L’utilisation de fluides non vaporisables tels que les gaz pour tremper différentes pièces d’acier rend possible, avec les outils numériques actuels, la simulation de l’ensemble des phénomènes physiques mis en jeu dans ce traitement thermique et ainsi de prédire les comportements thermique, métallurgique et mécanique des pièces. Plusieurs auteurs s’intéressent à la construction de ce type de modèles dont les enjeux sont de promouvoir l’utilisation de la trempe gazeuse haute pression, en cherchant à remplacer les trempes à l’huile plus polluantes et/ou à maîtriser les déformations pendant ou après la trempe. Lors de notre travail, un modèle décrivant ces phénomènes physiques, de l’écoulement gazeux aux déformations, et leurs couplages a été construit par étapes en couplant les deux codes de calcul commerciaux Fluent et Sysweld. Les résultats de simulations ont ensuite été confrontés à des mesures de vitesses d’écoulements de gaz (par PIV), de températures et de déformations in situ (détection de contours). Malgré quelques écarts dont les origines ont été analysées, la comparaison a révélé une très bonne concordance des résultats de calculs et expérimentaux, validant ainsi la démarche de calcul. Le modèle pourrait maintenant être testé pour des refroidissements plus rapides que ceux considérés mais son utilisation pour des applications industrielles (pièces de géométrie plus complexe, refroidissement de charges entières, …) peut d’ores et déjà être envisagée avec confiance / The use of non vaporizable fluids such as gas to quench steel bodies makes the simulation of all the coupled physical phenomena involved in this heat treatment possible thanks to current numerical simulation tools. It gives access to the prediction of thermal, metallurgical and mechanical behaviour of steel pieces during quenching operation. Several authors have tried and build such kind of models in order to promote gas quenching use either by trying to replace less environmental friendly oil treatments or by trying to control distortions during or after quenching. In our work a model describing the physical coupled phenomena, from gas flow to distortion has been built step by step by coupling both commercial numerical codes Fluent and Sysweld. Simulation results have then been compared to gas flow velocities measurements (by PIV), temperature measurements and in situ distortions measurements (contour’s detection method). This confrontation revealed a very good agreement between calculated and experimental data despite some slight differences, which have been analysed in detail. This validated the calculation method used in the model. One of the perspectives of this work could be the validation of the model for higher quenching rate. However, some industrial applications (tridimensional more complex bodies quenching simulation, quenching of full loads, …) can be run from now on with confidence

Dans cette thèse, nous avons étudié la simulation numérique des phénomènes d'interaction fluide-structure entre un fluide compressible et une structure déformable. En particulier, nous nous sommes intéressés au couplage par une approche partitionnée entre une méthode de Volumes Finis pour résoudre les équations de la mécanique des fluides compressibles et une méthode d'Eléments discrets pour le solide, capable de prendre en compte la fissuration. La revue des méthodes existantes de domaines fictifs ainsi que des algorithmes partitionnés couramment utilisés pour le couplage conduit à choisir une méthode de frontières immergées conservative et un schéma de couplage explicite. Il est établi que la méthode d'Eléments Discrets utilisée permet de retrouver le comportement macroscopique du matériau et que le schéma symplectique employé assure la préservation de l'énergie du solide. Puis nous avons développé un algorithme de couplage explicite entre un fluide compressible non-visqueux et un solide indéformable. Nous avons montré des propriétés de conservation exacte de masse, de quantité de mouvement et d'énergie du système ainsi que de consistance du schéma de couplage. Cet algorithme a été étendu au couplage avec un solide déformable, sous la forme d'un schéma semi-implicite. Cette méthode a été appliquée à l'étude de problèmes d'écoulements non-visqueux autour de structures mobiles : les comparaisons avec des résultats numériques et expérimentaux existants démontrent la très bonne précision de notre méthode / This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an undeformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi-implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method

The current demands on Swedish steel industry to produce low quantity batches of specialized products requires research on steel casting processes. There are several physical processes that need be taken into account for this problem to be viewed in full light such as thermal-processes, solidification and fluid dynamics. This work focuses on the fluid-dynamics part; more specifically, the dependence of flow quality within the caster on nozzle and mould geometry. The simulations are carried out using a scale-resolving method, in specific LES (Large Eddy Simulation) which is coupled with a DPM (Discrete Phase Model) to model Argon behaviour. The results of these simulations are presented and validated against physical experiment and data from industrial trials. Conclusions are drawn regarding optimal nozzle types in respect to different mould geometries. The mould eigenfrequencies are shown to exhibit a connection with the casting velocity. This results in so called sweet spots in casting velocity where flow irregularities due to sloshing is minimal. It is shown that the mountain type nozzle is preferable for smaller geometries whilst comparatively larger geometries benefit from a cup type. / FLOWFLEX CC

