Velocity dependence of dispersion for transport through a single fracture of variable roughness

Abstract

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 average fluid velocity within the fracture. It is not apparent that this 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 raised to a power, n. Further, it is assumed that transport within the fracture follows classic advection‐dispersion behavior (e.g., Fickian dispersion). The present study focuses on the value of the power n in a series of artificial fractures. In particular, an experimental apparatus is utilized to run controlled tracer experiments through a single fracture. When the fracture consists of smooth parallel plates, the results from the experiments indicate that the dispersion coefficient is proportional to the velocity squared (consistent with the early work by Taylor (1953) for transport dominated by transverse diffusion). As the 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 fracture roughness, the results followed the general relationship in which dispersion is proportional to velocity raised to the power n. The power n, however, was strongly dependent on the fracture roughness, taking on a value of 2.0 for smooth parallel plates and decreasing to a value of approximately 1.3 for rough plates.