Impact of nonaqueous phase liquid (NAPL) source zone architecture on mass removal mechanisms in strongly layered heterogeneous porous media during soil vapor extraction

An existing multiphase flow simulator was modified in order to determine the effects of four mechanisms on NAPL mass removal in a strongly layered heterogeneous vadose zone during soil vapor extraction (SVE): a) NAPL flow, b) diffusion and dispersion from low permeability zones, c) slow desorption from sediment grains, and d) rate-limited dissolution of trapped NAPL. The impacts of water and NAPL saturation distribution, NAPL-type (i.e., free, residual, or trapped) distribution, and spatial heterogeneity of the permeability field on these mechanisms were evaluated. Two different initial source zone architectures (one with and one without trapped NAPL) were considered and these architectures were used to evaluate seven different SVE scenarios. For all runs, slow diffusion from low permeability zones that gas flow bypassed was a dominant factor for diminished SVE effectiveness at later times. This effect was more significant at high water saturation due to the decrease of gas-phase relative permeability. Transverse dispersion contributed to fast NAPL mass removal from the low permeability layer in both source zone architectures, but longitudinal dispersion did not affect overall mass removal time. Both slow desorption from sediment grains and rate-limited mass transfer from trapped NAPL only marginally affected removal times. However, mass transfer from trapped NAPL did affect mass removal at later time, as well as the NAPL distribution. NAPL flow from low to high permeability zones contributed to faster mass removal from the low permeability layer, and this effect increased when water infiltration was eliminated. These simulations indicate that if trapped NAPL exists in heterogeneous porous media, mass transfer can be improved by delivering gas directly to zones with trapped NAPL and by lowering the water content, which increases the gas relative permeability and changes trapped NAPL to free NAPL.     

Magnetic resonance imaging of nonaqueous phase liquid during soil vapor extraction in heterogeneous porous media

Soil vapor extraction (SVE) is commonly used to remediate nonaqueous phase liquids (NAPLs) from the vadose zone. This paper aims to determine the effect of grain size heterogeneity on the removal of NAPL in porous media during SVE. Magnetic resonance imaging (MRI) was used to observe and quantify the amount and location of NAPL in flow-through columns filled with silica gel grains. MRI is unique because it is nondestructive, allowing three-dimensional images to be taken of the phases as a function of space and time. Columns were packed with silica gel in three ways: coarse grains (250-550 microm) only, fine grains (32-63 microm) only, and a core of fine grains surrounded by a shell of coarse grains. Columns saturated with water were drained under a constant suction head, contaminated with decane, and then drained to different decane saturations. Each column was then continuously purged with water-saturated nitrogen gas and images were taken intermittently. Results showed that at residual saturation, a sharp volatilization front moved through the columns filled with either coarse-grain or fine-grain silica gel. In the heterogeneous columns, the volatilization front in the core lagged just behind the shell because gas flow was greater through the shell and decane in the core diffused outward to the shell. When decane saturation in the core was above residual saturation, decane volatilization occurred near the inlet, the relative decane saturation throughout the core dropped uniformly, and decane in the core flowed in the liquid phase to the shell to replenish volatilized decane. These results indicate that NAPL trapped in low-permeability zones can flow to replenish areas where NAPL is lost due to SVE. However, when residual NAPL saturation is reached, NAPL flow no longer occurs and diffusion limits removal from low-permeability zones.     

Mass flux from a non-aqueous phase liquid pool considering spontaneous expansion of a discontinuous gas phase

