Academic literature on the topic 'Non-Fickian dispersion'

In this study, four homogeneous porous media (HPM1-HPM4), consisting of distinct proportions of sand-sized and clay-sized solid beads, were prepared and used as single fracture infills. Flow and nonreactive solute transport experiments in HPM1-HPM4 under three flow rates were conducted, and the measured breakthrough curves (BTCs) were quantified using conventional advection-dispersion equation (ADE), mobile-immobile model (MIM), and continuous time random walk (CTRW) model with truncated power law transition time distribution. The measured BTCs showed stronger non-Fickian behaviour in HPM2-HPM4 (which had clay) than in HPM1 (which had no clay), implying that clay enhanced the non-Fickian transport. As the fraction of clay increased, the global error of ADE fits also increased, affirming the inefficiency of ADE in capturing the clay-induced non-Fickian behaviour. MIM and CTRW performed better in capturing the non-Fickian behaviour. Nonetheless, CTRW’s performance was robust. 12.5% and 25% of clay in HPM2 and HPM3, respectively, decreased the flowing fluid region and increased the solute exchange rate between the flowing and stagnant fluid regions in MIM. For CTRW, the power law exponent ( β CTRW ) values were 1.96, 1.75, and 1.63 in HPM1-HPM3, respectively, implying enhanced non-Fickian behaviour. However, for HPM4, whose clay fraction was 50%, the β CTRW value was 1.87, implying a deviation in the trend of non-Fickian enhancement with increasing clay fraction. This deviation indicated that non-Fickian behaviour enhancement depended on the fraction of clay present. Moreover, increasing flow rate enhanced the non-Fickian transport based on β CTRW .

In this study, the performance of two routing procedures were evaluated to estimate the two-dimensional dispersion coefficients. The two-dimensional Stream-Tube Routing Procedure (2D ST-RP) has been widely used to obtain the dispersion coefficients from measured concentration-time curves under the frozen cloud assumption. Meanwhile, the Spatial Routing Procedure (2D S-RP) employs the spatial distributions of concentration to estimate the dispersion coefficients. The performance of the two routing methods were evaluated in aspect of the validity of the frozen cloud assumption and the applicability in the non-Fickian mixing. From the estimation results of dispersion coefficients, the results by the 2D ST-RP included errors due to skewed concentration-time curves which were created by violating the frozen cloud assumption. On the other hand, the 2D S-RP provides accurate dispersion coefficients in the same condition. The estimated results of dispersion coefficients in the meandering channel show that both the 2D ST-RP and the 2D S-RP contained errors due to the non-Fickian mixing properties of the test case. Even with the discrepancies, the 2D S-RP presented more appropriate spatial variabilities along the meander cycle than the results by the 2D ST-RP.

Abstract. During a risk assessment procedure as well as when dealing with cleanup and monitoring strategies, accurate predictions of solute propagation in fractured rocks are of particular importance when assessing exposure pathways through which contaminants reach receptors. Experimental data obtained under controlled conditions such as in a laboratory allow to increase the understanding of the fundamental physics of fluid flow and solute transport in fractures. In this study, laboratory hydraulic and tracer tests have been carried out on an artificially created fractured rock sample. The tests regard the analysis of the hydraulic loss and the measurement of breakthrough curves for saline tracer pulse inside a rock sample of parallelepiped shape (0.60 × 0.40 × 0.08 m). The convolution theory has been applied in order to remove the effect of the acquisition apparatus on tracer experiments. The experimental results have shown evidence of a non-Darcy relationship between flow rate and hydraulic loss that is best described by Forchheimer's law. Furthermore, in the flow experiments both inertial and viscous flow terms are not negligible. The observed experimental breakthrough curves of solute transport have been modeled by the classical one-dimensional analytical solution for the advection–dispersion equation (ADE) and the single rate mobile–immobile model (MIM). The former model does not properly fit the first arrival and the tail while the latter, which recognizes the existence of mobile and immobile domains for transport, provides a very decent fit. The carried out experiments show that there exists a pronounced mobile–immobile zone interaction that cannot be neglected and that leads to a non-equilibrium behavior of solute transport. The existence of a non-Darcian flow regime has showed to influence the velocity field in that it gives rise to a delay in solute migration with respect to the predicted value assuming linear flow. Furthermore, the presence of inertial effects enhance non-equilibrium behavior. Instead, the presence of a transitional flow regime seems not to exert influence on the behavior of dispersion. The linear-type relationship found between velocity and dispersion demonstrates that for the range of imposed flow rates and for the selected path the geometrical dispersion dominates the mixing processes along the fracture network.

