A constitutive model for air-NAPL-water flow in the vadose zone accounting for immobile, non-occluded (residual) NAPL in strongly water-wet porous media

A hysteretic constitutive model describing relations among relative permeabilities, saturations, and pressures in fluid systems consisting of air, nonaqueous-phase liquid (NAPL), and water is modified to account for NAPL that is postulated to be immobile in small pores and pore wedges and as films or lenses on water surfaces. A direct outcome of the model is prediction of the NAPL saturation that remains in the vadose zone after long drainage periods (residual NAPL). Using the modified model, water and NAPL (free, entrapped by water, and residual) saturations can be predicted from the capillary pressures and the water and total-liquid saturation-path histories. Relations between relative permeabilities and saturations are modified to account for the residual NAPL by adjusting the limits of integration in the integral expression used for predicting the NAPL relative permeability. When all of the NAPL is either residual or entrapped (i.e., no free NAPL), then the NAPL relative permeability will be zero. We model residual NAPL using concepts similar to those used to model residual water. As an initial test of the constitutive model, we compare predictions to published measurements of residual NAPL. Furthermore, we present results using the modified constitutive theory for a scenario involving NAPL imbibition and drainage.     

Wettability hysteresis and its implications for DNAPL source zone distribution

Subsurface heterogeneity at sites contaminated with nonaqueous phase liquids (NAPLs) reduces the effectiveness of traditional remediation measures. One cause may be the increased proportion of NAPL that is hydraulically isolated due to capillary trapping in heterogeneously-wetted materials. This study examines the wettability of ten materials, ranging from minerals, such as calcite and dolomite, to carbonaceous materials, such shale and coal, in air and water, NAPL and air, and NAPL and water systems. The wettability differed depending on which phase the solid material was initially immersed in: the less crystalline solids, if initially contacted by water were water-wet, but if initially contacted by NAPL were NAPL-wet. This difference, termed here wettability hysteresis, was observed for a suite of halogenated NAPLs and was independent of equilibration time. The degree of wettability hysteresis was greatest in the NAPL and water systems, with the magnitude of the difference increasing with the carbonaceous materials. Since the degree of capillary trapping in subsurface materials is related to wettability, the phenomenon of wettability hysteresis suggests that system history is a factor that may increase the heterogeneity of NAPL source zones.     

The effect of changes in surface wettability on two-phase saturated flow in horizontal replicas of single natural fractures

By using translucent epoxy replicas of natural single fractures, it is possible to optically measure aperture distribution and directly observe NAPL flow. However, detailed characterization of epoxy reveals that it is not a sufficiently good analogue to natural rock for many two-phase flow studies. The surface properties of epoxy, which is hydrophobic, are quite unlike those of natural rock, which is generally assumed to be hydrophilic. Different surface wettabilities result in dramatically different two-phase flow behavior and residual distributions. In hydrophobic replicas, the NAPL flows in well-developed channels, displacing water and filling all of the pore space. In hydrophilic replicas, the invading NAPL is confined to the largest aperture pathways and flow frequently occurs in pulses, with no limited or no stable channel development, resulting in isolated blobs with limited accessible surface area. The pulsing and channel abandonment behaviors described are significantly different from the piston-flow frequently assumed in current modeling practice. In addition, NAPL never achieved total saturation in hydrophilic models, indicating that significantly more than a monolayer of water was bound to the model surface. Despite typically only 60-80% NAPL saturation, there was generally good agreement between theoretically calculated Young-Laplace aperture invasion boundaries and the observed minimum apertures invaded. The key to determining whether surface wettability is negligible, or not, lies in accurate characterization of the contaminant-geologic media system under study. As long as the triple-point contact angle of the system is low (<20 degrees), the assumption of perfect water wettability is not a bad one.     

Large-scale effects on resistivity index of porous media

The estimation of humidity in the unsaturated zone of soils and NAPL saturation in contaminated aquifers may be based on the interpretation of electrical resistivity index logs. In the present work, concepts of the theory of the two-phase flow in pore networks are employed to interpret the form of the equilibrium and dynamic resistivity index curves of large porous samples. A resistivity cell is constructed to measure the capillary and electrical properties of large samples of unconsolidated porous media. The drainage capillary pressure and resistivity index curves of a sand column are measured by using the micropore membrane (porous plate) method, where a 0.5% wt/vol NaCl aqueous solution is displaced by n-dodecane. The dynamic resistivity index curves are measured by using the continuous injection technique for various orientations of the sand column. Based on concepts of the two-phase flow theory, concerning the dominant displacement growth pattern in a pore network and arising from the cooperative effects of capillary, buoyancy, and viscous forces, approximate relationships are developed for the resistivity index and saturation exponent as functions of the water saturation. The saturation exponent decreases as the displacement advances and the fluid distribution across the sand column tends to be homogenized after oil breakthrough. Both the resistivity index and saturation exponent increase as the displacement pattern tends to become compact and stable. In the destabilized flow pattern, as the Bond number decreases, the resistivity index may increase respectably within a narrow range of values of the Bond number. This happens when the thickness of the unstable capillary finger exceeds the lateral dimension of the porous sample and becomes a fractal percolation cluster. The saturation exponent becomes almost constant and independent of water saturation only over the destabilized displacement pattern at high values of the Bond number.     

