This thesis presents procedures to properly simulate naturally fractured reservoirs using dual-porosity models. The main objectives of this work are to: (1) determine if the spontaneous imbibition can be simulated using a two phase CMG simulator and validate it with laboratory experiments in the literature; (2) study the effect of countercurrent imbibition in field scale applications; and (3) develop procedures for using the dual-porosity to simulate fluid displacement in a naturally fractured reservoir. Reservoir simulation techniques, analytical solutions and numerical simulation for a two phase single and dual-porosity are used to achieve our objectives. Analysis of a single matrix block with an injector and a producer well connected by a single fracture is analyzed and compared with both two phase single and dual-porosity models. Procedures for obtaining reliable results when modeling a naturally fractured reservoir with a two phase dual-porosity model are presented and analyzed.

Particle technology affects the entire human population. It is involved in the manufacture of agriculture chemicals, asphalt, paint, and pharmaceuticals, just to name a few. The size and shape of the particles play an important role in the manufacturing processes. A change in size or shape can change the product produced. Experiments were run to test the effects of agitation rate, magma density, and residence time on adipic acid and sodium chloride crystals. Experiments were executed in a one-liter, double-jacketed, stirred vessel. Digital images of the broken crystals were taken with a microscope/digital camera combo. ImagePro Plus was used to analyze the size of the broken crystals. The greatest change was seen between the two magma densities. It can be determined that change in size and shape based on the variables does exist. A specific set of variables should be introduced for each process in industry to achieve the desired results.

Castings made of aluminum 319 and A356.2 alloy were examined to determine the effectiveness of using pressure application during solidification to reduce porosity levels. Pyknometry was the method chosen to measure porosity. It was determined that the porosity of castings poured in both alloys was reduced in some instances. During the study, the surfaces of these castings were also examined and some were found to have defects present. After the porosity was evaluated, specimens of castings poured in both alloys were tested to determine whether or not the surface intrusions affected the castings. The defects were found to reduce the strength of the castings poured in aluminum 319. The castings poured in A356.2 did not have surface intrusions or any significant decreases in strength. Therefore it was concluded that of the two alloys tested, A356.2 alloy is most suited for using pressurization as a method of reducing porosity.

