Uma área de aplicação da Ressonância Magnética (RM) que tem crescido recentemente é a de meios porosos, principalmente devido ao interesse da indústria petrolífera. Entretanto, até o presente momento, muito do que foi feito se baseia em medidas de relaxometria, o que impossibilita qualquer tipo de avaliação espacial desses meios. O presente trabalho teve como objetivo principal desenvolver, implementar e avaliar a aplicabilidade de métodos de imagens por RM para o estudo da morfologia de meios porosos. Esses sistemas apresentam tempos de relaxação bastante curtos, além de diferenças de susceptibilidade entre as paredes da rocha e os poros, o que compromete a qualidade dos dados de RM. Por essa razão, no presente trabalho nos concentramos em avaliar as imagens obtidas por RM, no que se refere à morfologia, usando imagens obtidas por microtomografia como referência. Os resultados revelaram que, apesar da variação na susceptibilidade do meio e dos baixos tempos de relaxação, o comprometimento na avaliação final esteve abaixo da resolução espacial da técnica e, portanto, não se configura como um limitante. Isso sugere que a técnica de imagens por RM pode contribuir para o estudo de meios porosos. Embora a microtomografia já ofereça bons resultados para o estudo de morfologia, imagens por RM devem viabilizar a investigação não invasiva de problemas nos quais a dinâmica de fluidos é relevante, o que ainda representa um desafio na área de estudos de meios porosos. / A recently growing application area of Magnetic Resonance (MR) is that of porous media, mainly due to the interest from the petrol industry. However, until the present moment, however, most of what has been done is based on relaxometry measures, which forbids any kind of special evaluation of these media. The objective of this work was to develop, implement and evaluate the applicability of MR imaging methods for the study of the morphology of porous media. These systems have very short relaxation times and considerable susceptibility differences between the rock walls and the pores, both of which compromise the quality of the data obtained via MR. For this reason, in this current work we focused on evaluating the MR images, with respect to morphology, using images obtained via microtomography as reference. Our results showed that, despite the susceptibility variations on the media and the short relaxation times, the errors in the final evaluation were below the spatial resolution threshold and, therefore, are not considered as a limiting factor. This suggests that MR imaging techniques can indeed contribute to the study of porous media. Although microtomography already offers good results on morphology studies, MR imaging can turn feasible the non-invasive investigation of problems on which the fluid dynamics is relevant, an issue which still represents a challenge in the study of porous media.

