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Published: 4 June 2021
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1

Welsh, Wendy Denise, and wendywelsh@yahoo com au. "Groundwater balance modelling with Darcy's Law." The Australian National University. Faculty of Science, 2007. http://thesis.anu.edu.au./public/adt-ANU20070703.165654.

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The sustainability of groundwater resources is important for the environment, the economy and communities where surface water is scarce. It is a hidden resource, but additional information can be extracted by combining groundwater measurements and lithological information with groundwater flow equations in groundwater models. The models convert data and knowledge about the groundwater systems into information, such as relative inflow and outflow rates and water-level predictions that can be readily understood by groundwater managers. ¶ The development of models to effectively inform groundwater management policies is, however, a complex task that presents a fundamental scientific challenge. This thesis presents methods and results for water balances calculated using groundwater flow models. Groundwater flow modelling methods and approaches are discussed, and their capabilities and limitations are reviewed. Two groundwater systems are studied for the Great Artesian Basin (GAB) and for the irrigation area near Bowen, Queensland. Three approaches to water balance modelling are applied in comprehensive model-development frameworks that take into account model objectives, data and knowledge availability and sensitivity analysis techniques. The three models show numerical methods of increasing complexity. The Bowen study area is well-suited to the least-complex method because data collection has been a priority there. As a contrast, the GAB is a large, poorly-monitored basin for which more knowledge of the groundwater system can be gained from its simulation by the steady state and transient groundwater flow models. The Bowen impact assessment model calculates dynamic historical water balances. The GAB aquifer models are high-complexity representations of the groundwater system that include predicted responses of the system to changes in hydrological conditions. These are comprehensive and well-documented attempts to model these systems. They provide a platform for scenario investigation and future improvements. ¶ Darcy’s Law was used in a GIS (Geographic Information System) to calculate dynamic water balances for an aquifer near the Queensland town of Bowen. This is the first time this approach has been applied to generate a complete groundwater balance. Over the period 1989-1997 the model estimates average total inflows to be 87 % groundwater recharge by rainfall and irrigation return flow, 12 % river recharge and 1 % inflow across the study area boundary. Outflows are estimated to be 66 % evapotranspiration, 28 % water bore discharge, 4 % discharge to the ocean and 2 % groundwater loss to rivers. Analyses show that evapotranspiration is the most uncertain parameter value. The GIS method was found to be useful for calculating water balances more accurately than analytical methods, because of their simplifying assumptions, and less time consuming than the more complex numerical models developed for the GAB aquifer. ¶ For the GAB, a steady state numerical model was developed and tested and predictive scenarios were run. The purpose of this modelling was both to gain a better understanding of the water balance of the GAB and to provide a tool that could predict water level recoveries under different bore rehabilitation scenarios. The model complexity is greater than in any previous numerical groundwater model of the GAB. In particular, the model uses more data, extends over a larger area and uses a generally finer discretisation than previous models. For the nearest surface artesian aquifer in 1960 the model estimates total inflows to be 60 % groundwater recharge and 40 % diffuse vertical inter-aquifer leakage. The model estimates outflows to be 53 % diffuse vertical leakage, 43 % water bore discharge, 3 % spring discharge and 1 % discharge to the ocean. Analyses show that the model is most sensitive to changes in horizontal hydraulic conductivity and recharge. The model-predicted heads match field measurements with a Scaled RMS error of 0.8 %, which is well within the guideline error of 5 %. The predictive scenarios show net vertical leakage into the aquifer decreasing and net vertical leakage out of the aquifer increasing, as bore flows are reduced. These estimates of inflows and outflows complement other studies of the Basin and add to our understanding of its hydrodynamics. In this way the water balance helps provide a sound basis for the development of GAB groundwater management plans and policies. Through its water level recovery predictions, the model has also been used to support the GAB Sustainability Initiative. ¶ A transient numerical model of the GAB was also developed and tested, and predictive scenarios were run. This model builds on the steady state model, and is more complex, with a calibration period (1965-1999) that is longer than in any previous GAB model. During calibration the model observations were expressed and weighted so that the minimisation of the objective function reflected the relative importance of the model’s potential uses, these being respectively: to simulate the impact of changing bore flows, to more generally inform water management plans and to provide an estimate of the water balance. It was found that the 1960 steady state assumption was not correct. Discluding anthropogenic discharge, the model is most sensitive to recharge and hydraulic conductivity. The model-predicted heads match field measurements with a Scaled RMS error of 2.7 %, which is well within the guideline error of 5 %, but the increased data requirements of the transient model highlighted deficiencies in the data available for the modelling. In particular, the uneven spread of the groundwater measurements over both time and space, the questionable accuracy of measurements from both high temperature and pressure bores, and corroded bores, and the type of discharge measured (for example, maximum yield or flow-as-found), became evident during the calibration of the model. Insights and the value of this work indicates for the first time that at the start of 2005 outflows were estimated to exceed inflows by 266 GL/year, or 62 % of total inflows, and, assuming that inflows through the aquifer’s boundary will not be reduced due to climate change, it will be possible to recover some of the lost groundwater pressure if all stock and domestic bores are rehabilitated and new extractions are limited. In this case the modelling estimates that inflows could exceed outflows by up to 40 % of total outflows.
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2

Punpocha, Mahosut. "Flow in a porous medium driven by differential heating." Thesis, City University London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340050.

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3

Hood, Jonathan Patrick. "Changes in Oriented Strandboard Permeability During Hot-Pressing." Thesis, Virginia Tech, 2004. http://hdl.handle.net/10919/10049.

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Convective heat transfer during hot pressing in wood-based composite panel manufacturing is widely accepted as the most important means of heat transport for resin curing. The rate of convective heat transfer to the panel core is controlled by its permeability. Permeability in the plane of the panel also controls the flow of vapor to the panel edges, thereby influencing the potential for panel "blowing". This research considers how flake thickness, flake alignment and changing mat density during hot-pressing influences OSB mat permeability, through its thickness and in the plane of the panel. Some previous research exists but it fails to address the affects of horizontal and vertical density gradients as well as flake alignment. An apparatus was designed to allow cold pressing of aligned flakes to desired densities while enabling permeability measurements through the mat thickness. An additional apparatus was designed to allow the measuring of permeability in the plane of the mat. These designs permitted permeability measurements in mats that had no vertical density gradient, allowing for the direct study of permeability versus density (compaction ratio). Superficial permeability was determined using Darcy's law and for each sample, multiple readings were made at five different pressure differentials. Permeability through the mat thickness was highly dependent on compaction ratio and to a lesser extent flake thickness. As the compaction ratio is increased, the initial reduction in permeability is severe, once higher compaction ratios are achieved the reduction in permeability is less pronounced. Permeability decreased with decreasing flake thickness. Permeability in the plane of the mat decreases with increasing compaction ratio but in a less severe manner than through the mat thickness. In this case, the permeability-compaction ratio relationship appears linear in nature. Again, permeability decreases with decreasing flake thickness.
Master of Science
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4

Arimoto, Shinichi. "Numerical method for coupled analysis of Navier-Stokes and Darcy flows." Kyoto University, 2018. http://hdl.handle.net/2433/232352.

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Kyoto University (京都大学)
0048
新制・課程博士
博士(農学)
甲第21151号
農博第2277号
新制||農||1059(附属図書館)
学位論文||H30||N5125(農学部図書室)
京都大学大学院農学研究科地域環境科学専攻
(主査)教授 村上 章, 教授 川島 茂人, 教授 藤原 正幸
学位規則第4条第1項該当
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5

Franks, Susan J. "Mathematical modelling of tumour growth and stability." Thesis, Nottingham Trent University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366363.

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6

Tangpithakkul, Rawee. "Study of permeability of pavement base materials." Ohio University / OhioLINK, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1184344573.

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7

Zafar, Saleem. "Strength and hydraulic conductivity characteristics of roller compacted concrete." Ohio : Ohio University, 1997. http://www.ohiolink.edu/etd/view.cgi?ohiou1184617589.

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8

Mattos, Tiago Souza. "Avaliação do impacto da substituição de pastagem por eucalipto na recarga de aquífero freático." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/18/18138/tde-14082015-144441/.

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As plantações florestais, historicamente, estão associada a intensos debates sobre o seu impacto na dinâmica da água do solo ou subterrânea. Nesse contexto, este trabalho buscou avaliar os possíveis impactos da mudança de cobertura do solo, de pastagem para eucalipto, sobre o aquífero freático em zona de afloramento do Sistema Aquífero Guarani. A área de pesquisa está localizada na bacia do Ribeirão da Onça, situada no município de Brotas, no centro-leste do Estado de São Paulo. Essa é monitorada desde 2004. Foram utilizados dois métodos para avaliar o impacto da mudança de uso do solo, o método iWTF e o método de Darcy. A partir desses métodos, estimou-se as taxas de recarga subterrânea, fluxo lateral, variação de armazenamento e percolação profunda. Além disso foram obtidas a variação do nível freático, espessura saturada e gradiente hidráulico horizontal para o aquífero na área de estudo. Durante os anos hidrológicos de 2005 a 2011, a recarga direta variou de 255 e 876 mm (iWTF), equivalente a 21% e 51% da precipitação anual correspondente. Após 2011, com a mudança de cobertura do solo de pastagem para eucalipto, não obstante os anos hidrológicos de 2012 e 2013 apresentarem precipitação próxima da média de longo período, a recarga direta foi estimada em cerca de 210 mm (2012) e 147 mm (2013), equivalentes a 13% e 10% da precipitação anual. A diminuição na recarga direta levou à redução da espessura saturada, variação do nível freático, gradiente hidráulico horizontal, fluxo lateral e armazenamento anual. Além disso, pode-se perceber que a plantação florestal está exercendo influência sobre a área de pastagem adjacente à plantação. Tem-se observado essa influência através da existência de fluxo transversal em direção à plantação florestal, o qual tem elevado o armazenamento no período de estiagem. Os resultados indicam que a plantação de eucalipto afetou significativamente o comportamento sazonal e anual do balanço hídrico na área de estudo.
Historically forest plantations are associated with intense debate about its impact on soil water dynamics or groundwater. Thus, the objective of this study was to evaluate the potential impacts of land cover change of pasture to eucalyptus on the groundwater in an outcrop zone of the Guarani Aquifer System. The study area is located in the Ribeirão da Onça watershed, located in the municipality of Brotas, in the center-east of the state of São Paulo. To assess the impact of land cover change, I used two methods: i. iWTF and ii. Darcy. From these methods, we estimated groundwater recharge rates, lateral flow, water storage variation and deep percolation. Furthermore, I obtained the water table variation, saturated thickness and horizontal hydraulic gradient into the aquifer in the study area. During the hydrological years 2005-2011, the direct recharge through the results of iWTF method varied between 256 and 876 mm, equivalent to 21% and 51% of the corresponding annual precipitation. After 2011, with the land cover change of pasture to eucalyptus, the direct recharge was computed at about 210 mm (2012) and 147 mm (2013), equivalent to 13% and 10% of the annual precipitation. I did not find significant difference in the annual precipitation in these years compared to the historical mean. Therefore, my findings have shown that the decrease of direct recharge are associated to the land cover change of pasture to eucalypts. The decrease in direct recharge leads to the reduction of saturated thickness, the water level variation, horizontal hydraulic gradient, lateral flow and annual storage. Moreover, it can be seen that the forest plantation has influenced the pasture area, adjacent to the plantation. It has been observed that influence through the existence of cross flow toward the forest plantation, which has high storage, especially in the dry season. The results indicate that the eucalyptus plantation significantly affected the seasonal and annual behavior of the water balance in the study area.
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9

Erdmann, Robert Gerald. "Image-Based Numerical Simulation of Stokes Flow in Porous Media." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/195724.

