Image-based modeling of gas adsorption and deformation in porous media

Understanding adsorption of CO₂ in porous formations is crucial to its sequestration in geological formations. We describe a model for adsorption of CO₂ and the deformation that it induces in a sandstone formation over wide ranges of temperature and pressure. The model couples the thermodynamics of sorption with elastic deformation of the solid. Finite-element computations are then used in order to compute CO₂ adsorption isotherms along with the induced strain in the formation. We also compute the Darcy permeability of the porous medium using the lattice-Boltzmann method. All the computations are carried out with a three-dimensional image of a core sample from Mt. Simon sandstone, the target porous formation for a pilot CO₂ sequestration project that is currently being carried out by Illinois State Geological Survey. Thus, no assumptions are made regarding the shape and sizes of the pore throats and pore bodies. The computed CO₂ sorption isotherm at 195 K is in excellent agreement with our experimental data. The computed permeability is also in good agreement with the measurement. As a further test we also compute the sorption isotherm of N₂ in the same formation at 77.3 K, and show that it is also in good agreement with our experimental data. The model is capable of predicting adsorption of CO₂ (or any other gas for that matter) in porous formations at high pressures and temperatures. Thus, it is used to study the effect of hydrostatic pressure on adsorption and deformation of the porous formation under various conditions. We find that the effect of the confining pressure is more prominent at higher temperatures. Also computed is the depth-dependence of the capacity of the formation for CO₂ adsorption, along with the induced volumetric strain.