Scaling of spontaneous imbibition data with wettability included

Wettability is a dominant parameter governing spontaneous imbibition. However less attention has been paid to the effect of wettability on the scaling of spontaneous imbibition data. Actually few models can include wettability in scaling of spontaneous imbibition data. To this end, a scaling model has been developed for NAPL (oil)-saturated porous media with different wettability based on the fluid flow mechanisms in porous media. Relative permeability, capillary pressure, initial water saturation, and wettability are considered in the scaling model. Theoretically this scaling model is suitable for both cocurrent and countercurrent spontaneous imbibition. The experimental data of countercurrent spontaneous water imbibition at different wettability cannot be scaled using the frequently used scaling model but can be scaled satisfactorily using the scaling model developed in this study. An analytical solution to the relationship between recovery and imbibition time for linear spontaneous imbibition has also been derived in the case in which gravity is ignored. The analytical solution predicts a linear correlation between the recovery by spontaneous water imbibition and the square root of imbibition time, which has been verified against experimental data.     

The effect of changes in surface wettability on two-phase saturated flow in horizontal replicas of single natural fractures

By using translucent epoxy replicas of natural single fractures, it is possible to optically measure aperture distribution and directly observe NAPL flow. However, detailed characterization of epoxy reveals that it is not a sufficiently good analogue to natural rock for many two-phase flow studies. The surface properties of epoxy, which is hydrophobic, are quite unlike those of natural rock, which is generally assumed to be hydrophilic. Different surface wettabilities result in dramatically different two-phase flow behavior and residual distributions. In hydrophobic replicas, the NAPL flows in well-developed channels, displacing water and filling all of the pore space. In hydrophilic replicas, the invading NAPL is confined to the largest aperture pathways and flow frequently occurs in pulses, with no limited or no stable channel development, resulting in isolated blobs with limited accessible surface area. The pulsing and channel abandonment behaviors described are significantly different from the piston-flow frequently assumed in current modeling practice. In addition, NAPL never achieved total saturation in hydrophilic models, indicating that significantly more than a monolayer of water was bound to the model surface. Despite typically only 60–80% NAPL saturation, there was generally good agreement between theoretically calculated Young–Laplace aperture invasion boundaries and the observed minimum apertures invaded. The key to determining whether surface wettability is negligible, or not, lies in accurate characterization of the contaminant-geologic media system under study. As long as the triple-point contact angle of the system is low (< 20°), the assumption of perfect water wettability is not a bad one.     

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

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

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.     

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.     

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.     

A functional relation for field-scale nonaqueous phase liquid dissolution developed using a pore network model

A pore network model with cubic chambers and rectangular tubes was used to estimate the nonaqueous phase liquid (NAPL) dissolution rate coefficient, Kdissai, and NAPL/water total specific interfacial area, ai. Kdissai was computed as a function of modified Peclet number (Pe') for various NAPL saturations (SN) and ai during drainage and imbibition and during dissolution without displacement. The largest contributor to ai was the interfacial area in the water-filled corners of chambers and tubes containing NAPL. When Kdissai was divided by ai, the resulting curves of dissolution coefficient, Kdiss versus Pe' suggested that an approximate value of Kdiss could be obtained as a weak function of hysteresis or SN. Spatially and temporally variable maps of Kdissai calculated using the network model were used in field-scale simulations of NAPL dissolution. These simulations were compared to simulations using a constant value of Kdissai and the empirical correlation of Powers et al. [Water Resour. Res. 30(2) (1994b) 321]. Overall, a methodology was developed for incorporating pore-scale processes into field-scale prediction of NAPL dissolution.     

