Reconstruction of 3D Porous Media Using Multiple-Point Statistics Based on a 2D Training Image

Abstract

Abstract Macroscopic transport properties of porous media essentially rely on the geometry and topology of their pore space. The premise of predicting these transport properties is to construct an accurate 3D pore space. To date the methods of modeling porous media are divided into two main groups, direct measurements by some equipment and stochastic statistical methods. Direct measurements of pore structure can be acquired with current equipment such as X-ray computed tomography and laser scanning confocal microscopy, but the unavailability of the equipment and the high cost of the measurement make their widespread application impossible. Many stochastic statistical methods, such as truncated Gaussian random field and simulated annealing methods, reconstruct 3D porous media based on some 2D thin sections by means of lower-order statistical functions. However these functions cannot reproduce the long-range connectivity of pore structure. Therefore, this paper will present a stochastic technique of reconstructing 3D pore space using multiple-point statistics with the purpose of solving the proposed problems. The single normal equation simulation algorithm (SNESIM), one of the most common methods for discrete variable simulation in multiple-point statistics, is the main tool to reproduce the long-range feature of pore space. To test the method, Berea sandstone was used as a sample. In the simulation process, a 2D thin section was taken as the training image for providing patterns of pore structure and some pixels were extracted from it as the conditioning data. The models were reconstructed using the SNESIM algorithm that serves as the simulation engine. In order to test the accuracy of these reconstructed models, pore geometry and topology and transport properties of the reconstructed models were compared with those of the real model obtained by X-ray computed tomography scanning. The comparison result shows that the reconstructed models are good agreement with the real model obtained by X-ray computed tomography scanning in the two-point correlation function, the pore space features and single- and two-phase flow permeabilities, which verifies that the long-range connectivity of pore space can be reproduced by this method. Comparing with other stochastic methods, a more accurate stochastic technique of reconstructing 3D porous media is put forward when only some 2D thin sections are available.