The groundwater specialists and the reservoir engineers share the same interest in simulating multiphase flow in soil with heterogeneous intrinsic properties. They also both face the challenge of going from a well-modeled micrometer scale to the reservoir scale with a controlled loss of information. This upscaling process is indeed worthy to make simulation over an entire reservoir manageable and stochastically repeatable. Two upscaling steps can be defined: one from the micrometer scale to the Darcy scale, and another from the Darcy scale to the reservoir scale. In this thesis, a new second upscaling multiscale algorithm Finite Volume Mixed Hybrid Multiscale Methods (Fv-MHMM) is investigated. Extension to a two-phase flow system is done by weakly and sequentially coupling saturation and pressure via IMPES-like method.

[pt] No método de injeção de água, o óleo no reservatório é varrido até os poços produtores através de frentes de deslocamento não uniformes, deixando óleo estagnado em grandes regiões do reservatório. Frentes uniformes de deslocamento e uma melhor varredura do reservatório podem ser obtidas diminuindo a razão de mobilidade entre a água e o óleo. Normalmente, esta diminuição é feita através da modificação da razão de viscosidade entre ambas as fases. No método de injeção de emulsões, o controle da mobilidade é alcançado bloqueando os poros ou caminhos gerados pela água com gotas da fase dispersa com diâmetro da mesma ordem ou maior do que o tamanho de poro. A aplicação de emulsões no controle da mobilidade e o efeito do bloqueio de poro podem ser desenvolvidos mediante a análise de diferentes regimes de escoamento de emulsões em meios porosos. Neste trabalho, o estudo do escoamento de emulsões em meios porosos foi realizado mediante duas abordagens experimentais utilizando um micro-capilar com garganta para modelar uma garganta conectando dois poros adjacentes. Na primeira abordagem experimental, quantificou-se a queda de pressão para diferentes vazões com emulsões de três tamanhos de gota e duas concentrações de óleo em dois capilares diferentes. Os resultados confirmam que a razão entre o diâmetro da garganta do capilar e o tamanho de gota influencia fortemente a relação vazão-queda de pressão. Os resultados mostram que, para baixos números de capilaridade, o escoamento de emulsões é dominado por efeitos capilares e leva a uma diminuição da mobilidade local. Na segunda montagem experimental, o sistema de micro-velocimetria por imagem de partículas ou u-PIV foi utilizado para medir campos de velocidade do escoamento através de micro-capilares com garganta. Resoluções espaciais da ordem de 20um foram obtidas para o campo de velocidade calculado pela média amostral de vários campos instantâneos de velocidade. Os resultados experimentais da relação vazão-queda de pressão e os campos de velocidade obtidos mediante o u-PIV representam informação de grande valor para o desenvolvimento de modelos de redes de capilares no estudo do escoamento de emulsões em meios porosos. / [en] During water injection, oil is swept through the reservoir to production wells by non-uniform displacement fronts originating large areas of entrapped oil in the reservoir. Uniform displacement fronts and better reservoir sweep can be achieved by improving the mobility ratio between water and oil. Usually, mobility ratio is reduced by changing the viscosity ratio between both phases. When injecting emulsions, mobility control is achieved by blocking water paths with dispersed phase drops with diameter of the same order of magnitude of the pore throats size. The application of emulsions as mobility control agents and the pore blocking effect may be developed by analyzing different flow regimes of emulsions through porous media. In the analysis presented here, two experimental setups were used using a constricted quartz capillary to represent a pore throat that connects two adjacent pore bodies to study the flow of emulsions in the pore scale. In the first experiment, pressure drop was measured at different imposed volumetric flow rates for three oil drop size emulsions at two oil concentrations and two different quartz capillaries. The results show that the ratio between the capillary constriction diameter and the oil drop size has a strong influence on the flow rate-pressure drop relation. Experimental results also indicate that the emulsion flow dominated by capillary effects (low capillary number) leads to a decrease of local mobility. In the second experiment, a microscopic particle image velocimetry (u-PIV) system was used to measure velocity fields of the flow of emulsion through a constricted micro-capillary. Ensemble-average was used in order to obtain resolution in the order of 20 um. The flow rate-pressure drop relation results and the u-PIV velocity fields of the emulsion flow through a constricted micro-capillary represent invaluable information that can be used in the development of a capillary network model to study the flow of emulsions through porous media.

