Reactive silica transport in fractured porous media: Analytical solution for a single fracture

A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a single fracture embedded in an impervious host rock matrix. This solution differs from previous analyses in that it takes into account both hydrodynamic dispersion and advection of silica transport along the fracture, and hence takes the form of an infinite integral. Several illustrative calculations are undertaken to confirm that neglecting the dispersion term may lead to erroneous silica distribution along the fracture and within the host matrix, and the error becomes severe with a smaller rate of fluid flow in the fracture. The longitudinal dispersion is negligible only at steady state or when the flow rate in the fracture is higher. The analytical solution can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.