Rozprawy doktorskie: „Transport in fractured porous media”

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Kang, Peter Kyungchul. "Anomalous transport through porous and fractured media". Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90043.

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Thesis: Ph. D. in Hydrology, Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 132-144).
Anomalous transport, understood as the nonlinear scaling with time of the mean square displacement of transported particles, is observed in many physical processes, including contaminant transport through porous and fractured geologic media, animal and human foraging patterns, tracer diffusion in biological systems, and transport in complex networks. Understanding the origin of anomalous transport is essential, because it determines the likelihood of high-impact, low-probability events and therefore exerts a dominant control over the predictability of a system. The origin of anomalous transport, however, remains a matter of debate. In this thesis, we first investigate the pore-scale origin of anomalous transport through sandstone. From high-resolution (micron-scale) 3D numerical flow and transport simulation, we find that transport at the pore scale is markedly anomalous. We demonstrate that this anomalous behavior originates from the intermittent structure of the velocity field at the pore scale, which in turn emanates from the interplay between velocity heterogeneity and velocity correlation. Finally, we propose a continuous time random walk (CTRW) model that honors this intermittent structure at the pore scale and captures the anomalous 3D transport behavior at the macroscale. To show the generality of our finding, we study transport through lattice networks with quenched disorder. We again observe anomalous transport originating from the interplay between velocity heterogeneity and velocity correlation. We extend the developed CTRW model to capture the full multidimensional particle transport dynamics for a broad range of network heterogeneities and for both advection- and diffusion-dominated flow regimes. We then study anomalous transport through fractured rock at the field-scale. We show that the interplay between heterogeneity and correlation in controlling anomalous transport can be quantified by combining convergent and push-pull tracer tests because flow reversibility is strongly dependent on correlation, whereas late-time scaling of breakthrough curves is mainly controlled by velocity heterogeneity. Our transport model captures the anomalous behavior in the breakthrough curves for both push-pull and convergent flow geometries, with the same set of parameters. Moreover, the inferred flow correlation length shows qualitative agreement with geophysical measurements. Thus, the proposed correlated CTRW modeling approach furnishes a simple yet powerful framework for characterizing the impact of flow correlation and heterogeneity on transport in porous and fractured media. Finally, we propose a joint flow-seismic inversion methodology for characterizing fractured reservoirs. Traditionally, seismic interpretation of subsurface structures is performed without any account of flow behavior. With the proposed methodology, we reduce the uncertainty by integrating dynamic flow measurements into the seismic interpretation, and improve the predictability of reservoir models by this joint use of seismic and flow data. This work opens up many possibilities of combining geophysical and flow information for improving subsurface characterization.
by Peter Kyungchul Kang.
Ph. D. in Hydrology

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Deng, Hailin. "Upscaling reactive transport parameters for porous and fractured porous media". Tallahassee, Florida : Florida State University, 2009. http://etd.lib.fsu.edu/theses/available/etd-10292009-103844/.

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Thesis (Ph. D.)--Florida State University, 2009.
Advisor: Ming Ye, Zhenxue Dai, Florida State University, College of Arts and Sciences, Dept. of Geological Sciences. Title and description from dissertation home page (viewed on Apr. 26, 2010). Document formatted into pages; contains xxii, 167 pages. Includes bibliographical references.

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ALVARENGA, JULIO ERNESTO MACIAS. "NUMERICAL MODELING OF VIRUS TRANSPORT IN FRACTURED-POROUS MEDIA". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=11744@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
GRUPO DE TECNOLOGIA DE COMPUTAÇÃO GRÁFICA - PUC-RIO
A avaliação do potencial de contaminação de capatações de água, por causa das águas residuais provenientes dos sistemas de tanque séptico, é feita a partir da definição da distância de separação mínima que deve existir entre a captação e o local de infiltração do efluente. A determinação dessa distância define a zona de proteção da captação. Existem três metodologias para definir o tamanho dessa zona de proteção: metodologias baseadas em distâncias fixas e tempos de trânsito, metodologias baseadas na vulnerabilidade e metodologias baseadas no risco de infecção. No caso da Costa Rica, as avaliações são feitas através do uso da metodologia baseada no tempo de trânsito. O tempo de trânsito empregado corresponde ao tempo de sobrevivência dos vírus. Nesta análise determina-se a distância máxima percorrida pelos vírus durante esse tempo, e essa distância define a separação mínima. Esse método considera que o transporte ocorre por percolação vertical saturada através da zona não saturada, e por transporte ao longo da interface água-ar na zona saturada segundo o gradiente natural. Neste trabalho apresenta-se um novo procedimento, baseado no risco de infecção, para a determinação da distância de separação considerando os efeitos da saturação variável e o fraturamento. Este procedimento determina a distância máxima percorrida, a partir do cálculo das concentrações de vírus. A distância de separação mínima corresponde à distância entre a fonte de injeção e o ponto aonde a concentração atinge o valor máximo de concentração permitida. Para o desenvolvimento deste novo procedimento foi implementado um código de programação que inclui: fluxo saturado-não saturado e transporte explícito nos poros e nas fraturas, advecção, dispersão, decaimento, sorção na superfície dos sólidos, sorção nas interfaces água-ar e água-sólido, filtração mecânica e exclusão de poros. Foi realizada uma análise comparativa entre as metodologias acima descritas para três geometrias tipo representativas das condições estratigráficas de algumas áreas do Vale Central da Costa Rica. Os resultados obtidos indicaram que a metodologia normalmente empregada na Costa Rica pode ser inadequada para prever na maioria dos casos a possibilidade de contaminação.
Setback distances of wellhead and catchments from septic tanks are establised by three aproaches: methods based on fixed setback distances or fixed travel times; methods based on vulnerability analysis and methods based on infection risk. In Costa Rica, the determination of setback distances is based on fixed travel times. This approach considers that during and specified travel time all microorganisms will be inactivated, and that the distance traveled during this time defines the minimum safe separation. In this approach a unitary hydraulic gradient and saturated hydraulic conductivity are considered for transport in the unsaturated zone and the natural hydraulic gradient and saturated conductivity for transport in the saturated zone. Only advection is considered as the responsible mechanism for virus transport. A new procedure is presented in this document to define the setback distance. This procedure is based on the infection risk approach. According to this approach the minimum required setback distance is defined as the distance between the injection point and the location where the contaminant reaches a maximum allowable concentration. This procedure was implemented in a computer code that considers variable saturated water flow, fractured-porous media, advection, dispersion, dynamic sorption, inactivation and mechanical filtration. A comparative analysis was performed for three hypothetical geometries using the two approaches described. The results indicate the approach normally used in Costa Rica may no reproduce adequately the possibility of catchments and wellhead contamination.

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Botros, Farag Elia Farag. "On upscaling groundwater flow and transport parameters in porous and fractured media". abstract and full text PDF (free order & download UNR users only), 2007. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3275828.

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Pollard, Adam Spencer. "A numerical study of flow and contaminant transport in fractured porous media". Thesis, University of Exeter, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284632.

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Graf, Thomas. "Modeling coupled thermohaline flow and reactive solute transport in discretely-fractured porous media". Thesis, Québec : Université Laval, 2005. http://www.theses.ulaval.ca/2005/23197/23197.pdf.

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Graf, Thomas. "Modeling coupled thermohaline flow and reactive solute transport in discretely-fractured porous media". Doctoral thesis, Université Laval, 2006. http://hdl.handle.net/20.500.11794/18230.

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Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2005-2006
Un modèle numérique tridimensionnel a été développé pour la simulation du système chimique quartz-eau couplé avec l’écoulement à densité et viscosité variable dans les milieux poreux discrètement fracturés. Le nouveau modèle simule aussi le transfert de chaleur dans les milieux poreux fracturés en supposant que l’expansion thermique du milieu est négligeable. Les propriétés du fluide, densité et viscosité, ainsi que les constantes chimiques (constant de taux de dissolution, constant d’équilibre, coefficient d’activité) sont calculées en fonction de la concentration des ions majeurs et de la température. Des paramètres de réaction et d’écoulement, comme la surface spécifique du minéral et la perméabilité sont mis jour à la fin de chaque pas de temps avec des taux de réaction explicitement calculés. Le modèle suppose que des changements de la porosite et des ouvertures de fractures n’ont pas d’impact sur l’emmagasinement spécifique. Des pas de temps adaptatifs sont utilisés pour accélérer et ralentir la simulation afin d’empêcher des résultats non physiques. Les nouveaux incréments de temps dépendent des changements maximum de la porosité et/ou de l’ouverture de fracture. Des taux de réaction au niveau temporel L+1 (schéma de pondération temporelle implicite) sont utilisés pour renouveler tous les paramètres du modèle afin de garantir la stabilité numérique. Le modèle a été vérifié avec des problèmes analytiques, numériques et physiques de l’écoulement à densité variable, transport réactif et transfert de chaleur dans les milieux poreux fracturés. La complexité de la formulation du modèle permet d’étudier des réactions chimiques et l’écoulement à densité variable d’une façon plus réaliste qu’auparavant possible. En premier lieu, cette étude adresse le phénomène de l’écoulement et du transport à densité variable dans les milieux poreux fracturés avec une seule fracture à inclinaison arbitraire. Une formulation mathématique générale du terme de flottabilité est dérivée qui tient compte de l’écoulement et du transport à densité variable dans des fractures de toute orientation. Des simulations de l’écoulement et du transport à densité variable dans une seule fracture implanté dans une matrice poreuse ont été effectuées. Les simulations montrent que l’écoulement à densité variable dans une fracture cause la convection dans la matrice poreuse et que la fracture à perméabilité élevée agit comme barrière pour la convection. Le nouveau modèle a été appliqué afin de simuler des exemples, comme le mouvement horizontal d’un panache de fluide chaud dans un milieu fracturé chimiquement réactif. Le transport thermohalin (double-diffusif) influence non seulement l’écoulement à densité variable mais aussi les réactions chimiques. L’écoulement à convection libre dépend du contraste de densité entre le fluide (panache chaud ou de l’eau salée froide) et le fluide de référence. Dans l’exemple, des contrastes de densité sont généralement faibles et des fractures n’agissent pas comme des chemins préférés mais contribuent à la dispersion transverse du panache. Des zones chaudes correspondent aux régions de dissolution de quartz tandis que dans les zones froides, la silice mobile précipite. La concentration de silice est inversement proportionnelle à la salinité dans les régions à salinité élevée et directement proportionnelle à la température dans les régions à salinité faible. Le système est le plus sensible aux inexactitudes de température. Ceci est parce que la température influence non seulement la cinétique de dissolution (équation d’Arrhenius), mais aussi la solubilité de quartz.
A three-dimensional numerical model is developed that couples the quartz-water chemical system with variable-density, variable-viscosity flow in fractured porous media. The new model also solves for heat transfer in fractured porous media, under the assumption of negligible thermal expansion of the rock. The fluid properties density and viscosity as well as chemistry constants (dissolution rate constant, equilibrium constant and activity coefficient) are calculated as a function of the concentrations of major ions and of temperature. Reaction and flow parameters, such as mineral surface area and permeability, are updated at the end of each time step with explicitly calculated reaction rates. The impact of porosity and aperture changes on specific storage is neglected. Adaptive time stepping is used to accelerate and slow down the simulation process in order to prevent physically unrealistic results. New time increments depend on maximum changes in matrix porosity and/or fracture aperture. Reaction rates at time level L+1 (implicit time weighting scheme) are used to renew all model parameters to ensure numerical stability. The model is verified against existing analytical, numerical and physical benchmark problems of variable-density flow, reactive solute transport and heat transfer in fractured porous media. The complexity of the model formulation allows chemical reactions and variable-density flow to be studied in a more realistic way than previously possible. The present study first addresses the phenomenon of variable-density flow and transport in fractured porous media, where a single fracture of an arbitrary incline can occur. A general mathematical formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulations of variable-density flow and solute transport are conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the highpermeability fracture acts as a barrier for convection. The new model was applied to simulate illustrative examples, such as the horizontal movement of a hot plume in a chemically reactive fractured medium. Thermohaline (double-diffusive) transport impacts both buoyancy-driven flow and chemical reactions. Free convective flow depends on the density contrast between the fluid (hot brine or cool saltwater) and the reference fluid. In the example, density contrasts are generally small and fractures do not act like preferential pathways but contribute to transverse dispersion of the plume. Hot zones correspond to areas of quartz dissolution while in cooler zones, precipitation of imported silica prevails. The silica concentration is inversely proportional to salinity in high-salinity regions and directly proportional to temperature in low-salinity regions. The system is the most sensitive to temperature inaccuracy. This is because temperature impacts both the dissolution kinetics (Arrhenius equation) and the quartz solubility.

