Stochastic Analysis of Surface Roughness, Aperture And Flow In a Single Fracture

ABSTRACT:

Sets of precise measurements of the surface roughness on natural and man-made fractures in six relatively impermeable rocks have been carried out with a specially built non-contact optical system employing a laser displacement meter. It has an excellent positional reproducibility relative to the fracture plane and allows one to compute fracture aperture by comparison of the opposing fracture surfaces. Surface roughness and fracture aperture were statistically analyzed, with respect to spatial variation and correlation. The observed spatial variation of aperture in a fracture is almost homogeneous, isotropic and uncorrelated, except for the sandstone and schist in this study.



RESUME:

Un serie de mesures precises de la rugosite de surface de fractures naturelles et anificielles a ete effectuee dans six roches relativement impermeables avec un nouvean système optique sans-contact utilisant des measures de distance par laser. Les mesures ont une exellente reproductibilitè de position dans Ie plan de la fracture et permettent de determiner l'ouverture de la fracture en comparant les surfaces opposes. La rugosite de la surface et l'ouverture de la fracture etaient analysees particulièrernent concernant la variation et correlation spatiale. La variation spatiale de l'ouvenure observee dans une fracture est presque homogène, isotrope et non-corelee, sauf pour Ie grès et le schiste dans cette etude.



ZUSAMMENFASSUNG :

An einer Serie natuerlicher und kuenstlicher Kluefte, die von sechs relativ undurchlassigen Gesteinsproben stammen, wurde mittels eines beruehrungsfreien Lasermessverfahrens die Kluftoberflaohenrauhigkeit bestimmt. Das angewandte Messverfahren ermöglicht eine genaue Rekonstruktion der gegenueberliegenden Kluftoberflachen und damit der Kluftöffnung. Die Kluftöffnungen wurden in der Folge staustisch ausgewertet, vor allem was die raumliche Variation und Korrelation betrifft. Die gemessene raumliche Variation der Kluftöffnung ist beinahe homogen, isotrop und unkorreliert mit Ausnahme der Sandstein und Schieferkluefte.



1 INTRODUCTION AND BACKGROUND

Flow through fractured rock is important in many areas, such as extraction of oil as well as geothermal energy and underground disposal of nuclear waste; all this requires a detailed understanding of the groundwater flow system. The theory of flow through fractured rock is, however, not yet fully developed, mainly due to the difficulty of defining the geometry of the fracture system and understanding the flow mechanism through an individual fracture. The latter can be complicated since it is affected by surface roughness, fracture aperture and infilling material. Several models exist to describe fracture aperture. In the parallel plate model, an individual fracture is represented by two infinite smooth parallel plates, and the flow is assumed to be laminar with a parabolic velocity profile. This leads to the well-known "cubic law" relating fluid flux to aperture. On the other hand, the results by Abelin et al. (1985) and Hakami (1988) revealed tortuous flow behavior through a fracture, the so-called channeling, both in the field and in the laboratory respectively. Brown (1987), Tsang and Tsang (1987), Tsang et al. (1988) and Moreno et al. (1988) have all confirmed this behavior by numerical analyses using realistically generated fracture apertures. Also the theoretical and experimental studies have been carried out to investigate the effect of aperture variation on flow through a single fracture (Neuzil and Tracy 198I, Raven and Gale 1985, Schraufand Evans 1986, Silliman 1989 and Brown 1989). Aperture variation and correlation may be important in describing the channeling nature of flow through a fracture. To observe and characterize fracture aperture variation, several methods have been proposed using profilometers (Barton et al. 1985, Brown et al. 1986) or injection and casting techniques (Pyrac- Nolte et al. 1987, Hakami 1988, Gentier et al. 1989) as well as optical techniques (Kimura and Esaki 1992).