A sorption-kinetics coupled dual-porosity poromechanical model for organic-rich shales

The flow of gas in shale formations is influenced by several coupled processes including matrix and fractures deformations, and gas sorption. An increase in effective stress by pore-pressure decline, for example, reduces the formation’s porosity and permeability whereas gas desorption results in shrinkage of the rock matrix, causing an increase in permeability. The sorption-driven characteristics of such coupled systems, however, are dependent on gas sorption kinetics. In this study, we thus utilized the concepts of non-equilibrium thermodynamics and continuum mechanics to develop a fully coupled sorptive-poroelastic constitutive equations to describe the impact of sorption kinetics induced deformation on the dual porosity behaviour of gas-shales. These developed constitutive equations were then solved using the finite element method. After verifying the model performance against existing analytical solutions and experimental data from the literature, numerical sensitivity analyses were performed to specifically investigate the gas sorption kinetics on multi-physical processes. Additional numerical sensitivity analyses were performed to assess the importance of the newly derived coupling thermodynamics coefficients. The results showed that the effect of the coupling coefficient between the chemical potential of the adsorbed gas and the porosity of the bedding planes is important in gas production, especially in the long term. Numerical results also showed that the effect of sorption kinetics on gas production is a strong function of gas diffusivity in the matrix and desorption rate. It is also realized that the effect of sorption kinetics on gas production cannot be ignored when the matrix has high gas diffusivity.