Pour les structures de génie civil avec un rôle d’étanchéité, lors d’un accident grave, la perméabilité du béton est une question clé. Les mesures de perméabilités actuelles ne permettent d'avoir que des grandeurs moyennes (structurelles) qui ne conviennent pas pour des éprouvettes hétérogènes (fissures et/ou armatures). La compréhension des détails de l'écoulement des fluides est cruciale en raison des implications sur les voies préférentielles (interface acier/béton, fissures, etc.). Le but de cette thèse est de proposer une nouvelle méthodologie et de tester un nouveau dispositif expérimental par imagerie neutronique à la ligne de faisceaux D50 à l’Institut Laue Langevin à Grenoble. Le test consiste à injecter de l’eau normale (H2O), sous haute pression, dans un échantillon de béton coulé et saturé en eau lourde (D2O), afin de suivre la progression d’un front d’eau dans le temps par différence d’atténuation entre ces deux eaux. Une campagne expérimentale a été lancée sur des éprouvettes de béton sous différentes configurations (béton sain, béton fissuré et béton avec une armature) et des mesures de perméabilité locale dans les singularités (zone fissurée, interface armature-béton, etc.) ont été faites. Les essais ont montré que les mesures classiques de perméabilité sont sous-estimées et les écoulements dans le béton sont contrôlés par les défauts. / For civil engineering structures, especially containment buildings during a severe accident, the permeability of concrete is a key issue. Current permeability measurements allow only average (structural) magnitudes, which are not suitable for heterogeneous samples (cracks and/or reinforcements). Understanding the details of fluid flow is crucial because of the implications of preferred pathways (steel/concrete interface, cracks, etc.). The aim of this thesis is to propose a new methodology, and to test a new experimental setup, using neutron imaging at the D50 beam line at the Institute Laue Langevin in Grenoble to measure flow directly. The test consists of injecting normal water (H2O) under high pressure, into a concrete sample casted and saturated with heavy water (D2O), in order to follow the evolution of a waterfront over time by difference of attenuation between these two waters. An experimental campaign was launched on concrete specimens in different configurations (proper concrete, cracked concrete and concrete with reinforcement) and measurements of local permeability in singularities (cracked zone, reinforcement-concrete interface, etc.) were done. Tests have shown that classical permeability measurements are underestimated and flows in concrete are controlled by defects.

[pt] 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. / [en] 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.

Desde a década de 70, há um crescente interesse em simulações em computador de fenômenos físicos visto sua diversidade de aplicações. Dentre esses fenômenos, podem ser destacados a interação entre corpos rígidos, elásticos, plásticos, quebráveis e também fluidos. Neste trabalho realizamos a simulação de um desses fenômenos, o escoamento de fluidos, por um método conhecido como Smoothed Particles Hydrodynamics, uma abordagem lagrangeana baseada em partículas para resolução das equações que modelam o movimento do fluido. Várias são as vantagens de métodos lagrangeanos usando partículas sobre os que usam malhas, por exemplo, as propriedades do material transladam com as partículas como função do tempo, além da capacidade de lidar com grandes deformações. Dentre as desvantagem, destacamos uma deficiência relacionada ao ganho de energia total do sistema e estabilidade das partículas. Para lidar com isso, utilizamos uma abordagem baseada na lei da conservação da energia: em um sistema isolado a energia total se mantém constante e ela não pode ser criada ou destruida. Dessa forma, alterando o integrador temporal nós restringimos o aumento arbitrário de energia, tornando a simulação mais tolerante às condições iniciais / Since the late 70s, there is a growing interest in physically-based simulations due to its increasing range of application. Among these simulations, we may highlight interaction between rigid, elastic, plastic and breakable bodies and also fluids. In this work, one of these phenomena, fluid flow, is simulated using a technique known as Smoothed Particle Hydrodynamics, a meshless lagrangean method that solves the equations of the flow behavior of fluids. There are several advantages of meshless methods over mesh-based methods, for instance, the material properties are translated along with particles as a function of time and the ability to handle arbitrary deformations. Among the disadvantages, we may highlight a problem related to the gain of energy by the system and stability issues. In order to handle this, we used an approach based on the law of conservation of energy: in an isolated system the total energy remains constant and cannot be created or destroyed. Based on this, we used a technique that bounds the total energy and the simulation becomes less sensitive to initial conditions

