[pt] O objetivo principal deste trabalho foi apresentar um modelo matemático que permitisse uma descrição local do processo de transferência de energia num escoamento saturado através de um meio poroso rígido. Este modelo teve como base o ponto de vista da Teoria de Misturas. Neste contexto, fluido e sólido (o meio poro) foram tratados como constituintes contínuos de uma mistura binária, coexistindo superpostos em todo o volume da mistura. Um importante aspecto levado em conta no presente trabalho foi permitir que os constituintes fluido e sólido possuíssem seus próprios campos de temperatura, de tal que a hipótese de equilíbrio térmico não foi suposta a priori. Problemas envolvendo convecção livre e forçada foram simulados numericamente. A transferência de calor por convecção forçada num canal poroso limitado por duas placas planas isotérmicas foi considerado em três casos diferentes. No primeiro, foram consideradas quatro condições de contorno na direção x. No segundo, a ausência de condição de contorno para o constituinte fluido na saída do canal, levou à utilização de um esquema iterativo, a única condição de contorno prescrita na direção x foi a temperatura do constituinte fluido na entrada do canal. Um trocador de calor de leito poroso num arranjo em contra-corrente também foi considerado. O trocador consistia de dois canais porosos, separados por uma parede impermeável sem resistência térmica. A convecção natural numa cavidade porosa foi também simulada, sendo considerado o efeito de alguns parâmetros adimensionais. Linhas de corrente e isotermas (para os dois constituintes) foram plotadas em alguns casos representativos. / [en] The main of tis work was to present a mathematical model, suitable for a local description of energy transfer process in a saturated flow thorough a rigid porous medium. This model was constructed based upon the Theory of Mixtures viewopoint. In this context, fluid and solid (the porous medium) were treated as continuous constituents of a binary mixture, coexisting supperposed in the whole volume of the mixture. One important aspect focused on the present work was that fluid and solid constituents were allowed to hav their own temperature fields, so that no thermal equilibrium between them was supposed a priori. Forced and free convection problems were numerically simulated. The forced convection heat transfer in a porous channel bounded by two isothermal flat plates was considered in three different cases.In the first one, four boundary conditions on x-direction were considered. In the second case, the absence of boundary condition for the fluid constituent at the channels exit, led to the utilization of an iterative procedure. Finally, in the third case, in which an iterative algorithm was presented, the fluid constituent inlet temparature was the only boundary condition prescribed on x-direction. A packed-bed heat exchanger in counter-flow arrangement was alo considered. The heat exchanger consisted of two porous channels, separated by impermeable wall without thermal resistence. The natural convection flow in a porous cavity was also simulated. The effect of some dimensionless parameters was considered. Stream lines and isotherms (for both constituents) were plotted for some representative cases.

Biofilms are microbial communities developing at the interface between two phases, usually solidliquid, where the micro-organisms are nested in a self-secreted polymer matrix. The biofilm mode of growth is predominant in nature (for e.g. the slimy matter forming on rocks at river bottoms, the viscous deposit in water pipes or even dental plaque) and confers a suitable environment for the development of the micro-organisms. This is particularly the case for porous media which provide favourable substrates given their significant surface to volume ratio. The multi-physical framework of biofilms in porous media is highly complex where the mechanical, chemical and biological aspects interacting at different scales are poorly understood and very partially controlled. An example is the feedback mechanism between flow, spatial distribution of the micro-organisms and the transport of nutrient (by diffusion and advection). Biofilms developing in porous media are a key process of many engineering applications, for example biofilters, soil bio-remediation, CO2 storage and medical issues like infections. Progress in this domain is substantially hindered by the limitations of experimental techniques in metrology and imaging in opaques structures. The main objective of this thesis is to propose robust and reproducible experimental methodologies for the investigation of biofilms in porous media. An experimental workbench