VELOCITY DEPENDENCE OF DISPERSION FOR TRANSPORT THROUGH A SINGLE FRACTURE OF VARIABLE ROUGHNESS

Several authors have recently expressed interest in chemical transport within fractured media. The majority of these efforts have been based on a linear relationship between the dispersion coefficient and the a verage fluid velocity within the fracture. It is not apparent that thi s relationship is fully justified in all applications. For the present study, it is assumed (as suggested by authors working in porous media ) that the dispersion coefficient is proportional to the velocity rais ed to a power, n. Further, it is assumed that transport within the fra cture follows classic advection-dispersion behavior (e.g., Fickian dis persion). The present study focuses on the value of the power n in a s eries of artificial fractures. In particular, an experimental apparatu s is utilized to run controlled tracer experiments through a single fr acture. When the fracture consists of smooth parallel plates, the resu lts from the experiments indicate that the dispersion coefficient is p roportional to the velocity squared (consistent with the early work by Taylor (1953) for transport dominated by transverse diffusion). As th e fracture roughness is increased through use of blockages within the fracture and/or addition of surface roughness along the fracture walls , the relationship between dispersion and velocity varied. For each fr acture roughness, the results followed the general relationship in whi ch dispersion is proportional to velocity raised to the power n. The p ower n, however, was strongly dependent on the fracture roughness, tak ing on a value of 2.0 for smooth parallel plates and decreasing to a v alue of approximately 1.3 for rough plates.