The influence of field-scale heterogeneity on the infiltration and entrapment of dense nonaqueous phase liquids in saturated formations

Numerical simulations are used for the systematic exploration of the migration and entrapment of dense nonaqueous phase liquids (DNAPLs) in heterogeneous formations. Ensembles of realizations of random, spatially correlated permeability fields are generated and employed in model simulations of a spill event. Statistical techniques are then used to quantify the sensitivity of model predictions to input parameters, thereby identifying the parameters or processes that may be of primary importance in the determination of organic liquid distributions in heterogeneous systems. Results of the study indicate that the most critical factors in modeling organic entrapment include the spill release rate, reliable estimates of the mean, variance, and vertical correlation scale of the formation permeability, and an accurate representation of the correlation between the capillary pressure–saturation function and the permeability. In contrast, the hydraulic gradient and cross-correlation of residual saturations with permeabilities are found to have only minor influence on organic liquid distributions in such heterogeneous formations.     

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.     

Infiltration of PCE in a system containing spatial wettability variations

A two-dimensional infiltration experiment was conducted to investigate and quantify the effect of spatial wettability variations on DNAPL migration and entrapment in saturated sands. Experimental observations of tetrachloroethylene (PCE) infiltration showed that organic-wet sand lenses acted as very effective capillary barriers, retaining PCE and inhibiting its downward migration. A multiphase numerical simulator was used to model this sand box experiment. The simulator incorporates wettability-modified van Genuchten and Brooks-Corey capillary pressure/saturation relationships as well as Burdine and Mualem relative permeability relationships. PCE mass distributions, estimated by image analysis of digital photographs taken during the infiltration event, were compared to simulation results. Although both relative permeability models were qualitatively able to predict the PCE retention in the organic-wet layers, simulations with the Mualem model failed to capture the observed rate of PCE migration. A traditional multiphase simulator, incorporating water-wet capillary retention relations, failed to predict both PCE pathways and retention behavior. This study illustrates the potential influence of subsurface wettability variations on DNAPL migration and entrapment and supports the use of modified capillary relations in conjunction with the Burdine model in multiphase flow simulators.     

Comparison of capillary pressure relationships of organic liquid-water systems containing an organic acid or base

The presence of surface-active solutes such as organic acids and bases may have a profound influence on the transport of organic liquid contaminants through their impact on the constitutive relationship of capillary pressure vs. saturation. This relationship is a function of the interfacial tension and wettability of the system, which, in turn, depend on the pH and the concentration of organic acids and bases that are present. This study examines the impact of pH and the concentration on the interfacial tension, contact angle, and capillary pressure of systems consisting of tetrachloroethylene, water, and quartz containing either octanoic acid or dodecylamine. In general, the ionic form of the solute tended to remain in the aqueous phase and reduced the capillary pressure through its impact on the interfacial tension and contact angle; on the other hand, the neutral form of the solute partitioned into the organic liquid phase and had a lesser impact on the capillary pressure for the same total mass of solute. A comparison of these data with data generated in previous research in similar systems where o-xylene was the organic liquid showed that the trends are analogous. Thus, the behavior of these two solvent systems seems to be driven primarily by the aqueous phase speciation of the solute, and the differences between the capillary pressure relationships for the two systems could be attributed to the pure system interfacial tension.     

Estimation of primary drainage three-phase relative permeability for organic liquid transport in the vadose zone

The modeling of transport of organic liquid contaminants through the vadose zone often requires three-phase relative permeabilities. Since these are difficult to measure, predictive models are usually used. The objective of this study is to assess the ability of eight common models to predict the drainage relative permeability to oil in a three-phase system (water-oil-air). A comparison of the models' estimates using data set from Oak [Oak, M.J., 1990. Three-phase relative permeability of water-wet Berea. In: Seventh Symposium on Enhanced Oil Recovery, Paper SPE/Doe 20183. Tulsa, OK, April 22-25] showed that they provide very different predictions for the same system. The goodness of the models does not increase with the amount of data or computation that the models require. Also, the calculations showed how different interpretations of the models and of the terminology associated with them can significantly impact the predictions. Thus, considerable error may be introduced into the simulations of organic liquid transport in the vadose zone depending on the selection and interpretation of the three-phase relative permeability model.     

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

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

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.     

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.     

More general capillary pressure and relative permeability models from fractal geometry

More general capillary pressure and relative permeability models were derived theoretically from fractal modeling of a porous medium. It was found that the new capillary pressure model could be reduced to the frequently-used Brooks–Corey capillary pressure model and the Li–Horne imbibition model when the fractal dimension of a porous medium takes specific values. This also demonstrates that the Brooks–Corey model and the Li-Horne model have a further confirmed theoretical basis. Capillary pressure data measured using mercury intrusion techinque were used to verify the model. The results demonstrated that the new capillary pressure model could represent the capillary pressure curves in those rocks with fracures or with great heterogeneity while the existing models cannot. The new relative permeability models can be reduced to the Brooks–Corey relative permeability model in a specific case. It has been proved theoretically that the relative permeability of each phase in a smooth fracture is only a linear function of its own saturation. Relative permeability data were calculated using the new models and the model results were compared with experimental data measured using a steady-state technique. The comparison demonstrated that the relative permeability models and experimental results were consistent with each other.     

