Analytical solutions of solute transport in a fracture-matrix system with different reaction rates for fracture and matrix

- Solute transport with different fracture and matrix reaction rates.
- Analytical solutions obtained for non-reactive transport.
- Steady-state analytical solutions with the first-order reactions.
- The first-order reaction shortens the penetration distance.

SummaryThis study deals with the problem of reactive solute transport in a fracture-matrix system using both analytical and numerical modeling methods. The groundwater flow velocity in the fracture is assumed to be high enough (no less than 0.1 m/day) to ensure the advection-dominant transport in the fracture. The problem includes advection along the fracture, transverse diffusion in the matrix, with linear sorption as well as first-order reactions operative in both the fracture and the matrix. A constant-concentration boundary condition and a decay source boundary condition in the fracture are considered. With a constant-concentration source, we obtain closed-form analytical solutions that account for the transport without reaction as well as steady-state solutions with different first-order reactions in the two media. With a decay source, a semi-analytical solution is obtained. The analytical and semi-analytical solutions are in excellent agreement with the numerical simulation results obtained using COMSOL Multiphysics. Sensitivity analysis is conducted to assess the relative importance of matrix diffusion coefficient, fracture aperture, and matrix porosity. We conclude that the first-order reaction as well as the matrix diffusion in the fractured rock would decrease the solute peak concentration and shorten the penetration distance into the fracture. The solutions can be applied to assess the spatial-temporal distribution of concentrations in the fracture and the matrix as well as to assess the contaminant mass stored in the rock matrix. All of these are useful for designing remediation plans for contaminated fractured rocks or for risk assessment of contaminated fracture-matrix systems.