under controlled physical and biological conditions is proposed along with a validated 3D imaging protocol based on X-ray micro-tomography (XR MT) using a novel contrast agent (barium sulfate and agarose gel) to quantify the spatial distribution of the biofilm. At first, the XR MT-based methodology is compared to a commonly used techniques for biofilm observation: one or multiple photon excitation fluorescence microscopy, here two-photon laser scanning microscopy (TPLSM). This comparison is performed on Pseudomonas Aeruginosa biofilms grown in transparent glass capillaries which allows for the use of both imaging modalities. Then, the study of uncertainty associated to different metrics namely volume, 3D surface area and thickness, is achieved via an imaging phantom and three different segmentation algorithms. The quantitative analysis show that the protocol enables a visualisation of the biofilm with an uncertainty of approximately 17% which is comparable to TPLSM (14%). The reproducibility and robustness of the XR MT-based methodology is demonstrated. The last step of this work is the achievement of a novel bioreactor elaborated by additive manufacturing and controlled by a high-performance micro-fluidic system. The experimental workbench that we have designed enables to monitor in real-time the evolution of transport properties (effective permeability), O2 concentrations and biofilm detachment by spectrophotometry, all under controlled hydrodynamical conditions. Our methodology allows to investigate the influence of biophysical parameters on the colonisation of the porous medium, for example, the influence of flow rate or nutrient concentration on the temporal development of the biofilm. In conclusion, the thesis work proposes a robust and reproducible experimental methodology for the controlled growth and 3D imaging of biofilms in porous media; while providing versatility in the control of the substrate’s micro-architecture as well as on the flow and biochemical culture conditions. To our knowledge, the scientific approach followed, along with the experimental apparatus, form the most complete methodology, at this time, for the study of biofilms in porous media.

[pt] Evidências experimentais demonstram o potencial da injeção de emulsões no aumento do fator de recuperação de óleo. O mecanismo responsável por esta melhor varredura do reservatório é a redução da mobilidade da água em regiões do reservatório já varridas por água. Esta redução pode ser associada ao bloqueio parcial de gargantas do meio poroso por gotas da fase dispersa da emulsão. A eficiência deste bloqueio parcial depende fortemente da geometria do poro, das características morfológicas e propriedades físicas da emulsão injetada. A utilização eficiente deste método de recuperação é limitada pela falta de entendimento fundamental de como emulsões escoam através de um meio poroso. Este trabalho tem como objetivo estudar o escoamento de emulsões através de gargantas de poros, que são modeladas fisicamente por micro- capilares com garganta nos experimentos desenvolvidos nesta pesquisa. Os resultados mostram como a permeabilidade varia com as propriedades e características morfológicas da emulsão e parâmetros geométricos do micro-capilar. Estes dados definem as propriedades necessárias de emulsões em função das características do reservatório para a obtenção do efeito de bloqueio parcial desejado e servem de entrada de dados para modelo de rede de capilares de escoamento de emulsões em meios porosos. / [en] Experimental evidences show the potential of emulsion injection in the improvement of oil recovery factor. The responsible mechanism for this better reservoir sweep is the water mobility reduction in regions already swept by water. This reduction can be associated with partial blockage of porous media throats by droplets of emulsion dispersed phase. The efficiency of this partial blockade strongly depends on pore geometry, morphological characteristics and physical properties of the injected emulsion. The efficient use of this recovery method is limited by the lack of fundamental understanding of how emulsions flow through a porous medium. This work aims to study the flow of emulsions through pores throats, which are physically modeled by constricted micro- capillaries in the experiments presented here. The results show how permeability varies with geometrical parameters of micro-capillaries, emulsion properties and morphological characteristics. These data define the necessary properties of emulsions according to the reservoir characteristics to obtain the desired blocking effect and serve as input data to capillaries network model of flow of emulsions in porous media.