Secondary imbibition in NAPL-invaded mixed-wet sediments

A previously developed pore network model is used here to study the spontaneous and forced secondary imbibition of a NAPL-invaded sediment, as in the displacement of NAPL by waterflooding a mixed-wet soil. We use a 3D disordered pore network with a realistic representation of pore geometry and connectivity, and a quasi-static displacement model that fully describes the pore-scale physics. After primary drainage (NAPL displacing water) up to a maximum capillary pressure, we simulate secondary imbibition (water displacing NAPL). We conduct a parametric study of imbibition by varying systematically the controlling parameters: the advancing contact angles, the fraction of NAPL-wet pores, the interfacial tension, and the initial water saturation. Once the secondary imbibition is completed, the controlling displacement mechanisms, capillary pressures, relative permeabilities, and trapped NAPL saturations are reported. It is assumed that NAPL migrates into an initially strongly water-wet sediment, i.e., the receding contact angles are very small. However, depending on the surface mineralogy and chemical compositions of the immiscible fluid phases, the wettability of pore interiors is altered while the neighborhoods of pore corners remain strongly water-wet-resulting in a mixed-wet sediment. Here, we compare three different levels of wettability alteration: water-wet (advancing contact angles (20 degrees to 55 degrees), intermediate-wet (55 degrees to 120 degrees), and NAPL-wet (120 degrees to 155 degrees). The range of advancing contact angles and the fraction of NAPL-wet pores have dramatic effects on the NAPL-water capillary pressures and relative permeabilities. The spatially inhomogeneous interfacial tension has a minor impact on the trapped NAPL saturation and relative permeability to NAPL, and a slight effect on the relative permeability to water. The initial water saturation has a slight effect on the two-phase flow characteristics of water-wet sediments; however, with more NAPL-wet pores in the sediment, it starts to have a profound effect on the water and NAPL relative permeabilities.     

A multi-flowpath model for the interpretation of immiscible displacement experiments in heterogeneous soil columns

This work focuses on the phenomenon of the immiscible two-phase flow of water and oil in saturated heterogeneous soil columns. The goal is to develop a fast and reliable method for quantifying soil heterogeneities for incorporation into the relevant capillary pressure and relative permeability functions. Such data are commonly used as input data in simulators of contaminant transport in the subsurface. Rate-controlled drainage experiments are performed on undisturbed soil columns and the transient response of the axial distribution of water saturation is determined from electrical measurements. The transient responses of the axial distribution of water saturation and total pressure drop are fitted with the multi-flowpath model (MFPM) where the pore space is regarded as a system of parallel paths of different permeability. The MFPM enables us to quantify soil heterogeneity at two scales: the micro-scale parameters describe on average the effects of pore network heterogeneities on the two-phase flow pattern; the macro-scale parameters indicate the variability of permeability at the scale of interconnected pore networks. The capillary pressure curve is consistent with that measured with mercury intrusion porosimetry over the low pressure range. The oil relative permeability increases sharply at a very low oil saturation (< 10^− 3) and tends to a high end value. The water relative permeability decreases abruptly at a low oil saturation (~ 0.1), whereas the irreducible wetting phase saturation is quite high. The foregoing characteristics of the two-phase flow properties are associated with critical (preferential) flowpaths that comprise a very small percentage of the total pore volume, control the overall hydraulic conductivity, and are consistent with the very broad range of pore-length scales usually probed in soil porous matrix.     

Predictive modelling of NAPL injection tests in variable aperture spatially correlated fractures.

In preparation for a field experiment where a NAPL will be injected into a fractured sandstone aquifer, a 2D invasion percolation model of DNAPL migration in a single horizontal fracture with varying aperture has been developed. This simulation investigated the effect of spatially correlated fracture aperture fields on pressure-saturation relationships as a function of variable aperture mean, standard deviation, and spatial correlation statistics under hydrostatic conditions. Results from spatially correlated variable aperture fields can be significantly different from random fields. Longer ranges decreased entry pressures and higher standard deviations decreased nonwetting phase saturations. Mean aperture is the major control on displacement pressure, entry pressure and the form of the pressure-saturation curve. Simulation results using statistical parameters for a variable aperture natural sandstone fracture as described by Yeo et al. [International Journal of Rock Mechanics and Mining Sciences 35 (1998) 1051] closely resemble a Brooks-Corey pressure-saturation function, and exhibit a distinct entry pressure followed by a rapid increase in nonwetting phase saturation. Graphical estimates of entry pressure provide a good approximation of the critical aperture controlling the formation of a continuous nonwetting phase pathway in a variable aperture fracture. Consequently, we show that multiphase flow concepts developed for porous media can successfully be applied to variable aperture fractures. Entry pressure correlates well to the mean aperture in these simulations when using a Gaussian distribution of fracture aperture. Interpreted aperture distributions from NAPL injection experiments do not fit the true distribution well at low nonwetting phase saturations, but do at higher saturations above the entry pressure. Consequently, true, mechanical aperture variation within a fracture plane cannot be determined from NAPL injection experiments either in the field or laboratory.     

