Étude expérimentale de la dispersion active d'un polluant hydrocarboné en milieu poreux hétérogèneActive dispersion of a hydrocarbon pollutant in heterogeneous porous media: experimental study

This study deals with Non Aqueous Phase Liquid (NAPL) dissolution in subsurface water in order to predict the pollutant plume development and to optimize remediation processes. An experimental study of NAPL dissolution in porous media is presented. Local water saturation and effluent pollutant concentration measurements are presented for several kinds of porous media. Experimental results show clearly the influence of microscopic and/or macroscopic heterogeneities of the porous media and the distribution of the pollutant on the active dispersion of the NAPL. The NAPL dissolution occurs in several steps which highlights the existence of non-local equilibrium related to the heterogeneity of the porous media. To cite this article: A. Yra et al., C. R. Mecanique 334 (2006).     

Pore-Scale Analysis of NAPL Blob Dissolution and Mobilization in Porous Media

A pore-scale analysis of nonaqueous phase liquid (NAPL) blob dissolution and mobilization in porous media was presented. Dissolution kinetics of residual NAPLs in an otherwise water-saturated porous medium was investigated by conducting micromodel experiments. Changes in residual NAPL volume were measured from recorded video images to calculate the mass transfer coefficient, K and the lumped mass transfer rate coefficient, k. The morphological characteristics of the blobs such as specific and intrinsic area were found to be independent of water flow rate except at NAPL saturations below 2%. Dissolution process was also investigated by separating the mass transfer into zones of mobile and immobile water. The fractions of total residual NAPL perimeters in contact with mobile water and immobile water were measured and their relationship to the mass transfer coefficient was discussed. In general, residual NAPLs are removed by dissolution and mobilization. Although these two mechanisms were studied individually by others, their simultaneous occurrence was not considered. Therefore, in this study, mobilization of dissolving NAPL blobs was investigated by an analysis of the forces acting on a trapped NAPL blob. A dimensional analysis was performed to quantify the residual blob mobilization in terms of dimensionless Capillary number (Ca _I). If Ca _I is equal to or greater than the trapping number defined as , then blob mobilization is expected.     

Conditional Stochastic Analysis for Multiphase Trsnsport in Randomly Heterogeneous,variably Saturated Media

Groundwater contamination of organics has recently become a problem of growing concern over the resulting health and environmental problems. In general, the multiphase system of nonaqueous phase liquid (NAPL), water and air has to be studied in order to realistically describe the movement of such materials in the subsurface. Numerous models have been developed to study multiphase flow and/or multispecies transport in porous media. However, using models to study the influence of medium heterogeneity on such flow and transport is only a recent event. It has been demonstrated for single-phase flow and transport in saturated and unsaturated media that the study of medium heterogeneity is amenable to stochastic analysis. In this paper, we extend our Eulerian–Lagrangian stochastic theory for single-phase transport to the problem of multiphase–multispecies transport in randomly heterogeneous media under the conditions that the flow is steady-state and the phases are in local chemical equilibrium. We present theoretical expressions to describe the first two conditional moments of the random concentration of any species in any phase. Though they reveal some of the fundamental properties and help gaining insight into the nature of the problem, these expressions cannot be evaluated without either high resolution Monte Carlo simulation or approximation (closure). Therefore, we propose two sets of workable approximations, one being a weak approximation and the other being a linearized pseudo-Fickian approximation. The former yields a nonlinear integro-differential equation for the first conditional moment and the latter yields a linear differential equation. Then the second moments can be computed from explicit expressions from either the weak or pseudo-Fickian approximation.     