[pt] Objetivo: Transporte de emulsões num meio poroso é relevante para diversas aplicações em sub-superfície. Muitos processos de recuperação melhorada de petróleo envolvem formação de emulsões. A modelagem do fluxo de emulsões num meio poroso é extremamente desafiante. As descrições disponíveis baseadas na viscosidade efetiva não são validas quando o tamanho das gotas é da mesma ordem de magnitude que o tamanho dos corpos de poros num meio poroso. Neste caso, intercepção e captura de gotas podem bloquear parcialmente a passagem dos poros e um modelo apropriado deve ser capaz de descrever estas mudanças locais de mobilidade. O modelo desenvolvido neste trabalho é baseado na relação vazão e queda de pressão do escoamento de emulsões através de capilares com constri ção. Um modelo de redes de capilares é construído com objetivo de obter parâmetros macroscópicos a partir do comportamento microscópico. Os resultados mostram a variação da permeabilidade com o número de capilaridade e propriedades da emulsão. Para baixas vazões, ou baixos números de capilaridade, as gotas maiores bloqueiam parcialmente os poros pequenos, resultando em uma redução da permeabilidade. Para altas vazões, o gradiente de pressão em cada capilar é alto o suficiente para forçar as gotas fluir através da constrição. Consequentemente, a permeabilidade aumenta com o número de capilaridade. Um programa, escrito na linguagem Fortran, é desenvolvido neste trabalho para simular o escoamento monofásico e bifásico de emulsões através de um meio poroso utilizando o modelo de rede de capilares. Na modelagem monofásica, os resultados apresentam uma boa concordância com as medidas experimentais feitas em mostras de arenito. Na modelagem bifásica, a comparação dos resultados entre a injeção da fase continua da emulsão e a injeção de emulsões (fase continua mais gotas) sobre uma rede inicialmente saturada com óleo mostra um aumento no fator de recuperação de óleo e uma frente de deslocamento mais uniforme no caso de injeçãode emulsão. / [en] Objective: Transport of emulsions in porous media is relevant to several subsurface applications. Many enhanced oil recovery processes involve emulsion formation and their flow in some form. Modeling the flow of emulsion in porous media is extremely challenging. The available descriptions based on effective viscosity are not valid when the drop size is of the same order of magnitude as the pore-throat size. In this case, drop straining and capturing may partially block the pore passage and an accurate model should be able to describe this local changes on mobility. The model developed in this work is based on the flow rate-pressure drop relationship of emulsion flow through constricted capillaries. A capillary network model is constructed in order to obtain macroscopic parameters from upscaling of the microscopic behavior. The results show how the permeability changes with Darcy velocity and emulsion properties. At low flow rates, the large drops partially block the smallest pores, leading to a low permeability. At high flow rates, the pressure gradient in each capillary is strong enough to force the drops to flow through the constrictions. Consequently, the permeability rises with capillary number. A program, written in Fortram language, based on network model is developed in this work to simulate the single phase and two phase flow of emulsion through a porous medium. In the single phase model, the results show good agreement with experimental measurements on samples of sandstone. In the two phase model, the comparison of results between the injection of the continuous phase of emulsion and the injection of emulsions (with drops) on a network initially saturated with oil shows an increase in the oil recovery factor and a more uniform displacement front in the case of emulsion injection.