Multidimensional validation of a numerical model for simulating a DNAPL release in heterogeneous porous media

A fixed-volume release of 1,2-DCE, tracked in space and time with a light transmission/image analysis system, provided a data set for the infiltration, redistribution, and immobilisation of a dense non-aqueous phase liquid (DNAPL) in a heterogeneous porous medium. The two-dimensional bench scale flow cell was packed with a spatially correlated, random heterogeneous distribution of six sand types. In order to provide the necessary modelling parameters, detailed constitutive relationships were measured at the local scale for the six sands. These experiments revealed that nonwetting phase (NWP) relative permeability-saturation (k(rN)-S(W)) relationships are strongly correlated to sand type. Trends in the best-fit k(rN)-S(W) parameters reflected a positive correlation between mean grain diameter and the maximum NWP relative permeability, k(rN)(max). Multiphase flow simulations of the bench scale experiment best reproduced the experimental observations, producing excellent matches in both time and space, when the measured, correlated local scale k(rN)-S(W) relationships were employed.     

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.     

Entrapment and dissolution of DNAPLs in heterogeneous porous media

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

Macro-scale effective constitutive relationships for two-phase flow processes in heterogeneous porous media with emphasis on the relative permeability-saturation relationship

Macro-scale simulations often play an important role in the assessment and remediation of contamination by dense non-aqueous phase liquids (DNAPLs) in the subsurface. Effective parameters for the macro scale are required for these simulations in order to avoid a detailed discretisation of the geological structures. Starting from the observed influence of heterogeneities on multiphase flow processes at the macro scale, we present an upscaling procedure from the local to the macro scale for the derivation of constitutive relationships for multiphase flow processes. The approach is based on the assumption of an equilibrium of (capillary) forces, which allows the application of a percolation model. This results in saturation distributions for different capillary pressures. Averaging these distributions gives rise to a macroscopic capillary pressure-saturation relationship. For the saturation distribution, relative permeabilities and effective conductivities are computed depending on the structure and the flow direction. These are averaged with the help of the renormalisation method. The evolving relative permeability-saturation relationship for the macro scale shows a saturation-dependent anisotropy and pronounced residual saturations of the nonwetting phase (which were not assumed for the local scale). The anisotropy reflects the underlying structure of the considered system that needs not to be known in detail.     

Prediction of two-phase capillary pressure-saturation relationships in fractional wettability systems

Capillary pressure/saturation data are often difficult and time consuming to measure, particularly for non-water-wetting porous media. Few capillary pressure/saturation predictive models, however, have been developed or verified for the range of wettability conditions that may be encountered in the natural subsurface. This work presents a new two-phase capillary pressure/saturation model for application to the prediction of primary drainage and imbibition relations in fractional wettability media. This new model is based upon an extension of Leverett scaling theory. Analysis of a series of DNAPL/water experiments, conducted for a number of water/intermediate and water/organic fractional wettability systems, reveals that previous models fail to predict observed behavior. The new Leverett–Cassie model, however, is demonstrated to provide good representations of these data, as well as those from two earlier fractional wettability studies. The Leverett–Cassie model holds promise for field application, based upon its foundation in fundamental scaling principles, its requirement for relatively few and physically based input parameters, and its applicability to a broad range of wetting conditions.     

Kinetic limitations on tracer partitioning in ganglia dominated source zones

Quantification of the relationship between dense nonaqueous phase liquid (DNAPL) source strength, source longevity and spatial distribution is increasingly recognized as important for effective remedial design. Partitioning tracers are one tool that may permit interrogation of DNAPL architecture. Tracer data are commonly analyzed under the assumption of linear, equilibrium partitioning, although the appropriateness of these assumptions has not been fully explored. Here we focus on elucidating the nonlinear and nonequilibrium partitioning behavior of three selected alcohol tracers - 1-pentanol, 1-hexanol and 2-octanol in a series of batch and column experiments. Liquid-liquid equilibria for systems comprising water, TCE and the selected alcohol illustrate the nonlinear distribution of alcohol between the aqueous and organic phases. Complete quantification of these equilibria facilitates delineation of the limits of applicability of the linear partitioning assumption, and assessment of potential inaccuracies associated with measurement of partition coefficients at a single concentration. Column experiments were conducted under conditions of non-equilibrium to evaluate the kinetics of the reversible absorption of the selected tracers in a sandy medium containing a uniform entrapped saturation of TCE-DNAPL. Experimental tracer breakthrough data were used, in conjunction with mathematical models and batch measurements, to evaluate alternative hypotheses for observed deviations from linear equilibrium partitioning behavior. Analyses suggest that, although all tracers accumulate at the TCE-DNAPL/aqueous interface, surface accumulation does not influence transport at concentrations typically employed for tracer tests. Moreover, results reveal that the kinetics of the reversible absorption process are well described using existing mass transfer correlations originally developed to model aqueous boundary layer resistance for pure-component NAPL dissolution.