Ces travaux ont pour objectif de modéliser les mécanismes de dispersion dans les aquifères. L’hétérogénéité du champ de vitesse et le transfert de masse entre zones immobiles et mobiles sont deux origines possibles du comportement non-Fickéen, jusqu’alors étudiées de façon séparée. Notre hypothèse de départ est que ces deux mécanismes coexistent. Nos travaux comprennent : 1) des expériences de traçage sur colonnes de billes de verre et carottes de grès de Berea, en mode flow-through et push-pull, et 2) des simulations numériques réalisées à partir d’images en microtomographie RX segmentées en trois phases : solide, vide et microporosité. L’analyse du champ de vitesse (Stokes) montre l’importance de la discrétisation spatiale et de la prise en compte de la microporosité. Les résultats des simulations de transport (en utilisant la méthode time domain random walk) permettent de quantifier l’effet combiné de l’hétérogénéité du champ de vitesse et des transferts diffusifs dans la fraction micro-poreuse de la roche sur la dispersion non-Fickéenne, caractérisée à partir des courbes de restitution (BTC). Ces résultats sont cohérents avec les observations expérimentales. Nous concluons que ces deux effets doivent être pris en compte même si leur identification à partir de la forme des BTCs issues des traçages des milieux naturels (souvent caractérisés par de faible valeurs du nombre de Peclet ) reste difficile. Enfin, un modèle moyen macroscopique 1D est proposé dans le cadre d’une approche de type continuous time random walk dans laquelle des distributions spécifiques du temps de transfert des particules sont construites pour chacun des deux mécanismes de transport
His work aims at modeling hydrodynamic dispersion mechanisms in aquifers. So far both flow field heterogeneity and mobile-immobile mass transfer have been studied separately for explaining the ubiquitously observed non-Fickian behaviors, but we postulate that both mechanisms contribute simultaneously. Our investigations combine laboratory experiments and pore scale numerical modeling. The experimental rig was designed to enable push-pull and flow through tracer tests on glass bead columns and Berea sandstone cores. Modeling consists in solving Stokes flow and solute transport on 3D X-ray microtomography images segmented into three phases: solid, void and microporosity. Transport is modeled using time domain random walk. Statistical analysis of the flow field emphasizes the importance of the mesh resolution and the inclusion of the microporosity. Results from the simulations show that both the flow field heterogeneity and the diffusive transport in the microporous fraction of the rock contribute to the overall non-Fickian transport behavior observed, for instance, on the breakthrough curves (BTC). These results are supported by our experiments. We conclude that, in general, this dual control must be taken into account, even if these different influences can hardly be distinguished from a qualitative appraisal of the BTC shape, specifically for the low values of the Peclet number that occurs in natural conditions. Finally, a 1D up-scaled model is developed in the framework of the continuous time random walk, where the influences of the flow field heterogeneity and mobile-immobile mass transfer are both taken into account using distinct transition time distributions

Until present, many researchers relied on the conventional plug flow dispersion models to analyse the concentration profiles obtained from the tracer injection experiments to evaluate the dispersion coefficients in packed beds. The Fickian concept in the limit of long time duration is assumed to be applicable and it implies that the mean-square displacement of the tracer profile is constant with time and the concentration profile is Gaussian. There were very few studies on identifying the conditions under which this assumption is valid and delineate the range of applicability of the existing plug flow dispersion models. If the time scales of a tracer injection experiment are not sufficient for a tracer to traverse the bed radius and sample the velocity variations, this could give rise to persisting non-Fickian transients where the mean-square displacement of the tracer profile is not constant with time and the concentration profile deviates from the normal Gaussian distribution. These transients cannot be predicted by the conventional plug dispersion models. An extended axial non-Fickian macroscopic dispersion model is derived to describe the transient development of a solute tracer when injected into a fluid flowing through a cylindrical packed bed or empty tube and some non-Fickian effects in the dispersion process. The flow profile in beds packed with uniform particles exhibits radial non-uniformity due to the oscillatory variation in porosity because of the wall confinement (wall effect). Compared with the axial plug flow dispersion model, the extended model contains time-dependent coefficients such as the transient axial dispersion coefficient and higher order derivatives (higher than second order) of the cross-sectionally averaged concentration. Including them provides