SILVA, Jorge Roberto Pereira da. Invasões múltiplas em meios porosos desordenados. 2013. 73 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2013. / Submitted by francisco lima (admir@ufc.br) on 2014-03-20T13:24:31Z No. of bitstreams: 1 2013_dis_jrpdasilva.pdf: 6783022 bytes, checksum: 56a0994d2bd89d4081cf4955dce1d3dc (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2014-05-16T21:51:28Z (GMT) No. of bitstreams: 1 2013_dis_jrpdasilva.pdf: 6783022 bytes, checksum: 56a0994d2bd89d4081cf4955dce1d3dc (MD5) / Made available in DSpace on 2014-05-16T21:51:28Z (GMT). No. of bitstreams: 1 2013_dis_jrpdasilva.pdf: 6783022 bytes, checksum: 56a0994d2bd89d4081cf4955dce1d3dc (MD5) Previous issue date: 2013 / In this dissertation, we investigate by means of numerical simulations geometrical and transport properties related with the invasion phenomena through disordered porous media in a very slow invasion regime, using two and three dimensions porous medias. Here, the porous media is modeling by means of a random structure, where each pore is represented by a random number comes from a uniform distribution. We assume that the invasion process occurs in the limit of very low viscous force, which means that the invasion process is controlled by capillary force. In this limit the invasion percolation model without trap is suitable. The new aspect incorporated here, consists basically of a multiple invasion process, where after the first invasion takes place only part of the structure of the porous, that was invaded previous, can be invaded again. We study, how the multiple invasion changes the fractal dimension of the invaded cluster. Estimated values for the fractal dimension of the invaded region reveal that the critical exponents vary as a function of the generation number G, i.e., where the number of times the invasion takes place. On base in numerical datas, we show the averaged mass M of the invaded region decreases with a power law as a function of G, M ∼ G{−β} , where the exponents β ≈ 0.59 (2D) and β ≈ 0.73 (3D). We also investigated, how the fractal dimension changes as a function of G, find that the fractal dimension of the invaded cluster changes from df = 1.89 ± 0.02 to ds = 1.22 ± 0.02 and df = 2.52 ± 0.02 to ds = 1.46 ± 0.02 for (2D) and (3D), respectively. These results confirm that the multiple invasion process follows a continuous transition from one universality class (nontrapping invasion percolation) to another (optimal path), furthermore these change are continuos for both dimensionality. Another aspect investigated, was the avalanche distribution in the invasion process. We analyzed how the distribution of avalanche changes as function of G, more precisely, how the multiple invasion process changes the exponent τ of the power law distribution. Regardless the values, we find that the behaviour of the exponents τ looks like the same for both dimensions studied. The exponents τ , initially change in a very slow way until reach a region, of certain value of G which depend on the dimension, they start to decrease in a deep way until reach the saturation value. The saturation value is close, for (2D), to one-dimension cas / Nesta dissertação, investigamos por meio de simulação computacional propriedades geométricas e de transportes relacionadas ao fenômeno de invasão em meios porosos desordenados no regime de invasão muito lento em sistemas bidimensionais e tridimensionais. O meio poroso considerado aqui é representado por meio de uma estrutura desordenada onde a cada poro que compõe este meio se associa um número aleatório obtido a partir de uma distribuição uniforme. Considerando o regime lento de invasão, onde as forças capilares dominam o escoamento em relação as forças viscosas, utilizando para a dinâmica de invasão o modelo de percolação invasiva sem aprisionamento. Introduzimos um variante no modelo de percolação invasiva, assumindo o aspecto de múltiplas invasões, onde a cada nova invasão apenas parte do substrato utilizado na invasão anterior pode ser invadido novamente. Em uma primeira parte, estudamos como o processo de múltipla invasão altera as características do agregado invadido. Valores estimados para a dimensão fractal da região invadida revelam que os expoentes críticos variam em função do número de geração G, isto é, o número de vezes que o processo de invasão foi repetido. Com base em dados numéricos, mostramos que a massa média do agregado invadido decresce na forma de uma lei de potência como função de G, M ~ G^{-β}, com o expoente β = 0.59 (2D) e 0.73 (3D). Investigamos como a dimensão fractal do agregado invadido varia em função dos repetitivos processo de invasão, mostrando que as mesmas variam de df = 1.89 ± 0.02 até ds = 1.22 ± 0.02 para o caso (2D) e df = 2.52 ± 0.02 até ds = 1.46 ± 0.02 para o caso (3D). Os resultados confirmam que o processo de múltiplas invasões segue uma transição continua entre as classes de universalidade do modelo de percolação invasiva sem aprisionamento e ótimo caminho, sendo este comportamento observado em duas e três dimensões. Um outro aspecto investigado nessa dissertação, foi o fenômeno de avalanche que ocorre durante o processo de invasão. Investigamos como a distribuição de tamanhos de avalanche, que se comporta na forma de uma lei de potência P(S, L) ~ S^{-τ} , altera-se em função das múltiplas invasões. Mais precisamente, calculamos como o expoente que governa o comportamento das avalanches se altera em função do número de geração G. Verificamos que este comportamento do expoente em função de G é semelhante para duas e três dimensões, apresentando uma região de mudança suave seguida por uma mudança mais acentuada até atingir um limite de saturação, onde o sistema se comporta de maneira parecida com o caso unidimensional.

