The influence of confining stress and pore pressure on effective stress coefficient for permeability: A novel Discretized Clay Shell Model for clayey sandstone

Abstract

The effective stress coefficient $\alpha$ determines the effective stress and dominates the permeability of rocks. This study proposes a novel theoretical model called the Discretized Clay Shell Model (DCSM) that modifies the Clay Shell Model (CSM) by incorporating the stress-dependent elastic modulus of clay into a discretized multi-layer clay domain to depict the relationship between $\alpha$, pore pressure, and confining stress. The proposed model was successfully used to provide insights into the stress-dependent $\alpha$ of clayey sandstones. We found that $\alpha$ always decreased with increasing pore pressure and could decrease or increase with increasing confining stress. The modelling trends, which are also observed in the previous laboratory tests, can be well explained using two effects due to the heterogeneity of radial stress within clay domain, that is, the bulk and differential clay hardening effects. The bulk clay hardening effect generates a decreasing trend in $\alpha$ with increasing pore pressure, while the differential clay hardening effect competes with the bulk clay hardening effect and yields a reverse trend, that is, $\alpha$ first decreases with increasing confining stress and then decreases when the confining stress reaches a certain critical value. This study provides synthetic cases to quantify the influence of stress-dependent $\alpha$ evaluated by the DCSM on the evaluation of the permeability-depth relation. Based on the laboratory testing data, the calibrated parameters of the stress-dependent permeability model assuming $\alpha =1$ are significantly overestimated, and the prediction model yields overestimated permeability up to three to four orders of magnitude. Meanwhile, the synthetic in-situ case shows that the predicted permeability could be underestimated by up to one third, and the errors due to laboratory analysis that neglect the stress dependency of $\alpha$ will propagate to and amplify the errors of prediction for the in-situ permeability-depth relation.