A variação da densidade de um compacto de partículas de vidro durante o aquecimento pode ser calculada aproximadamente pelo Modelo de Clusters de sinterização de vidros por escoamento viscoso com cristalização superficial concorrente. Nesse modelo, o efeito do formato das partículas é tratado como um fator de correção e determinado como um parâmetro de ajuste a dados experimentais. Portanto, um parâmetro de forma independente do modelo ainda deve ser considerado para que a cinética de sinterização de vidros possa ser precisamente calculada. A cinética de cristalização de vidros em pó também depende do formato das partículas e pode ser determinada através de Calorimetria Diferencial Exploratória (DSC). Assim, o objetivo desse trabalho foi acessar o formato de partículas de vidro através do estudo da cinética de cristalização das mesmas, visando posteriormente usar as informações de formato em cálculos cinéticos de sinterização. Para isso, o pico de cristalização de um compacto de diopsídio vítreo em pó foi determinado por DSC e avaliado em função do formato de partículas considerando diferentes morfologias regulares. A cinética de cristalização foi calculada considerando modelos distintos de cristalização de partículas de vidro com nucleação heterogênea na superfície. Os picos de cristalização foram determinados por DSC para um vidro de diopsídio (\'Ca\'\'O\'.\'Mg\'\'O\'.2\'Si\'\'O IND.2\') de composição próxima à estequiométrica, em amostras com diferentes granulometrias, e taxa de aquecimento de 10°C/min. As curvas experimentais foram comparadas com picos de cristalização calculados para pós de vidro de diopsídio com diferentes formatos regulares e granulometrias. A caracterização do formato das partículas iniciais e da microestrutura de compactos de vidros sinterizados não isotermicamente auxiliou na interpretação dos resultados. Os intervalos de temperatura onde ocorrem os picos de cristalização calculados coincidiram com os experimentais, mas o máximo dos picos variou em função da cinética de cristalização para diferentes formatos de partículas. Para o propósito do presente trabalho, observou-se um bom acordo, porém não perfeito, entre as curvas calculadas e experimentais, demostrando-se que DSC é uma técnica promissora para a caracterização de um fator de forma efetivo para o cálculo da cinética de sinterização de partículas de vidro com cristalização concorrente. / The densification rate of glass particle compacts during a temperature rise can approximately be calculated from the so-called Clusters model of sintering with concurrent crystallization, in which the particle shape effect is treated as a correction factor and determined as a fitting parameter. Thus, a model-independent particle shape parameter still has to be considered so that glass sintering kinetics can be precisely calculated. Aiming to access the particle shape effect on the glass sintering kinetics with concurrent crystallization, the crystallization peak of a glass particle compact was determined by Differential Scanning Calorimetry (DSC) and evaluated as a function of particle shape, regarding distinct regular morphologies. The crystallization kinetics was calculated considering distinct models of glass particle phase transformation. Crystals were considered to nucleate heterogeneously on particles surface. The expected DSC crystallization peaks were calculated for glass particles with near-stoichiometric diopside composition (\'Ca\'\'O\'.\'Mg\'\'O\'.2\'Si\'\'O IND.2\') heated up at a constant rate (10°C/min), and compared with the crystallization peak experimentally obtained for diopside glass powders with irregular shape and different granulometries. The characterization of the initial particle shape and the microstructure of non-isothermally sintered glass compacts aided in the interpretation of the results. The calculated crystallization peaks stand in the same temperature range as the experimental one, although the peak maxima vary as a function of crystallization kinetics due to the different particle shapes. For the purposes of the present research, there was a clear agreement, yet not perfect, between the calculated curves and experimental data, showing that DSC is a promise technique to characterize an effective shape factor to assess the glass particle sinter-crystallization kinetics.

The purpose of this study was to compare the phase characteristics of the countermovement jump (CMJ) force-time (F-t) curve between athletes based on jumping ability. An initial sample of one-hundred fifty Division-I collegiate athletes were ranked based on CMJ height. Three performance groups were then formed by taking the top, middle, and lower 30 athletes (15 men and 15 women) from the sample. Phases of the CMJ F-t curve were determined and then characterized by their duration, magnitude, area (impulse), and shape (shape factor). A series of 3-way mixed analysis of variance were used to determine statistical differences in phase characteristics between performance groups as well as between male and female athletes. Statistically significant phase-by-performance group interactions were observed for relative phase magnitude (p < 0.001), relative phase impulse (p < 0.001), and shape factor (p = 0.002). Phase-by-sex interactions were statistically significant for both relative phase magnitude (p < 0.001) and relative phase impulse (p < 0.001). Post hoc comparisons indicated that higher jumpers exhibited larger relative magnitude and impulse in the phases contained within the positive area of the F-t curve. Similarly, relative phase magnitude and impulse were the only phase characteristics to be statically different between men and women. Finally, the relative shape of the phase representing the initial rise in force was found to relate to jump height. These results provide some information regarding the diagnostic value of qualitative analysis of the CMJ F-t curve.

