Measurement and analysis of non-Fickian dispersion in heterogeneous porous media

Contaminant breakthrough behavior in a variety of heterogeneous porous media was measured in laboratory experiments, and evaluated in terms of both the classical advection-dispersion equation (ADE) and the continuous time random walk (CTRW) framework. Heterogeneity can give rise to non-Fickian transport patterns, which are distinguished by "anomalous" early arrival and late time tails in breakthrough curves. Experiments were conducted in two mid-scale laboratory flow cells packed with clean, sieved sand of specified grain sizes. Three sets of experiments were performed, using a "homogeneous" packing, a randomly heterogeneous packing using sand of two grain sizes, and an exponentially correlated structure using sand of three grain sizes. Concentrations of sodium chloride tracer were monitored at the inflow reservoir and measured at the outflow reservoir. Breakthrough curves were then analyzed by comparison to fitted solutions from the ADE and CTRW formulations. In all three systems, including the "homogeneous" one, subtle yet measurable differences between Fickian and non-Fickian transport were observed. Quantitative analysis demonstrated that the CTRW theory characterized the full shape of the breakthrough curves far more effectively than the ADE.     

Determination of spatially-resolved porosity, tracer distributions and diffusion coefficients in porous media using MRI measurements and numerical simulations

This work is focused on measuring the concentration distribution of a conservative tracer in a homogeneous synthetic porous material and in heterogeneous natural sandstone using MRI techniques, and on the use of spatially resolved porosity data to define spatially variable diffusion coefficients in heterogeneous media. The measurements are made by employing SPRITE, a fast MRI method that yields quantitative, spatially-resolved tracer concentrations in porous media. Diffusion experiments involving the migration of H(2)O into D(2)O-saturated porous media are conducted. One-dimensional spatial distributions of H(2)O-tracer concentrations acquired from experiments with the homogeneous synthetic calcium silicate are fitted with the one-dimensional analytical solution of Fick's second law to confirm that the experimental method provides results that are consistent with expectations for Fickian diffusion in porous media. The MRI-measured concentration profiles match well with the solution for Fick's second law and provide a pore-water diffusion coefficient of 1.75×10(-9)m(2)s(-1). The experimental approach was then extended to evaluate diffusion in a heterogeneous natural sandstone in three dimensions. The relatively high hydraulic conductivity of the sandstone, and the contrast in fluid density between the H(2)O tracer and the D(2)O pore fluid, lead to solute transport by a combination of diffusion and density-driven advection. The MRI measurements of spatially distributed tracer concentration, combined with numerical simulations allow for the identification of the respective influences of advection and diffusion. The experimental data are interpreted with the aid of MIN3P-D - a multicomponent reactive transport code that includes the coupled processes of diffusion and density-driven advection. The model defines local diffusion coefficients as a function of spatially resolved porosity measurements. The D(e) values calculated for the heterogeneous sandstone and used to simulate diffusive and advective transport range from 5.4×10(-12) to 1.0×10(-10)m(2)s(-1). These methods have broad applicability to studies of contaminant migration in geological materials.     

A numerical model for transient-hysteretic flow and solute transport in unsaturated porous media

A two-dimensional flow and transport model was developed for simulating transient water flow and nonreactive solute transport in heterogeneous, unsaturated porous media containing air and water. The model is composed of a unique combination of robust and accurate numerical algorithms for solving the Richards', Darcy flux, and advection-dispersion equations. The mixed form of Richards' equation is solved using a finite-element formulation and a modified Picard iteration scheme. Mass lumping is employed to improve solution convergence and stability behavior. The flow algorithm accounts for hysteresis in the pressure head-water content relationship. Darcy fluxes are approximated with a Galerkin and Petrov-Galerkin finite-element method developed for random heterogeneous porous media. The transport equation is solved using an Eulerian-Lagrangian method. A multi-step, fourth-order Runge-Kutta, reverse particle tracking technique and a quadratic-linear interpolation scheme are shown to be superior for determining the advective concentration. A Galerkin finite-element method is used for approximating the dispersive flux. The unsaturated flow and transport model was applied to a variety of rigorous problems and was found to produce accurate, mass-conserving solutions when compared to analytical solutions and published numerical results.     

