Abstract
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.
Highlights
To obtain the equilibrium state of the porous medium and its fluid content, which is in contact with a bulk reservoir at temperature T and chemical potential μ, we minimize the total energy with respect to the fluid density and strain ui of the solid
One must first determine the size of the representative elementary volume (REV) for the sample, i.e., the minimum image size such that its properties will not change if larger images and computational grids are used
After some preliminary simulations in which various grid resolutions were utilized in order to identify the most accurate grid with affordable computational time, a grid with 373,607 tetrahedral elements was determined to be accurate enough, as the porosity and computed adsorption isotherm of CO2 did not change significantly if grids with higher resolutions were used
Summary
Where Ef, Es, and Efs represent, respectively, the energy due to the fluid, the solid, and the interactions between the two. Es, the energy of the solid is represented by where Ki is the elastic stiffness, and σi and (∇ ⋅ u)i are the stress and strain in element i, respectively.
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