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Numerical models for the simulation of longitudinal and transverse Stokes flow in cylindrical periodic porous media are presented. The models, which are based on a finite-volume formulation in primitive variables, utilize digital image representations of the geometries to simulate, making them particularly well-suited for the rapid automated analysis of creeping flow in porous media with complex morphologies. Complete details of the model formulations are given, including extensive treatment of the pressure boundary conditions at the solid-liquid interface needed to guarantee convergence with all possible geometries. The convergence behavior of both models is tested, and the models are shown to be second-order accurate.The models are used to simulate flow over the whole range of volume fractions of liquid in several regular geometries. The longitudinal model is used to simulate flow in square arrays of circular and square ducts, and both models are used to simulate flow in square and hexagonal arrays of circular cylinders and square arrays of square cylinders rotated by varying amounts. For each of the geometries, accurate empirical expressions for the Darcy permeability as a function of volume fraction solid are presented. Where applicable, model predictions of permeability are compared to existing analytical results.Subsequently, the models are used to simulate Stokes flow in random domains over a wide range of fractions liquid. The sequential random packing algorithm is used to generate 1,000 random packings of circular cylinders at each of 14 fractions of liquid, and longitudinal and transverse flow simulations are performed for each geometry. Histograms and summary statistics are computed for the permeability for each fraction liquid, and empirical expressions for mean permeability as a function of fraction liquid are given. The autocorrelation structure of the geometry and of the fluid velocity is analyzed, and an analysis of the scaling of longitudinal permeability variance is presented. In transverse flow at high packing densities, it is found that lightning-like patterns emerge in the fluid velocity. It is also found that the details of flows in such geometries are strongly sensitive to the placement of individual solid obstacles.
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10

Hendrick, Angus Greer. "Effects of domain size on transverse permeability through random arrays of cylinders." Thesis, The University of Arizona, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3592730.

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Researchers using Darcy's law to model flow in porous media must satisfy the requirement for sufficient scale separation between the pore scale and the model scale. This requirement is analogous to that for any continuum model, where application is restricted to scales larger than the underlying discrete structure. In the case of Darcy's law when the model scale becomes too small, the measurement of the permeability—the material property required to close the relationship—becomes polluted by the boundary conditions, either physical or numerical. The requirements for adequate scale separation to obtain permeability measurements (also known as satisfying the conditions for a representative elementary volume, or REV, for permeability) have not been previously reported. Likewise, the behavior of Darcy models when applied at sub-REV length scales has not been reported.

Here, the results of Stokes simulations of transverse flow in 90,000 sequential random packings of monodisperse cylinders at a variety of liquid fractions and averaging-volume sizes show that approximately 200 cylinders must be present in an averaging volume before the effects of periodic boundary conditions on the Stokes simulations (the conventional choice for permeability measurements using Stokes flow) are no longer evident in the measured permeability. Direct comparisons between flow predictions from a two-dimensional, tensor-based Darcy model and a Stokes model for additional 10,000 domains show that the Darcy model is an unbiased predictor of the flow distribution in the system, even when the permeability is expected to contain boundary-condition artifacts. Though unbiased, the Darcy models do show considerable reduction in accuracy as the model scale shrinks toward the pore scale, with significant declines observed after the side length of a square averaging volume reaches 10 times the cylinder diameter. Finally, a novel approach for visualizing flows using the linear properties of the Stokes equations shows how the periodic boundary conditions affect the flow, and motivates the development of a generalized approach for obtaining permeability that does not require periodic boundary conditions. Modest improvements in the Darcy model relative to the actual Stokes flow result when the new approach is used to obtain permeability at small averaging volumes.

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11

Yamashita, Hiroshi, Shingo Satake, and Kazuhiro Yamamoto. "Microstructure and particle-laden flow in diesel particulate filter." Elsevier, 2009. http://hdl.handle.net/2237/20047.

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12

Carling, Gregory T. "The rate and timing of direct mountain front recharge in an arid environment, Silver Island Mountains, Utah." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2187.pdf.

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13

Mat, Isa Zaiton. "Mathematical modelling of fumigant transport in stored grain." Thesis, Queensland University of Technology, 2014. https://eprints.qut.edu.au/75420/1/Zaiton_Mat%20Isa_Thesis.pdf.

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Computational fluid dynamics, analytical solutions, and mathematical modelling approaches are used to gain insights into the distribution of fumigant gas within farm-scale, grain storage silos. Both fan-forced and tablet fumigation are considered in this work, which develops new models for use by researchers, primary producers and silo manufacturers to assist in the eradication grain storage pests.
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14

Sita, Ram Rao K. V. "Wall Effects In Packed Beds." Thesis, Indian Institute of Science, 1994. https://etd.iisc.ac.in/handle/2005/126.

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Packed beds find extensive application in a wide variety of industries. The objective of the present work is to analyze and evaluate the effects of the wall on structural characteristics, hydrodynamics and heat transfer in packed beds of spheres. As a first attempt, spheres of uniform size are considered. The cylindrical wall of the bed confines the location of the particles thus leading to significant radial variations in void fraction and specific lateral surface area. The two characteristics at any given radial position r* are estimated by defining a concentric cylindrical channel (CCC) of an arbitrary thickness such that its boundaries are equidistant from the cylindrical surface passing through r* and accounting for the solid volumes or lateral surface areas of the segments of spheres (cap, slice, rod and annular ring) contained in the CCC and with centers lying within a distance of a particle radius from r*.The curved boundaries of the sphere segments are rigorously accounted for. The low aspect ratio beds (aspect ratio less than or equal to 2) show three distinct types of behavior. In beds of aspect ratio 2, the void fraction starts from a value of unity at the wall and decreases to a minimum and then increases to unity at the center of the bed. In beds with aspect ratio between l\/¯3/2, there is a continuous decrease in void fraction from unity at the wall to a fairly low value towards the axis and then a slight increase followed by another decrease. The profiles for aspect ratio less than l\/¯3/2 show a continuous decrease from a value of unity at the wall to zero towards the axis. In contrast, beds of high aspect ratio show heavily damped oscillations in the void fraction up to about five particle diameters from the wall and then a constant value. The lateral surface area variations in low aspect ratio beds show a steep fall from a very high value near the wall, and in high aspect ratio beds an oscillatory nature, though not as strong as in the corresponding void fraction profiles. The distribution of flow in packed beds for steady flow of an incompressible Newtonian fluid under isothermal conditions is modeled by using Ergun equation with Brinkman-type correction to account for the viscous effects in the region close to the wall. The confining effect of the wall is incorporated through the radial variations in void fraction and specific lateral surface area. The hydraulic radius in the region next to the wall is modified to take into account the resistance of the wall surface to flow. The resulting model equations with appropriate boundary conditions are solved numerically by collocation technique. The influence of aspect ratio in the range 1.25 to 20.3 and Reynolds number from 0.1 to 1000, the two most important factors affecting the flow behavior, is evaluated. The velocity profiles show a peak in the region close to the wall thus indicating severe channeling effect in this region. The magnitude and location of the peak depend on aspect ratio and Reynolds number. The model predictions agree remarkably with reported experimental data on velocity profiles in a bed of aspect ratio 10.7, and on the effect of Reynolds number on friction factors in beds of low aspect ratio. The radial variations in void fraction, velocity and effective thermal conductivity are incorporated in the two-dimensional pseudo-homogeneous steady-state model to analyze the wall effects on heat transfer in packed beds. Both constant wall temperature and constant wall flux boundary conditions are adopted. The equations are solved numerically using finite difference technique. The radial temperature profiles are seen to be fairly uniform in beds of low aspect ratio thus showing that the often made assumption of complete radial thermal mixing in low aspect ratio beds is valid. Beds of high aspect ratio show strong radial gradients. For constant heat flux condition the slope of the temperature profile remains constant after a small distance from the Inlet thus leading to thermally fully-developed flow. For this condition the heat transfer equations are solved analytically to obtain expressions for Nusselt number and the radial temperature profiles. There is a significant difference in the temperature profiles evaluated in the presence and absence of wall effects. Good agreement is found between the Nusselt numbers obtained from the model and reported experimental data.
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15

Sita, Ram Rao K. V. "Wall Effects In Packed Beds." Thesis, Indian Institute of Science, 1994. http://hdl.handle.net/2005/126.

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Packed beds find extensive application in a wide variety of industries. The objective of the present work is to analyze and evaluate the effects of the wall on structural characteristics, hydrodynamics and heat transfer in packed beds of spheres. As a first attempt, spheres of uniform size are considered. The cylindrical wall of the bed confines the location of the particles thus leading to significant radial variations in void fraction and specific lateral surface area. The two characteristics at any given radial position r* are estimated by defining a concentric cylindrical channel (CCC) of an arbitrary thickness such that its boundaries are equidistant from the cylindrical surface passing through r* and accounting for the solid volumes or lateral surface areas of the segments of spheres (cap, slice, rod and annular ring) contained in the CCC and with centers lying within a distance of a particle radius from r*.The curved boundaries of the sphere segments are rigorously accounted for. The low aspect ratio beds (aspect ratio less than or equal to 2) show three distinct types of behavior. In beds of aspect ratio 2, the void fraction starts from a value of unity at the wall and decreases to a minimum and then increases to unity at the center of the bed. In beds with aspect ratio between l\/¯3/2, there is a continuous decrease in void fraction from unity at the wall to a fairly low value towards the axis and then a slight increase followed by another decrease. The profiles for aspect ratio less than l\/¯3/2 show a continuous decrease from a value of unity at the wall to zero towards the axis. In contrast, beds of high aspect ratio show heavily damped oscillations in the void fraction up to about five particle diameters from the wall and then a constant value. The lateral surface area variations in low aspect ratio beds show a steep fall from a very high value near the wall, and in high aspect ratio beds an oscillatory nature, though not as strong as in the corresponding void fraction profiles. The distribution of flow in packed beds for steady flow of an incompressible Newtonian fluid under isothermal conditions is modeled by using Ergun equation with Brinkman-type correction to account for the viscous effects in the region close to the wall. The confining effect of the wall is incorporated through the radial variations in void fraction and specific lateral surface area. The hydraulic radius in the region next to the wall is modified to take into account the resistance of the wall surface to flow. The resulting model equations with appropriate boundary conditions are solved numerically by collocation technique. The influence of aspect ratio in the range 1.25 to 20.3 and Reynolds number from 0.1 to 1000, the two most important factors affecting the flow behavior, is evaluated. The velocity profiles show a peak in the region close to the wall thus indicating severe channeling effect in this region. The magnitude and location of the peak depend on aspect ratio and Reynolds number. The model predictions agree remarkably with reported experimental data on velocity profiles in a bed of aspect ratio 10.7, and on the effect of Reynolds number on friction factors in beds of low aspect ratio. The radial variations in void fraction, velocity and effective thermal conductivity are incorporated in the two-dimensional pseudo-homogeneous steady-state model to analyze the wall effects on heat transfer in packed beds. Both constant wall temperature and constant wall flux boundary conditions are adopted. The equations are solved numerically using finite difference technique. The radial temperature profiles are seen to be fairly uniform in beds of low aspect ratio thus showing that the often made assumption of complete radial thermal mixing in low aspect ratio beds is valid. Beds of high aspect ratio show strong radial gradients. For constant heat flux condition the slope of the temperature profile remains constant after a small distance from the Inlet thus leading to thermally fully-developed flow. For this condition the heat transfer equations are solved analytically to obtain expressions for Nusselt number and the radial temperature profiles. There is a significant difference in the temperature profiles evaluated in the presence and absence of wall effects. Good agreement is found between the Nusselt numbers obtained from the model and reported experimental data.
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16

Bernales, chavez Braulio. "Modélisation de l'hydrodynamique et des transferts dans les procédés de filtration membranaire." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4779/document.