This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

This work deals with the study of heat transfer between a porous medium and a free medium, using multi scale approaches. First, we derive the boundary conditions that must be applied at a free-porous interface for laminar heat transfer at local thermal equilibrium and, then, at local thermal non-equilibrium. For turbulent heat transfer, a direct numerical simulation is performed supplying a better understanding of the physic at the free-porous interface. Then, we determine a turbulent model with associated jump conditions. These studies answer fundamental questions regarding the physical meaning of the jump conditions, the values of the jump parameters and the location of the interface for heat transfer.

The genus Phytophthora comprises numerous plant pathogens in both natural and managed ecosystems. For Phytophthora spp. that infect roots, dispersal occurs in soil water through a combination of advection and swimming of specialized motile propagules (zoospores). Specific biological and physico-chemical processes, however, remain poorly understood, due to difficulties in studying phenomena in opaque media and lack of a theoretical framework for analyzing transport of motile microorganisms. The goal of this research was to elucidate the impacts of advection and swimming on zoospore movement in a saturated, ideal soil. The work was accomplished in two stages, (i) conceptualization of 3-dimensional topography and flow field heterogeneity at the subpore-scale, and (ii) observation of behavior of zoospore suspensions infiltrated into saturated media. Chapter 2 introduces a 3-dimensional particle tracking method and presents two studies investigating particle transport in simplified 'ideal pores'. The first study describes 'avoidance' by latex microspheres of a volume surrounding orthogonal grain contacts and the second describes 'capture', translation, and retention of microspheres under conditions unfavorable to deposition. Chapter 3 expands on the first study and demonstrates, with the aid of computational fluid dynamics, that low flow zones associated with orthogonal grain contacts are minimally connected to the main flow. Thus, probability of entry into these regions for large, non-Brownian particles by advection alone is low. In zoospore infiltration experiments, zoospore plumes 'converged' rather than dispersing as expected. To assess the possibility of zoospore auto-aggregation driving this 'convergence', Chapter 4 delves into the 'pattern swimming' observed in free-swimming zoospore suspensions, concluding that the concentrating is an example of bioconvection. Chapter 5 introduces a conceptual model to explain the anomalous zoospore plume behavior. Random walk simulations replicated plume convergence but were less successful at modeling anisotropic dispersion. At low infiltration rates (<100 μm s⁻¹), simulations predict that zoospores will remain at or near the soil surface, resulting in greater opportunity to find host tissues or to be transported with surface water. Further investigation is necessary to develop a robust theoretical framework with appropriate conceptualization of the subpore hydrodynamic environment for predicting transport of zoospores and other motile microorganisms in porous media. / Graduation date: 2011

Motivated by the reservoir engineering concept of the productivity index of a producing oil well in an isolated reservoir, we analyze a time dependent functional, diffusive capacity, on the solutions to initial boundary value problems for a parabolic equation. Sufficient conditions providing for time independent diffusive capacity are given for different boundary conditions. The dependence of the constant diffusive capacity on the type of the boundary condition (Dirichlet, Neumann or third-type boundary condition) is investigated using a known variational principle and confirmed numerically for various geometrical settings. An important comparison between two principal constant values of a diffusive capacity is made, leading to the establishment of criteria when the so-called pseudo-steady-state and boundary-dominated productivity indices of a well significantly differ from each other. The third type boundary condition is shown to model the thin skin effect for the constant wellbore pressure production regime for a damaged well. The questions of stabilization and uniqueness of the time independent values of the diffusive capacity are addressed. The derived formulas are used in numerical study of evaluating the productivity index of a well in a general three-dimensional reservoir for a variety of well configurations.

