Error of labeling pages or Page 102 Not included in thesis. / <p> A semi-explicit scheme for the solution of transient multdimensional natural convection is made to study natural convection in porous media. The conservation equations are phrased in primitive form. Heat tranfer between the solid and liquid phases is modelled by representing the porous medium as an assemblage of spherical particles, and solving the conduction problem for such a system at every time step. Nusselt numbers were calculated from the temperature and velocity profiles. Numerical results for heat transfer through fluid saturated porous media heated from below are in good agreement with published experiments.</p> / Thesis / Master of Engineering (MEngr)

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Accurate predictions of macroscopic multiphase flow properties, such as relative permeability and capillary pressure, are necessary for making key decisions in reservoir engineering. These properties are usually measured experimentally, but pore-scale network modeling has become an efficient alternative for understanding fundamental flow behavior and prediction of macroscopic properties. In many cases network modeling gives excellent agreement with experiment by using models physically representative of real media. Void space within a rock sample can be extracted from high resolution images and converted to a topologically equivalent network of pores and throats. Multiphase fluid transport is then modeled by imposing mass conservation at each pore and implementing the Young-Laplace equation in pore throats; the resulting pressure field and phase distributions are used to extract macroscopic properties. Advancements continue to be made in making network modeling predictive, but one limitation is that artificial (e.g. constant pressure gradient) boundary conditions are usually assumed; they do not reflect the local saturations and pressure distributions that are affected by flow and transport in the surrounding media. In this work we demonstrate that flow behavior at the pore scale, and therefore macroscopic properties, is directly affected by the boundary conditions. Pore-scale drainage is modeled here by direct coupling to other pore-scale models so that the boundary conditions reflect flow behavior in the surrounding media. Saturation couples are used as the mathematical tool to ensure continuity of saturations between adjacent models. Network simulations obtained using the accurate, coupled boundary conditions are compared to traditional approach and the resulting macroscopic petrophysical properties are shown to be largely dependent upon the specified boundary conditions. The predictive ability of network simulations is improved using the novel network coupling scheme. Our results give important insight into upscaling as well as approaches for including pore-scale models directly into reservoir simulators. / text

This research addresses a number of fundamental issues concerning convective mass transfer across fluid-fluid interfaces in porous media. Mass transfer to/from distributed sinks/sources is considered for i) the slow dissolution of liquid filaments of a wetting non-aqueous phase liquid (NAPL) held in the corners of angular pores or throats and ii) the fate of gas bubbles generated during the flow of a supersaturated aqueous phase in porous media. 1. Effects of the stability of NAPL films on wetting NAPL dissolution Wettability profoundly affects the distribution of residual NAPL contaminants in natural soils. Under conditions of preferential NAPL wettability, NAPL is retained within small pores and in the form of thick films (liquid filaments) along the corners and crevices of the pore walls. NAPL films in pore corners provide capillary continuity between NAPL-filled pores, dramatically influencing the behaviour of NAPL dissolution to the flowing aqueous phase by convection and diffusion. A pore network model is developed to explore the dissolution behaviour of wetting NAPL in porous media. The effects of initial NAPL distribution and NAPL film stability on dissolution behaviour are studied using the simulator. NAPL phase loses continuity and splits into disconnected clusters of NAPL-filled pores due to rupture of NAPL films. Quasi-state drainage and fingering of the aqueous phase into NAPL-filled pores is treated as an invasion percolation process and a stepwise procedure is adopted for the solution of flow and solute concentration fields. NAPL film stability is shown to critically affect the rate of mass transfer as such that stable NAPL films provide for more rapid dissolution. The network simulator reproduces the essential physics of wetting NAPL dissolution in porous media and explains the concentration-tailing behaviour observed in experiments, suggesting also new possibilities for experimental investigation. 2. Convective Mass Transfer across Fluid Interfaces in Straight Angular Pores Steady convective mass transfer to or from fluid interfaces in pores of angular cross-section is theoretically investigated. The model incorporates the essential physics of capillarity and solute mass transfer by convection and diffusion in corner fluid filaments. The geometry of the corner filaments, characterized by the fluid-fluid contact angle, the corner half-angle and the interface meniscus curvature, is accounted for. Boundary conditions of zero surface shear (???perfect-slip???) and infinite surface shear (???no-slip???) at the fluid-fluid interface are considered. The governing equations for laminar flow within the corner filament and convective diffusion to or from the fluid-fluid interface are solved using finite-element methods. Flow computations are verified by comparing the dimensionless resistance factor and hydraulic conductance of corner filaments against recent numerical solutions by Patzek and Kristensen [2001]. Novel results are obtained for the average effluent concentration as a function of flow geometry and pore-scale Peclet number. These results are correlated to a characteristic corner length and local pore-scale Peclet number using empirical equations appropriate for implementation in pore network models. Finally, a previously published ???2D-slit??? approximation to the problem at hand is checked and found to be in considerable error. 3. Bubble evolution driven by solute diffusion during the process of supersaturated carbonated water flooding In situ bubble growth in porous media is simulated using a pore network model that idealizes the pore space as a lattice of cubic chambers connected by square tubes. Evolution of the gas phase from nucleation sites is driven by the solute mass transfer from the flowing supersaturated water solution to the bubble clusters. Effects of viscous aqueous phase flow and convective diffusion in pore corners are explicitly accounted for. Growth of bubble clusters is characterised by a pattern of quasi-static drainage and fingering in the gas phase, an invasion percolation process controlled by capillary and gravitational forces. A stepwise solution procedure is followed to determine the aqueous flow field and the solute concentration field in the model by solving the conservation equations. Mobilization of bubbles driven by buoyancy forces is also studied. Results of bubble growth pattern, relative permeability and macroscopic mass transfer coefficient are obtained under different gas saturations and aqueous flow conditions.

