Analysis of the long-term behavior of solute transport with nonlinear equilibrium sorption using breakthrough curves and temporal moments

We analyzed the long-term behavior of breakthrough curves (BTCs) and temporal moments of a solute subjected to Freundlich equilibrium sorption (s = kc(n)). For one-dimensional transport in a homogeneous porous medium, we derived a power-law relation between travel time, tau, and solute displacement, chi, with the exponent being equal to the Freundlich n exponent. The mean solute velocity, derived from the first time moment, was found to change as tau(n-1). For n values larger than 0.66, the second time moment could be related to c chi(2/n), where c is a constant. An approach based on the use of a critical concentration was developed to estimate the presence of the asymptotic regime in the tail of the BTC. This approach was tested successfully using numerical case studies. One-dimensional numerical simulations with varying values of k, n and initial mass were run to verify the closed form analytical expressions for the large time behavior of temporal moments and the tailing part of breakthrough curves. Good agreement between the slope of the tailing part of log-log transformed BTCs and the predicted slope using asymptotic theory was found. Asymptotic theory in general underestimated the magnitude of the concentration in the tail. The quality of the estimated concentrations in the tail improved for small values of the dispersivity. Experimental BTCs of uranin and benazolin were analyzed in combination with sorption/desorption batch experiments using asymptotic theory. A good agreement between the value of n parameter derived from desorption experiment with benazolin and the value of the n parameter derived from the tail of the BTC was found.     

Entrapment and dissolution of DNAPLs in heterogeneous porous media

Two-dimensional multiphase flow and transport simulators were refined and used to numerically investigate the entrapment and dissolution behavior of tetrachloroethylene (PCE) in heterogeneous porous media containing spatial variations in wettability. Measured hydraulic properties, residual saturations, and dissolution parameters were employed in these simulations. Entrapment was quantified using experimentally verified hydraulic property and residual saturation models that account for hysteresis and wettability variations. The nonequilibrium dissolution of PCE was modeled using independent estimates of the film mass transfer coefficient and interfacial area for entrapped and continuous (PCE pools or films) saturations. Flow simulations demonstrate that the spatial distribution of PCE is highly dependent on subsurface wettability characteristics that create differences in PCE retention mechanisms and the presence of subsurface capillary barriers. For a given soil texture, the maximum and minimum PCE infiltration depth was obtained when the sand had intermediate (an organic-wet mass fraction of 25%) and strong (water- or organic-wet) wettability conditions, respectively. In heterogeneous systems, subsurface wettability variations were also found to enhance or diminish the performance of soil texture-induced capillary barriers. The dissolution behavior of PCE was found to depend on the soil wettability and the spatial PCE distribution. Shorter dissolution times tended to occur when PCE was distributed over large regions due to an increased access of flowing water to the PCE. In heterogeneous systems, capillary barriers that produced high PCE saturations tended to exhibit longer dissolution times.     

Evaluating non-equilibrium solute transport in small soil columns

Displacement studies on leaching of bromide and two pesticides (atrazine and isoproturon) were conducted under unsaturated steady state flow conditions in 24 small undisturbed soil columns (5.7 cm in diameter and 10 cm long) each collected from two sites differing in soil structure and organic carbon content in North Germany. There were large and irregular variabilities in the characteristics of both soils, as well as in the shapes of breakthrough curves (BTCs) of different columns, including some with early breakthrough and increased tailing, qualitatively indicating the presence of preferential flow. It was estimated that one preferential flow column (PFC) at site A, and four at site B, contributed, respectively to 11% and 58% of the accumulated leached fraction and to more than 80% of the maximum observed standard deviation (SD) in the field-scale concentration and mass flux of pesticides at two sites. The bromide BTCs of two sites were analyzed with the equilibrium convection-dispersion equation (CDE) and a non-equilibrium two-region/mobile-immobile model. Transport parameters of these models for individual BTCs were determined using a curve fitting program, CXTFIT, and by the time moment method. For the CDE based equilibrium model, the mean values of retardation factor, R, considered separately for all columns, PFCs or non-preferential flow columns (NPFCs) were comparable for the two methods; significant differences were observed in the values of dispersion coefficients of two sites using the two estimation methods. It was inferred from the estimated parameters of non-equilibrium model that 5-12% of water at site A, and 12% at site B, was immobile during displacement in NPFCs. The corresponding values for PFCs of two sites were much larger, ranging from 25% to 51% by CXTFIT and from 24% to 72% by the moment method, suggesting the role of certain mechanisms other than immobile water in higher degrees of non-equilibrium in these columns. Peclet numbers in PFCs of both sites were consistently smaller than five, indicating the inadequacy of the non-equilibrium model to incorporate the effect of all forms of non-equilibrium in PFCs. Overall, the BTCs of individual NPFCs, PFCs and of field average concentration at the two sites were better reproduced with parameters obtained from CXTFIT than by the moment method. The moment method failed to capture the peak concentrations in PFCs, but tended to describe the desorption and tail branches of BTCs better than the curve fitting approach.     

