No description available.

Este trabalho apresenta uma solução analítica obtida pelo método de expansão para cinética espacial usando o modelo de difusão e considerando meios homogêneos multiplicativos subcríticos acionados por fonte externa. Em particular, partindo de modelos mais simples e aumentando a complexidade do sistema, resultados foram obtidos para diferentes tipos de transientes. Inicialmente, uma solução analítica foi obtida considerando um grupo de energia sem nêutrons atrasados, em seguida considerou-se um sistema de um grupo de energia e uma família de precursores. A solução para o caso G grupos de energia e R famílias de precursores em forma fechada é obtida, apesar do fato que não possa ser resolvido analiticamente, uma vez que não existe forma explícita para os autovalores e métodos numéricos devem ser utilizados para resolver tal problema. Para ilustrar a solução geral um problema de multigrupo (três grupos de energia) dependente do tempo sem precursores é apresentada e os resultados numéricos obtidos usando um código de diferenças finitas são comparados com os resultados exatos para diferentes tipos de transientes. / This work describes an analytical solution obtained by the expansion method for the spatial kinetics using the diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. An analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent problem without precursors was solved and the numerical results of a finite difference code were compared with the exact results for different transients.

Horizontal wells have been used to increase reservoir recovery, especially in unconventional reservoirs, and hydraulic fracturing has been applied to further extend the contact with the reservoir to increase the efficiency of development. In the past, many models, analytical or numerical, were developed to describe the flow behavior in horizontal wells with fractures. Source solution is one of the analytical/semi-analytical approaches. To solve fractured well problems, source methods were advanced from point sources to volumetric source, and pressure change inside fractures was considered in the volumetric source method. This study aims at developing a method that can predict horizontal well performance and the model can also be applied to horizontal wells with multiple fractures in complex natural fracture networks. The method solves the problem by superposing a series of slab sources under transient or pseudosteady-state flow conditions. The principle of the method comprises the calculation of semi-analytical response of a rectilinear reservoir with closed outer boundaries. A statistically assigned fracture network is used in the study to represent natural fractures based on the spacing between fractures and fracture geometry. The multiple dominating hydraulic fractures are then added to the natural fracture system to build the physical model of the problem. Each of the hydraulic fractures is connected to the horizontal wellbore, and the natural fractures are connected to the hydraulic fractures through the network description. Each fracture, natural or hydraulically induced, is treated as a series of slab sources. The analytical solution of superposed slab sources provides the base of the approach, and the overall flow from each fracture and the effect between the fractures are modeled by applying superposition principle to all of the fractures. It is assumed that hydraulic fractures are the main fractures that connect with the wellbore and the natural fractures are branching fractures which only connect with the main fractures. The fluid inside of the branch fractures flows into the main fractures, and the fluid of the main fracture from both the reservoir and the branch fractures flows to the wellbore. Predicting well performance in a complex fracture network system is extremely challenged. The statistical nature of natural fracture networks changes the flow characteristic from that of a single linear fracture. Simply using the single fracture model for individual fracture, and then adding the flow from each fracture for the network could introduce significant error. This study provides a semi-analytical approach to estimate well performance in a complex fracture network system.

An alongshore sediment transport and shoreline change analysis on Galveston Island in the period of 1990-2001 is conducted in this study using the Generalized Model for Simulating Shoreline Change (GENESIS). The study is divided into three main parts: 1. Assessment of the numerical accuracy of GENESIS, 2. Assessment of the alongshore sediment transport and shoreline change on the Galveston coast in the period of 1990-2001, and 3. Assessment of several erosion control practices on the Galveston coast for the period of 2001-2011. The first assessment shows that GENESIS has a numerical error which tends to be large for low energy wave (small breaking wave height) and large breaking wave angle. This numerical inaccuracy cannot be neglected and needs to be compensated for. This can be done, for instance, by adjusting the transport parameter K1. In the second assessment, good agreement between the calculated and measured transport/shoreline is achieved, particularly on the West Beach. Comparison between the potential alongshore sediment transport and sediment budget-inferred alongshore transport provides a systematic way of selecting the proper wave data set for the alongshore and shoreline change calculation. The third assessment proves that beach nourishment is the best alternative to overcome/reduce the erosion problem on the Galveston coast. Constructing coastal structure (groins, offshore breakwater) on the West Beach does not resolve the problem of erosion, but instead shifts it further west.

Im Folgenden wird die analytische Lösung der eindimensionalen, instationären Wärmeleitungsgleichung mit einer Randbedingung 3. Art gegeben. Die Außentemperatur wird dabei als harmonische Schwingung angenommen. Abhängig von den materialspezifischen Eigenschaften des Bauteils (Wärmeleitfähigkeit, Rohdichte, spezifische Wärmekapazität) kommt es zur Dämpfung und zeitlichen Verschiebung der Temperaturwelle im Bauteil. Die analytische Lösung liefert den raum- und zeitaufgelösten Temperaturverlauf innerhalb des Bauteils. Die analytische Lösung ist primär für die Kalibrierung und Validierung numerischer Approximationsverfahren relevant. Die zeitliche Verfügbarkeit von thermischer Speichermasse ist für die thermische Gebäude- und Raumsimulation von besonderer Wichtigkeit. Daher muss ein numerisches Berechnungsverfahren diese Prozesse gut abbilden können. Die hier gezeigte analytische Lösung kann daher zur Bewertung der Güte der gewählten numerischen Approximation verwendet werden. Zu diesem Zweck werden Ergebnisse beispielhaft für zwei getrennte Konstruktionen angegeben.

