Time-Dependent Dispersivity of Linearly Sorbing Solutes in a Single Fracture with Matrix Diffusion

Abstract

Field studies show that the variance of travel distance often increases nonlinearly with time elapsed after release of solute tracers. The nonlinear relationship between variance of travel distance and time is attributed to the heterogeneity of the porous media. To describe the transport in such a heterogeneous system, a time-dependent dispersivity is necessary. Though more attention has been devoted toward the study of non-Fickian dispersion at early time, there are no known studies that explicitly describe the dispersivity behavior in a fracture–matrix-coupled system. The observation from numerical results suggests that dispersivity has a time-dependent behavior and it reaches asymptotic values after a long time. The preasymptotic behavior of a solute front in fracture is characterized by increasing effective dispersivity with time. The role of fracture and matrix transport parameters on this behavior is analyzed for linearly sorbing solutes. Approximate expression is provided for the time-dependent dispersivity of the solute front in a single fracture with matrix diffusion and the expression for the time required to attain the asymptotic behavior is also obtained. A comparison of the front dispersivity behavior between parallel multiple fractures with a constant aperture width model and smooth parallel multiple fractures with a varying aperture width model is done.