some insight on non-Fickian transport in the dispersion process. The model provides time criteria on the basis that the effelongitudinal dispersion coefficient in the packed bed reaches its asymptotic value and the non-Fickian transients will die out. Some experimental conditions in the literature were checked by these criteria and found to be either marginally satisfied, or not satisfied at all, which indicates that the Fickian concept is not valid. The model results for tracer dispersion in cylindrical packed beds show that the longitudinal dispersion coefficient converges to its asymptotic value on a time scale proportional to R2/(DT) where R is the column radius and (DT) is the area averaged lateral dispersion coefficient. The extended model encouraged study of the consequences of the additional dispersion terms in other applications such as the pulse spread in the field of capillary column inverse gas chromatography (CCIGC). CCIGC is used to evaluate the solute-polymer diffusion coefficient Dp and the partition coefficient K at infinite dilute conditions. The tube geometry in CCIGC is more complex than the conventional Taylor dispersion problem due to the polymer coating on the inside of the capillary wall. The extended CCIGC model presented in this study has advantages over the previous models by including the effects of Taylor dispersion and higher order derivatives of the pulse area-averaged concentration. Taylor dispersion effect causes more pulse spread in the longitudinal direction and by not including it in the CCIGC regression models may cause a significant error in the measured Dp values. The extended CCIGC model provides for the first time criteria on capillary dimensions for the transient coefficients (multiplying the second and higher order derivatives) to become constant and for the non-Fickian effects associated with the higher order derivatives to be neglected. Model results show that Taylor dispersion effect has a significant effect on the elution profiles at high values of Dp and/or low values of gas diffusion coefficients Dg and it can be used to increase the sensitivity range of the previous CCIGC models at extremely low and high Dp values.

L'activité humaine a un impact significatif sur la vadose, une zone située au-dessus des nappes phréatiques, qui n'est que partiellement saturée en eau. La vadose peut être polluée par les activités agricoles ou industrielles, ce qui constitue une menace pour les ressources en eau. De plus, la saturation varie considérablement, notamment en raison des sécheresses plus fréquentes dues au changement climatique. Prévoir le transport de contaminants en milieux insaturées est donc essentiel. Cependant, la compréhension de la dispersion dans les milieux poreux insaturés reste limitée, en raison de l'interaction complexe des flux multiphasiques non miscibles avec le milieu poreux. Les modèles traditionnels tels que le modèle Fickien, décrit par l'équation d'Advection-Diffusion, ne parviennent pas à rendre compte avec précision de la dispersion dans les milieux poreux insaturés. L'objectif est d'aborder la question du transport dans les milieux poreux insaturés en identifiant les propriétés pertinentes à l'échelle du pore pour comprendre la dispersion à plus grande échelle. Il s'agit notamment de déterminer si la dispersion est fickienne ou non-fickienne, ce qui est crucial pour prédire la propagation des polluants. Une double approche est adoptée : des expériences de transport à l'échelle du pore et des simulations de Lattice Boltzmann. La visualisation directe des fluides dans les milieux poreux est un défi. Nous utilisons donc des micromodèles, réseaux poreux transparents interconnectés, pour permettre la visualisation optique à l'échelle du pore. Tout d'abord, un dispositif expérimental micromodèle a été établi et optimisé pour étudier l'écoulement et le transport multiphasiques. Des méthodes d'analyse ont été développées, ainsi que des techniques de caractérisation de la dispersion par l'analyse des moments spatiaux. Une première série d'expériences mène à des résultats préliminaires, l'évolution de la saturation et des distributions de phases avec le nombre capillaire a été caractérisée. Les expériences de transport réalisées pour toute la gamme de saturation montrent que la dispersion augmente à mesure que la saturation diminue. Cependant, l'analyse des faibles saturations s'est avérée difficile en raison de l'augmentation significative de la dispersion et des limites imposées par la taille du micromodèle, empêchant l'étude de la dispersion à long terme. Pour surmonter cette limitation, des simulations Lattice-Boltzmann ont été utilisées pour l'écoulement et le transport, car elles sont flexibles en taille et seulement limitées par le temps de calcul. Toutefois, simuler la distribution de deux phases après un écoulement multiphasique dans un milieu poreux complexe reste un défi. Générer des images à grande échelle de milieux poreux insaturés à partir de données expérimentales s'est donc avéré nécessaire pour observer la dispersion à temps long. Un algorithme de statistique multipoints (MPS) a été utilisé pour générer à la