The partitioning of non-aqueous phase liquid (NAPL) compounds to a discontinuous gas phase results in the repeated spontaneous expansion, snap-off, and vertical mobilization of the gas phase. This mechanism has the potential to significantly affect the mass transfer processes that control the dissolution of NAPL pools by increasing the vertical transport of NAPL mass and increasing the total mass transfer rate from the surface of the pool. The extent to which this mechanism affects mass transfer from a NAPL pool depends on the rate of expansion and the mass of NAPL compound in the gas phase. This study used well-controlled bench-scale experiments under no-flow conditions to quantify for the first time the expansion of a discontinuous gas phase in the presence of NAPL. Air bubbles placed in glass vials containing NAPL increased significantly in volume, from a radius of 1.0 mm to 2.0 mm over 215 days in the presence of tetrachloroethene (PCE), and from a radius of 1.2 mm to 2.3 mm over 22 days in the presence of trans-1,2-dichloroethene (tDCE). A one-dimensional mass transfer model, fit to the experimental data, showed that this expansion could result in a mass flux from the NAPL pool that was similar in magnitude to the mass flux expected for the dissolution of a NAPL pool in a two-fluid (NAPL and water) system. Conditions favouring the significant effect of a discontinuous gas phase on mass transfer were identified as groundwater velocities less than ~0.01 m/day, and a gas phase that covers greater than ~10% of the pool surface area and is located within ~0.01 m of the pool surface. Under these conditions the mass transfer via a discontinuous gas phase is expected to affect, for example, efforts to locate NAPL source zones using aqueous concentration data, and predict the lifetime and risk associated with NAPL source zones in a way that is not currently included in the common conceptual models used to assess NAPL-contaminated sites.     

Effect of soil moisture dynamics on dense nonaqueous phase liquid (DNAPL) spill zone architecture in heterogeneous porous media

The amount, location, and form of NAPL in contaminated vadose zones are controlled by the spatial distribution of water saturation and soil permeability, the NAPL spill scenario, water infiltration events, and vapor transport. To evaluate the effects of these processes, we used the three-phase flow simulator STOMP, which includes a new permeability-liquid saturation-capillary pressure (k-S-P) constitutive model. This new constitutive model considers three NAPL forms: free, residual, and trapped. A 2-D vertical cross-section with five stratigraphic layers was assumed, and simulations were performed for seven cases. The conceptual model of the soil heterogeneity was based upon the stratigraphy at the Hanford carbon tetrachloride (CT) spill site. Some cases considered co-disposal of NAPL with large volumes of wastewater, as also occurred at the Hanford CT site. In these cases, the form and location of NAPL were most strongly influenced by high water discharge rates and NAPL evaporation to the atmosphere. In order to investigate the impact of heterogeneity, the hydraulic conductivity within the lower permeability layer was modeled as a realization of a random field having three different classes. For six extreme cases of 100 realizations, the CT mass that reached the water table varied by a factor of two, and was primarily controlled by the degree of lateral connectivity of the low conductivity class within the lowest permeability layer. The grid size at the top boundary had a dramatic impact on NAPL diffusive flux just after the spill event when the NAPL was present near the ground surface. NAPL evaporation with a fine grid spacing at the top boundary decreased CT mass that reached the water table by 74%, compared to the case with a coarse grid spacing, while barometric pumping had a marginal effect for the case of a continuous NAPL spill scenario considered in this work. For low water infiltration rate scenarios, the distribution of water content prior to a NAPL spill event decreased CT mass that reached the water table by 98% and had a significant impact on the formation of trapped NAPL. For all cases simulated, use of the new constitutive model that allows the formation of residual NAPL increased the amount of NAPL retained in the vadose zone. Density-driven advective gas flow from the ground surface controlled vapor migration in strongly anisotropic layers, causing NAPL mass flux to the lower layer to be reduced. These simulations indicate that consideration of the formation of residual and trapped NAPLs and dynamic boundary conditions (e.g., areas, rates, and periods of different NAPL and water discharge and fluctuations of atmospheric pressure) in the context of full three-phase flow are needed, especially for NAPL spill events at the ground surface. In addition, NAPL evaporation, density-driven gas advection, and NAPL vertical movement enhanced by water flow must be considered in order to predict NAPL distribution and migration in the vadose zone.     

Non-aqueous phase liquid spreading during soil vapor extraction

Many non-aqueous phase liquids (NAPLs) are expected to spread at the air-water interface, particularly under non-equilibrium conditions. In the vadose zone, this spreading should increase the surface area for mass transfer and the efficiency of volatile NAPL recovery by soil vapor extraction (SVE). Observations of spreading on water wet surfaces led to a conceptual model of oil spreading vertically above a NAPL pool in the vadose zone. Analysis of this model predicts that spreading can enhance the SVE contaminant recovery compared to conditions where the liquid does not spread. Experiments were conducted with spreading volatile oils hexane and heptane in wet porous media and capillary tubes, where spreading was observed at the scale of centimeters. Within porous medium columns up to a meter in height containing stagnant gas, spreading was less than ten centimeters and did not contribute significantly to hexane volatilization. Water film thinning and oil film pinning may have prevented significant oil film spreading, and thus did not enhance SVE at the scale of a meter. The experiments performed indicate that volatile oil spreading at the field scale is unlikely to contribute significantly to the efficiency of SVE.     

