Um parâmetro físico essencial na modelagem matemática de qualidade de água visando a análise do impacto causado pelo lançamento de efluentes nos corpos d\'água superficiais é o coeficiente de dispersão longitudinal (DL). Portanto, a devida quantificação desse parâmetro é de grande importância para garantir a confiabilidade dos resultados de um modelo matemático de qualidade de água. Sendo assim, o presente trabalho propôs a quantificação de tal parâmetro. Para isso foram efetuados ensaios de campo de estímulo-resposta com traçador salino (cloreto de sódio) em dois cursos d\'água de pequeno porte localizados no município de Uberaba - MG. Após a realização dos ensaios de campo foram utilizados métodos diretos para a quantificação do parâmetro a partir dos dados experimentais. Os valores de DL mais confiáveis derivaram do método da convolução (routing procedure), variando de 0,70 a 10,44 m2/s. Também foi desenvolvido um modelo matemático de previsão do coeficiente de dispersão longitudinal a partir dos resultados experimentais com base em análise dimensional e a técnica de regressão linear múltipla. O r2 da equação gerada foi de 0,87, o que sugere que esta equação é adequada para a estimativa do coeficiente de dispersão longitudinal para os cursos d\'água estudados. Foi efetuada também a validação da aplicabilidade do modelo matemático desenvolvido a outras condições de campo diferentes daquelas utilizadas em sua dedução, com base em resultados experimentais obtido por outros autores. Por fim foi obtida, para os trechos dos cursos d\'água estudados, os coeficientes de dispersão longitudinal pelas equações empíricas e semi-empíricas de previsão mais conhecidas na literatura, comparando-se o desempenho de tais equações com a equação desenvolvida no trabalho através de análise estatística. A equação produzida no presente trabalho gerou melhores estimativas do coeficiente de dispersão longitudinal para os cursos d\'água estudados do que as equações utilizadas para comparação. / An essential parameter in the mathematical modeling of water quality in order to analyze the impact caused by the release of effluents into surface water bodies is the longitudinal dispersion coefficient (DL) . Therefore, proper quantification of this parameter is of great importance to ensure the reliability of the results of a mathematical model of water quality. Thus, this paper proposed to quantify this parameter. For this, field tests were conducted with stimulus-response tracer salt (sodium chloride) in two small streams located in Uberaba - MG. After completion of the field tests, direct methods to quantify the parameter from experimental data were used. The most reliable DL values derived from the routing procedure method, with valuer between 0.70 to 10.44 m2/s. Also we developed a mathematical model to predict the longitudinal dispersion coefficient from the experimental results based on dimensional analysis and multiple linear regression technique. The equation r2 generated was 0.87, suggesting that this equation is suitable for the estimation of longitudinal dispersion in the studied streams. We also performed the validation of the applicability of the developed mathematical model to other field conditions different from those of your deduction, based on experimental results obtained by other authors. Finally we obtained in the literature for the sections of the studied streams, the longitudinal dispersion coefficients by the best known empirical and semiempirical equations, comparing the performance of such equations with the equation developed in this work through statistical analysis. The equation produced in this study gave better predictions of the longitudinal dispersion coefficient for the studied streams than the equations used for comparison.