Impact of edible oil injection on the permeability of aquifer sands

Recent laboratory and field studies have shown that food-grade edible oils can be injected into the subsurface for installation of in-situ permeable reactive barriers. However to be effective, the oil must be distributed out away from the oil injection points without excessive permeability loss. In this work, we examine the distribution of soybean oil in representative aquifer sediments as non-aqueous phase liquid oil (NAPL oil) or as an oil-in-water emulsion. Laboratory columns packed with sands or clayey sands were flushed with either NAPL oil or a soybean emulsion followed by plain water, while monitoring permeability loss and the final oil residual saturation. NAPL oil can be injected into coarse-grained sands. However NAPL injection into finer grained sediments requires high injection pressures which may not be feasible at some sites. In addition, NAPL injection results in high oil residual saturations and moderate permeability losses. In contrast, properly prepared emulsions can be distributed through sands with varying clay content without excessive pressure buildup, low oil retention and very low to moderate permeability loss. For effective transport, the emulsion must be stable, the oil droplets must be significantly smaller than the mean pore size of the sediment and the oil droplets should have a low to moderate tendency to stick to each other and the aquifer sediments. In our work, oil retention and associated permeability loss increased with sediment clay content and with the ratio of droplet size to pore size. For sandy sediments, the permeability loss is modest (0-40% loss) and is proportional to the oil residual saturation.     

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.     

A micromodel analysis of factors influencing NAPL removal by surfactant foam flooding

A methodology to study the trichloroethylene (TCE) and dodecane removal in porous media by surfactant foams (SF) was presented by using etched-glass micromodels. The purpose of this work was to systematically evaluate the impact of various physicochemical factors such as gas fraction (GF), surfactant concentration, pore structure and nonaqueous phase liquid (NAPL) types on NAPL removal during SF flooding. The TCE displacement by SF was dependent on the gas fraction of SF. Low GFs (50% and 66%) were more efficient for TCE removal and sweep efficiencies than a high GF (85%). An increase in TCE removal was observed with increasing surfactant concentration at a fixed GF. TCE removal by SF flooding appeared to be dependent more to the value of Capillary number rather than to the concentration of surfactant solution. The effect of the pore heterogeneity was evaluated by employing two different types of micromodels. The Capillary number is an important parameter in the determination of sweep efficiency or gas saturation of SF in a nonhomogeneous porous medium. However, the TCE removal from a nonhomogeneous porous medium may not be associated with sweep efficiency. The initial configuration of residual TCE blobs in a nonhomogeneous porous medium would also be influential in displacing TCE. Sweep efficiencies and pressure responses of two NAPL systems (TCE and dodecane) were monitored to evaluate foam stability when the foam contacts the NAPLs. Stable foam contacting with TCE is implied, while it appears that dodecane cause the SF to collapse. All results indicate that the Capillary number (a ratio of viscous forces to capillary forces) is the most important parameter for TCE removal by SF flooding. Micromodel visualizations of water, surfactant and SF floods were showed and also discussed.     

Multispectral image analysis method to determine dynamic fluid saturation distribution in two-dimensional three-fluid phase flow laboratory experiments

The need for measuring dynamic fluid saturation distribution in multi-dimensional three-fluid phase flow experiments is hampered by lack of appropriate techniques to monitor full field transient flow phenomena. There is no conventional technique able to measure dynamic three-fluid phase saturation at several array points of the flow field at the same time. A multispectral image analysis technique was developed to determine dynamic NAPL, water and air saturation distribution in two-dimensional three-fluid phase laboratory experiments. Using a digital near-infrared camera, images of sand samples with various degrees of NAPL, water and air saturation were taken, under constant lighting conditions and within three narrow spectral bands of the visible and near-infrared spectrum. It was shown that the optical density defined for the reflected luminous intensity was a linear function of the NAPL and the water saturation for each spectral band and for any two and three-fluid phase systems. This allowed the definition of dimensionless lump reflection coefficients for the NAPL and the water phase within each spectral band. Consequently, at any given time, two images taken within two different spectral bands provided two linear equations which could be solved for the water and the NAPL saturation. The method was applied to two-dimensional three-phase flow experiments, which were conducted to investigate the migration and the distribution of LNAPL in the vadose zone. The method was used to obtain continuous, quantitative and dynamic full field mapping of the NAPL saturation as well as the variation of the water and the air saturation during NAPL flow. The method provides a non-destructive and non-intrusive tool for studying multiphase flow for which rapid changes in fluid saturation in the entire flow domain is difficult to measure using conventional techniques.     

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.     

