A nonequilibrium model for reactive contaminant transport through fractured porous media: Model development and semianalytical solution

Abstract

[1] In this study a conceptual model that accounts for the effects of nonequilibrium contaminant transport in a fractured porous media is developed. Present model accounts for both physical and sorption nonequilibrium. Analytical solution was developed using the Laplace transform technique, which was then numerically inverted to obtain solute concentration in the fracture matrix system. The semianalytical solution developed here can incorporate both semi-infinite and finite fracture matrix extent. In addition, the model can account for flexible boundary conditions and nonzero initial condition in the fracture matrix system. The present semianalytical solution was validated against the existing analytical solutions for the fracture matrix system. In order to differentiate between various sorption/ transport mechanism different cases of sorption and mass transfer were analyzed by comparing the breakthrough curves and temporal moments. It was found that significant differences in the signature of sorption and mass transfer exists. Applicability of the developed model was evaluated by simulating the published experimental data of Calcium and Strontium transport in a single fracture. The present model simulated the experimental data reasonably well in comparison to the model based on equilibrium sorption assumption in fracture matrix system, and multi rate mass transfer model.

Application of nonequilibrium fracture matrix model in simulating reactive contaminant transport through fractured porous media

“…However, very few studies consider the nonequilibrium sorption in the fractured porous media [ Maloszewski and Zuber , ; Lee and Teng , ; Berkowitz and Zhou , ; Xu and Worman , ; Bodin et al ., , Ojha et al ., ; Joshi et al ., ; Sharma et al ., ]. Most of the available models neglect the effect of sorption kinetics in the fracture‐matrix system and are based on the local equilibrium assumption (LEA).…”

“…The details about the conceptualization, their assumptions, and limitations have been reported elsewhere [ Committee on Fracture Characterization and Fluid Flow, National Research Council , ]. The governing equation for the fracture‐matrix system can be solved using either analytical techniques [ Tang et al ., ; Neretnieks , ; Grisak et al ., 1981; Bibby , ; Sudicky and Frind , ; Barker , ; Moreno and Rasmuson , ; Maloszewski and Zuber , ; Roubinet et al ., ] or numerical techniques [ Grisak et al ., ; Noorishad and Mehran , ; Huyakorn et al ., ; Sekhar et al ., ; Suresh Kumar , ; Ojha et al ., ; Joshi et al ., ]. However, the numerical techniques are more common due to its ability to handle complex initial and boundary conditions along with the sorption nonlinearity.…”

“…Joshi et al . [] developed a generalized model, which can incorporate the nonequilibrium sorption in both fracture and porous matrices. Semianalytical solutions for the model, considering both finite and semi‐infinite fracture and matrix extent were developed.…”

“…The nonequilibrium fracture‐matrix model of Joshi et al . [] was modified to incorporate the sorption nonlinearity. Two different nonlinear sorption isotherms namely nonlinear Freundlich and Langmuir sorption isotherm were used to represent the instantaneous sorption in the fracture‐matrix system.…”

Semi-analytical Solutions of Multiprocessing Non-equilibrium Transport Equations with Linear and Exponential Distance-Dependent Dispersivity

“…They obtained semi-analytical solutions with linear and exponential distance-dependent dispersivity. The de Hoog's algorithm has been widely applied on numerous flow and transport problems and has been found to perform satisfactorily on both advection and dispersion dominated cases (de Hoog et al 1982;Joshi et al 2012). Dentz et al (2011) derived an effective reactive transport equation for the mobile solute that is characterized by non-local physical mass transfer and reaction terms.…”