Um parâmetro físico essencial na modelagem matemática de qualidade de água visando a análise do impacto causado pelo lançamento de efluentes nos corpos d\'água superficiais é o coeficiente de dispersão longitudinal (DL). Portanto, a devida quantificação desse parâmetro é de grande importância para garantir a confiabilidade dos resultados de um modelo matemático de qualidade de água. Sendo assim, o presente trabalho propôs a quantificação de tal parâmetro. Para isso foram efetuados ensaios de campo de estímulo-resposta com traçador salino (cloreto de sódio) em dois cursos d\'água de pequeno porte localizados no município de Uberaba - MG. Após a realização dos ensaios de campo foram utilizados métodos diretos para a quantificação do parâmetro a partir dos dados experimentais. Os valores de DL mais confiáveis derivaram do método da convolução (routing procedure), variando de 0,70 a 10,44 m2/s. Também foi desenvolvido um modelo matemático de previsão do coeficiente de dispersão longitudinal a partir dos resultados experimentais com base em análise dimensional e a técnica de regressão linear múltipla. O r2 da equação gerada foi de 0,87, o que sugere que esta equação é adequada para a estimativa do coeficiente de dispersão longitudinal para os cursos d\'água estudados. Foi efetuada também a validação da aplicabilidade do modelo matemático desenvolvido a outras condições de campo diferentes daquelas utilizadas em sua dedução, com base em resultados experimentais obtido por outros autores. Por fim foi obtida, para os trechos dos cursos d\'água estudados, os coeficientes de dispersão longitudinal pelas equações empíricas e semi-empíricas de previsão mais conhecidas na literatura, comparando-se o desempenho de tais equações com a equação desenvolvida no trabalho através de análise estatística. A equação produzida no presente trabalho gerou melhores estimativas do coeficiente de dispersão longitudinal para os cursos d\'água estudados do que as equações utilizadas para comparação. / An essential parameter in the mathematical modeling of water quality in order to analyze the impact caused by the release of effluents into surface water bodies is the longitudinal dispersion coefficient (DL) . Therefore, proper quantification of this parameter is of great importance to ensure the reliability of the results of a mathematical model of water quality. Thus, this paper proposed to quantify this parameter. For this, field tests were conducted with stimulus-response tracer salt (sodium chloride) in two small streams located in Uberaba - MG. After completion of the field tests, direct methods to quantify the parameter from experimental data were used. The most reliable DL values derived from the routing procedure method, with valuer between 0.70 to 10.44 m2/s. Also we developed a mathematical model to predict the longitudinal dispersion coefficient from the experimental results based on dimensional analysis and multiple linear regression technique. The equation r2 generated was 0.87, suggesting that this equation is suitable for the estimation of longitudinal dispersion in the studied streams. We also performed the validation of the applicability of the developed mathematical model to other field conditions different from those of your deduction, based on experimental results obtained by other authors. Finally we obtained in the literature for the sections of the studied streams, the longitudinal dispersion coefficients by the best known empirical and semiempirical equations, comparing the performance of such equations with the equation developed in this work through statistical analysis. The equation produced in this study gave better predictions of the longitudinal dispersion coefficient for the studied streams than the equations used for comparison.

Dispersion has been shown to degrade miscibility in miscible displacements by lowering the concentration of the injected solute at the displacement fronts. Dispersion can also improve oil recovery by increasing sweep efficiency. Either way, dispersion is an important factor in understanding miscible displacement performance. Conventionally, dispersion is measured in the laboratory by fitting the solution of one-dimensional convection-dispersion equation (CDE) to the effluent concentration from a core flood. However dispersion is anisotropic and mixing occurs in both longitudinal and transverse directions. This dissertation uses the analytical solution of the two-dimensional CDE to simultaneously determine longitudinal and transverse dispersion. The two-dimensional analytical solution for an instantaneous finite volume source is used to investigate anisotropic mixing in miscible displacements. We conclude that transverse mixing becomes significant with large a concentration gradient in the transverse direction and significant local variation in flow directions owing to heterogeneity. We also utilized simulation models similar to Blackwell's (1962) experiments to determine transverse dispersion. This model coupled with the