The effect of local-scale physical heterogeneity and nonlinear,rate-limited sorption/desorption on contaminant transport in porous media

Nonideal transport of contaminants in porous media has often been observed in laboratory characterization studies. It has long been recognized that multiple processes associated with both physical and chemical factors can contribute to this nonideal transport behavior. To fully understand system behavior, it is important to determine the relative contributions of these multiple factors when conducting contaminant transport and fate studies. In this study, the relative contribution of physical-heterogeneity-related processes versus those of nonlinear, rate-limited sorption/desorption to the observed nonideal transport of trichloroethene in an undisturbed aquifer core was determined through a series of miscible-displacement experiments. The results of experiments conducted using the undisturbed core, collected from a Superfund site in Tucson, AZ, were compared to those obtained from experiments conducted using the same aquifer material packed homogeneously. The results indicate that both physical and chemical factors, specifically preferential flow and associated rate-limited diffusive mass-transfer and rate-limited sorption/desorption, respectively, contributed to the nonideal behavior observed for trichloroethene transport in the undisturbed core. A successful prediction of trichloroethene transport in the undisturbed core was made employing a mathematical model incorporating multiple sources of nonideal transport, using independently determined model parameters to account for the multiple factors contributing to the nonideal transport behavior. The simulation results indicate that local-scale physical heterogeneity controlled the nonideal transport behavior of trichloroethene in the undisturbed core, and that nonlinear, rate-limited sorption/desorption were of secondary importance.     

Nonideal transport of reactive contaminants in heterogeneous porous media: 7. distributed-domain model incorporating immiscible-liquid dissolution and rate-limited sorption/desorption

The purpose of this work is to present a distributed-domain mathematical model incorporating the primary mass-transfer processes that mediate the transport of immiscible organic liquid constituents in water-saturated, locally heterogeneous porous media. Specifically, the impact of grain/pore-scale heterogeneity on immiscible-liquid dissolution and sorption/desorption is represented in the model by describing the system as comprising a continuous distribution of mass-transfer domains. With this conceptualization, the distributions of the initial dissolution rate coefficient and the sorption/desorption rate coefficient are represented as probability density functions. Several sets of numerical experiments are conducted to examine the effects of heterogeneous dissolution and sorption/desorption on contaminant transport and elution. Four scenarios with different combinations of uniform/heterogeneous rate-limited dissolution and uniform/heterogeneous rate-limited sorption/desorption are evaluated. The results show that both heterogeneous rate-limited sorption/desorption and heterogeneous rate-limited dissolution can significantly increase the time or pore volumes required to elute immiscible-liquid constituents from a contaminated porous medium. However, sorption/desorption has minimal influence on elution behavior until essentially all of the immiscible liquid has been removed. For typical immiscible-liquid constituents that have relatively low sorption, the asymptotic elution tailing produced by heterogeneous rate-limited sorption/desorption begins at effluent concentrations that are several orders of magnitude below the initial steady-state concentrations associated with dissolution of the immiscible liquid. Conversely, the enhanced elution tailing associated with heterogeneous rate-limited dissolution begins at concentrations that are approximately one-tenth of the initial steady-state concentrations. Hence, dissolution may generally control elution behavior of immiscible-liquid constituents in cases wherein grain/pore-scale heterogeneity significantly influences both dissolution and sorption/desorption.     

Nonequilibrium sorption of phenols onto geosorbents: the impact of pH on intraparticle mass transfer

While the pH effect on sorption equilibrium of weak acids on natural sorbents was investigated in a number of studies, less is known about the pH dependence of sorption kinetics. This paper investigates the impact of pH on sorption kinetics during the transport of some selected phenols through a sandy aquifer material. Breakthrough curves measured in column experiments were analyzed using a mass transfer based nonequilibrium model designated as dispersed flow, film and particle diffusion model (DF-FPDM). In this model, the rate limiting intraparticle diffusion is characterized by the mass transfer coefficient, kSaV, which can be determined from breakthrough curves by curve fitting. The experimental results indicate that the kSaV is pH-dependent and inversely correlated with the pH-dependent distribution coefficient, K(d,app). Regression equations are presented that may be used to estimate approximate values of intraparticle mass transfer coefficients on the basis of experimentally determined or LFER predicted distribution coefficients.     

