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.     

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.     

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.     

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.     

Surfactant-induced changes in gravity fingering of water through a light oil

Gravity-driven preferential flow (fingering) can greatly affect how one fluid displaces another in the subsurface. We have studied the internal properties of these preferential flow paths for water, with and without surfactants, infiltrating into oil saturated porous media using synchrotron X-rays, and miniature tensiometers to characterize fluid content and pressure relationships. We also used a light transmission technique to visualize overall flow pattern. Capillary pressure and water content decrease behind the front, similar to fingers in air-dry sand, with quantitative differences for five different surfactants with surface tensions ranging from 4–21 g/s². Using unstable flow theory, the finger widths, capillary pressure drops within the fingers, finger tip lengths, and finger splitting dynamics were scaled successfully with interfacial tension, fluid density, and the contact angle using the fingers in air–water systems as the reference.     

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.     

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.     

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.     

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.     

Microbial physiology-based model of ethanol metabolism in subsurface sediments

Dense non-aqueous phase liquids (DNAPLs) present in the subsurface may contain surface active compounds that impact DNAPL migration and distribution. While a number of studies have revealed the role surface active compounds play in altering the wettability of quartz sand, few have considered the implications for other minerals common to contaminated sites. This study extends understanding of DNAPL/surfactant wettability to iron oxide surfaces. Specifically, quartz and iron oxide-coated sands in a tetrachloroethene (PCE)/water system containing the organic base (an organic molecule that acts as a base) dodecylamine (DDA) were compared at a variety of scales. Wettability of the minerals' surfaces, and the impact of wettability on capillary resistance to DNAPL entry, were assessed as a function of pH through: (i) advancing and receding contact angles, (ii) primary drainage capillary pressure-saturation experiments, and (iii) small, two-dimensional, flow cell experiments. The work revealed that, at neutral pH and under identical boundary capillary pressures, DNAPL invaded quartz sand but not iron oxide-coated sand; however, at low pH, DNAPL invaded both sands equally. These differences were demonstrated to be due to wettability alterations associated with the strength of attractive forces between DDA and the mineral surface, dictated by the isolectric point of the minerals and system pH. Observed differences in DNAPL invasion behavior were consistent with measured intrinsic contact angles and P(c)-S relationships, the latter requiring scaling by the operative contact angle inside the porous medium for a meaningful comparison. This study suggests that the distribution of minerals (and, more specifically, their isoelectric points), as well as the aqueous phase pH at a given site, may have a significant impact on the DNAPL source zone architecture.     

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.     

Single- and dual-porosity modelling of flow in reclaimed mine soil cores with embedded lignitic fragments

Lignitic mine soils represent a typical two-scale dual-porosity medium consisting of a technogenic mixture of overburden sediments that include lignitic components as dust and as porous fragments embedded within a mostly coarse-textured matrix. Flow and transport processes in such soils are not sufficiently understood to predict the course of soil reclamation or of mine drainage. The objective of this contribution is to identify the most appropriate conceptual model for describing small-scale heterogeneity effects on flow on the basis of the physical structure of the system. Multistep flow experiments on soil cores are analyzed using either mobile–immobile or mobile–mobile type 1D dual-porosity models, and a 3D numerical model that considers a local-scale distribution of fragments. Simulations are compared with time series' of upward infiltration and matric potential heads measured at two depths using miniature tensiometers. The 3D and the 1D dual-permeability models yielded comparable results as long as pressure heads are in local equilibrium; however, could describe either the upward infiltration or the matric potential curves but not both at the same time. The mobile–immobile type dual-porosity model failed to describe the data. A simultaneous match with pressure heads and upward infiltration data could only be obtained with the 1D dual-permeability model (i.e., mobile–mobile) by assuming an additional restriction of the inter-domain water transfer. These results indicate that for unsaturated flow conditions at higher matric potential heads (i.e., here >− 40 hPa), water in a restricted part of the fragment domain must be more mobile as compared to water in the sandy matrix domain. Closer inspections of the pore system and first neutron radiographic imaging support the hypothesis that a more continuous pore region exists at these pressure heads in the vicinity of the lignitic fragments possibly formed by fragment contacts and a lignitic dust interface-region between the two domains. The results suggest that the small-scale structure is too complex as to be represented by weighted contributions of individual components alone.     

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.     

地下水中轻质有机污染物(LNAPL)透镜体研究

在二维砂槽模型中模拟了轻质油在均匀多孔介质地下水非饱和区中的运移过程。模拟结果表明,地下水毛细区是轻质油污染的重点区,除了ＬＮＡＰＬ的残留以外,进入地下水饱和的ＬＮＡＰＬ终将被地下水顶托回到毛细区中,毛细区以上的约大多民将在重力作用下进入毛细区中,试验中观察到达稳定状态时ＬＮＡＰＬ透镜体的上边缘略微高出毛细区。利用多孔介质毛细管模型,建立了利用界面张力、接触角、介质特征孔隙直径等物理量估算不同位置     

Full and boundary-layer solutions of the steady air sparging problem

The one previous analytical solution to the steady sparging problem in a homogeneous soil was in the boundary-layer approximation that neglects the vertical capillary pressure gradient. The present study gives an analytical solution to the full air-flow equation, with the corresponding boundary-layer solution for comparison. The full solution predicts sparging below the air-injection point, whereas the boundary-layer solution does not. Solutions are expressed both in terms of the dimensionless Kirchhoff potential θ (increasing monotonically with capillary pressure and air saturation also) and the dimensionless Stokes stream function F (mapping the pattern of air flow). Both θ and F show the full solution predicting more effective sparging near the injection point than does the boundary-layer solution. The overall boundary-layer relative error, however, decreases as dimensionless air-injection depth below the undisturbed water-table increases.     

