Mass transfer at fracture intersections: An evaluation of mixing models

Abstract

Models of solute transport in fractured geologic media that are based on the discrete network approach require that a method be adopted for transferring mass through each fracture intersection. The two usual models for mass partitioning between the outflow branches of crossing fractures assume either stream tube routing or complete mixing. A mathematical analysis of two‐dimensional, laminar flow through the intersection of two orthogonal fractures with smooth walls is carried out to examine the mixing process. Mixing ratios are expressed in terms of a local Peclet number (Pe = υr/D), where υ is an average fluid velocity within the fracture intersection, r is the radius of the fracture intersection, and D is the diffusion coefficient. As a general observation the concept of complete mixing within a fracture intersection does not properly represent the mass transfer process at any value of the Peclet number. A mixing ratio equivalent to complete mixing may be observed, but only for particular flow geometries and in a limited range of the Peclet number. Stream tube routing models provide a good approximation for Peclet numbers greater than 1; and in some cases this limit may be as low as 10−2. The actual value of the lower limit depends upon the geometry of the bounding streamline that separates the flow into the two outflow fractures, in relation to the fracture through which solute enters the intersection. There is a range in the Peclet number, of roughly 3 orders of magnitude, where the extent of mixing is dependent upon the value of Pe within the intersection.