This work is devoted to the numerical analysis of saturated porous media, taking into account the damage phenomenon on the solid skeleton. The porous media is taken into poroelastic framework, in full-saturated condition, based on the Biot's Theory. A scalar damage model is assumed for this analysis. An implicit Boundary Element Method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and the elasto-damage problems. The integration over boundary elements is evaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear system is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficiency.; Este trabalho trata da análise numérica de meios porosos saturados, considerando danificação na matriz sólida. O meio poroso é admitido em regime poroelástico, em condição saturada, com base na teoria de Biot. Um modelo de dano escalar é empregado nesta análise. Uma formulação implícita do Método dos Elementos de Contorno (MEC), baseada em soluções fundamentais independentes do tempo...

A Ressonância Magnética Nuclear (RMN) é uma importante técnica empregada nas principais áreas de conhecimento, tais como, Física, Química e Medicina. Importantes trabalhos da RMN aplicada ao estudo da dinâmica de moléculas em fluidos presentes em meios porosos permitiram que esta técnica ganhasse também notoriedade na indústria do petróleo. O presente projeto é fundamentado em alguns destes trabalhos seminais, reproduzindo, através de modelos físico-computacionais, os principais efeitos físicos da difusão e a consequente relaxação dos spins dos núcleos atômicos presentes nas moléculas dos fluidos imersos nos meios porosos. Os métodos teóricos utilizados para a interpretação dos parâmetros de relaxação transversal (T2) e longitudinal (T1), levam em consideração as propriedades macroscópicas da dinâmica de um ensemble de spins nucleares. Para a compreensão da difusão e relaxação nuclear em meios porosos, é de fundamental importância o emprego de métodos físico-computacionais que levam em consideração tanto a microestrutura quanto a difusão translacional dos spins nucleares através desses meios. Dentro dos modelos propostos nesta dissertação, foram utilizados conceitos básicos de mecânica estatística e de relaxação nuclear...

Queimadores cuja combustão é realizada em meios porosos apresentam vantagens, tais como dimensões mais compactas, maior eficiência térmica e alta razão de operação (razão entre máxima e a mínima potências entre as quais podem operar com estabilidade). Este trabalho busca estudar diferentes condições de entrada do fluido de trabalho no meio poroso e quais implicações das mudanças nas principais características de funcionamento do queimador. O fluido de trabalho será uma mistura de gás metano e ar. O queimador apresenta apenas uma camada de material poroso (Al2O3) e os parâmetros testados são a razão de equivalência e a velocidade de entrada da mistura. Para tanto, são realizadas simulações numéricas em um modelo de queimador nas condições descritas anteriormente. A metodologia numérica utilizada é a dos volumes finitos. As simulações numéricas são feitas em linguagem de programação FORTRAN. Observou-se que a adequação do modelo ao processo de combustão merece um esforço adicional, ficando como proposta para futuros trabalhos. Foram então analisados os escoamentos dentro do modelo proposto, obtendo-se resultados adequados aos encontrados na literatura.; Porous media burners are characterized by advantages like compacity...

Queimadores que utilizam meios porosos representam uma tecnologia relativamente recente e que apresenta vantagens em relação a outros processos de queima, como excelente desempenho, estabilidade de chama, baixos níveis de emissão de poluentes e largos intervalos de potência disponível. Este trabalho objetiva estudar numericamente diferentes modos de operação de um queimador poroso, analisando-se os efeitos nas variações de parâmetros como razão de excesso de ar e potência de operação. Usa-se misturas de ar e metano como fluido de trabalho. A matriz porosa é constituída de alumina (Al2O3). O código utilizado na programação é escrito na linguagem Fortran, utiliza algoritmo SIMPLE e método de volumes finitos. Obteve-se perfis de temperatura para diferentes parâmetros de operação do queimador. Conseguiu-se estabilizar chamas no interior de matrizes porosas, observando-se escoamentos homogêneos que preenchem toda a geometria. Observou-se que a análise de diferentes geometrias e estruturas para queimadores enriqueceriam o estudo do escoamento e do processo de combustão que ocorre no interior do equipamento, bem como a evolução do código de programação para acoplar mecanismos de reação de cinética química detalhada seriam de grande valor científico...