Influence of surfactant-facilitated interfacial tension reduction on chlorinated solvent migration in porous media: observations and numerical simulation

The ability of a multiphase flow model to capture the migration behavior of chlorinated solvents under conditions of surfactant-facilitated interfacial tension (IFT) reduction is assessed through comparison of model predictions with observations from controlled laboratory experiments. Tetrachloroethene (PCE) was released in two-dimensional saturated systems, packed with sandy media that incorporated rectangular lenses of capillary contrast. Spatially uniform interfacial tension conditions were created in the tanks by pre-flushing the porous medium with either Milli Q water or an aqueous surfactant solution. Experimental observations showed that surfactant-facilitated IFT reductions substantially lowered capillary resistance to the vertical downward migration of PCE and enabled PCE to enter finer grained, less permeable lenses that were not penetrated in the absence of surfactant. An immiscible flow model was used to simulate the conditions of the laboratory experiments. Under higher IFT conditions (47.5 and 5 dyn/cm), the model could successfully predict the general migration behavior of the organic liquid. Model predictions, however, exhibited poorer agreement with observed migration pathways under low IFT conditions (0.5 dyn/cm). In all cases, the predicted PCE distributions were influenced by selection of the parametric model for capillary retention and relative permeability. Simulated migration rates were more consistent with observed behavior when the Brooks-Corey/Burdine model was employed. For low interfacial tensions, improved predictions of migration pathways were obtained through grid refinement and incorporation of small-scale packing variability. Simulations highlight the substantial sensitivity of model predictions to the capillary pressure-scaling factor, grid resolution, and small-scale porosity variations at interfaces of permeability contrast under reduced IFT conditions.     