A set of constitutive relationships accounting for residual NAPL in the unsaturated zone

Although laboratory experiments show that non-aqueous phase liquid (NAPL) is retained in the unsaturated zone, no existing multiphase flow model has been developed to account for residual NAPL after NAPL drainage in the unsaturated zone. We developed a static constitutive set of saturation-capillary pressure relationships for water, NAPL and air that accounts for both this residual NAPL and entrapped NAPL. The set of constitutive relationships is formulated similarly to the set of scaled relationships that is frequently applied in continuum models. The new set consists of three fluid-phase systems: a three-phase system and a two-phase system, that both comply with the original constitutive model, and a newly introduced residual NAPL system. The new system can be added relatively easily to the original two- and three-phase systems. Entrapment is included in the model. The constitutive relationships of the non-drainable residual NAPL system are based on qualitative fluid behavior derived from a pore scale model. The pore scale model reveals that the amount of residual NAPL depends on the spreading coefficient and the water saturation. Furthermore, residual NAPL is history-dependent. At the continuum scale, a critical NAPL pressure head defines the transition from free, mobile NAPL to residual NAPL. Although the Pc-S relationships for water and total liquid are not independent in case of residual NAPL, two two-phase Pc-S relations can represent a three-phase residual system of Pc-S relations. A newly introduced parameter, referred to as the residual oil pressure head, reflects the mutual dependency of water and oil. Example calculations show consistent behavior of the constitutive model. Entrapment and retention in the unsaturated zone cooperate to retain NAPL. Moreover, the results of our constitutive model are in agreement with experimental observations.     

Push-pull partitioning tracer tests using radon-222 to quantify non-aqueous phase liquid contamination

Naturally occurring radon in groundwater can be used as an in situ partitioning tracer for locating and quantifying non-aqueous phase liquid (NAPL) contamination in the subsurface. When combined with the single-well, push-pull test, this methodology has the potential to provide a low-cost alternative to inter-well partitioning tracer tests. During a push-pull test, a known volume of test solution (radon-free water containing a conservative tracer) is first injected ("pushed") into a well; flow is then reversed and the test solution/groundwater mixture is extracted ("pulled") from the same well. In the presence of NAPL radon transport is retarded relative to the conservative tracer. Assuming linear equilibrium partitioning, retardation factors for radon can be used to estimate NAPL saturations. The utility of this methodology was evaluated in laboratory and field settings. Laboratory push-pull tests were conducted in both non-contaminated and trichloroethene NAPL (TCE)-contaminated sediment. The methodology was then applied in wells located in non-contaminated and light non-aqueous phase liquid (LNAPL)-contaminated portions of an aquifer at a former petroleum refinery. The method of temporal moments and an approximate analytical solution to the governing transport equations were used to interpret breakthrough curves and estimate radon retardation factors; estimated retardation factors were then used to calculate TCE saturations. Numerical simulations were used to further investigate the behavior of the breakthrough curves. The laboratory and field push-pull tests demonstrated that radon retardation does occur in the presence of TCE and LNAPL and that radon retardation can be used to calculate TCE saturations. Laboratory injection-phase test results in TCE-contaminated sediment yielded radon retardation factors ranging from 1.1 to 1.5, resulting in calculated TCE saturations ranging from 0.2 to 0.9%. Laboratory extraction-phase test results in the same sediment yielded a radon retardation factor of 5.0, with a calculated TCE saturation of 6.5%. Numerical simulation breakthrough curves provided reasonably good matches to the approximate analytical solution breakthrough curves. However, non-equilibrium radon partitioning and heterogeneous TCE distributions may affect the retardation factors and TCE saturation estimates.     

Effects of heterogeneities on capillary pressure-saturation-relative permeability relationships

In theories of multiphase flow through porous media, capillary pressure-saturation and relative permeability-saturation curves are assumed to be intrinsic properties of the medium. Moreover, relative permeability is assumed to be a scalar property. However, numerous theoretical and experimental works have shown that these basic assumptions may not be valid. For example, relative permeability is known to be affected by the flow velocity (or pressure gradient) at which the measurements are carried out. In this article, it is suggested that the nonuniqueness of capillary pressure-relative permeability-saturation relationships is due to the presence of microheterogeneities within a laboratory sample. In order to investigate this hypothesis, a large number of "numerical experiments" are carried out. A numerical multiphase flow model is used to simulate the procedures that are commonly used in the laboratory for the measurement of capillary pressure and relative permeability curves. The dimensions of the simulation domain are similar to those of a typical laboratory sample (a few centimeters in each direction). Various combinations of boundary conditions and soil heterogeneity are simulated and average capillary pressure, saturation, and relative permeability for the "soil sample" are obtained. It is found that the irreducible water saturation is a function of the capillary number; the smaller the capillary number, the larger the irreducible water saturation. Both drainage and imbibition capillary pressure curves are found to be strongly affected by heterogeneities and boundary conditions. Relative permeability is also found to be affected by the boundary conditions; this is especially true about the nonaqueous phase permeability. Our results reveal that there is much need for laboratory experiments aimed at investigating the interplay of boundary conditions and microheterogeneities and their effect on capillary pressure and relative permeability.