Cette thèse porte sur les capacités d'extraction d'une mousse déposée sur un support poreux dans le but d'y déloger un contaminant ayant imprégné la porosité. Nous avons donc considéré l'imprégnation forcée de fluides dans un pore unique, étudiée pour deux cas particuliers : (i) lors de l'impact d'une goutte de liquide à l'aplomb d'un pore unique vertical cette situation visant à modéliser l'imprégnation du poreux par le contaminant, et (ii) lors de l'aspiration d'une mou sse liquide à travers le pore qui illustre la compétition d'aspiration entre la mousse et le poreux. Dans chaque cas, le diamètre du pore est inférieur à celui des gouttes ou des bulles.Pour le premier cas, nous nous sommes intéressés au volume et à la profondeur d'imprégnation pour des surfaces hydrophiles et hydrophobes. Nous établissons les diagrammes d'imprégnation en fonction du diamètre du pore et de la vitesse d'impact et un travail de modélisation nous permet de déterminer les limites entre les différentes régions de ces digrammes.Pour le second cas, nous montrons que lors de l'aspiration, la mousse entre dans le pore uniquement dans un domaine bien déterminé dans le diagramme fraction liquide, rapport de taille pore/bulle et débit d'aspiration. En dehors de ce domaine, l'aspiration peut faire entrer soit le gaz seul, soit le liquide seul. La encore, un travail de modélisation nous permet de prédire les limites des différentes zones du diagramme. Dans une dernière partie, nous revenons à un problème pratique d'imprégnation sur support textile et quantifions les capacités d'extraction d'une mousse dans cette configuration dans le but d'y déloger un contaminant / This thesis is about the ability of foam to extract a pollutant trapped in a fabric. We studied the forced impregnation of fluids into a single pore, in two particular cases : (i) when a liquid droplet impact vertically on the pore (this situation corresponds to the model of the impregnation of the pollutant into the fabric), and (ii) when a foam is sucked through a pore, which illustrate the competition between the suction on the foam and those of the porous media. For each case, the diameter of the pore is smaller than the diameter of droplet or bubble. At first, we studied the volume and how deep penetrates the liquid penetrates, for hydrophobic and hydrophilic surfaces. We established diagrams of impregnation as a function of the pore diameter and impact velocity, and a model determines the limits between the different areas of the diagram. For the second case, we showed that during the suction, the foam go into the pore only for one delimited area of the diagram liquid fraction, ration pore diameter / bubble diameter. Out of this area, suction force solely liquid or solely gas into the pore. Again, a model determines the limits between the different areas of the diagram. Finally an applied part of our work is about the ability of foam to extract a pollutant trapped in a fabric