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TELLES, ISABELLE DE ARAUJO. "DEVELOPMENT OF AN INTEGRATED SYSTEM FOR THE MODELLING OF FLOW AND TRANSPORT IN POROUS AND FRACTURED MEDIA". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2006. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8662@1.

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AGÊNCIA NACIONAL DE PETRÓLEO
Este trabalho apresenta o desenvolvimento de um sistema integrado de modelagem, tridimensional, de fluxo e transporte em meios porosos e fraturados. O sistema é composto de seis programas computacionais, que são responsáveis pela geração de superfícies geológicas (Gocad), geração de sistemas de fraturas (FracGen3D), modelagem geométrica (MG), análise numérica de fluxo e transporte (soluto e partículas) (FTPF-3D) e visualização dos resultados (Pos3D e Matlab). Dos programas, dois foram desenvolvidos neste trabalho (FracGen3D e o FTPF-3D) e quatro foram integrados ao sistema (Gocad, MG, Pos3D e Matlab). O sistema é capaz de modelar os meios porosos, fraturados, porosos fraturados (meio poroso e fraturado interposto) e uma combinação entre os meios. Nos meios fraturados ou porosos fraturados, as fraturas geradas podem ser do tipo determinísticas e/ou estatísticas. As características das fraturas estatísticas podem ser geradas segundo distribuições probabilísticas ou com valores constantes. O programa de análise numérica utiliza o Método dos Elementos Finitos para resolver as equações governantes, considerando os regimes permanente e transiente, em condições saturadas e não saturadas. Para a solução da não linearidade da equação de fluxo, é adotado o método de Picard ou o método BFGS. No transporte de solutos, os mecanismos de advecção, dispersão, difusão, sorção e decaimento podem ser considerados. O trabalho apresenta exemplos numéricos utilizados na validação das implementações computacionais realizadas, e apresenta também, outros exemplos utilizados para demonstrar o sistema desenvolvido.
This work presents the development of an integrated system for the threedimensional modelling of flow and transport in porous and fractured media. The system is composed of six computational programs, which are responsible for the generation of geologic surface (Gocad), generation of fracture network (FracGen3D), geometric modelling (MG), numerical analysis of flow and transport (solute and particles) (FTPF-3D) and results visualization (Pos3D and Matlab). Of the programs, two had been developed in this work (FracGen3D and the FTPF-3D) and four had been integrated to the system (Gocad, MG, Pos3D and Matlab). The system is able to model the porous, fractured, fractured porous media (porous and fractured medias interposed) and a combination between the media. In the fractured or fractured porous media, the fractures generated can be of the type deterministic and/or statistical. The characteristics of the statistical fractures can be generated according to probabilistic distributions or with constant values. The numerical analysis program uses the Finite Element Method to solve the governance equations, considering steady-state and transient flow, in saturated and unsaturated conditions. For the solution of non linearity of the flow equation, the Picard scheme or the BFGS scheme are adopted. In the solute transport, the advection, dispersion, diffusion, sorption and decay mechanisms can be considered. This work also presents numerical examples used in the validation of the carried through computational implementations and other examples used to demonstrate the system that has been developed.

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Koohbor, Behshad. "Modeling water flow and mass transport in fractured porous media : application to seawater intrusion and unsaturated zone". Thesis, Strasbourg, 2020. http://www.theses.fr/2020STRAH013.

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Ce mémoire de thèse traite de la modélisation des écoulements et du transport dans les milieux poreux fracturés, avec deux applications : l'intrusion saline dans les aquifères côtiers et l'écoulement dans la zone non saturée fracturée. Les principaux objectifs sont d'améliorer l'efficacité et la précision des modèles numériques afin de renforcer leur capacité à traiter des situations réelles de terrain. Une partie importante est consacrée au développement de solutions semi-analytiques pour l'intrusion d'eau de mer avec le modèle d'écoulement densitaire. Ces solutions sont utiles à des fins d'analyse comparative et de compréhension des processus physiques. Une technique robuste d’analyse de sensibilité avec un modèle de substitution est également développée pour étudier les incertitudes liées aux fractures sur l'intrusion saline. Une autre partie du mémoire décrit un schéma numérique efficace élaboré pour la simulation des écoulements variablement saturés dans les domaines fracturés. Ce nouveau schéma est utilisé pour étudier l'effet du changement climatique sur les ressources en eau souterraine dans un système fracturé au Liban
This work addresses the numerical modeling of flow and mass transport in fractured porous media with a focus on two applications: seawater intrusion in coastal aquifers and flow in the fractured vadose zone. The main objectives of this work are to improve the efficiency and accuracy of numerical models to enhance their capacity in dealing with real-world studies. A significant part is dedicated to the development of semi-analytical solutions for seawater intrusion with the variable density flow model. These solutions are useful for benchmarking purposes and understanding the physical processes. An appropriate and robust technique based on surrogate modeling is also developed to investigate the uncertainties related to fractures on seawater intrusion. An efficient numerical scheme is developed for the simulation of variably saturated flow in fractured domains. The new developed scheme is used to investigate the effect of climate change on groundwater resources in a karst aquifer/spring system in Lebanon

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Süß, Mia. "Analysis of the influence of structures and boundaries on flow and transport processes in fractured porous media". [S.l. : s.n.], 2005. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11759360.

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Momeni, Sina. "Non-linear diffusion in fractured porous media and application to dual-medium inter-porosity flux". Electronic Thesis or Diss., Sorbonne université, 2022. http://www.theses.fr/2022SORUS496.

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Les transferts en milieu poreux fracturés sont importants dans de nombreuses applications industrielles telles que la production pétrolière, l'exploitation géothermique, la dépollution des sols ou le stockage géologique. L'analyse dimensionnelle des transferts matrice-fracture doit prendre en compte tous les mécanismes physiques entraînant les transferts, la diffusivité de la pression, la gravité/ségrégation, la force capillaire, l'écoulement visqueux, la diffusion moléculaire pour les transferts de composition et l'altération chimique du fluide/de la roche. La modélisation et la mise à l'échelle de ces transferts décrits par des équations de transport linéaires et non linéaires font l'objet de recherches actives. Le modèle double milieu est un outil puissant pour la mise à l'échelle des transferts à l'échelle des blocs matriciels des réservoirs naturellement fracturés, mais, malheureusement, la plupart de leurs formulations reposent sur la valeur asymptotique (aux temps longs) impliquant un « facteur de forme » déterminé dans un contexte d'écoulement monophasique. Nos travaux visent à améliorer la fiabilité de la mise à l'échelle des modèles matrice-fracture bi-milieu qui sont adoptés pour simuler le transport et les échanges de fluides à l'échelle des réservoirs géologiques. Les solutions analytiques pour la pression monophasique ou la diffusion moléculaire sont bien connues à l'échelle de Darcy. Ces modèles à l'échelle de Darcy ont fourni des solutions de référence dont l'analyse physique aide à mettre en place les méthodes de mise à l'échelle pour paramétrer les modèles à macro-échelle basés sur le concept de double milieu. Cette étude fournit un facteur de forme analytique pour la diffusion linéaire dans le modèle à double milieu avec des conditions aux limites de fracture spécifiques et suggère une correction pour améliorer le simulateur numérique à double milieu. Le transfert matrice-fracture est caractérisé par des comportements précoces et tardifs qui ont orienté notre méthodologie pour résoudre le transfert non linéaire en deux phases. Nous revisitons le problème non linéaire avec condition aux limites de Dirichlet en présentant deux solutions asymptotiques exactes valables pour les temps courts et longs, sous l'hypothèse que la diffusivité s'annule comme une loi de puissance des deux saturations de phase aux valeurs extrêmes de la saturation du fluide. Aux temps, courts une solution auto-similaire exacte déjà connue par ailleurs est adaptée. Dans le domaine des temps longs, un Ansatz s’écrivant sous la forme d'une décroissance temporelle en loi de puissance de la saturation Liquide en Phase Non Aqueuse. Les variations spatiales de la solution sont données analytiquement pour un milieu poreux unidimensionnel. La solution analytique est en très bon accord avec les résultats de simulations numériques impliquant divers ensembles réalistes de paramètres de transport d'entrée. Dans le cas multidimensionnel de forme arbitraire, un algorithme à convergence rapide basé sur une séquence en virgule fixe a été développé. Les comparaisons avec des simulations complètes pour plusieurs géométries de blocs typiques montrent un excellent accord. Ces solutions analytiques généralisent la représentation linéaire monophasique du terme d'échange matrice-fracture au transfert d'imbibition capillaire biphasique. Cette formulation tient compte de la non-linéarité des équations d'écoulement locales en utilisant la dépendance en loi de puissance de la conductivité pour une faible saturation en NAPL. L'exposant correspondant peut être prédit à partir des paramètres de conductivité d'entrée. La généralisation des résultats à des blocs matriciels représentatifs à deux ou trois dimensions est également présentée, et les résultats sont confirmés. Enfin, nous présentons un modèle de transfert matrice-fracture avec un temps caractéristique portant sur toute la gamme d'une imbibition capillaire à contre-courant dans un système de blocs 2D ou 3D
Transfers in fractured porous media are involved in many industrial applications such as oil production, geothermal exploitation, soil remediation, or geological storage. Dimensional analysis of matrix-fracture transfers must consider all physical mechanisms driving transfers, pressure diffusivity, gravity/segregation, capillary force, viscous flow, molecular diffusion for compositional transfers, and chemical alteration of fluid/rock. Modeling and up-scaling these transfers in linear and non-linear forms remain a major challenge in many applications. The “dual-medium” model is a powerful tool for up-scaling transfers in the matrix block scale of Naturally Fractured Reservoirs but, unfortunately, most of their formulations rely on the asymptotic value (at large/late times) of a so-called “shape factor” in a single-phase flow context. This research increases the reliability of up-scaling of matrix-fracture dual-medium models that are adopted to simulate fluid or heat transport at the scale of geological reservoirs. Analytical solutions for single-phase diffusion are well-known in Darcy-scale. These Darcy-scale models provided reference solutions whose physical analysis helps in setting up the upscaling methods for parameterizing the macro-scale models based on the dual-medium concept. This study derived an analytical shape factor for linear diffusion in the dual-medium model with specific fracture boundary conditions and suggested a correction function to modify the dual-medium numerical simulator. The matrix-fracture transfer time is characterized by early- and late-time behaviors that turned to our methodology to solve the non-linear two-phase transfer. In many situations of practical interest, capillarity is the dominant driving force and the saturation-dependent diffusion coefficient vanishes at the saturation end points, which renders the driving equation highly singular. We revisit this non-linear problem with Dirichlet boundary condition by presenting two exact asymptotic solutions valid for early- and late-times, under the assumption that the diffusivity vanishes as a power-law of both phase saturations at the extreme values of the fluid saturation. In the early-time an exact self-similar solution is adopted. Focusing on the late-time domain, the asymptotic solution is derived using an Ansatz that is written under the form of a power-law time decay of the NAPL saturation. The spatial variations of the solution are given analytically for a one-dimensional porous medium corresponding to parallel fracture planes. The analytical solution is in very good agreement with the results of numerical simulations involving various realistic sets of input transport parameters. Generalization to the case of two- or three-dimensional matrix blocks of arbitrary shape is proposed using a similar Ansatz. A fast converging algorithm based on a fixed-point sequence starting from a suitable first guess was developed. Comparisons with full-time simulations for several typical block geometries show an excellent agreement. These analytical results generalize linear single-phase representation of matrix-to-fracture exchange term to two-phase capillary imbibition transfer. This formulation accounts for the non-linearity of the local flow equations using the power-law dependence of the conductivity for low NAPL saturation. The corresponding exponent can be predicted from the input conductivity parameters. Similar findings are also presented and validated numerically for two- or three-dimensional matrix blocks. Finally, we present a matrix-fracture transfer model with a characteristic time that scales the full range of a counter-current capillary imbibition in a multi-dimensional system.That original approach paves the way to research leading to a more faithful description of matrix-to-fracture exchanges when considering a realistic fractured medium composed of a population of matrix blocks of various size and shapes

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Langer, Vera Waltraud. "Investigation of trichloroethene (TCE) transport in fractured porous media with emphasis on sorption onto stylolites and matrix diffusion". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0011/NQ41616.pdf.

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Zhang, Keni. "The modal reduction method for simulation of groundwater flow and multi-species contaminant transport in fractured porous media". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0026/NQ51676.pdf.

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Samardzioska, T. "Boundary element dual reciprocity method with multi domains for modelling fractured porous media : single and two-phase flow and transport". Thesis, Cardiff Metropolitan University, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.521506.

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Süß, Mia [Verfasser]. "Analysis of the influence of structures and boundaries on flow and transport processes in fractured porous media / Institut für Wasserbau der Universität Stuttgart. Vorgelegt von Mia Süß". Stuttgart : Inst. für Wasserbau, 2005. http://d-nb.info/974748897/34.