One-dimensional simulation of solute transfer in saturated-unsaturated porous media using the discontinuous finite elements method

A one-dimensional transport model for simulating water flow and solute transport in homogeneous-heterogeneous, saturated-unsaturated porous media is presented. The model is composed of a combination of accurate numerical algorithms for solving the nonlinear Richard's and advection-dispersion equations (ADE). The mixed form of Richard's equation is solved using a standard finite element method (FEM) with primary variable switching. The transport equation is solved using operator splitting, with the discontinuous finite element method (DFE) for discretization of the advective term. A slope limiting procedure for DFE avoids numerical instabilities but creates very limited numerical dispersion for high Peclet numbers. An implicit finite differences scheme (FD) is used for the dispersive term. The unsaturated flow and transport model (Wamos-T) is applied to a variety of rigorous problems including transient flow, heterogeneous medium and abrupt variations of velocity in magnitude and direction due to time-varying boundary conditions. It produces accurate and mass-conservative solutions for a very large range of grid Peclet numbers. The Wamos-T model is a good and robust alternative for the simulation of mass transport in unsaturated domain.     

Evidence of one-dimensional scale-dependent fractional advection-dispersion

A semi-analytical inverse method and the corresponding program FADEMain for parameter estimation of the fractional advection-dispersion equation (FADE) were developed in this paper. We have analyzed Huang et al.'s [Huang, K., Toride, N., van Genuchten, M.Th., 1995. Experimental investigation of solute transport in large homogeneous and heterogeneous saturated soil columns. Trans. Porous Media 18, 283-302.] laboratory experimental data of conservative solute transport in 12.5-m long homogeneous and heterogeneous soil columns to test the non-Fickian dispersion theory of FADE. The dispersion coefficient was calculated by fitting the analytical solution of FADE to the measured data at different transport scales. We found that the dispersion coefficient increased exponentially with transport scale for the homogeneous column, whereas it increased with transport scale in a power law function for the heterogeneous column. The scale effect of the dispersion coefficient in the heterogeneous soil was much more significant comparing to that in the homogeneous soil. The increasing rate of dispersion coefficient versus transport distance was smaller for FADE than that for the advection-dispersion equation (ADE). Finite difference numerical approximations of the scale-dependent FADE were established to interpret the experimental results. The numerical solutions were found to be adequate for predicting scale-dependent transport in the homogeneous column, while the prediction for the heterogeneous column was less satisfactory.     

One-dimensional simulation of solute transfer in saturated–unsaturated porous media using the discontinuous finite elements method

A one-dimensional transport model for simulating water flow and solute transport in homogeneous–heterogeneous, saturated–unsaturated porous media is presented. The model is composed of a combination of accurate numerical algorithms for solving the nonlinear Richard's and advection–dispersion equations (ADE). The mixed form of Richard's equation is solved using a standard finite element method (FEM) with primary variable switching. The transport equation is solved using operator splitting, with the discontinuous finite element method (DFE) for discretization of the advective term. A slope limiting procedure for DFE avoids numerical instabilities but creates very limited numerical dispersion for high Peclet numbers. An implicit finite differences scheme (FD) is used for the dispersive term.The unsaturated flow and transport model (Wamos-T) is applied to a variety of rigorous problems including transient flow, heterogeneous medium and abrupt variations of velocity in magnitude and direction due to time-varying boundary conditions. It produces accurate and mass-conservative solutions for a very large range of grid Peclet numbers. The Wamos-T model is a good and robust alternative for the simulation of mass transport in unsaturated domain.     

Computation of the interfacial area for two-fluid porous medium systems

We develop a method to compute interfacial areas from three-dimensional digital representations of multiphase systems. We approximate the interfaces with the isosurface generated by the standard marching-cube algorithm from the discrete phase distribution. We apply this approach to two-fluid pore-scale simulations by (1) simulating a random packing of spheres that obeys the grain-size distribution and porosity of an experimental porous medium system, and (2) using a previously developed pore-morphology-based model in order to predict the phase distribution for a water-wet porous medium that undergoes primary drainage. The predicted primary drainage curve and interfacial areas are in good agreement with the experimental values reported in the literature, where interfacial areas were measured using interfacial tracers. The energy dissipation during Haines jumps is significant: thus, the mechanical work done on the system is not completely converted into surface energy, and interfacial areas may not be deduced from the primary drainage curve.     

