利用格子Boltzmann方法计算页岩渗透率

Permeability calculation in shale using lattice Boltzmann method

关键词:  格子Boltzmann方法  页岩  Knudsen数  数字岩心

Key words:  lattice Boltzmann method  shale  Knudsen number  digital core

摘要:

针对页岩中孔隙主要分布在纳米尺度的特点,建立Knudsen数修正固体边界并考虑镜面反弹的格子Boltzmann模型。利用二维平板模型,考察Knudsen数对渗透率的影响,得出在一定误差条件下,须考虑Knudsen数修正的最大孔隙宽度。由页岩的SEM扫描图像重构得到三维数字岩心,利用新模型进行模拟流动,并计算得到绝对渗透率。结果表明:利用Knudsen数修正后,通道中间部分流体速度增大,固体边界处速度变小;压力不变,随着孔隙直径变小,Knudsen数增大,渗透率变小。

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.