Fluid Flow Through a Crack Network in Rocks

Abstract

A network of cracks pervading a rock is modeled by a random distribution of two-dimensional intersecting, complex, narrow cracks. The percolation properties of the resulting network are studied as functions of the crack-area density and size of the medium. Gas flow commences at a finite value of the crack density which in Arkansas Novaculite rocks amounts according to our model to 670 cracks per cm2. The mean probability of finding at least one crack intersecting another is 0.57 at the threshold density. Above that, the rock gas-flow permeability increases superlinearly with crack density due to the enhancement of short percolative paths.

Permeability, porosity, and percolation properties of two-dimensional disordered fracture networks

“…Over the past three decades, many research groups have developed 2D models of networks of fractures of finite lengths, represented by sticks or lines. Notable among them are the works of Long and coworkers [7], Englman et al [8], Schwartz and Smith [9], Charlaix et al [10], Robinson [11], Guéguen and Dienes [12], Robinson and Gale [13], and Mukhopadhyay and Sahimi [14], in which the fractures were represented by 1D finite line segments to which an effective permeability was attributed. Such models can even be a reasonable representation of a 3D network of interconnected fractures, if most of the hydraulic conductivity is in the intersections between the fractures, or if fluid flow is channelized in the fractures.…”

Models for the effect of rising water in abandoned mines on seismic activity

“…Evidently the water level in the fault will eventually reach H w and our aim is to determine the dependence of this In the lower range (W o 6 μm) the flux is independent of aperture, see Cook [28]. (b, c) Other results from Engelder and Scholz [36] and Gale [32]; results varied with the test run, see text.…”

“…All such procedures require on-site experimental tuning. There have also been attempts to numerically model flows in a network of cracks, see for example Englman et al [36], but the geometry of the connections is normally unknown and in the end one must rely on empirical fits. In the present context a detailed hydraulic model is not required so such on-site network issues will not be addressed; simple generic models will be examined.…”

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

“…In some early works, due to the lack of in-situ measurement of fracture length, fractures were typically assumed to have constant lengths (Englman et al 1983;Robinson 1983Robinson , 1984Balberg et al 1984;Balberg et al 1991;Gueguen and Dienes Fig. 1 Schematic view of the geometric parameters involved in a fracture network, including: (i) fracture length, (ii) aperture, (iii) surface roughness, (iv) dead-end, (v) number of intersections, (vi) hydraulic gradient, (vii) boundary stress, (viii) anisotropy, and (ix) scale 1989).…”