Problems involving coupled thermo-poro-chemo-mechanical processes are of great importance in geothermal and petroleum reservoir systems. In particular, economic power production from enhanced geothermal systems, effective water-flooding of petroleum reservoirs, and stimulation of gas shale reservoirs are significantly influenced by coupled processes. During such procedures, stress state in the reservoir is changed due to variation in pore fluid pressure and temperature. This can cause deformation and failure of weak planes of the formation with creation of new fractures, which impacts reservoir response. Incorporation of geomechanical factor into engineering analyses using fully coupled geomechanics-reservoir flow modeling exhibits computational challenges and numerical difficulties. In this study, we develop and apply efficient numerical models to solve 3D injection/extraction geomechanics problems formulated within the framework of thermo-poro-mechanical theory with reactive flow. The models rely on combining Displacement Discontinuity (DD) Boundary Element Method (BEM) and Finite Element Method (FEM) to solve the governing equations of thermo-poro-mechanical processes involving fracture/reservoir matrix. The integration of BEM and FEM is accomplished through direct and iterative procedures. In each case, the numerical algorithms are tested against a series of analytical solutions. 3D study of fluid injection and extraction into the geothermal reservoir illustrates that thermo-poro-mechanical processes change fracture aperture (fracture conductivity) significantly and influence the fluid flow. Simulations that consider joint stiffness heterogeneity show development of non-uniform flow paths within the crack. Undersaturated fluid injection causes large silica mass dissolution and increases fracture aperture while supersaturated fluid causes mineral precipitation and closes fracture aperture. Results show that for common reservoir and injection conditions, the impact of fully developed thermoelastic effect on fracture aperture tend to be greater compare to that of poroelastic effect. Poroelastic study of hydraulic fracturing demonstrates that large pore pressure increase especially during multiple hydraulic fracture creation causes effective tensile stress at the fracture surface and shear failure around the main fracture. Finally, a hybrid BEFEM model is developed to analyze stress redistribution in the overburden and within the reservoir during fluid injection and production. Numerical results show that fluid injection leads to reservoir dilation and induces vertical deformation, particularly near the injection well. However, fluid withdrawal causes reservoir to compact. The Mandel-Cryer effect is also successfully captured in numerical simulations, i.e., pore pressure increase/decrease is non-monotonic with a short time values that are above/below the background pore pressure.

This thesis considers various strongly correlated quantum phases in solid state and cold atom spin systems. In the first part we focus on phases emerging in multi-orbital materials. We study even-parity spin-triplet superconductivity originating from Hund's coupling between t2g orbitals and investigate the effect of spin-orbit interaction on spin-triplet and spin-singlet pairing. Various aspects of the pairing state are discussed against the backdrop of the spin-triplet superconductor Sr2RuO4. Motivated by the remarkable phenomena observed in the bilayer compound Sr3Ru2O7, which point to the formation of an electronic nematic phase in the presence of critical fluctuations, we investigate how such a broken symmetry state emerges from electronic interactions. Since the broken x-y symmetry is revealed experimentally by applying a small in-plane magnetic field component, we examine nematic phases in a bilayer system and the role of the in-plane magnetic field using a phenomenological approach. In addition, we propose a microscopic mechanism for nematic phase formation specific to Sr3Ru2O7. The model is based on a realistic multi-orbital band structure and local and nearest neighbour interactions. Considering all t2g-orbital derived bands on an equal footing, we find a nematic quantum critical point and a nearby meta-nematic transition in the phase diagram. This finding harbours important implications for the phenomena observed in Sr3Ru2O7. The second part is devoted to the study of the anisotropic bilinear biquadratic spin-1 Heisenberg model, where the existence of an unusual direct phase transition between a spin-nematic phase and a dimerized valence bond solid phase in the quasi-1D limit was conjectured based on Quantum Monte Carlo simulations. We establish the quasi-1D phase diagram using a large-N Schwinger boson approach and show that the phase transition is largely conventional except possibly at two particular points. We further discuss how to realize and to detect such phases in an optical lattice.