NAPL (non-aqueous phase liquid) blob mobilization and solubilization models were developed to predict residual NAPL fate and describe flow dynamics of various displacing phases (water and surfactant foam). The models were achieved by pore-scale mass and force balances and were focused on the understanding of the physico-chemical interactions between NAPL blobs and the displacing phases. The pore-level mass balance indicated changes in NAPL saturation instead of mass reduction occurring with blob solubilization. The force balance was used to explain the complex flow configurations among NAPL blobs and the displacing phases. Some factors such as the wettability and the spreading/entering coefficients were useful in determining flow configurations. From the models developed in this study, dimensional analysis was performed to identify NAPL blob motion during water or surfactant foam flooding. In non-dimensionalized forms, a Trapping number employed as an indicator of blob displacement performance was modified to quantify the onset of blob mobilization. Its value for water flooding was nearly 2-3 orders of magnitude greater than that of surfactant foam flooding. Next, to investigate the blob flow regime in porous media, a blob velocity was computed. Regardless of the displacing phases, a blob’s velocity increased with increasing blob sizes after commencement of blob motion, and the velocity of DNAPL (dense non-aqueous phase liquid) blobs was greater than that of LNAPL (light non-aqueous phase liquid) blobs. From this investigation, it is expected that the pore-scale solubilization and mobilization models would provide better understanding leading to a predictive capability for the flow behavior of NAPL blobs removed by various displacing phases in a porous medium. Additionally, the models based on newly approached concepts and modified governing equations would be useful in conceptualization, as well as the model prediction of other immiscible or miscible fluids flowing through a porous medium. Further, the models developed in our study would be a useful contribution to the study of small-scale contaminants or substances such as particle and bacterial transport in porous media.

As a hygroscopic salt, granular potash can easily absorb large quantities of water vapor from humid air during storage and transportation processes. Subsequent drying will result in potash particles sticking together to form clumps or cakes. In order to avoid or decrease caking, it is essential to know the local history of moisture content and moisture movement in a bed of potash. In this thesis, experimental measurements and numerical simulations are used to investigate moisture transport and redistribution by capillarity, gravity and diffusion effects within a potash bed. <p> The important properties required to model moisture transfer in granular porous potash (i.e. porosity, permeability, specific surface area and irreducible saturation) are investigated experimentally and theoretically. It is shown that for a mixture with a wide range of particle sizes the potash bed properties can be predicted knowing the properties for each narrow range of particle size in the mixture. <p> An experimental test facility was designed and constructed to test moisture transfer within a potash bed. The test procedures are presented along with an uncertainty analysis. The moisture content spatial distribution for different particle sizes under different initial conditions is investigated and data are presented. <p>A one-dimensional transient numerical model of moisture transport accounting for diffusion, capillarity and gravity effects within potash beds is developed. Two different moisture transport mechanisms are presented. In a wet region, where local moisture saturation level, S, is larger than an irreducible saturation, S0, liquid water exists as continuous liquid film on the particles; moisture is transferred by liquid film movement due to capillarity and gravity effects. In a dry region where S is less than S0, water vapor diffusion is the only mechanism of moisture transfer and water is adsorbed in layers on the surfaces. <p> From the experimental data and numerical simulation analysis, it is shown that the irreducible saturation, S0, is a strong function of particle size. It will decrease with a particle size increase. <p> The numerical model is validated by comparison with some typical experimental case studies. Agreement between the experimental data and simulation results is well within the experimental 95% uncertainty bounds. It is concluded from this research that the complex moisture transport process by diffusion, capillarity and gravity effects within a potash bed can be modeled and simulated. Experimental and simulation results indicate that direct water drainage will more readily occur for large particle sizes than for small particles for the same initial moisture content.