Tracer test for the measurement of gas diffusion and non-aqueous phase liquid (NAPL) saturation in soil

During soil bioremediation, the diffusion of oxygen into the soil is an important prerequisite for aerobic biodegradation, and the decrease of petroleum products is the ultimate goal. Both processes need to be monitored. The aim of this work was to develop a gas tracer test that yields information on both, gas diffusion and residual saturation with non-aqueous phase liquids (NAPLs) in unsaturated soil heaps. One conservative tracer (methane) and 4 partitioning gas tracers (diethylether, methyl tert-butyl ether, chloroform and n-heptane) were injected as vapors into laboratory columns filled with unsaturated sand with increasing NAPL saturation. Breakthrough curves of gaseous compounds were measured at two points and compared to analytical solutions of an analytical diffusive-reactive transport equation. By fitting of methane data, robust results for effective diffusivity (tortuosity) were obtained. NAPL saturation was most accurately measured by the moderately water soluble tracers (ethers and chloroform). The hydrophobic tracer n-heptane did not partition into water-immersed NAPL. An easy and accurate way to assess air-NAPL partitioning constants from gas chromatography retention times is furthermore reported. It is concluded that gas tracer tests have the potential for measuring two important properties in soil bioremediation systems easily and quickly.     

Investigation of surfactant-enhanced mass removal and flux reduction in 3D correlated permeability fields using magnetic resonance imaging

Magnetic resonance imaging (MRI) was used to visualize the NAPL source zone architecture before and after surfactant-enhanced NAPL dissolution in three-dimensional (3D) heterogeneously packed flowcells characterized by different longitudinal correlation lengths: 2.1 cm (aquifer 1) and 1.1 cm (aquifer 2). Surfactant flowpaths were determined by imaging the breakthrough of a paramagnetic tracer (MnCl(2)) analyzed by the method of moments. In both experimental aquifers, preferential flow occurred in high permeability materials with low NAPL saturations, and NAPL was preferentially removed from the top of the aquifers with low saturation. Alternate flushing with water and two surfactant pulses (5-6 pore volumes each) resulted in approximately 63% of NAPL mass removal from both aquifers. However, overall reduction in mass flux (Mass Flux 1) exiting the flowcell was lower in aquifer 2 (68%) than in aquifer 1 (81%), and local effluent concentrations were found to increase by as high as 120 times at local sampling ports from aquifer 2 after surfactant flushing. 3D MRI images of NAPL revealed that NAPL migrated downward and created additional NAPL source zones in previously uncontaminated areas at the bottom of the aquifers. The additional NAPL source zones were created in the direction transverse to flow in aquifer 2, which explains the higher mass flux relative to aquifer 1. Analysis using a total trapping number indicates that mobilization of NAPL trapped in the two coarsest sand fractions is possible when saturation is below 0.5 and 0.4, respectively. Results from this study highlight the potential impacts of porous media heterogeneity and NAPL source zone architecture on advanced in-situ flushing technologies.     

Plant aided bioremediation in the vadose zone: model development and applications

Phytoremediation has the potential to enhance clean up of land contaminated by various pollutants. A mathematical model that includes a two-fluid phase flow model of water flow as well as a two-region soil model of contaminant reactions was developed and applied to various bioremediation scenarios in the unsaturated zone, especially to plant-aided bioremediation. To investigate model behavior and determine the main parameters and mechanisms that affect bioremediation in unplanted and planted soils, numerical simulations of theoretical scenarios were conducted before applying the model to field data. It is observed from the results that parameters affecting the contaminant concentration in the water phase, such as aqueous solubility, the octanol-water partition coefficient, and organic carbon content of the soil controlled the contaminant fate in the vadose zone. Simulation using the developed model also characterized the fate and transport of the contaminants both in planted and unplanted soils satisfactorily for field applications. Although phytoremediation has the potential for remediation of contaminated soils, results from both modeling and field studies suggested that plants may not always enhance the remediation efficiency when the soil already has a high microbial concentration, when the contaminant bioavailability is low, or when the overall reaction is mass transfer-limited. Therefore, other steps to increase contaminant bioavailability are needed in phytoremediation applications; natural purification mechanisms such as aging, volatilization, and natural bioremediation should be considered to maximize the plant effect and minimize the cost.     

