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.

This research addresses a number of fundamental issues concerning convective mass transfer across fluid-fluid interfaces in porous media. Mass transfer to/from distributed sinks/sources is considered for i) the slow dissolution of liquid filaments of a wetting non-aqueous phase liquid (NAPL) held in the corners of angular pores or throats and ii) the fate of gas bubbles generated during the flow of a supersaturated aqueous phase in porous media. 1. Effects of the stability of NAPL films on wetting NAPL dissolution Wettability profoundly affects the distribution of residual NAPL contaminants in natural soils. Under conditions of preferential NAPL wettability, NAPL is retained within small pores and in the form of thick films (liquid filaments) along the corners and crevices of the pore walls. NAPL films in pore corners provide capillary continuity between NAPL-filled pores, dramatically influencing the behaviour of NAPL dissolution to the flowing aqueous phase by convection and diffusion. A pore network model is developed to explore the dissolution behaviour of wetting NAPL in porous media. The effects of initial NAPL distribution and NAPL film stability on dissolution behaviour are studied using the simulator. NAPL phase loses continuity and splits into disconnected clusters of NAPL-filled pores due to rupture of NAPL films. Quasi-state drainage and fingering of the aqueous phase into NAPL-filled pores is treated as an invasion percolation process and a stepwise procedure is adopted for the solution of flow and solute concentration fields. NAPL film stability is shown to critically affect the rate of mass transfer as such that stable NAPL films provide for more rapid dissolution. The network simulator reproduces the essential physics of wetting NAPL dissolution in porous media and explains the concentration-tailing behaviour observed in experiments, suggesting also new possibilities for experimental investigation. 2. Convective Mass Transfer across Fluid Interfaces in Straight Angular Pores Steady convective mass transfer to or from fluid interfaces in pores of angular cross-section is theoretically investigated. The model incorporates the essential physics of capillarity and solute mass transfer by convection and diffusion in corner fluid filaments. The geometry of the corner filaments, characterized by the fluid-fluid contact angle, the corner half-angle and the interface meniscus curvature, is accounted for. Boundary conditions of zero surface shear (‘perfect-slip’) and infinite surface shear (‘no-slip’) at the fluid-fluid interface are considered. The governing equations for laminar flow within the corner filament and convective diffusion to or from the fluid-fluid interface are solved using finite-element methods. Flow computations are verified by comparing the dimensionless resistance factor and hydraulic conductance of corner filaments against recent numerical solutions by Patzek and Kristensen [2001]. Novel results are obtained for the average effluent concentration as a function of flow geometry and pore-scale Peclet number. These results are correlated to a characteristic corner length and local pore-scale Peclet number using empirical equations appropriate for implementation in pore network models. Finally, a previously published “2D-slit” approximation to the problem at hand is checked and found to be in considerable error. 3. Bubble evolution driven by solute diffusion during the process of supersaturated carbonated water flooding In situ bubble growth in porous media is simulated using a pore network model that idealizes the pore space as a lattice of cubic chambers connected by square tubes. Evolution of the gas phase from nucleation sites is driven by the solute mass transfer from the flowing supersaturated water solution to the bubble clusters. Effects of viscous aqueous phase flow and convective diffusion in pore corners are explicitly accounted for. Growth of bubble clusters is characterised by a pattern of quasi-static drainage and fingering in the gas phase, an invasion percolation process controlled by capillary and gravitational forces. A stepwise solution procedure is followed to determine the aqueous flow field and the solute concentration field in the model by solving the conservation equations. Mobilization of bubbles driven by buoyancy forces is also studied. Results of bubble growth pattern, relative permeability and macroscopic mass transfer coefficient are obtained under different gas saturations and aqueous flow conditions.

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.

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.

<p>The need for an improved ability to "see into the earth" has resulted in the use of geophysical techniques, especially the electrical resistivity method, in engineering and environmental investigations. The major challenge in the use of electrical resistivity measurements however is the interpretation of the electrical response. This is due to the lack of adequate understanding of the relationships between the physical factors controlling the engineering behavior of geomaterials (earth materials) and their measurable electrical parameters. This research work therefore sets out to investigate the linkages between engineering and petrophysical properties of geomaterials and their geoelectrical parameters. This goal is achieved through the development of laboratory equipments and the conduction of both laboratory and field studies. The laboratory experiments involve the measurement of the complex resistivity responses of natural and artificial soil samples under varying effective stress conditions. The field study involves the characterization of subsurface fracture parameters from field electrical measurements in complex fractured terrains at selected farming communities in Ghana.</p><p>The results from this study improve on our knowledge and understanding of the influence of fundamental engineering properties of geomaterials on their electrical responses. It results will aid in the interpretation of field electrical measurements and provide a means for engineering properties of geomaterials to be estimated from measurable electrical parameters. It will also contribute towards using non-invasive electrical measurements to locate weak zones in the subsurface, assess and monitor the stability conditions of soil units and assist in the environmental impact assessment of anthropogenic activities on groundwater resources in complex fractured terrain.</p> / Dissertation

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Pulse Tube Cryocoolers (PTC) is widely used in aerospace and missile guiding systems where extreme reliability and ruggedness are crucial. PTCs, in particular, are a class of rugged refrigeration systems that are capable of maintaining temperatures as low as 4 K, without a moving part in their cold end. The operation of PTCs is based on complicated and poorly-understood solid-fluid interactions involving periodic flows of a cryogenic fluid in micro porous structures. Currently, PTCs is often modeled as one-dimensional flow fields using methods whose relevance to cryocoolers is at best questionable. Furthermore, recent CFD-based investigations have underscored the need for adequate closure relations representing periodic flows in anisotropic micro porous media, and have shown that multi-dimensional effects can be significant in PTCs. The objectives of this investigation were to experimentally measure and correlate the anisotropic hydrodynamic parameters for typical micro porous structures that are used in the regenerators of PTCs fillers; perform modeling and CFD-based simulations to elucidate the component and system-level thermo-fluidic processes in modern pulse tube cryocooler designs; and perform a preliminary CFD-based assessment of the effect of miniaturization on the thermal performance of a current PTC design. In the experiments, the measurement and correlation of the directional (axial and radial) permeabilities and Forchheimer s inertial coefficients of meshed screen, sintered mesh, foam metal, and stacked micro-machined plate regenerator fillers were of interest. Hydrodynamic parameters under steady-state conditions were addressed first. Pressure drops were measured for purely axial flow in cylindrical test sections and predominantly radial flows in annular test sections that contained regenerator fillers of interest, under steady-state conditions. The permeabilities and Forchheimer s inertial coefficients were then obtained in an iterative process where agreement between the data and the predictions of detailed CFD simulations addressing the entire test sections and their surroundings were sought. Periodic flows were then addressed. Using high frequency pressure transducers and hot wire anemometry, instantaneous pressures and mass fluxes are measured under periodic purely axial flow conditions. CFD simulations of the experiments were then performed, whereby permeabilities and Forchheimer coefficients that bring about agreement between data and simulation results were calculated.

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 e&#64256;ect 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 e&#64256;ective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a &#64257;nite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coe&#64259;cients. For linear coe&#64259;cients, the multiscale &#64257;nite volume element method is viewed as a perturbation of multiscale &#64257;nite element method. The analysis uses substantially the existing &#64257;nite element results and techniques. The multiscale method for nonlinear coe&#64259;cients will be analyzed in the &#64257;nite 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 &#64258;ow in porous media. Problems that we will consider are multiphase immiscible &#64258;ow, multicomponent miscible &#64258;ow, and soil in&#64257;ltration in saturated/unsaturated &#64258;ow.