A variação da densidade de um compacto de partículas de vidro durante o aquecimento pode ser calculada aproximadamente pelo Modelo de Clusters de sinterização de vidros por escoamento viscoso com cristalização superficial concorrente. Nesse modelo, o efeito do formato das partículas é tratado como um fator de correção e determinado como um parâmetro de ajuste a dados experimentais. Portanto, um parâmetro de forma independente do modelo ainda deve ser considerado para que a cinética de sinterização de vidros possa ser precisamente calculada. A cinética de cristalização de vidros em pó também depende do formato das partículas e pode ser determinada através de Calorimetria Diferencial Exploratória (DSC). Assim, o objetivo desse trabalho foi acessar o formato de partículas de vidro através do estudo da cinética de cristalização das mesmas, visando posteriormente usar as informações de formato em cálculos cinéticos de sinterização. Para isso, o pico de cristalização de um compacto de diopsídio vítreo em pó foi determinado por DSC e avaliado em função do formato de partículas considerando diferentes morfologias regulares. A cinética de cristalização foi calculada considerando modelos distintos de cristalização de partículas de vidro com nucleação heterogênea na superfície. Os picos de cristalização foram determinados por DSC para um vidro de diopsídio (\'Ca\'\'O\'.\'Mg\'\'O\'.2\'Si\'\'O IND.2\') de composição próxima à estequiométrica, em amostras com diferentes granulometrias, e taxa de aquecimento de 10°C/min. As curvas experimentais foram comparadas com picos de cristalização calculados para pós de vidro de diopsídio com diferentes formatos regulares e granulometrias. A caracterização do formato das partículas iniciais e da microestrutura de compactos de vidros sinterizados não isotermicamente auxiliou na interpretação dos resultados. Os intervalos de temperatura onde ocorrem os picos de cristalização calculados coincidiram com os experimentais, mas o máximo dos picos variou em função da cinética de cristalização para diferentes formatos de partículas. Para o propósito do presente trabalho, observou-se um bom acordo, porém não perfeito, entre as curvas calculadas e experimentais, demostrando-se que DSC é uma técnica promissora para a caracterização de um fator de forma efetivo para o cálculo da cinética de sinterização de partículas de vidro com cristalização concorrente. / The densification rate of glass particle compacts during a temperature rise can approximately be calculated from the so-called Clusters model of sintering with concurrent crystallization, in which the particle shape effect is treated as a correction factor and determined as a fitting parameter. Thus, a model-independent particle shape parameter still has to be considered so that glass sintering kinetics can be precisely calculated. Aiming to access the particle shape effect on the glass sintering kinetics with concurrent crystallization, the crystallization peak of a glass particle compact was determined by Differential Scanning Calorimetry (DSC) and evaluated as a function of particle shape, regarding distinct regular morphologies. The crystallization kinetics was calculated considering distinct models of glass particle phase transformation. Crystals were considered to nucleate heterogeneously on particles surface. The expected DSC crystallization peaks were calculated for glass particles with near-stoichiometric diopside composition (\'Ca\'\'O\'.\'Mg\'\'O\'.2\'Si\'\'O IND.2\') heated up at a constant rate (10°C/min), and compared with the crystallization peak experimentally obtained for diopside glass powders with irregular shape and different granulometries. The characterization of the initial particle shape and the microstructure of non-isothermally sintered glass compacts aided in the interpretation of the results. The calculated crystallization peaks stand in the same temperature range as the experimental one, although the peak maxima vary as a function of crystallization kinetics due to the different particle shapes. For the purposes of the present research, there was a clear agreement, yet not perfect, between the calculated curves and experimental data, showing that DSC is a promise technique to characterize an effective shape factor to assess the glass particle sinter-crystallization kinetics.

