The Characteristics and Estimation of Flow Through a Single Rough-Walled Fracture

Abstract

Abstract:The Àow through a single fracture is numerically studied by means of the Fluent Software. The results show that the roughness of the fracture significantly affects the hydraulic conductivity in the fracture as compared with the cubic law model widely used to describe the flow between two smooth parallel plates. A new model is proposed in this paper, the non-symmetric sinusoidal fracture model, to simulate the flow in a real fracture. This model involves two sinusoidal-varying walls with different phases to replace the flat planes in the cubic law model. The relationships between the effective hydraulic apertures and the phase retardation for different relative amplitudes and wavelengths are numerically investigated. A simple expression of the effective hydraulic aperture of the fracture is obtained, together with the law of the effective hydraulic aperture against the amplitude, the phase retardation and the wavelength of two sinusoidal-varying walls.

On the cubic law and variably saturated flow through discrete open rough-walled discontinuities

“…19 [63], where  refers to the aperture's standard deviation. Roughness was also found to generally cause mechanical aperture to exceed hydraulic aperture, with the latter decreasing significantly with increase in roughness or decrease in mechanical aperture [29].…”

“…Measurement of aperture in a rough fracture: (i) the vertical aperture, perpendicular to the discontinuity, (ii) normal-to-local-centerline aperture, (iii) ball aperture, or (iv) average segment aperture [54] Hydraulic apertures, on the other hand, can possibly be determined through knowledge of the means and standard deviations of fracture apertures [28]. Hydraulic aperture decreases as Re increases, and it increases with increase in roughness and decrease in mechanical aperture, further emphasising the sensitivity of the cubic law [29].…”

“…[5]) and sinusoidally varying aperture with shorter wavelengths and larger amplitudes deviate more from the cubic law [29].  Further investigation on contact obstacles and variable aperture based on numerical flow simulations, resulting in corrections terms to better predict fracture flow [58].…”

“… Geometrical-related modifications account for roughness through treating the rough walls as sinusoidally varying along the length of the fracture, even more recently incorporating roughness profiles not in phase [29].…”

Power law breakthrough curve tailing in a fracture: The role of advection

“…The LCL is not strictly valid under all circumstances. At large Reynolds or Peclet numbers (Detwiler et al, 2000;Konzuk and Kueper, 2004), in the presence of asperities or inclusions in the aperture that may create eddies (Konzuk and Kueper, 2004;Liu and Fan, 2012;Oron and Berkowitz, 1998;Qian et al, 2012) or under conditions of hydromechanical dilation and/or normal stress (Cornet et al, 2003;Gentier et al, 2013;Liu et al, 2013;Witherspoon et al, 1980), the rate of flow may not scale with the cube of the local aperture. However, for the development herein we do not need to invoke the LCL directly; we assume only small variations in aperture will cause large variations local advective velocity.…”