Parameters that control the cleanup of fractured permeable aquifers

This study develops a modeling approach for simulating and evaluating entrapped light nonaqueous-phase liquid (light NAPL-LNAPL) dissolution and transport of the solute in a fractured permeable aquifer (FPA). The term FPA refers to an aquifer made of porous blocks of high permeability that embed fractures. The fracture network is part of the domain characterized by high permeability and negligible storage. Previous studies show that sandstone aquifers often represent FPAs. The basic model developed in this study is a two-dimensional (2-D) model of permeable blocks that embed oblique equidistant fractures with constant aperture and orientation. According to this model, two major parameters govern NAPL dissolution and transport of the solute. These parameters are: 1) the dimensionless interphase mass transfer coefficient, K(f0), and 2) the mobility number, N(M0). These parameters represent measures of heterogeneity affecting flow, NAPL dissolution, and transport of the solute in the domain. The parameter K(f0) refers to the rate at which organic mass is transferred from the NAPL into the water phase. The parameter N(M0) represents the ratio of flow through the porous blocks to flow through the fracture network in regions free of entrapped NAPL. It also provides a measure of groundwater flow bypassing regions contaminated by entrapped NAPL. In regions contaminated by entrapped NAPL our simulations have often indicated very low permeability of the porous blocks, enabling a significant increase of the fracture flow at the expense of the permeable block flow. Two types of constitutive relationships also affect the rate of FPA cleanup: 1) the relationship between the saturation of the entrapped NAPL and the permeability of the porous blocks, and 2) the relationships representing effects of the entrapped NAPL saturation and the permeable block flow velocity on rates of interphase mass transfer. This study provides basic tools for evaluating the characteristics of pump-and-treat cleanup of FPAs by referring to sets of parameters and constitutive relationships typical of FPAs. The numerical simulations carried out in this study show that at high initial saturation of the entrapped NAPL, during initial stages of the FPA cleanup the contaminant concentration increases, but later it decreases. This phenomenon originates from significant groundwater bypassing the NAPL entrapped in the permeable blocks via the fracture network.     

The effects of surfactant formulation on nonequilibrium NAPL solubilization

Surfactant-enhanced aquifer remediation (SEAR) involves the injection of surfactant solutions into aquifers contaminated with nonaqueous phase liquids (NAPL). Batch and column experiments were used to assess the effect of surfactant formulation on the rate of NAPL solubilization. The experimental variables were surfactant type, surfactant concentration, electrolyte concentration, and cosolvent concentration. Model equations were proposed and solved to describe solubilization under the conditions of each type of experiment. Using these models, a solubilization rate constant, kappa(b), and an overall mass transfer rate coefficient, kappa, were estimated from the batch and column experiments, respectively. The solubilization rate constant was consistently sensitive to surfactant type, surfactant concentration, and electrolyte concentration. The estimated solubilization rate constants varied over two orders of magnitude. The results of the column experiments also were sensitive to the surfactant formulation. Variations in the fitted mass transfer rate coefficient parameter, beta(0), were related to variations in the surfactant formulations. A comparison between the results of the batch and column experiments yields an apparent relationship between beta(0) and kappa(b). This relationship suggests that the mass transfer rate coefficient is directly related to the formulation of the surfactant solution.     

Characterization of pore scale NAPL morphology in homogeneous sands as a function of grain size and NAPL dissolution

In this study, we investigate pore scale morphology of nonaqueous phase liquids (NAPLs) trapped in different pore sizes using tracer techniques. Specific interfacial area and saturation of NAPL trapped in homogeneous sands were measured using the interfacial and partitioning tracer techniques. The observed NAPL-water interfacial areas increased in a log-linear fashion with decreasing sand grain size, but showed no clear trend with residual NAPL saturation formed in the various grain sizes. The measured values were used to calculate the NAPL morphology index, which characterizes the spatial NAPL distribution within the pore space. The NAPL morphology indices, increased exponentially with decreasing grain size, indicating that the NAPL becomes smaller, but more blobs. For a fixed grain size, the specific interfacial area and saturation of the NAPL were measured following changes caused by dissolution using alcohol. The observed interfacial areas showed a decrease linearly as a function of the NAPL saturation.     

