Suresh Kumar Govindarajan

Diffusive mass transfer between fracture and matrix accompanied with sorption significantly influences the efficiency of natural attenuation in hard rocks. While these processes have extensively been studied in a fractured formation, limited information exists on the sorption nonlinearity. For this purpose, a numerical model is developed that couples matrix diffusion and nonlinear sorption at the scale of a single fracture using the dual-porosity concept. The study is limited to a constant continuous solute source boundary condition. The influence of both favorable and unfavorable sorption intensities on solute mobility is investigated using the method of spatial moments. The differing capacities of available sorption sites between fracture surfaces at the fracture-matrix interface and the solid grain surfaces within the rock matrix result in a slower migration of solutes along the fracture, and a larger amount of diffusive mass transfer away from the high permeability fracture. © 2009 ASCE.

Matrix diffusion and sorption are among the key processes impacting the efficiency of natural attenuation in the subsurface. While these processes have been studied extensively in fractured media, limited information exists on the sorption nonlinearity. To address this shortfall, a numerical model has been developed that couples matrix diffusion and nonlinear sorption at the scale of a single fracture using the dual-porosity concept. The study is limited to a constant continuous-solute-source boundary condition. The influence of sorption intensities on dispersivity and macro-dispersion coefficient is investigated using a method of spatial moments. Results suggest that mixing of solutes is significantly lowered by nonlinear sorptive behavior, with respect to the mixing caused by matrix diffusion for linearly sorbing solutes. Also, the magnitude of time dependent dispersivity during the pre-asymptotic regime is lower for nonlinearly sorbing solutes with respect to the linearly sorbing solutes. Reduced mixing is also observed for nonlinearly sorbing solutes under combined mechanisms of matrix diffusion and decay. © Springer-Verlag 2007.

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. © 2008 ASCE.