruction techniques are often used to characterize the pore space topology and geometry. However, the wide range of pore sizes encountered in carbonates, including submicron microporosity, usually renders these techniques unsuitable. A classic technique to approximate the pore size distribution (Ritter and Drake) is based on inversion of the mercury intrusion capillary pressure (MICP) curve. However, this technique is inaccurate due to the lack of accessibility of the large pores before the percolation threshold is reached. In this paper, we use a simple lattice network, characterized by an average co-ordination number, a pore volume-vs-radius power law and a pore (radius) size distribution (PSD) with an arbitrarily large range of radii, to match the MICP curve. Efficient optimization methods have been implemented to estimate these principal parameters, as outlined below. The overall aim of this work is to predict rock flow functions for different floods or saturations paths that are difficult and expensive to obtain from laboratory experiments, based on the PSD estimations. In the present approach the PSD has a given number of non-constant radius classes (bins), for which the probabilities need to be determined. As an initial guess, we take the Ritter and Drake PSD, based on which the non-fixed bin widths are determined, using principal theorems derived in information theory and data compression. Then, the pore-network parameters including the PSD class probabilities are optimized to match the experimental MICP, using two methods that are based on the link between the Boltzmann - Maxwell equation describing the molecular state probabilities in statistical physics and the Bayes method for posterior distribution. The first method is the classic Metropolis Markov Chain Monte Carlo method and the second, hybrid, method adds Hamiltonian Dynamics to avoid the random nature of the classic Metropolis algorithm, thus enhancing the convergence of the classical approach. The methods have successfully been applied to two synthetic cases and three carbonate samples from a Middle East reservoir presenting three different carbonate facies. The hybrid method improves the Markov Chain Monte Carlo efficiency in terms of the accepted system parameters states by a factor of 4 to 5.