Unconventional resources will play an important role in filling the gap between supply and demand for future world energy. In North America, the impact of unconventional resources on energy supplies is growing continuously. However, around the world they have yet to serve as a major contributor to the energy supply, partly due to the scarcity of information about the exploration and development technologies required to produce them. Basin analogy can be used to estimate the undiscovered petroleum potential in a target basin by finding a geological analog that has been explored enough that its resource potential is fully understood. In 2006, Singh developed a basin analog system BASIN (Basin Analog Systems INvestigation) in detail that could rapidly and consistently identify analogous reference basins for a target basin. My research focused on continuing that work, comprehensively improving the basin analog system in four areas: the basin analog method; the database; the software functionality; and the validation methods. The updated system compares basins in terms of probability distributions of geological parameters. It compensates for data that are sparse or that do not represent basin-level geological parameters, and it expands the system's ability to compare widely varying quantitative parameters. Because the updated BASIN database contains more geologic and petroleum systems information on reference (existing) basins, it identifies analog basins more accurately and efficiently. The updated BASIN software was developed by using component-based design and data visualization techniques that help users better manage large volumes of information to understand various data objects and their complicated relationships among various data objects. Validation of the improved BASIN software confirms its accuracy: if a basin selected as the target basin appears in the reference basin list with other basins, the target basin is 100% analogous only to itself. Furthermore, when a target basin is analyzed by both BASIN and PRISE (Petroleum Resources Investigation and Summary Evaluation) software, results of the improved BASIN closely matched the PRISE results, which provides important support for using BASIN and PRISE together to quantitatively estimate the resource potential in frontier basins.

This thesis considers various strongly correlated quantum phases in solid state and cold atom spin systems. In the first part we focus on phases emerging in multi-orbital materials. We study even-parity spin-triplet superconductivity originating from Hund's coupling between t2g orbitals and investigate the effect of spin-orbit interaction on spin-triplet and spin-singlet pairing. Various aspects of the pairing state are discussed against the backdrop of the spin-triplet superconductor Sr2RuO4. Motivated by the remarkable phenomena observed in the bilayer compound Sr3Ru2O7, which point to the formation of an electronic nematic phase in the presence of critical fluctuations, we investigate how such a broken symmetry state emerges from electronic interactions. Since the broken x-y symmetry is revealed experimentally by applying a small in-plane magnetic field component, we examine nematic phases in a bilayer system and the role of the in-plane magnetic field using a phenomenological approach. In addition, we propose a microscopic mechanism for nematic phase formation specific to Sr3Ru2O7. The model is based on a realistic multi-orbital band structure and local and nearest neighbour interactions. Considering all t2g-orbital derived bands on an equal footing, we find a nematic quantum critical point and a nearby meta-nematic transition in the phase diagram. This finding harbours important implications for the phenomena observed in Sr3Ru2O7. The second part is devoted to the study of the anisotropic bilinear biquadratic spin-1 Heisenberg model, where the existence of an unusual direct phase transition between a spin-nematic phase and a dimerized valence bond solid phase in the quasi-1D limit was conjectured based on Quantum Monte Carlo simulations. We establish the quasi-1D phase diagram using a large-N Schwinger boson approach and show that the phase transition is largely conventional except possibly at two particular points. We further discuss how to realize and to detect such phases in an optical lattice.

<p>This dissertation presents two essays on Markov-Switching dynamic stochastic general equilibrium models.</p><p>The first essay is "Perturbation Methods for Markov-Switching Models," which is co-authored with Juan Rubio-Ramirez, Dan Waggoner, and Tao Zha. This essay develops an perturbation-based approach to solving dynamic stochastic general equilibrium models with Markov-Switching, which implies that parameters governing policies or the environment evolve over time in a discrete manner. Our approach has the advantages that it introduces regime switching from first principles, allows for higher-order approximations, shows non-certainty equivalence of first-order approximations, and allows checking the solution for determinacy. We explain the model setup, introduce an iterative procedure to solve the model, and illustrate it using a real business cycle example.</p><p>The second essay considers a model with financial frictions and studies the role of expectations and unconventional monetary policy during financial crises. During a financial crisis, the financial sector has</p><p>reduced ability to provide credit to productive firms, and the central bank may help lessen the magnitude of the downturn by using unconventional monetary policy to inject liquidity into credit markets. The model allows agents in the economy to expect policy changes by allowing parameters to change according to a Markov process, so agents have expectations about the probability of the central bank intervening during a crisis, and also have expectations about the central bank's exit strategy post-crisis. </p><p>Using this Markov Regime Switching specification, the paper addresses three issues. First, it considers the effects of different exit strategies, and shows that, after a crisis, if the central bank sells off its accumulated assets too quickly, the economy can experience a double-dip recession. Second, it analyzes the effects of expectations of intervention policy on pre-crisis behavior. In particular, if the central bank commits to always intervening during crises, there is a loss of output in pre-crisis times relative to if the central bank commits to never intervening. Finally, it considers the welfare implications of committing to intervening during crises, and shows that committing can raise or lower welfare depending upon the exit strategy used, and that committing before a crisis can be welfare decreasing but then welfare increasing once a crisis occurs.</p> / Dissertation