[pt] Emulsões podem ser utilizadas como agentes de controle de mobilidade em diferentes processos de recuperação melhorada de petróleo e armazenamento de carbono em reservatórios porosos. A aplicação desta técnica, com a escolha correta das características das emulsões injetadas e a determinação das condições de operação ótimas, requer um entendimento adequado do escoamento de emulsões em meios porosos. As características macroscópicas do fluxo de emulsões através de meios porosos estão diretamente ligadas ao escoamento bifásico na escala de poros. Modelos de rede de capilares permitem a implementação dos mecanismos de fluxo das gotas nas gargantas de poros e fornecem parâmetros macroscópicos do escoamento. Neste trabalho, o escoamento de emulsões em meios porosos é analisado através de um modelo dinâmico de rede de capilares tridimensional e não-estruturada. A distribuição de pressão nos poros, e consequentemente o fluxo em cada capilar da rede, é determinada pelo balanço de massa em cada poro. O efeito das gotas da fase dispersa no comportamento do escoamento em cada elemento da rede é descrito por um fator de bloqueio de fluxo baseado em resultados experimentais de escoamento de emulsões através de micro capilares com gargantas. O fator de bloqueio descreve a mudança da condutividade de cada elemento e é uma função da geometria da garganta, do tamanho e concentração volumétrica da fase dispersa e do número de capilaridade local. A distribuição de concentração da fase dispersa ao longo da rede é descrita através de uma equação de transporte de massa, permitindo assim o estudo do processo de filtragem de gotas nos poros e o estudo da injeção alternada de água e emulsão. A integração no tempo do modelo dinâmico é feita por um método semi-implícito e o sistema de equações não linear obtido a cada passo de tempo é resolvido através de um método iterativo. Os resultados apresentam a evolução da redução da permeabilidade e concentração de gotas na saída do meio poroso em função do tamanho das gotas, da vazão de injeção, da concentração da emulsão injetada e do volume injetado de emulsão. A análise da injeção alternada de água-emulsão mostra claramente o bloqueio de poros por gotas da emulsão e a alteração no padrão de escoamento após reiniciada a injeção de água. / [en] Emulsions can be used as mobility control agents in different enhanced oil recovery and carbon storage methods in oil reservoirs. The application of this technique, with the correct choice of the injected emulsion characteristics and the determination of optimal operating conditions, requires an adequate understanding of the emulsion flow in porous media. The macroscopic characteristics of the emulsion flow through porous media are directly linked to the two-phase flow at the pore scale. Capillary network models allow the implementation of the drop flow mechanisms in the pore throats and the determination of macroscopic flow parameters. In this work, emulsion flow in porous media is analyzed through an unstructured 3D dynamic network model. The pressure distribution, and consequently the flow rate in each capillary of the network, isdetermined by mass balance equation in each pore. The effects of the drops of dispersed phase in the flow behavior within each element of the network is described by a flow blocking factor based on experimental results on emulsion flow through single microcapillary tubes with throats. The blocking factor describes the changes in the conductivity of each element and it is a function of the throat geometry, the size and volumetric concentration of the dispersed phase and the local capillary number. The concentration distribution of the dispersed phase along the network is described by a mass transport equation, allowing the study of the filtration process of the drops in the pores and the analysis of the alternate injection of water and emulsion.Time integration in the dynamic model is performed by a semi-implicit method and the non-linear system of equations obtained in each time step is solved by an iterative method. The results illustrate the evolution of the permeability reduction and the effluent concentration of drops as a function of the drops size, injection flow rate, concentration of the injected emulsion and injected volume of emulsion. The analysis of the emulsion/water alternate injection clearly shows the pore blockage by the emulsion drops and the change in the flow pattern after the reinjection of water.

This thesis describes a new dynamic network model for imbibition which is based on a physically realistic description of the complex dynamics of corner film flow, swelling and snap-off. The model shows that film flow is a capillary driven non-linear diffusive process and that the competition between snapoff and frontal displacements is rate dependent and results in rate dependent relative permeabilities and residual saturations. In contrast to previously published models in which length scales for snap-off are either specified a priori or calculated assuming steady-state film flow and constant film conductivities, in the present model, snap-off arises as a natural consequence of the fully transient nature of film flow and swelling. The network model is used to analyse the complex interaction between displacement rate, contact angle, aspect ratio and pore and throat shape on relative permeability and residual saturation. Computed relative permeabilities and residual saturations are compared with laboratory measurements reported in the literature. It is concluded that the magnitude of the rate effect on imbibition relative permeabilities and residual saturations for a particular rock microstructure and wettability condition depends largely on the pore-throat aspect ratio. Higher aspect ratios result in stronger rate effects than do smaller aspect ratios.

In this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales effect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more effective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a finite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coefficients. For linear coefficients, the multiscale finite volume element method is viewed as a perturbation of multiscale finite element method. The analysis uses substantially the existing finite element results and techniques. The multiscale method for nonlinear coefficients will be analyzed in the finite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the flow in porous media. Problems that we will consider are multiphase immiscible flow, multicomponent miscible flow, and soil infiltration in saturated/unsaturated flow.