analytical solution for two-dimensional CDE for continuous injection source is used to determine longitudinal and transverse dispersivity for the flow medium. The validated model is used to investigate the effect of heterogeneity and other first contact miscible (FCM) scaling groups on dispersion. We derive the dimensionless scaling groups that affect FCM displacements and determine their impact on dispersion. Experimental design is used to determine the impact and interactions of significant scaling groups and generate a response surface function for dispersion based on the scaling groups. The level of heterogeneity is found to most significantly impact longitudinal dispersion, while transverse dispersion is most significantly impacted by the dispersion number. Finally, a mathematical procedure is developed to use the estimated dispersivities to determine a-priori the maximum grid-block size to maintain an equivalent level of dispersion between fine-scale and upscaled coarse models. Non-uniform coarsening schemes is recommended and validated for reservoir models with sets of different permeability distributions. Comparable sweep and recovery are observed when the procedure was extended to multi-contact miscible (MCM) displacements. / text

A cross-section averaged Advection-Dispersion equation (ADE) model was developed to simulate the transport of fertilizer in furrow irrigation. The advection and dispersion processes were solved separately by implementing the method of the characteristics with cubic spline interpolation (and natural boundary condition) and weighted finite difference scheme respectively. A zero-flux boundary condition during advance and an advective gradient at the downstream end of an open furrow were established. Local pseudo-steady state was assumed in order to apply Fischer's longitudinal dispersion equation under non-uniform and unsteady furrow flow conditions. Also, several parameters were used to evaluate the ADE model and fertigation performance.A field tracer experiment in two types of downstream-end furrow and two treatments was conducted and described. Infiltration and roughness parameters were calibrated by implementing a volume balance approach. The calibrated parameters were used as input data to run the surface irrigation model (SRFR). The roughness coefficient was 0.045 for wheel and 0.055 for non-wheel furrow treatment for bare soil. The root mean square error (RMSE) comparing the computed and observed infiltrated volume was in the range of 0.09-0.38 m3. The close match between simulated and observed data indicates an acceptable calibration. Pulses of fertilizer injected at the head end of four furrows each having unique management characteristics were simulated satisfactorily during the entire duration of the irrigation event. The constant value of the longitudinal dispersion coefficient was 1 m2 min-1 and yielded an acceptable space-time evolution of the pulses of tracer injected. Similar results for the dispersion coefficient were obtained with Fischer's equation in non-uniform and unsteady stream flow conditions in the furrow. An evaluation of several fertigation strategies for furrow systems indicated that fertigation by pulses could help reduce leaching and runoff losses in surface irrigation systems.

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ZUSAMMENFASSUNG Die vorliegende Dissertation befasst sich mit den komplexen physikalischen und biologischen Prozessen in Flachlandflüssen, die mit der saisonalen Entwicklung submerser aquatischer Vegetation im Zusammenhang stehen. Vorrangige Ziele der durchgeführten Arbeiten waren sowohl Untersuchungen zum Einfluss elastischer submerser Vegetation auf die Struktur der turbulenten Strömung, als auch die damit verbundenen Effekte auf Transport- und Mischungsprozesse sowie mögliche Auswirkungen auf Morphodynamik und Ökologie. Erkenntnisse zur Struktur der turbulenten Strömung, die sich über Beständen submerser elastischer Vegetation entwickelt, konnten aus originären Feldexperimenten gewonnen werden. Die Resultate wurden mit der hydrodynamischen Modellierung der Entwicklung einer Mischungsschicht verglichen. Theoretische Analysen der Mischungsschicht über submerser Vegetation führten zu einer Erweitung des Modells. Dabei zeigt sich, in welcher Weise die Interaktion zwischen Strömung und Pflanzen die Entwicklung der Scherschicht und der Turbulenz beeinflusst. Die abgeleiteten theoretischen Lösungen stehen in engem Zusammenhang mit der theoretischen Beschreibung der biomechanischen Eigenschaften elastischer Vegetation. Die Dissertation beschäftigt sich vorwiegend mit Effekten der Wechselwirkung von Strömung und Bewuchs in Bezug auf eindimensionale Ansätze der Modellierung von Transport und Vermischung in Flüssen. In der Arbeit werden quantitative Ansätze zur Modellierung der longitudinalen Dispersion für einen bestimmten Typ von Vegetation vorgeschlagen, die die komplexe Struktur der Strömung bei Bewuchs berücksichtigen. Darüber hinaus wird gezeigt, wie die entwickelte