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L'accumulation du soluté à la surface d'une membrane entraîne le phénomène de polarisation de concentration. Ceci est un problème qui affecte tous les systèmes de filtration membranaire car il a pour effet une augmentation de la pression osmotique et par conséquence une réduction substantielle du flux de perméat. Afin de comprendre ce phénomène, nous avons d'abord mené une étude analytique de la filtration tangentielle en solvant pur prenant en compte de l'influence de la pression motrice locale sur le taux de perméation. Lors de cette étude, des solutions analytiques qui augmentent en précision avec l'ordre développé ont ete dérivées. Ensuite nous avons développé une approche analytique qui couple l'hydrodynamique aux transferts de matière pour le cas d'un système de filtration qui opère sous haute pression avec un taux de récupération faible. Dans le but d'intégrer à la fois la dépendance de la pression transmembranaire locale sur le flux de perméat et l'influence de la polarisation de concentration à travers leurs effets osmotiques sur la pression effective, nous avons développé un modèle numérique qui résout l'équation de conservation du soluté couplée aux équations de Navier-Stokes en régime stationnaire dans l'approximation de Prandtl. Nous avons validé cette approche grâce aux solutions analytiques précédemment dérivées. Ensuite, nous avons testé l'influence des principaux paramètres de fonctionnement sur la performance du système et comparé nos résultats avec ceux d'autres modèles numériques. Finalement, la pertinence du modèle a été quantitativement vérifiée grâce à des données tirées des expériences bien documentées en osmose inverse
Concentration polarization of solute at the membrane surface, because of osmotic pressure effects, is an important phenomenon that can cause substantial reductions in permeation. To understand these phenomena: we first analyze the filtration process for a pure solvent, imposing the influence of the driving pressure on permeation at the membrane. We obtain accurate analytical solutions for the flow fields. We then derive an analytical solution that coupled hydrodynamics to mass transfer for filtration systems working in a situation of High Pressure and Low Recovery. Second, we develop a numerical model that incorporates both physical aspects: the dependency of pressure on permeation and the influence of concentration polarization and their related osmotic effects in the effective pressure at the membrane. For that, the numerical approach solves the solute conservation equation coupled with the Navier-Stokes equations under the steady Prandtl approximation. The solution of the system is performed using a finite difference method of order 2. The validity of this approach is successfully demonstrated with the previous analytical solutions for hydrodynamics, as well as for the coupling with mass transfer. We then test the influence of the main operating parameters (inlet concentration, axial flow rate, operating pressure and membrane permeability) on the performance of the filtration system and compare the results with other numerical models that takes into account concentration polarization phenomenon. Finally, the validity of this model is quantitatively well-proved when using the reported data resulting from reverse osmosis experiments
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17

Bailly, David. "Vers une modélisation des écoulements dans les massifs très fissurés de type karst : étude morphologique, hydraulique et changement d'échelle." Thesis, Toulouse, INPT, 2009. http://www.theses.fr/2009INPT027H/document.

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Les aquifères fissurés de type karst contiennent d'importantes ressources en eau. Ces aquifères sont complexes et hétérogènes sur une gamme d'échelles importantes. Leur gestion nécessite l'utilisation d'outils et de méthodologies adaptés. Dans le cadre de cette étude, différents outils et méthodologies numériques d'étude ont été développés pour la modélisation des aquifères karstiques, et plus généralement, des milieux poreux très fissurés 2D et 3D - en mettant l'accent sur la morphologie et sur le comportement hydrodynamique du milieu à travers la notion de changement d'échelle ("second changement d'échelle", reposant sur un modèle d'écoulement local de type Darcy et/ou Poiseuille avec quelques généralisations). Plusieurs axes sont explorés concernant la morphologie du milieu poreux fissuré (milieux aléatoires, milieux booléens avec réseaux statistiques de fissures, mais aussi, modèles morphogénétiques). L'étude du changement d'échelle hydrodynamique tourne autour du concept de macro perméabilité. Dans un premier temps, l'étude porte sur un modèle de perte de charge linéaire darcien. Les perméabilités effectives sont calculées numériquement en termes des fractions volumiques de fissures et du contraste de perméabilité matrice/fissures. Elles sont analysées et comparées à des modèles théoriques (analytiques). Une étude particulière des effets de quasi-percolation pour les grands contrastes aboutit à la définition de trois fractions critiques liées à des seuils de percolation. Pour tenir compte des effets inertiels dans les fissures, l'étude est étendue au cas d'une loi locale comprenant un terme quadratique en vitesse (Darcy/Ward-Forchheimer). Une perméabilité macroscopique équivalente non linéaire est définie et analysée à l'aide d'un modèle inertiel généralisé (linéaire/puissance). Enfin, l'anisotropie hydraulique à grande échelle du milieu fissuré est étudiée, en termes de perméabilités directionnelles, à l'aide d'une méthode numérique d'immersion
Karstic aquifers contain large subsurface water resources. These aquifers are complex and heterogeneous on a large range of scales. Their management requires appropriate numerical tools and approaches. Various tools and numerical methodologies have been developed to characterize andmodel the geometry and hydraulic properties of karstic aquifers, more generally, of highly fissured 2D and 3D porous media. In this study, we emphasize morphological characterization, and we analyze hydrodynamic behavior through the concept of upscaling ("second upscaling"). Concerning the morphology of fissured porous media, several axes are explored : random media, composite random Boolean media with statistical properties, and morphogenetic models. Hydrodynamic upscaling is developed using the macro-permeability concept. This upscaling method is based on either Darcy's linear law, or on a linear/quadratic combination of Darcy's and Ward-Forchheimer's quadratic law (inertial effects). First, the study focuses on Darcy's linear head loss law, and Darcian effective permeabilities are calculated numerically in terms of volume fractions of fissures and "fissure/matrix" permeability contrasts. The results are analysed and compared with analytical results and bounds. A special study of percolation and quasi-percolation effects, for high contrasts, leads to defined three critical fractions. These critical fractions are "connected" to percolation thresholds. Secondly, in order to consider inertial effect in fissures, the study is extended to a local law with a quadratic velocity term (Darcy/Ward-Forchheimer). Then, an equivalent nonlinear macroscopic permeability is defined and analysed using a generalized inertial model (linear/power). Finally, the large scale hydraulic anisotropy of fissured medium is studied, in terms of directional permeabilities, using an "immersion" numerical method
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18

Dib, Serena. "Méthodes d'éléments finis pour le problème de Darcy couplé avec l'équation de la chaleur." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066294/document.

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Dans cette thèse, nous étudions l'équation de la chaleur couplée avec la loi de Darcy à travers de la viscosité non-linéaire qui dépend de la température pour les dimensions d=2,3 (Hooman et Gurgenci ou Rashad). Nous analysons ce problème en introduisant la formulation variationnelle équivalente et en la réduisant à une simple équation de diffusion-convection pour la température où la vitesse dépend implicitement de la température.Nous démontrons l'existence de la solution sans la restriction sur les données par la méthode de Galerkin et du point fixe de Brouwer. L'unicité globale est établie une fois la solution est légèrement régulière et les données se restreignent convenablement. Nous introduisons aussi une formulation variationnelle alternative équivalente. Toutes les deux formulations variationnelles sont discrétisées par quatre schémas d'éléments finis pour un domaine polygonal ou polyédrique. Nous dérivons l'existence, l'unicité conditionnée, la convergence et l'estimation d'erreur a priori optimale pour les solutions des trois schémas. Par la suite, ces schémas sont linéarisés par des algorithmes d'approximation successifs et convergentes. Nous présentons quelques expériences numériques pour un problème modèle qui confirme les résultats théoriques de convergence développées dans ce travail. L'estimation d'erreur a posteriori est établie avec deux types d'indicateurs d'erreur de linéarisation et de discrétisation. Enfin, nous montrons des résultats numériques de validation
In this thesis, we study the heat equation coupled with Darcy's law by a nonlinear viscosity depending on the temperature in dimension d=2,3 (Hooman and Gurgenci or Rashad). We analyse this problem by setting it in an equivalent variational formulation and reducing it to an diffusion-convection equation for the temperature where the velocity depends implicitly on the temperature.Existence of a solution is derived without restriction on the data by Galerkin's method and Brouwer's Fixed Point. Global uniqueness is established when the solution is slightly smoother and the dataare suitably restricted. We also introduce an alternative equivalent variational formulation. Both variational formulations are discretized by four finite element schemes in a polygonal or polyhedral domain. We derive existence, conditional uniqueness, convergence, and optimal a priori error estimates for the solutions of the three schemes. Next, these schemes are linearized by suitable convergent successive approximation algorithms. We present some numerical experiments for a model problem that confirm the theoretical rates of convergence developed in this work. A posteriori error estimates are established with two types of errors indicators related to the linearisation and discretization. Finally, we show numerical results of validation
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19

Zhang, Andi. "Numerical investigation of multiphase Darcy-Forchheimer flow and contaminant transport during SO₂ co-injection with CO₂ in deep saline aquifers." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/49065.

