Lattice Boltzmann Modeling of Gas Adsorption and Desorption in Shale Matrix

Study of hydrocarbon adsorption in shale has gained significant attention in petroleum industry since it is directly related to reserve estimation and production forecast. However, due to nanometer scale pore sizes and complex surface properties, the mechanism and behavior of hydrocarbon adsorption in shale matrix remain elusive. Existing theoretical models generally fail to capture either the microscale kinetics or the complex pore structure which are both essential for accurately reproducing the correct phase behavior under nanometer scale confinement.

In this study, we present a novel 3D lattice Boltzmann model that accounts for the interaction between fluid molecules by incorporating Peng-Robinson equation of state (PR-EOS), as well as the rock-fluid interaction in the form of a surface force. We validate our model against Ono-Kondo theory for subcritical and supercritical gas adsorption. We then create a 3D statistical reconstruction of the shale matrix informed by a series of 2D scanning electron microscopy (SEM) images and perform CH₄ and CO₂ adsorption and desorption simulation. The evolvement of fluid density profile at different sorption stages is visualized in 3D and the total adsorption uptake is calculated and plotted as a function of pressure. It is shown that adsorbed gas contributes a significant portion to the total gas storage in shale reservoirs, and the adsorption amount is highly affected by surface area and pore size distribution, especially the existence of micropores. Moreover, the effect of solid-fluid interaction strength on gas adsorption is studied in detail. We finally simulate the desorption process during which the hydrocarbon stored in the shale matrix is produced into the open fractures as a result of the induced pressure difference. The production rate as a function of time is calculated and compared for a variety of initial pressure differences.

The model developed in this study provides a tool to study phase behavior in any complex geometry under nanoscale confinement and can be integrated with existing nanoscale flow models to study multiphase flow behavior in shale.