A variedade dos meios porosos é evidente na pluralidade de seus usos. Não por acaso, a avaliação dos escoamentos que neles sucedem é comum a diversos campos de conhecimento. Avanços nas técnicas experimentais e numéricas têm sido observados recentemente. No entanto, progressos posteriores no assunto encontram-se condicionados à evolução da contraparte teórica. Em virtude disso, no presente estudo, foi desenvolvido um modelo analítico para o escoamento em meios porosos. Este modelo se baseia no princípio da entropia máxima (PEM), advindo da teoria da informação. Por meio dele, foi possível a determinação estatística das velocidades locais de um fluido e puderam ser deduzidas expressões embasadas nas Equações de Navier-Stokes, tais quais as Leis de Darcy, de Forchheimer e a Equação de Darcy-Weisbach. Ele permitiu, também, a atribuição de significados físicos mais precisos para grandezas intervenientes no escoamento em meios porosos, como o número de Reynolds e o coeficiente de permeabilidade intrínseca. Dele emergiu, ainda, o parâmetro de entropia, modelador da distribuição de velocidades, capaz de delimitar os regimes de escoamento e que viabiliza a conexão entre a micro e a macroescala do problema. Verificou-se uma grande aderência do modelo proposto a resultados obtidos em escala de bancada, piloto e real, constantes na literatura científica. Por essas razões e pelo fato de o modelo proposto ter como base um número bastante reduzido de premissas, conclui-se que ele é geral e robusto, sendo aplicável às mais distintas áreas que requeiram uma descrição analítica do escoamento em meios porosos. / Given the wide-ranging uses of porous media, it is no coincidence that several distinct fields of knowledge require analysis and evaluation of flows occurring therein. Recent advances in this area have included experimental and numerical techniques. However, further developments in the subject are conditioned to (and held back by) the evolution in its theoretical counterpart. As a result, this study proposes a new analytical model for the flow through porous media, based on information theory\'s principle of maximum entropy (POME). The proposed model allows for the statistical determination of a fluid\'s local velocities. Further, it also permits the deduction of expressions based on the Navier-Stokes Equations, such as Darcy\'s and Forchheimer\'s Laws and the Darcy-Weisbach Equation. It bestows more precise physical meanings to the quantities typically involved in the flow through porous media, such as the Reynolds number and the intrinsic permeability coefficient, as well. Furthermore, the proposed model introduces an entropy parameter, which represents the statistical distribution of velocities and is capable of delimiting flow regimes. This parameter also permits a clear connection between both micro and macro scales of the problem. The proposed model showed great adherence to bench, pilot and real scale results found in scientific literature. For these reasons, and due to its reduced number of premises, the proposed model is concluded to be general and robust, and that it can be applied to countless areas in which an analytical description of flow through porous media is required.

