基于格子Boltzmann方法的页岩气微观流动模拟

页岩中的主要孔隙类型是纳米孔隙,气体在纳米孔隙中的流动不同于在常规孔隙中的流动,其存在微尺度效应,因此基于连续介质假设的达西方程不再适用。由于页岩气藏一般处于高压环境,气体比较稠密,理想气体状态方程也不再适用。而格子Boltzmann方法是一种介观流动模拟方法,其不基于连续介质假设,适用于从滑移区到过渡区的气体流动模拟,并且能够考虑气体稠密性和非理想气体状态方程的影响。基于考虑努森层影响和微尺度效应的非理想气体格子Boltzmann方法,结合镜面反射格式与反弹格式组合的滑移边界条件,采用二维平板模型,研究了孔隙尺寸、压力和温度等因素对微尺度效应的影响,并对影响机理进行了分析。结果表明:努森数是微尺度气体流动的控制参数;在滑移区和自由分子流区,各因素对微尺度效应的影响较小,而在过渡区,各因素对微尺度效应的影响较大;通过表观渗透率与固有渗透率比值随努森数的变化关系,并与常用的页岩气藏表观渗透率计算模型进行对比,验证了目前常用页岩气藏表观渗透率计算模型的准确性。

Microscale shale gas flow simulation based on Lattice Boltzmann method

Nano-pores are dominantly developed in shale. Due to microscale effect, the gas flow in nano-pores is different from that in conventional pores. Therefore, Darcy's law based on the continuous medium assumption is no longer applicable. Shale gas reservoirs are generally under a high pressure environment with denser gas, so that the ideal gas state equation is also inapplicable. However, the lattice Boltzmann method is a mesoscopic flow simulation method, which is not based on the continuum assumption, but suitable for gas flow simulation from slip zones to transition zones as considering the influences of gas denseness and non-ideal gas state equation. Based on the lattice Boltzmann method for non-ideal gas in considerations of the influences of Knudsen layer and microscale effect, as well as slip boundary conditions in mirror reflection-bounce back pattern, a two-dimensional plate model was used to study the influences of pore size, pressure and temperature on microscale effect and analyze the influence mechanisms. The results show that Knudsen number is the control parameter of microscale gas flow. The influences of various parameters on microscale effect are smaller in slip zones and free molecular flow zones, but it is opposite to the transition zones. The variation relationship between Knudsen number and the ratios of apparent permeability and intrinsic permeability, the accuracy of the commonly-used calculation model of apparent permeability in shale gas reservoirs is verified through comparison with the two-dimensional plate model.