Ternary segmentation and estimation of permeability for porous rocks based on 3D X-ray computed tomographic images by hidden Markov random field and Brinkman-force lattice Boltzmann model

Three-dimensional X-ray computed tomographic (CT) images of specimens often serve as a flow simulation domain for numerical analysis, particularly for permeability estimation, but there exists uncertainty in classifying image pixels into pore or solid structures due to the complex pore geometry and limited resolution of X-ray CT image. This limitation has been tackled by ternary segmentation of CT images into resolved pore, unresolved pore, and solid phases, but it is still challenging to segment each phase and estimate local permeability of unresolved pore. This study proposed the estimation of the hydraulic diameter of each unresolved pore voxel in CT images to evaluate the local permeability by a general porosity-permeability model. Hidden Markov random field (HMRF) was implemented to achieve reliable ternary segmentation of porous rock images with different resolutions by considering the statistical and spatial distribution of CT numbers. Brinkman-force lattice Boltzmann method (BF-LBM) was then used to compute permeability. The results showed that the estimated permeability of Berea sandstone and limestone was analogous to experimentally measured values. The proposed procedure, which does not require experimental characterization of the pore size distribution, can be used to nondestructively estimate the permeability of porous rocks using X-ray CT images while being less sensitive to image resolution.