Theorie zur Wechselwirkung von Strömung und Vegetation mit einem phänologischen Modell für das Wachstum der Pflanzenbiomasse gekoppelt werden kann, womit ein nahezu geschlossener Lösungsansatz für die behandelte Fragestellung vorliegt. Schlagwörter: Makrophyten, Flussströmung ,Turbulenz, longitudinale Dispersion. / SUMMARY The thesis is focused on complex physical and biological processes occurring in natural lowland streams due to the seasonal development of submerged aquatic vegetation. The primary goal of the studies was an exploration of the effects that submerged flexible vegetation sets upon turbulent flow structure, their consequences for transport and mixing processes, and implications for morphodynamics and ecology. A deeper insight into the structure of turbulent flow evolving over a patch of flexible submerged vegetation was gained completing an original field experimental study which results were examined in a context of a hydrodynamic model of the mixing layer. The model was expanded by theoretical analysis of evolution of the mixing layer over the vegetation patch yielding knowledge on how do interactions of flow and vegetation produce the velocity shear and turbulence across the flow. The obtained theoretical solutions are linked to the theoretical description of biomechanical properties for flexible buoyant vegetation. The thesis is concentrated on examining the consequences of flow – plants interactions in respect to the one-dimensional approach to the modeling of transport and mixing in rivers. In this study the longitudinal dispersion model was re-examined to account for the complex structure of flow in vegetation mosaic and possible quantitative approaches are proposed to infer the model parameters for a known type of vegetation. It was also shown how the developed theory of flow-plants interactions can be coupled with a phenological model of biomass growth providing a nearly complete approach to the problem. Keywords: macrophytes, river flow, turbulence, longitudinal dispersion.

The longitudinal solute transport modeling is critical in river and stream water quality management, control, and the mitigation of hazardous riverine spills. One of the widely used "deadzone" model is the transient storage model (TSM). TSM is a significant improvement over the advection-dispersion model (ADM), but it cannot simulate the breakthrough curve (BTC) immediately after a large pool. Additionally, the calibration (parameterization) method is challenged by the non-identifiability which is common to all inverse modeling, and it seems TSM cannot be easily used as a predictive tool, more of an interpretive tool of solute transport, i.e., is the parameter set calibrated via inverse modeling transferable? Pools are fundamental stream morphology unit in streams with mixed bed materials in pool-riffle or pool-step sequences. Understanding of how a pool impacts the longitudinal solute transport is the first step towards improving current model such as TSM or developing new models. By introducing a dimensionless group, e= Q/(Dt W) (where, Q is the average volumetric flow rate; Dt is an average transverse dispersion coefficient; W is the channel flow width), derived from non-dimensionalization of the governing equations of one of the most rigorous 2-dimansional (2D) (depth-averaged) model, Mike21, this work presents an alternative way of longitudinal solute transport investigation. Using the 2D fully hydrodynamic Mike21, numerical experiments were conducted on hypothetical streams in this dissertation. Simulation study on hypothetical stream with pool reveals that a pool's effects on longitudinal solute transport are manifested by three aspects: boosting longitudinal spreading (concentration peak attenuation), causing a solute plume delay and increasing solute residence time. These effects fade like a "wake" as the solute plume moves downstream. e provides an insight into the physics of longitudinal transport; it outlines a relative transverse mixing intensity of a stream. The internal transport and mixing condition (including the secondary circulations) in a pool together with the pool's dimensions determine the pool's storage effects especially when e >>1. The BTCs downstream from a pool may be "heavy tailed" (i.e., have enormously slow decaying rate) which cannot be modeled by the TSM. Results also suggest that the falling limb of a BTC more accurately characterizes the pool's storage effects because the corresponding solute has more chance to sample the entire storage area. n a more fundamental perspective, the predictive ability of inverse modeling parameterized model is discussed and conclusion is made about the role of a stream/river system's nonlinearity in determining the predictability; a misleading mis-nomenclature in TSM application is also demonstrated with a numerical experiment. / Civil Engineering

