In this thesis, we consider the two-space homogenization method, which produces macroscopic expressions out of descriptions of the behaviour of the microstructure. Specifically, we focus on its application to poroelastic media. After describing the method, we provide examples to demonstrate that the resultant expressions are equivalent to an explicit derivation, which might not always be possible, and to outline the method for proving that the expressions converge to their macroscopic equivalents. Upon providing the basis for this method, we follow Burridge and Keller’s work for using this to prove the existence of Biot’s consolidation equations for poroelastic media and to provide expressions for the derivation of the parameters of these equations from the microstructure [5]. We then discuss the benefits and challenges that arise from this formulation of Biot’s consolidation equations.

Within fractured reservoirs, such as tight gas reservoir, coupled processes between matrix deformation and fluid flow are very important for predicting reservoir behavior, pore pressure evolution and fracture closure. To study the coupling between gas desorption and rock matrix/fracture deformation, a poroelastic constitutive relation is developed and used for deformation of gas shale. Local continuity equation of dry gas model is developed by considering the mass conservation of gas, including both free and absorbed phases. The absorbed gas content and the sorption-induced volumetric strain are described through a Langmiur-type equation. A general porosity model that differs from other empirical correlations in the literature is developed and utilized in a finite element model to coupled gas diffusion and rock mass deformation. The dual permeability method (DPM) is implemented into the Finite Element Model (FEM) to investigate fracture deformation and closure and its impact on gas flow in naturally fractured reservoir. Within the framework of DPM, the fractured reservoir is treated as dual continuum. Two independent but overlapping meshes (or elements) are used to represent these kinds of reservoirs: one is the matrix elements used for deformation and fluid flow within matrix domain; while the other is the fracture element simulating the fluid flow only through the fractures. Both matrix and fractures are assumed to be permeable and can accomodate fluid transported. A quasi steady-state function is used to quantify the flow that is transferred between rock mass and fractures. By implementing the idea of equivalent fracture permeability and shape-factor within the transfer function into DPM, the fracture geometry and orientation are numerically considered and the complexity of the problem is well reduced. Both the normal deformation and shear dilation of fractures are considered and the stress-dependent fracture aperture can be updated in time. Further, a non-linear numerical model is constructed by implementing a poroviscoelastic model into the dual permeability (DPM)-finite element model (FEM) to investigate the coupled time-dependent viscoelastic deformation, fracture network evolution and compressible fluid flow in gas shale reservoir. The viscoelastic effect is addressed in both deviatoric and symmetric effective stresses to emphasize the effect of shear strain localization on fracture shear dilation. The new mechanical model is first verified with an analytical solution in a simple wellbore creep problem and then compared with the poroelastic solution in both wellbore and field cases.

In this thesis, we consider the two-space homogenization method, which produces macroscopic expressions out of descriptions of the behaviour of the microstructure. Specifically, we focus on its application to poroelastic media. After describing the method, we provide examples to demonstrate that the resultant expressions are equivalent to an explicit derivation, which might not always be possible, and to outline the method for proving that the expressions converge to their macroscopic equivalents. Upon providing the basis for this method, we follow Burridge and Keller’s work for using this to prove the existence of Biot’s consolidation equations for poroelastic media and to provide expressions for the derivation of the parameters of these equations from the microstructure [5]. We then discuss the benefits and challenges that arise from this formulation of Biot’s consolidation equations.

Stress and permeability variations around a wellbore and in the reservoir are of much interest in petroleum and geothermal reservoir development. Water injection causes significant changes in pore pressure, temperature, and stress in hot reservoirs, changing rock permeability. In this work, two- and three-dimensional finite element methods were developed to simulate coupled reservoirs with damage mechanics and stress-dependent permeability. The model considers the influence of fluid flow, temperature, and solute transport in rock deformation and models nonlinear behavior with continuum damage mechanics and stress-dependent permeability. Numerical modeling was applied to analyze wellbore stability in swelling shale with two- and three-dimensional damage/fracture propagation around a wellbore and injection-induced microseismic events. The finite element method (FEM) was used to solve the displacement, pore pressure, temperature, and solute concentration problems. Solute mass transport between drilling fluid and shale formation was considered to study salinity effects. Results show that shear and tensile failure can occur around a wellbore in certain drilling conditions where the mud pressure lies between the reservoir pore pressure and fracture gradient. The fully coupled thermo-poro-mechanical FEM simulation was used to model damage/fracture propagation and microseismic events caused by fluid injection. These studies considered wellbore geometry in small-scale modeling and point-source injection, assuming singularity fluid flux for large-scale simulation. Damage mechanics was applied to capture the effects of crack initiation, microvoid growth, and fracture propagation. The induced microseismic events were modeled in heterogeneous geological media, assuming the Weibull distribution functions for modulus and permeability. The results of this study indicate that fluid injection causes the effective stress to relax in the damage phase and to concentrate at the interface between the damage phase and the intact rock. Furthermore, induced-stress and far-field stress influence damage propagation. Cold water injection causes the tensile stress and affects the initial fracture and fracture propagation, but fracture initiation pressure and far-field stress are critical to create a damage/fracture plane, which is normal to the minimum far-field stress direction following well stimulation. Microseismic events propagate at both well scale and reservoir-scale simulation; the cloud shape of a microseismic event is affected by permeability anisotropy and far-field stress, and deviatoric horizontal far-field stress especially contributes to the localization of the microseismic cloud.