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Of all the strategies to reduce carbon emissions, carbon dioxide (CO₂) geological sequestration is an immediately available option for removing large amounts of the gas from the atmosphere. However, our understanding of the transition behavior between Forchheimer and Darcy flow through porous media during CO₂ injection is currently very limited. In addition, the kinetic mass transfer of SO₂ and CO₂ from CO₂ stream to the saline and the fully coupling between the changes of porosity and permeability and multiphase flow are two significant dimensions to investigate the brine acidification and the induced porosity and permeability changes due to SO₂ co-injection with CO₂. Therefore, this dissertation develops a multiphase flow, contaminant transport and geochemical model which includes the kinetic mass transfer of SO₂ into deep saline aquifers and obtains the critical Forchheimer number for both water and CO₂ by using the experimental data in the literature. The critical Forchheimer numbers and the multiphase flow model are first applied to analyze the application problem involving the injection of CO₂ into deep saline aquifers. The results show that the Forchheimer effect would result in higher displacement efficiency with a magnitude of more than 50% in the Forchheimer regime than that for Darcy flow, which could increase the storage capacity for the same injection rate and volume of a site. Another merit for the incorporation of Forchheimer effect is that more CO₂ would be accumulated in the lower half of the domain and lower pressure would be imposed on the lower boundary of the cap-rock. However, as a price for the advantages mentioned above, the injection pressure required in Forchheimer flow would be higher than that for Darcy flow. The fluid flow and contaminant transport and geochemical model is then applied to analyze the brine acidification and induced porosity and permeability changes due to SO₂ co-injection. The results show that the co-injection of SO₂ with CO₂ would lead to a substantially acid zone near the injecting well and it is important to include the kinetic dissolution of SO₂ from the CO₂ stream to the water phase into the simulation models, otherwise considerable errors would be introduced for the equilibrium assumption. This study provides a useful tool for future analysis and comprehension of multiphase Darcy-Forchheimer flow and brine acidification of CO₂ injection into deep saline aquifers. Results from this dissertation have practical use for scientists and engineers concerned with the description of flow behavior, and transport and fate of SO₂ during SO₂ co-injection with CO₂ in deep saline aquifers.
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20

Qin, Xiaowen. "Modeling Study of Pyrolysis of Composite Materials : Application to Wood and Carbon/Epoxy Composite." Thesis, Chasseneuil-du-Poitou, Ecole nationale supérieure de mécanique et d'aérotechnique, 2021. http://www.theses.fr/2021ESMA0006.

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Les matériaux composites prennent une place importante dans les applications industrielles ou plus largement dans notre vie courante. Les composites synthétiques substituent les matériaux métalliques en raison du gain de poids pour des propriétés mécaniques identiques. Ce type de matériaux est largement répandu dans les domaines du transport et du stockage de l’énergie. Les composites naturels (bois) sont également très utilisés notamment dans le domaine de l’habitat. L’inconvénient de ces matériaux réside dans leur difficulté à maintenir leurs caractéristiques mécaniques en cas d’incendie ; l’étude de leur tenue au feu est donc un enjeu majeur. Ce travail de thèse vise à développer un modèle numérique de décomposition d’un matériau composite soumis à un flux de chaleur. La simulation de différents cas d’attaque thermique permet d’étudier les interactions entre les processus de transferts de masses, de chaleur et de réactions chimiques au sein du solide. Le modèle développé, 3D décrit les transports au sein des pores du matériau à l’échelle de Darcy. Le transfert de chaleur par conduction est écrit sous forme tensoriel permettant de définir des conductivités dans les 3 directions de l’espace. Pour les 2 types de matériaux, un schéma réactionnel multi-étapes est défini afin de décrire le processus de pyrolyse. Les essais en cône calorimètre qui ont servi à développer le modèle ont été réalisées sous atmosphère inertes (N2) ce qui permet « d’éliminer » la présence de la flamme à la surface du matériau ainsi que les réactions hétérogènes pouvant se produire en présence d’oxygène. Les conditions aux limites définis sont donc plus simples et mieux maitrisées car le caractère instationnaire de la flamme n’est pas pris en compte. Les schémas réactionnels se composent donc uniquement des réactions de pyrolyse excluant ainsi toutes réactions hétérogènes. Les gaz de pyrolyse sont assimilés à un gaz inerte. Les réactions intra-pores sont donc négligées et l’hypothèse de l’équilibre thermique locale entre les phases solides et le gaz environnant est assumée. La construction du modèle décomposition thermique des 2 types de matériaux suit une démarche de séparation des échelles. Les différents processus de transport de chaleur, de masses et de réactions chimiques sont étudiés séparément afin de s’affranchir des interactions et de valider séparément les modèles. Le modèle global est ensuite reconstruit afin de tenir compte de ces interactions. La dégradation thermique est d’abord étudiée à une échelle « 0D » afin de développer les schémas réactionnels. L’Analyse Thermogravimétrique est alors utilisée à cette étape ou des expériences sont conduites à différentes vitesses de chauffage sous atmosphère inerte. Les phénomènes de transports au sein de la particule solide peuvent être négligés, la température de la particule est homogène et sa dynamique est connue. A cette étape, seul le processus de pyrolyse est mis en jeu. Les différentes familles de réactions sont identifiées et décrites au sein du modèle par des réactions apparentes de type Arrhenius. Les constantes cinétiques sont calculées par des méthodes mathématiques inverses. L’influence de la vitesse de chauffage sur le processus de pyrolyse est analysée. Une simulation 2D est réalisée à 2 vitesses de chauffages afin d’analyser l’évolution des gradients thermiques et de pression au sein de la particule. Les phénomènes de transports de chaleur et de masses sont pris en compte à l’échelle du matériau et étudiés par des expériences réalisées en cône calorimètre. A cette échelle, les phénomènes de transports de masses et de chaleur sont calculés. Des simulations sont réalisées pour 2 flux de chaleurs. Les interactions entre les processus de transport de masses, de chaleur et de pyrolyse sont étudiées en analysant les échelles locales de temps et de longueurs afin d’identifier quels sont les phénomènes limitant sur le processus global de décomposition thermique
Composite materials occupy a critical position in industrial applications or more broadly in our daily life. Synthetic composites substitute metallic materials due to their lightweight properties to achieve identical mechanical performance. They are widely used in the fields of energy transportation and storage. Natural composites (wood) are also widely used, especially in construction industry. The disadvantage of these materials involves the disability in maintaining their mechanical characteristics in a fire scenario, and the study of their fire resistance is therefore a major issue. This thesis aims to develop a mathematical model of thermal decomposition of composite materials subjected to different heating conditions. The simulations of different cases of thermal decomposition make it possible to study the interactions among the processes of heat and mass transfer as well as chemical reactions within the solid. The developed 3D model describes the gas transport within the pores of materials at the Darcy scale. Thermal conductivity is formulated in a tensor form allowing the definition of heat transfer in three directions of the domain. For the two types of materials, a multi-step reaction scheme is defined to describe the pyrolysis process. The cone calorimeter tests used to validate the model were carried out under an inert atmosphere (Nitrogen) which makes it possible to eliminate the presence of flame on the material surface as well as the heterogeneous reactions which can occur in the presence of oxygen. Therefore, the defined boundary conditions are quite simple and well-controlled to characterize without considering the unsteady flame. Pyrolysis gasses are assembled into inert gas, therefore, the gas reactions in the pore are neglected and the local thermal equilibrium between the solid and gas phase is assumed. The implementation of this pyrolysis model follows a scale separation process with two types of materials. The different heat and mass transfer processes, as well as chemical reactions, are studied separately to avoid the interactions, then the model is reconstructed to take these interactions into account. The pyrolysis behavior is firstly studied at a "0D" scale to develop the part of chemical reactions. The thermogravimetric analysis (TGA) is used at this scale and related experiments are conducted at different heating rates under an inert atmosphere. At this scale, only the chemical reactions are involved with known kinetics, and the heat and mass transport within the solid can be neglected with homogeneous temperature distribution. The different chemical reactions are described with the Arrhenius-type equation. The kinetic parameters are calculated by the inverse modeling method. The influence of the heating rate on the pyrolysis process is analyzed and 2D simulations are conducted at two heating rates to analyze the evolution of thermal and pressure gradients within the solid. The phenomena of heat and mass transport are considered and studied by bench-scale experiments which are conducted in the cone calorimeter. The corresponding simulations are implemented under two heat flux. The interactions among the heat and mass transport as well as chemical reaction processes are studied by analyzing the local time and length scales to identify what are the dominant phenomena through the whole pyrolysis process
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21

Zhang, Wenxiang. "Optimization of protein concentration from alfalfa juice by high shear rate dynamic filtration." Thesis, Compiègne, 2016. http://www.theses.fr/2016COMP2281/document.

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Les protéines extraites des feuilles de luzerne sont une source importante de protéines. La filtration membranaire, technologie de séparation respectueuse de l’environnement avec une productivité élevée et de faible coût a été utilisée pour séparer et concentrer les protéines des feuilles de luzerne à partir de leur jus. Cependant le phénomène du colmatage de la membrane qui réduit sérieusement le flux et la séparation des protéines est un facteur limitant important dans l'application de la filtration membranaire. Pour améliorer la récupération des protéines et amenuiser le phénomène du colmatage, la filtration membranaire associée à fort cisaillement a été utilisée pour la filtration du jus de luzerne. Toujours dans l’objectif d'optimiser le processus de la filtration, "le mode de la filtration" et "les paramètres de fonctionnement" ont été étudiés pour réduire le colmatage de la membrane et améliorer le rendement de la filtration. Puis, l’effluent du jus de luzerne a été filtré par des membranes dans des conditions de fort cisaillement afin de recycler les protéines. En outre, le mécanisme du colmatage a été étudié et a permis d’évaluer les stratégies de contrôle du colmatage. L'optimisation du procédé membranaire, via l’étude du "mode de filtration" et des "paramètres de fonctionnement" a été conduit dans le but d’améliorer la séparation et la concentration des protéines et de réduire le colmatage. Trois types de « mode de filtration » ont été testés : la filtration frontale sur le module de la cellule amicon (DA), la filtration tangentielle dynamique sur le module à disque rotatif (CRDM) et la filtration frontale sur le module à disque rotatif (DRDM)). Les « paramètres de fonctionnement » qui ont été étudiés sont les suivants : le type de membranes (ultrafiltration (UF) et microfiltration (MF)), la vitesse de rotation, la température et la pression transmembranaire (TMP). Le comportement du débit (évolution du flux du perméat au cours de la filtration), les performances de la séparation (taux de clarification et de concentration), l’efficacité du nettoyage de la membrane (récupération de la perméabilité membranaire) et la productivité lors des tests de recyclage et de concentration ont été étudiés dans le but de définir des stratégies dans le contrôle du colmatage. Puis, l’effluent de luzerne a été filtré par UF afin de séparer et purifier les protéines. Le mécanisme du phénomène du colmatage des membranes lors de la filtration du jus de luzerne a été étudié. Le processus du colmatage de la membrane a montré une tendance d’un colmatage multi-site progressif. Le modèle du colmatage multisite progressif selon la loi de Darcy (SMDM) a été proposé afin de mieux décrire et comprendre le processus du colmatage. Les effets de la composition du fluide d’alimentation, du choix de la membrane et des conditions hydraulique ont joué un rôle important dans le processus progressif du colmatage. De plus, les coefficients de résistance et de compressibilité dans les différentes étapes et sites ont été calculés afin d’expliquer le processus complexe du colmatage et d’évaluer l'efficacité des stratégies du contrôle du colmatage. Une série d'essais avec de longues durées de filtration a été réalisée pour étudier le déclin du flux et le colmatage de la membrane à diverses étapes du processus. Ces résultats présentent une utilité pour améliorer la récupération des protéines et contrôler le colmatage dans le processus de la filtration membranaire à fort cisaillement du jus de luzerne. Ces résultats sont aussi utiles pour la conception et la mise en place des technologies membranaires dans les processus industriels
Alfalfa leaf proteins extracted from plants are an important protein source. As an environmentally friendly separation technology with high productivity and low cost, membrane filtration was used to separate and concentrate leaf protein from alfalfa juice. However membrane fouling seriously reduces flux and protein separation and is an important limitation in the application of membrane filtration. To improve protein recovery and fouling control, dynamic shear-enhanced membrane filtration with high shear rate on membrane surface and excellent anti-fouling capacity was used for alfalfa juice filtration in this work. In order to optimize filtration process, filtration mode and operation parameters were investigated to reduce membrane fouling and improve separation performance. Then, alfalfa wastewater was also treated by dynamic shear-enhanced membrane filtration to recycle proteins. Furthermore, the fouling mechanism was studied and served as a valuable evaluation for fouling strategies. In this study, process optimization including “Filtration mode” and “Operation parameters” was studied to improve protein recovery and fouling control. In “Filtration mode”, three types of filtration modules (dead end filtration using laboratory Amicon cell (DA), dynamic cross filtration using rotating disk module (CRDM) and dead end filtration using rotating disk module (DRDM)) were used to investigate the filtration performance. As for “Operation parameters”, the operation parameters including membranes (ultrafiltration (UF) and microfiltration (MF)), rotating speed, temperature and transmembrane pressure (TMP) were studied to optimize the filtration process. Flux behavior (permeate flux and flux decline), separation performance (clarification and concentration capacity), membrane cleaning efficiency (permeability recovery) and productivity in full recycling tests and concentration tests were utilized to evaluate the various operation strategies. In addition, alfalfa wastewater was treated by UF membrane, while waste proteins were recycled. Fouling mechanism for alfalfa juice filtration was investigated. The fouling process showed significantly stepwise multisite patterns. Based on Darcy’s law, the stepwise multisite Darcy’s law model (SMDM) was proposed to better describe and understand the fouling process. The effects of feed composition, membrane and hydraulic conditions played an important role in stepwise fouling process. Moreover, the resistance coefficient and compressibility for different steps and sites were calculated to explain the complex fouling process and estimate the efficiency of flux decline control strategies. Besides, a series of long tests were utilized to study flux decline and membrane fouling at various fouling step process. These results can be used to understand the protein recovery and fouling control during shear-enhanced membrane filtration process of alfalfa juice. They have important implications for process design of membrane technology in industrial scale
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22

