Absolute permeability assessment of porous structures under different boundary conditions using lattice Boltzmann method

Abstract

Digital rock physics is now recognized as a satisfactory solution for studying fluid dynamics phenomena within porous structures. On the other hand, the lattice Boltzmann method shown its capabilities in this field well. However, choosing the suitable boundary condition with the most negligible effect on flow behavior is a challenge. Therefore, this study aims to introduce the most common boundary conditions, such as periodic, constant pressure, and periodic-pressure, so it focuses on investigating their performance in predicting the permeability of synthetic and natural structures. Hence, three benchmark tests are initially considered to validate the model. First, the Poiseuille flow test has been addressed, so the observations reveal that the results are in close agreement with the analytical solution. In the following, synthetic models are introduced as square and hexagonal arrangements. The details have shown that using different boundary conditions in permeability prediction is associated with a good agreement between the results and the analytical data. Finally, the digital image obtained by x-ray tomography of a real porous sample has been studied. Also, the sensitivity analysis for permeability estimation has been done on pressure gradient and relaxation time. Detailed investigations show that the increase in pressure gradient under the pressure-periodic boundary condition is associated with an increase in permeability, but it has practically no effect on the result of the periodic boundary condition. In contrast, increasing this parameter under constant pressure did not affect the permeability curve, though it grows slightly with further increase, which is quite reliable considering the compressibility error and non-Darcy flow. On the other hand, increasing the relaxation time has resulted in increased permeability. However, it is recommended to use periodic and constant pressure boundary conditions because of the lower rate of change.