A note on fracture flow dispersion mechanisms in the ground

Abstract

Two mechanisms for spreading of a tracer pulse in fissured media are discussed: channeling and diffusion in the rock matrix. Dispersion has traditionally been treated as a random mechanism, comparable to diffusion. It is not quite clear if this is applicable to such geologic media as sparsely fissured rock or other stratified media. In this paper, two other mechanisms for dispersion are treated. One is stratified flow; the other is due to interaction with a solid material. A very idealized case of stratified flow is treated. A case is modeled where the medium flows in parallel channels. Each channel is assumed to consist of the space between two parallel plates. The flow is laminar. The various channel widths are assumed to be randomly distributed with a lognormal frequency distribution. This is a distribution which has been found experimentally in fissured crystalline rock. For this case, it is shown that an equivalent dispersion coefficient will increase with the distance between injection and observation point. For this case the normal Fickian diffusion dispersion description is not applicable if the usual assumption is made that the dispersion coefficient is constant. There are several interaction mechanisms of interest between a solute and the solid material. The one treated here is the diffusion of the solute into the porous rock matrix and sorption of the inner surfaces of the matrix. This interaction will also lead to the spreading of a tracer front, in a similar way to what other dispersion mechanisms do. It is demonstrated that if the solid material has very long extension, the dispersion due to this mechanism is so large that a Fickian dispersion coefficient cannot be evaluated without explicitly accounting for this mechanism. Attempts to evaluate Fickian dispersion coefficients by the method of moments will give values which are entirely dependent on the observation accuracy of the tail.