LATTICE BOLTZMANN SIMULATION OF NON-DARCY FLOW IN STOCHASTICALLY GENERATED THREE-DIMENSIONAL GRANULAR POROUS MEDIA

The fluid velocity is higher in the near wellbore region or in the hydraulic fractured wells, which would lead to non-Darcy flow and significantly decrease the deliverability of the well. In this work, the inertia resistance factor and transition point between Darcy flow and non-Darcy flow are investigated by using lattice Boltzmann method based on stochastically constructed three-dimensional porous media, with porosity ranging from 0.19 to 0.39. The results show that gas flow in porous media shows a transition from Darcy flow to non-Darcy flow with an increase of Reynolds number. The transition occurs when the Reynolds number is between 0.2 and 0.3. Meanwhile, the inertia resistance factor of porous media decreases with increasing porosity and permeability. Compared with the porous media generated by regular grains, the stochastically constructed three-dimensional porous media better represents the reservoir rocks, and the derived inertia resistance factors are closer to rock samples. Finally, a relation of inertial resistance factor with porosity and permeability was established for the porous media with irregular grain sizes and shapes. This work provides a useful method to investigate non-Darcy flows in reservoir rocks.