Field study of TCE diffusion profiles below DNAPL to assess aquitard integrity

An area where a free-product accumulation of trichloroethylene (TCE) dense non-aqueous phase liquid (DNAPL) occurs at the bottom of a 10-m-thick surficial sand aquifer was studied to determine the integrity of the underlying, 20-m-thick, clayey silt aquitard formed of glaciolacustrine sediment. TCE concentration-versus-depth profiles determined from aquitard cores collected at five locations indicated penetration of detectable TCE 2.5 to 3.0 m into the aquitard. Two of the profiles show persistent DNAPL at the aquitard interface, while two others indicate that DNAPL, present initially, was completely dissolved away producing concentration declines at the aquitard interface. The fifth profile suggests shallow DNAPL penetration (<0.5 m) into the aquitard, however, this penetration, which was likely caused by cross-contamination during core collection or cone penetrometry (CPT) of the aquitard interface, did not increase the maximum depth of TCE penetration. Combining the field profiles with one-dimensional model simulations, downward migration of the aqueous TCE front, defined as the EPA MCL of 5 microg/l, which was below the analytical detection limit, was projected to a distance between 4 and 5 m below the top of the aquitard. Using a single set of estimated aquitard parameter values, simulations of aqueous TCE migration into the aquitard provided a good fit to four of the field profiles with a migration time of 35 to 45 years, consistent with the history of TCE use at the site. These simulations indicate aqueous TCE migration is diffusion-dominated with only small advective influence by the downward groundwater velocity of 2 to 3 cm/year or less in the aquitard due to pumping of the underlying aquifer to supply water to the facility in the past 50 years. The applicability of the parameter values was confirmed by in situ diffusion experiments of 1-year duration, in which stainless steel cylinders containing DNAPL were inserted into the aquitard. The diffusion-dominated nature of the profiles indicates that the aquitard provides long-term protection of the underlying aquifer from contamination from this DNAPL zone. Simulations of long-term migration of the TCE solute front indicate breakthrough to the lower aquifer at 1200 years for the no advection scenario and at 500 years if the strong downward hydraulic gradient persists. However, even after breakthrough, the mass flux through the aquitard to the underlying aquifer remains relatively low, and when considered in terms of potential impacts to pumping wells, concentrations are not expected to increase significantly above present-day MCLs. The use of contaminant profiles of different time and distance scales, in addition to hydraulic data, dramatically improves the ability to assess aquitard integrity, and provides improved transport parameter values for estimating contaminant arrival times and fluxes. The apparent lack of deep preferential pathways for TCE migration, such as open fractures, is probably due to the softness of the silty aquitard deposit and minimal physical or chemical weathering of the aquitard provides long-term protection of the underlying aquifer from contamination from this DNAPL zone. Simulations of long-term migration of the TCE solute front indicate breakthrough to the lower aquifer at 1200 years for the no advection scenario and at 500 years if the strong downward hydraulic gradient persists. However, even after the breakthrough, the mass flux through the aquitard to the underlying aquifer remains relatively low, and when considered in terms of potential impacts to pumping wells , concentrations are not expected to increase significantly above present-day MCLs. The use of contaminant profiles of different time and distance scales, in addition to hydraulic data, dramatically improves the ability to assess aquitard integrity, and provides improved transport parameter values for estimating contaminant arrival times and fluxes. The apparent lack of deep preferential pathways for TCE migration, such as open fractures, is probably due to the softness of the silty aquitard deposit and minimal physical or chemical weathering of the aquitard.     

The effect of entrapped nonaqueous phase liquids on tracer transport in heterogeneous porous media: laboratory experiments at the intermediate scale

This work considers the applicability of conservative tracers for detecting high-saturation nonaqueous-phase liquid (NAPL) entrapment in heterogeneous systems. For this purpose, a series of experiments and simulations was performed using a two-dimensional heterogeneous system (10x1.2 m), which represents an intermediate scale between laboratory and field scales. Tracer tests performed prior to injecting the NAPL provide the baseline response of the heterogeneous porous medium. Two NAPL spill experiments were performed and the entrapped-NAPL saturation distribution measured in detail using a gamma-ray attenuation system. Tracer tests following each of the NAPL spills produced breakthrough curves (BTCs) reflecting the impact of entrapped NAPL on conservative transport. To evaluate significance, the impact of NAPL entrapment on the conservative-tracer breakthrough curves was compared to simulated breakthrough curve variability for different realizations of the heterogeneous distribution. Analysis of the results reveals that the NAPL entrapment has a significant impact on the temporal moments of conservative-tracer breakthrough curves.     

Abiotic behavior of entrapped petroleum products in the subsurface during leaching

Petroleum products are generally volatile hydrocarbon mixtures. These mixtures may contaminate land surfaces, the unsaturated zone and ground waters at numerous sites and thus represent a long-term source of environmental subsurface pollution. Based on laboratory and field evidence obtained by our research groups and others we emphasize in the present review paper the effect of leaching on the abiotic processes controlling the fate of volatile petroleum hydrocarbon mixtures (VPHMs) in the soil environment. The modification of petroleum hydrocarbon mixtures due to changes in the soil water content is considered the result of a “leaching phenomenon”. The experimental evidence of VPHM behavior in the porous media is linked to four major processes: retention, redistribution and attenuation in the subsurface, and dissolution in the soil water.

Once VPHMs reach the soil surface, their residual concentration and composition is influenced by the amount and quality of the leaching water. The transport and natural attenuation of the VPHMs in the unsaturated zone is affected by the amount and rate of leaching. Since VPHM are a mixture of volatile and non-volatile hydrocarbons whose components differ by several orders of magnitude in their vapor pressure and water solubility, their fates in the soil environment under leaching will be diverse too. This will influence the temporal concentrations of the VPHM components and their distributions with depth, as vapors, solutes, or water-immiscible solutions. Wetting the soil before or after the VPHMs reach it, differentially affects the abiotic processes governing petroleum products behavior into the porous media.     