Neste trabalho é investigada a relaxação longitudinal da magnetização nuclear de água impregnada em pastilhas de pó de alumina (Al IND. 2 O IND. 3) com grau de pureza de 99,8%, objetivando a determinação do diâmentro de poro de uma espuma cerâmica do mesmo material a partir de medidas do tempo de relaxação longitudinal T IND. 1. O trabalho fundamenta-se no fato dos tempos de relaxação da magnetização nuclear T IND. 1 e T IND. 2, spin-rede e spin-spin respectivamente, de um fluido confinado em um meio poroso serem menores que tempos T IND. 1B e T IND. 2B para o mesmo fluido não confinado. Mediram-se os tempos T IND. 1 para graus de impregnação de água nas amostras entre 10 e 100% usando um espectrômetro montado a partir de módulos comerciais e de um gerador de pulsos desenvolvido no IFSC-USP. A partir dos tempos T IND. 1 e dos diâmetros de poro das pastilhas de pó, determinou-se o valor da relaxatividade longitudinal ou intensidade de relaxação superficial (mu IND. 1), um parâmetro que caracteriza a interface água-alumina nestas amostras. Usando o valor de (mu IND. 1) obtido para o pó e o tempo de relaxação T IND. 1 medido nas amostras de espuma cerâmica foi determinado o diâmetro de poro desta. Última, o qual é comparado com os valores obtidos com a microscopia eletrônica e com a injeção de mercúrio. O caráter não invasivo desta técnica em contraste com as outras, faz dela a única possível em algumas aplicações. / Nuclear magnetization relaxation of water imbibed on 99,8% purê alumina (Al IND. 2 O IND. 3) grain packs is investigated aiming to determine the mean pore diameter of ceramic foam pieces of the same material. The work rely on the shortening of the relaxation times T IND. 1 spin-lattice and T IND. 2 spin-spin of the nuclear magnetization of fluids confined on porous media as compared with their T IND. 1B e T IND. 2B bulk values. Relaxation times T IND. 1 were measured, using a spectrometer built from commercial modules and a pulse generator developed at the IFSC-USP, varying the content of water imbibed from 10 to 100%. The longitudinal relaxation (mu IND. 1), or surface sink strength, was determined from the measured T IND. 1 values and the mean pore diameter of the powder packs. This parameter characterizes the water-alumina interface of these samples. Using the (mu IND. 1) value from the powder and the relaxation times T IND. 1 measured on the ceramic foam pieces, the mean pore diameter of these samples were determined and are compared with the values obtained from mercury intrusion and electron microscopie. The non-invasive character of this technique distinguishes it from the other, making it the only possible in some applications.

A teoria da percolação tem se revelado muito útil no tratamento de inúmeros fenômenos da natureza. Devido a sua grande versatilidade, esta teoria é objeto de intensa pesquisa. Aqui, propomos novas formas de percolação e as estudamos através de simulações numéricas. Na primeira parte de nosso trabalho, investigamos a estrutura dos aglomerados gerados pelo modelo de percolação por invasão múltipla. Estimamos os valores das dimensões fractais do esqueleto, do esqueleto elástico, dos pontos de estrangulamento e dos menores caminhos, como função dos parâmetros do modelo. Por ter uma estrutura geométrica bastante estabilizada, o modelo otimizado pode vir a ser muito útil no tratamento de problemas com diluição da mecânica estatística. O modelo de percolação atenuada foi concebido para permitir que, durante o processo de invasão, os poros grandes possam também ser ocupados. Esta ocupação ocorre com uma probabilidade que diminui quando o tamanho do poro aumenta.Estimamos cuidadosamente os limiares de percolação e construímos os diagramas de fase correspondentes. Verificamos que os limiares de percolação de nosso modelo não satisfazem a conjectura de Galam e Mauger. Estudamos o efeito da inércia em fluidos escoando através de meios porosos incorporando uma caminhada de N passos ao modelo de percolação por invasão. A magnitude da inércia é proporcional ao parâmetro N, que representa o número de poros seqüencialmente invadidos após a ruptura do perímetro, em cada etapa do processo. Investigamos este modelo em duas e três dimensões. Verificamos que no caso bidimensional, as caminhadas de N passos são facilmente bloqueadas o que leva ao surgimento de um limite superior para o número de passos efetivamente realizados. Nossas estimativas das dimensões fractais dos aglomerados (como função do parâmetro N), indicam que este modelo pertence a uma classe de universalidade diferente daquela da percolação por invasão ordinária. Propomos um modelo de percolação para tratar um processo de solidificação de dois fluidos imiscíveis na presença de impurezas móveis. O movimento das impurezas ocorre devido a uma interação repulsiva de curto alcance observada experimentalmente por Ulhmann, Chalmers e Jackson (UCJ). Dependendo das concentrações de fluidos e impurezas, pode haver a formação de uma fase sólida que percola todo o sistema. Construímos o diagrama de fases deste modelo no espaço das concentrações e calculamos seus expoentes críticos. Nossos resultados indicam que o modelo pertence à mesma classe de universalidade que a percolação ordinária. Finalmente, estudamos um processo de percolação por invasão na presença de impurezas que se movem segundo o mecanismo UCJ. Encontramos um valor crítico para a concentração de impurezas, acima do qual não mais existe percolação. O perfil de aceitação aproxima-se de uma função de Heavyside, com o ponto de descontinuidade dependendo da concentração de impurezas. / Percolation theory provides a quantitative and conceptual model for the understanding of many natural phenomena. Here, we present new kinds of percolation and study them using Monte Carlo simulation techniques. We start studying the cluster, the backbone and the elastic backbone structures of the multiple invasion percolation for both the perimeter and the optimized versions. The behavior of the mass, the number of cutting sites and loops are investigated and their corresponding scaling exponents are estimated. By construction, the mass of the optimized model scales exactly with the gyration radius of the cluster - we verify that this also happens with the backbone. Our simulation shows that the red sites almost disappear, indicating that the cluster has achieved a high degree of connectivity. We propose a new kind of invasion percolation, which permits that, besides small pores, large pores being also occupied. In our model, the occupation probability of a pore diminishes with the pore\'s size. We estimate their corresponding percolation thresholds and show that they do not satisfy the Galam and Mauger conjecture. In order to take into account the inertia of the invader fluid, a new kind of invasion percolation is introduced. In this model, which we named N-steps invasion percolation, the inertia forces are controlled by the number N of pores (or steps) invaded after the perimeter rupture. The new model belongs to a different class of universality and has its fractal dimension depending on N. A blocking phenomenon takes place in two dimensions. It imposes an upper bound value on N. For pores sizes larger than the critical threshold, the acceptance profile exhibits a permanent tail. We also introduce a model for the solidification process of two immiscible fluids interacting repulsively with mobile impurities on a two dimensional square lattice. In the space of the fluids and impurities concentrations the phase diagram exhibits a critical curve separating a percolating from a non-percolating phase. Estimated values for the fractal dimension and the exponent ? of the order parameter, reveal that the critical exponents do not vary along this curve, i.e., they are independent of the impurities concentration. The universality class we find is that of the ordinary percolation. Finally, based on the main ideas of the dynamic epidemic and invasion percolation models, we propose a model to describe the cleaning process of a dirty porous medium by fluid injection. An analysis of the acceptance profiles strongly indicates that this model is a kind of self-organized system.