A review and numerical assessment of the random walk particle tracking method

We review the basic mathematical concepts of random walk particle tracking (RWPT) and its advantages and limitations. Three different numerical approaches to overcome the local mass conservation problem of the random walk methodology are examined: (i) the interpolation method, (ii) the reflection principle, and (iii) the generalized stochastic differential equations (GSDE). Analytical solutions of the spatial moments for a two-layer system are compared to model predictions using the different techniques and results demonstrate that the interpolation method reproduces correctly average velocity, but fails to reproduce macrodispersion at higher hydraulic conductivity contrasts between the two layers. On the contrary, the reflection principle and the GSDE approach underestimate average velocity, but reproduce macrodispersion better for high contrasts. The different behavior is based on an artificial shift of mass for increasing heterogeneities for the GSDE approach and the reflection principle, whereas the interpolation method suffers from the smoothing of the dispersion tensor. The behavior of these approaches was furthermore analyzed in two-dimensional heterogeneous hydraulic conductivity fields, which are characterized by different random function models. Solute transport was simulated correctly by all three approaches for the reference fields having Gaussian structures or non-Gaussian structures with an isotropic spatial correlation, even for a variance of the natural log of hydraulic conductivity of sigma(lnK)(2)=4. However, for the non-Gaussian model with a strong anisotropic spatial correlation and a variance of sigma(lnK)(2)=2 and higher, the interpolation method was the only technique modelling solute transport correctly. Furthermore, we discuss the general applicability of random walk particle tracking in comparison to the standard transport models and conclude that in advection-dominated problems using a high spatial discretization or requiring the performance of many model runs, RWPT represents a good alternative for modelling contaminant transport.     

Modeling solute transport in one-dimensional homogeneous and heterogeneous soil columns with continuous time random walk

In this paper, we used the continuous time random walk (CTRW) framework to characterize the transport process in 1250-cm long one-dimensional homogenous and heterogeneous soil columns at the experiments conducted by Huang et al. [Huang, K., Toride, N., van Genuchten, M.Th., 1995. Experimental investigation of solute transport in large, homogeneous and heterogeneous, saturated soil columns. Trans. Porous Media. 18, 283-302]. The transport process was also simulated by using the advection-dispersion equation (ADE) and the spatial fractional advection-dispersion equation (FADE) for comparison. In the homogeneous soil column, the non-Fickian behavior is found at the distances less than 1000cm with beta values larger than 1.60, but less than 2, and Fickian form transport is obtained at distances larger than 1000cm with beta values larger than 2. In the heterogeneous soil column, we found the most anomalous behavior at distances from 200cm to 700cm with beta values ranging from 0.894 to 0.958, and non-Fickian transport process is observed at distances larger than 800cm with beta values in the range between 1 and 1.3. More significant non-Fickian behavior is found for transport in the heterogeneous soil column than that in the homogeneous soil column. The CTRW fits to the breakthrough curves (BTCs) have lower values of root mean square error (RMSE) and higher values of determination coefficient (r(2)), with respect to the fits of ADE and FADE. The CTRW model also is better captures the full evolution of BTCs, and especially their tails.     

Non-Fickian dispersion in a single fracture

Solute transport in fractured rocks is of major interest in many applications, from the petroleum industry to ground water management. This work focuses on the dispersion process in a transparent replica of a real single fracture. The fracture exhibits strong changes in heterogeneity, with the first half very heterogeneous and the second half fairly homogeneous. Three models have been used to interpret the tracer experiments: the classical advection-dispersion equation (ADE), the continuous time random walk (CTRW), and the stratified model. The main goals were to test these models and to study possible correlations between fitting parameters and heterogeneities. As expected, the solution derived from the ADE equation appears to be unable to model long-time tailing behavior. On the other hand, the results confirm the CTRW robustness and the coefficient beta seems well correlated to heterogeneities. Finally, the stratified model is also able to describe non-Fickian dispersion. The parameters defined by this model are correlated to the heterogeneities of the fracture.     

Kinematic analysis of solute mass flows in rock fractures with spatially random parameters

Field data of physical properties in heterogeneous crystalline bedrock, like porosity and fracture aperture, is associated with uncertainty that can have a significant impact on the analysis of solute transport in rock fractures. Solutions to the central temporal moments of the residence time probability density function (PDF) are derived in a closed form for a solute Dirac pulse. The solutions are based on a model that takes into account advection along the fracture plane, diffusion into the rock matrix and sorption kinetics in the rock matrix. The most relevant rock properties including fracture aperture and several matrix properties as well as flow velocity are assumed to be spatially random along transport pathways. The mass transport is first solved in a general form along one-dimensional pathways, but the results can be extended to multi-dimensional flows simply by substituting the expected travel time for inert water parcels. Based on data obtained with rock samples taken at Asp? Hard Rock Laboratory in Sweden, the solutions indicate that the heterogeneity of the rock properties contributes to increasing significantly both the variance and the skewness of the residence time probability density function for a pulse travelling in a fracture. The Asp? data suggests that the bias introduced in the variance of the residence time PDF by neglecting the effect of heterogeneity of the rock properties on the radionuclide migration is very large for fractures thinner than a few tenths of a millimetre.     