Nonequilibrium transport of organic chemicals: The impact of pore-water velocity

The impact of variations in pore-water velocity on the nonequilibrium sorption and transport of organic chemicals was investigated. Miscible displacement experiments were performed with four organic chemicals (dichlorobenzene, naphthalene, tetrachloroethene and p-xylene) and three aquifer materials having low organic-carbon contents (0.02–0.1%). The results of the experiments were analyzed by using a one-dimensional advective-dispersive transport model, wherein sorption is considered instantaneous for a fraction of the sorbent and rate-limited for the remainder. An inverse relationship between the reverse sorption rate constant and the equilibrium sorption constant was evident for each of two velocities. However, there was an order-of-magnitude difference between the rate constants obtained at the two velocities. This suggests the existence of a time-scale effect, which must be accounted for when modeling the transport of organic solutes.     

Development of a continuously stirred flow cell for investigating sorption mass transfer

This paper introduces a new reversible-flow design for a continuously stirred reactor used to study sorption mass transfer in soil and solvent systems. The stirred reactor has potential advantages over conventional packed column or batch reactors because it isolates intraparticle sorption rate limitations from advective-dispersive transport, yet allows changes to flux through the reactor for analysis of sorption kinetics under dynamic conditions. Previously, stirred reactors have often failed due to clogging of sediment on the effluent frit. The reverse-flow backwashing design allows longer life and higher confidence in maintaining mixed conditions than previous designs. Mass transfer 'rate coefficients estimated from stirred and column experiments are compared; both techniques produced results consistent with a published correlation. The data also show that fitted sorption mass transfer coefficients can be strongly dependent on the choice of equilibrium partition coefficient (i.e. batch or first-moment derived values), and that the conventional two-site sorption kinetics model fails to accurately predict sorption mass transfer in the presence of changing solvent velocity through the reactor.     

Reactive solute transport in macroscopically homogeneous porous media: analytical solutions for the temporal moments

In this work, we investigate one-dimensional solute transport affected by rate-limited sorption, first-order mass transfer, and first-order transformation. Analytical expressions are obtained for the temporal moments of the solute in the solution phase. The effect of various rate coefficients on the temporal moments is examined. It was found that, in the presence of transformation reactions, the mean arrival time, and the spread and skewness of the breakthrough curves, are not monotonic functions of the rate coefficients. These solutions will be useful as a preliminary analysis tool for ascertaining the relative importance of various processes under given conditions. They may also be used to analyze the accuracy of various numerical techniques used for simulation of reactive transport.     

Application of continuous time random walk theory to nonequilibrium transport in soil

Continuous time random walk (CTRW) formulations have been demonstrated to provide a general and effective approach that quantifies the behavior of solute transport in heterogeneous media in field, laboratory, and numerical experiments. In this paper we first apply the CTRW approach to describe the sorbing solute transport in soils under chemical (or) and physical nonequilibrium conditions by curve-fitting. Results show that the theoretical solutions are in a good agreement with the experimental measurements. In case that CTRW parameters cannot be determined directly or easily, an alternative method is then proposed for estimating such parameters independently of the breakthrough curve data to be simulated. We conduct numerical experiments with artificial data sets generated by the HYDRUS-1D model for a wide range of pore water velocities (υ) and retardation factors (R) to investigate the relationship between CTRW parameters for a sorbing solute and these two quantities (υ, R) that can be directly measured in independent experiments. A series of best-fitting regression equations are then developed from the artificial data sets, which can be easily used as an estimation or prediction model to assess the transport of sorbing solutes under steady flow conditions through soil. Several literature data sets of pesticides are used to validate these relationships. The results show reasonable performance in most cases, thus indicating that our method could provide an alternative way to effectively predict sorbing solute transport in soils. While the regression relationships presented are obtained under certain flow and sorption conditions, the methodology of our study is general and may be extended to predict solute transport in soils under different flow and sorption conditions.     

