Semi‐analytical solutions for solute transport and exchange in fractured porous media

Abstract

[1] Fracture-matrix interactions can significantly affect solute transport in fractured porous media and rocks, even when fractures are major (or sole) conduits of flow. We develop a semi-analytical solution for transport of conservative solutes in a single fracture. Our solution accounts for two-dimensional dispersion in the fracture, two-dimensional diffusion in the ambient matrix, and fully coupled fracture-matrix exchange, without resorting to simplifying assumptions regarding any of these transport mechanisms. It also enables one to deal with arbitrary initial and boundary conditions, as well as with distributed and point sources. We investigate the impact of transverse dispersion in a fracture and longitudinal diffusion in the ambient matrix on the fracture-matrix exchange, both of which are neglected in standard models of transport in fractured media.Citation: Roubinet, D., J.-R. de Dreuzy, and D. M. Tartakovsky (2012), Semi-analytical solutions for solute transport and exchange in fractured porous media, Water Resour. Res., 48, W01542,

Report on THMC Modeling of the Near Field Evolution of a Generic Clay Repository: Model Validation and Demonstration

“…For these situations, longitudinal and transverse dispersion are independent processes and can be incorporated into the transport solution in the same way. The system analyzed by Roubinet et al (2012) general orientation of the principal axes relative to the fracture results in transverse and longitudinal matrix diffusion/dispersion processes that are not independent; therefore, the superposition method presented here for incorporating longitudinal diffusion and dispersion is not applicable.…”

“…For solute release in the matrix, solute that has not interacted with the fracture remains at 0   (the solute release location in a coordinate system moving at the matrix longitudinal velocity) unless longitudinal diffusion is included. Roubinet et al (2012) have shown that at low Peclet numbers, longitudinal diffusion in the matrix can have a significant effect on solute transport through the fracture. For solute that has interacted with the fracture, differential advection caused by fracture-matrix interaction can overshadow other dispersion/diffusion processes, as shown here for the low fracture-dispersion case based on parallel-plate fracture geometry.…”

“…They also compared their analytical solutions with numerical simulations that included longitudinal and transverse matrix advection and longitudinal dispersion in the macropore. Roubinet et al (2012) added the effects of transverse dispersion in a fracture and longitudinal diffusion in the matrix to these mechanisms, and found that transverse dispersion in fractures had little effect on solute transport, but that longitudinal diffusion in the matrix becomes important at low Peclet numbers. The solution provided by Roubinet et al (2012) also is capable of treating spatially varying and time-dependent source conditions.…”

“…These values of Ω indicate that longitudinal dispersion and diffusion should have negligible effects on longitudinal spreading for cases 7 and 10, which use the low longitudinal dispersion coefficient, a minor effect for Case 8, and an even smaller effect for Case 11, both of which use the moderate longitudinal dispersion coefficient; and significant effects for cases 9 and 12, where the high longitudinal dispersion coefficient is used. Roubinet et al (2012) investigated the effects of longitudinal diffusion in the matrix on transport for an instantaneous point source and computed three cases for different Peclet numbers. They found that longitudinal matrix diffusion effects are less significant as the Peclet number increases (Roubinet et al, 2012).…”

“…Roubinet et al (2012) investigated the effects of longitudinal diffusion in the matrix on transport for an instantaneous point source and computed three cases for different Peclet numbers. They found that longitudinal matrix diffusion effects are less significant as the Peclet number increases (Roubinet et al, 2012). Application of Equation (3-89) to these cases gives values of Ω of 0.2, 0.8, and 20 for high-, middle-, and low-Peclet-number cases, respectively.…”