Advective-diffusive-reactive solute transport due to non-Newtonian fluid flows in a fracture surrounded by a tight porous medium

A mathematical model is presented for advective-diffusive-reactive solute transport due to non-Newtonian fluid flows in a fracture surrounded by a tight porous medium. The interaction between the two media is handled by the continuity of solute concentration and diffusive flux at the interface. The semi-analytical solutions and their asymptotic behaviours are derived for concentration inside the tight porous medium, average concentration within the fracture, and average diffusive flux through the interface. The developed model is verified using a numerical simulation of the original governing equations and then it is compared with the existing theoretical models for solute transport in a fracture with porous walls. It is revealed that the Damkohler number in the finite fracture affects the breakthrough of the solute much more considerably compared to that in the matrix. However, the larger the rate of reaction in the fracture the slower the breakthrough of the solute. Also, the shear-thinning fluids lead to faster breakthrough of the solute than the Newtonian fluid and the shear-thickening fluids yield slower breakthrough of the solute respect to the Newtonian fluid. Moreover, the average diffusive flux through interface generally increases as the advection coefficient becomes larger. In addition, the Damkohler number in the fracture influences the average diffusive flux through interface more noticeably compared to that in the matrix. Nevertheless, the higher the rate of reaction in the fracture the lower the average diffusive flux through interface. Finally, the breakthrough of the solute occurs faster within the infinite fracture respect to the finite fracture. (C) 2018 Elsevier Ltd. All rights reserved.