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability–possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.     

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.     

A multi-directional tracer test in the fractured Chalk aquifer of E. Yorkshire, UK

A multi-borehole radial tracer test has been conducted in the confined Chalk aquifer of E. Yorkshire, UK. Three different tracer dyes were injected into three injection boreholes and a central borehole, 25 m from the injection boreholes, was pumped at 330 m(3)/d for 8 days. The breakthrough curves show that initial breakthrough and peak times were fairly similar for all dyes but that recoveries varied markedly from 9 to 57%. The breakthrough curves show a steep rise to a peak and long tail, typical of dual porosity aquifers. The breakthrough curves were simulated using a 1D dual porosity model. Model input parameters were constrained to acceptable ranges determined from estimations of matrix porosity and diffusion coefficient, fracture spacing, initial breakthrough times and bulk transmissivity of the aquifer. The model gave equivalent hydraulic apertures for fractures in the range 363-384 microm, dispersivities of 1 to 5 m and matrix block sizes of 6 to 9 cm. Modelling suggests that matrix block size is the primary controlling parameter for solute transport in the aquifer, particularly for recovery. The observed breakthrough curves suggest results from single injection-borehole tracer tests in the Chalk may give initial breakthrough and peak times reasonably representative of the aquifer but that recovery is highly variable and sensitive to injection and abstraction borehole location. Consideration of aquifer heterogeneity suggests that high recoveries may be indicative of a high flow pathway adjacent, but not necessarily connected, to the injection and abstraction boreholes whereas low recoveries may indicate more distributed flow through many fractures of similar aperture.     

A sensibility analysis of model selection in modeling the reactive transport of cesium in crushed granite

We performed a sensibility analysis of model selection in modeling the reactive transport of cesium in crushed granite through model calibration and validation. Based on some solid phase analysis data and kinetic batch experimental results, we hypothesized three two-site sorption models in the LEHGC reactive transport model to fit the breakthrough curves (BTCs) from the corresponding column experiments. The analysis of breakthrough curves shows that both the empirical two-site kinetic linear sorption model and the semi-mechanistic/semi-empirical two-site kinetic surface complexation model, regardless of their complexity, can match our experimental data fairly well under given test conditions. A numerical experiment to further compare the two models shows that they behave differently when the pore velocity is not of the same order of magnitude as our test velocities. This result indicates that further investigations to help determine a better model are needed. We suggest that a multistage column experiment, which tests over the whole range of practical flow velocities, should be conducted to help alleviate inadequate hypothesized models.     

Transport of volatile compounds in porous media in the presence of a trapped gas phase

The presence of an immobile gaseous phase in an otherwise-saturated porous medium affects the transport of volatile compounds. The linear theory of partitioning tracers suggests that a volatile tracer introduced into such a system should be retarded with a constant retardation factor. Using high concentrations, however, the saturation of the gaseous phase will change as an effect of the tracer test itself. Competitive gas transfer among all volatile compounds and the change of saturation may lead to tracer concentrations that are temporarily higher than those injected. We analyze the system in the framework of the coherence theory by Helfferich [Soc. Pet. Eng. J. 21 (1) (1981) 51]. The governing equations are formulated as functions of total concentration, i.e., the mass of solutes in all phases per pore volume. Neglecting dispersion and mass-transfer kinetics, we derive the characteristic form of the resulting system of hyperbolic equations. In a system with N volatile compounds, a variation of the concentrations splits up into N waves, each traveling with its own characteristic velocity. If the presence of a gaseous phase is sustained, one wave will be a standing one. We perform numerical model calculations for tracers with various Henry's law coefficients and show that the results agree with the semi-analytical solution obtained by coherence theory.     