To safely store carbon dioxide in enhanced oil recovery/ CO2 sequestration projects it is important to ensure the integrity of the caprock during and after production and injection. A change in fluid pressure and temperature within a porous reservoir will generally induce stress changes within the reservoir and the rocks that surround it. Amongst the potential hazards resulting from these induced stress changes is the reactivation of existing faults or fractures and inducing new fractures, which may breach the hydraulic integrity of the caprock that bounds the reservoir.<p> The theories of inclusions and inhomogeneities have been used in this research to derive semi-analytical and closed-form solutions for induced stress change during pore pressure change within a reservoir and in the surrounding rock, under plane strain and axisymmetric conditions. Methods have been developed to assess fault reactivation and induced fracturing during injection or production within a reservoir. The failure stress change concept for a Coulomb failure criterion has been used to study the likelihood of fault reactivation and induced fracturing within the reservoir. Formulations have been adopted to calculate the critical pressure change for fault reactivation and induced fracturing within the reservoir and in the surrounding rock during injection and production. Sensitivity analysis has been performed to study the effects of different parameters such as initial in-situ stress, reservoir geometry, reservoir depth, reservoir tilt or dip , material property contrast between the reservoir and surrounding rock, fault geometry, fault strength, and intact rock strength. General patterns of induced stress change, in-situ stress evolution, fault reactivation, and induced fracturing have been identified.<p> The developed methodologies have been applied to six different case studies: fault reactivation analysis in the entire field for a synthetic case study; induced fracturing analysis in the entire field in a synthetic case study; fault reactivation and induced stress change analysis within the Ekofisk oil reservoir in North Sea; fault reactivation analysis in the Lacq gas reservoir in France; the Weyburn-Midale EOR/CO2 Storage project in southeast Saskatchewan; and acid gas injection in Zama oil field, Alberta. The results of these case studies show good consistency with field observation, and physical and numerical models.<p> The generality, simplicity, and straightforwardness of the developed methodologies, along with their flexibility to model different plausible scenarios and their ease of implementation for systematic sensitivity analyses makes them suitable for decision-making and uncertainty management, specifically in early stages of reservoir development or site assessment for geological sequestration of carbon dioxide.

Transcapillary exchange is the movement of fluid and molecules through the porous capillary wall, and is important in maintaining homeostasis of bodily tissues. The classical view of this process is that of Starling's hypothesis, in which the forces driving filtration or absorption are the hydrostatic and osmotic pressure differences across the capillary wall. However, experimental evidence has emerged suggesting the importance of the capillary wall ultrastructure, and thus rather than the global differences between capillary and tissue, it is the local difference across a structure lining the capillary wall known as the endothelial glycocalyx that determines filtration. Hu and Weinbaum presented a detailed cellular level microstructural model of this phenomenon which was able to explain some experimental discrepancies. In this Thesis, rather than describing the microstructural details, the capillary wall is treated as a poroelastic material. The assumptions of poroelasticity theory are such that the detailed pore structure is smeared out and replaced by an idealized homogeneous system in which the fluid and solid phases coexist at each point. The advantage of this approach is that the mathematical problem is greatly simplified such that analytical solutions of the governing equations may be obtained. This approach also allows calculation of the stress and strain distribution in the tissue. We depart from classical poroelasticity, however, due to the fact that since there are concentration gradients within the capillary wall, the filtration is driven by both hydrostatic and osmotic pressure gradients. The model predictions for the filtration flux as a function of capillary pressure compares favourably with both experimental observations and the predictions of the microstructural models. An important factor implicated in transcapillary exchange is the endothelial glycocalyx, which was shown experimentally to protect against edema formation. Using our theory in combination with the experimental measurements of glycocalyx thickness and pericapillary space dimension (PSD), we make a quantitative comparison for the excess flow as a result of a deteriorated glycocalyx, which shows reasonably good agreement with the data. Since many of the parameters in the model are difficult to measure, a sensitivity analysis was performed on the most important of these. Finally, since there was variation in the measurements of glycocalyx thickness and PSD, we used probability distributions to represent the data, and performed further calculations to obtain ranges of likely values for the various parameters. This work could find applications in cardiovascular disease, where the glycocalyx is degraded or absent, and in cancer research, where the abnormal vasculature is an impediment to the efficient delivery of anti-cancer drugs.