The ever increasing energy demand brings about widespread interest to rapidly, profitably and efficiently develop unconventional resources, among which tight gas sands hold a significant portion. However, optimization of development strategies in tight gas fields is challenging, not only because of the wide range of depositional environments and large variability in reservoir properties, but also because the evaluation often has to deal with a multitude of wells, limited reservoir information, and time and budget constraints. Unfortunately, classical full-scale reservoir evaluation cannot be routinely employed by small- to medium-sized operators, given its timeconsuming and expensive nature. In addition, the full-scale evaluation is generally built on deterministic principles and produces a single realization of the reservoir, despite the significant uncertainty faced by operators. This work addresses the need for rapid and cost-efficient technologies to help operators determine optimal well spacing in highly uncertain and risky unconventional gas reservoirs. To achieve the research objectives, an integrated reservoir and decision modeling tool that fully incorporates uncertainty was developed. Monte Carlo simulation was used with a fast, approximate reservoir simulation model to match and predict production performance in unconventional gas reservoirs. Simulation results were then fit with decline curves to enable direct integration of the reservoir model into a Bayesian decision model. These integrated tools were applied to the tight gas assets of Unconventional Gas Resources Inc. in the Berland River area, Alberta, Canada.

With the rapidly increasing demand for energy and the increasing prices for oil and gas, the role of unconventional gas reservoirs (UGRs) as energy sources is becoming more important throughout the world. Because of high risks and uncertainties associated with UGRs, their profitable development requires experts to be involved in the most critical development stages, such as drilling, completion, stimulation, and production. However, many companies operating UGRs lack this expertise. The advisory system we developed will help them make efficient decisions by providing insight from analogous basins that can be applied to the wells drilled in target basins. In North America, UGRs have been in development for more than 50 years. The petroleum literature has thousands of papers describing best practices in management of these resources. If we can define the characteristics of the target basin anywhere in the world and find an analogous basin in North America, we should be able to study the best practices in the analogous basin or formation and provide the best practices to the operators. In this research, we have built an advisory system that we call the Unconventional Gas Reservoir (UGR) Advisor. UGR Advisor incorporates three major modules: BASIN, PRISE and Drilling & Completion (D&C) Advisor. BASIN is used to identify the reference basin and formations in North America that are the best analogs to the target basin or formation. With these data, PRISE is used to estimate the technically recoverable gas volume in the target basin. Finally, by analogy with data from the reference formation, we use D&C Advisor to find the best practice for drilling and producing the target reservoir. To create this module, we reviewed the literature and interviewed experts to gather the information required to determine best completion and stimulation practices as a function of reservoir properties. We used these best practices to build decision trees that allow the user to take an elementary data set and end up with a decision that honors the best practices. From the decision trees, we developed simple computer algorithms that streamline the process.

Hydraulic fracturing is an important stimulation method for producing unconventional gas reserves. Natural fractures are present in many low-permeability gas environments and often provide important production pathways for natural gas. The production benefit from natural fractures can be immense, but it is difficult to quantify. The Mesaverde Group in the Piceance Basin in Colorado is a gas producing reservoir that has low matrix permeability but is also highly naturally fractured. Wells in the Piceance Basin are hydraulically fractured, so the production enhancements due to natural fracturing and hydraulic fracturing are difficult to decouple. In this thesis, dipole sonic logs were used to quantify geomechanical properties by combining stress equations with critically-stressed faulting theory. The properties derived from this log-based evaluation were used to numerically model hydraulic fracture treatments that had previously been pumped in the basin. The results from these hydraulic fracture models, in addition to the log-derived reservoir properties were used to develop reservoir models. Several methods for simulating the reservoir were compared and evaluated, including layer cake models, geostatistical models, and models simulating the fracture treatment using water injection. The results from the reservoir models were compared to actual production data to quantify the effect of both hydraulic fractures and natural fractures on production. This modeling also provided a framework upon which completion techniques were economically evaluated. / text