O foco desta dissertação de mestrado consiste em um estudo computacional de equações pseudo-parabólicas em mecânica dos fluidos e fenômenos de transporte de fluidos em meios porosos. Serão considerados problemas de valor de contorno e inicial associados a duas classes de modelos de equações de evolução pseudo-parabólicas: um modelo de advecção-difusão com termo pseudo-parabólico que exibe um certo caráter dispersivo e um outro modelo pseudo-parabólico "puro", i.e., sem a presença do termo de advecção. O primeiro modelo se relaciona com a modelagem física do fluxo de duas fases incompressíveis em dinâmica de fluidos em meios porosos, onde são considerados modelos de pressão capilar dinâmica, ou seja, em que os efeitos dinâmicos são também incluídos na diferença de pressão entre as fases fluidas. Uma discussão sobre a relevância física em aplicações e da importância matemática do sistema governante de equações para pressão capilar dinâmica em fenômenos de transporte de fluidos em meios porosos é também feita de modo a indicar algum suporte à escolha dos métodos estudados para aproximação numérica dos modelos consideradores. Além disso, um conjunto de experimentos numéricos é apresentado e discutido para avaliar a qualidade das soluções obtidas do estudo proposto...

This paper deals with possibility of information entropy usage for porous media structure characteristics description. The paper presents the results of preliminary investigation of the possibility using information entropy parameter for porous media. The first approach of the method presented in the paper confirmed the possibility to get the join characteristic of porous media. The method may give a new point of view on the problem of porous media modelling. The examples of entropy calculation for distributions of pore by size and length as well as for multi-layers porous media joint entropy are given.; Junta de Investigação Científica e Tecnológica (JNICT)

We present a compact finite differences method for the calculation of two-dimensional viscous flows in porous media. This is achieved by using body forces that allow for the imposition of boundary conditions that coincide with the computational grid. An implementation of the forcing of Mohd-Yusof is used in order to implement the immersed boundary. A detailed description of the original compact finite difference method used can be found in Ferreira de Sousa et al.. The unsteady, incompressible Navier-Stokes equations are solved in a Cartesian staggered grid with fourth-order Runge-Kutta temporal discretization and fourth-order compact schemes for spatial discretization, used to achieve highly accurate calculations. Special attention is given to the boundary condition implementation on the immersed media. In this paper, two different flows are calculated. First, the flow over a 2D square cylinder located along the centreline of a channel with free-slip boundary conditions. The computed drag coefficient is compared with numerical results available in the literature. The second flow configuration analyzed is the flow over a porous matrix composed of staggered square cylinders. Results for the pressure drop across the porous matrix are presented for a wide range of Reynolds numbers...

Porous media exposed to humid air absorb moisture which can lead to extensive internal damage and failure. In this paper, we analyze numerically the influence of the moisture intrusion in a two-layer viscoelastic porous media. The relationship between air humidity and moisture content inside the porous media was examined. It was also found that the local stress increases with the exposure time to humid air but decreases with initial moisture content of the porous medium. Furthermore, the stress components were tensile at the centre of the medium and compressive near the medium surface. The ultimate strength of the medium was only exceeded for the stresses in axial and tangential directions.

This chapter demonstrates the potential of the immersed boundary method for the direct numerical simulation of the flow through porous media. A 2D compact finite differences method was employed to solve the unsteady incompressible Navier-Stokes equations with fourth-order Runge-Kutta temporal discretization and fourth-order compact schemes for spatial discretization. The solutions were obtained in a Cartesian grid, with all the associated advantages. The porous media is made of equal size square cylinders in a staggered arrangement and is bounded by solid walls. The transverse and longitudinal distances between cylinders are equal to two cylinder diameters and at the inlet a fully developed velocity profile is specified. The Reynolds number based on the cylinder diameter and maximum inlet velocity ranges from 40 to 80. The different flow regimes are identified and characterised, along with the prediction of the Reynolds number at which transition from steady to unsteady flow takes place. Additionally, the average drag and lift coefficients are presented as a function of the Reynolds number.

This paper reports a theoretical and experimental research in the field of mass transport through porous media. Thermodynamics was employed to model the change of mass inside porous media and the fluid flow through porous media. An experimental study was carried out to provide a thermodynamic chart of a porous medium and to infer the parameters required by the theoretical approach. The e ffect of the moisture content and temperature on fluid transport properties was also investigated.

