Chen Li, Fang Wenzhen, Kang Qinjun, De'Haven Hyman Jeffrey, Viswanathan Hari S, Tao Wen-Quan
Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China.
Computational Earth Science, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Mar;91(3):033004. doi: 10.1103/PhysRevE.91.033004. Epub 2015 Mar 3.
Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. [Phys. Rev. E 65, 046308 (2002)]. The second-order Beskok and Karniadakis-Civan's correlation [A. Beskok and G. Karniadakis, Microscale Thermophys. Eng. 3, 43 (1999) and F. Civan, Transp. Porous Med. 82, 375 (2010)] is adopted to calculate the apparent permeability based on intrinsic permeability and the Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate the model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicate that Klinkenberg's effect plays a significant role on fluid flow in low-permeability porous media, and it is more pronounced as the Knudsen number increases. Fluid flow in a shale matrix with and without fractures is also studied, and it is found that the fractures greatly enhance the fluid flow and Klinkenberg's effect leads to higher global permeability of the shale matrix.
当气体分子的平均自由程与多孔介质的特征孔径处于同一数量级时，就会发生气体滑脱现象。这种现象导致了克林肯贝格效应，即气体的测量渗透率（表观渗透率）高于液体的渗透率（固有渗透率）。基于Guo等人[《物理评论E》65, 046308 (2002)]的模型，提出了一种用于模拟包含克林肯贝格效应的多孔介质中流动的广义格子玻尔兹曼模型。采用二阶Beskok和Karniadakis-Civan关联式[A. Beskok和G. Karniadakis, 《微观尺度热物理学工程》3, 43 (1999)以及F. Civan, 《多孔介质传输》82, 375 (2010)]，根据固有渗透率和克努森数来计算表观渗透率。对填充有多孔介质的两个平行板之间的流体流动进行了模拟，以验证该模型。在具有不同孔隙率和渗透率组分的非均质多孔介质中进行的模拟表明，克林肯贝格效应在低渗透率多孔介质中的流体流动中起着重要作用，并且随着克努森数的增加而更加显著。还研究了有裂缝和无裂缝的页岩基质中的流体流动，发现裂缝极大地增强了流体流动，并且克林肯贝格效应导致页岩基质具有更高的整体渗透率。