The objective of this dissertation is to investigate the non-Darcy flow effects on field base data by considering gas viscosity, gas deviation factor and gas density as variables. To achieve it, different correlations from the literature and field data have been combined to Sawyer-Brown Method, thus a contribution has been achieved. Production history of selected gas field has been implemented to a numerical simulator. To find out non-Darcy effects quantitatively, Darcy flow conditions have also been run in the simulator for each scenario in addition to non-Darcy flow correlation runs. Extracted data from simulation runs have been analyzed on the basis of Sawyer-Brown Method by introducing several correlations to consider gas viscosity, gas deviation factor and gas density as variables. Engineering and scientific research on non-Darcy flow is still being conducted in order for better understanding the nonlinear flow behavior of fluids through porous media. The deviations from Darcy&rsquo / s Law are attributed to the occurrence of all or alternating combinations of factors that can be categorized as the anisotropy of porosity and permeability, multi-phase flow of fluids in varying phases, magnitude of pressure drop and the subsequent phase change in fluids, and the change in flow regime at elevated rates of flow in porous media. Throughout this dissertation, the factors causing deviations from Darcy flow behavior have been investigated.

An acoustic frequency-swept wave was investigated as a means for determining Snow Water Equivalent (SWE) in cold wind-swept prairie and sub-alpine environments. Building on previous research conducted by investigators who have examined the propagation of sound in snow, digital signal processing was used to determine acoustic pressure wave reflection coefficients at the interfaces between 'layers' indicative of changes in acoustic impedance. Using an iterative approach involving boundary conditions at the interfaces, the depth-integrated SWE was determined using the Berryman equation from porous media physics. Apparatuses used to send and receive sound waves were designed and deployed during the winter season at field sites situated near the city of Saskatoon, Saskatchewan, and in Yoho National Park, British Columbia. Data collected by gravimetric sampling was used as comparison for the SWE values determined by acoustic sounding. The results are encouraging and suggest that this procedure is similar in accuracy to SWE data collected using gravimetric sampling. Further research is required to determine the applicability of this technique for snow situated at other geographic locations.

Porous media flows are encountered in many natural and man-made systems such as gas adsorption, filtration, heat exchangers, combustion, catalytic reactors and groundwater hydrology. This study experimentally investigates these flows as function of pore Reynolds number, Re[subscript pore]. The pore Reynolds number is based on the porous bed hydraulic diameter, D[subscript H] =φD[subscript Β]/(1−φ) where φ is bed porosity and D[subscript B] is solid phase bead diameter and average bed interstitial velocity, V[subscript int]= V[subscript Darcy]/φ, where VDarcy= Q/A[subscript bed], with Q being the volumetric flow rate and A[subscript bed] the bed cross section normal to the flow. The flow characteristics are studied through application of a particle displacement technique called particle image velocimetry, PIV. In the case of PIV, flow fields are estimated by seeding the flow with tracer particles and then evaluating their displacements. Application of quantitative imaging technique such as PIV to a complex flow domain like porous bed requires matching refractive index of liquid phase to that of the solid phase. Firstly, the effect of slight index mismatch, due to experimental uncertainties, on obtaining highly accurate PIV measurements as expressed as an experimental uncertainty was explored. Mismatch of refractive indices leads to error in estimation of particle positions and their displacements due to refraction at solid-liquid interfaces. Slight mismatch, in order of 10⁻³, in refractive indices also leads to reduction in particle density, particle signal peak intensity and degrade the particle image. These effects on velocity field estimation using PIV is studied experimentally and numerically. The numerical model, after validating against experimental results, is used to generate an expression for the error in PIV measurements as a function of refractive index mismatch for a range of bead diameters, bed widths, bed porosity, and optical magnification. After refractive index matching, planar PIV measurements were taken at discrete locations throughout a randomly packed bed with aspect ratio (bed width to bead diameter) of 4.67 for steady, low pore Reynolds number flows, Re[subscript pore] ~ 6, intermediate Re[subscript pore] of 54 and unsteady flow with high Re[subscript pore] ranging from 400-4000. Details of the measurement uncertainties as well as methods to determine local magnification and determination of the dynamic velocity range are presented. The data are analyzed using the PIV correlation averaging method for steady flows and multigrid and multipass correlation methods for unsteady turbulent flows with the largest velocity uncertainties arising from in plane image loss and out of plane motion. Results for low Re[subscript pore] flows show the correspondence of the geometric and velocity correlation functions across the bed, and that the centerline of the bed shows a random-like distribution of velocity with an integral length scale on the order of one hydraulic diameter (or 0.38 bead diameters based on the porosity for this bed). The velocity variance is shown to increase by a factor of 1.8 when comparing the center plane data versus using data across the entire bed. It is shown that the large velocity variance contributes strongly to increased dispersion estimates, and that based on the center plane data of the variance and integral length scales, the dispersion coefficient matches well with that measured in high aspect ratio beds using global data. For unsteady and turbulent flow, velocity data were used to determine the following turbulence measures: (i) turbulent kinetic energy components, (ii) turbulent shear production rate, (iii) integral Eulerian length and time scales, and (iv) energy spectra all for a range of pore Reynolds numbers, Re[subscript pore], from 418 to 3964. These measures, when scaled with the bed hydraulic diameter, DH, and average interstitial velocity, V[subscript int], all collapse for Re[subscript pore], beyond approximately 2800, except that the integral scales collapse at a lower value near 1300-1800. The results show that the pore turbulence characteristics are remarkably similar from pore to pore and that scaling based on bed averaged variables like D[subscript H] and V[subscript int] characterizes their magnitudes despite very different local mean flow conditions. In the case of high Re[subscript pore] flows, large scale structures such as stationary and convected vortices and structures resembling jets were also identified. These structures were analyzed in detail using decomposition techniques like Large Eddy Scale decomposition and critical point analysis like swirl strength analysis. Direct velocity measurements were used to estimate Lagrangian statistics through Eulerian measures and then estimate contribution of flow structures to turbulent mechanical dispersion. Results agree well with those in the literature obtained using global measurements in very high aspect ratio, long test beds. Stationary vortical or recirculation regions were seen to play a dominant role in contributing to overall dispersion in porous beds. / Graduation date: 2013