Effect of water content on transient nonequilibrium NAPL-gas mass transfer during soil vapor extraction

The effect of water content on the volatilization of nonaqueous phase liquid (NAPL) in unsaturated soils was characterized by one-dimensional venting experiments conducted to evaluate the lumped mass transfer coefficient. An empirical correlation based upon the modified Sherwood number, Peclet number, and normalized mean grain size was used to estimate initial lumped mass transfer coefficients over a range of water content. The effects of water content on the soil vapor extraction SVE process have been investigated through experimentation and mathematical modeling. The experimental results indicated that a rate-limited NAPL-gas mass transfer occurred in water-wet soils. A severe mass transfer limitation was observed at 61.0% water saturation where the normalized effluent gas concentrations fell below 1.0 almost immediately, declined exponentially from the initiation of venting, and showed long tailing. This result was attributed to the reduction of interfacial area between the NAPL and mobile gas phases due to the increased water content. A transient mathematical model describing the change of the lumped mass transfer coefficient was used. Simulations showed that the nonequilibrium mass transfer process could be characterized by the exponent beta, a parameter which described the reduction of the specific area available for NAPL volatilization. The nonequilibrium mass transfer limitations were controlled by the soil mean grain size and pore gas velocity, were well described by beta values below 1.0 at low water saturation, and were well predicted with beta values greater than 1.0 at high water saturation.     

Adsorption and transport of arsenate in carbonate-rich soils: coupled effects of nonlinear and rate-limited sorption

The transport and fate of arsenate in carbonate-rich soil under alkaline conditions was investigated with multiple approaches combining batch, sequential extraction and column experiments as well as transport modeling studies. Batch experiments indicated that sorption isotherm was nonlinear over a wide range of concentration (0.1-200 mg L(-1)) examined. As(V) adsorption to the calcareous soil was initially fast but then continued at a slower rate, indicating the potential effect of rate-limited sorption on transport. Column experiments illustrated that transport of As(V) was significantly retarded compared to a non-reactive tracer. The degree of retardation decreased with increasing As(V) concentration. As(V) breakthrough curves exhibited nonideal transport behavior due to the coupled effects of nonlinear and rate-limited sorption on arsenate transport, which is consistent with the results of modeling studies. The contribution of nonlinear sorption to the arsenate retardation was negligible at low concentration but increased with increasing As(V) concentration. Sequential extraction results showed that nonspecifically sorbed (easily exchangeable, outer sphere complexes) fraction of arsenate is dominant with respect to the inner-sphere surface bound complexes of arsenate in the carbonate soil fraction, indicating high bioavailability and transport for arsenate in the carbonate-rich soils of which Fe and Al oxyhydroxide fractions are limited.     

Washing of marine coastal sand in a batch reactor: sorption and desorption of BTEX

This study addresses the issues related to decontamination of marine beach sand accidentally contaminated by petroleum products. Sorption and desorption of BTEX (i.e., benzene, toluene, ethylbenzene, and xylene) onto the sand from Uran Beach, located near the city of Mumbai, India, were studied, and isotherms were determined using the bottle point method to estimate sorption coefficients. Alternatively, QSARs (i.e., quantitative structure activity relationships) were developed and used to estimate the sorption coefficients. Experiments for kinetics of volatilization as well as for kinetics of sorption and desorption in the presence of volatilization were conducted in a fabricated laboratory batch reactor. A mathematical model describing the fate of volatile hydrophobic organic pollutants like BTEX (via sorption and desorption in presence of volatilization) in a batch sediment-washing reactor was proposed. The experimental kinetic data were compared with the values predicted using the proposed models for sorption and desorption, and the optimum values of overall mass transfer coefficients for sorption (K(s)a(s)) and desorption (K(d)a(d)) were estimated. This was achieved by minimization of errors while using the sorption coefficients (Kp) obtained from either laboratory isotherm studies or the QSARs developed in the present study. Independent experimental data were also collected and used for calibration of the model for volatilization, and the values of the overall mass transfer coefficient for volatilization (K(g)a(g)) were estimated for BTEX. In these exercises of minimization of errors, comparable cumulative errors were obtained from the use of Kp values derived from experimental isotherms and QSARs.     