Significance of Mass–Concentration Relation on the Contaminant Source Depletion in the Nonaqueous Phase Liquid (NAPL) Contaminated Zone

This study develops a new numerical model adopting a generic relation between the nonaqueous phase liquid (NAPL) mass and aqueous-phase NAPL concentration to simulate the relationship between NAPL contaminant mass discharge and contaminant mass reduction in the source zone, which plays a critical role to assist with site management decisions on contaminated zone remediation. The model can accommodate any contaminant mass and concentration relations and applicable to the situations when groundwater flowrate in the NAPL source zone varies in any form temporally. Therefore, the combined effects of mass–concentration relation and groundwater flowrate variations can be examined. It is hypothesized that the NAPL mass–concentration relations reflect the spatial variability of porous media in the subsurface. The developed model is compared with results from field monitoring sites and found to exhibit high flexibility and capability in capturing the observed complex NAPL source zone dynamics. Using six contaminant mass and concentration functions of varying shapes, we show that contaminant mass and concentration relation has pronounced effects on contaminant mass discharge dynamics in addition to the groundwater flowrate temporal variations. In general, the coupled mass–concentration relation and groundwater flowrate variations demonstrate stronger capability in capturing the NAPL source zone dynamics under a wide range of field porous medium conditions reported in the literature than the models that only consider groundwater flux variations. In particular, the concave mass–concentration models can be used in less heterogeneous porous media, while the convex mass–concentration models are more appropriate in more heterogeneous site conditions.

     

Density-driven Transport of Volatile Organic Compounds and its Impact on Contaminated Groundwater Plume Evolution

Density-driven advection of gas phase due to vaporization of chlorinated volatile organic compounds (VOCs) has a significant effect on fate and transport of contaminants. In this study, we investigated the effects of density-driven advection, infiltration, and permeability on contaminant plume evolution and natural attenuation of VOCs in the subsurface system. To analyze these effects, multiphase flow and contaminant transport processes were simulated using a three-dimensional Galerkin-finite-element-based model. Trichloroethylene (TCE) is selected as a target contaminant. Density-driven advection of gas phase elevated the potential of groundwater pollution in the saturated zone by accelerating downward migration of vaporized contaminant in the unsaturated zone. The advection contributed to increased removal rates of non-aqueous phase liquid (NAPL) TCE source and reduced dissolved TCE plume development in the downstream area. Infiltration reduced the velocity of the density-driven advection and its influence zone, but raised TCE transfer from the unsaturated to the saturated zone. The variation in soil permeability showed greater impact on contaminant migration within water phase in the saturated zone than within gas phase in the unsaturated zone. Temporal variations of TCE mass within two-dimensional (2D) and three-dimensional (3D) domains under several modeling conditions were compared. These results are important in evaluation of natural attenuation processes, and should be considered to effectively design monitored natural attenuation as a remedial option.     

Flow behaviour in the presence of wettability heterogeneities

The physical processes occurring during fluid flow and displacement within porous media having wettability heterogeneities have been investigated in specially designed heterogeneous visual models. The models were packed with glass beads, areas of which were treated with a water repellent to create wettability variations. Immiscible displacement experiments show visually the effect of wettability heterogeneities on the formation of residual oil and recovery due to capillary trapping. This work demonstrates by experiment the importance of incorporating reservoir heterogeneity into pore displacement analysis, essential for the correct interpretation of core data and for directing the route for scale-up of the processes to reservoir scale.     

Nonaqueous Phase Liquid Dissolution in Porous Media: Current State of Knowledge and Research Needs

