Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Avaliação da influência de cinza da casca de arroz em cimentos para poços de petróleo submetidos à injeção de vapor

Reservoirs that present highly viscous oils require methods to aid in their recovery to the surface. The elev ated oil viscosity hinders its flow through porous media and conventional recovery methods have not obtained significant efficiency. As such, the injection of steam into the reservoir through an injection well has been the most widely used method of therma l recovery, for it allows elevated volumes of recovery due to the viscosity reduction of the oil, facilitating the oil’s mobility within the rock formation and consequently into the production well where it will be exploited. On the other hand, the injecti on of vapor not only affects the fluids found in the rock pores, but the entire structure that composes the well where it is injected due to the high temperatures used in the process. This temperature increment is conducted to the cement, found in the annu lus, responsible for the isolation of the well and the well casing. Temperatures above 110 ̊C create new fazes rich in calcium in the cement matrix, resulting in the reduction of its permeability and the consequential phenomenon of mechanical resistance ret rogression. These alterations generate faults in the cement, reducing the well’s hydraulic isolation, creating insecurity in the operations in which the well will be submitted as well as the reduction of its economic life span. As a way of reducing this re trograde effect, this study has the objective of evaluating the incorporation of rice husk ash as a mineral additive substitute of silica flour , commercially utilized as a source of silica to reduce the CaO/SiO 2 ratio in the cement pastes submitted to high temperatures in thermal recovery. Cement pastes were formulated containing 20 and 30% levels of ash, apart from the basic paste (water + cement) and a reference paste (water + cement + 40% silica flour) for comparison purposes. The tests were executed th rough compression resistance tests, X - Ray diffraction (XRD) techniques, thermogravimetry (TG), scanning electron microscopy (SEM) and chemical anal ysis BY X - ray fluorescence (EDS) on the pastes submitted to cure at low temperatures (45 ̊C) for 28 days following a cure at 280 ̊C and a pressure of 2,000 PSI for 3 days, simulating vapor injection. The results obtained show that the paste containing 30% r ice shell ash is satisfactory, obtaining mechanical resistance desired and equivalent to that of the paste containing 40% silica flour, since the products obtained were hydrated with low CaO/SiO 2 ratio, like the Tobermorita and Xonotlita fases, proving its applicability in well subject to vapor injection.

Análise da eficácia de um refrigerador doméstico com condensador modificado: revestimento com meio poroso dissipativo

The development of home refrigerators generally are compact and economic reasons for using simplified configuration. The thermodynamic coefficient of performance ( COP ) is limited mainly in the condenser design for reasons of size and arrangement ( layout ) of the project ( design ) and climatic characteristics of the region where it will operate. It is noteworthy that this latter limitation is very significant when it comes to a country of continental size like Brazil with diverse climatic conditions. The COP of the cycle depends crucially on the ability of heat dissipated in the condenser. So in hot climates like the northeast, north, and west-central dispel ability is highly attenuated compared to the south and southeast regions with tropical or subtropical climates when compared with other regions. The dissipation in compact capacitors for applications in domestic refrigeration has been the focus of several studies, that due to its impact on reducing costs and power consumption, and better use of the space occupied by the components of refrigeration systems. This space should be kept to a minimum to allow an increase in the useful storage volume of refrigerator without changing the external dimensions of the product. Due to its low cost manufacturing, wire on tube condensers continue to be the most advantageous option for domestic refrigeration. Traditionally, these heat exchangers are designed to operate under natural convection. Not always, the benefits of greater compactness of capacitors for forced outweigh the burden of pumping air through the external heat exchanger. In this work we propose an improvement in convective condenser changing it to a transfer mechanism combined in series with conductive pipes and wire to a moist convective porous medium and the porous medium to the environment. The porous media used in the coating was composed of a gypsum plaster impregnated fiber about a mesh of natural cellulosic molded tubular wire mesh about the original structure of the condenser , and then dried and calcined to greater adherence and increased porosity. The proposed configuration was installed in domestic refrigeration system ( trough ) and tested under the same conditions of the original configuration . Was also evaluated in the dry condition and humidified drip water under natural and forced with an electro - fan ( fan coil ) convection. Assays were performed for the same 134- refrigerant charge e under the same thermal cooling load. The performance was evaluated in various configurations, showing an improvement of about 72 % compared with the original configuration proposed in humidification and natural convection.

