Quantifying matrix diffusion effect on solute transport in subsurface fractured media

Abstract. Matrix diffusion is an important process for solute transport in subsurface fractured media. The effect of matrix diffusion on solute transport depends on various fracture and matrix parameters as well as the underlying temporal-spatial scales. In the present study, we quantitatively analyze the dependency of matrix diffusion effect on these parameters through analytical solutions, and then propose a new unified parameter to quantify the significance of matrix diffusion effect. A comprehensive analysis is performed to verify the applicability of the unifed parameter through both analytical and field/laboratory data. Compared with previous unified parameters, the new unifed parameter exhibits a stronger capability in quantifying the strength of matrix diffusion. Based on the field/laboratory data, a threshold of the unified parameter is recommended as a criterion to assess whether matrix diffusion effect is significant or negligible. We also derive an equivalent solute release function to compensate for matrix diffusion so that a fracture-matrix coupled model could be simplified to a fracture-only model, largely mitigating the computational burden associated with solute transport modeling. Although the unifed parameter and the equivalent solute release function are derived with 1D analytical solutions, they also show satisfactory performance in a 3D numerical model with a nonuniform fracture flow field. Results of the present study offer an accurate method to quantify matrix diffusion effect on solute transport in fractured media, and are particularly useful to improve the computational efficiency of solute transport modeling for prediction and inversion purposes.