The Influence of Grain Shape and Size on the Relationship Between Porosity and Permeability in Sandstone

An accurate and reliable description of the relationship between porosity and permeability in geological materials is valuable in understanding subsurface fluid movement. This is of great importance for studies of reservoir characterisation, useful for energy exploitation, carbon capture, use and storage (CCUS) and groundwater contamination and remediation. Whilst the relationship between pore characteristics and porosity and permeability are well examined, there is scope for further investigation into the influence of grain characteristics on porosity and permeability due to the inherent relationship between grains and related pores. In this work we use digital image analysis (DIA) of reconstructed 3D X-ray micro computed tomographic (μCT) images to measure porosity, permeability and segment individual grains enabling the measurement of grain shape (sphericity) and size (Feret diameter). We compare two marker-based watershed workflows to grain boundary segmentation before applying the most reliable one to our images. We found there to be a positive relationship between grain sphericity and porosity according to ϕ=1.22ϕs-0.42 whereas no such relationship exists with grain size. We applied our grain shape and size measurements to calculate a Kozeny-Carman (K-C) porosity-permeability fit which was found to be unsatisfactory, possibly due to significant deviation from the K-C assumption that grains are spherical. Therefore, we show that a simpler fit of the form K= 10^5.54 ϕ^3.7, excluding any influence of grain characteristics, is most suitable for the studied materials and that grain shape and size is not influential on the porosity-permeability relationship in a K-C paradigm.