Fluxo de fluído através de um meio poroso fractal desordenado. Análise das tensões de cisalhamento e efeito de escala na estimativa das forças viscosas

In this work we have investigated some aspects of the two-dimensional flow of a viscous Newtonian fluid through a disordered porous medium modeled by a random fractal system similar to the Sierpinski carpet. This fractal is formed by obstacles of various sizes, whose distribution function follows a power law. They are randomly disposed in a rectangular channel. The velocity field and other details of fluid dynamics are obtained by solving numerically of the Navier-Stokes and continuity equations at the pore level, where occurs actually the flow of fluids in porous media. The results of numerical simulations allowed us to analyze the distribution of shear stresses developed in the solid-fluid interfaces, and find algebraic relations between the viscous forces or of friction with the geometric parameters of the model, including its fractal dimension. Based on the numerical results, we proposed scaling relations involving the relevant parameters of the phenomenon, allowing quantifying the fractions of these forces with respect to size classes of obstacles. Finally, it was also possible to make inferences about the fluctuations in the form of the distribution of viscous stresses developed on the surface of obstacles.

The critical role of intracavity dynamics in high-power mode-locked fiber lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile. © 2010 Copyright SPIE - The International Society for Optical Engineering.

Intracavity dynamics in mode-locked lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile. © 2010 American Institute of Physics.

Intracavity dynamics for power and energy enhancement in mode-locked lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile.

Constructal Design of Energy Systems

This dissertation shows the use of Constructal law to find the relation between the morphing of the system configuration and the improvements in the global performance of the complex flow system. It shows that the better features of both flow and heat transfer architecture can be found and predicted by using the constructal law in energy systems. Chapter 2 shows the effect of flow configuration on the heat transfer performance of a spiral shaped pipe embedded in a cylindrical conducting volume. Several configurations were considered. The optimal spacings between the spiral turns and spire planes exist, such that the volumetric heat transfer rate is maximal. The optimized features of the heat transfer architecture are robust. Chapter 3 shows the heat transfer performance of a helically shaped pipe embedded in a cylindrical conducting volume. It shows that the optimized features of the heat transfer architecture are robust with respect to changes in several physical parameters. Chapter 4 reports analytically the formulas for effective permeability in several configurations of fissured systems, using the closed-form description of tree networks designed to provide flow access. The permeability formulas do not vary much from one tree design to the next, suggesting that similar formulas may apply to naturally fissured porous media with unknown precise details, which occur in natural reservoirs. Chapter 5 illustrates a counterflow heat exchanger consists of two plenums with a core. The results show that the overall flow and thermal resistance are lowest when the core is absent. Overall, the constructal design governs the evolution of flow configuration in nature and energy systems.

Bridging the Scale Gap from Leaf to Canopy in Biosphere-Atmosphere Gas and Particle Exchanges

Terrestrial ecosystems, occupying more than 25% of the Earth's surface, can serve as

`biological valves' in regulating the anthropogenic emissions of atmospheric aerosol

particles and greenhouse gases (GHGs) as responses to their surrounding environments.

While the signicance of quantifying the exchange rates of GHGs and atmospheric

aerosol particles between the terrestrial biosphere and the atmosphere is

hardly questioned in many scientic elds, the progress in improving model predictability,

data interpretation or the combination of the two remains impeded by

the lack of precise framework elucidating their dynamic transport processes over a

wide range of spatiotemporal scales. The diculty in developing prognostic modeling

tools to quantify the source or sink strength of these atmospheric substances

can be further magnied by the fact that the climate system is also sensitive to the

feedback from terrestrial ecosystems forming the so-called `feedback cycle'. Hence,

the emergent need is to reduce uncertainties when assessing this complex and dynamic

feedback cycle that is necessary to support the decisions of mitigation and

adaptation policies associated with human activities (e.g., anthropogenic emission

controls and land use managements) under current and future climate regimes.