L’hydrodynamique et la probabilité de minéralisation (R²AI) autour des intrusions magmatiques ont été étudiées par modélisation numérique couplant transfert de chaleur et circulation de fluide. L’objectif principal de ce travail est de tester la nature du lien génétique entre l’intrusion et le processus de minéralisation. La première série de résultats s’appuie sur une comparaison avec des exemples naturels de gisements bien connus : i) L’hydrodynamique et la localisation des zones probables de minéralisation sont fortement dépendantes de la profondeur de mise en place du pluton. Au-dessus de 4.5km de profondeur de mise en place, le seuil de perméabilité de 10-16 m² est atteint et les cellules convectives peuvent créer des zones de décharge additionnelles où des minéralisations peuvent avoir lieu ; ii) Pour toutes les profondeurs d’emplacement, la zone en dessous du pluton n'est pas favorable à la précipitation minérale ; iii) Les apophyses focalisent les fluides convectifs et les zones de minéralisation autour d’elles ; iv) La phase de refroidissement n'est pas la phase majeure de convection. La zone advective principale et celle de haute favorabilité peuvent se produire avant et pendant la phase la plus chaude d’emplacement, avant que le magma ne cristallise complètement; v) Les détachements sont capables de fortement modifier et de re-localiser les flux convectifs déclenchés par une intrusion syn-tectonique; vi) Les conditions physiques favorables à la minéraliser sont produites pendant une durée courte autour de la phase la plus chaude de l'intrusion. Même si les arguments chimiques sont absents, la circulation de fluide (induite par la mise en place de magma) joue un rôle principal dans la genèse des gisements d'or associés aux intrusions. De plus, la formation de ce type de gisement est favorisée par l'occurrence d'une auréole thermique fracturée autour de l'intrusion. La seconde série de résultats concerne l’étude du cas naturel de la minéralisation W-Au de Tighza (Jebel Aouam) au Maroc Central. Une campagne d’acquisition de données gravimétriques, l’inversion données et l’utilisation de logiciel 3D, ont permis d’obtenir la géométrie 3D complexe du pluton de Tighza. Les résultats sont les suivants : i) la zone probable de la minéralisation apparaît au début de la mise en place du magma dans la zone perméable (veine W1) et s'étend pour remplir W1 et couvrir la région autour du pluton pendant la phase la plus chaude de mise en place; ii) lors du refroidissement, la zone probable est réduite et limitée à la zone perméable (W1) pendant 0,6 Ma; iii) L’application de la température de fermeture isotopique de la muscovite et de la biotite avec la distribution du R²AI montre que les âges de refroidissement entre la minéralisation au niveau de la veine W1 et l'intrusion ne sont pas séparés de plus de 0,10 Ma. Ceci est confirmé par la datation absolue de la minéralisation de Tighza et permet de discuter la fiabilité des âges obtenus pour la minéralisation dans la veine W1. / Coupled hydro-thermal numerical modeling has been used to simulate the hydrothermal fluid flow regime and the mineralization probability (R²AI) around plutons. The main objective behind this work is to test the nature of the genetic link between mineralization and intrusions. The first series of results comes from comparison with well-constrained mineral deposits: i) Fluid circulation and mineralization patterns are strongly dependent of the emplacement depth of the pluton. Deep seated plutons emplaced below 10 km do not induce an advective heat dissipation. For emplacement depth less than 4.5 km, the permeability threshold of 10-16 m2 is reached and second order convection cells may create additional discharge zones where mineralization are expected; ii) For all emplacement depths, the pluton floor zone is not favorable for mineral deposition; iii) The apexes strongly modified the fluid flow patterns by focusing convective fluids and mineralization zones around them; iv) The cooling phase is not the main phase of convection for large pluton often associated with long-lived magma emplacement. Major advective heat dissipation and mineral deposition zone may also occur sometime before and during the hottest phase of emplacement; v) Extensional detachments faults are able to delocalize and strongly modify classical fluid flow patterns induced by coeval intrusion; vi) Favorable physical conditions for mineral deposition are encountered around middle crust pluton, during a short time span bracketing the hottest phase of intrusion. We conclude that, even if chemical arguments are absent, fluid circulation induced by granite emplacement plays a key role in the genesis of granite-related Au deposits. Moreover, formation of this type of deposit is promoted and controlled by the occurrence of a fractured thermal aureole around the intrusion. The second series of results deals with the W-Au granite related Tighza deposits (Jebel Aouam, Morocco). Based on gravimetric data, inversion, and 3D modeling software, we were able to construct the most probable complex geometry of the Tighza pluton. The 3D geometries of the pluton and major fractures (W1 vein) were injected in the hydro-thermal modeling procedure. The results are: i) the probable zone of mineralization appears at the beginning of magma emplacement within the permeable zone (W1 vein) and extends to fill up W1 and covers the area around pluton at the hottest phase; ii) During the cooling phase, the story was reversed; the probable zone was reduced and restricted in the permeable zone (W1) during 0.6 Myr of cooling; iii) Application of isotopic closure temperature of muscovite and biotite coupled with R²AI distribution shows that the cooling ages between mineralization in W1 veins and the intrusion are not separated by more than 0.10 Myr. This is confirmed by the absolute dating obtained for Tighza Au mineralization and allows discussing the significance of older ages obtained for the mineralization in W1 veins.