It is widely known in oil industry that changes in fluid flow conditions such as water breakthrough or unsteady flow due to well shut-in can lead to sand destabilization, with a possible consequent sand production. In this research, different flow situations are incorporated into stress and stability analysis for the region around a wellbore producing oil from weak or unconsolidated sands, and the analyses involve strength weakening, stress redistribution, and decrease of rock stiffness. Two main mechanisms, chemical reactions of rock with formation water and variations of rock capillary strength, are identified and analyzed to study strength weakening after water breakthrough, both qualitatively and quantitatively. Using theories from particle mechanics, rock mechanics, and interfacial science, four novel capillarity models are developed and verified to analytically capture the physical behaviors of capillary strength at the grain scale. Based on model calculations, significantly better understanding of strength behavior in two-phase fluid environments is achieved. Based on a simplified model that can conservatively but efficiently quantify capillary strength with only two input parameters (i. e. particle radius and water saturation), a verified new method that physically calculates pore pressure in a multiphase environment, and a coupled poro-inelastic stress model, the redistributions of effective stresses with water saturation around a wellbore are solved. In terms of stress changes and growth of a plastic radius defining shear-failure zone, the effects of different stability factors, including capillarity through water-oil menisci, pore pressure changes due to the variations of fluid relative permeabilities, and loss of strength through chemical reactions of water-sensitive cementation materials, are quantified and compared in order to clarify when and how they contribute to sand production after water breakthrough. The nonlinearities of rock elastic properties in stressed and biphasic fluid environments is analytically addressed, based on an improved nonlinear theory that considers both a failure-based mechanism and a confining-stress-based mechanism, the strength model, and the coupled stress model. The calculations demonstrate the redistributions of stress-dependent rock stiffness around a wellbore and its evolution with increase of water saturation, clarify the relative importance of each mechanism in reducing rock stiffness, and fundamentally explain why current predictive technologies are invalid when water appears in a flowing wellbore. To quantify the effect of well shut-down on rock stability, the redistributions of fluid pressure in reservoir are analytically solved and coupled with the stress model, while the water hammer equations provide a boundary condition for the bottom-hole pressure. This approach allows direct solution of the relationships among fluid properties, rock properties and production parameters, within the context of rock stability. The proposed new approaches and models can be applied to evaluate sand production risk in multiphase and unsteady fluid flow environment. They can also serve as points of departure to develop more sophisticated models, or to develop more useful constitutive laws for numerical solutions.