fois des images de milieux poreux non saturés plus larges et un grand ensemble de d'images plus petites pour augmenter la signification statistique de l'étude. Des simulations d'écoulement et de transport ont été réalisées sur l'ensemble des images générées afin d'explorer l'influence de la saturation sur l'écoulement et le transport. Cette étude révèle que la diminution de la saturation augmente de manière significative l'hétérogénéité de l'écoulement, ce qui entraîne une dispersion accrue. Notamment, la nature non fickienne de l'écoulement tend à être plus prononcée à faible saturation. De plus, la transition d'un transport fickien à un transport non fickien dépend du nombre de Peclet. Il existe une compétition entre l'advection et la diffusion dans des conditions saturées, ce qui entraîne un régime Fickien diffusif pour les faibles nombres de Peclet. Cependant, le transport en conditions non saturées est principalement advectif, même à faible nombre de Peclet, et présente donc un comportement non Fickien
Human activity has a significant impact on the vadose zone, an area located below the land surface and above the water tables, only partially saturated with water. The vadose is susceptible to pollution from agricultural or industrial activities, posing a threat to water resources. Plus, saturation levels vary greatly, especially with the increasing frequency of droughts due to climate change. Hence, predicting contaminant transport in unsaturated conditions is crucial. However, the understanding of dispersion in unsaturated porous media remains limited, due to the complex interaction of multiphase non-miscible flows with the porous medium. Traditional models such as the Fickian model, described by the Advection-Diffusion Equation, fail to accurately capture dispersion in unsaturated porous media.The objective is to address the issue of transport in unsaturated porous media by identifying relevant properties at the pore scale to understand dispersion at a larger scale. One of the goals is to determine whether dispersion follows Fickian or non-Fickian behavior, as this understanding is crucial for predicting the spreading of pollutant in the vadose zone.To investigate transport in unsaturated porous media, a dual approach is being employed: pore scale transport experiments and Lattice Boltzmann simulations. Direct visualization of fluid structure in natural porous media is challenging. Thus, we use micromodels, transparent interconnected porous networks, to enable optical visualization at the pore scale. First, a micromodel experimental setup was established and optimized to study multiphase flow and transport. Analysis methods were developed, along with techniques for characterizing dispersion through spatial moment analysis.A series of experiments were conducted to obtain initial results on multiphase flow and dispersion. The evolution of saturation and phase distributions with the capillary number was characterized. Transport experiments were performed for the entire range of saturations, showing that dispersion increases as saturation decreases. However, analyzing low saturations was challenging due to the significant increase in dispersion and limitations imposed by the micromodel size, preventing the study of long-term dispersion.To overcome this limitation, Lattice Boltzmann simulations were used for flow and transport, as there is no size limitation except for computational time. However, simulating the distribution of two phases after a multiphase flow in a complex porous medium remains challenging. Generating large-scale images of unsaturated porous media based on experimental data was then crucial for observing late-time dispersion. Machine learning techniques, specifically the Multiple Point Statistic algorithm, were employed to generate images of wider unsaturated porous media and a large dataset of smaller images to increase the statistical significance of the study.Flow and transport simulations were conducted using the generated image dataset to explore the influence of saturation on flow and transport. This involved examining flow properties under saturated and unsaturated conditions. The nature of transport, specifically whether it exhibited Fickian or non-Fickian behavior was investigated. Furthermore, the effect of the Peclet number (a measure of the balance between advection and diffusion) on dispersion for different saturation levels was analyzed.This study revealed that decreasing saturation significantly increases flow heterogeneity, leading to increased dispersion. Notably, the non-Fickian nature of flow tends to be more pronounced with low saturations. Plus, the transition from Fickian to non-Fickian depends on the Peclet number. There is a competition between advection and diffusion in saturated conditions, resulting in a diffusive Fickian regime for low Peclet numbers. However, transport in unsaturated conditions is mainly advective, even at low Peclet, and thus displays a non-Fickian behavior