Hot water flushing for immiscible displacement of a viscous NAPL

Thermal remediation techniques, such as hot water flooding, are emerging technologies that have been proposed for the removal of nonaqueous phase liquids (NAPLs) from the subsurface. In this study a combined laboratory and modeling investigation was conducted to determine if hot water flooding techniques would improve NAPL mass removal compared to ambient temperature water flushing. Two experiments were conducted in a bench scale two-dimensional sandbox (55 cmx45 cmx1.3 cm) and NAPL saturations were quantified using a light transmission apparatus. In these immiscible displacement experiments the aqueous phase, at 22 degrees C and 50 degrees C, displaced a zone with initial NAPL saturations on the order of 85%. The interfacial tension and viscosity of the selected light NAPL, Voltesso 35, are strongly temperature-dependent. Experimental results suggest that hot water flooding reduced the size of the high NAPL saturation zone, in comparison to the cold water flood, and yielded greater NAPL mass recovery (75% NAPL removal vs. 64%). Hot water flooding did not, however, result in lower residual NAPL saturations. A numerical simulator was modified to include simultaneous flow of water and organic phases, energy transport, temperature and pressure. Model predictions of mass removal and NAPL saturation profiles compared well with observed behavior. A sensitivity analysis indicates that the utility of hot water flooding improves with the increasing temperature dependence of NAPL hydraulic properties.     

Radon as a naturally occurring tracer for the assessment of residual NAPL contamination of aquifers

The noble gas radon has a strong affinity to non-aqueous phase-liquids (NAPLs). That property makes it applicable as naturally occurring partitioning tracer for assessing residual NAPL contamination of aquifers. In a NAPL contaminated aquifer, radon dissolved in the groundwater partitions preferably into the NAPL. The magnitude of the resulting radon deficit in the groundwater depends on the NAPL-specific radon partition coefficient and on the NAPL saturation of the pore space. Hence, if the partition coefficient is known, the NAPL saturation is attainable by determination of the radon deficit. After a concise discussion of theoretical aspects regarding radon partitioning into NAPL, related experimental data and results of a field investigation are presented. Aim of the laboratory experiments was the determination of radon partition coefficients of multi-component NAPLs of environmental concern. The on-site activities were carried out in order to confirm the applicability of the "radon method" under field conditions.     

Volatilization of 1,2-dibromo-3-chloropropane (DBCP) from soils.

The volatilization of DBCP from soils, as affected by the soil characteristics and application techniques, was studied in a laboratory experiment. The volatilization rate of DBCP applied in water was higher from sandy and silty loam soils than from clay soil. Water added after DBCP application acted as a soil cover, decreasing the volatilization rate. The results obtained with DBCP application in hexane to air-dry soils, indicate that adsorption could be an important factor in reducing the volatilization losses. Diffusion coefficients were calculated from the volatilization parameters, by using a simplified relationship between volatilization losses and diffusion through soil.     

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.     

Analysis of a gas-phase partitioning tracer test conducted in an unsaturated fractured-clay formation

The gas-phase partitioning tracer method was used to estimate non-aqueous phase liquid (NAPL), water, and air saturations in the vadose zone at a chlorinated-solvent contaminated field site in Tucson, AZ. The tracer test was conducted in a fractured-clay system that is the confining layer for the underlying regional aquifer. Three suites of three tracers were injected into wells located 14, 24, and 24 m from a single, central extraction well. The tracers comprised noble gases (traditionally thought to be nonsorbing), alkanes (primarily water partitioning), perfluorides (primarily NAPL partitioning), and halons (both NAPL and water partitioning). Observations of vacuum response were consistent with flow in a fractured system. The halon tracers exhibited the greatest amount of retardation, and helium and the perfluoride tracers the least. The alkane tracers were unexpectedly more retarded than the perfluoride tracers, indicating low NAPL saturations and high water saturations. An NAPL saturation of 0.01, water saturation of 0.215, and gas saturation of 0.775 was estimated based on analysis of the suite of tracers comprising helium, perfluoromethylcyclohexane and dibromodifluoromethane, which was considered to be the most robust set. The estimated saturations compare reasonably well to independently determined values.     