Surfactant enhanced recovery of tetrachloroethylene from a porous medium containing low permeability lenses. 1. Experimental studies

A matrix of batch, column and two-dimensional (2-D) box experiments was conducted to investigate the coupled effects of rate-limited solubilization and layering on the entrapment and subsequent recovery of a representative dense NAPL, tetrachloroethylene (PCE), during surfactant flushing. Batch experiments were performed to determine the equilibrium solubilization capacity of the surfactant, polyoxyethylene (20) sorbitan monooleate (Tween 80), and to measure fluid viscosity, density and interfacial tension. Results of one-dimensional column studies indicated that micellar solubilization of residual PCE was rate-limited at Darcy velocities ranging from 0.8 to 8.2 cm/h and during periods of flow interruption. Effluent concentration data were used to develop effective mass transfer coefficient (Ke) expressions that were dependent upon the Darcy velocity and duration of flow interruption. To simulate subsurface heterogeneity, 2-D boxes were packed with layers of F-70 Ottawa sand and Wurtsmith aquifer material within 20-30 mesh Ottawa sand. A 4% Tween 80 solution was then flushed through PCE-contaminated boxes at several flow velocities, with periods of flow interruption. Effluent concentration data and visual observations indicated that both rate-limited solubilization and pooling of PCE above the fine layers reduced PCE recovery to levels below those anticipated from batch and column measurements. These experimental results demonstrate the potential impact of both mass transfer limitations and subsurface layering on the recovery of PCE during surfactant enhanced aquifer remediation.     

A method for estimating distributions of mass transfer rate coefficients with application to purging and batch experiments

Mass transfer between aquifer material and groundwater is often modeled as first-order rate-limited sorption or diffusive exchange between mobile zones and immobile zones with idealized geometries. Recent improvements in experimental techniques and advances in our understanding of pore-scale heterogeneity demonstrate that two (or even a few) rate coefficients are insufficient in many cases. Here, we investigate a piece-wise linear model for a continuous distribution of rate coefficients, that has several advantages over previously used ‘statistical' distribution models (with functional form from gamma or lognormal PDF's): (1) distributions of arbitrary, even bimodal, shapes can be represented; (2) linear estimation methods can be applied to determine the distribution from experimental data; (3) the uncertainty in the distribution can be determined for each of its sections; and (4) the relationship between the time scales of available data and those of estimatable mass transfer processes can be investigated. A statistical model refinement algorithm is presented that reduces the number of parameters (sections of the piece-wise linear model) to the admissible minimum. We show that purging experiments allow estimation of a wider zone of the rate distribution than do batch experiments, and hence will provide predictions that are accurate over a wider range of time scales. Finally, in an application to TCE gas-purging desorption data, the piece-wise linear rate-distribution model has a higher probability of being adequate than those using a gamma or lognormal distribution or a single rate coefficient.     

Estimating first-order reaction rate coefficient for transport with nonequilibrium linear mass transfer in heterogeneous media

A travel-time based approach is developed for estimating first-order reaction rate coefficients for transport with nonequilibrium linear mass transfer in heterogeneous media. Tracer transport in the mobile domain is characterized by a travel-time distribution, and mass transfer rates are described by a convolution product of concentrations in the mobile domain and a memory function rather than predefining the mass transfer model. A constant first-order reaction is assumed to occur only in the mobile domain. Analytical solutions in Laplace domain can be derived for both conservative and reactive breakthrough curves (BTCs). Temporal-moment analyses are presented by using the first and second moments of conservative and reactive BTCs and the mass consumption of the reactant for an inverse Gaussian travel-time distribution. In terms of moment matching, there is no need for one to specify the mass transfer model. With the same capacity ratio and the mean retention time, all mass transfer models will lead to the same moment-derived reaction rate coefficients. In addition, the consideration of mass transfer generally yields larger estimations of the reaction rate coefficient than models ignoring mass transfer. Furthermore, the capacity ratio and the mean retention time have opposite influences on the estimation of the reaction rate coefficient: the first-order reaction rate coefficient is positively linearly proportional to the capacity ratio, but negatively linearly proportional to the mean retention time.     

A two-region nonequilibrium model for solute transport in solution conduits in karstic aquifers

A two-region nonequilibrium model was used to calibrate initial solute-transport parameter estimates generated from tracer-breakthrough curves (TBCs) developed from tracer tests conducted in uni-axial solution conduits in karstic aquifers. Two-region nonequilibrium models account for partitioning of solute into mobile- and immobile-fluid regions to produce a more representative model fit to the strong tails associated with TBCs than do equilibrium models. The nonequilibrium model resulted in an increase in average flow velocities and a decrease in longitudinal dispersion coefficients over comparable estimates using an equilibrium model. Increases in velocity and decreases in dispersion were obtained at the expense of including parameters that describe solute partitioning and mass transfer rate for the mobile- and immobile-fluid regions. In addition, nonidentifiable sorption and mass transfer parameters for the immobile-fluid regions could only be described in terms of upper and lower bounds using readily determined identifiable ratios representing solute partitioning and system constraints based on known physical properties. The identifiable ratios and system constraints serve to minimize model nonuniqueness and renders the nonidentification problem trivial.     