<p>The compressible turbulent boundary layer developing over atwo-dimensional bump which leads to a supersonic pocket with aterminating shock wave has been studied. The measurements havebeen made with hot-wire anemometry and Particle ImageVelocimetry (PIV).</p><p>A method to calibrate hot-wire probes in compressible ow hasbeen developed which take into account not only the ow velocitybut also the inuence of the Mach number, stagnation temperatureand uid density. The calibration unit consists of a small jetow facility, where the temperature can be varied. The hot wiresare calibrated in the potential core of the free jet. The jetemanates in a container where the static pressure can becontrolled, and thereby the gas density. The calibration methodwas verfied in the at plate zero pressure gradient turbulentboundary layer in front of the bump at three different Machnumbers, namely 0.3, 0.5 and 0.7. The profiles were alsomeasured at different static pressures in order to see theinuence of varying density. Good agreement between the profilesmeasured at different pressures, as well as with the standardlogarithmic profile was obtained.</p><p>The PIV measurements of the boundary layer ow in front ofthe 2D bump showed good agreement with the velocity profilesmeasured with hotwire anemometry. The shock wave boundary layerinteraction was investigated for an inlet Mach number of 0.69.A lambda shock wave was seen on the downstream side of thebump. The velocity on both sides of the shock wave as measuredwith the PIV was in good agreement with theory. The shock wavewas found to cause boundary layer separation, which was seen asa rapid growth of the boundary layer thickness downstream theshock. However, no back ow was seen in the PIV-data, probablybecause the seeding did not give enough particles in theseparated region. The PIV data also showed that the shock wavewas oscillating, i.e. it was moving approximately 5 mm back andforth. This distance corresponds to about five boundary layerthicknesses in terms of the boundary layer upstream theshock.</p><p><b>Descriptors:</b>Fluid mechanics, compressible ow,turbulence, boundary layer, hot-wire anemometry, PIV, shockwave boundary layer interaction, shape factor.</p>

Multiquadric collocation method is highly efficient for solving partial differential equations due to its exponential error convergence rate. More amazingly, there are two ways to reduce the error: the traditional way of refining the grid, and the unexpected way of simply increasing the value of shape constant $c$ contained in the multiquadric basis function, $sqrt{r^2 + c^2}$. The latter is accomplished without increasing computational cost. It has been speculated that in a numerical solution without roundoff error, infinite accuracy can be achieved by letting $c ightarrow infty$. The ability to obtain infinitely accurate solution is limited only by the roundoff error induced instability of matrix solution with large condition number. Using the arbitrary precision computation capability of {it Mathematica}, this paper tests the above conjecture. A sharper error estimate than previously obtained is presented in this paper. A formula for a finite, optimal $c$ value that minimizes the solution error for a given grid size is obtained. Using residual errors, constants in error estimate and optimal $c$ formula can be obtained. These results are supported by numerical examples.

abstract: Pseudo-steady state (PSS) flow is an important time-dependent flow regime that quickly follows the initial transient flow regime in the constant-rate production of a closed boundary hydrocarbon reservoir. The characterization of the PSS flow regime is of importance in describing the reservoir pressure distribution as well as the productivity index (PI) of the flow regime. The PI describes the production potential of the well and is often used in fracture optimization and production-rate decline analysis. In 2016, Chen determined the exact analytical solution for PSS flow of a fully penetrated vertically fractured well with finite fracture conductivity for reservoirs of elliptical shape. The present work aimed to expand Chen’s exact analytical solution to commonly encountered reservoirs geometries including rectangular, rhomboid, and triangular by introducing respective shape factors generated from extensive computational modeling studies based on an identical drainage area assumption. The aforementioned shape factors were generated and characterized as functions for use in spreadsheet calculations as well as graphical format for simplistic in-field look-up use. Demonstrative use of the shape factors for over 20 additional simulations showed high fidelity of the shape factor to accurately predict (mean average percentage error remained under 1.5 %) the true PSS constant by modulating Chen’s solution for elliptical reservoirs. The methodology of the shape factor generation lays the ground work for more extensive and specific shape factors to be generated for cases such as non-concentric wells and other geometries not studied. / Dissertation/Thesis / Masters Thesis Chemical Engineering 2017

The aim of this thesis is to determine influence of porosity and shape-factor over mechanical properties, performed on cast samples from Aalen foundry (Germany), that were high pressure die casted from AZ91 D Alloy. Evaluation of these quantities was done using computer software Olympus Five. Measured values were subjected to statistical analysis in order to eliminate gross errors and determine linear dependence between mechanical properties and porosity eventually voids shape factor.