Analytical solutions for solute transfer characteristics at continuous fracture junctions

Simple analytical solutions for the mixing characteristics and transfer probabilities of solute at the continuous fracture junction are proposed in this study. The proposed analytical solution considers the effects of diffusion, and it is simple enough to be applied to the junctions in discrete fracture network. The analytical solutions are compared with the complete-mixing and the streamline-routing models. As the Peclet number increases, the analytical solutions indicate the transition from complete solute mixing to streamline routing at a fracture junction. It is clear from the results that the transfer characteristics at the junctions are a function not only of one dimensionless parameter but of complex combinations of discharge pattern, geometry, and concentration distribution in the related fractures. Comparisons with the existing numerical solutions and possible underestimation of the solute mixing by the analytical solutions are discussed.