Volatilization of 1,2‐dibromo‐3‐chloropropane (DBCP) from soils

Abstract

The volatilization of DBCP from soils, as affected by the soil characteristics and application techniques, was studied in a laboratory experiment. The volatilization rate of DBCP applied in water was higher from sandy and silty loam soils than from clay soil. Water added after DBCP application acted as a soil cover, decreasing the volatilization rate. The results obtained with DBCP application in hexane to air‐dry soils, indicate that adsorption could be an important factor in reducing the volatilization losses.

Diffusion coefficients were calculated from the volatilization parameters, by using a simplified relationship between volatilization losses and diffusion through soil.     

Multiphase flow and transport caused by spontaneous gas phase growth in the presence of dense non-aqueous phase liquid

Disconnected bubbles or ganglia of trapped gas may occur below the top of the capillary fringe through a number of mechanisms. In the presence of dense non-aqueous phase liquid (DNAPL), the disconnected gas phase experiences mass transfer of dissolved gases, including volatile components from the DNAPL. The properties of the gas phase interface can also change. This work shows for the first time that when seed gas bubbles exist spontaneous gas phase growth can be expected to occur and can significantly affect water-gas-DNAPL distributions, fluid flow, and mass transfer. Source zone behaviour was observed in three different experiments performed in a 2-dimensional flow cell. In each case, a DNAPL pool was created in a zone of larger glass beads over smaller glass beads, which served as a capillary barrier. In one experiment effluent water samples were analyzed to determine the vertical concentration profile of the plume above the pool. The experiments effectively demonstrated a) a cycle of spontaneous gas phase expansion and vertical advective mobilization of gas bubbles and ganglia above the DNAPL source zone, b) DNAPL redistribution caused by gas phase growth and mobilization, and c) that these processes can significantly affect mass transport from a NAPL source zone.     

DNAPL source depletion: linking architecture and flux response

The relationship between dense non-aqueous phase liquid (DNAPL) mass reduction and contaminant mass flux was investigated experimentally in four model source zones. The flow cell design for the experiments featured a segmented extraction well that allowed for analysis of spatially resolved flux information. This flux information was coupled with image analysis of the NAPL spatial distribution to investigate the relationship between flux and the up-gradient NAPL architecture. Results indicate that in the systems studied, the relationship between DNAPL mass reduction and contaminant mass flux was primarily controlled by the NAPL architecture. A specific definition of NAPL architecture was employed where the source zone is resolved into a collection of streamtubes with spatial variability in NAPL saturation along each streamtube integrated and transformed into an effective NAPL content for each streamtube. The distribution of NAPL contents among the streamtubes (NAPL architecture) controlled dissolution dynamics. Two simplified models, a streamtube model and an effective Damkohler number model, were investigated for their ability to simulate dissolution dynamics.     

A proposed model to include a residual NAPL saturation in a hysteretic capillary pressure-saturation relationship

A residual non-aqueous phase liquid (NAPL) present in the vadose zone can act as a contaminant source for many years as the compounds of concern partition to infiltrating groundwater and air contained in the soil voids. Current pressure-saturation-relative permeability relationships do not include a residual NAPL saturation term in their formulation. This paper presents the results of series of two- and three-phase pressure cell experiments conducted to evaluate the residual NAPL saturation and its impact on the pressure-saturation relationship. A model was proposed to incorporate a residual NAPL saturation term into an existing hysteretic three-phase parametric model developed by Parker and Lenhard [Water Resour. Res. 23(12) (1987) 2187], Lenhard and Parker [Water Resour. Res. 23(12) (1987) 2197] and Lenhard [J. Contam. Hydrol. 9 (1992) 243]. The experimental results indicated that the magnitude of the residual NAPL saturation was a function of the maximum total liquid saturation reached and the water saturation. The proposed model to incorporate a residual NAPL saturation term is similar in form to the entrapment model proposed by Parker and Lenhard, which was based on an expression presented by Land [Soc. Pet. Eng. J. (June 1968) 149].