Our understanding of nonaqueous phase liquid (NAPL) dissolution in the subsurface environment has been increasing rapidly over the past decade. This knowledge has provided the basis for recent developments in the area of NAPL recovery, including cosolvent and surfactant flushing. Despite these advances toward feasible remediation technologies, there remain a number of unresolved issues to motivate environmental researchers in this area. For example, the lack of an effective NAPLlocation methodology precludes effective deployment of NAPL recovery technologies. The objectives of this paper are to critically review the state of knowledge in the area of stationary NAPL dissolution in porous media and to identify specific research needs. The review first compares NAPL dissolutionbased mass transfer correlations reported for environmental systems with more fundamental results from the literature involving model systems. This comparison suggests that our current understanding of NAPL dissolution in smallscale (on the order of cm) systems is reasonably consistent with fundamental mass transfer theory. The discussion then expands to encompass several issues currently under investigation in NAPL dissolution research, including: characterizing NAPL morphology (i.e. effective size and surface area); multicomponent mixtures; scale-related issues (dispersion, flow by-passing); locating NAPL in the subsurface and enhanced NAPL recovery. Research needs and potential approaches are discussed throughout the paper. This review supports the following conclusions: (1) Our knowledge related to local dissolution and remediation issues is maturing, but should be brought to closure with respect to the link between NAPL emplacement theory (as it impacts NAPL morphology) and NAPL dissolution; (2) The role of nonideal NAPL mixtures, and intra-NAPL mass transfer processes must be clarified; (3) Valid models for quantifying and designing NAPL recovery schemes with chemical additives need to be refined with respect to chemical equilibria, mass transfer and chemical delivery issues; (4) Computational and large-scale experimental studies should begin to address parameter up-scaling issues in support of model application at the field scale; and (5) Inverse modeling efforts aimed at exploiting the previous developments should be expanded to support field-scale characterization of NAPL location and strength as a dissolving source.     

Comparison of Kinetic and Hybrid-Equilibrium Models Simulating Colloid-Facilitated Contaminant Transport in Porous Media

The presence of colloidal particles in groundwater can enhance contaminant transport by reducing retardation effects and carrying them to distances further than predicted by a conventional advective/dispersive equation with normal retardation values. When colloids exist in porous media and affect contaminant migration, the system can best be simulated as a three-phase medium. Mechanisms of mass transfer from one phase to another by colloids and contaminants can be kinetic or equilibrium-based, depending on the sorption–desorption reaction rate between the aqueous and solid phases. When the rate of sorption between the water phase and the solid phase(s) is not much greater than the rate of change in contaminant concentration in the water phase, kinetic sorption models may better describe the phenomenon. In some cases of modeling one or more mass transfer processes, a useful simplification may be to introduce the local equilibrium assumption. In this study, the local equilibrium assumption for sorption processes on colloidal surfaces (hybrid equilibrium model) was compared with kinetic-based models. Sensitivity analyses were conducted to deduce the effect of major parameters on contaminant transport. The results obtained from the hybrid equilibrium model in predicting the transport of colloid-facilitated groundwater contaminant are very similar to those of the kinetic model, when the point of interest is not at contaminant and colloid source vicinities and the time of interest is sufficiently long for imposed sources.     

A Fickian diffusion model for the spreading of liquid plumes infiltrating in heterogeneous media

Infiltration of water and non-aqueous phase liquids (NAPLs) in the vadose zone gives rise to complex two- and three-phase immiscible displacement processes. Physical and numerical experiments have shown that ever-present small-scale heterogeneities will cause a lateral broadening of the descending liquid plumes. This behavior of liquid plumes infiltrating in the vadose zone may be similar to the familiar transversal dispersion of solute plumes in single-phase flow. Noting this analogy we introduce a mathematical model for ‘phase dispersion’ in multiphase flow as a Fickian diffusion process. It is shown that the driving force for phase dispersion is the gradient of relative permeability, and that addition of a phase-dispersive term to the governing equations for multiphase flow is equivalent to an effective capillary pressure which is proportional to the logarithm of the relative permeability of the infiltrating liquid phase. The relationship between heterogeneity-induced phase dispersion and capillary and numerical dispersion effects is established. High-resolution numerical simulation experiments in heterogeneous media show that plume spreading tends to be diffusive, supporting the proposed convection-dispersion model. Finite difference discretization of the phase-dispersive flux is discussed, and an illustrative application to NAPL infiltration from a localized source is presented. It is found that a small amount of phase dispersion can completely alter the behavior of an infiltrating NAPL plume, and that neglect of phase-dispersive processes may lead to unrealistic predictions of NAPL behavior in the vadose zone.     