A practical and important class of scientific images are the 2D/3D images obtained from porous materials such as concretes, bone, active carbon, and glass. These materials constitute an important class of heterogeneous media possessing complicated microstructure that is difficult to describe qualitatively. However, they are not totally random and there is a mixture of organization and randomness that makes them difficult to characterize and study. In order to study different properties of porous materials, 2D/3D high resolution samples are required. But obtaining high resolution samples usually requires cutting, polishing and exposure to air, all of which affect the properties of the sample. Moreover, 3D samples obtained by Magnetic Resonance Imaging (MRI) are very low resolution and noisy. Therefore, artificial samples of porous media are required to be generated through a porous media reconstruction process. The recent contributions in the reconstruction task are either only based on a prior model, learned from statistical features of real high resolution training data, and generating samples from that model, or based on a prior model and the measurements. The main objective of this thesis is to some up with a statistical data fusion framework by which different images of porous materials at different resolutions and modalities are combined in order to generate artificial samples of porous media with enhanced resolution. The current super-resolution, multi-resolution and registration methods in image processing fail to provide a general framework for the porous media reconstruction purpose since they are usually based on finding an estimate rather than a typical sample, and also based on having the images from the same scene -- the case which is not true for porous media images. The statistical fusion approach that we propose here is based on a Bayesian framework by which a prior model learned from high resolution samples are combined with a measurement model defined based on the low resolution, coarse-scale information, to come up with a posterior model. We define a measurement model, in the non-hierachical and hierarchical image modeling framework, which describes how the low resolution information is asserted in the posterior model. Then, we propose a posterior sampling approach by which 2D posterior samples of porous media are generated from the posterior model. A more general framework that we propose here is asserting other constraints rather than the measurement in the model and then propose a constrained sampling strategy based on simulated annealing to generate artificial samples.

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, but not in synthetic calcite. The high adsorption is due to the strong electrostatic interactions between the cationic surfactants and negative binding sites in silica and/or clay. There are a number of commercial foam simulators, but an approach to estimate foam modeling parameters from laboratory experiments is needed to simulate foam transport. A one-dimensional foam simulator is developed to simulate foam flow. Chromatographic retardation of surfactants caused by adsorption and by partition between phases is investigated. The parameters in the foam model are estimated with an approach utilizing both steady-state and transient experiments. By superimposing contour plots of the transition foam quality and the foam apparent viscosity, one can estimate the reference mobility reduction factor (fmmob) and the critical water saturation (fmdry) using the STARS foam model. The parameter epdry, which regulates the abruptness of the foam dry-out effect, can be estimated by a transient foam experiment in which 100% gas displaces surfactant solution at 100% water saturation. Micromodel experiments allow for pore-level visualization of foam transport. We have developed model porous media systems using polydimethylsiloxane. We developed a simple method to tune and pattern the wettability of polydimethylsiloxane (PDMS) to generate porous media models with specific structure and wettability. The effect of wettability on flow patterns is observed in gas-liquid flow. The use of foam to divert flow from high permeable to low permeable regions is demonstrated in a heterogeneous porous micromodel. Compared with 100% gas injection, surfactant-stabilized foam effectively improves the sweep of the aqueous fluid in both high and low permeability regions of the micromodel. The best performance of foam on fluid diversion is observed in the lamella-separated foam regime, where the presence of foam can enhance gas saturation in the low permeable region up to 45.1% at the time of gas breakthrough. In conclusion, this thesis provides new findings in surfactant adsorption onto mineral surfaces, in the methodology of estimating foam parameters for reservoir simulation, and in micromodel observations of foam flow through porous media. These findings will be useful to design foam flooding in EOR processes.