Solutes In Heterogeneous Porous Media Research Articles

Transport of rate‐limited sorbing solutes in heterogeneous porous media: Application of a one‐dimensional multifactor nonideality model to field data

The results of several experiments reported in the literature indicate that the assumptions of porous media homogeneity and instantaneous sorption are generally invalid for transport of sorbing solute at the field scale. In addition, it is probable that the “nonideal” transport observed is caused by more than one factor. The purpose of this work was to evaluate the ability of a one‐dimensional, multifactor nonideality model to represent the nonideal transport of sorbing solutes at the field scale. For this model the two‐domain approach is used to represent heterogeneity, and sorption is represented as being essentially instantaneous for a portion of the sorbent and rate limited for the remainder. Data (breakthrough curves) obtained from four field experiments reported in the literature were used to test the performance of the model. With one exception, data from laboratory or field experiments were used to identify values for input parameters; the exception concerned an assumption of a uniform distribution of sorbent between the advective and nonadvective pore water domains. Specification of input parameters independent of the data being simulated allowed the model to be used in a predictive mode. On the basis of the good match between predictions produced with the model and the data, it appears that the model provides a valid representation of sorption dynamics and solute transport for field‐scale systems influenced by heterogeneity and rate‐limited sorption. The model should be useful in situations where the extensive input data required for more complex models (e.g., stochastic) are not available.

An analytical solution for one‐dimensional transport in porous media with an exponential dispersion function

An analytical solution describing the transport of dissolved substances in heterogeneous porous media with an asymptotic distance‐dependent dispersion relationship has been developed. The solution has a dispersion function which is linear near the origin (i.e., for short travel distances) and approaches an asymptotic value as the travel distance becomes infinite. This solution can be used to characterize differences in the transport process relative to both the classical convection‐dispersion equation which assumes that the hydrodynamic dispersion in the porous medium remains constant and a dispersion solution which has a strictly linear dispersion function. The form of the hydrodynamic dispersion function used in the analytical solution is , where α(x) = a L[1 − e−bx/L] and is the average pore water velocity. The proposed model may provide an alternate means for obtaining a description of the transport of solutes in heterogeneous porous media, when the scale dependence of the dispersion relationship follows the behavior given by α(x). The overall behavior of the model is illustrated by several examples for constant concentration and flux boundary conditions.

Modeling solute advection coupled with sorption kinetics in heterogeneous formations

A method for coupling sorption kinetics and solute advection in particle‐tracking models is proposed; this method is efficient for the case where sorption rate coefficients can be assumed constant field scale parameters. A simulation example of reactive solute advection in two‐dimensional heterogeneous porous media is presented. The effect of sorption kinetics on solute advection is investigated. Nonequilibrium effects are exhibited as enhanced tailing in the solute breakthrough. Because high variability in the hydraulic conductivity also yields enhanced tailing, the nonequilibrium effect is more pronounced for the case of low variability. Moreover, it may be difficult to distinguish cases of low variability with nonequilibrium sorption from cases of high variability with equilibrium sorption. A comparison of Monte Carlo ensemble results is made with an analytical model for the mass arrival of kinetically sorbing solute in heterogeneous porous media obtained using first‐order perturbation. The comparison indicates that the analytical model provides reasonable approximations of the expected solute breakthrough if the variance of the natural logarithm of the hydraulic conductivity is smaller than 1.

Mass arrival of sorptive solute in heterogeneous porous media

The stochastic arrival time analysis of nonreactive solute movement in heterogeneous porous media is extended to consider solute that undergo sorption‐desorption governed by first‐order linear kinetics. For an instantaneous solute injection, a general expression for the expected mass flux at any distance from the injection point is derived in terms of the three‐dimensional velocity field and the forward‐ and reverse‐sorption rate coefficients. This general expression is reduced for three special cases: (1) equilibrium sorption‐desorption where the retardation coefficient is either correlated or uncorrelated with the hydraulic conductivity field, (2) solute degradation where the rate coefficient is uncorrelated with the hydraulic conductivity, and (3) nonequilibrium sorption‐desorption with constant sorption rate coefficients. These cases are analyzed for a lognormally distributed and statistically isotropic spatial correlation of the hydraulic conductivity; other assumptions of spatial correlation in the hydraulic conductivity can also be used. The influence of spatial variability in the sorption rate coefficients for nonequilibrium sorption‐desorption is investigated for the special case of a stratified porous medium. For equilibrium sorption‐desorption, the spatial variability in the retardation coefficient may notably delay the breakthrough of solute at a given location. The spatial variability in the degradation parameter does not influence solute breakthrough significantly for the considered range of parameters. For a stratified porous medium, spatial variability in the sorption rate coefficients has a significant effect on the cumulative mass arrival at a given location. Using the harmonic mean of the sorption rate coefficients most closely approximates the results generated using variable sorption‐rate coefficients for the stratified formation case.