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Kordilla, Jannes Verfasser], Martin [Akademischer Betreuer] Sauter, Alexandre [Akademischer Betreuer] Tartakovsky i Insa [Akademischer Betreuer] [Neuweiler. "Flow and transport in saturated and unsaturated fractured porous media: Development of particle-based modeling approaches / Jannes Kordilla. Gutachter: Martin Sauter ; Alexandre Tartakovsky ; Insa Neuweiler. Betreuer: Martin Sauter". Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2014. http://d-nb.info/1059570092/34.

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Lekmine, Gregory. "Caractérisation de la dynamique de transports dans les milieux fractures par tomographie de resistivité électrique : développements méthodologiques et expérimentaux". Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112097.

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La tomographie de résistivité électrique (ERT) est une méthode courante géophysique de terrain, souvent utilisée pour détecter et l’évolution suivre les panaches de polluants en zone saturée. L’ERT est cependant une méthode intégratrice dont la fiabilité des modèles est confronte aux problèmes de non unicité des solutions du problème inverse. Ces contraintes limitent l’interprétation des modèles a un aspect qualitatif de la distribution des contrastes de résistivité modélises en 2D ou 3D, résultant du choix des paramètres d’inversion et de l’association de paramètres du milieu non identifiables a l’échelle du volume poreux.Cette thèse propose de tester la faisabilité de la méthode pour quantifier les paramètres de transport de polluants et de solutés miscibles au contact des eaux souterraines, ainsi que la sensibilité des paramètres d’inversion les plus influents sur la modélisation.Les tests expérimentaux sont réalisés en laboratoire sur des empilements 2D de billes de verre sphériques (de l’ordre de la 100èn de μm) dans un réservoir en plexiglas transparent. Deux réseaux verticaux de 21 électrodes sont disposes sur les bords latéraux du réservoir pour effectuer le suivi ERT du traceur sale (NaCl dissout) a partir de 210 points de mesures en dipôle-dipôle transverse acquis toutes les 5 minutes afin d’optimiser la résolution temporelle. Le dispositif est également dispose face a un panneau lumineux permettant de réalise un suivi vidéo simultané du colorant.L’analyse vidéo révèle une propagation plus rapide du colorant sur les bords latéraux qui reste somme toute négligeable pour les débits a la pompe les plus faibles. En revanche les mesures ERT sont fortement perturbées par les effets résistant de la cellule plexiglas qui se répercutent sur les modèles. La normalisation des mesures de résistivité apparente à partir d’une série acquise à l’état initial permet de les atténuer fortement.La modélisation est particulièrement sensible au choix du maillage, aux normes appliques (L1 ou L2) sur les données et les paramètres, et au facteur d’amortissement _. Des valeurs trop élevées de _ et du facteur d’acceptance tendent à lisser les contrastes au niveau du front de dispersion et augmentent l’impact des effets des bords horizontaux sur D et _. A l’inverse, une modélisation contrainte par de faibles valeurs de α et du facteur d’acceptante donne des résultats plus proches l’analyse vidéo, mais produit des effets de bosses à l’avant et à l’arrière du front.La vitesse interstitiel u est indépendante du choix des paramètres d’inversion pour l’ERT. Pour les deux méthodes u est toujours inférieure au débit impose par la pompe, dont le décalage est exprimé par le facteur retard Rf . Les effets de retard résultent de l’adsorption du Na+ sur les surfaces des billes de verre chargées négativement qui retarde le front de dispersion du suivi ERT. Pour le suivi vidéo, la taille importante de la molécule du colorant favorise son piégeage dans les zones ou la perméabilité est plus faible, en plus d’une éventuelle affinité avec la surface solide. Les contrastes de conductivité et la stabilité de l’interface créent par la différence de densité entre les fluides testes ici n’ont pas d’influences significatives sur la dispersion qui est dominée par le débit impose a la pompe. Les estimations du coefficient de dispersion D en fonction du nombre de Péclet sont cohérentes avec la courbe théorique de Bachmat (1968). Cependant la dispersivité α augmente pour les vitesses d’écoulement les plus élevées. Les premières expérimentations de terrain réalises en 2D sur des sables de Fontainebleau présentent l’avantage de s’affranchir des effets de bords inhérents au laboratoire. En revanche la recalibration des données normalisées par la loi de Archie est plus complexe puisqu’il est nécessaire de tenir compte de l’état de saturation de la résistivité des fluides initialement présents. De plus l’erreur importante sur les modèles ne permet pas de déduire une estimation fiable des paramètres de transport u, α (ou D), et Rf
Electrical resistivity tomography is a common geophysical method often used to detect and follow plumepollutants in aquifers. However ERT is an integrative method whose reliability of the models is faced tothe non-unicity of the inverse problem solutions. These constraints limit the interpretation to a qualitativeview of the resistivity contrasts modelled in 2D or 3D, resulting of the chosen inverse parameters and thecombination of several hydrodynamic paramaters related to the poral network.The purpose of this thesis was to test the abilities of the ERT imaging to quantify solute transport parametersin miscible displacement occurred in groundwater and the sensitivity of inverse parameters most aﬀectingthe modelled dispersion front.Laboratory experiments are conducted on glass beads poured into a transparent plexiglas container. Twovertical lines of 21 stainless steel electrodes are ﬁxed on the lateral sides of the container to perform the ERTmonitoring, of the NaCl dissolved in the tracer, from a sequence of 210 quadripole measurements acquiredin transverse dipole-dipole each 5 minutes. A light panel is placed behind the experimental device and avideo follow up of the dyed part of the tracer is acquired from the other side.Video analysis reveal a faster propagation of the dye in contact of the vertical edge, which is negligible forthe lowest ﬂow rates imposed by the pump. In contrast, ERT mesurements are strongly disturbed by theresistant edges of the plexiglas container which aﬀect the resulting models. Normalisation of the apparentresisitivity measurements acquired at the experimental stage and by the Archie’s law strongly tones downthese resistive artefacts.ERT modelling is here particularly sensitive to the grid mesh, the norm (L1 or L2 ) applied on data andparameters, and the damping factor λ. High values of λ and the cutoﬀ factor tend to smooth the resistivityconstrasts in the area of the mixing front and increase the weight of the horizontal edge eﬀects on D andα. While results from inverse modelling constraint by low λ and cutoﬀ factors are much closer to the videoanalysis but with enhanced side slope eﬀects at the rear and the front of the mixing area.The interstitial velocity u is independant of the chosen inverse parameters. For both methods u is alwaysinferior to the ﬂow rate provided by the pump, whose the gap is expressed as a retardation factor Rf . Thisretardation is due to adsorption of Na+ on the beads surfaces, which contributes to delay the dispersionfront followed by ERT. The retardation expressed by the video analysis can be due to the important sizeof the molecule of the dye which is easily slowed down in lower permeability areas, added to an eventualaﬃnity to the solid surface.The ranges of ﬂuid conductivity contrasts and stability of the interfaces tested here have no inﬂuences onthe dispersion which is dominated by the ﬂow velocity u. Estimations of the dispersion coeﬃcient D asfunction of the Péclet is consistent with the theoretical curve of Bachmat (1968) and Bĳeljic & al (2004).Field experiments are ﬁrst conducted in 2D on homogeneous unsaturated sand which is considered as aninﬁnite half-space. However, data normalisation is much more complicated since the saturation state andthe initial ﬂuid conductivities need to be estimated to calibrate the Archie’s law. Because of the 3D tracerinﬂitration, the RMS error of 2D-ERT models highlights that the inversion process is not enough constraintby data which does not allow to quantify the transport parameters. 3D experiments were then adaptedto detect and follow plumes of saline tracers injected in the centre of the electrode device. From 3D ERTmeasurements we are able to produce reliable models in order to estimate such transport parameters as themean ﬂow velocity, and transverse and longitudinal dispersivities

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Dashti, Hameeda. "Miscible displacement in fractured porous media". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/mq64994.pdf.

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PAITAN, CESAR AUGUSTO TORRES. "NUMERICAL MODELLING OF FLOW IN FRACTURED AND FRACTURED POROUS MEDIA". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=23503@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Este trabalho apresenta o desenvolvimento/montagem de um sistema computacional para análise de fluxo em meios porosos, meios fraturados, porosos fraturados e em combinações destes meios, considerando regime permanente ou transiente, sob condições saturadas e não saturadas. O sistema consiste de quatro programas, três programas de funções específicas interligadas por rotinas de programação feitas na linguagem Cmaismais e o quarto é um visualizador de resultados. O FracGen 3D (Telles, 2006) gera fraturas ou famílias de fraturas de forma determinística ou probabilística. O programa ICEM CFD v.14 divide o domínio de interesse em sub-dominios, através da geração de malha de elementos finitos. O programa FTPF-3D (Telles, 2006) utiliza o método de elementos finitos para discretizar as equações governantes no espaço e em diferenças finitas no tempo, e para resolver a não linearidade, utiliza o método iterativo de Picard ou o método iterativo BFGS e finalmente O Pos3D é o responsável pela visualização dos resultados. Neste trabalho foram desenvolvidos cinco exemplos, dois deles para a validação deste procedimento, e três aplicados a um talude típico do Rio de Janeiro, os quais incluem fraturas verticais e juntas de alívio. Estes casos estudados verificam a influência das fraturas nos meios porosos em termos de carga de pressão, totais e campo de velocidades, para a verificação do comportamento hidráulico dos maciços e de eventuais instabilidades.
This work presents the development/assembly of a computational system for flow analysis in porous media, fractured and fractured porous media and in combination of both media, considering steady or transient states under saturated and unsaturated conditions. The system comprehends four computational programs, three of them of specific functions interconnected by Cplusplus programing routines and the last program is an output viewer. FracGen 3D program (Telles, 2006) generates fractures or fracture families in a determinist or probabilistic way. ICEM CFD v.14 program divides the interest domain in sub-domains by means of the element finite mesh generation. FTPF-3D program (Telles, 2006) uses the element finite method to discretize the governing equations in the space domain and the difference finite method for the time domain and for solving the nonlinearity is used the iterative Picard or BFGS method, so that, finally, Pos3D viewer program is answerable by visualization of the results. In the present dissertation five examples were developed, two of them for the validation of this procedure and the three others applied to a typical slope in Rio de Janeiro, which include vertical fractures and relief joints on their slopes. All those studied cases evaluate the influence of the fractures on porous media in terms of pressure and total heads and velocity fields for verifying of the hydraulic behavior of solid masses and eventual instabilities.

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Daher, Ibrahim. "Salt transport experiments in fractured media". Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/45285.

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During the sequestration of CO2 into down-hole rock formations, salt precipitation may occur due to the drying of the formation brine if the injected CO2 is dry. This can negatively affect the performance of injection wells and can even lead to well clogging, which is a serious risk for such operations. Further, the salt deposition can alter the flow of the CO2 in the formation altering the storage capacity. Therefore, it is very important to explore the effect on CCS (Carbon Capture and Storage) process of drying out and salt precipitation during CO2 injection. This study is focused on CCS in fractured aquifers, which has received less attention than their un-fractured counterparts and particularly, the flow impairment associated with salt precipitation during the injection of dry CO2. When CO2 is injected into a conductive fracture network, the brine will rapidly be displaced from the fractures near the point of injection and the subsequent mass transfer between the matrix and the fracture; orthogonal to the flow direction in the fracture, is the major target of the project. The dry-out that occurs due to the evaporation of water from the brine filled region of the matrix into the under-saturated CO2 filling the fracture can cause deposition of salt in the matrix or the fracture, locally reducing permeability. This thesis reports on an investigation of the evaporative drying kinetics and salt precipitation using a combination of gravimetric and X-ray µ-CT techniques to measure the water and brine saturation, salt precipitation and distribution of salt deposition in two rocks; a sandstone, Bentheimer and a carbonate, Ketton. Based on the experimental results for de-ionised water, two main regimes occur during the dry-out process: a capillarity driven regime which seems to be dominant for most of the dry-out process in the experiments, during which evaporation happens only at the surface of the fracture, followed by a diffusion limited regime after the liquid bridge to the surface breaks and pores near the surface become dry for the first time. In pure water, this results in an almost constant evaporation flux in the first regime followed by a mass loss that is linear when plotted against the square root of time. The experiments with brine were initially similar with an evaporative flux almost constant with time. However, a short time into the process the evaporative flux started to decrease approximately linearly with the square root of time, following the deposition of salt at the surface of the fracture. At the end of gravimetric dry-out tests, µ-CT images were obtained showing that salt was mainly precipitated at the surface of the sample; however, relatively small amount of salt was observed precipitated in the interior of the sample. The pore structure of the precipitated salt at the end of the dry-out tests maintained connectivity between the surface of the deposit and the rock matrix. Dynamic µ-CT imaging of Bentheimer during brine drying showed that during the early stage of evaporation, salt was continuously deposited at the surface of the matrix. During this stage in the evaporation of brine, advection dominates the transport of dissolved salt, indicated by a large Peclet number, and this resulted in an increased salt concentration very local to the site of evaporation. The ongoing formation of an efflorescence therefore, is evidence for the continuity of the liquid connections to the outside of the sample, despite the evaporation becoming linear against the square root of time. Unfortunately, the liquid bridges to the surface were too small to be seen directly in the µ-CT imaging. The volume of precipitated salt increased with time and this resulted in a change in the pore structure at the surface of the sample structure, consequently reducing the brine-drying rate. However, as the salt deposition and therefore the location of the evaporation continued to be at the exposed surface, vapour diffusion cannot account for the mass lost by evaporation becoming linear in the square root time as is usually stated. Some other mechanism must account for the observed behaviour and we speculate that the surface area for evaporation was reduced by the appearance of dry patched on the surface. At a very late stage of evaporation, it was observed that no further salt precipitated at the surface of the sample; and subsequently, salt precipitation progressed with time towards the interior of the sample core with small amount of salt. At this stage the liquid connection to the surface must finally have broken and a true diffusion controlled process occurred. In the limited sample size used in this study, this mechanism accounted for only a small fraction of the total salt deposited. From permeability measurements before and after the complete drying of the samples, it was demonstrated that the permeability of Bentheimer was reduced by 81 % from 2.2 D to 0.41 D by the salt deposition. However, Lattice Boltzmann simulations of single phase permeability in the segmented µ-CT images, showed a reduction by 54% from 2.27 D to 1.28 D at 6 µm scanned voxel resolution and 54% from 2.7D to 1.48D at 15um scanned voxel resolution. From these results, it can be concluded that salt precipitation during the injection of CO2 into a fractured porous medial result in a significant reduction in formation permeability, but connectivity between the matrix and the fracture is maintained.

