The Effect of Tortuosity on Fluid Flow Through a Single Fracture

Abstract

Calculations to investigate the effect of path tortuosity and connectivity on fluid flow rate through a single rough fracture were carried out. The flow paths are represented by electrical resistors placed on a two‐dimensional grid, and the resistances vary as the inverse of the fracture aperture cubed. The electric current through the circuit bears a one‐to‐one correspondence to the fluid flow rate. Both fracture apertures derived from measurements and from hypothetical analytic functions were used in a parameter study to investigate the dependence of tortuosity on fracture roughness characteristics. It was found that the more small apertures there are in the aperture distribution, the larger is the effect of tortuosity. When the fraction of contact area between the fracture surfaces rises above 30%, the aperture distributions are invariably large at small apertures, and the effect of fracture roughness and flow path tortuosity depresses flow rate from the value predicted by the parallel plate representation of a fracture by three or more orders of magnitude. The impact of these results on the calculations and measurements in fracture hydrology is discussed.

Channel model of flow through fractured media

“…The two fracture surfaces are matched, so the difference of the measurements for the top and bottom surfaces gives the apertures. When all the apertures measurements over the fracture were pooled together, it was found (Tsang, 1984) that the aperture density distribution (Fig. 4b) can be approximated by a Gamma function ( Fig.…”

“…The relationship of fracture wall roughness to the fluid flowrate though a single fracture subject to normal stress has been analyzed in a series of theoretical papers (Tsang and Witherspoon, 1981;Tsang and Witherspoon, 1983;Tsang, 1984). Their investigations show that only at low applied stress, when the fracture is essentially open, does the parallel-plate idealization adequately describe fluid flow.…”

“…Rather, the fracture needs to be mathematically described by the aperture density distribution, n(b ), where n(b )db gives the probability of finding apertures with values between b and (b+d b). Furthermore, because of the con tact areas and constrictions of the fracture subject to stress, flow through a single fracture becomes a two-dimensional flow through a few channels which are tortuous, have variable aperture along their length, and which -2-may or may not intersect each other (Tsang, 1984). The field experiment of Abelin et al (1983) on a single fracture showed that the equivalent fracture aperture derived from the constant head permeability measurements was a few orders of magnitude smaller than that derived from the tracer migration experiments.…”

Hydrological characterization of variable-aperture fractures

“…In the past decade researchers have employed more realistic description of a rock joint with a range of apertures and the impact of the aperture variation within a single rock joint on its flow properties has been recognized (e.g. Tsang and Witherspoon, 1981, Tsang 1984, Gentier 1986, Brown 1987. Detailed measw-ements of fracture apertures have been obtained by joint swface profiling (Bandis et al 1981, Brown and Scholz 1985, Gentier 1986), low melting-point metal injecticm (Pyrak-Nolte et aI.…”

Flow Simulation of Artificially Induced Microfractures Using Digital Rock and Lattice Boltzmann Methods

“…Researchers made use of many techniques to obtain the structure of fractures in rocks, such as stylus profilemeters [19,20], surface laser scanning [21,22], nuclear magnetic-resonance imaging [14,23], and computed tomography (CT) scanning [3,24,25]. CT scanning and nuclear magnetic-resonance imaging are two methods by which we can get the structure of fractures without destroying the core.…”