Following the development of an immersed boundary method for the study of flow through porous media [1,2], this paper presents direct numerical simulations for structured porous media composed of equal size staggered square cylinders. Different Reynolds numbers are simulated in order to capture the dependence of the pressure drop and friction factor with the Reynolds number. Results are compared to available and widely used empirical correlations. These correlations assume that the additional pressure drop caused by the entrance and exit flow adjustments is unimportant as compared to the pressure drop imposed by the porous medium core. Following this line of though, many of the studies and books on flow though porous media neglect these entrance and exit effects and at best mention them in passing. Through the representation of the pressure drop per unit length for several Reynolds numbers, the authors obtain for a regular matrix composed of equal size square cylinders, the influence of the porous medium entrance. This influence is a function of the Reynolds number.

The flow of Bingham liquids through porous media has been studied. Experiments have been performed to determine the flow rate / pressure drop relationship for the flow of a grease of Binghamian rheological behavior through an array of rods of circular cross section. The yield stress and plastic viscosity of the grease have been determined with the aid of a controlled stress rotational rheometer. To investigate a wider range of the flow parameters, the mass and momentum conservation equations have been solved numerically, in conjunction with the generalized Newtonian constitutive law and the bi-viscosity model. The finite volume method has been employed to obtain the numerical solution. These numerical results also yielded a flow rate / pressure drop relationship, which is in very good agreement with the experimental results. A capillaric theory has been developed to determine an analytical relationship between the flow rate and pressure drop for flows of Bingham liquids through porous media. It is shown that the predictions of this theory are in good agreement with the experimental and numerical results.

In this paper, the volume averaging transport equations of two reactive processes in porous media are presented. The porous media are characterized by different length scales and the information describing the mass transfer mechanisms is transferred hierarchically between scales by applying the volume averaging method. This development provides the theoretical definition of effective transport coefficients, which can be predicted through solution of the closure problems. The theoretical calculation of effective diffusion tensors of the species in the particle pores is presented. Two closure problems are deduced through mathematical formulation of two different scales: microporous (process 1) and macroporous (process 2). In order to solve these closure problems, the volume finite method is used as the numerical methodology. Good agreement is verified between the numerical solutions obtained in this study and the data found in the literature for the closure problems considered.

É apresentado um estudo para o desenvolvimento e resolução das equações do acoplamento fluxo - deformação em meios porosos saturados com fluido compressível. Os casos analisados são sistemas transientes, bidimensionais e tridimensionais, e são estudados com o objetivo de se obter informações sobre os deslocamentos superficiais, campo de tensões e deformações nos maciços geotécnicos submetidos a carregamentos superficiais. O processo permite a simulação do comportamento de solos e rochas, constituídos de diferentes propriedades elásticas e hidráulicas quando submetidos a efeitos estáticos, cíclicos ou harmônicos superficiais. Um campo de pressão nos poros é gerado devido ao efeito do carregamento na superfície do maciço. O modelo matemático desenvolvido simula o campo de tensões e de deslocamentos no interior do meio poroso, acoplando o escoamento do fluido nos poros com a deformação da estrutura porosa constituinte do maciço. O estudo é feito considerando que as partículas sólidas constituintes do meio geotécnico, solo ou rocha, são incompressíveis. As equações que regem o fenômeno são resolvidas numericamente através da técnica do método espectral, usando uma malha de pontos de colocação no domínio analisado e acompanhando evolução da pressão nos poros com o tempo. A dissipação da pressão se acopla com os deslocamentos no meio poroso...

The use of foam-forming surfactants offers promise to improve sweep efficiency and mobility control for enhanced oil recovery (EOR). This thesis provides an in depth understanding of transport of surfactant and foam through porous media using a combination of laboratory experiments and numerical simulations. In particular, there are several issues in foam EOR processes that are examined. These include screening of surfactant adsorption onto representative rock surfaces, modeling of foam flow through porous media, and studying the effects of surface wettability and porous media heterogeneity. Surfactant adsorption onto rock surfaces is a main cause of foam chromatographic retardation as well as increased process cost. Successful foam application requires low surfactant adsorption on reservoir rock. The focus of this thesis is natural carbonate rock surfaces, such as dolomite. Surfactant adsorption was found to be highly dependent on electrostatic interactions between surfactants and rock surface. For example, the nonionic surfactant Tergitol 15-S-30 exhibits low adsorption on dolomite under alkaline conditions. In contrast, high adsorption of cationic surfactants was observed on some natural carbonate surfaces. XPS analysis reveals silicon and aluminum impurities exist in natural carbonates...