Analytical Solutions for Partitioned Diffusion in Laminates: I. Initial Value Problem with Steady Cauchy Conditions

Studies of the transport of contaminants and nutrients in industrial and environmental systems are complicated by the heterogeneous nature of the supporting porous or permeable media, and by the numerical problems associated with high Peclet number advection and sharp interface models. In order to provide independent theoretical checks of numerical transport theories, this set of papers presents analytical solutions to diffusive transport equations in simplified (one-dimensional) laminate systems subject to partitioning interactions. Here, in Part I, a standard separation of variables technique is used to develop analytical eigenfunction expansions of the concentration solution in an N-laminate system subject to steady Cauchy (third-type) nonhomogeneous boundary conditions. Both Cartesian and radial (axisymmetric) coordinate systems are considered. The solutions are developed for two different interface partitioning formulations, allowing the partitioning processes to be described by instantaneous equilibration mechanisms, or in terms of gradual equilibration mediated by mass transfer coefficients. Worked examples are presented and limitations of the approach discussed.     

Modeling the Transport of Contaminants Originating from the Dissolution of DNAPL Pools in Aquifers in the Presence of Dissolved Humic Substances

A twodimensional finite difference numerical model was developed to describe the transport of dissolved organics originating from nonaqueous phase liquid (NAPL) pool dissolution in saturated porous media in the presence of dissolved humic substances. A rectangular NAPL pool was considered in a homogeneous porous medium with unidirectional interstitial groundwater velocity. It was assumed that dissolved humic substances and aqueous phase contaminants may sorb onto the solid matrix under local equilibrium conditions. The contaminant in the aqueous phase may undergo firstorder decay. Also, the dissolved contaminant may sorb onto humic substances. The transport properties of dissolved humic substances are assumed to be unaffected by sorbing contaminants, because dissolved humic macromolecules are much larger than dissolved contaminants and sorption of nonpolar contaminants onto humic substances do not affect the overall surface charge of humic substances. The sorption characteristics of dissolved humic substances onto clean sand were determined from column experiments. An effective local mass transfer rate coefficient accounting for the presence of dissolved humic substances was developed. Model simulations indicate that dissolved humic substances substantially increase NAPL pool dissolution, and consequently reduce the required pumpandtreat aquifer remediation time.     

Upscaling of Nonwetting Phase Residual Transport in Porous Media: A Network Approach

Based on the volume averaging method, a macroscopic model is developed for the upscaling of NAPL transport in a porous medium idealised by a network model. Under the assumption of local mass non-equilibrium, a macroscopic equation involving a dispersion tensor, additional convective terms and a linear form for the interfacial mass flux is obtained. The resolution of the two local closure problems obtained allow the determination of the local properties without adjustable parmeters. These problems are solved in a semi-analytical, semi-numerical manner on the network. The originality of this work is the association of the upscaling by volume averaging method with the network approach. The local properties, including the dispersion tensor and the mass exchange coefficient, can therefore be calculated over a large number of pore-bodies and pore-throats in a computationaly tractable manner, thus leading to more significant results. Results are presented for 3D, spatially periodic models of porous media.     

多孔介质在压力梯度作用下的热质耦合数值模拟

多孔介质干燥导致热质耦合传输过程。本文基于连续介质力学的宏观尺度,对多孔介质的热、湿和气三者耦合迁移进行数值模拟,研究压力梯度对热质传输的影响。多孔介质传质机理主要为水汽和空气的对流和扩散传输、吸附水在含湿量梯度作用下的自由扩散和其在温度梯度即Soret效应驱动下的流动。采用Galerkin加权余量的有限元方法,提出了...     

