Advective-diffusive-reactive solute transport due to non-Newtonian fluid flows in a fracture surrounded by a tight porous medium. (January 2019) - Dejam, Morteza
Graphical abstract: Sketch of a physical system (comprised of a fracture surrounded by a tight porous medium) where the advective-diffusive-reactive solute transport due to non-Newtonian fluid flows occurs. Highlights: Transport in non-Newtonian fluid flows in a fracture surrounded by a tight matrix is modeled. Developed model is verified using a numerical simulation of original governing equations. The larger the rate of reaction in fracture the slower the breakthrough of solute. Shear-thinning fluids lead to faster breakthrough of solute than shear-thickening fluids. The higher the rate of reaction in fracture the lower the average diffusive flux through interface. Abstract: 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 Damköhler 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 Damköhler 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.