Geostatistical analysis of soil hydrologic properties in a field plot

A 91-m transect was set up in an irrigated field near Las Cruces, New Mexico to obtain soil water tension and water content data to investigate their spatial variability. A total of 455 sampling points were monitored along a grid consisting of 91 stations placed 1 m apart by 5 depths per station (at 0.3, 0.6, 0.9, 1.2 and 1.5 m below the surface). Post-irrigation tension and wetness measurements were recorded over 45 days at 11 time periods. Soil water tension was measured with tensiometers using a hand-held pressure transducer. A neutron probe was used to obtain volumetric water content. Using the observed wetness and tension data, unsaturated hydraulic conductivity values were derived (using a cubic spline function to estimate the gradient), and an exponential model was used to fit the calculated conductivity-tension curves to obtain hydraulic conductivity parameter values. The spatial and temporal variability of wetness, tension, saturated hydraulic conductivity and pore-size distribution parameters, and texture at the 0.3-m depth were examined using geostatistical techniques.The exponential model was found to inadequately describe the hydraulic conductivity/tension relationship for the full range of tension, particularly in the tension range near saturation. The derived values of the saturated hydraulic conductivity parameter were much greater than expected and do not correspond to reasonable saturated hydraulic conductivity values.All of the soil parameters studied exhibited large spatial variability horizontally and vertically in the field. Ranges of dependence determined from semivariogram analysis over the 44-day drainage period are 3–32 m for wetness, 6–34 m for soil water tension, 5–35 m for natural log of saturated hydraulic conductivity parameters, 5–11 m for pore-size distribution parameter, and 8–24 m for percent sand, silt and clay at the 0.3 m depth. An alternate hole-effect model is suggested to describe the texture semivariograms.It was determined that the variance of volumetric water content generally increased at each depth over the measured time periods, which is consistent with certain past field studies and a stochastic analysis of unsaturated flow in heterogeneous soils. Future research is recommended relating soil texture to soil hydrologic parameters with the goal of predicting soil behavior with less extensive sampling schemes.     

Re-evaluation of metal bioaccumulation and chronic toxicity in Hyalella azteca using saturation curves and the biotic ligand model

Bioaccumulation by Hyalella of all metals studied so far in our laboratory was re-evaluated to determine if the data could be explained satisfactorily using saturation models. Saturation kinetics are predicted by the biotic ligand model (BLM), now widely used in modelling acute toxicity, and are a pre-requisite if the BLM is to be applied to chronic toxicity. Saturation models provided a good fit to all the data. Since these are mechanistically based, they provide additional insights into metal accumulation mechanisms not immediately apparent when using allometric models. For example, maximum Cd accumulation is dependent on the hardness of the water to which Hyalella are acclimated. The BLM may need to be modified when applied to chronic toxicity. Use of saturation models for bioaccumulation, however, also necessitates the need for using saturation models for dose-response relationships in order to produce unambiguous estimates of LC50 values based on water and body concentrations. This affects predictions of toxicity at very low metal concentrations and results in lower predicted toxicity of mixtures when many metals are present at low concentrations.     

Simulating the fate and transport of TCE from groundwater to indoor air

This work provides an exploratory analysis on the relative importance of various factors controlling the fate and transport of volatile organic contaminants (in this case, TCE) from a DNAPL source zone located below the water table and into the indoor air. The analysis is conducted using the multi-phase compositional model CompFlow Bio, with the base scenario problem geometry reminiscent of a field experiment conducted by Rivett [Rivett, M.O., (1995), Soil–gas signatures from volatile chlorinated solvents: Borden field experiments. Groundwater, 33(1), 84–98.] at the Borden aquifer where groundwater was observed to transport a contaminant plume a substantial distance without vertical mass transport of the contaminant across the capillary fringe and into the vadose zone. Results for the base scenario model indicate that the structure of the permeability field was largely responsible for deflecting the groundwater plume upward towards the capillary fringe, permitting aqueous phase diffusion to transport the TCE into the vadose zone. Alternative permeability realizations, generated as part of a Monte Carlo simulation process, at times deflected the groundwater plume downwards causing the extended thickness of the saturated zone to insulate the vadose zone from exposure to the TCE by upward diffusive transport. Comparison of attenuation coefficients calculated using the CompFlow Bio and Johnson and Ettinger [Johnson, P.C. and Ettinger, R.A., (1991), Heuristic model for predicting the intrusion rate of contaminant vapors into buildings. Environmental Science and Technology, 25, 1445–1452.] heuristic model exhibited fortuitous agreement for the base scenario problem geometry, with this agreement diverging for the alternative permeability realizations as well as when parameters such as the foundation slab fracture aperture, the indoor air pressure drop, the capillary fringe thickness, and the infiltration rate were varied over typical ranges.