Evaluation of surface diffusion in microporous/mesoporous media using a numerical model applied to rate-of-adsorption data: Implications for improved gas permeability estimation in shales/tight rocks using drill cuttings

Abstract

Adsorbed-phase surface diffusion has been recognized as an important controlling factor on gas apparent permeability in micropores and smaller mesopores. However, for the estimation of surface diffusion coefficients of shales, the commonly used empirical methods cannot account for the complexity of rock fabric in the matrix system of tight rocks. Further, the small sample sizes and amounts (<5 g) of drill cuttings, which are usually the only reservoir samples available from horizontal wells, significantly limit the feasibility and reliability of current experimental methods for the direct quantification of surface diffusion coefficients. The primary objectives of this study are therefore to: 1) establish an integrated experimental and modeling approach to evaluate surface diffusion and permeability using drill cuttings, and 2) investigate the significance of surface diffusion in different adsorbate/adsorbent systems. In this work, a bidisperse numerical model is developed to extract surface diffusion coefficients and permeability/diffusivity values from porous materials by matching the pressure transient data recorded during gas adsorption. A high-resolution gas adsorption apparatus is employed to measure gas sorption kinetics under low-temperature (N2, −196 °C; CO2, 0 °C), low-pressure (<0.1 MPa) conditions, using small amounts (<2 g) of powdered/crushed samples. The proposed model successfully matched rate-of-adsorption (ROA) pressure transient data on two synthetic micro/mesoporous materials (Activated Carbon and SBA-15) and five organic-rich shale samples. It was observed that surface diffusion is a dominant flow mechanism and enhances permeability/diffusivity in micropores and smaller mesopores. The new model improves upon the results of a previously-developed ROA model.