With the goal to improve the predictions for the biosphere-atmosphere exchange

of biologically active gases and atmospheric aerosol particles, the main focus of this

dissertation is on revising and up-scaling the biotic and abiotic transport processes

from leaf to canopy scales. The validity of previous modeling studies in determining

iv

the exchange rate of gases and particles is evaluated with detailed descriptions of their

limitations. Mechanistic-based modeling approaches along with empirical studies

across dierent scales are employed to rene the mathematical descriptions of surface

conductance responsible for gas and particle exchanges as commonly adopted by all

operational models. Specically, how variation in horizontal leaf area density within

the vegetated medium, leaf size and leaf microroughness impact the aerodynamic attributes

and thereby the ultrane particle collection eciency at the leaf/branch scale

is explored using wind tunnel experiments with interpretations by a porous media

model and a scaling analysis. A multi-layered and size-resolved second-order closure

model combined with particle

uxes and concentration measurements within and

above a forest is used to explore the particle transport processes within the canopy

sub-layer and the partitioning of particle deposition onto canopy medium and forest

oor. For gases, a modeling framework accounting for the leaf-level boundary layer

eects on the stomatal pathway for gas exchange is proposed and combined with sap

ux measurements in a wind tunnel to assess how leaf-level transpiration varies with

increasing wind speed. How exogenous environmental conditions and endogenous

soil-root-stem-leaf hydraulic and eco-physiological properties impact the above- and

below-ground water dynamics in the soil-plant system and shape plant responses

to droughts is assessed by a porous media model that accommodates the transient

water

ow within the plant vascular system and is coupled with the aforementioned

leaf-level gas exchange model and soil-root interaction model. It should be noted

that tackling all aspects of potential issues causing uncertainties in forecasting the

feedback cycle between terrestrial ecosystem and the climate is unrealistic in a single

dissertation but further research questions and opportunities based on the foundation

derived from this dissertation are also brie

y discussed.

On the statistics of transverse permeability of randomly distributed fibers

An RVE–based stochastic numerical model is used to calculate the permeability of randomly generated porous media at different values of the fiber volume fraction for the case of transverse flow in a unidirectional ply. Analysis of the numerical results shows that the permeability is not normally distributed. With the aim of proposing a new understanding on this particular topic, permeability data are fitted using both a mixture model and a unimodal distribution. Our findings suggest that permeability can be fitted well using a mixture model based on the lognormal and power law distributions. In case of a unimodal distribution, it is found, using the maximum-likelihood estimation method (MLE), that the generalized extreme value (GEV) distribution represents the best fit. Finally, an expression of the permeability as a function of the fiber volume fraction based on the GEV distribution is discussed in light of the previous results.

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.

Employment of the Technique of Radiotracers for Analysis of Industrial Filters

The main aim of this work is to develop a methodology to evaluate the characteristics of porous media in filter using the radio-tracing technique. To do this, an experimental prototype filter made up of an acrylic cylinder, vertically mounted and supported on the lower side by a controlled leaking valve was developed. Two filters (spheres of acrylic and silica crystals) were used to check the movement of the water through the porous media using 123I in its MIBG (iodine-123-meta-iodo benzyl-guanidine) form. Further up the filter an instantaneous injection of the substance makes it possible to see the passage of radioactive clouds through the two scintillatory detectors NaI (2x2)” positioned before and immediately after the cylinder with the filtering element (porous media). The are caused by the detectors on the passage of the radioactive cloud are analyzed through statistical functions using the weighted moment method which makes it possible to calculate the Residence-Time (the amount of time the tracer takes to thoroughly pass through the filter) per the equation of dispersion in tubular flow and the one-directional flow of the radiotracer in the porous media.