Analytical solutions for aquifer response to pumping are commonly used to infer the hydraulic properties of aquifers. This dissertation develops new analytical solutions for the analysis of pumping test data from confined and unconfined aquifer.An analytical solution for flow to a partially penetrating well of infinitesimally small radius in a compressible unconfined aquifer is developed that allows inferring its saturated and unsaturated hydraulic properties from drawdowns recorded in the saturated and/or the unsaturated zone. The effects of unsaturated zoneconstitutive parameters and thickness on drawdowns in the saturated and unsaturated zones as functions of position and time is investigated; the solution is validated against numerical simulations of drawdown in a synthetic aquifer having unsaturated properties described by the van Genuchten (1980) - Mualem (1976)constitutive model; used to analyze drawdown data from a pumping test conducted by the US Geological Survey at Cape Cod,Massachusetts; and corresponding estimates of van Genuchten - Mualem parameters are compared with laboratoryvalues obtained for similar materials in the area.Drawdowns generated by extracting water from a large diameter (e.g. water supply) well are affected by wellbore storage. An analytical solution in Laplace transformed space for drawdown in a uniformanisotropic confined aquifer caused by withdrawing water at a constant rate from a partially penetrating well with storage is developed. When the pumping well is fully penetrating the solution reduces to that of Papadopulos and Cooper (1967); to that of Hantush (1964) when the pumping well has no wellbore storage; to the solution of Theis (1935) when both conditions are fulfilled; and to that of Yang et al. (2006) when the pumping well is partially penetrating, having finite radius but lacking storage. The solutionis validated against synthetic pumping test data and used to explore graphically the effects of partial penetration, wellbore storage and anisotropy on time evolutions of drawdown in the pumping well and in observation wells.The analytical solution for unconfined aquifers is extended to the case of a finite diameter pumping well with storage. The extended analytical solution is used to investigate the effects of storage in the pumping well and delayed piezometer response on drawdowns in the saturated and unsaturated zones as functions of position and time. The solution is validated against numerical simulations of drawdown in a synthetic aquifer having unsaturated properties described by the van Genuchten (1980) - Mualem (1976) model. It is then used to analyze a seven-day pumping test conducted by University of Waterloo researchers at the Canadian Forces Base Borden in Ontario, Canada; and to compare our results with those ofMoench (2008).

No description available.

No description available.

Removal of CO2 directly from anthropogenic sources (capture) and its disposal in geological formations can take place for medium-term time periods (storage), or it can be permanent (sequestration), with the CO2 eventually becoming dissolved in the aqueous phase. The latter is the main subject of this dissertation. Carbon dioxide sequestration covers a wide range of strategies and alternatives. The main objective of CO2 sequestration alternatives is secure disposal of carbon in large amounts and for a lengthy time scale (typically 1000 years). Injection of CO2 into subsurface formations is generally considered as the main option for CO2 sequestration. Geological sequestration through injection covers a broad variety of target formations: disposal in depleted oil and gas reservoirs, trapping in oil reservoirs, replacing CH4 in coal bed methane recovery processes, trapping in deep aquifers, and salt cavern placement are the major CCS alternatives in geologic formations. In this thesis, hydrogeologic interaction between the injectant (CO2) and the host fluid (saline water) during injection is the main subject of the project. Because of the density and viscosity contrast of displacing and displaced fluids, the pattern of saturation progression is complicated. A set of semi-analytical solutions is developed for quick estimation of the position of isosats (contours of saturation) during primary injection in homogenous cases with simple geometry. All of the mathematical solutions are developed based on two assumptions; incompressible fluids and rocks and vertical equilibrium (capillary-gravity condition) for geometries with large aspect ratio (L >> H). First, a series of analytical solutions for primary drainage for a set of linear relative permeability functions is developed. The first analytical solution is based on the assumption of locally linearized Leverett-J functions, and by using the method of characteristics, a formulation for the isosats’ geometry is obtained. A semi-analytical solution is then proposed for calculation of the position of isosats with linearized relative permeability functions and arbitrary capillary-saturation correlation. The analytical solution is extended to incorporate a specific form of nonlinearity of the relative permeability function. Nonlinear relative permeability functions are also incorporated in another semi-analytical solution, and the positions of the isosats for any arbitrary Leverett-J function and relative permeability functions are developed. Sequential gas-saline injection is also modeled in that chapter. For approximate verification of the analytical solutions, a FEM numerical model is developed and the results of the analytical solutions are compared with the numerical solutions. These new analytical solutions provide powerful tools for prediction of saturation distribution during injection in vertical and horizontal wells, as well as for carrying out stochastic assessments (Monte Carlo simulations) and parametric weight assessment. The domain of applications of the new solutions go far beyond the limited question of CO2 sequestration: they can be used for injection of any less viscous fluid into a reservoir, whether the fluid is lighter or denser than the host fluid (gas injection, water-alternating gas injection, water injection into viscous oil reservoirs, solvent injection).

The optimal replacement policy for an asset subject to a stochastic deteriorating operating cost is determined for three different tax depreciation schedules and a known re-investment cost, as the solution to a two-factor model using a quasi-analytical method. We find that tax depreciation exerts a critical influence over the replacement policy by lowering the operating cost thresholds. Although typically a decline in the corporate tax rate, increase in any initial capital allowance, or decrease in the depreciation lifetime (increase in depreciation rate) results in a lower operating cost threshold which justifies replacing older equipment, these results are not universal, and indeed for younger age assets the result may be the opposite. An accelerating depreciation schedule may incentivize early replacement in a deterministic context, but not necessarily for an environment of uncertainty.