Analytical model of solute transport by unsteady unsaturated gravitational infiltration

Penetration of reactive solute into a soil during a cycle of water infiltration and redistribution is investigated by deriving analytical closed form solutions for fluid flux, moisture content and contaminant concentration. The solution is developed for gravitational flow and advective transport and is applied to two scenarios of solute applications encountered in the applications: a finite pulse of solute dissolved in irrigation water and an instantaneous pulse broadcasted onto the soil surface. Through comparison to simulations of Richards' flow, capillary suction is shown to have contrasting effects on the upper and lower boundaries of the fluid pulse, speeding penetration of the wetting front and reducing the rate of drying. This leads to agreement between the analytical and numerical solutions for typical field and experimental conditions. The analytical solution is further incorporated into a stochastic column model of flow and transport to compute mean solute concentration in a heterogeneous field. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying stage. The mean concentration profiles match those of the Monte-Carlo simulations for capillary length scales typical of sandy soils.     

Using the multiple cell balance method to solve the problem of two-dimensional groundwater flow and contaminant transport with nonequilibrium sorption

The problem of large-scale contamination of groundwater by relatively low levels of organic contaminants is most frequently addressed by extracting and treating the impacted groundwater. This pump-and-treat strategy is often unsuccessful because of difficulties encountered in recovering the contaminants from relatively immobile zones within the porous medium. These zones can exist at the particle scale, as intraparticle or intra-aggregate porosity, and at the larger scales, as low-permeability layers or lenses interspersed in substantially more permeable layers. This work focuses on achieving an efficient numerical solution to a system of groundwater flow and contaminant transport equations that sufficiently captures the dynamics of slow desorption in a two-dimensional porous medium. The conceptual model and governing equations are presented. A numerical method for solving the governing equations, the upstream-weighted, multiple cell balance (UMCB) method, is proposed. The UMCB algorithm has been employed previously for the case of solute transport with equilibrium sorption, and is extended here to the nonequilibrium case. The approach employs a finite-element basis function and a finite-difference local mass balance, and is designed to reduce computational and storage requirements, while minimizing the mass balance error. The computational grid is formed by division of the flow domain into triangular elements. An invented node at the center of each element divides the element into three subtriangular regions. By linking the center of each triangular element and the mid-point of each elemental side, a multiangular region, referred to as an exclusive subdomain, is defined. The discretized system of governing equations is derived from the integral form that describes the mass balance in the exclusive subdomain of each node. The paper details the application of the numerical method, and demonstrates that the method is reasonably accurate and computationally efficient for a two-dimensional domain subject to nonequilibrium sorption.     

Pore-scale modeling of dispersion in disordered porous media

We employ a direct pore-level model of incompressible flow that uses the modified moving particle semi-implicit (MMPS) method. The model is capable of simulating both unsteady- and steady-state flow directly in microtomography images of naturally-occurring porous media. We further develop this model to simulate solute transport in disordered porous media. The governing equations of flow and transport at the pore level, i.e., Navier-Stokes and convection-diffusion, are solved directly in the pore space mapped by microtomography techniques. Three naturally-occurring sandstones are studied in this work. We verify the accuracy of the model by comparing the computed longitudinal dispersion coefficients against the experimental data for a wide range of Peclet numbers, i.e., 5×10(-2)相似文献   

Travel time and trajectory moments of conservative solutes in two-dimensional convergent flows