Söderberg, Karolina. "Utredning av igensättningsproblematik i markfilter av sorbtionstyp vid Gräfsåsens avfallsanläggning." Thesis, Mittuniversitetet, Avdelningen för ekoteknik och hållbart byggande, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-29261.

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Markfilter för rening av vatten har utvecklats under årens lopp till att besitta skräddarsydda egenskaper anpassade för rening av lakvatten. Lakvatten innehåller en rad olika föroreningar, vilka beror på det deponerade materialets beskaffenhet. I sorptionsfilter kombineras ett traditionellt filters mekaniska förmåga att avskilja partiklar och biologiska förmåga att bryta ner organiskt material, med en eller flera sorbenter, vilka verkar för att fastlägga eller fälla föroreningar. Inte sällan drabbas dock denna typ av filter av igensättningar, vilket reducerar filtrets kapacitet och livslängd. Vid deponin i Gräfsåsen, tillhörande Östersunds kommun, installerades 2013 ett markfilter av sorptionstyp framtaget av konsult, vilket uppgavs ha en livslängd på 10-15 år. Efter installering av filtret visar sig kapaciteten vara sämre än förväntat och dessutom snabbt sjunkande över tid. Justeringar i filtermaterialets sammansättning sker efter ett par månades drift, men problemet med igensättningar/låg kapacitet kvarstår. Detta examensarbete utformades i syfte att utreda igensättningsproblematiken med sorptionsfiltret vid Gräfsåsen och att föreslå förbättringsåtgärder. Den andra delen bestod av att kontrollera konsultens dimensioneringsberäkningar och jämföra med olika beräkningsmodeller för markfilter. Analysresultaten och beräkningarna kompletterades med ett praktiskt försök att filtrera lakvatten och kranvatten i varsin filterkolonn som utformades med samma proportioner och material som det aktuella filtret. Avsikten med kolonnfiltreringen var att bedöma materialets hydrauliska kapacitet och undersöka om det fanns eventuella skillnader i rinntider för lak- respektive kranvatten. Filtreringen visade att packningsgraden av filtermaterialet är av stor betydelse för genomsläppligheten, inga slutsatser om vattenkvaliténs påverkan kunde dock dras. Karaktäriseringen visade att lakvattnet i Gräfsåsen innehöll höga halter BOD, POC, aluminium, svavel, kalcium och fosfor. Analyserna och jämförelserna sammantaget indikerade att metalloxider och karbonater fälldes i filtret. Beräkningarna visade att filtret dimensionerats för ett genomsnittligt mindre flöde än vad som bedömdes vara lämpligt. Den hydrauliska konduktiviteten för filtermaterialet var lägre än konsultens rekommendationer, vilket i praktiken innebar att kapaciteten för filtret var en tredjedel av flödet man avsett att dimensionera för..
Filters for treatment of leachate have been developed over the years to hold tailor-made properties for the treatment of leachate. Leachate contains a variety of pollutants, which depends on the waste upon the landfill. In sorption-filters the traditional filter’s mechanical ability to remove particles and biological ability to break down organic material, is combined with one or several sorbents which act to precipitate or trap contaminants. However, it is rather common that these types of filters suffer from clogging which result in reduction of the filter’s capacity and lifetime. At the landfill in Gräfsåsen, belonging to the municipality of Östersund, a sorption filter developed by a consultant was installed in 2013, which was estimated to have a lifespan of 10-15 years. When installed, the capacity of the filter was lower than expected and also decreased rapidly over time. The filter media had to be redesigned after a couple of months in operation, but the problem with clogging/low capacity remained. This thesis was shaped to investigate the causes of the clogging problem of the filter at Gräfsåsen and to suggest improvements. The study consisted mainly of two parts, one part consisted of interpreting and comparing test results and characterize the leachate from a study of leachate from IVL (Swedish Environmental Research Institute). The second part consisted of controlling the consultant’s sizing and compare with other models for sizing filters. The analytical results and calculations were supplemented with a practical test to filter leachate and tap water in separate filter columns, designed with the same proportions and materials as the existing filter. The purpose of the filtering columns was to assess the material's hydraulic capacity and to examine whether there were any differences in the flow times of the leachate and tap water. The filtering showed that the degree of compaction of the filter material is of great importance for the permeability, no conclusions regarding the water quality’s impact could be drawn. The characterization indicated that the leachate in Gräfsåsen contained high concentrations of BOD, POC, aluminum, sulfur, calcium and phosphorus. Analyzes and comparisons collectively indicated that metal oxides and carbonates precipitated in the filter. The calculations showed that the filter is dimensioned for an average flow rate less than what was assessed appropriate. The hydraulic conductivity of the filter material was lower than the consultant's recommendations, which in practice meant that the capacity of the filter was a third of the flow it intended to be designed for.
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23

Alastal, Khalil. "Ecoulements oscillatoires et effets capillaires en milieux poreux partiellement saturés et non saturés : applications en hydrodynamique côtière." Thesis, Toulouse, INPT, 2012. http://www.theses.fr/2012INPT0039/document.

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Dans cette thèse, on étudie les écoulements oscillatoires en milieux poreux (non saturés ou partiellement saturés) dus à des oscillations tidales des niveaux d'eau dans des milieux ouverts adjacents aux milieux poreux. L'étude est centrée sur le cas des plages de sable en hydrodynamique côtière, mais les applications concernent, potentiellement et plus généralement, les problèmes d'oscillation et de variation temporelle des niveaux d'eau dans des systèmes couplés, lorsque ceux-ci mettent en jeu des interactions entre les écoulements de sub-surface (milieux poreux) et les eaux de surface (milieux ouverts) : plages naturelles et artificielles; digues portuaires; barrages en terre; berges de fleuves; estuaires. Le forçage tidal des écoulements souterrains est représenté et modélisé ici, tant expérimentalement que numériquement, par une oscillation quasi-statique du niveau d'eau dans un réservoir externe ouvert, connecté au domaine poreux. On s'intéresse plus particulièrement aux écoulements verticaux forcés par une pression oscillatoire imposée au bas d'une colonne de sol. Sur le plan expérimental, ce type de forçage est obtenu par une machine à marée équipée d'un arbre rotatif. Au total, on utilise dans ce travail trois types d'approches (expérimentale, numérique, analytique), l'objectif étant d'étudier le mouvement vertical de la surface "libre" et l'écoulement non saturé sus-jacent, de façon à prendre en compte aussi bien les pertes de charge dans la zone saturée que les gradients de pression capillaire dans la zone non saturée. […]
In this thesis, we study hydrodynamic oscillations in porous bodies (unsaturated or partially saturated), due to tidal oscillations of water levels in adjacent open water bodies. The focus is on beach hydrodynamics, but potential applications concern, more generally, time varying and oscillating water levels in coupled systems involving subsurface / open water interactions (natural and artificial beaches, harbor dykes, earth dams, river banks, estuaries). The tidal forcing of groundwater is represented and modeled (both experimentally and numerically) by quasi-static oscillations of water levels in an open water reservoir connected to the porous medium. Specifically, we focus on vertical water movements forced by an oscillating pressure imposed at the bottom of a soil column. Experimentally, a rotating tide machine is used to achieve this forcing. Overall, we use three types of methods (experimental, numerical, analytical) to study the vertical motion of the groundwater table and the unsaturated flow above it, taking into account the vertical head drop in the saturated zone as well as capillary pressure gradients in the unsaturated zone. Laboratory experiments are conducted on vertical sand columns, with a tide machine to force water table oscillations, and with porous cup tensiometers to measure both positive pressures and suctions along the column (among other measurement methods). Numerical simulations of oscillatory water flow are implemented with the BIGFLOW 3D code (implicit finite volumes, with conjugate gradients for the matrix solver and modified Picard iterations for the nonlinear problem). In addition, an automatic calibration based on a genetic optimization algorithm is implemented for a given tidal frequency, to obtain the hydrodynamic parameters of the experimental soil. Calibrated simulations are then compared to experimental results for other non calibrated frequencies. Finally, a family of quasi-analytical multi-front solutions is developed for the tidal oscillation problem, as an extension of the Green-Ampt piston flow approximation, leading to nonlinear, non-autonomous systems of Ordinary Differential Equations with initial conditions (dynamical systems). The multi-front solutions are tested by comparing them with a refined finite volume solution of the Richards equation. Multi-front solutions are at least 100 times faster, and the match is quite good even for a loamy soil with strong capillary effects (the number of fronts required is small, no more than N≈ to 20 at most). A large set of multi-front simulations is then produced in order to analyze water table and flux fluctuations for a broad range of forcing frequencies. The results, analyzed in terms of means and amplitudes of hydrodynamic variables, indicate the existence, for each soil, of a characteristic frequency separating low frequency / high frequency flow regimes in the porous system
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24

RASOLOARIJAONA, MAMY NIRINA. "Non-linearites de la loi de darcy : etudes theorique, numerique et experimentale." Grenoble 1, 1993. http://www.theses.fr/1993GRE10124.

