The effect of pore structure on non-Darcy flow in porous media using the lattice Boltzmann method

Non-Darcy flows associated with high Reynolds numbers often occur in the near-wellbore regions of gas reservoirs or hydraulic fractures and thus should not be ignored. However, investigating non-Darcy flow in these porous rocks through laboratory experiments is always expensive and time-consuming. As such, this article sought an alternative method, and a lattice Boltzmann study of non-Darcy flow in various porous models was performed. The applicability of two non-Darcy correlations in porous media and the effect of pore structure on non-Darcy flow were examined. In addition, the reasons for the deviation from the linear Darcy flow and different flow patterns related to inertial effects of the fluid were also studied. The results showed that the characterization of non-Darcy flow in porous media with the cubic law can only be valid in a narrow range of Reynolds number beyond the Darcy regime, outside of which the strong inertia-dominated flow yields to the quadratic correction. On the whole, representing the non-Darcy flows using the quadratic correction is acceptable, especially for porous media with a higher complexity. The features of non-Darcy flow greatly depend on the pore structure of a porous medium, and more heterogeneous pore models always have a faster cessation for Darcy flow and a higher beta factor. Furthermore, for simple porous media a small amount of parameters may be adequate for the prediction of the beta factor; while the correlations involving more parameters would be needed to determine the beta factor for more intricate porous models, although such correlations may not be widely used in various industries. Besides, the non-Darcy flow that occurs in porous media is collectively controlled by different mechanisms. At elevated velocities, the inertial core effect in a large channel will lead the flow to be more homogeneous and less tortuous, while in porous models with complicated pore space, the steady eddy and reversal flow resulting from drag force will make the flow paths more tortuous. As such, it is the hope of this study to provide some new insights into the non-Darcy flow in porous media.