Solute transport through fractured rock: Radial diffusion into the rock matrix with several geological layers for an arbitrary length decay chain

- A model is developed for reactive solute transport in heterogeneous fractured rocks.
- Semi-analytical solution is derived for cylindrical channels with radial matrix diffusion.
- Solutes are more retarded by radial matrix diffusion than by linear matrix diffusion.

SummaryThe paper presents a model development to derive a semi-analytical solution to describe reactive solute transport through a single channel in a fracture with cylindrical geometry. The model accounts for advection through the channel, radial diffusion into the adjacent heterogeneous rock matrix comprising different geological layers, adsorption on both the channel surface, and the geological layers of the rock matrix and radioactive decay chain. Not only an arbitrary-length decay chain, but also as many number of the rock matrix layers with different properties as observed in the field can be handled. The solution, which is analytical in the Laplace domain, is transformed back to the time domain numerically e.g. by use of de Hoog algorithm. The solution is verified against experimental data and analytical solutions of limiting cases of solute transport through porous media. More importantly, the relative importance and contribution of different processes on solute transport retardation in fractured rocks are investigated by simulating several cases of varying complexity. The simulation results are compared with those obtained from rectangular model with linear matrix diffusion. It is found that the impact of channel geometry on breakthrough curves increases markedly as the transport distance along the flow channel and away into the rock matrix increase. The effect of geometry is more pronounced for transport of a decay chain when the rock matrix consists of a porous altered layer.