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Nous etudions la filtration en milieu poreux de fluides newtoniens en utilisant la theorie d'homogeneisation des structures periodiques. Dans un premier temps nous rappelons les resultats obtenus grace a la methode dans les cas de l'ecoulement stationnaire de fluides incompressibles ou compressibles, et de l'acoustique de fluides incompressibles. Dans le premier cas, la filtration est decrite par la loi de darcy, la compressibilite etant prise en compte dans le bilan de masse. Dans le second cas, la loi macroscopique est une loi de darcy generalisee: le tenseur de permeabilite est a valeur complexe et depend de la frequence. Nous etendons ensuite notre etude a la recherche d'une correction faiblement non lineaire a la loi de darcy, le nombre de reynolds re microscopique etant suppose petit. L'ecoulement est suppose stationnaire et le fluide incompressible. Le nombre de reynolds microscopique est pris re=0(). En appliquant les resultats aux filtrations unidirectionnelles, la loi macroscopique est une loi cubique sans terme quadratique. On retrouve le meme terme cubique auquel est adjoint un terme du type (v. Grad)v dans le cas d'un milieu isotrope et homogene. Lorsque re0(), le terme cubique n'apparait pas et lorsque 0()re1, on obtient le terme cubique seul. Finalement, nous effectuons une etude experimentale ainsi qu'un calcul numerique sur un modele monodimensionnel. Les deux etudes portent sur un nombre de reynolds local allant de 0 a 150. Il existe une bonne correspondance entre les resultats numeriques et experimentaux. Ces resultats confirment la loi cubique
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25

Bergman, Karin, Linn Berkelund, Maria Nylander, Malin Olsson, and Terese Renström. "HYDROGEOLOGISKA FÖRHÅLLANDEN I GÄVLEÅSEN : Analys av stabila syreisotoper och kemiska parametrar samt beräkning av flöden i Gävleåsen." Thesis, Uppsala universitet, Institutionen för geovetenskaper, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-295020.

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Detta projekt behandlar hur vatten rör sig i Gävleåsen, det vill säga åsens hydrogeologiska förhållanden. Gävle kommun tar sitt dricksvatten från Gävleåsens grundvattenmagasin. För att öka grundvattenbildningen i åsen används konstgjord infiltration av åvatten och grundvatten genom infiltrationsbassänger, infiltrationsbrunnar och en sprinkleranläggning. Projektet initierades med bakgrund att grundvattennivåerna i Gävle kommuns grundvattentäkt sjunker på grund av vattenuttaget. Syftet med projektet var att bestämma om variationer i halt löst syre, organiskt material, an- och katjoner samt stabila syre- och väteisotoper kunde användas för att förklara de hydrogeologiska förhållandena i Gävleåsen. Även storleken på flödet uppströms och nedströms om infiltrationsanläggningen samt blandningsförhållandet nedströms skulle fastställas. Tre modeller över hur flödet varierade i åsen utformades på grund av den stora osäkerhet som fanns vid uppskattning av åsens mättade hydrauliska konduktivitet som användes vid flödesberäkningarna. I den första modellen antogs att flödesmassbalansen i åsen stämde, det vill säga att flödet nedströms var en summa av flödet uppströms om och flödet från infiltrationsanläggningen. Den andra modellen byggde på att det skedde ett okänt nettoutflöde från åsen mellan flödet uppströms och flödet nedströms om infiltrationsanläggningen. Att vatten istället skulle ha tillkommit till akviferen från exempelvis Gavleån eller genom inträngning av äldre grundvatten undersöktes med den tredje modellen. Uppställning av en isotopmassbalans för de olika modellerna tydde på att alla modeller kunde vara en möjlig bild av hur flödena i Gävleåsens akvifer förhöll sig till varandra och infiltrationsflödet genom infiltrationsanläggningen. Vid beräkning av blandningsförhållandet mellan grund- och åvatten nedströms om infiltrationsanläggningen visade både syreisotopsberäkningar och beräkningar med kloridjoner att cirka 25 procent åvatten tillkommit i akviferen. De kemiska parametrarna löst syre och organiskt material visade sig inte vara lämpliga som spårämnen för att bestämma källor till ett flöde. Dock kan dessa parametrar användas för att bedöma om det skett en förändring i vattenkvaliteten.
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26

Pegaz-fiornet, Sylvie. "Etude de modèles pour la migration des hydrocarbures dans les simulateurs de bassin." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10049.

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La modélisation de la migration des hydrocarbures dans les bassins sédimentaires a pour but d'évaluer leur potentiel pétrolier, en localisant et en quantifiant les accumulations d'hydrocarbures au sein des formations géologiques. Dans cette thèse, nous étudions les modèles de migration de type "Darcy" ainsi que des modèles simplifiés de types "ray-tracing" et "invasion percolation"; l'objectif est de mener une analyse critique et de proposer des améliorations tout en fournissant un guide pour une utilisation pertinente sur des cas d'étude.Tout d'abord, nous faisons une revue des mécanismes de la migration depuis l'échelle des pores jusqu'à l'échelle des bassins, puis nous présentons chacun des modèles.Dans le volet suivant, nous proposons deux algorithmes d'invasion percolation : le premier, adapté aux maillages structurés; le second, permettant de mieux prendre en compte les maillages non structurés. Dans un troisième volet, nous nous intéressons à la comparaison entre ces modèles, en nous concentrant sur ceux de types "Darcy" et "invasion percolation". Nous nous focalisons en premier lieu sur les aspects numériques en nous appuyant sur plusieurs cas tests; puis nous effectuons une comparaison formelle en étudiant la limite asymptotique de la solution du modèle de type "Darcy" en temps long. Nous présentons ensuite une série d'applications dont notamment l'étude d'un cas réel 3D en géométrie complexe.Finalement, nous concluons ce travail avec deux articles. Le premier montre une évolution des modèles de type "Darcy" en utilisant la méthode du raffinement local de maillage, avec une illustration sur un cas d'étude du nord du Koweït. Le deuxième synthétise les principaux résultats obtenus concernant les méthodes de "Darcy" et "d'invasion percolation"
Hydrocarbon migration modeling in sedimentary basins aims to localize and to quantify hydrocarbon accumulations in geological formations in order to estimate their petroleum potential. In this thesis, we study “Darcy” migration models and also simplified migration models such as “ray-tracing” and “invasion percolation”; the purpose is to conduct a critical analysis and to offer improvements while providing a guide for a relevant use on case studies.We start by a review of migration mechanisms from the pore scale to the basin scale, then we present each model.In a following part, we propose two invasion percolation algorithms: the first one is suited to structured grids, the second one allows to take better account of unstructured grids.In a third part, we take an interest in the comparison between the different models and particularly between “Darcy” and “invasion percolation” approaches. First we devote our attention to numerical aspects supported by several use cases; then we realize a formal comparison by studying the asymptotic limit of the “Darcy” model large time solution. Afterwards, we present several applications including the study of a 3D real case in complex geometry.Finally, we conclude this work with two articles. The first one shows an evolution of “Darcy” models by using the method of local grid refinement with an illustration on a case study from northern Kuwait. The second one synthesizes the main results on “Darcy” and “invasion percolation” methods
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27

Keiser, Ludovic. "Formation et déplacement de gouttes confinées : Instabilités et dynamiques." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC080/document.

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Les écoulements biphasiques en milieux poreux sont généralement accompagnés par des phénomènes d'émulsification d'une phase dans l'autre. Les causes peuvent être nombreuses, de la digitation visqueuse aux instabilités purement capillaires. Cette thèse expérimentale a pour objet l'étude d'un mécanisme particulier d'émulsification de l'huile en milieu poreux, ainsi que le transport des gouttes produites dans des milieux confinés. Dans la première partie de cette thèse, l'instabilité gravito-capillaire de Rayleigh-Taylor est revisitée dans un coin formé entre deux plaques de verre centimétriques. La présence d'un gradient de confinement introduit une force capillaire supplémentaire à cette instabilité canonique, susceptible de stabiliser une couche de liquide suspendue au-dessus du vide. Le seuil de stabilité, les longueurs d'onde caractéristiques et les taux de croissance sont bien modélisés par une analyse de stabilité linéaire de l'interface. La caractérisation de cette force capillaire induite par le gradient de confinement nous amène par la suite à l'étude d'une instabilité purement capillaire se produisant lorsqu'un fluide en mouillage très favorable migre vers les régions les plus confinées d'un coin, occupées initialement par un fluide en mouillage moins favorable. Le gradient de confinement introduit alors une force déstabilisante, aboutissant à l'inversion de la position respective des deux phases. Le liquide le moins mouillant est complètement émulsifié et transporté vers les régions les moins confinées sous la forme de gouttelettes. Une analyse de stabilité linéaire de l'interface permet, là encore, de prédire cette sélection de taille. Les taux de croissance mesurés ne sont en revanche pas en accord avec la modélisation, basée sur la loi de Darcy. Leur valeur suggère une localisation de la dissipation visqueuse dans les lignes de contact déplacées durant le développement de l'instabilité, ainsi que dans les films de lubrification également déposés. Ces dynamiques "non-darciennes" nous ont amenés dans une seconde partie de la thèse à l'étude du transport de gouttes d'huile très visqueuses confinées dans de l'eau en mouillage total. Dans cette configuration, la présence de films de lubrification d'eau entre la goutte et le substrat assure la localisation de la dissipation dans les films peu visqueux, favorisant ainsi la mobilité des gouttes. Nous montrons également que la présence de rugosités sur les parois du confinement induit un ralentissement significatif de la vitesse des gouttes, lié à l'amincissement du film de lubrification par ces rugosités. L'interdépendance subtile entre friction visqueuse à l'avant de la goutte et dans son volume est notamment mise en lumière. Dans une dernière partie, nous étudions l'instabilité capillaire se produisant lorsqu'une goutte binaire d'eau et d'alcool est déposée à la surface d'un bain d'huile. L'évaporation majoritaire de l'alcool à la surface de la goutte induit des variations locales de la tension de surface. Des écoulements interfaciaux de Marangoni se produisent, et aboutissent à la déstabilisation spectaculaire de la goutte en étalement
Biphasic flows in porous media generally lead to the emulsification of one phase into the other. This may be due to several phenomena, such as viscous fingering or pure capillary instabilities. In this experimental thesis, we study a particular emulsifying phenomenon of oil in a model porous medium, as well as the transport of the produced droplets in confined regions. In the first part of the manuscript, the Rayleigh-Taylor instability is revisited in a wedge formed between two centimetric glass plates. The gradient of confinement leads to a capillary force not present in the canonical Rayleigh-Taylor instability. This new force can stabilize liquid layer above air submitted to gravity. The threshold of the instability, the characteristic wavelength and the growth rate are captured by a linear stability analysis of the interface. This characterization of the confinement-induced capillary force drove us to the study of a pure capillary instability occurring when a wetting liquid migrates toward the most confined regions of a wedge, initially filled with a less wetting liquid. The gradient of confinement generates a destabilizing force, leading to the complete inversion of the position of both phases. The less wetting liquid is fully emulsified and the produced droplets are convected towards the less confined regions. A linear stability analysis of the interface here again predicts the characteristic size of the droplets. However, the measured growth rates are not in agreement with the model, based on the Darcy law. This suggests a localization of viscous dissipation in the contact lines displaced during the development of the instability. Another source of viscous dissipation can be in the deposited lubrication films. Those "non-Darcian" dynamics motivated the second part of this thesis, which focuses on the motion of very viscous and non-wetting droplets confined in water. In this configuration, the lubrication film of water between the drop and the substrate ensures the localization of viscous dissipation in those films of low viscosity. This favors the extremely high mobility of the droplets. We also show that wall roughness may induce a thinning of these lubrication films. We shed light on the intricate coupling between viscous friction at the front of the drop and in its bulk. In a last part of this work, we study the capillary instability occurring when a binary droplet of water and alcohol is deposited at the surface of a vegetable oil bath. The dominant evaporation of alcohol at the surface of the drop induces local variations of surface tension. Interfacial Marangoni flows are thus observed, leading to the spectacular destabilization of the spreading droplet
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28

Chevalier, Thibaud. "Écoulements de fluides à seuil en milieux confinés." Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00903850.