This thesis focuses on solute transport upscaling. Upscaling of solute transport is usually required to obtain computationally efficient numerical models in many field applications such as, remediation of aquifers, environmental risk to groundwater resources or the design of underground repositories of nuclear waste. The non-Fickian behavior observed in the field, and manifested by peaked concentration profiles with pronounced tailing, has questioned the use of the classical advection-dispersion equation to simulate solute transport at field scale using numerical models with discretizations that cannot capture the field heterogeneity. In this context, we have investigated the use of the advection-dispersion equation with mass transfer as a tool for upscaling solute transport in a general numerical modeling framework. Solute transport by groundwater is very much affected by the presence of high and low water velocity zones, where the contaminant can be channelized or stagnant. These contrasting water velocity zones disappear in the upscaled model as soon as the scale of discretization is larger that the size of these zones. We propose, for the modeling solute transport at large scales, a phenomenological model based on the concept of memory functions, which are used to represent the unresolved processes taking place within each homogenized block in the numerical models. We propose a new method to estimate equivalent blocks, for which transport and mass transfer parameters have to be provided. The new upscaling technique consists in replacing each heterogeneous block by a homogeneous one in which the parameters associated to a memory functions are used to represent the unresolved mass exchange between highly mobile and less mobile zones occurring within the block. Flow upscaling is based on the Simple Laplacian with skin, whereas transport upscaling is based in the estimation of macrodispersion and mass transfer parameters as a result of the interpretation of the r
Llerar Meza, G. (2009). Upscaling nonreactive solute transport [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/5848
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This report describes activity conducted in several lines of research associated with field-scale water and solute processes. A major effort was put forth developing a stochastic continuum analysis for an important class of problems involving flow of reactive and non reactive chemicals under steady unsaturated flow. The field-scale velocity covariance tensor has been derived from local soil properties and their variability, producing a large-scale description of the medium that embodies all of the local variability in a statistical sense. Special cases of anisotropic medium properties not aligned along the flow direction of spatially variable solute sorption were analysed in detail, revealing a dependence of solute spreading on subtle features of the variability of the medium, such as cross-correlations between sorption and conductivity. A novel method was developed and tested for measuring hydraulic conductivity at the scale of observation through the interpretation of a solute transport outflow curve as a stochastic-convective process. This undertaking provided a host of new K(q) relationships for existing solute experiments and also laid the foundation for future work developing a self-consistent description of flow and transport under these conditions. Numerical codes were developed for calculating K(q) functions for a variety of solute pulse outflow shapes, including lognormal, Fickian, Mobile-Immobile water, and bimodal. Testing of this new approach against conventional methodology was mixed, and agreed most closely when the assumptions of the new method were met. We conclude that this procedure offers a valuable alternative to conventional methods of measuring K(q), particularly when the application of the method is at a scale (e.g. and agricultural field) that is large compared to the common scale at which conventional K(q) devices operate. The same problem was approached from a numerical perspective, by studying the feasibility of inverting a solute outflow signal to yield the hydraulic parameters of the medium that housed the experiment. We found that the inverse problem was solvable under certain conditions, depending on the amount of noise in the signal and the degree of heterogeneity in the medium. A realistic three dimensional model of transient water and solute movement in a heterogeneous medium that contains plant roots was developed and tested. The approach taken was to generate a single realization of this complex flow event, and examine the results to see whether features were present that might be overlooked in less sophisticated model efforts. One such feature revealed is transverse dispersion, which is a critically important component in the development of macrodispersion in the longitudinal direction. The lateral mixing that was observed greatly exceeded that predicted from simpler approaches, suggesting that at least part of the important physics of the mixing process is embedded in the complexity of three dimensional flow. Another important finding was the observation that variability can produce a pseudo-kinetic behavior for solute adsorption, even when the local models used are equilibrium.