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Mettier, Ralph. "Mass transport in fractured media transition to anomalous transport /". [S.l. : s.n.], 2007.

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Reichenberger, Volker. "Numerical simulation of multiphase flow in fractured porous media". [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970266049.

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Hyun, Yunjung. "Multiscale anaylses of permeability in porous and fractured media". Diss., The University of Arizona, 2002. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu_e9791_2002_321_sip1_w.pdf&type=application/pdf.

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Dyrdahl, Joachim. "Thermal flow in fractured porous media and operator splitting". Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-25927.

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Thermal flow in fractured porous medium is an area of interest for both the oil and the geothermal energy industry. The mathematical model consists of multiple equations, often various conservation laws and constitutive relations. Solving these equations simultaneously is called the fully implicit approach, an alternative is sequential splitting. We investigate and compare these approaches, applied on incompressible and compressible cases of single-phase and two-phase fluid flow. The experiments show that the difference of the solutions between our approaches is small, and that the results from the sequentially split solver are obtained significantly faster than the fully implicit solver scheme.

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Jing, Wen 1966. "Virus transport through porous media". Thesis, The University of Arizona, 1992. http://hdl.handle.net/10150/291550.

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Investigated in laboratory column experiments were the effects of 0.01 M and 0.001 M CaPO₄ concentrations and pH on the attachment-detachment of bacteriophages PRD-1 and MS-2. Bacteriophages PRD-1 and MS-2 exhibited attachment to the soil at concentrations of 0.01M CaPO₄ and 0.5M NaCl. Release of attached phage at 0.001 M CaPO₄ and without NaCl was observed. The pH was also found to affect the attachment-detachment of PRD-1 and MS-2. However, they attached at pH 5.5 and detached at pH 8.0 at a limited extent and over an extented long period of time. The effect of salt concentration on deattachment was greater than the effect of pH. Similar results were obtained when glass beads were used as the adsorbent. These results suggest that changes in pH and ionic strength (as might occur after a rainfall) can result in the rapid release of previously adsorbed virus. (Abstract shortened by UMI.)

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Kilchherr, Rudolf. "Transport phenomena in porous media". Thesis, Kingston University, 2003. http://eprints.kingston.ac.uk/20729/.

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Non-Newtonian flow in heterogeneous media is of enormous theoretical and industrial importance. This phenomenon is studied to reveal macroscopic effects that arise due to the interaction between the non-linear flow behaviour and the spatial variation of the medium through which it is forced to move. The heterogeneity is achieved by using porous granular media, which is naturally non-homogeneous. The non-Newtonian properties of the fluid may have many causes and is an intrinsic property of the fluid that is used: One way of achieving it is by studying dense slurries of neutral particles or naturally occurring magmatic flows. Another way is to study the case where the flow is dominated by its ionic content and where the double layer thickness (the effective size of the ionic entities) is of the order of magnitude of the pore size. All cases studied in this thesis pertain to slow flow (low Reynolds number), though the fluid may be compressible. The variations in the flow are calculated in first order and these turn out to be coupled to the spatial variations in the porous medium. In this way structure formation is predicted. The structures may be either aligned with or may be perpendicular to the mean flow direction. 'Experiments to decide on which regime is relevant have been conducted. The genesis of structure formation is studied as a temporal development by considering a compressible flow. The constitutive equation that is required to couple the compressibility to the flow parameters is investigated. Two possible mechanisms have been identified: compressibility coupled to the pressure field and compressibility associated with the fluctuations in the flow. Using linear analysis the structure formation patterns associated with these two mechanisms are established for the steady state. Flow of ionically laden fluids has also been studied. Experiments done at Loughborough University (Department of Chemical Engineering) on electrowashing of filter cakes has been used to prove a major macroscopic effect. This effect takes place when the ionic diameter (which is approximately twice the double layer thickness) is of the order of magnitude of the pore size. A phenomenological set of transport equations has been set up. These contain coefficients, such as transition probabilities and mean ionic flow rates, that can be obtained from experiments by doing a first order solution of the equations for short times. A more involved numerical solution is also supplied and confirms the initial analytical estimates.

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Rhodes, Matthew Edward. "Transport in heterogeneous porous media". Thesis, Imperial College London, 2008. http://hdl.handle.net/10044/1/1296.

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We present a new algorithm for modelling single phase transport of a tracer in porous media which demonstrates that structure on all scales affects macroscopic transport behaviour. We marry the robustness of the continuous time random walk (CTRW) framework with the simplicity of a Monte Carlo approach to reservoir simulation. We simulate transport as a series of particles transitioning between nodes with probability (t).dt that a particle will first arrive at a nearest neighbor in a time t to t + dt. To this end we first determine the mixing rules and transition probability ADE(t) for transport governed by the advection-dispersion equation (ADE) (Rhodes and Blunt, 2006). We validate our algorithm by simulating advective transport in bond percolation clusters at the critical point. We compute the histogram of flow speeds using the velocities from the bonds on the backbone and find the multifractal spectrum for two-dimensional lattices with linear dimension L _ 2000 and in three dimensions for L _ 250. We demonstrate that in the limit of large systems all the negative moments of the velocity distribution become ill-defined. However, to model transport, the velocity histogram should be weighted by the flux to obtain a well-defined mean travel time. Finally, we use CTRWtheory to demonstrate that anomalous transport is observed whose characteristics can be related to the multifractal properties of the system. We next demonstrate a pore-to-reservoir simulation methodology which is consistent across all scales of interest. At the micron scale, we fit a truncated power law (t) for the distribution of particle transition times from pore to pore simulations. To do this we use our transport algorithm on a geologically representative network model of Berea sandstone and compare the results to the explicit modelling of advection and molecular diffusion by Bijeljic and Blunt (2006). We find that the results are similar. We then demonstrate the effect of increasing pore scale heterogeneity on the power law exponent (_) by stretching the distribution of throat radii in our network model. We show that by increasing the spread of velocities within the network we decrease _ making the transport more anomalous - in keeping with the consensus currently in the literature. This (t) is then used to calculate transport on the mm to cm scale. We can then move up to the metre/grid block scale by using the transit time distribution from the mm-cm simulation to model transport in an explicit, geologically representative model of heterogeneity found within a grid block of the reservoir. From these numerical experiments we determine the (t) appropriate for transport on grid block scale systems characterized by Peclet (Pe) number and the type of heterogeneity within the system. This allows us to account for small scale uncertainty by interpreting (t) probabilistically and running simulations for different possible realizations of the reservoir heterogeneity. At the field scale, we represent the reservoir as an unstructured network of nodes connected by links. For each node-to-node transition, we use our upscaled (t) from a simulation of transport at the smaller scale. We account for small-scale uncertainty by parameterising (t) in terms of sub-scale heterogeneity and Peclet number. We demonstrate the methodology by finding a (t) for each scale of interest taking into consideration the relevant physics at that scale and using the appropriate function in a million-cell reservoir model. We show that the macroscopic behaviour can be very different from that predicted by assuming that the ADE operates at the small scale. Small-scale structure dramatically retards the advance of the plume with the particles becoming trapped in the slow moving pores/regions increasing breakthrough times by an order of magnitude compared to those predicted by the ADE.

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Ruthven, Douglas M. "Diffusion through porous media". Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-188922.

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This paper considers permeation through microporous or nanoporous inorganic membranes under the influence of an applied pressure gradient. In general membrane permeation may be considered as a diffusive process, driven by the gradient of chemical potential (which depends on both composition and pressure). The relative importance of these two factors varies greatly for different types of system. The general features of such processes are reviewed and the diffusional behavior of selected systems is examined. (membrane permeation, osmosis, diffusion, zeolite membrane, DDR-3, SAPO-34)

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Ekanem, Aniekan Martin. "Analysis of P-wave attenuation anisotropy in fractured porous media". Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/7621.

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Fractures exert a strong influence on fluid flow in subsurface reservoirs, and hence an adequate understanding of fracture properties could provide useful information on how they may be managed optimally to produce oil and gas or to be used as repositories for carbon dioxide (CO2) to mitigate climate change. Since fractures are commonly aligned by the stress field, seismic anisotropy is a key tool in investigating their properties. Velocity anisotropy is now a well-established technique for determining properties such as fracture orientation and density, but in recent years, attention has focused on quantifying azimuthal variations in Pwave attenuation to provide additional information, especially on the fracture size. However, the practical application of this attribute in geophysical exploration is still limited due to the uncertainty associated with its measurement and the difficulty in its interpretation in terms of rock properties. There is still a lack of proper understanding of the physical processes involved in the mechanisms of attenuation anisotropy. In this thesis, I use the seismic modelling approach to study the effects of attenuation anisotropy in fractured porous media using P-waves with the main aim of improving the understanding of these effects and exploring the physical basis of using attenuation anisotropy as a potential tool for the characterization of fractured reservoirs. Fractures with length on the order of the seismic wavelength in reservoir rocks cause scattering of seismic waves which exhibits characteristic azimuthal variations. I study these scattering effects using complementary seismic physical (scale-model laboratory experiments) and numerical (finite difference) modelling approaches. The results of both approaches are consistent in delineating fracture properties from seismic data. The scattered energy is quantified through estimates of the attenuation factor (the inverse of the seismic quality factor Q) and shown to be anisotropic, with elliptical (cos2θ) variations with respect to the survey azimuth angle θ. The minor axis of the Q ellipse corresponds to the fracture normal. In this direction, i.e. across the material grain, the attenuation is a maximum. The major axis corresponds to the fracture strike direction (parallel to the material grain) where minimum attenuation occurs. Empirically, the magnitude of P-wave attenuation anisotropy is greater in fluid-saturated rocks than in dry rocks. I study the influence of fluid saturation on P-wave attenuation through synthetic modelling and compare the attenuation signature to that of dry fractured rocks. The results of the analysis show that the relaxation time strongly controls the frequency range over which attenuation occurs. The magnitude of the induced attenuation increases with polar angle and also away from the fracture strike direction. The attenuation exhibits elliptical variations with azimuth which are also well fitted with a cos2θ function. The magnitude of the attenuation anisotropy is higher in the case of the fluid-saturated rocks. All of these properties of the numerical model are in agreement with the results of empirical experiments in the laboratory. The same crack density can result from many small cracks, from a few large cracks, or from an equal number of cracks of various sizes with varying thicknesses in the same volume of background material. This makes it difficult to distinguish between the anisotropy caused by micro-cracks and that caused by macro-cracks. I study the effects of fracture thickness or aperture on P-wave scattering attenuation through seismic physical modelling, and find that the induced attenuation has a direct relationship with the fracture thickness or aperture. This result indicates the potential of using P-wave attenuation to get information which might be useful in examining the effects of voids in the rocks, and also provides a basis for further future theoretical development to distinguish the effects caused by thin micro cracks and large open fractures. Finally, I study the effects of two types of fluid saturation (brine and CO2 in the supercritical state) on P-wave attenuation through synthetic modelling, with particular attention to varying CO2 saturation using the CO2 properties at the Sleipner gas Field in the North Sea. The presence of CO2 causes more attenuation in the numerical model output than when the rock is saturated with only brine. The induced attenuation increases with decreasing percentage of CO2 saturation and has a maximum magnitude at 10 % CO2 saturation. Further work is needed to quantify the additional effect of fractures on these results.