Smoothed Particle Hydrodynamics Model of Non-Aqueous Phase Liquid Flow and Dissolution

A smoothed particle hydrodynamics model was developed to simulate the flow of mixtures of aqueous and non-aqueous phase liquids in porous media and the dissolution of the non-aqueous phase in the aqueous phase. The model was used to study the effects of pore-scale heterogeneity and anisotropy on the steady state dense non-aqueous phase liquid (DNAPL) saturation when gravity driven DNAPL displaces water from initially water saturated porous media. Pore-scale anisotropy was created by using co-oriented non-overlapping elliptically shaped grains to represent the porous media. After a steady state DNAPL saturation was reached, water was injected until a new steady state DNAPL saturation was reached. The amount of trapped DNAPL was found to be greater when DNAPL is displaced in the direction of the major axes of the soil grains than when it is displaced in the direction of the minor axes of the soil grains. The amount of trapped DNAPL was also found to increase with decreasing initial saturation of the continuous DNAPL phase. For the conditions used in our simulations, the saturation of the trapped DNAPL with a smaller initial DNAPL saturation was more than 3 times larger than the amount of trapped DNAPL with a larger initial saturation. These simulations were carried out assuming that the DNAPL did not dissolve in water. Simulations including the effect of dissolution of DNAPL in the aqueous phase were also performed, and effective (macroscopic) mass transfer coefficients were determined. The U.S. Government’s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Heterogeneity Effects on Evaporation-Induced Halite and Gypsum Co-precipitation in Porous Media

Understanding evaporation from porous media in the presence of soluble salts plays a key role in describing many environmental processes. Several studies done in this field led to a wide acceptance that the prediction of soil salinization driven by evaporation from the unsaturated zone and mainly encountered in arid and semiarid regions is a challenging task because of the temporal and spatial variabilities of soil rocks combined with different interactions between the porous medium and the atmosphere. In this work, we present a reactive transport model developed with the aim of describing the processes of evaporation, salt accumulation and precipitation. We took the model presented in our previous paper (Jambhekar et al. in Transp Porous Media 114:341–369, 2016) as the basis and developed it with the required geochemical model to account for evaporative salt co-precipitation. The salts considered in this work are halite (NaCl) and gypsum (CaSO\(_{4}\cdot 2\mathrm{H}_{2}\)O). We focus particularly on the influence of spatial heterogeneities in the porous medium on the dynamics of the physical processes. In the numerical simulations performed in this work, we distinguished different heterogeneity configurations. The results show that the drying from heterogeneous porous media initially affects the coarser pores, where the salt crystals first appear.     

Homogenization Modeling and Parametric Study of Moisture Transfer in an Unsaturated Heterogeneous Porous Medium

The classical mass balance equation is usually used to model the transfer of humidity in unsaturated macroscopically homogeneous porous media. This equation is highly non-linear due to the pressure-dependence of the hydrodynamic characteristics. The formal homogenization method by asymptotic expansions is applied to derive the upscaled form of this equation in case of large-scale heterogeneities of periodic structure. The nature of such heterogeneities may be different, resulting in locally variable hydrodynamic parameters. The effective capillary capacity and the effective hydraulic conductivity are defined as functions of geometry and local characteristics of the porous medium. A study of a two-dimensional stone-mortar system is performed. The effect of the second medium (the mortar), on the global behavior of the system is investigated. Numerical results for the Brooks and Corey hydrodynamic model are provided. The sensitivity analysis of the parameters of the model in relation to the effective hydrodynamic parameters of the porous structure is presented.     

Influence of Porous Media and Airflow Rate on the Fate of NAPLs Under Air Sparging

