Yazdi Anoosheh, Hamzehpour Hossein, Sahimi Muhammad
Department of Physics, K. N. Toosi University of Technology, Tehran 15875-4416, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Oct;84(4 Pt 2):046317. doi: 10.1103/PhysRevE.84.046317. Epub 2011 Oct 20.
Using extensive Monte Carlo simulations, we study the effective permeability, porosity, and percolation properties of two-dimensional fracture networks in which the fractures are represented by rectangles of finite widths. The parameters of the study are the width of the fractures and their number density. For low and intermediate densities, the average porosity of the network follows a power-law relation with the density. The exponent of the power law itself depends on the fractures' width through a power law. For an intermediate range of the densities, the effective permeability scales with the fractures' width as a power law, with an exponent that depends on the density. For high densities the effective permeability also depends on the porosity through a power law, with an exponent that depends on the fractures' width. In agreement with the results, experimental data also indicate the existence of a power-law relationship between the effective permeability and porosity in consolidated sandstones and sedimentary rocks with a nonuniversal exponent. The percolation threshold or critical number density of the fractures depends on their width and is maximum if they are represented by squares, rather than rectangles.
通过广泛的蒙特卡罗模拟，我们研究了二维裂缝网络的有效渗透率、孔隙率和渗流特性，其中裂缝由具有有限宽度的矩形表示。研究参数为裂缝宽度及其数密度。对于低密度和中等密度，网络的平均孔隙率与密度遵循幂律关系。幂律的指数本身通过幂律取决于裂缝宽度。对于中等密度范围，有效渗透率与裂缝宽度呈幂律关系，其指数取决于密度。对于高密度，有效渗透率也通过幂律取决于孔隙率，其指数取决于裂缝宽度。与结果一致，实验数据也表明在固结砂岩和沉积岩中有效渗透率与孔隙率之间存在幂律关系，且指数不具有普遍性。裂缝的渗流阈值或临界数密度取决于其宽度，如果用正方形而非矩形表示裂缝，该阈值最大。
