Modelagem multiescala de fenômenos eletrocinéticos em meios porosos carregados eletricamente: aplicação a meios porosos argilosos

In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.

Modelagem multiescala de fenômenos eletrocinéticos em meios porosos carregados eletricamente: aplicação a meios porosos argilosos

In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.

Evaluation of Gaseous Fluid Dispersion Through Packed Bed Using Radiotracers Technique

In this study, it was developed a methodology for the determination of the dispersion of a gaseous tracer in porous media using the radiotracer technique. In order to evaluate several porous media, a cylindrical filter was constructed in PVC and connected to a system with constant flow. Inside this unit silica crystals (16-20) mesh was used as porous media and CH3Br (Methyl Bromide) marked with 82Br was used as radiotracer. An instantaneous pulse of tracer was applied in the system entrance and registered by two NaI (3x3)” scintillation detectors located one before and the other after the filter. The curves produced by the radioactive cloud and recorded by the detector were analyzed statistically using the weighted moment method. The mathematical model one considered as great dispersion of tracer was used to evaluate the flow conditions inside the filter system. The results show us that the weight moment method associated with radiotracer techniques is useful to evaluated an industrial filter and allows to measure the residence time distribution, τ, and the axial dispersion, DAB, gas in a porous medium.

Simulação numérica da convecção mista em cavidade preenchida com meio poroso heterogêneo e homogêneo

In this work is presented mixed convection heat transfer inside a lid-driven cavity heated from below and filled with heterogeneous and homogeneous porous medium. In the heterogeneous approach, the solid domain is represented by heat conductive equally spaced blocks; the fluid phase surrounds the blocks being limited by the cavity walls. The homogeneous or pore-continuum approach is characterized by the cavity porosity and permeability. Generalized mass, momentum and energy conservation equations are obtained in dimensionless form to represent both the continuum and the pore-continuum models. The numerical solution is obtained via the finite volume method. QUICK interpolation scheme is set for numerical treatment of the advection terms and SIMPLE algorithm is applied for pressure-velocity coupling. Aiming the laminar regime, the flow parameters are kept in the range of 102≤Re≤103 and 103≤Ra≤106 for both the heterogeneous and homogeneous approaches. In the tested configurations for the continuous model, 9, 16, 36, and 64 blocks are considered for each combination of Re and Ra being the microscopic porosity set as constant φ=0,64 . For the pore-continuum model the Darcy number (Da) is set according to the number of blocks in the heterogeneous cavity and the φ. Numerical results of the comparative study between the microscopic and macroscopic approaches are presented. As a result, average Nusselt number equations for the continuum and the pore continuum models as a function of Ra and Re are obtained.

A new method for conditioning stochastic groundwater flow models in fractured media

Many geological formations consist of crystalline rocks that have very low matrix permeability but allow flow through an interconnected network of fractures. Understanding the flow of groundwater through such rocks is important in considering disposal of radioactive waste in underground repositories. A specific area of interest is the conditioning of fracture transmissivities on measured values of pressure in these formations. This is the process where the values of fracture transmissivities in a model are adjusted to obtain a good fit of the calculated pressures to measured pressure values. While there are existing methods to condition transmissivity fields on transmissivity, pressure and flow measurements for a continuous porous medium there is little literature on conditioning fracture networks. Conditioning fracture transmissivities on pressure or flow values is a complex problem because the measurements are not linearly related to the fracture transmissivities and they are also dependent on all the fracture transmissivities in the network. We present a new method for conditioning fracture transmissivities on measured pressure values based on the calculation of certain basis vectors; each basis vector represents the change to the log transmissivity of the fractures in the network that results in a unit increase in the pressure at one measurement point whilst keeping the pressure at the remaining measurement points constant. The fracture transmissivities are updated by adding a linear combination of basis vectors and coefficients, where the coefficients are obtained by minimizing an error function. A mathematical summary of the method is given. This algorithm is implemented in the existing finite element code ConnectFlow developed and marketed by Serco Technical Services, which models groundwater flow in a fracture network. Results of the conditioning are shown for a number of simple test problems as well as for a realistic large scale test case.

Modelagem e previsão da perda de injetividade em poços canhoneados

Waterflooding is a technique largely applied in the oil industry. The injected water displaces oil to the producer wells and avoid reservoir pressure decline. However, suspended particles in the injected water may cause plugging of pore throats causing formation damage (permeability reduction) and injectivity decline during waterflooding. When injectivity decline occurs it is necessary to increase the injection pressure in order to maintain water flow injection. Therefore, a reliable prediction of injectivity decline is essential in waterflooding projects. In this dissertation, a simulator based on the traditional porous medium filtration model (including deep bed filtration and external filter cake formation) was developed and applied to predict injectivity decline in perforated wells (this prediction was made from history data). Experimental modeling and injectivity decline in open-hole wells is also discussed. The injectivity of modeling showed good agreement with field data, which can be used to support plan stimulation injection wells