Flow and transport phenomena in the subsurface often span a wide range of length (nanometers to kilometers) and time (nanoseconds to years) scales, and frequently arise in applications of CO₂ sequestration, pollutant transport, and near-well acid stimulation. Reliable field-scale predictions depend on our predictive capacity at each individual scale as well as our ability to accurately propagate information across scales. Pore-scale modeling (coupled with experiments) has assumed an important role in improving our fundamental understanding at the small scale, and is frequently used to inform/guide modeling efforts at larger scales. Among the various methods, there often exists a trade-off between computational efficiency/simplicity and accuracy. While high-resolution methods are very accurate, they are computationally limited to relatively small domains. Since macroscopic properties of a porous medium are statistically representative only when sample sizes are sufficiently large, simple and efficient pore-scale methods are more attractive. In this work, two Eulerian pore-network models for simulating single-phase flow and solute transport are developed. The models focus on capturing two key pore-level mechanisms: a) partial mixing within pores (large void volumes), and b) shear dispersion within throats (narrow constrictions connecting the pores), which are shown to have a substantial impact on transverse and longitudinal dispersion coefficients at the macro scale. The models are verified with high-resolution pore-scale methods and validated against micromodel experiments as well as experimental data from the literature. Studies regarding the significance of different pore-level mixing assumptions (perfect mixing vs. partial mixing) in disordered media, as well as the predictive capacity of network modeling as a whole for ordered media are conducted. A mortar domain decomposition framework is additionally developed, under which efficient and accurate simulations on even larger and highly heterogeneous pore-scale domains are feasible. The mortar methods are verified and parallel scalability is demonstrated. It is shown that they can be used as “hybrid” methods for coupling localized pore-scale inclusions to a surrounding continuum (when insufficient scale separation exists). The framework further permits multi-model simulations within the same computational domain. An application of the methods studying “emergent” behavior during calcite precipitation in the context of geologic CO₂ sequestration is provided. / text

Les phénomènes de transport en milieux poreux sont étudiés depuis près de deux siècles, cependant les travaux concernant les milieux fortement poreux sont encore relativement peu nombreux. Les modèles couramment utilisés pour les poreux classiques (lits de grains par exemple) sont peu applicables pour les milieux fortement poreux (les mousses par exemple), un certain nombre d’études ont été entreprises pour combler ce manque. Néanmoins, les résultats expérimentaux et numériques caractérisant les pertes de charge dans les mousses sont fortement dispersés. Du fait des progrès de l’imagerie 3D, une tendance émergente est la détermination des paramètres des lois d’écoulement à partir de simulations directes sur des géométries reconstruites. Nous présentons ici l’utilisation d’une nouvelle approche cinétique pour résoudre localement les équations de Navier-Stokes et déterminer les propriétés d’écoulement (perméabilité, dispersion, ...). / A novel kinetic scheme satisfying an entropy condition is developed, tested and implemented for the simulation of practical problems. The construction of this new entropic scheme is presented. A classical hyperbolic system is approximated by a discrete velocity vector kinetic scheme (with the simplified BGK collisional operator), but applied to an inviscid compressible gas dynamics system with a small Mach number parameter, according to the approach of Carfora and Natalini (2008). The numerical viscosity is controlled, and tends to the physical viscosity of the Navier-Stokes system. The proposed numerical scheme is analyzed and formulated as an explicit finite volume flux vector splitting (FVS) scheme that is very easy to implement. It is close in spirit to Lattice Boltzmann schemes, but it has the advantage to satisfy a discrete entropy inequality under a CFL condition and a subcharacteristic stability condition involving a cell Reynolds number. The new scheme is proved to be second-order accurate in space. We show the efficiency of the method in terms of accuracy and robustness on a variety of classical benchmark tests. Some physical problems have been studied in order to show the usefulness of both schemes. The LB code was successfully used to determine the longitudinal dispersion of metallic foams, with the use of a novel indicator. The entropic code was used to determine the permeability tensor of various porous media, from the Fontainebleau sandstone (low porosity) to a redwood tree sample (high porosity). These results are pretty accurate. Finally, the entropic framework is applied to the advection-diffusion equation as a passive scalar.