Comparison of nonideal sorption formulations in modeling the transport of phthalate esters through packed soil columns

Sorption of dimethyl phthalate (DMP), diethyl phthalate (DEP) and dipropyl phthalate (DPP) to two soil materials that vary in organic matter content was investigated using miscible displacement experiments under saturated flow conditions. Generated breakthrough curves (BTCs) were inversely simulated using linear, equilibrium sorption (LE), nonlinear, equilibrium sorption (NL), linear, first-order nonequilibrium sorption (LFO), linear, radial diffusion (LRD), and nonlinear, first-order nonequilibrium sorption (NFO) models. The Akaike information criterion was utilized to determine the preferred model. The LE model could not adequately describe phthalate ester (PE) BTCs in higher organic matter soil or for more hydrophobic PEs. The LFO and LRD models adequately described the BTCs but a slight improvement in curve-fitting was gained in some cases when the NFO model was used. However, none of the models could properly describe the desorptive tail of DPP for the high organic matter soil. Transport of DPP through this soil was adequately predicted when degradation or sorption hysteresis was considered. Using the optimized parameter values along with values reported by others it was shown that the organic carbon distribution coefficient (K(oc)) of PEs correlates well with the octanol/water partition coefficient (K(ow)). Also, a strong relationship was found between the first-order sorption rate coefficient normalized to injection pulse size and compound residence time. A similar trend of timescale dependence was found for the rate parameter in the radial diffusion model. Results also revealed that the fraction of instantaneous sorption sites is dependent on K(ow) and appears to decrease with the increase in the sorption rate parameter.     

Modelling the solute transport under nonequilibrium conditions on the basis of mass transfer equations

A solute transport model that describes nonequilibrium adsorption in soil/groundwater systems by mass transfer equations for film and intraparticle diffusion is presented. The model is useful in cases where breakthrough curve spreading cannot be explained by dispersion only. To evaluate its validity, the model was applied to several data sets from column experiments. The validity was also proved by a comparison with an analytical solution for the limiting case of predominating dispersion. Furthermore, a sensitivity analysis was performed to illustrate the influence of different process and sorption parameters (pore water velocity, intraparticle mass transfer coefficient, isotherm nonlinearity) on the shape of the calculated breakthrough curves. The application of the proposed model is discussed in comparison to the widely used dispersed flow/local equilibrium model, and a relationship between both models, which is based on a lumped parameter approach, is shown.     

Relationship between mass-flux reduction and source-zone mass removal: analysis of field data

The magnitude of contaminant mass-flux reduction associated with a specific amount of contaminant mass removed is a key consideration for evaluating the effectiveness of a source-zone remediation effort. Thus, there is great interest in characterizing, estimating, and predicting relationships between mass-flux reduction and mass removal. Published data collected for several field studies were examined to evaluate relationships between mass-flux reduction and source-zone mass removal. The studies analyzed herein represent a variety of source-zone architectures, immiscible-liquid compositions, and implemented remediation technologies. There are two general approaches to characterizing the mass-flux-reduction/mass-removal relationship, end-point analysis and time-continuous analysis. End-point analysis, based on comparing masses and mass fluxes measured before and after a source-zone remediation effort, was conducted for 21 remediation projects. Mass removals were greater than 60% for all but three of the studies. Mass-flux reductions ranging from slightly less than to slightly greater than one-to-one were observed for the majority of the sites. However, these single-snapshot characterizations are limited in that the antecedent behavior is indeterminate. Time-continuous analysis, based on continuous monitoring of mass removal and mass flux, was performed for two sites, both for which data were obtained under water-flushing conditions. The reductions in mass flux were significantly different for the two sites (90% vs. approximately 8%) for similar mass removals ( approximately 40%). These results illustrate the dependence of the mass-flux-reduction/mass-removal relationship on source-zone architecture and associated mass-transfer processes. Minimal mass-flux reduction was observed for a system wherein mass removal was relatively efficient (ideal mass-transfer and displacement). Conversely, a significant degree of mass-flux reduction was observed for a site wherein mass removal was inefficient (non-ideal mass-transfer and displacement). The mass-flux-reduction/mass-removal relationship for the latter site exhibited a multi-step behavior, which cannot be predicted using some of the available simple estimation functions.     