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Galvin, Robert John. "Elastic wave attenuation, dispersion and anisotropy in fractured porous media /". Full text available, 2007. http://adt.curtin.edu.au/theses/available/adt-WCU20071218.143340.

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Galvin, Robert. "Elastic wave attenuation, dispersion and anisotropy in fractured porous media". Thesis, Curtin University, 2007. http://hdl.handle.net/20.500.11937/1735.

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Development of a hydrocarbon reservoir requires information about the type of fluid that saturates the pore space, and the permeability distribution that determines how the fluid can be extracted. The presence of fractures in a reservoir can be useful for obtaining this information. The main objectives of this thesis are to investigate how fracturing can be detected remotely using exploration seismology. Fracturing will effect seismic data in a number of ways. Firstly, if the fractures are aligned preferentially in some direction, the medium will exhibit long wavelength anisotropy. In turn, if wave propagation is not aligned with one of the symmetry axes of the effective medium then shear wave splitting will depend upon the properties of the fracture filling fluid. Secondly, elastic waves will experience attenuation and dispersion due to scattering and wave-induced fluid flow between the fractures and matrix porosity. This occurs because the fractures are more compliant than the background medium and therefore there will be a pressure gradient formed during passage of the wave, causing fluid to flow between fractures and background. If the direction of shear-wave propagation is not perpendicular or parallel to the plane of fracturing, the wave polarized in the plane perpendicular to the fractures is a quasi-shear mode, and therefore the shear-wave splitting will be sensitive to the fluid bulk modulus.The magnitude of this sensitivity depends upon the extent to which fluid pressure can equilibrate between pores and fractures during the period of the deformation. In this thesis I use the anisotropic Gassmann equations and existing formulations for the excess compliance due to fracturing to estimate the splitting of vertically propagating shear-waves as a function of the fluid modulus for a porous medium with a single set of dipping fractures and with two conjugate fracture sets dipping with opposite dips to the vertical. This is achieved using two alternative approaches. In the first approach it is assumed that the deformation taking place is quasi-static. That is, the frequency of the elastic disturbance is low enough to allow enough time for fluid to flow between both the fractures and the pore space throughout the medium. In the second approach I assume that the frequency is low enough to allow fluid flow between a fracture set and the surrounding pore space, but high enough so that there is not enough time during the period of the elastic disturbance for fluid flow between different fracture sets to occur. It is found that the second approach yields a much stronger dependency of shear-wave splitting on the fluid modulus than the first one. This is a consequence of the fact that at higher wave frequencies there is not enough time for fluid pressure to equilibrate and therefore the elastic properties of the fluid have a greater effect on the magnitude of the shear-wave splitting. I conclude that the dependency of the shear-wave splitting on the fluid bulk modulus will be at its minimum for quasi-static deformations, and will increase with increasing wave frequency.In order to treat the problem of dispersion and attenuation due to wave-induced fluid flow I consider interaction of a normally incident time-harmonic longitudinal plane wave with a circular crack imbedded in a porous medium governed by Biot’s equations of dynamic poroelasticity. The problem is formulated in cylindrical coordinates as a system of dual integral equations for the Hankel transform of the wave field, which is then reduced to a single Fredholm integral equation of the second kind. It is found that the scattering that takes place is predominantly due to wave induced fluid flow between the pores and the crack. The scattering magnitude depends on the size of the crack relative to the slow wave wavelength and has its maximum value when they are of the same order. I conclude that this poroelastic effect should not be neglected, at least at seismic frequencies. Using the solution of the scattering problem for a single crack and multiple-scattering theory I estimate the attenuation and dispersion of elastic waves taking place in a porous medium containing a sparse distribution of such cracks. I obtain from this analysis an effective velocity which at low frequencies reduces to the known static Gassmann result and a characteristic attenuation peak at the frequency such that the crack size and the slow wave wavelength are of the same order.When comparing with a similar model in which multiple scattering effects are neglected I and that there is agreement at high frequencies and discrepancies at low frequencies. I conclude that the interaction between cracks should not be neglected at low frequencies, even in the limit of weak crack density. Since the models only agree with each other at high frequencies, when the time available for fluid diffusion is small, I conclude that the interaction between cracks that takes place as a result of fluid diffusion is negligible at high frequencies. I also compare my results with a model for spherical inclusions and find that the attenuation for spherical inclusions has exactly the same dependence upon frequency, but a difference in magnitude that depends upon frequency. Since the attenuation curves are very close at low frequencies I conclude that the effective medium properties are not sensitive to the shape of an inclusion at wavelengths that are large compared to the inclusion size. However at frequencies such that the wavelength is comparable to or smaller than the inclusion size the effective properties are sensitive to the greater compliance of the flat cracks, and more attenuation occurs at a given frequency as a result.

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32

Galvin, Robert. "Elastic wave attenuation, dispersion and anisotropy in fractured porous media". Curtin University of Technology, Department of Exploration Geophysics, 2007. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=17486.

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Development of a hydrocarbon reservoir requires information about the type of fluid that saturates the pore space, and the permeability distribution that determines how the fluid can be extracted. The presence of fractures in a reservoir can be useful for obtaining this information. The main objectives of this thesis are to investigate how fracturing can be detected remotely using exploration seismology. Fracturing will effect seismic data in a number of ways. Firstly, if the fractures are aligned preferentially in some direction, the medium will exhibit long wavelength anisotropy. In turn, if wave propagation is not aligned with one of the symmetry axes of the effective medium then shear wave splitting will depend upon the properties of the fracture filling fluid. Secondly, elastic waves will experience attenuation and dispersion due to scattering and wave-induced fluid flow between the fractures and matrix porosity. This occurs because the fractures are more compliant than the background medium and therefore there will be a pressure gradient formed during passage of the wave, causing fluid to flow between fractures and background. If the direction of shear-wave propagation is not perpendicular or parallel to the plane of fracturing, the wave polarized in the plane perpendicular to the fractures is a quasi-shear mode, and therefore the shear-wave splitting will be sensitive to the fluid bulk modulus.
The magnitude of this sensitivity depends upon the extent to which fluid pressure can equilibrate between pores and fractures during the period of the deformation. In this thesis I use the anisotropic Gassmann equations and existing formulations for the excess compliance due to fracturing to estimate the splitting of vertically propagating shear-waves as a function of the fluid modulus for a porous medium with a single set of dipping fractures and with two conjugate fracture sets dipping with opposite dips to the vertical. This is achieved using two alternative approaches. In the first approach it is assumed that the deformation taking place is quasi-static. That is, the frequency of the elastic disturbance is low enough to allow enough time for fluid to flow between both the fractures and the pore space throughout the medium. In the second approach I assume that the frequency is low enough to allow fluid flow between a fracture set and the surrounding pore space, but high enough so that there is not enough time during the period of the elastic disturbance for fluid flow between different fracture sets to occur. It is found that the second approach yields a much stronger dependency of shear-wave splitting on the fluid modulus than the first one. This is a consequence of the fact that at higher wave frequencies there is not enough time for fluid pressure to equilibrate and therefore the elastic properties of the fluid have a greater effect on the magnitude of the shear-wave splitting. I conclude that the dependency of the shear-wave splitting on the fluid bulk modulus will be at its minimum for quasi-static deformations, and will increase with increasing wave frequency.
In order to treat the problem of dispersion and attenuation due to wave-induced fluid flow I consider interaction of a normally incident time-harmonic longitudinal plane wave with a circular crack imbedded in a porous medium governed by Biot’s equations of dynamic poroelasticity. The problem is formulated in cylindrical coordinates as a system of dual integral equations for the Hankel transform of the wave field, which is then reduced to a single Fredholm integral equation of the second kind. It is found that the scattering that takes place is predominantly due to wave induced fluid flow between the pores and the crack. The scattering magnitude depends on the size of the crack relative to the slow wave wavelength and has its maximum value when they are of the same order. I conclude that this poroelastic effect should not be neglected, at least at seismic frequencies. Using the solution of the scattering problem for a single crack and multiple-scattering theory I estimate the attenuation and dispersion of elastic waves taking place in a porous medium containing a sparse distribution of such cracks. I obtain from this analysis an effective velocity which at low frequencies reduces to the known static Gassmann result and a characteristic attenuation peak at the frequency such that the crack size and the slow wave wavelength are of the same order.
When comparing with a similar model in which multiple scattering effects are neglected I and that there is agreement at high frequencies and discrepancies at low frequencies. I conclude that the interaction between cracks should not be neglected at low frequencies, even in the limit of weak crack density. Since the models only agree with each other at high frequencies, when the time available for fluid diffusion is small, I conclude that the interaction between cracks that takes place as a result of fluid diffusion is negligible at high frequencies. I also compare my results with a model for spherical inclusions and find that the attenuation for spherical inclusions has exactly the same dependence upon frequency, but a difference in magnitude that depends upon frequency. Since the attenuation curves are very close at low frequencies I conclude that the effective medium properties are not sensitive to the shape of an inclusion at wavelengths that are large compared to the inclusion size. However at frequencies such that the wavelength is comparable to or smaller than the inclusion size the effective properties are sensitive to the greater compliance of the flat cracks, and more attenuation occurs at a given frequency as a result.

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33

Awan, Faisal Ur Rahman. "Electrokinetic investigation of coal fines in fractured and porous media". Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2022. https://ro.ecu.edu.au/theses/2523.

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Coal seams are unconventional subsurface formations that host methane and are weaker (relative to conventional subsurface) formations. Coal seams are prone to coal fines generation within the fractured porous space throughout the life of the reservoir. These coal fines damage the permeability, deliverability and productivity of coal seams. Furthermore, the coal fines mobility/blockage in the hydraulically induced fractures and proppant packs negatively impacts the proppant conductivity. In this work, a comprehensive study has been conducted to augment the understanding of coal fines and their behaviour within porous and proppant pack systems. Systematic experiments were conducted to address the coal fines by developing various approaches presented in this work. The approaches adopted to achieve the study objectives were: i) streaming zeta potential on coal and sandstone, ii) nano-treated proppant surface modification for coal fines adsorption, and iii) coal fines mobility/attachment in the proppant packs. One of the electrokinetic parameters that is crucial in releasing/mobilising coal fines is coal’s zeta potential. The coal surface is generally hydrophobic and possesses negative zeta potential. Researchers have used the electrophoretic zeta potential technique to indicate charge identification of coal particles, denoting repulsion or attraction of the particle. In chapter 3, a robust study investigates streaming zeta potential measurements of an in-situ sub-bituminous coal core saturated with saline water of 0.1, 0.3 and 0.6 mol.dm-3 NaCl salinities. Thus, the novel study determines the charge carried by percolating fluid when passing through coal rock. The zeta potential is directly proportional to saline water salinity. The trends found in the research were consistent with reported zeta potential measured using other techniques, while the magnitude varied. The findings reported in the study apply to subsurface coal seams at salinity up to 0.6 mol.dm-3 NaCl. Coal seams are hydraulically fractured for commercial production, and sand-based proppants occupy the fractured space. Before understanding the electrokinetics of coal fines, the behaviour of these sand-based proppants should be determined. Sand-based proppants are predominantly silica, and so are sandstones. Furthermore, the selection of sandstone was further motivated by two reasons, i) for comparison and benchmarking, and ii) correlation with coals (as sandstone and coal both are negatively charged). The research presented in chapter 4 considered clay-rich (i.e. clay ≥ 5 wt.%) sandstones for the first time (as coal can have clay ingredients). Specifically, streaming potential measurements were conducted on Bandera Grey sandstone (clay-rich and -poor) saturated with saline water in pressurised environments. Additionally, the streaming potential was determined at identical conditions for the effect of two surfactants, sodium dodecylbenzene sulfonate (SDBS) and cetrimonium bromide (CTAB), at concentrations of 0.01 and 0.1 wt. % on the clay-poor sample. Moreover, a comparison of electrophoretic and streaming zeta potentials was conducted. Accordingly, the work analyses the effects of mineralogy and surfactants within this process. Clay-rich sandstone possessed lower zeta-potentials than clay-poor sandstone at the two tested salinities. SDBS reduced zeta-potential and yielded higher repulsive forces rendering the rock more hydrophilic. Additionally, electrophoretic zeta-potentials were higher when compared to streaming zeta-potentials. Mechanisms for the observed phenomena are also provided. Following the observations from the two studies, proppant column experiments with glass bead proppant and high volatile bituminous were conducted and are presented in chapter 5. One of the approaches to handling coal fines is its dispersal within the aqueous suspension. Proppant column experiments were conducted to test various schemes. It was found that coal zeta potential using SDBS reaches a maximum, and regardless of the pH, it effectively delivers the maximum output of coal fines in the effluent. Thus, a 0.001 wt.% SDBS could effectively disperse coal fines suspension through proppant packs. Nano-treated proppant surface modification was developed to investigate coal fines mobility/attachment within the proppant packs. Succinctly, four (alumina, magnesia, silica and zirconia) nanoparticles (NPs) were adsorbed onto synthetic porous media (glass bead) using a robust pseudo-continuous fixed-bed (PCFB) adsorption method in work presented in chapter 6. A wide range of salinity (0 to 10.5 wt.% NaCl), temperature (298.15 to 348.15 K), NPs loading (0.01 to 0.2 wt.%), and injection rate (1 to 50 mL.min-1) were tested. Results showed that PCFB adsorption of NPs with higher specific surface area resulted in faster adsorption (adsorbed in ~25 mins) with > 99% immobilisation of NPs on the proppant pack. Adsorption kinetics showed reasonable conformity with the pseudo-first-order model, where isothermal adsorption followed the Sips model. The adsorption capacity of magnesia NPs (specific surface area 50 to 80 m2.g-1, 7 wt.% NaCl) at 298.15 K was higher than silica NPs. Accordingly, the newly developed PCFB method can be used for onsite treatment of proppants with nanoparticles, which can then be injected into a fractured formation to achieve multiple objectives such as fines fixation, wettability alteration and sand control. In this work, another study explored the application of nano-treated proppant packs on the adsorption of coal fines, presented in chapter 7. In this study, the objective was to identify silica nano-formulations (0 – 0.1 wt.%), and coal fines concentration of 0.1 to 1 wt.% were examined to determine the fixation of coal fines within the glass bead synthetic proppant pack. The quantitative results showed that the proppant pack with nanoparticle treatment strongly affects the fixation ability of coal fines. The non-NP treated pack yielded 30% adsorption, whilst the NP treated pack yielded 74% adsorption. It was noted that greater adsorption is also related to the higher zeta potential of silica NPs (i.e. nearer to iso-electric point). A set of laboratory experiments on industrial-grade proppants was conducted as the definitive work, presented in chapter 8. The work involved sensitivity experiments as a function of coal rank, pH, salinity, and surfactants. These conductivity results were compared with established analytical models to interpret the mechanistic coal-proppant interaction in the presence of an electrolyte. It was found that fines dispersion and its mobility within the proppant pack is easier at high pH, low salinity, temperature, anionic surfactants, and lower concentration of coal fines. However, fines mobility is reduced at neutral pH, high salinity, temperature, and cationic surfactants.