We address advective transport of a solute traveling toward a single pumping well in a two-dimensional randomly heterogeneous aquifer. The two random variables of interest are the trajectory followed by an individual particle from the injection point to the well location and the particle travel time under steady-state conditions. Our main objective is to derive the predictors of trajectory and travel time and the associated uncertainty, in terms of their first two statistical moments (mean and variance). We consider a solute that undergoes mass transfer between a mobile and an immobile zone. Based on Lawrence et al. [Lawrence, A.E., Sánchez-Vila, X., Rubin, Y., 2002. Conditional moments of the breakthrough curves of kinetically sorbing solute in heterogeneous porous media using multirate mass transfer models for sorption and desorption. Water Resour. Res. 38 (11), 1248, doi:10.1029/2001WR001006.], travel time moments can be written in terms of those of a conservative solute times a deterministic quantity. Moreover, the moments of solute particles trajectory do not depend on mass transfer processes. The resulting mean and variance of travel time and trajectory for a conservative species can be written as functions of the first, second moments and cross-moments of trajectory and velocity components. The equations are developed from a consistent second order expansion in sigmaY (standard deviation of the natural logarithm of hydraulic conductivity). Our solution can be completely integrated with the moment equations of groundwater flow of Guadagnini and Neuman [Guadagnini, A., Neuman, S.P., 1999a. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 1. Theory and computational approach. Water Resour. Res. 35(10), 2999-3018.,Guadagnini, A., Neuman, S.P., 1999b. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 2. Computational examples. Water Resour. Res. 35(10), 3019-3039.], it is free of distributional assumptions regarding the log conductivity field, and formally includes conditioning. We present analytical expressions for the unconditional case by making use of the results of Riva et al. [Riva, M., Guadagnini, A., Neuman, S.P., Franzetti, S., 2001. Radial flow in a bounded randomly heterogeneous aquifer. Transport in Porous Media 45, 139-193.]. The quality of the solution is supported by numerical Monte Carlo simulations. Potential uses of this work include the determination of aquifer reclamation time by means of a single pumping well, and the demarcation of the region potentially affected by the presence of a contaminant in the proximity of a well, whenever the aquifer is very thin and Dupuit-Forchheimer assumption holds.     

Laboratory analog and numerical study of groundwater flow and solute transport in a karst aquifer with conduit and matrix domains

New mathematical and laboratory methods have been developed for simulating groundwater flow and solute transport in karst aquifers having conduits imbedded in a porous medium, such as limestone. The Stokes equations are used to model the flow in the conduits and the Darcy equation is used for the flow in the matrix. The Beavers–Joseph interface boundary conditions are adopted to describe the flow exchange at the interface boundary between the two domains. A laboratory analog is used to simulate the conduit and matrix domains of a karst aquifer. The conduit domain is located at the bottom of the transparent plexiglas laboratory analog and glass beads occupy the remaining space to represent the matrix domain. Water flows into and out of the two domains separately and each has its own supply and outflow reservoirs. Water and solute are exchanged through an interface between the two domains. Pressure transducers located within the matrix and conduit domains of the analog provide data that is processed and stored in digital format. Dye tracing experiments are recorded using time-lapse imaging. The data and images produced are analyzed by a spatial analysis program. The experiments provide not only hydraulic head distribution but also capture solute front images and mass exchange measurements between the conduit and matrix domains. In the experiment, we measure and record pressures, and quantify flow rates and solute transport. The results present a plausible argument that laboratory analogs can characterize groundwater water flow, solute transport, and mass exchange between the conduit and matrix domains in a karst aquifer. The analog validates the predictions of a numerical model and demonstrates the need of laboratory analogs to provide verification of proposed theories and the calibration of mathematical models.     

Simulation and analysis of solute transport in 2D fracture/pipe networks: the SOLFRAC program

The Time Domain Random Walk (TDRW) method has been recently developed by Delay and Bodin [Delay, F. and Bodin, J., 2001. Time domain random walk method to simulate transport by advection-dispersion and matrix diffusion in fracture networks. Geophys. Res. Lett., 28(21): 4051-4054.] and Bodin et al. [Bodin, J., Porel, G. and Delay, F., 2003c. Simulation of solute transport in discrete fracture networks using the time domain random walk method. Earth Planet. Sci. Lett., 6566: 1-8.] for simulating solute transport in discrete fracture networks. It is assumed that the fracture network can reasonably be represented by a network of interconnected one-dimensional pipes (i.e. flow channels). Processes accounted for are: (1) advection and hydrodynamic dispersion in the channels, (2) matrix diffusion, (3) diffusion into stagnant zones within the fracture planes, (4) sorption reactions onto the fracture walls and in the matrix, (5) linear decay, and (6) mass sharing at fracture intersections. The TDRW method is handy and very efficient in terms of computation costs since it allows for the one-step calculation of the particle residence time in each bond of the network. This method has been programmed in C++, and efforts have been made to develop an efficient and user-friendly software, called SOLFRAC. This program is freely downloadable at the URL (labo.univ-poitiers.fr/hydrasa/intranet/telechargement.htm). It calculates solute transport into 2D pipe networks, while considering different types of injections and different concepts of local dispersion within each flow channel. Post-simulation analyses are also available, such as the mean velocity or the macroscopic dispersion at the scale of the entire network. The program may be used to evaluate how a given transport mechanism influences the macroscopic transport behaviour of fracture networks. It may also be used, as is the case, e.g., with analytical solutions, to interpret laboratory or field tracer test experiments performed in single fractures.     

