Prediction of Non-Darcy Coefficients for Inertial Flows Through the Castlegate Sandstone Using Image-Based Modeling

Near wellbore flow in high rate gas wells shows the deviation from Darcy’s law that is typical for high Reynolds number flows, and prediction requires an accurate estimate of the non-Darcy coefficient (β factor). This numerical investigation addresses the issues of predicting non-Darcy coefficients for a realistic porous media. A CT-image of real porous medium (Castlegate Sandstone) was obtained at a resolution of 7.57 μm. The segmented image provides a voxel map of pore-grain space that is used as the computational domain for the lattice Boltzmann method (LBM) based flow simulations. Results are obtained for pressure-driven flow in the above-mentioned porous media in all directions at increasing Reynolds number to capture the transition from the Darcy regime as well as quantitatively predict the macroscopic parameters such as absolute permeability and β factor (Forchheimer coefficient). Comparison of numerical results against experimental data and other existing correlations is also presented. It is inferred that for a well-resolved realistic porous media images, LBM can be a useful computational tool for predicting macroscopic porous media properties such as permeability and β factor.