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34

Ippisch, Olaf. "Coupled transport in natural porous media". [S.l. : s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=96376022X.

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Ippisch, Olaf. "Coupled transport in natural porous media". [S.l. : s.n.], 2003. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10605053.

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36

Maghami, Nick Hamidreza. "Towards large-scale modelling of fluid flow in fractured porous media". Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/6118.

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To date, the complexity of fractured porous media still precludes the direct incorporation of small-scale features into field-scale modelling. These features, however, can be instrumental in shaping and triggering coarsening instabilities and other forms of emergent behaviour which need to be considered on the field-scale. Here we develop numerical simulation methods for this purpose and demonstrate their improved performance in single-and two-phase flow simulations with models of fractured porous media. Material discontinuities in fractured porous media strongly influence single-and multi-phase fluid flow. When continuum methods are used to model transport across such interfaces, they smear out jump discontinuities of concentration or saturation. To overcome this drawback, we “explode” hybrid finite-element node-centred finite-volume models along these introducing complementary finite-volumes along the material interfaces. With this embedded discontinuity discretization we develop a transport scheme that realistically represents the dependent variable discontinuities arising at these interfaces. The main advantage of this new scheme is its ability to honour the flow effects that we know that these discontinuities have in physical experiments. We have also developed a new time-stepping control scheme for the transport equation. It allows the user to specify the volume fraction of the model in which he/she is prepared to relax the CFL condition. This scheme is applied in a study of the impact of fracture pattern development on solute transport. These two-dimensional simulations quantify the effect of the fractures on macro-scale dispersion in geomechanically generated fracture geometries, as opposed to stochastically generated ones. Among other insights, the results indicate that fracture density, fracture spacing, and the fracture-matrix flux ratio control anomalous mass transport in such media. We also find that it is crucial to embed discontinuities into large-scale models of heterogeneous porous media.

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37

Watanabe, Norihiro. "Finite element method for coupled thermo-hydro-mechanical processes in discretely fractured and non-fractured porous media". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-104411.

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Numerical analysis of multi-field problems in porous and fractured media is an important subject for various geotechnical engineering tasks such as the management of geo-resources (e.g. engineering of geothermal, oil and gas reservoirs) as well as waste management. For practical usage, e.g. for geothermal, simulation tools are required which take into account both coupled thermo-hydro-mechanical (THM) processes and the uncertainty of geological data, i.e. the model parametrization. For modeling fractured rocks, equivalent porous medium or multiple continuum model approaches are often only the way currently due to difficulty to handle geomechanical discontinuities. However, they are not applicable for prediction of flow and transport in subsurface systems where a few fractures dominates the system behavior. Thus modeling coupled problems in discretely fractured porous media is desirable for more precise analysis. The subject of this work is developing a framework of the finite element method (FEM) for modeling coupled THM problems in discretely fractured and non-fractured porous media including thermal water flow, advective-diffusive heat transport, and thermoporoelasticity. Pre-existing fractures are considered. Systems of discretely fractured porous media can be considered as a problem of interacted multiple domains, i.e. porous medium domain and discrete fracture domain, for hydraulic and transport processes, and a discontinuous problem for mechanical processes. The FEM is required to take into account both kinds of the problems. In addition, this work includes developing a methodology for the data uncertainty using the FEM model and investigating the uncertainty impacts on evaluating coupled THM processes. All the necessary code developments in this work has been carried out with a scientific open source project OpenGeoSys (OGS). In this work, fluid flow and heat transport problems in interactive multiple domains are solved assuming continuity of filed variables (pressure and temperature) over the two domains. The assumption is reasonable if there are no infill materials in fractures. The method has been successfully applied for several numerical examples, e.g. modeling three-dimensional coupled flow and heat transport processes in discretely fractured porous media at the Gross Schoenebck geothermal site (Germany), and three-dimensional coupled THM processes in porous media at the Urach Spa geothermal site (Germany). To solve the mechanically discontinuous problems, lower-dimensional interface elements (LIEs) with local enrichments have been developed for coupled problems in a domain including pre-existing fractures. The method permits the possibility of using existing flow simulators and having an identical mesh for both processes. It enables us to formulate the coupled problems in monolithic scheme for robust computation. Moreover, it gives an advantage in practice that one can use existing standard FEM codes for groundwater flow and easily make a coupling computation between mechanical and hydraulic processes. Example of a 2D fluid injection problem into a single fracture demonstrated that the proposed method can produce results in strong agreement with semi-analytical solutions. An uncertainty analysis of THM coupled processes has been studied for a typical geothermal reservoir in crystalline rock based on the Monte-Carlo method. Fracture and matrix are treated conceptually as an equivalent porous medium, and the model is applied to available data from the Urach Spa and Falkenberg sites (Germany). Reservoir parameters are considered as spatially random variables and their realizations are generated using conditional Gaussian simulation. Two reservoir modes (undisturbed and stimulated) are considered to construct a stochastic model for permeability distribution. We found that the most significant factors in the analysis are permeability and heat capacity. The study demonstrates the importance of taking parameter uncertainties into account for geothermal reservoir evaluation in order to assess the viability of numerical modeling.

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38

Amoah, Nelson. "Experimental and numerical study of solute transport through saturated fractured porous aquifer". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq25764.pdf.

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39

Ghafouri, H. R. "Finite element modelling of multi-phase flow through deformable fractured porous media". Thesis, Swansea University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.637047.

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Based on the theory of 'Double-Porosity', three-phase fluid flow in a fractured porous media has been formulated using continuity and equilibrium equations where displacement is also a primary unknown. Unlike previous models used for fractured media, the pressure of each fluid phase within the fracture network and porous rock has been considered to be coupled with the deformation of porous media. Also coupling between the fracture network and the porous rock is carried out using 'Transfer Function' or 'Leakage Term'. The derived equations are then discretised using 'Finite Element Method' where the displacements as well as pressure of fluids within matrix and fracture are primary unknowns. The resulting set of equations, is an implicit, fully coupled formulation which is capable of modelling three phase (Oil, Gas and Water) flow in a fractured reservoir where the deformation and consequent surface subsidence is of particular interest i.e. a case frequently encountered in petroleum engineering. In its extreme case, the presented formulation turns to the conventional one-phase models for heterogeneous porous media and by further simplification, the governing equations for ordinary single porosity models could be obtained. A computer code based on the mathematical model is developed and validated. Important aspects of the developed code, based on the double porosity theory, are presented together with several example problems. The model is also employed to solve a field scale example where the results are compared to those of ten other uncoupled models. As a genuine application of the present model, it is employed to solve the real field problem of the subsidence at the Ekofisk oil field in the Norwegian sector of the North Sea. The impact of various parameters of the model are verified by conducting sensitivity analyses. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered.

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40

Bajaj, Reena. "An unstructured finite volume simulator for multiphase flow through fractured-porous media". Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/54839.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 77-78).
Modeling of multiphase flow in fractured media plays an integral role in management and performance prediction of oil and gas reserves. Geological characterization and nmultiphase flow simulations in fractured media are challenging for several reasons, such as uncertainty in fracture location, complexity in fracture geometry. dynamic nature of fractures etc. There is a need for complex sinmulation models that resolve the flow dynamics along fractures and the interaction with the porous matrix. The unstructured finite volume model provides a tool for the numerical simulation of multiphase flow (inmmiscible and incompressible two-phase flow) in two-dimensional fractured media. We use a finite volume formulation, which is locally imass conservative and it allows the use of fully unstructured grids to represent the coimplex geometry of the fracture networks. Fractures are represented as objects of lower diniensionality than that of the domain (in this case, ID objects in a 2D domain). The model permits fine-scale simulation of multiphase transport through fractured media. The non-Fickian transport resulting due to the presence of heterogeneity (as fractures or inhomogeneous permeability distribution) is captured by the traditional advection-diffusion equation using a highly discretized system. Today. many macroscopic flow models are being developed which account for the non-Fickian. non-local flow more accurately and efficiently with less computation. The finite volume simulator niodel described in this thesis will be instrumental as a tool to train and validate the macroscopic flow models which account for anomialous transport behavior.
(cont.) We illustrate the performance of this simulator on several synthetic cases with different fracture geometries and conclude the model effectively captures the miiultiphase fluid flow pattern in fractured media.
by Reena Bajaj.
S.M.

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41

Robertson, Mark Donald. "A statistical continuum approach for mass transport in fractured media". Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/29740.

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The stochastic-continuum model developed by Schwartz and Smith [1988] is a new approach to the traditional continuum methods for solute transport in fractured media. Instead of trying to determine dispersion coefficients and an effective porosity for the hydraulic system, statistics on particle motion (direction, velocity and fracture length) collected from a discretely modeled sub-domain network are used to recreate particle motion in a full-domain continuum model. The discrete sub-domain must be large enough that representative statistics can be collected, yet small enough to be modeled with available resources. Statistics are collected in the discrete sub-domain model as the solute, represented by discrete particles, is moved through the network of fractures. The domain of interest, which is typically too large to be modeled discretely is represented by a continuum distribution of the hydraulic head. A particle tracking method is used to move the solute through the continuum model, sampling from the distributions for direction, velocity and fracture length. This thesis documents extensions and further testing of the stochastic-continuum two-dimensional model and initial work on a three-dimensional stochastic-continuum model. Testing of the model was done by comparing the mass distribution from the stochastic-continuum model to the mass distribution from the same domain modeled discretely. Analysis of the velocity statistics collected in the two-dimensional model suggested changes in the form of the fitted velocity distribution from a gaussian distribution to a gamma distribution, and the addition of a velocity correlation function. By adding these changes to the statistics collected, an improvement in the match of the spatial mass distribution moments between the stochastic-continuum and discrete models was effected. This extended two-dimensional model is then tested under a wide range of network conditions. The differences in the first spatial moments of the discrete and stochastic-continuum models were less than 10%, while the differences in the second spatial moments ranged from 6% to 30%. Initial results from the three-dimensional stochastic-continuum model showed that similar statistics to those used in the two-dimensional stochastic-continuum model can be used to recreate the nature of three-dimensional discrete particle motion.
Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate

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42

Shao, Haibing. "Modelling reactive transport processes in porous media". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-61738.