Os meios rochosos são compostos por blocos de rochas intactos e por descontinuidades. As descontinuidades representam zonas de baixa rigidez, onde as propriedades do maciço estão degradadas, reduzindo a resistência do mesmo. Elas também constituem caminhos para o fluxo de fluidos no interior da rocha. O estudo do comportamento hidráulico-mecânico acoplado existente nos meios porosos é realizado pela poroelasticidade, que relaciona os campos de tensões e deformações no maciço, gerados pela deformação mecânica do esqueleto e pela ação do fluido pressurizado nos poros. Uma abordagem micromecânica permite estender os resultados clássicos da teoria de poroelasticidade para o caso de juntas que são capazes de transferir esforços ao longo de suas faces. Neste contexto, o meio rochoso heterogêneo é substituído por um meio homogêneo equivalente, pela aplicação do conceito de mudança de escala da teoria da homogeneização, que possibilita a determinação das propriedades efetivas do maciço. Demonstra-se que, para certas distribuições geométricas das juntas, é possível obter soluções analíticas para o comportamento do maciço pela aplicação de estimativas como, por exemplo, o esquema Mori-Tanaka, onde as juntas são modeladas como esferoides. Um modelo numérico via método dos elementos finitos, que considera explicitamente as juntas, é usado para comparar os resultados obtidos. / Rock media are composed by blocks of intact rock and discontinuities. Discontinuities represent zones of low stiffness, where the mass properties of the rock are degraded, with reduced resistance. They also provide ways for fluid flow within the rock. The study of coupled mechanical-hydraulic behavior existing in porous media is perfomed by poroelasticity, which relates the stress and strain fields in a rock mass generated by the mechanical deformation of the skeleton and the action of pressurized fluid in the pores. A Micromechanics approach allows to extend the classical results of the theory of poroelasticity to the case of joints that are able to transfer stresses along their faces. In this context, a heterogeneous rock media is replaced by an equivalent homogeneous medium by applying the micro-macro approach from the theory of homogenization, which allows the determination of the effective properties of the rock mass. It is shown that, for some geometric distributions of the joints, it is possible to obtain analytical solutions for the rock behavior by applying estimates methods as the Mori-Tanaka scheme, where the joints are modeled as oblong spheroids. A numerical model via the finite element method, where the joints are considering explicitly, is used in order to compare the results.

abstract: This study was designed to provide insight into microbial transport kinetics which might be applied to bioremediation technology development and prevention of groundwater susceptibility to pathogen contamination. Several pilot-scale experiments were conducted in a saturated, 2 dimensional, packed porous media tank to investigate the transport of Escherichia coli bacteria, P22 bacteriophage, and a visual tracer and draw comparisons and/or conclusions. A constructed tank was packed with an approximate 3,700 cubic inches (in3) of a fine grained, homogeneous, chemically inert sand which allowed for a controlled system. Sampling ports were located at 5, 15, 25, and 25 vertical inches from the base of the 39 inch saturated zone and were used to assess the transport of the selected microorganisms. Approximately 105 cells of E. coli or P22 were injected into the tank and allowed to move through the media at approximately 10.02 inches per day. Samples were collected intermittently after injection based off of an estimated sampling schedule established from the