Reconstruction of pore-space images using multiple-point statistics

Quantitative prediction of petrophysical properties for reservoir rocks frequently employs representative microscopic models of the pore space as input. Recently digital imaging techniques such as microtomography have been used to provide void space images at the resolution of a few microns. However, the sample size is normally only a few mm when the highest resolutions are used, and even this may be insufficient to capture some structures, particularly in carbonates. A larger image may be necessary to predict representative flow properties. Focused ion beam images can provide better resolution but only on even smaller samples. Two-dimensional (2D) thin sections can image micro-porosity, but do not directly capture the three- dimensional (3D) pore space. We use 2D thin-sections and 3D microtomography images as training data sets to generate 3D pore space representations at high resolution using multiple point statistics. The training images provide multiple-point statistics, which describe the statistical relation between multiple spatial locations and allow the connectivity of the void space to be reproduced accurately. The method is tested on sandstones and carbonates for which 3D images are available: these images capture the connectivity of the larger pore spaces, while 2D thin sections accurately characterize small-scale structure. The statistically generated images have permeabilities computed using the lattice-Boltzmann method (LBM) that are similar to laboratory-measured values.