Naturally fractured reservoirs (NFRs) hold a significant amount of the world's hydrocarbon reserves. Compared to conventional reservoirs, NFRs exhibit a higher degree of heterogeneity and complexity created by fractures. The importance of fractures in production of oil and gas is not limited to naturally fractured reservoirs. The economic exploitation of unconventional reservoirs, which is increasingly a major source of short- and long-term energy in the United States, hinges in part on effective stimulation of low-permeability rock through multi-stage hydraulic fracturing of horizontal wells. Accurate modeling and simulation of fractured media is still challenging owing to permeability anisotropies and contrasts. Non-physical abstractions inherent in conventional dual porosity and dual permeability models make these methods inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent approaches for discrete fracture modeling may require large computational times and hence the oil industry has not widely used such approaches, even though they give more accurate representations of fractured reservoirs than dual continuum models. We developed an embedded discrete fracture model (EDFM) for an in-house fully-implicit compositional reservoir simulator. EDFM borrows the dual-medium concept from conventional dual continuum models and also incorporates the effect of each fracture explicitly. In contrast to dual continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity and heterogeneity of a typical fractured reservoir. EDFM employs a structured grid to remediate challenges associated with unstructured gridding required for other discrete fracture models. Also, the EDFM approach can be easily incorporated in existing finite difference reservoir simulators. The accuracy of the EDFM approach was confirmed by comparing the results with analytical solutions and fine-grid, explicit-fracture simulations. Comparison of our results using the EDFM approach with fine-grid simulations showed that accurate results can be achieved using moderate grid refinements. This was further verified in a mesh sensitivity study that the EDFM approach with moderate grid refinement can obtain a converged solution. Hence, EDFM offers a computationally-efficient approach for simulating fluid flow in NFRs. Furthermore, several case studies presented in this study demonstrate the applicability, robustness, and efficiency of the EDFM approach for modeling fluid flow in fractured porous media. Another advantage of EDFM is its extensibility for various applications by incorporating different physics in the model. In order to examine the effect of pressure-dependent fracture properties on production, we incorporated the dynamic behavior of fractures into EDFM by employing empirical fracture deformation models. Our simulations showed that fracture deformation, caused by effective stress changes, substantially affects pressure depletion and hydrocarbon recovery. Based on the examples presented in this study, implementation of fracture geomechanical effects in EDFM did not degrade the computational performance of EDFM. Many unconventional reservoirs comprise well-developed natural fracture networks with multiple orientations and complex hydraulic fracture patterns suggested by microseismic data. We developed a coupled dual continuum and discrete fracture model to efficiently simulate production from these reservoirs. Large-scale hydraulic fractures were modeled explicitly using the EDFM approach and numerous small-scale natural fractures were modeled using a dual continuum approach. The transport parameters for dual continuum modeling of numerous natural fractures were derived by upscaling the EDFM equations. Comparison of the results using the coupled model with that of using the EDFM approach to represent all natural and hydraulic fractures explicitly showed that reasonably accurate results can be obtained at much lower computational cost by using the coupled approach with moderate grid refinements. / text

This dissertation consists of three essays on topics in macroeconomics. In the first chapter, I construct a macroeconomic model with a heterogeneous banking sector and an interbank lending market. Banks differ in their ability to transform deposits from households into loans to firms. Bank size differences emerge endogenously in the model, and in steady state, the induced bank size distribution matches two stylized facts in the data: bigger banks borrow more on the interbank lending market than smaller banks, and bigger banks are more leveraged than smaller banks. I use the model to evaluate the impact of increasing concentration in US banking on the severity of potential downturns. I find that if the banking sector in 2007 was only as concentrated as it was in 1992, GDP during the Great Recession would have declined by 40% less it did, and would have recovered twice as fast. In the second chapter, my co-author and I investigate the impact of firm capacity constraints on aggregate production and productivity when the economy is driven by aggregate and idiosyncratic demand shocks. We are motivated by three observed regularities in US GDP: business cycles are asymmetric, in that large absolute changes in output are more likely to be negative than positive; capacity and capital utilization are procyclical, and increase the procyclicality of measured productivity; the dispersion of firm productivity increases in recessions. We devise a model of demand shocks and endogenous capacity constraints that is qualitatively consistent with these observations. We then calibrate the model to aggregate utilization data using standard Bayesian techniques. Quantitatively, we find that the calibrated model also exhibits significant asymmetry in output, on the order of the regularities observed in GDP. The third chapter explores the role of distance in equilibrium selection. I consider a model economy with multiple steady state equilibria where a high productivity and a low productivity technology are available for use in production. The high productivity technology requires a fixed set up cost for production. Sectors are linked by localized production complementarities. I consider selection under a learning rule in which agents imitate their most successful neighbor. As distance between neighbors decreases, the possible profits from industrialization increase, and the likelihood that the learning rule process converges to a steady state matching the H equilibrium increases. The result suggests that, in the presence of localized technology spillovers, there may be important gains to economic growth from infrastructure development. / text