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Afin de mieux comprendre les spécificités de l'écoulement des fluides en seuil en géométries confinées, nous avons opté pour une approche multi-échelle expérimentale et/ou numérique dans des milieux poreux complexes et modèles. Nous montrons qu'il est possible d'utiliser la RMN pour visualiser des écoulements de fluides à seuil en géométrie complexe. Dans un milieu poreux, il est également possible de mesurer la distribution statistique des vitesses, ceci sans problème de résolution spatiale, grâce à la méthodologie de réglage d'une expérience d'injection sous IRM que nous avons mise en place. A l'aide de ces techniques, nous montrons que l'écoulement d'un fluide à seuil dans un pore modèle (une expansion-contraction axisymétrique) se localise dans la partie centrale du pore, dans le prolongement du tube d'entrée, tandis que les régions extérieures restent dans le régime solide. Des simulations numériques confirment ces résultats et montrent que la localisation de l'écoulement provient du confinement engendré par la géométrie. A l'inverse, nous montrons que pour un fluide à seuil s'écoulant dans un milieu poreux réel (en trois dimensions), il n'existe pas de zones au repos. De plus, la distribution de vitesse est identique à celle d'un fluide newtonien. Une analyse de ces résultats nous permet de prédire la forme de la loi de Darcy pour les fluides à seuil et de comprendre l'origine physique des paramètres déterminés par des expériences d'injection " macroscopiques "
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29

Copol, Cédrick Nicolas. "Etudes mathématiques et numériques pour la modélisation des systèmes hydrothermaux. Applications à la géothermie haute énergie." Thesis, Antilles, 2016. http://www.theses.fr/2016ANTI0093/document.

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L’objectif de notre étude est de modéliser un réservoir géothermique. Si nous supposons que le réservoir géothermique n’est composé que d’eau pure le transfert de matière et d’énergie est classiquement décrit par deux équations de conservation : la conservation de la matière et la conservation de l’énergie. À ces deux équations vient s’ajouter la vitesse du fluide classiquement donnée par la loi de Darcy tandis que les propriétés thermodynamiques, obtenues grâce à des équations théoriques ou empiriques (les équations d’état), ferment le modèle mathématique. Dès lors, ce modèle fermé, il existe différents schémas de résolution. Le premier est de résoudre en pression et température puis de procéder à un changement de variables lors du passage de monophasique à diphasique ou de diphasique à monophasique. TOUGH2 utilise le couple pression-saturation dans la zone diphasique.La seconde approche est de résoudre en pression et enthalpie afin d’accroître la stabilité lors de la transition entre l’état monophasique et l’état diphasique (voir Hydrotherm). Nous avons adopté la seconde option, résoudre en pression et enthalpie. De plus la résolution spatiale est faite avec les volumes finis.La modélisation d’un réservoir géothermique fait intervenir des équations fortement dépendantes l’une de l’autre. Cependant nous avons fait le choix de découpler la résolution afin de se libérer de la complexité de la résolution du système couplé. En effet, cette méthode possède l’avantage d’être moins consommatrice de mémoire puisque nous travaillons toujours avec le même nombre de données, mais dans une matrice deux fois moins importante. Nous montrerons que cette méthode demeure suffisamment précise pour une utilisation aussi bien dans le domaine industriel que dans celui de la recherche.Nous offrons à l’utilisateur une grande liberté grâce à l’implémentation de plusieurs méthodes : Euler implicite, explicite, Runge-Kutta ou BDF2 pour les solveurs temporels ou GMRES et BICGSTAB pour les solveurs linéaires. Nous pouvons gérer des conditions aux limites très variées telles que des flux nuls (décrivant une frontière qui n’échange pas de matière avec l’extérieur) ou une condition mixte (un Dirichlet sur la pression et un Dirichlet ou condition « sortie libre » sur la température… Cette dernière situation décrit une zone de recharge ou de décharge. Nous avons développé un outil multilangage : Python,Fortran et C++ (une implémentation de l’IAPWS provenant du projet freesteam incluant la zone supercritique). Tous ces langages sont orientés objet. L’IAPWS est l’outil permettant de calculer les propriétés physiques inconnues et par conséquent il ferme le système.Enfin nous avons appliqué le modèle sur le bassin parisien, France, sur plusieurs systèmes 1D et un autre système 2D réalisés par Coumou avec la plateforme CSMP++. Le bassin parisien est un réservoir exploité pour produire de la chaleur par le biais du pompage d’une eau à 70 _C et réinjecté à 40 _C. Les simulations 1D permettent de visualiser le déplacement d’un front de chaleur en haute enthalpie. La simulation 2D montre la convection naturelle de l’eau dans une faille. Chaque simulation a été comparée aux résultats obtenus avec un autre code (CSMP++, HYDROTHERM ou TOUGH2) et les résultats sont en accord
The purpose of our study is to model a geothermal reservoir. When geothermal reservoirs are assumed to be composed of pure water, the transfer of mass and energy is classically described by two balance equations: the mass balance equation and the energy balance equation. In addition to those equations, fluid velocity is classically given by the Darcy law while thermodynamic properties, inferred from theoretical or empirical equations of state, are used to close the mathematical system. Once this system is closed, there exist different solutions. The first one is to solve for pressure and temperature with a variable switch to saturation in the two-phase region (e.g. TOUGH2). The second one is to solve for pressure and enthalpy to increase the stability of phase transition between single and two-phase states (e.g. Hydrotherm). We adopted the second option. We solve the system by using a splitting method — to get rid of the complexity of coupling equations — and a finite volume method for the spatial discretization. We offer some freedom to users thanks to the implementation of several methods like explicit or implicit Euler, Runge-Kutta or BDF2 for time solvers or GMRES and BICGSTAB for the linear solver. We can handle several boundary conditions like no-flow — describing a boundary which cannot exchange matter withthe exterior — or like a mixed-therm condition — a Dirichlet condition to the pressure and a Dirichlet or an outflow condition to the temperature in order to describe a recharge or a discharge zone — …Selecting object-oriented languages, we developed a multi-language framework, combining Python, Fortran and a C++ implementation of IAPWS (from the freesteam project) including the supercritical equations. To close the system physical propertiesare determined by the IAPWS- IF97 thermodynamic formulation. We’ve applied this simulation model to the dogger in Paris, France, to several onedimensional systems and a two-dimensional one made by Coumou with the CSMP++platform. The dogger is a reservoir exploited to produce heat by pumping water at 70 _C and reinjecting it in the reservoir at 40 _C. In the one-dimensional systems we wanted to observe the process of heat transfer from a higher temperature boundary to a smaller one in a high-energy domain. The last simulation shows the natural convection of water in a fault. For every simulation we compared the solutions we found with another code (TOUGH2 or CSMP++) and they agreed
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30

Marusic-Paloka, Eduard. "Modélisation par homogénéisation des écoulements en milieux poreux fissurés." Saint-Etienne, 1995. http://www.theses.fr/1995STET4008.

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Dans cette thèse nous présentons plusieurs résultats qui concernent l'homogénéisation appliquée à la modélisation des milieux poreux. Elle est composée de quatre chapitres indépendants. Dans les premier et deuxième chapitres nous étudions le comportement effectif des solutions de l'équation de Laplace et du système de Stokes dans un milieu poreux, contenant une fissure mince. Suivant la relation entre la taille caractéristique des pores et l'épaisseur de la fissure nous trouvons trois modèles différents. Le troisième chapitre présente un résultat qui concerne les estimations d'erreur pour les correcteurs dans l'homogénéisation du système de Stokes et de Navier-Stokes, pour un milieu poreux. Dans le dernier chapitre nous étudions les effets inertiels pour un écoulement visqueux, rapide dans une couche ondulée. Nous trouvons une loi globale non linéaire
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31

Mostefai, Mohamed Sadek. "Déduction rigoureuse de l'équation de Reynolds à partir d'un système modélisant l'écoulement à faible épaisseur d'un fluide micropolaire, et étude de deux problèmes à frontière libre : Hele-Shaw généralisé et Stephan à deux phases pour un fluide non newtonien." Saint-Etienne, 1997. http://www.theses.fr/1997STET4019.

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Dans le chapitre 1, on considère le modèle micropolaire de Navier-Stokes avec conditions de bords de type Dirichlet non homogènes en dimension deux. On donnera un résultat d'existence d'une solution faible en utilisant le théorème du point fixe de Leray-Schauder, puis on prouvera l'unicité de la solution faible du problème sous certaines hypothèses. On établiera une justification mathématique de l’équation de Reynolds généralisé à partir de ce modèle là. On étudiera ensuite la forme de l'équation de Reynolds suivant le choix de la viscosité et des données initiales. Dans le chapitre 2, nous considérons le modèle de Hele-Shaw généralisé dans une cellule laminaire, qui consiste à injecter du fluide, avec un débit non constant w 0, à travers un trou de frontière 1, situé sur l'une des deux surfaces ; et à tenir compte que l'une des surfaces a une géométrie quelconque et animée d'un mouvement relatif vertical. En introduisant un changement de variable de type Baiocchi, le problème initial se ramène à l'étude d'une inéquation variationnelle avec terme de Volterra. L'existence d'une solution pour cette dernière est donnée par le théorème du point fixe de Banach. Des résultats de régularité en espace pour la solution seront prouvés en introduisant un problème pénalisé et en utilisant la méthode de Rothe (semi-discrétisation en temps), puis on montrera que la dérivée par rapport à t de la solution de l'inéquation variationnelle est dans l#(0, t, h#2()), ce dernier résultat nous permet de revenir au problème initial. Dans le chapitre 3, on considère un problème de Stefan à deux phases avec convection. Le problème est gouverné par un système couple non linéaire, comprenant la loi de Darcy pour un fluide non newtonien et l'équation d'équilibre d'énergie avec second membre dans l#1. Pour prouver l'existence de solutions du problème faible on introduira une famille de solutions approchées (#, p#), > 0, définies sur le domaine entier , en insérant une fonction de pénalité convenable dans l'équation de pression. On considère ensuite séparement les problèmes en # et p#, respectivement, et en utilisant le principe de point fixe de Schauder, on montre l'existence de couples solutions (#, p#) du problème approché, pour tout > 0. En faisant tendre vers zéro, on montre que les solutions du problème approché convergent vers une limite (, p) qui est une solution faible du problème variationnel. On montre aussi que la fonction est continue d'où le domaine où > 0 est un ensemble ouvert, et l'interface des deux phases est définie a posteriori comme l'ensemble de niveau = 0. On établira, enfin, quelques relations entre les solutions faibles et classiques, dans le cas d’une courbe assez régulière
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Thibaud, Laurent. "Contribution à l'étude de la convection naturelle à l'intérieur d'un cylindre vertical poreux soumis à une densité de flux thermique parietal constante : application aux silos à grains." Poitiers, 1988. http://www.theses.fr/1988POIT2299.