Elemental sulphur (S0) is produced from processing bitumen from the oil sands region, Alberta. Long term storage of this S0 is under consideration. The objective of the current study was to determine the controls on water migration in variably saturated S0 blocks. Based on visual observations of S0 blocks, they were characterized as a hydrophobic fractured porous media. Thus, measurements of the hydraulic characteristics, including porosity (n) and hydraulic conductivity (K) of the matrix and the fractured media, were undertaken. These data were used to create characteristic relationships of unsaturated K (Kunsat) and volumetric moisture content (è) change with change in positive injection pressure (Ø).<p>Analyses showed that the mean total matrix n (nm) was 0.094 ± 0.035 (n = 280), the mean n available for water migration (na) was 0.065 ± 0.044 (n = 8) and the mean (geometric) K for the matrix was 2.0 x 10-6 ± 2.1 x 10-6 ms-1. In the case of vertical fractures, the aperture frequencies were measured to be 2.5, 10.0 and 21.0 m-1 for fractures with apertures > 1.4, 1.4 to 0.6 and < 0.6 mm respectively while the frequency of horizontal fractures, were measured to be 1.7 and 3.7 m-1 for with apertures > 1.4, and < 1.4 mm respectively. The fracture n (nf) was determined to be 0.0135. è Ø relationships were determined for both the fractured and non fractured media. From these plots, water entry values of 9 mm and 1 m were determined for the fracture pore space and the matrix pore space, respectively.<p>Simulations of packer tests resulted in a bulk saturated K (Kb) values ranging from 8.5 x 10-5 to 2 x 10-4 ms-1 above 9 m depth and 3 x 10-6 to 1.5 x 10-5 ms-1 below 9 m depth. Coupled Kunsat Ø and è Ø relationships were used to conceptually describe water migration in S0 blocks under different precipitation and mounding conditions. These plots also showed that the Kb is dominated by the fractures.

As a hygroscopic salt, granular potash can easily absorb large quantities of water vapor from humid air during storage and transportation processes. Subsequent drying will result in potash particles sticking together to form clumps or cakes. In order to avoid or decrease caking, it is essential to know the local history of moisture content and moisture movement in a bed of potash. In this thesis, experimental measurements and numerical simulations are used to investigate moisture transport and redistribution by capillarity, gravity and diffusion effects within a potash bed. <p> The important properties required to model moisture transfer in granular porous potash (i.e. porosity, permeability, specific surface area and irreducible saturation) are investigated experimentally and theoretically. It is shown that for a mixture with a wide range of particle sizes the potash bed properties can be predicted knowing the properties for each narrow range of particle size in the mixture. <p> An experimental test facility was designed and constructed to test moisture transfer within a potash bed. The test procedures are presented along with an uncertainty analysis. The moisture content spatial distribution for different particle sizes under different initial conditions is investigated and data are presented. <p>A one-dimensional transient numerical model of moisture transport accounting for diffusion, capillarity and gravity effects within potash beds is developed. Two different moisture transport mechanisms are presented. In a wet region, where local moisture saturation level, S, is larger than an irreducible saturation, S0, liquid water exists as continuous liquid film on the particles; moisture is transferred by liquid film movement due to capillarity and gravity effects. In a dry region where S is less than S0, water vapor diffusion is the only mechanism of moisture transfer and water is adsorbed in layers on the surfaces. <p> From the experimental data and numerical simulation analysis, it is shown that the irreducible saturation, S0, is a strong function of particle size. It will decrease with a particle size increase. <p> The numerical model is validated by comparison with some typical experimental case studies. Agreement between the experimental data and simulation results is well within the experimental 95% uncertainty bounds. It is concluded from this research that the complex moisture transport process by diffusion, capillarity and gravity effects within a potash bed can be modeled and simulated. Experimental and simulation results indicate that direct water drainage will more readily occur for large particle sizes than for small particles for the same initial moisture content.