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Experimental and Numerical Analysis of Gas Flows in Microchannels and Micro Heat Exchanger

Due to increased interest in miniaturization, great attention has been given in the recent decade to the micro heat exchanging systems. Literature survey suggests that there is still a limited understanding of gas flows in micro heat exchanging systems. The aim of the current thesis is to further the understanding of fluid flow and heat transfer phenomenon inside such geometries when a compressible working fluid is utilized. A combined experimental and numerical approach has been utilized in order to overcome the lack of employable sensors for micro dimensional channels. After conducting a detailed comparison between various data reduction methodologies employed in the literature, the best suited methodology for gas microflow experimentalists is proposed. A transitional turbulence model is extensively validated against the experimental results of the microtubes and microchannels under adiabatic wall conditions. Heat transfer analysis of single microtubes showed that when the compressible working fluid is used, Nusselt number results are in partial disagreement with the conventional theory at highly turbulent flow regime for microtubes having a hydraulic diameter less than 250 microns. Experimental and numerical analysis on a prototype double layer microchannel heat exchanger showed that compressibility is detrimental to the thermal performance. It has been found that compressibility effects for micro heat exchangers are significant when the average Mach number at the outlet of the microchannel is greater than 0.1 compared to the adiabatic limit of 0.3. Lastly, to avoid a staggering amount of the computational power needed to simulate the micro heat exchanging systems with hundreds of microchannels, a reduced order model based on the porous medium has been developed that considers the compressibility of the gas inside microchannels. The validation of the proposed model against experimental results of average thermal effectiveness and the pressure loss showed an excellent match between the two.

Analytical methods for modeling elastic metasurfaces

This dissertation aims at developing advanced analytical tools able to model surface waves propagating in elastic metasurfaces. In particular, four different objectives are defined and pursued throughout this work to enrich the description of the metasurface dynamics. First, a theoretical framework is developed to describe the dispersion properties of a seismic metasurface composed of discrete resonators placed on a porous medium considering part of it fully saturated. Such a model combines classical elasticity theory, Biot’s poroelasticity and an effective medium approach to describe the metasurface dynamics and its coupling with the poroelastic substrate. Second, an exact formulation based on the multiple scattering theory is developed to extend the two-dimensional classical Lamb’s problem to the case of an elastic half-space coupled to an arbitrary number of discrete surface resonators. To this purpose, the incident wavefield generated by a harmonic source and the scattered field generated by each resonator are calculated. The substrate wavefield is then obtained as solutions of the coupled problem due to the interference of the incident field and the multiple scattered fields of the oscillators. Third, the above discussed formulation is extended to three-dimensional contexts. The purpose here is to investigate the dynamic behavior and the topological properties of quasiperiodic elastic metasurfaces. Finally, the multiple scattering formulation is extended to model flexural metasurfaces, i.e., an array of thin plates. To this end, the resonant plates are modeled by means of their equivalent impedance, derived by exploiting the Kirchhoff plate theory. The proposed formulation permits the treatment of a general flexural metasurface, with no limitation on the number of plates and the configuration taken into account. Overall, the proposed analytical tools could pave the way for a better understanding of metasurface dynamics and their implementation in engineered devices.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.

Surface diffusion of adsorbed molecules in porous media: Monolayer, multilayer, and capillary condensation regimes

This review provides an overview of surface diffusion and capillary condensate flow in porous media. Emphasis has been placed on the distinction between purely surface diffusion, multilayer surface diffusion, and, capillary condensate flow.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Development of porous glass-fiber reinforced composite for bone implants. Evaluation of antimicrobial effect and implant fixation

Cranial bone reconstructions are necessary for correcting large skull bone defects due to trauma, tumors, infections and craniotomies. Traditional synthetic implant materials include solid or mesh titanium, various plastics and ceramics. Recently, biostable glass-fiber reinforced composites (FRC), which are based on bifunctional methacrylate resin, were introduced as novel implant solution. FRCs were originally developed and clinically used in dental applications. As a result of further in vitro and in vivo testing, these composites were also approved for clinical use in cranial surgery. To date, reconstructions of large bone defects were performed in 35 patients. This thesis is dedicated to the development of a novel FRC-based implant for cranial reconstructions. The proposed multi-component implant consists of three main parts: (i) porous FRC structure; (ii) bioactive glass granules embedded between FRC layers and (iii) a silver-polysaccharide nanocomposite coating. The porosity of the FRC structure should allow bone ingrowth. Bioactive glass as an osteopromotive material is expected to stimulate the formation of new bone. The polysaccharide coating is expected to prevent bacterial colonization of the implant. The FRC implants developed in this study are based on the porous network of randomly-oriented E-glass fibers bound together by non-resorbable photopolymerizable methacrylate resin. These structures had a total porosity of 10–70 volume %, of which > 70% were open pores. The pore sizes > 100 μm were in the biologically-relevant range (50-400 μm), which is essential for vascularization and bone ingrowth. Bone ingrowth into these structures was simulated by imbedding of porous FRC specimens in gypsum. Results of push-out tests indicated the increase in the shear strength and fracture toughness of the interface with the increase in the total porosity of FRC specimens. The osteopromotive effect of bioactive glass is based on its dissolution in the physiological environment. Here, calcium and phosphate ions, released from the glass, precipitated on the glass surface and its proximity (the FRC) and formed bone-like apatite. The biomineralization of the FRC structure, due to the bioactive glass reactions, was studied in Simulated Body Fluid (SBF) in static and dynamic conditions. An antimicrobial, non-cytotoxic polysaccharide coating, containing silver nanoparticles, was obtained through strong electrostatic interactions with the surface of FRC. In in vitro conditions the lactose-modified chitosan (chitlac) coating showed no signs of degradation within seven days of exposure to lysozyme or one day to hydrogen peroxide (H2O2). The antimicrobial efficacy of the coating was tested against Staphylococcus aureus and Pseudomonas aeruginosa. The contact-active coating had an excellent short time antimicrobial effect. The coating neither affected the initial adhesion of microorganisms to the implant surface nor the biofilm formation after 24 h and 72 h of incubation. Silver ions released to the aqueous environment led to a reduction of bacterial growth in the culture medium.