Prediction of contaminant transport in fractured carbonate aquifer types: a case study of the Permian Magnesian Limestone Group (NE England,UK)

Viruses and bacteria which are characterized by finite lives in the subsurface are rapidly transported via fractures and cavities in fractured and karst aquifers. Here, we demonstrate how the coupling of a robust outcrop characterization and hydrogeophysical borehole testing is essential for prediction of contaminant velocities and hence wellhead protection areas. To show this, we use the dolostones of the Permian Magnesian Limestone aquifer in NE England, where we incorporated such information in a groundwater flow and particle tracking model. Within this aquifer, flow in relatively narrow (mechanical aperture of ~?10^?1–1 mm) fractures is coupled with that in pipe cavities (~?0.20-m diameter) following normal faults. Karstic cavities and narrow fractures are hydraulically very different. Thus, the solutional features are represented within the model by a pipe network (which accounts for turbulence) embedded within an equivalent porous medium representing Darcian flowing fractures. Incorporation of fault conduits in a groundwater model shows that they strongly influence particle tracking results. Despite this, away from faulted areas, the effective flow porosity of the equivalent porous medium remains a crucial parameter. Here, we recommend as most appropriate a relatively low value of effective porosity (of 2.8?×?10^?4) based on borehole hydrogeophysical testing. This contrasts with earlier studies using particle tracking analyses on analogous carbonate aquifers, which used much higher values of effective porosity, typically ~?10² times higher than our value, resulting in highly non-conservative estimates of aquifer vulnerability. Low values of effective flow porosities yield modelled flow velocities ranging from ~?100 up to ~?500 m/day in un-faulted areas. However, the high fracturing density and presence of karstic cavities yield modelled flow velocities up to ~?9000 m/day in fault zones. The combination of such flow velocities along particle traces results in 400-day particle traces up to 8-km length, implying the need for large well protection areas and high aquifer vulnerability to slowly degrading contaminants.

     

The influence of mass transfer on solute transport in column experiments with an aggregated soil

The spreading of concentration fronts in dynamic column experiments conducted with a porous, aggregated soil is analyzed by means of a previously documented transport model (DFPSDM) that accounts for longitudinal dispersion, external mass transfer in the boundary layer surrounding the aggregate particles, and diffusion in the intra-aggregate pores. The data are drawn from a previous report on the transport of tritiated water, chloride, and calcium ion in a column filled with Ione soil having an average aggregate particle diameter of 0.34 cm, at pore water velocities from 3 to 143 cm/h. The parameters for dispersion, external mass transfer, and internal diffusion were predicted for the experimental conditions by means of generalized correlations, independent of the column data. The predicted degree of solute front-spreading agreed well with the experimental observations. Consistent with the aggregate porosity of 45%, the tortuosity factor for internal pore diffusion was approximately equal to 2. Quantitative criteria for the spreading influence of the three mechanisms are evaluated with respect to the column data. Hydrodynamic dispersion is thought to have governed the front shape in the experiments at low velocity, and internal pore diffusion is believed to have dominated at high velocity; the external mass transfer resistance played a minor role under all conditions. A transport model such as DFPSDM is useful for interpreting column data with regard to the mechanisms controlling concentration front dynamics, but care must be exercised to avoid confounding the effects of the relevant processes.     

Three-fluid retention in porous media involving water, PCE and air

A classical way to obtain three-fluid retention curves in porous media from measured two-fluid retention curves is based on the Leverett concept, which states that the total volumetric liquid content in a water-wet porous medium, containing water, a nonaqueous-phase liquid (NAPL) and air, is a function of the capillary pressure across the interface between the continuous NAPL and air. This functional relationship results from the assumed condition that in a three-fluid porous medium, the intermediate wetting fluid spreads over the water-air interface. Application of Leverett's concept may not be valid, however, for nonspreading NAPLs like perchloroethylene (PCE). This paper discusses measurements of both PCE-air and water-PCE-air retention curves using a long vertical column in conjunction with a dual-energy gamma radiation system. The data indicate that the Leverett concept was applicable only until a critical PCE saturation had been reached.