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Reactive transport modelling has wide applications in geosciences. In the ﬁeld of hydrogeology, it has been utilised to simulate the biogeochemical processes that disperse and degrade contaminants in the aquifer. For geotechnical applications, such as geological CO2 sequestration, the reaction of CO2 with the ambient saline aquifer determines the ﬁnal success of storage. In a radioactive waste repository, scientists rely on reactive transport models to predict the mobilisation of hazardous radionuclides within space and time. In this work, the multi-component mass transport code OpenGeoSys, was coupled with two geochemical solvers, the Gibbs Energy Minimization Selektor (GEM) and the Biogeochemical Reaction Network Simulator (BRNS). Both coupled codes were veriﬁed against analytical solutions and simulation results from other numerical models. Moreover, the coupling interface was developed for parallel simulation. Test runs showed that the speed-up of reaction part had a very good linearity with number of nodes in the mesh. However, for three dimensional problems with complex geochemical reactions, the model performance was dominated by solving transport equations of mobile chemical components. OpenGeoSys-BRNS was applied to a two dimensional groundwater remediation problem. Its calculated concentration proﬁles ﬁtted very well with analytical solutions and numerical results from TBC. The model revealed that natural attenuation of groundwater contaminants is mainly controlled by the mixing of carbon source and electron donor. OpenGeoSys-GEM was employed to investigate the retardation mechanism of radionuclides in the near ﬁeld of a nuclear waste repository. Radium proﬁles in an idealised bentonite column was modelled with varying clay/water ratios. When clay content is limited, Ba-Sr-Ra sulfate solid solutions have a very strong retardation eﬀect on the aqueous radium. Nevertheless, when clay mineral is abundant, cation exchange sites also attract Sr and Ba, thus dominates the transport of Ra.

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43

Nguyen, Khac Long. "Multiscale analysis of transport in porous media". Thesis, Aix-Marseille, 2019. http://theses.univ-amu.fr.lama.univ-amu.fr/190522_NGUYEN_156sqbpnr595zlxet195ycj854nvqyn_TH.pdf.

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La corrélation entre les propriétés structurales des matériaux et les propriétés de transport d’un fluide à travers les matériaux poreux intervient dans de nombreux procédés en physique, chimie, géologie et ingénierie. Les propriétés telles que la porosité et la distribution de taille de pore ne reflètent pas la complexité du réseau poreux qui consiste en un réseau de pores interconnectés irrégulier et de différentes sections. La complexité est décrite par un paramètre appelé la tortuosité. La tortuosité est déterminé par des mesures électriques ou par chromatographie liquide. En chromatographie liquide la tortuosité intraparticulaire est calculée à partir du coefficient de diffusion intraparticulaire de polystyrènes déterminé à partir de l’élargissement des pics obtenus en mode dynamique et en mode statique en conditions non-adsorbantes avec le solvant tétrahydrofurane (THF). En mode dynamique, dans l’équation de van Deemter, le terme constant dépend de la diffusion d’eddy et de la polydispersité des polystyrènes. La silice poreuse Si100 présente une distribution de taille des pores assez large ce qui entraîne l’élargissement des pics chromatographiques. Le transport de polystyrènes à travers les silices en conditions adsorbantes a également été étudié en modifiant le solvant. En conditions adsorbantes, avec un mélange de THF et d’heptane, pour un polymère de taille donné, plusieurs pics sont obtenus en raison de la polydispersité du polystyrène. L’adsorption augmente avec la masse molaire du polystyrène. La diffusion de surface diminue lorsque le facteur de rétention augmente
The correlation of the structural parameters with the transfer properties of a fluid through a porous media is a significant subject in physics, chemistry, geology, and engineering. The architectural parameters such as porosity and pore size distribution do not describe the complexity of most porous organizations consisting of labyrinths of interconnected pores with random shapes and cross-sections. This complexity is described by a parameter called tortuosity. The apparent total and particle tortuosities are determined by electrical measurements or the analysis of the peak shape of chromatographic probes. In the latter case, the particle tortuosity of silica is calculated from effective intraparticle diffusion coefficient determined by modelling the chromatographic peak broadening of polystyrenes obtained either in dynamic or in static conditions under non-adsorbing conditions by using the solvent tetrahydrofuran (THF). In dynamic conditions, the constant term in the van Deemter equation is a combined contribution of eddy diffusion and polydispersity of the polystyrenes and depends on the size of the molecule. The broad pore size distribution of totally porous silica contributes also to the spreading of the peak. The transport of polystyrenes through silica columns has also been studied in adsorbing conditions by changing the solvent. With the mixture of n-Heptane and THF, one obtains many peaks for a polystyrene sample due to the polydispersity of the polystyrene. In fact, the adsorption increases with the molecular weight of the polystyrenes. The surface diffusion of polystyrene decreases with an increase in the retention factor

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44

Li, Shimin. "Modeling biocolloid transport in saturated porous media". Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186407.

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A forced-gradient experiment of virus and carboxylated microsphere transport was carried out at a two-well system in saturated aquifer at Borden, Ontario. The purpose of experiment was to qualitatively and quantitatively investigate bacteriophage transport relative to that of a conservative solute in porous media. A simplified plane radial advection dispersion equation coupled with reversible first-order and equilibrium mass transfer was found to be adequate to simulate the attachment and transport process. For simulating detachment and transport, all rate parameters were varied with time up/down (depending on the parameter) to reflect the changes in pH of groundwater with time from 7.4 to 8.4 then back to 7.4. Both constant and scale-dependent dispersivity were used in the modeling of the transport process. Time-moment analysis of the conservative-tracer breakthrough curves produced dispersivity values of 0.1-0.6 m, close to the macrodispersivity of 0.6 m obtained using a stochastic model to describe a previous larger-scale experiment at the site. The multiple-peak feature of all the breakthrough curves suggests that the aquifer heterogeneity may be more important than local dispersion in affecting the appearance of both electrical conductivity and phage breakthrough curves. Strack's model was found quite well to describe the hydraulic head profile during the whole period of experiment if proper values for transmissivity and cone radius are chosen. Virus traveled at least a few meters in the experiment, but virus concentrations at observation points 1-m to 2-m away were a small fraction of those injected. Though clearly not an equilibrium process, retardation involving a dynamic steady state between attachment and detachment is nevertheless a major determinant of transport versus retention of virus.

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45

Jewett, David Gordon. "Bacterial transport in variably saturated porous media". Diss., The University of Arizona, 1995. http://hdl.handle.net/10150/187285.

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The transport of Pseudomonas fluorescens strain P17 through saturated and unsaturated porous media was investigated. Continuous-flow column experiments examined the effects of ionic strength and pH on P17 transport in saturated porous media. Bacterial penetration was measured and filtration theory was used to calculate bacterial collision efficiencies (ɑ). A decrease in ionic strength from 10⁻¹ to 10⁻⁵ M produced an approximately 90% decrease in bacterial ɑ's (from 0.12 to 0.015). This change in a is consistent with double-layer theory, but suggests that very large changes in ionic strength are necessary to influence transport. Cell transport was unaffected by pH in the range of 5.5 < pH < 7.0. Column results were compared to a screening technique using large-pore filters. Filter ɑ's followed similar trends, but were about 1.5 times that of column ɑ's, likely due to the use of an idealized model to describe different porous media geometries and system hydraulics. Column results also indicate that uncertainty in measurements of culturable bacteria can preclude reliable estimation of low ɑ values. For ɑ < 0.01, a rapid and more reliable mini-column method is suggested for measuring biocolloid attenuation in saturated porous media. Laboratory experiments also determined P17 transport as a function of water content and the influence of the gas-liquid and solid-liquid interfaces in limiting microbial transport. Cells were suspended in artificial groundwater and injected into saturated and unsaturated quartz sand columns. Total P17 retention (R(t)) was inversely proportional to water content with approximately twice the cell retention at 46% water saturation (R(t) = 0.95) compared to saturated experiments (R(t) = 0.50). Retained cells were divided into fractions attached at the gas-liquid (R(g)) and solid-liquid (R(s)) interfaces. The ratio of R(g)/R(t), increased with decreasing water content suggesting increased bacterial removal was due to cell attachment at the gas-liquid interface and was in proportion to gas-liquid interfacial area. Bacterial transport under unsaturated conditions was enhanced by decreasing the ionic strength of the carrying solution and adding non ionic surfactant. Decreased cell attachment at both the gas-liquid and solid-liquid interfaces was likely due to changes in electrostatic interactions between the interfaces and cell surfaces brought on by water chemistry modifications.

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46

NASSI, Marianna. "Reactive transport of pollutants in porous media". Doctoral thesis, Università degli studi di Ferrara, 2012. http://hdl.handle.net/11392/2389259.

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Accidental or deliberate crude oil spills have been, and still continue to be, a significant source of environmental pollution, and pose a serious environmental problem, due to the possibility of air, water and soil contamination. Chlorinated volatile organic compounds (VOCs), such as 1,1-dichloroethylene (DCE) and aromatic hydrocarbons, BTEX (benzene, toluene, ethyl benzene and xylene) constitute a significant fraction of hazardous air and water pollution. Human beings are exposed to elevated levels of a wide spectrum of VOCs, many of which have been found to be toxic and potentially carcinogenic. Removal of these organic contaminants from water and wastewater has been achieved using several treatment technologies, such as advanced oxidation processes, air stripping, reverse osmosis, ultrafiltration and adsorption. Adsorption processes can be successfully used when contaminants are not amenable to fast biological degradation. Permeable Reactive Barriers (PRB) are one of the most promising passive treatment technologies, due to their effectiveness regarding various contaminants, and their low cost compared to other in situ technologies. Typical PRB configuration consists in a permeable treatment zone placed vertically to the flow path of groundwater, which contains reactive material that immobilises or decomposes the contaminants by adsorption as the groundwater flows through it. PRBs are installed as permanent, semi-permanent, or replaceable units. A wide variety of pollutants are degraded, precipitated, sorbed or exchanged in the reactive zone, including chlorinated solvents, heavy metals, radionuclides and other organic and inorganic species. Conventional permeable reactive barriers for the decontamination of water are based on systems which most widely use Granular Activated Carbon (GAC). GAC has been shown to be only slightly effective in treating water containing very soluble compounds, such as oxygenated organics, or low molecular weight compounds, such as DCE and vinyl chloride (VC). However, their use for the removal of organic contaminants in water and wastewater applications can be complicated by the presence of dissolved natural organic matter in the water stream being treated, which can decrease the removal efficiency of GAC. When activated carbon is saturated, it has to be regenerated or renewed, which is rather an expensive operation. The adsorbed molecules are then released and still have to be destroyed by thermal treatments. Moreover, this additional treatment also degrades the activated carbon adsorption properties in the long term [1]. Zero-valent iron (ZVI), which directly degrades several contaminants, appears to be ineffective too, both on irreducible compounds such as DCE and chlorobenzenes as well as on hydrocarbons. Furthermore, when ZVI is used, it causes a reduction in the permeability of the barrier due to encrustations or precipitation of minerals which derive from the reactions between the ions of the oxidised metal and the substances contained in the groundwater [1-2]. Therefore, when operating with a barrier based on metallic iron alone, the chemical reduction reaction of the reducible compounds can require from 1 to 2 days. In this case, it is only the thickness of the iron which can ensure the time necessary for completing the reactions and large quantities are required to guarantee the complete decontamination of the groundwater. Recently, high-silica zeolites were shown to be more effective than activated carbon or ZVI in removing certain organics from water [3-4]. The selection of zeolites from among the large variety of adsorbent materials is based on their stability and efficiency properties. To date, the adsorption mechanisms of zeolites in gas phase systems have been widely investigated. On the contrary, studies and applications on organic pollutants adsorption in microporous zeolitic materials from aqueous media have been relatively scarce. Adsorption from gas phase systems can significantly differ from that observed from the corresponding aqueous solutions, due to the highly polar nature of water molecules. In literature, it has been reported that water plays a very important role in the diffusion of hydrocarbons in the zeolite pore system. In particular, large amounts of co-adsorbed water molecules block the migration of host molecules such as alkanes and olefins, thus reducing the adsorption capacity of zeolites, especially at low adsorbate concentrations. As a consequence, water acts as a screen between the cationic sites of the zeolite and the hydrocarbon molecules (screening effect) and reduces both the sorption volume (steric effect) and the aperture of the zeolite windows (blocking effect). On the contrary, small amounts of co-adsorbed water lower the extent of specific adsorption without significant blocking effects. However, as mentioned above, this research on hydrocarbon adsorption has also mainly been focused on single components from air matrices, whereas there are few studies involving aqueous dilute solutions. Nonetheless, in most environmental applications, these pollutants are present as very dilute aqueous solution mixtures. The work developed in the present thesis is part of a wider project whose purpose is to study the interaction and mobility of groundwater pollutants adsorbed in zeolite pores, in order to improve the efficiency of permeable reactive barriers. This project involves Ferrara and Bologna Universities with the financial support of the ENI and the scientific support of Dr. Roberto Bagatin of the research centre of Novara. Several techniques were employed such as X ray diffraction, gas chromatography, IR spectroscopy, thermal analyses, as well as computational studies. In this thesis, combined diffractometric, thermogravimetric and gas chromatographic techniques were employed to study the adsorption process in order to: 1) investigate the adsorptive properties of these hydrophobic synthetic zeolites; 2) characterise their structure after the adsorption of selected contaminants (1-2 dichloroethane, tert-butyl methyl ether and toluene); 3) localise the organic species in the zeolite channel system; 4) probe the interactions between organic molecules and framework oxygen atoms; 5) compare the adsorption data for a mixture of these contaminants with concentrations in the ppb and ppm range; 6) characterise the kinetic of the adsorption processes. In particular, the thermodynamic and kinetic of the adsorption processes of contaminants on hydrophobic zeolites were obtained by using complementary, batch, linear and non-linear chromatography and thermogravimetry techniques. Batch and non-linear chromatography were mainly used to measure the adsorption isotherms for the compounds of interest. The adsorption isotherm is useful in representing the capacity of a zeolite to adsorb organics from waste, and in providing description of the functional dependence of capacity on the concentration of pollutants. Experimental determination of the isotherm allows to evaluate the feasibility of adsorption for treatment, to select a zeolite, and to estimate adsorbent dosage requirements. Moreover, it is possible to evaluate the adsorption energy distribution of the process from isotherm parameters. Batch and linear chromatography, instead, were employed to investigate the kinetic of the adsorption. Kinetics deals with changes in chemical properties in time and is especially concerned with the rate of changes and plays a fundamental role in determining the proper time contact for the removal of pollutant components from wastewater. In addition, an original theoretical model able to give information regarding the kinetic and the thermodynamic constants of systems in which both reactions and adsorption processes occur simultaneously was developed. To investigate the adsorption mechanism, diffraction techniques were employed to localize the organics adsorbed into the zeolite structure. The information gathered by this latter investigation – in cooperation with the Earth Science Department UNIFE - allows to define the interactions between organic molecules and zeolite framework. Finally, adsorption on mesoporous materials was investigated. It is well known that water is contaminated by different classes of substances, and zeolites are mainly suitable for molecules with dimensions comparable to that of their pores. However, many compounds belonging to the class of emergent contaminants have large molecular dimensions, and in such cases mesoporous materials can be more efficient than zeolites. To accomplish this task MCM-41 and HMS were synthesized and characterised – this work was carried out at the ‘Institut Charles Gerhardt (ICG), Matériaux Avancés pour la Catalyse et la Santé (MACS)’ at Montpellier (France) with the supervision of Prof. Francesco di Renzo and Dr. Anne Galarneau – and then the adsorption of acid perfluorooctanoic onto these mesoporous materials was performed.

