Abstract
The hydraulic permeability is a key parameter for simulating the flow-related phenomenon so that its accurate estimation is crucial in both experimental and numerical simulation studies. 3D pore structure can be readily taken by X-ray computed tomography (CT) and it often serves as a flow domain for pore-scale simulation. However, one encounters the challenges in segmenting the authentic pore structure owing to the finite size of image resolution and segmentation methods. Therefore, the loss of structural information in pore space seems unavoidable to result in the unreliable estimation of permeability. In this study, we propose a novel framework to overcome these limitations by using a flexible ternary segmentation scheme. Given the pore size distribution curve and porosity, three phases of pore, solid, and gray regions are segmented by considering the partial volume effect which holds the composition information of unresolved objects. The resolved objects such as solid and pore phases are taken to equivalently solve Stokes equation while the fluid flow through unresolved objects is simultaneously solved by Stokes-Brinkmann equation. The proposed numerical scheme to obtain the permeability is applied to Indiana limestone and Navajo sandstone. The results show that the computed hydraulic permeability is similar to the experimentally obtained value without being affected by image resolution. This approach has advantages of achieving consistent permeability values, less influenced by segmentation methods.
Highlights
A computed tomography (CT) number of a voxel in X-ray CT images represents the linear attenuation coefficient (LAC) of materials constituting the voxel
By using pore size distribution (PSD) obtained from mercury intrusion porosimetry test, we presented a flexible ternary segmentation classifying X-ray CT images into apparent pore, gray pore, and apparent solid: apparent pore stands for the voxel composed of pure void, gray pore stands for the mixture voxel composed of unresolved pore and solid particles, and apparent solid means the voxel composed of almost pure solid
Using the proposed methods to define the threshold for the three phases and define the hydraulic diameter for each gray pore voxel, voxel porosity, and voxel permeability for 3D voxel map of X-ray CT images are determined (Fig. 3)
Summary
A CT number of a voxel in X-ray CT images represents the linear attenuation coefficient (LAC) of materials constituting the voxel. It is known that when a voxel is composed of multiple end members, the LAC of the voxel ( μmix ) can be described as the combination of the LAC of each end member ( μi ), which is weighted by the volume fraction of the end member. This is called the partial volume effect (Johns et al, 1993). The binary segmentation schemes can make the accurate estimation of transport properties difficult as they classify the mixture voxel either into pure solid (so that the flow path of the voxel is neglected), or pure pore (so that the flow path is overestimated). We implemented the proposed methods with Brinkman-force LBM (BF-LBM) and validated the proposed methods by confirming the accurate estimation of permeability of two rock specimens
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