A pectina é uma substância polissacarídica originada de plantas, que pode ser utilizada como agente gelificante, estabilizante de compotas, em bebidas láticas e iogurtes. A gelatina, proteína, nesse caso de origem bovina, é principalmente utilizada como agente gelificante, pois, forma hidrogéis por resfriamento. O processo de irradiação por radiação gama pode causar uma variedade de modificações nas macromoléculas algumas de aplicação industrial, como é o caso de reticulação. A resposta dinâmica de materiais viscoelásticos pode ser usada para dar informação sobre o aspecto estrutural de um sistema a nível molecular. No presente trabalho, pectina com diferentes graus de metoxilação, gelatina e a mistura de ambas foram empregados para estudar a sensibilidade à radiação por meio de medidas de viscosidade. Amostras de soluções de pectina de alto teor de metoxilação (ATM) 1%, pectina de baixo teor (BTM) 1%, gelatina 0,5%,1% e 2%, e a mistura de ambas a 1% e 2% foram irradiadas com raios gama em doses de até 15kGy e taxa de dose em torno de 2kGy/h. Após irradiação, a viscosidade foi medida dentro de um período de 48 h. A viscosidade da pectina ATM e BTM diminuiu drasticamente com o aumento da dose de radiação. A gelatina, entretanto, apresentou grande resistência à radiação. Na mistura de ambas, houve predomínio do comportamento esperado para a pectina. / Pectin is a polysaccharide substance of plant origin that may be used as gelling agent, stabilizer in jams, in yogurt drinks and lactic acid beverages. Gelatin, a protein from bovine origin, in this case, is mainly used as gelling agent due to hydrogel formation during cooling. The 60 Co-irradiation process may cause various modifications in macromolecules, some with industrial application, as reticulation. The dynamic response of viscoelastic materials can be used in order to give information about the structural aspect of a system at molecular level. In the present work samples of pectin with different degree of methoxylation, gelatin and the mixture of both were employed to study the radiation sensitivity by means of viscosity measurements. Solutions prepared with citric pectin with high methoxylation content (ATM) 1 por cent, pectin with low content (BTM) 1 por cent, gelatin 0.5 por cent, 1 por cent and 2 por cent, and the mixture 1 por cent and 2 por cent were irradiated with gamma rays at different doses, up to 15 kGy with dose rate about 2 kGy/h. After irradiation the viscosity was measured within a period of 48 h. The viscosity of ATM and BTM pectin solutions decreased sharply with the radiation dose. However, the gelatin sample presented a great radiation resistance. When pectin and gelatin solutions were mixed a predominance of pectin behavior was found.

A variedade dos meios porosos é evidente na pluralidade de seus usos. Não por acaso, a avaliação dos escoamentos que neles sucedem é comum a diversos campos de conhecimento. Avanços nas técnicas experimentais e numéricas têm sido observados recentemente. No entanto, progressos posteriores no assunto encontram-se condicionados à evolução da contraparte teórica. Em virtude disso, no presente estudo, foi desenvolvido um modelo analítico para o escoamento em meios porosos. Este modelo se baseia no princípio da entropia máxima (PEM), advindo da teoria da informação. Por meio dele, foi possível a determinação estatística das velocidades locais de um fluido e puderam ser deduzidas expressões embasadas nas Equações de Navier-Stokes, tais quais as Leis de Darcy, de Forchheimer e a Equação de Darcy-Weisbach. Ele permitiu, também, a atribuição de significados físicos mais precisos para grandezas intervenientes no escoamento em meios porosos, como o número de Reynolds e o coeficiente de permeabilidade intrínseca. Dele emergiu, ainda, o parâmetro de entropia, modelador da distribuição de velocidades, capaz de delimitar os regimes de escoamento e que viabiliza a conexão entre a micro e a macroescala do problema. Verificou-se uma grande aderência do modelo proposto a resultados obtidos em escala de bancada, piloto e real, constantes na literatura científica. Por essas razões e pelo fato de o modelo proposto ter como base um número bastante reduzido de premissas, conclui-se que ele é geral e robusto, sendo aplicável às mais distintas áreas que requeiram uma descrição analítica do escoamento em meios porosos. / Given the wide-ranging uses of porous media, it is no coincidence that several distinct fields of knowledge require analysis and evaluation of flows occurring therein. Recent advances in this area have included experimental and numerical techniques. However, further developments in the subject are conditioned to (and held back by) the evolution in its theoretical counterpart. As a result, this study proposes a new analytical model for the flow through porous media, based on information theory\'s principle of maximum entropy (POME). The proposed model allows for the statistical determination of a fluid\'s local velocities. Further, it also permits the deduction of expressions based on the Navier-Stokes Equations, such as Darcy\'s and Forchheimer\'s Laws and the Darcy-Weisbach Equation. It bestows more precise physical meanings to the quantities typically involved in the flow through porous media, such as the Reynolds number and the intrinsic permeability coefficient, as well. Furthermore, the proposed model introduces an entropy parameter, which represents the statistical distribution of velocities and is capable of delimiting flow regimes. This parameter also permits a clear connection between both micro and macro scales of the problem. The proposed model showed great adherence to bench, pilot and real scale results found in scientific literature. For these reasons, and due to its reduced number of premises, the proposed model is concluded to be general and robust, and that it can be applied to countless areas in which an analytical description of flow through porous media is required.