A field experiment with variable-suction multi-compartment samplers to measure the spatio-temporal distribution of solute leaching in an agricultural soil

Solutes spread out in time and space as they move downwards from the soil surface with infiltrating water. Solute monitoring in the field is often limited to observations of resident concentrations, while flux concentrations govern the movement of solutes in soils. A recently developed multi-compartment sampler is capable of measuring fluxes at a high spatial resolution with minimal disturbance of the local pressure head field. The objective of this paper is to use this sampler to quantify the spatial and temporal variation of solute leaching below the root zone in an agricultural field under natural rainfall in winter and spring. We placed two samplers at 31 and 25 cm depth in an agricultural field, leaving the soil above undisturbed. Each sampler contained 100 separate cells of 31 × 31 mm. Water fluxes were measured every 5 min for each cell. We monitored leaching of a chloride pulse under natural rainfall by frequently extracting the collected leachate while leaving the samplers buried in situ. This experiment was followed by a dye tracer experiment. This setting yielded information that widely surpassed the information that can be provided by separate anionic and dye tracer trials, and solute transport monitoring by coring or suction cups. The detailed information provided by the samplers showed that percolation at the sampling depth started much faster (approximately 3 h after the start of rainfall) in initially wet soil (pressure head above − 65 cm) than in drier soil (more than 14 h at pressure heads below − 80 cm). At any time, 25% of the drainage passed through 5–6% of the sampled area, reflecting the effect of heterogeneity on the flow paths. The amount of solute carried by individual cells varied over four orders of magnitude. The lateral concentration differences were limited though. This suggests a convective–dispersive regime despite the short vertical travel distance. On the other hand, the dilution index indicates a slight tendency towards stochastic–convective transport at this depth. There was no evidence in the observed drainage patterns and dye stained profiles of significant disturbance of the flow field by the samplers.     

Migration of contaminants through the unsaturated zone overlying the Hesbaye chalky aquifer in Belgium: a field investigation

This paper presents the results of a detailed field investigation that was performed for studying groundwater recharge processes and solute downward migration mechanisms prevailing in the unsaturated zone overlying a chalk aquifer in Belgium. Various laboratory measurements were performed on core samples collected during the drilling of boreholes in the experimental site. In the field, experiments consisted of well logging, infiltration tests in the unsaturated zone, pumping tests in the saturated zone and tracer tests in both the saturated and unsaturated zones. Results show that gravitational flows govern groundwater recharge and solute migration mechanisms in the unsaturated zone. In the variably saturated chalk, the migration and retardation of solutes is strongly influenced by recharge conditions. Under intense injection conditions, solutes migrate at high speed along the partially saturated fissures, downward to the saturated zone. At the same time, they are temporarily retarded in the almost immobile water located in the chalk matrix. Under normal recharge conditions, fissures are inactive and solutes migrate slowly through the chalk matrix. Results also show that concentration dynamics in the saturated zone are related to fluctuations of groundwater levels in the aquifer. A conceptual model is proposed to explain the hydrodispersive behaviour of the variably saturated chalk. Finally, the vulnerability of the chalk to contamination issues occurring at the land surface is discussed.     

Local and distant residence times of contaminants in multi-compartment models. Part I: a review of the theoretical basis

In this, Part I of a two-part series, a review is presented of some generally appreciated residence time properties of multimedia models. The novel concept of “distant residence time” (DRT) is developed to provide additional insights into the characterization of environmental transport. DRT is the proportionality constant between the rate of emission of a contaminant into one compartment or region and the mass that results at steady-state in a distant compartment. The concept, which can be viewed as an expression of environmental mobility, is illustrated for various configurations of compartments and is shown to be consistent with the concepts of global fractionation and cold condensation. The dynamic responses of chemical quantities at distant locations to changing emission rates are also discussed. It is shown that approximate solutions for DRTs and their time dependence are useful for characterizing the long-range transport of chemicals and for interpreting monitoring data.     

Testing the importance of accurate meteorological input fields and parameterizations in atmospheric transport modelling using dream - validation against ETEX-1

A tracer model, the DREAM, which is based on a combination of a near-range Lagrangian model and a long-range Eulerian model, has been developed. The meteorological meso-scale model, MM5V1, is implemented as a meteorological driver for the tracer model. The model system is used for studying transport and dispersion of air pollutants caused by a single but strong source as, e.g. an accidental release from a nuclear power plant. The model system including the coupling of the Lagrangian model with the Eulerian model are described. Various simple and comprehensive parameterizations of the mixing height, the vertical dispersion, and different meterological input data have been implemented in the combined tracer model, and the model results have been validated against measurements from the ETEX-1 release. Several different statistical parameters have been used to estimate the differences between the parameterizations and meterological input data in order to find the best performing solution.