A model of dynamic adsorption-diffusion for modeling gas transport and storage in shale

Understanding gas transport and storage processes is essential for analysis of reservoir accumulation mechanisms and evaluation of a shale formation. Because organic matter such as kerogen is widely distributed in shale, it plays an important role in gas diffusion and adsorption. Although many mathematical models considering gas diffusion and adsorption have been proposed and evaluated, very few models consider the effect of organic matter on the dynamic adsorption process, and research studies systematically combining a mathematical model history-matched to experimental data is also rare. In this study, a dynamic, approaching equilibrium (hereinafter referred to as delayed) adsorption-diffusion (DAD) method is presented to analyze gas transport and storage processes in crushed particles of three different sizes. The delayed effect for adsorption results from the dynamic mechanisms of gas dissolution and adsorption in the semi-liquid layer of organic matter. The mathematical model for this phenomenon is based on dynamic adsorption experiments with a constant pressure condition. The general and approximate solutions for the DAD model are obtained to estimate the physical parameters through a multilevel single-linkage method. From the fitting results of the DAD method, it is found that the absolute permeability begins to decrease when particles are crushed into smaller sizes and observed that particle size plays more important role than permeability in the diffusion process for crushed shale samples. Isotherm measurements for total gas and free gas reveal that the difference in gas content between total gas and adsorbed gas become greater as pressure increases. Sensitivity analyses for the model disclose that the apparent diffusion coefficient and adsorption/desorption rate coefficient determine gas transport and storage processes together. Analysis and comparison of a diffusion model, an instantaneous adsorption-diffusion (IAD) model, and the DAD model reveal that the former two models are special forms of the DAD model, and the sequence of equilibrium times required for the gas transport and storage processes is: DAD > IAD > diffusion model. (C) 2016 Elsevier Ltd. All rights reserved.