Développement d'un senseur électrochimique pour le dosage des nitrates en laboratoire et en pépinière forestière

Le lessivage des nitrates, la contamination de la nappe phréatique et l’eutrophisation des cours d’eau figurent parmi les enjeux planétaires qui affectent la durabilité de l’agriculture et des ressources naturelles. Ce mémoire présente le développement d’une première génération d’un nouveau senseur électrochimique pour le dosage de précisions des nitrates. Celui-ci est basé sur la spectroscopie d’impédance électrochimique d’une membrane polymérique sélective aux ions. Grâce à cette approche, un senseur compact et abordable a été produit. Par son utilisation en solutions aqueuses et en substrats de croissance saturés, il a été montré que le senseur permettait de quantifier des ajouts contrôlés de nitrates allant de 0,6 ppm à 60 ppm. La mise en application en substrat de croissance a pu être étudiée en comparaison avec des méthodes certifiées ISO 17025 visant l’analyse de ces substrats. Le senseur a aussi montré une grande versatilité par son utilisation sur divers appareils de mesure d’impédance. En plus, il a démontré une stabilité possible suite à une implantation d’un mois directement en substrat de croissance sous les variables environnementales d’une pépinière forestière. Par l’étude du spectre d’impédance du senseur en solutions pures de différentes concentrations, il a aussi été possible de proposer le circuit électrique équivalent du système, qui met en évidence deux parcours compétitifs du courant, un au coeur de la membrane et un deuxième en solution. Les résultats de ces travaux sont au coeur de deux publications scientifiques dont le manuscrit est inclus à ce mémoire. Pour finir cette étude, des suggestions seront faites pour guider l’amélioration du senseur par le développement d’une deuxième génération de celui-ci.

Modelling of water removal during a paper vacuum dewatering process using a Level-Set method

Water removal in paper manufacturing is an energy-intensive process. The dewatering process generally consists of four stages of which the first three stages include mechanical water removal through gravity filtration, vacuum dewatering and wet pressing. In the fourth stage, water is removed thermally, which is the most expensive stage in terms of energy use. In order to analyse water removal during a vacuum dewatering process, a numerical model was created by using a Level-Set method. Various different 2D structures of the paper model were created in MATLAB code with randomly positioned circular fibres with identical orientation. The model considers the influence of the forming fabric which supports the paper sheet during the dewatering process, by using volume forces to represent flow resistance in the momentum equation. The models were used to estimate the dry content of the porous structure for various dwell times. The relation between dry content and dwell time was compared to laboratory data for paper sheets with basis weights of 20 and 50 g/m2 exposed to vacuum levels between 20 kPa and 60 kPa. The comparison showed reasonable results for dewatering and air flow rates. The random positioning of the fibres influences the dewatering rate slightly. In order to achieve more accurate comparisons, the random orientation of the fibres needs to be considered, as well as the deformation and displacement of the fibres during the dewatering process.

Finite difference calculations of permeability in large domains in a wide porosity range.

Determining effective hydraulic, thermal, mechanical and electrical properties of porous materials by means of classical physical experiments is often time-consuming and expensive. Thus, accurate numerical calculations of material properties are of increasing interest in geophysical, manufacturing, bio-mechanical and environmental applications, among other fields. Characteristic material properties (e.g. intrinsic permeability, thermal conductivity and elastic moduli) depend on morphological details on the porescale such as shape and size of pores and pore throats or cracks. To obtain reliable predictions of these properties it is necessary to perform numerical analyses of sufficiently large unit cells. Such representative volume elements require optimized numerical simulation techniques. Current state-of-the-art simulation tools to calculate effective permeabilities of porous materials are based on various methods, e.g. lattice Boltzmann, finite volumes or explicit jump Stokes methods. All approaches still have limitations in the maximum size of the simulation domain. In response to these deficits of the well-established methods we propose an efficient and reliable numerical method which allows to calculate intrinsic permeabilities directly from voxel-based data obtained from 3D imaging techniques like X-ray microtomography. We present a modelling framework based on a parallel finite differences solver, allowing the calculation of large domains with relative low computing requirements (i.e. desktop computers). The presented method is validated in a diverse selection of materials, obtaining accurate results for a large range of porosities, wider than the ranges previously reported. Ongoing work includes the estimation of other effective properties of porous media.