Colloid-facilitated transport of radionuclides through fractured media

The sorption of radionuclides on natural colloids may significantly modify their transport behaviour through fractured media, since radionuclides bound to colloids may not be subject to the important retardation mechanisms of matrix diffusion and sorption onto pore surfaces. This paper reports on theoretical and experimental work aimed at assessing the relevance of colloid-facilitated transport to repository safety analyses, with specific reference to the Swiss case. Transport models are presented, developed in conjunction with field- and laboratory-based studies of deep groundwater in the crystalline basement of northern Switzerland, in which colloid size distributions, compositions and sorption properties have been measured. Various potential mechanisms giving rise to both reversible and irreversible sorption are discussed. In the first case, a simple approach is examined which is based on previously reported models of colloid transport and assumes reversible, linear sorption on colloids, for which experimental data have been obtained. It is shown that transport of radionuclides would not, in general, be significantly enhanced because of this process. A more recently developed and more complex model is then described incorporating irreversible sorption, in which case the transport of radionuclides tends to be strongly dependent on the extent of colloid-fracture wall interaction.     

Influence of rate-limited sorption on the cleanup of layered soils by vapor extraction

The conditions under which rate-limited sorption is important for cleanup of layered soils by vapor extraction are investigated. The investigation includes two steps: (a) the cleanup time is estimated for a number of scenario cases by means of a numerical model and (b) the numerical results are approximated using analytical solutions derived for simplified models. In this way, equations are derived, which give insight into the influence of different parameters characterizing the properties of the soil, the geometry of the formation, the mass transfer mechanisms in it, and the distribution of the contaminant mass in the different phases (gas phase, water phase and solid phase). The numerical model used is based on the advection-dispersion differential equations for Darcian isothermal airflow, local equilibrium contaminant mass transfer between gas phase and soil water and first-order kinetics for mass transfer between soil water and solid phase. The numerical results are approximated combining an analytical solution to estimate cleanup time in layered formations for local equilibrium sorption, which has been presented in a previous work (J. Contam. Hydrol., 36 (1999) 105). with an analytical solution based on the well-mixed reservoir model under consideration of rate-limited sorption. The analytical approximation of the cleanup time is in reasonable agreement with the numerical results and allows its estimation with small computational effort.     

Model coupling intraparticle diffusion/sorption, nonlinear sorption, and biodegradation processes

Diffusion, sorption and biodegradation are key processes impacting the efficiency of natural attenuation. While each process has been studied individually, limited information exists on the kinetic coupling of these processes. In this paper, a model is presented that couples nonlinear and nonequilibrium sorption (intraparticle diffusion) with biodegradation kinetics. Initially, these processes are studied independently (i.e., intraparticle diffusion, nonlinear sorption and biodegradation), with appropriate parameters determined from these independent studies. Then, the coupled processes are studied, with an initial data set used to determine biodegradation constants that were subsequently used to successfully predict the behavior of a second data set. The validated model is then used to conduct a sensitivity analysis, which reveals conditions where biodegradation becomes desorption rate-limited. If the chemical is not pre-equilibrated with the soil prior to the onset of biodegradation, then fast sorption will reduce aqueous concentrations and thus biodegradation rates. Another sensitivity analysis demonstrates the importance of including nonlinear sorption in a coupled diffusion/sorption and biodegradation model. While predictions based on linear sorption isotherms agree well with solution concentrations, for the conditions evaluated this approach overestimates the percentage of contaminant biodegraded by as much as 50%. This research demonstrates that nonlinear sorption should be coupled with diffusion/sorption and biodegradation models in order to accurately predict bioremediation and natural attenuation processes. To our knowledge this study is unique in studying nonlinear sorption coupled with intraparticle diffusion and biodegradation kinetics with natural media.