To safely store carbon dioxide in enhanced oil recovery/ CO2 sequestration projects it is important to ensure the integrity of the caprock during and after production and injection. A change in fluid pressure and temperature within a porous reservoir will generally induce stress changes within the reservoir and the rocks that surround it. Amongst the potential hazards resulting from these induced stress changes is the reactivation of existing faults or fractures and inducing new fractures, which may breach the hydraulic integrity of the caprock that bounds the reservoir.<p> The theories of inclusions and inhomogeneities have been used in this research to derive semi-analytical and closed-form solutions for induced stress change during pore pressure change within a reservoir and in the surrounding rock, under plane strain and axisymmetric conditions. Methods have been developed to assess fault reactivation and induced fracturing during injection or production within a reservoir. The failure stress change concept for a Coulomb failure criterion has been used to study the likelihood of fault reactivation and induced fracturing within the reservoir. Formulations have been adopted to calculate the critical pressure change for fault reactivation and induced fracturing within the reservoir and in the surrounding rock during injection and production. Sensitivity analysis has been performed to study the effects of different parameters such as initial in-situ stress, reservoir geometry, reservoir depth, reservoir tilt or dip , material property contrast between the reservoir and surrounding rock, fault geometry, fault strength, and intact rock strength. General patterns of induced stress change, in-situ stress evolution, fault reactivation, and induced fracturing have been identified.<p> The developed methodologies have been applied to six different case studies: fault reactivation analysis in the entire field for a synthetic case study; induced fracturing analysis in the entire field in a synthetic case study; fault reactivation and induced stress change analysis within the Ekofisk oil reservoir in North Sea; fault reactivation analysis in the Lacq gas reservoir in France; the Weyburn-Midale EOR/CO2 Storage project in southeast Saskatchewan; and acid gas injection in Zama oil field, Alberta. The results of these case studies show good consistency with field observation, and physical and numerical models.<p> The generality, simplicity, and straightforwardness of the developed methodologies, along with their flexibility to model different plausible scenarios and their ease of implementation for systematic sensitivity analyses makes them suitable for decision-making and uncertainty management, specifically in early stages of reservoir development or site assessment for geological sequestration of carbon dioxide.

The present research seeks to study the decrease in diffusivity rate as relative humidity (RH) decreases and modeling drying shrinkage of hardened cement paste as a poroviscoelastic respose. Thin cement paste strips of 0.4 and 0.5 w/c at age 3 and 7 days were measured for mass loss and shrinkage at small RH steps in an environmental chamber at constant temperature. Non-linear drying diffusion rate of hardened cement was modeled with the use of Fick's second law of diffusion by assuming linearity of diffusion rate over short drops of ambient relative humidity. Techniques to determine drying isotherms prior to full equilibration of mass loss, as well as converting mass loss into concentration of water vapor were developed. Using the measured water vapor diffusivity, drying shrinkage strain was modeled by the theory of poroviscoelasticity. This approach was validated by determining viscoelastic properties from uniaxial creep tests considering the effect of aging by the solidification theory. A change in drying diffusion rate at different RH was observed in the 0.4 and 0.5 w/c pastes at different ages. Drying diffusion rate decreases as RH drops. This can be attributed to a change in diffusion mechanisms in the porous media at smaller pore radius. Shrinkage modeling with an average diffusion coefficient and with determined viscoelastic parameters from creep tests agreed well compared to the shrinkage data from experiments, indicating that drying shrinkage of cement paste may be considered as a poroviscoelastic reponse.

New elastographic techniques such as poroelastography and viscoelasticity imaging aim at imaging the temporal mechanical behavior of tissues. These techniques usually involve the use of curve fitting methods as applied to noisy data to estimate new elastographic parameters. As of today, however, image quality performance of these new elastographic imaging techniques is still largely unknown due to a paucity of data and the lack of systematic studies that analyze performance limitations of estimators suitable for these novel applications. Furthermore, current elastographic implementations of poroelasticity and viscoelasticity imaging methods are in general too slow and not optimized for clinical applications. In this paper, we propose a new elastographic time constant (TC) estimator, which is based on the use of the Least Square Error (LSE) curve-fitting method and the Levenberg-Marquardt (LM) optimization rule as applied to noisy elastographic data obtained from a tissue under creep compression. The estimator's performance is analyzed using simulations and quantified in terms of accuracy, precision, sensitivity, signal-to-noise ratio (SNR) and speed. Experiments are performed as a proof of principle of the technical applicability of the new estimator on real experimental data. The results of this study demonstrate that the new elastographic estimator described in this thesis can produce highly accurate, sensitive and precise time constant estimates in real-time and at high SNR. In the future, the use of this estimator could allow real-time imaging of the temporal behavior of complex tissues and provide advances in lymphedema and cancer imaging.

Encapsulated microbubbles, whose diameters are on the order of microns, are widely used to provide acoustic contrast in biomedical applications. But well below the resonance frequencies of these microbubbles, any acoustic contrast is due solely to their relatively high compressibility compared to the surrounding medium. To estimate how well microbubbles may function as acoustic contrast agents in applications such as borehole logging or underground flow mapping, it must be determined how they behave both at atmospheric and down-well conditions, and how their presence affects the bulk acoustic properties of the surrounding medium, most crucially its specific acoustic impedance. Resonance tube experiments were performed on several varieties of acoustic contrast agents to determine their compressibility as a function of pressure and temperature, and the results are used to estimate the effect on sound propagation when they are introduced into rock formations. / text