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33

Welsh, WD. "Groundwater balance modelling with Darcy's Law." Phd thesis, 2007. http://hdl.handle.net/1885/48015.

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The sustainability of groundwater resources is important for the environment, the economy and communities where surface water is scarce. It is a hidden resource, but additional information can be extracted by combining groundwater measurements and lithological information with groundwater flow equations in groundwater models. The models convert data and knowledge about the groundwater systems into information, such as relative inflow and outflow rates and water-level predictions that can be readily understood by groundwater managers. ¶ The development of models to effectively inform groundwater management policies is, however, a complex task that presents a fundamental scientific challenge. This thesis presents methods and results for water balances calculated using groundwater flow models. Groundwater flow modelling methods and approaches are discussed, and their capabilities and limitations are reviewed. Two groundwater systems are studied for the Great Artesian Basin (GAB) and for the irrigation area near Bowen, Queensland. Three approaches to water balance modelling are applied in comprehensive model-development frameworks that take into account model objectives, data and knowledge availability and sensitivity analysis techniques. The three models show numerical methods of increasing complexity...
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34

Karthigesu, Thayalan. "Validity of Darcy's law for low-gradient saturated flow through bentonite and sand mixtures." 1994. http://hdl.handle.net/1993/18130.

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Delchini, Marc Olivier. "A Preliminary Study to Assess Model Uncertainties in Fluid Flows." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-05-7793.

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In this study, the impact of various flow models is assessed under free and forced convection: compressible versus incompressible models for a Pressurized Water Reactor, and Darcy's law vs full momentum equation for High Temperature Gas Reactor. Euler equations with friction forces and a momentum and energy source/sink are used. The geometric model consists of a one-dimensional rectangular loop system. The fluid is heated up and cooled down along the vertical legs. A pressurizer and a pump are included along the horizontal legs. The compressible model is assumed to be the most accurate model in this study. Simulations show that under forced convection compressible and incompressible models yield the same transient and steady-state. As free convection is studied, compressible and incompressible models have different transient but the same final steady-state. As Darcy's law is used, pressure and velocity steady-state profiles yield some differences compared to the compressible model both under free and forced convections. It is also noted some differences in the transient.
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Lehr, Heather Lyn Arbogast Todd J. "Analysis of a Darcy-Stokes system modeling flow through vuggy porous media." 2004. http://wwwlib.umi.com/cr/utexas/fullcit?p3143297.

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Rath, James Michael 1975. "Multiscale basis optimization for Darcy flow." Thesis, 2007. http://hdl.handle.net/2152/3977.

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Simulation of flow through a heterogeneous porous medium with fine-scale features can be computationally expensive if the flow is fully resolved. Coarsening the problem gives a faster approximation of the flow but loses some detail. We propose an algorithm that obtains the fully resolved approximation but only iterates on a sequence of coarsened problems. The sequence is chosen by optimizing the shapes of the coarse finite element basis functions. As a stand-alone method, the algorithm converges globally and monotonically with a quadratic asymptotic rate. Computational experience indicates the number of iterations needed is independent of the resolution and heterogeneity of the medium. However, an externally provided error estimate is required; the algorithm could be combined as an accelerator with another iterative algorithm. A single "inner" iteration of the other algorithm would yield an error estimate; following it with an "outer" iteration of our algorithm would give a viable method.
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Lehr, Heather Lyn. "Analysis of a Darcy-Stokes system modeling flow through vuggy porous media." Thesis, 2004. http://hdl.handle.net/2152/1234.

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San, Martin Gomez Mario. "A three dimensional finite element method and multigrid solver for a Darcy-Stokes system and applications to vuggy porous media." Thesis, 2007. http://hdl.handle.net/2152/2929.

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San, Martin Gomez Mario 1968. "A three dimensional finite element method and multigrid solver for a Darcy-Stokes system and applications to vuggy porous media." 2007. http://hdl.handle.net/2152/13131.

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41

Liu, Kun. "Discontinuous Galerkin Methods for Parabolic Partial Differential Equations with Random Input Data." Thesis, 2013. http://hdl.handle.net/1911/71989.

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This thesis discusses and develops one approach to solve parabolic partial differential equations with random input data. The stochastic problem is firstly transformed into a parametrized one by using finite dimensional noise assumption and the truncated Karhunen-Loeve expansion. The approach, Monte Carlo discontinuous Galerkin (MCDG) method, randomly generates $M$ realizations of uncertain coefficients and approximates the expected value of the solution by averaging M numerical solutions. This approach is applied to two numerical examples. The first example is a two-dimensional parabolic partial differential equation with random convection term and the second example is a benchmark problem coupling flow and transport equations. I first apply polynomial kernel principal component analysis of second order to generate M realizations of random permeability fields. They are used to obtain M realizations of random convection term computed from solving the flow equation. Using this approach, I solve the transport equation M times corresponding to M velocity realizations. The MCDG solution spreads toward the whole domain from the initial location and the contaminant does not leave the initial location completely as time elapses. The results show that MCDG solution is realistic, because it takes the uncertainty in velocity fields into consideration. Besides, in order to correct overshoot and undershoot solutions caused by the high level of oscillation in random velocity realizations, I solve the transport equation on meshes of finer resolution than of the permeability, and use a slope limiter as well as lower and upper bound constraints to address this difficulty. Finally, future work is proposed.
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Gannavaram, Spandana. "Modeling and design optimization of a microfluidic chip for isolation of rare cells." Thesis, 2013. http://hdl.handle.net/1805/4442.

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Indiana University-Purdue University Indianapolis (IUPUI)
Cancer is still among those diseases that prominently contribute to the numerous deaths that are caused each year. But as technology and research is reaching new zeniths in the present times, cure or early detection of cancer is possible. The detection of rare cells can help understand the origin of many diseases. The current study deals with one such technology that is used for the capture or effective separation of these rare cells called Lab-on-a-chip microchip technology. The isolation and capture of rare cells is a problem uniquely suited to microfluidic devices, in which geometries on the cellular length scale can be engineered and a wide range of chemical functionalizations can be implemented. The performance of such devices is primarily affected by the chemical interaction between the cell and the capture surface and the mechanics of cell-surface collision and adhesion. This study focuses on the fundamental adhesion and transport mechanisms in rare cell-capture microdevices, and explores modern device design strategies in a transport context. The biorheology and engineering parameters of cell adhesion are defined; chip geometries are reviewed. Transport at the microscale, cell-wall interactions that result in cell motion across streamlines, is discussed. We have concentrated majorly on the fluid dynamics design of the chip. A simplified description of the device would be to say that the chip is at micro scale. There are posts arranged on the chip such that the arrangement will lead to a higher capture of rare cells. Blood consisting of rare cells will be passed through the chip and the posts will pose as an obstruction so that the interception and capture efficiency of the rare cells increases. The captured cells can be observed by fluorescence microscopy. As compared to previous studies of using solid microposts, we will be incorporating a new concept of cylindrical shell micropost. This type of micropost consists of a solid inner core and the annulus area is covered with a forest of silicon nanopillars. Utilization of such a design helps in increasing the interception and capture efficiency and reducing the hydrodynamic resistance between the cells and the posts. Computational analysis is done for different designs of the posts. Drag on the microposts due to fluid flow has a great significance on the capture efficiency of the chip. Also, the arrangement of the posts is important to contributing to the increase in the interception efficiency. The effects of these parameters on the efficiency in junction with other factors have been studied and quantified. The study is concluded by discussing design strategies with a focus on leveraging the underlying transport phenomena to maximize device performance.
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Kociánová, Barbora. "Matematické modelování perfúze jater." Master's thesis, 2019. http://www.nusl.cz/ntk/nusl-406142.

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Liver perfusion can be modelled by Darcy's flow in multiple connected com- partments. The first part of the present thesis shows in detail the existence of a solution to the multi-compartmental model. The flow in each compartment in this model is characterized by a permeability tensor, which is obtained from the geometry of liver vasculature. It turns out that this tensor might be singular, which potentially causes solvability problems. The second part deals with this abnormality in one compartment. By using the theory of degenerate Sobolev spaces, an appropriate weak formulation is defined. Analogues of Poincar'e and traces inequalities in this degenerate setting are proved, which also imply the existence of the weak solutions. In addition, this part justifies another possibil- ity how to deal with degenerate permeability, which is regularizing the tensor by adding a small isotropic permeability to it. In the third part, the aim is to find subdomains of autonomous perfusion with respect to the source positions. This is formulated as a minimization problem and several numerical results are presented. 1
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Chaudhary, Kuldeep. "Pore-scale controls of fluid flow laws and the cappillary trapping of CO₂." 2013. http://hdl.handle.net/2152/22083.

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A pore-scale understanding of fluid flow underpins the constitutive laws of continuum-scale porous media flow. Porous media flow laws are founded on simplified pore structure such as the classical capillary tube model or the pore-network model, both of which do not include diverging-converging pore geometry in the direction of flow. Therefore, modifications in the fluid flow field due to different pore geometries are not well understood. Thus this may translate to uncertainties on how flow in porous media is predicted in practical applications such as geological sequestration of carbon dioxide, petroleum recovery, and contaminant’s fate in aquifers. To fill this gap, we have investigated the role of a spectrum of diverging-converging pore geometries likely formed due to different grain shapes which may be due to a variety of processes such as weathering, sediment transport, and diagenesis. Our findings describe the physical mechanisms for the failure of Darcy’s Law and the characteristics of Forchheimer Law at increasing Reynolds Number flows. Through fundamental fluid physics, we determined the forces which are most responsible for the continuum-scale porous media hydraulic conductivity (K) or permeability. We show that the pore geometry and the eddies associated therein significantly modify the flow field and the boundary stresses. This has important implications on mineral precipitation-dissolution and microbial growth. We present a new non-dimensional geometric factor β, a metric for diverging-converging pore geometry, which can be used to predict K. This model for K based on β generalizes the original and now widely-used Kozeny (1927) model which was based on straight capillary tubes. Further, in order to better quantify the feasibility of geological CO2 sequestration, we have conducted laboratory fluid flow experiments at reservoir conditions to investigate the controls of media wettability and grain shapes on pore-scale capillary trapping. We present experimental evidence for the snap-off or formation of trapped CO2 ganglion. The total trapping potential is found to be 15% of porosity for a water-wet media. We show that at the pore-scale media wettability and viscous-fingering play a critical role in transport and trapping of CO2. Our investigations clearly show that that in single-phase flow pore geometry significantly modifies pore-scale stresses and impacts continuum-scale flow laws. In two-phase flows, while the media wettability plays a vital role, the mobility ratio of CO2 - brine system significantly controls the CO2 capillary trapping potential- a result which should be taken into consideration while managing CO2 sequestration projects.
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