A new mobile‐immobile model for reactive solute transport with scale‐dependent dispersion

Abstract

[1] This study proposed a new mobile-immobile model (MIM) to describe reactive solute transport with scale-dependent dispersion in heterogeneous porous media. The model was derived from the conventional MIM but assumed the dispersivity to be a linear or exponential function of travel distance. The linear adsorption and the first-order degradation of solute were also considered in the model. The Laplace transform technique and the de Hoog numerical Laplace inversion method were applied to solve the developed model. Solute breakthrough curves (BTCs) obtained from MIM with scale-dependent and constant dispersions were compared, and a constant effective dispersivity was provided to reflect the lumped scale-dependent dispersion effect. The effective dispersivity was calculated by arithmetically averaging the distance-dependent dispersivity. With this effective dispersivity, MIM could produce similar BTC as that from MIM with scale-dependent dispersion in porous media with moderate heterogeneity. The applicability of the proposed new model was tested with concentration data from a 1,250-cm long and highly heterogeneous soil column. The simulation results indicated that MIM with constant and linear distance-dependent dispersivities were unable to adequately describe the measured BTCs in the column, while MIM with exponential distance-dependent dispersivity satisfactorily captured the evolution of BTCs.

Numerical Study of Contaminant Transport in Fractured Porous Rock with Distance Dependent Dispersivity

“…For verification of the developed numerical model, the spatial relative concentration profiles (for a constant concentration boundary condition) were compared with the analytical solution of the transport equation with a distance-dependent dispersion coefficient [7]. Fig.…”

“…Also, analytical solutions have been derived for a porous medium with a linear and exponentially increasing dispersion coefficient [12][13]. A semi-analytical solution has been developed for the mobile-immobile model with distance-dependent dispersion [7]. It was found that the distance-dependent dispersion model describes the solute transport more effectively than the constant dispersion model.…”

“…For the heterogeneous porous media, there are a number of approaches that consider the dispersion coefficient to be either distance- [4][5][6][7] or time-dependent [8][9][10]. A stochastic approach has been used to represent the physical heterogeneity [2], and also several models such as the linear, power law, asymptotic and exponential dispersion models to represent the heterogeneity, of the porous media [4].…”

Finite volume model for reactive transport in fractured porous media with distance- and time-dependent dispersion

“…For heterogeneous porous media, there are several approaches which consider the dispersion coefficient to be either distance dependent (Pickens and Grisak 1981, Pang and Hunt 2001, Gao et al 2010 or time dependent (Srivastava et al 2002, Zhou and Selim 2003, Sharma and Srivastava 2012. Gelhar (1993) used a stochastic approach to represent the physical heterogeneity, while Pickens and Grisak (1981) used several models such as linear, power law, asymptotic and exponential dispersion models to represent the heterogeneity of porous media.…”

One-dimensional spatially dependent solute transport in semi-infinite porous media: an analytical solution

“…Sanskrityayn et al (2016) obtained analytical solution of advection dispersion equation with spatially and temporally dependent dispersion using Green's function. Gao et al (2010) was presented a new mobile-immobile model to account for solute transport with scale-dependent dispersion in heterogeneous porous media and the dispersivity was assumed to be a function of travel distance, also the linear adsorption and the first-order degradation of solute were considered. The linear and exponential functions were chosen to describe the relationship between dispersivity and distance.…”