Generalizamos o modelo de percolação por invasão de maneira que vários sítios possam ser simultaneamente invadidos. Propomos dois tipos de generalização: na primeira, o fluxo de fluido invasor e controlado através do perímetro do aglomerado, enquanto que na segunda modificação, o crescimento e governado pela relação de escala entre a massa e o raio de giração dos aglomerados. Estudamos cuidadosamente tanto o perfil de aceitação quanto as dimensões fractais (\'D IND.F\') dos aglomerados assim crescidos. No modelo baseado nas relações de escala, \'D IND.F\' pode ser tratado como um mero parâmetro real que pode assumir qualquer valor no intervalo (0, ?). Nos intervalos (0, \'91 SOB.48\') e (2, ?), o sistema e frustrado. Para \'D IND.F\' > 2, o modelo exibe um fenômeno interessante: em algumas etapas ocorrem explosões no crescimento da massa dos aglomerados (bursts). Na região [\'91 SOB.48\',2], os aglomerados obedecem exatamente e em qualquer escala a relação M ~ RgDF entre a massa m e o raio de giração \'RG\'. Acreditamos que estes fractais cuja estrutura completamente e estabilizada possam ser muito úteis no tratamento de problemas de diluição da mecânica estatística. / We generalize the standard site invasion percolation model to permit simultaneous invasion of several sites. We propose two kinds of generalizations: one in which the invasion flux is controlled by the perimeter size and another where the scaling properties command the growth process. The acceptance profile as well as the fractal dimension \'D IND.F\' are carefully studied. In the model based on scaling relation, \'D IND.F\' can be treated as a mere real parameter in the range (0, ?). In the intervals (0, \'91 SOB.48\') and (2, ?) the system is frustrated. For \'D IND.F\' > 2 the model exhibits also an interesting burst phenomenon that is explained in the text. In the region [\'91 SOB.48\',2], the clusters obey exactly and in any scale the relation M ~ RgDF between the mass M and gyration radius Rg. These stable random fractals may be very useful in the study of dilute systems.

Subglacial processes that control the water pressure and flow determine the large-scale behavior of the overlying ice by regulating basal resistance. We implement a model in which a steady-state subglacial conduit system is surrounded by fully saturated porous media. We investigate branching in this system at fixed angles of 15 degrees, 30 degrees and 45 degrees to the direction of ice flow and further assess these systems by calculating the hydraulic potential gradient to determine conduit flow path. We solve our governing equations for porous media flow and allow ice infiltration of the pore space to occur at a critical effective stress N infiltration. For low values of N infiltration, ice infiltration of sediment allows these conduits to follow their original paths. Where insufficient ice infiltration occurs, the conduit path instead lies parallel to the direction of ice flow. Our results speak to the importance of incorporating small-scale processes into models of subglacial hydrologic networks.