Nonequilibrium air–water mass transfer experiments using a laboratoryscale singleair channel setup were conducted to investigate the influence of porous media and air velocity on the fate of nonaqueous phase liquids (NAPLs) under air sparging conditions. Benzene was used as a NAPL while silica sand 30/50 (dp₅₀=0.305mm, uniformity coefficient, UC=1.41) and silica sand 70/100 (dp₅₀=0.168mm, UC=1.64) were used as porous media. Air velocities ranged from 0 to 1.4cm/s. Mass transfer coefficients for the dissolution of NAPLs were estimated by numerical methods using a twodimensional dissolution–diffusion–volatilization model. The study showed that the presence of advective airflow in air channels controlled the spreading of the dissolved phase but the overall removal efficiency was independent of airflow rate. Removal efficiencies and dissolution rates of the NAPL were found to be strongly affected by the mean particle size of the porous media during air sparging. More than 50% reduction in the removal rate of benzene was found when silica sand 70/100 was used instead of silica sand 30/50. Mass transfer coefficients for the dissolution of benzene NAPL were estimated to be 0.0041cm/min for silica sand 70/100 and 0.227cm/min for silica sand 30/50. Increasing the air velocity from 0.6 to 1.4cm/s for silica sand 30/50 did not result in a higher removal rate. Quantitative estimation of the dissolution rates of benzene NAPL indicated that the dissolution rates (between 0.227 and 0.265cm/min) were similar in magnitude for the same porous media but different air flow rates. Based on the visualization study, air sparging may be used to control the spreading of the dissolved phase even when the glob of NAPL is several centimeters away from the air–water interface of the air channels.     

Local Mass Transfer Correlations for Nonaqueous Phase Liquid Pool Dissolution in Saturated Porous Media

Local mass transfer correlations are developed to describe the rate of interface mass transfer of single component nonaqueous phase liquid (NAPL) pools in saturated subsurface formations. A threedimensional solute transport model is employed to compute local mass transfer coefficients from concentration gradients at the NAPL–water interface, assuming that the aqueous phase concentration along the NAPL–water interface is constant and equal to the solubility concentration. Furthermore, it is assumed that the porous medium is homogeneous, the interstitial fluid velocity steady and the dissolved solute may undergo firstorder decay or may sorb under local equilibrium conditions. Powerlaw expressions relating the local Sherwood number to appropriate local Peclet numbers are developed for both rectangular and elliptic/circular source geometries. The proposed power law correlations are fitted to numerically generated data and the correlation coefficients are determined using nonlinear least squares regression. The estimated correlation coefficients are found to be direct functions of the interstitial fluid velocity, pool dimensions, and pool geometry.     

考虑相变的近场动力学热?力耦合模型及多孔介质冻结破坏模拟

多孔介质的传热传质现象广泛存在于自然界和工业领域中. 低温条件可能导致多孔介质中的组分发生相变, 并由此诱发材料损伤, 甚至导致结构失效破坏. 对这类破坏现象的预测需要精细化建模, 以能够反映物质的相变过程和材料的破坏特征. 本文采用热焓法改写经典的热传导方程, 在近场动力学框架下, 建立了一种考虑物质相变的热?力耦合模型, 发展了交错显式求解的数值计算方法, 进行了方板角冻结、热致变形和多孔介质冻结破坏等问题的模拟, 得到了方板的冻结特征、温度场和变形场的分布规律以及多孔介质的冻结破坏过程, 与试验和其他数值方法的结果具有较好的一致性. 研究表明, 本文所建立的考虑物质相变的近场动力学热?力耦合模型能够反映材料的非局部效应和物质相变潜热的影响, 准确捕捉相变过程中液固界面的演化特征, 再现多孔介质中材料相变、基质热致变形和冻结破坏过程, 突破了传统连续性模型求解这类破坏问题时面临的瓶颈, 为深入研究多孔介质冻融破坏过程和破坏机理提供了有效途径.      

Pore-Network Modeling of Isothermal Drying in Porous Media

In this paper we present numerical results obtained with a pore-network model for the drying of porous media that accounts for various processes at the pore scale. These include mass transfer by advection and diffusion in the gas phase, viscous flow in the liquid and gas phases and capillary effects at the liquid--gas interface. We extend our work by studying the effect of capillarity-induced flow in macroscopic liquid films that form at the pore walls as the liquid--gas interface recedes. A mathematical model that accounts for the effect of films on the drying rates and phase distribution patterns is presented. It is shown that film flow is a major transport mechanism in the drying of porous materials, its effect being dominant when capillarity controls the process, which is the case in typical applications.