visual tracer. The results suggest that bacteriophages pass through soil faster and with greater recovery than bacteria. P22 in the tank reservoir experienced approximately 1 log reduction after 36 hours. After 85 hours, P22 was still detected in the reservoir after experiencing a 2 log reduction from the start of the experiment. E. coli either did not reach the outlet or died before sampling, while P22 was able to be recovered. Bacterial breakthrough curves were produced for the microbial indicators and illustrate the peak concentrations found for each sampling port. For E. coli, concentrations at the 5 inch port peaked at a maximum of 5170 CFU/mL, and eventually at the 25 inch port at a maximum of 90 CFU/mL. It is presumed that E. coli might have experienced significant filtration, straining and attachment, while P22 might have experienced little adsorption and instead was transported rapidly in long distances and was able to survive for the duration of the experiment. / Dissertation/Thesis / Masters Thesis Civil, Environmental and Sustainable Engineering 2017

Os meios rochosos são compostos por blocos de rochas intactos e por descontinuidades. As descontinuidades representam zonas de baixa rigidez, onde as propriedades do maciço estão degradadas, reduzindo a resistência do mesmo. Elas também constituem caminhos para o fluxo de fluidos no interior da rocha. O estudo do comportamento hidráulico-mecânico acoplado existente nos meios porosos é realizado pela poroelasticidade, que relaciona os campos de tensões e deformações no maciço, gerados pela deformação mecânica do esqueleto e pela ação do fluido pressurizado nos poros. Uma abordagem micromecânica permite estender os resultados clássicos da teoria de poroelasticidade para o caso de juntas que são capazes de transferir esforços ao longo de suas faces. Neste contexto, o meio rochoso heterogêneo é substituído por um meio homogêneo equivalente, pela aplicação do conceito de mudança de escala da teoria da homogeneização, que possibilita a determinação das propriedades efetivas do maciço. Demonstra-se que, para certas distribuições geométricas das juntas, é possível obter soluções analíticas para o comportamento do maciço pela aplicação de estimativas como, por exemplo, o esquema Mori-Tanaka, onde as juntas são modeladas como esferoides. Um modelo numérico via método dos elementos finitos, que considera explicitamente as juntas, é usado para comparar os resultados obtidos. / Rock media are composed by blocks of intact rock and discontinuities. Discontinuities represent zones of low stiffness, where the mass properties of the rock are degraded, with reduced resistance. They also provide ways for fluid flow within the rock. The study of coupled mechanical-hydraulic behavior existing in porous media is perfomed by poroelasticity, which relates the stress and strain fields in a rock mass generated by the mechanical deformation of the skeleton and the action of pressurized fluid in the pores. A Micromechanics approach allows to extend the classical results of the theory of poroelasticity to the case of joints that are able to transfer stresses along their faces. In this context, a heterogeneous rock media is replaced by an equivalent homogeneous medium by applying the micro-macro approach from the theory of homogenization, which allows the determination of the effective properties of the rock mass. It is shown that, for some geometric distributions of the joints, it is possible to obtain analytical solutions for the rock behavior by applying estimates methods as the Mori-Tanaka scheme, where the joints are modeled as oblong spheroids. A numerical model via the finite element method, where the joints are considering explicitly, is used in order to compare the results.