This work presents the extension of a compact finite difference immersed boundary method for the detailed calculation of fluid flow and heat transfer in porous media. The unsteady incompressible Navier-Stokes and energy conservation equations are solved with fourth-order Runge-Kutta temporal discretization and fourth-order compact schemes for spatial discretization, which allows achieving highly accurate calculations. Verification proves that the method is higher than third-order accurate. Three test cases were used for the validation of the method: (i) isothermal flow around a square cylinder in a plane parallel channel, (ii) isothermal flow through an infinite row of square cylinders and iii) flow and heat transfer around a square cylinder in a plane parallel channel. The validation tests establish confidence in the application of the method to porous media. As an example of such an application, direct numerical simulations are conducted for a staggered array of equal size square cylinders. Although the problem is rather complex from the geometrical point of view, a Cartesian grid is employed, with all its advantages. The potential of applying an immersed boundary method to the solution of a multiphase problem with complex internal boundaries is demonstrated.

Bi-orthogonality relationships are established for a vertically heterogeneous porous media in contact with a fluid, a solid, a second porous medium, and a free surface. Fraser's bi-orthgonality relation for propagation of Rayleigh-Lamb modes in a plate with traction free eurfaces is shown to be a special case of the bi-orthogonality relations derived herein in which the medium can be thought of as a porous slab with zero porosity.

Numerical experiments in multiple representative elementary volumes (REVs) were conducted to validate calculations of macroscopic parameters for porous media models carried out employing a unit periodic cell (single REV). The simulation of a microscopic flow that develops through a porous medium formed by staggered square cylinders is presented to that purpose. A laminar steady flow regime is considered together with Péclet numbers in the 1–103 range and porosities between 55 and 95%. In particular, the interfacial heat transfer coefficient (hsf) is analyzed by comparing results found in literature with those reported here. First, the outlet boundary condition that is generally employed in single REV simulations for the case of constant wall temperature was tested by comparing the values it imposes in the flow with those obtained far away from the outlet (unperturbed). It was found that this outlet boundary condition is adequate and moreover, that the flow rapidly develops to satisfy it (one or two REVs in simulated cases). Additionally, two definitions found in the literature to calculate the hsf were compared, and it was shown that both calculations differ in approximately 20% for the 55% porosity case and still present ignificant differences (>5%) for greater porosities. The hsf coefficient was also calculated as a function of the REV’s positions in the porous structure to show that it is position dependent or...

Carbon dioxide (CO2) sequestration in the sub-surface is a potential mitigation technique for global climate change caused by greenhouse gas emissions. In order to evaluate the feasibility of this technique, understanding the behaviour of CO2 stored in geological rock formations over a range of length- and time-scales is crucial. The work presented in this dissertation contributes to the knowledge in this field by investigating the two-phase flow and entrapment processes of CO2, as well as other relevant fluids, in porous media at the pore- and centimetre-scales using a combination of lab-based nuclear magnetic resonance (NMR) experimental techniques and lattice Boltzmann (LB) numerical simulation techniques. Pulsed field gradient (PFG) NMR techniques were used to acquire displacement distributions (propagators) of brine flow through a model porous medium (100 ?m glass bead packing) before and after the capillary (residual) trapping of gas-phase CO2 in the pore space. The acquired propagators were compared quantitatively with the corresponding LB simulations. In addition, magnetic resonance imaging (MRI) techniques were used to characterise the extent of CO2 trapping in the bead pack. The acquired NMR propagators were compared to LB simulations applied to various CO2 entrapment scenarios in order to investigate the pore morphology in which CO2 becomes entrapped. Subsequently...

A three-dimensional isothermal transient compressible two phase flow of liquid and gas in a low permeability fractured porous media model has been developed from the general mass and momentum balances using volume averaging techniques. The emphasis of the paper is on the available analytical and semi-empirical correlations and closure relations. The interfacial mass and momentum transfer terms in the averaged formulation are explained. The assumptions used in the model's formulation are that a condition of capillary equilibrium exists throughout the media, momentum transfer between mobile fluid phases is negligible in the porous media and exists in the fracture, and fluid phase change has been neglected. The pore size distribution of the studied porous media was represented by three mean pore diameters: liquid pore network, gas pore network, and fractures. An average pore diameter and length for each network were determined using the gamma distribution function. The model was validated and solved for a hypothetical porous media and fractured domain.