Permeability calculation in shale using lattice Boltzmann method

Key words:  lattice Boltzmann method  shale  Knudsen number  digital core

Abstract:

Considering the nano-scale pores in shale, a lattice Boltzmann model amended by Knudsen number was established with a specular bounceback condition on the solid boundary. The effect of Knudsen number on permeability was studied in a 2D flat model. The maximum of pore width can be calculated when the Knudsen number is considered at a given relative error range. A 3D digital core of shale was reconstructed using SEM images, which was used to simulate the flow behavior in the core based on the new model in order to calculate the permeability of the core. The results show that the flow velocity in the middle of the flat model becomes larger after the model was amended by Knudsen number, while the velocity near the solid boundaries becomes smaller. Permeability decreases with the increase of Knudsen number when the pore diameter becomes smaller at the same pressure.