Catalysis by Modified Pillared Clays and Porous Clay Heterostructures

In this venture three distinct class of catalysts such as, pillared clays and transition metal loaded pillared clays , porous clay heterostructures and their transition metal loaded analogues and DTP supported on porous clay heterostructures etc. were prepared and characterized by various physico chemical methods. The catalytic activities of prepared catalysts were comparatively evaluated for the industrially important alkylation, acetalization and oxidation reactions.The general conclusions drawn from the present investigation are  Zirconium, iron - aluminium pillared clays were synthesized by ion exchange method and zirconium-silicon porous heterostructures were Summary and conclusions 259 prepared by intergallery template method. Transition metals were loaded in PILCs and PCHs by wet impregnation method.  Textural and acidic properties of the clays were modified by pillaring and post pillaring modifications.  The shift in 2θ value to lower range and increase in d (001) spacing indicate the success of pillaring process.  Surface area, pore volume, average pore size etc. increased dramatically as a result of pillaring process.  Porous clay heterostructures have higher surface area, pore volume, average pore diameter and narrow pore size distribution than that of pillared clays.  The IR spectrum of PILCs and PCHs are in accordance with literature without much variation compared to parent montmorillonite which indicate that basic clay structure is retained even after modification.  The silicon NMR of PCHs materials have intense peaks corresponding to Q4 environment which indicate that mesoporous silica is incorporated between clay layers.  Thermo gravimetric analysis showed that thermal stability is improved after the pillaring process. PCH materials have higher thermal stability than PILCs.  In metal loaded pillared clays, up to 5% metal species were uniformly dispersed (with the exception of Ni) as evident from XRD and TPR analysis. Chapter 9 260  Impregnation of transition metals in PILCs and PCHs enhanced acidity of catalysts as evident from TPD of ammonia and cumene cracking reactions.  For porous clay heterostructures the acidic sites have major contribution from weak and medium acid sites which can be related to the Bronsted sites as evident from TPD of ammonia.  Pillared clays got more Lewis acidity than PCHs as inferred from α- methyl styrene selectivity in cumene cracking reaction.  SEM images show that layer structure is preserved even after modification. Worm hole like morphology is observed in TEM image of PCHs materials  In ZrSiPCHS, Zr exists as Zr 4+ and is incorporated to silica pillars in the intergallary of clay layers as evident from XPS analysis.  In copper loaded zirconium pillared clays, copper exists as isolated species with +2 oxidation state at lower loading. At higher loading, Cu exists as clusters as evident from reduction peak at higher temperatures in TPR.  In vanadium incorporated PILCs and PCHs, vanadium exist as isolated V5+ in tetrahedral coordination which is confirmed from TPR and UVVis DRS analysis.  In cobalt loaded PCHs, cobalt exists as CoO with 2+ oxidation state as confirmed from XPS.  Cerium incorporated iron aluminium pillared clay was found to be the best catalyst for the hydroxylation of phenol in aqueous media due to the additional surface area provided by ceria mesopores and its redox properties. Summary and conclusions 261  Cobalt loaded zirconium porous clay heterostructures were found to be promising catalyst for the tertiary butylation of phenol due to higher surface area and acidic properties.  Copper loaded pillared clays were found to be good catalyst for the direct hydroxylation of benzene to phenol.  Vanadium loaded PCHs catalysts were found to be efficient catalysts for oxidation of benzyl alcohol.  DTP was firmly fixed on the mesoporous channels of PCHs by Direct method and functionalization method.  DTP supported PCHs catalyst were found to be good catalyst for acetalization of cyclohexanone with more than 90% conversion.

The acoustic signature of fluid flow in complex porous media

Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/ porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic - viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown-Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown-Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz-clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks. (C) 2003 Elsevier B.V. All rights reserved.