L'objectif industriel de cette thèse est de proposer un modèle de transfert radiatif dans un réacteur de reformage de méthane. Dans ce procédé, des gaz réactifs circulent dans le réacteur tubulaire rempli de pastilles catalytiques.L'empilement de pastilles constitue un milieu poreux où le rapport de la taille caractéristique des pores sur la dimension radiale du réacteur est grand (1=10 à 1=5). De plus, les très forts gradients de porosité dus à l'organisation des pastilles au voisinage des parois ont un impact important sur les transferts thermiques et en particulier les transferts radiatifs.L'objectif scientifique est de développer et valider un modèle de transfert radiatif applicable à des milieux poreux fortement hétérogènes et anisotropes ne suivant pas la loi de Beer. Dans un premier temps, les propriétés radiatives du milieu homogénéisé équivalent au milieu poreux réel sont complètement déterminées par la fonction de distribution cumulée d'extinction Gext, la fonction de phase p et la porosité Π. Ces fonctions, précédemment introduites pour des milieux homogènes éventuellement anisotropes, sont calculées avec une grande précision par une méthode de Monte Carlo. Elles ont été généralisées ici à des milieux hétérogènes. Il a été montré à partir d'un nouveau critère de validité adapté aux milieux hétérogènes que le milieu homogénéisé équivalent ne suit pas la loi de Beer, en particulier au voisinage des parois.De ce fait, l'équation de transfert radiatif généralisée (GRTE) doit prendre en compte l'émission par un milieu non Beerien fortement hétérogène même à la limite optiquement mince : un coefficient d'absorption n'y a pas de sens physique et des corrélations entre émission et transmission apparaissent dues au caractère non Beerien. Le principe de réciprocité et les propriétés des fonctions d'extinction Gext ont permis d'exprimer rigoureusement les termes sources d'émission dans ce type de milieux fortement hétérogènes non Beeriens. Un facteur de corrélation émission-transmission a été introduit. La GRTE, sous forme intégrale, a été résolue par une méthode de transfert de Monte Carlo. Le modèle complet a été appliqué après validation aux réacteurs de reformage de méthane de Air Liquide. / The industrial goal of this work is to propose a radiative transfer model in a tubular reactor of steam methane reforming. During the reforming process, reactive gases are injected in the tubular reactor filled with catalytic pellets. The packed bed of pellets forms a porous medium, and a particular feature of it is that the characteristic pore size is large compared to the reactor inner dimension. In addition, the organization of the pellets in the near-wall region results in important porosity gradients which have a significant effect on the heat transfer, and more specifically on the radiative transfer.The scientific goal is to develop and validate a radiative transfer model applicable to strongly nonhomogeneous, anisotropic and non Beerian porous media.First, the radiative properties of the homogenised phase equivalent to the real porous medium are completely determined by the cumulated distribution function of extinction Gext, the phase function p, and the local porosity Π. These functions, previously introduced for statistically homogeneous and anisotropic porous media, are calculated very accurately by a Monte Carlo method. They have been extended to statistically non-homogeneous porous media. Similarly, the expression of the validity criterion of the Beer law is extended to statistically anisotropic and non-homogeneous porous media : it is proven that for the considered porous media the Beer law is not valid in the homogenised phase, in particular in the vicinity of the walls. As a result, the Generalized Radiative Transfer Equation (GRTE) is needed and the emission source terms must be determined in a strongly nonhomogeneous non Beerian even at the optically thin limit : an absorption coefficient doesn't have any physical meaning and correlations between emission and transmission appear due to the non-Beerian behavior.The reciprocity principle and the properties of the extinction functions Gext allow the emission source terms in this kind of strongly non-homogeneous and non-Beerian media to be accurately determined. A correlation factor emission-transmission has been introduced. The GRTE has been solved by a Monte Carlo method.The complete model is applied, after validation, to the steam methane reformers in use by Air Liquide.

Ce travail porte sur l’étude du transfert de chaleur entre un milieu poreux et un milieu libre en utilisant une approche multi-échelle. Dans un premier temps, nous dérivons les conditions limites à imposer à une interface libre-poreux dans le cas des transferts de chaleur à l’équilibre thermique local puis dans le cas du déséquilibre thermique local. Pour les transferts de chaleur turbulent, une simulation numérique directe est réalisée afin d’apporter une meilleur compréhension de la physique existant à l’interface libre poreux. Puis, nous déterminons un modèle turbulent avec des conditions de saut. Ces études répondent à des questions fondamentales liées à la compréhension physique des conditions de saut, des valeurs des paramètres des sauts et de la position de l’interface dans le cadre des transferts de chaleur. / This work deals with the study of heat transfer between a porous medium and a free medium, using multi scale approaches. First, we derive the boundary conditions that must be applied at a free-porous interface for laminar heat transfer at local thermal equilibrium and, then, at local thermal non-equilibrium. For turbulent heat transfer, a direct numerical simulation is performed supplying a better understanding of the physic at the free-porous interface. Then, we determine a turbulent model with associated jump conditions. These studies answer fundamental questions regarding the physical meaning of the jump conditions, the values of the jump parameters and the location of the interface for heat transfer.