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Ayalur-Karunakaran, Santhosh, i Siegfried Stapf. "Poly (dimethyl siloxane) films in porous media". Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-192162.

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Poly (Dimethyl siloxane) thin films were prepared by solvent evaporation method in porous alumina hosts. The thickness of these layers ranged from multilayer to sub-monolayer. Different NMR methods (FFC relaxometry, transverse relaxation, 1H Double quantum NMR) were applied to study the dynamics and order in these thin films. We found that dynamic restrictions and order increased with decreasing layer size. The increase of a short component of T2 from CPMG curves was attributed to the thawing of the adsorbed chains as seen in the decrease of the short component from Hahn echoes.

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48

Avesani, Diego. "A new Lagrangian method for transport in porous media (to model chemotaxis in porous media)". Doctoral thesis, Università degli studi di Trento, 2014. https://hdl.handle.net/11572/367738.

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As recently shown in laboratory bench scale experiments, chemotaxis, i.e.the movement of microorganisms toward or away from the concentration gradient of a chemical species, could have a fundamental role in the transport of bacteria through saturated porous media. Chemotactic bacteria could enhance bioremediation by directing their own motions to residual contaminants in less conductive zones in aquifers. The aim of the present work is to develop a proper numerical scheme to define and to quantify the magnitude and the role of chemotaxis in the complex groundwater system framework. We present a new class of meshless Lagrangian particle methods based on the Smooth Particle Hydrodinamics (SPH) formulation of Vila & Ben Moussa, combined with a new Weighted Essentially Non-Oscillatory (WENO) reconstruction technique on moving point clouds in multiple space dimensions. The purpose of this new scheme is to fully exploit the advantages of SPH among traditional meshbased and meshfree schemes and to overcome its inapplicability for modeling chemotaxis in porous media. The key idea is to produce for each particle first a set of high order accurate Moving Least Squares (MLS) reconstructions on a set of different reconstruction stencils. Then, these reconstructions are combined with each other using a nonlinear WENO technique in order to capture at the same time discontinuities and to maintain accuracy and low numerical dissipation in smooth regions. The numerical fluxes between interacting particles are subsequently evaluated using this MLS-WENO reconstruction at the midpoint between two particles, in combination with a Riemann solver that provides the necessary stabilization of the scheme based on the underlying physics of the governing equations. We propose the use of two different Riemann solvers: the Rusanov flux and an Osher-type flux. The use of monotone fluxes together with a WENO reconstruction ensures accuracy, stability, robustness and an essentially non oscillatory solution without the artificial viscosity term usually employed in conventional SPH schemes. To our knowledge, this is the first time that the WENO method, which has originally been developed for mesh-based schemes in the Eulerian framework on fixed grids, is extended to meshfree Lagrangian particle methods like SPH in multiple space dimensions. In the first part, we test the new algorithm on two dimensional blast wave problems and on the classical one-dimensional Sod shock tube problem for the Euler equations of compressible gas dynamics. We obtain a good agreement with the exact or numerical reference solution in all cases and an improved accuracy and robustness compared to existing standard SPH schemes. In the second part, the new SPH scheme is applied to advection-diffusion equation in heterogeneous porous media with anisotropic diffusion tensor. Several numerical test case shows that the new scheme is accurate. Unlike standard SPH, it reduces the occurrence of negative concentration. In the third part, we show the applicability of the new scheme for modeling chemotaxis in porous media. We test the new scheme against analytical reference solutions. Under the assumption of complete mixing at the Darcy scale, we perform different two-dimensional conservative solute transport simulations under steady-state conditions with instant injection showing that chemotaxis significantly affect the quantification of field-scale mixing processes.

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49

Avesani, Diego. "A new Lagrangian method for transport in porous media (to model chemotaxis in porous media)". Doctoral thesis, University of Trento, 2014. http://eprints-phd.biblio.unitn.it/1288/1/avesani_tesi.pdf.

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As recently shown in laboratory bench scale experiments, chemotaxis, i.e.the movement of microorganisms toward or away from the concentration gradient of a chemical species, could have a fundamental role in the transport of bacteria through saturated porous media. Chemotactic bacteria could enhance bioremediation by directing their own motions to residual contaminants in less conductive zones in aquifers. The aim of the present work is to develop a proper numerical scheme to define and to quantify the magnitude and the role of chemotaxis in the complex groundwater system framework. We present a new class of meshless Lagrangian particle methods based on the Smooth Particle Hydrodinamics (SPH) formulation of Vila & Ben Moussa, combined with a new Weighted Essentially Non-Oscillatory (WENO) reconstruction technique on moving point clouds in multiple space dimensions. The purpose of this new scheme is to fully exploit the advantages of SPH among traditional meshbased and meshfree schemes and to overcome its inapplicability for modeling chemotaxis in porous media. The key idea is to produce for each particle first a set of high order accurate Moving Least Squares (MLS) reconstructions on a set of different reconstruction stencils. Then, these reconstructions are combined with each other using a nonlinear WENO technique in order to capture at the same time discontinuities and to maintain accuracy and low numerical dissipation in smooth regions. The numerical fluxes between interacting particles are subsequently evaluated using this MLS-WENO reconstruction at the midpoint between two particles, in combination with a Riemann solver that provides the necessary stabilization of the scheme based on the underlying physics of the governing equations. We propose the use of two different Riemann solvers: the Rusanov flux and an Osher-type flux. The use of monotone fluxes together with a WENO reconstruction ensures accuracy, stability, robustness and an essentially non oscillatory solution without the artificial viscosity term usually employed in conventional SPH schemes. To our knowledge, this is the first time that the WENO method, which has originally been developed for mesh-based schemes in the Eulerian framework on fixed grids, is extended to meshfree Lagrangian particle methods like SPH in multiple space dimensions. In the first part, we test the new algorithm on two dimensional blast wave problems and on the classical one-dimensional Sod shock tube problem for the Euler equations of compressible gas dynamics. We obtain a good agreement with the exact or numerical reference solution in all cases and an improved accuracy and robustness compared to existing standard SPH schemes. In the second part, the new SPH scheme is applied to advection-diffusion equation in heterogeneous porous media with anisotropic diffusion tensor. Several numerical test case shows that the new scheme is accurate. Unlike standard SPH, it reduces the occurrence of negative concentration. In the third part, we show the applicability of the new scheme for modeling chemotaxis in porous media. We test the new scheme against analytical reference solutions. Under the assumption of complete mixing at the Darcy scale, we perform different two-dimensional conservative solute transport simulations under steady-state conditions with instant injection showing that chemotaxis significantly affect the quantification of field-scale mixing processes.

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PASSOS, NATHALIA CHRISTINA DE SOUZA TAVARES. "NUMERICAL MODELLING OF TWO-PHASE FLOW IN FRACTURED POROUS MEDIA WITH FLUIDMECHANICAL COUPLING". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36897@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Esse trabalho apresenta um modelo numérico para a análise de processos acoplados de efeitos mecânicos e escoamento bifásico em meios porosos fraturados, com a utilização de diferentes métodos numéricos combinados (Elementos finitos contínuos e descontínuos), e utilizando uma mesma malha de elementos finitos para representar uma célula de modelo de simulação de reservatório. As descontinuidades são inseridas na malha como elementos de nós duplicados colapsados. Empregam-se procedimentos numéricos desenvolvidos em dois grupos distintos. Um primeiro grupo de simulações trata de um procedimento numérico de escoamento bifásico, com ênfase à obtenção de um balanço de volumes verdadeiramente conservativo. Nesta fase, avalia-se uma formulação numérica que emprega um processo em três etapas: o método dos elementos finitos (EF), para a aproximação da equação da pressão; intermediariamente, utiliza-se o método de Raviart-Thomas de mais baixa ordem para aproximação da velocidade; e a aproximação da equação da saturação pelo método dos elementos finitos descontínuos (MEFD), que utiliza um limitador de inclinação multidimensional de modo a evitar oscilações na reconstrução dos dados de saturação. Para fins de validação da formulação desenvolvida, comparam-se os resultados obtidos com simulações utilizando o Método do Volumes Finitos (VF). O segundo grupo de simulações trata de acoplar o módulo mecânico (em EF) ao simulador de escoamento bifásico, de modo que a variação do estado de tensões, decorrente da explotação, seja considerada nas simulações. Essa análise permite uma melhor representação do fenômeno estudado além de proporcionar melhores resultados quanto à chegada da água nos poços produtores, afetando a produtividade do modelo.
This work presents a numerical model for the analysis of coupled processes of mechanical effects and two-phase flow in fractured porous media using different numerical methods (continuous and discontinuous finite elements), and using the same finite element mesh to represent a cell of reservoir simulation model. The discontinuities are inserted into the mesh as elements of collapsed duplicate nodes. Numerical procedures developed in two distinct groups are used. A first group of simulations deals with a numerical two-phase flow procedure, with special emphasis on obtaining a truly conservative volume balance. At this stage, a numerical formulation using a three-step process is evaluated: The Finite Element Method (EF), for the approximation of the pressure equation; the lower order of Raviart-Thomas method is used to velocity approximation; and the approximation of the saturation equation by the discontinuous finite element method (MEFD), using a multidimensional slope limiter in order to avoid oscillations in the reconstruction of the saturation data. For the validation of the developed formulation, the results obtained are compared with simulations using the Finite Volume Method (VF), with focus on the analysis of the conservation of volumes. The second group of simulations couple the mechanical module (in EF) to twophase flow computer program, so the variation of the stress state, due to exploitation, is considered in the simulations. This analysis allows a better representation of the phenomenon. In addition to providing better results regarding the arrival of water in the producing wells, affecting the productivity of the model.

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