Active magnetic bearings (AMBs) have the ability to act concurrently as support bearings and as load sensing measurement tools. Previous work in the area of AMB force measurement has relied upon basic magnetic equations requiring knowledge of coil currents and air gap lengths. Some researchers have utilized magnetic flux probes to eliminate the need for air gap measurements, but these are limited by physical size constraints and require complex hardware. This thesis presents a new method for measuring forces with AMBs that utilizes multiple current pairs with no gap measurement to provide accurate and precise force predictions. Previous methods for force measurement with AMBs rely on the controlled environment of a laboratory setting for accurate measurements. The goal of this work is to develop a robust force measurement procedure for use in industrial and field applications, as well as the laboratory. The harsh environment of a factory floor makes air gap measurements difficult, which limits the use of current-based force equations. Additionally, the flexibility of AMB-equipped thrust measurement systems (TMSs) to measure many types of forces with little to no reconfiguration or calibration makes them appealing. The multi-point method provides predictions of both shaft force and rotor position using only current pairs without air gap measurements. Static and dynamic load scenarios were investigated to determine the feasibility of this new approach to force measurement. For both, the effects of bearing load and rotor position within the bearing were analyzed. Under dynamic loading, different amounts of unbalance as well as various rotor speeds were used to provide multiple test cases. The multi-point predictions of rotor position were analyzed and compared with the measured rotor positions. It was shown that this new multiple-point method for measuring bearing loads with AMBs provides equivalent or better force predictions to analogous single-point methods for static loads while eliminating the need for measuring rotor position. / Master of Science

Paleokarst reservoirs consist of complex cave networks, which are formed by various mechanisms and associated collapsed cave facies. Traditionally, cave structures are defined using variogram-based methods in flow models and this description does not precisely represent the reservoir geology. Algorithms based on multiple-point statistics (MPS) are widely used in modeling complex geologic structures. Statistics required for these algorithms are inferred from gridded training images. However, structures like modern cave networks are represented by point data sets. Thus, it is not practical to apply rigid and gridded templates and training images for the simulation of such features. Therefore, a quantitative algorithm to characterize and model paleokarst reservoirs based on physical and geological attributes is needed. In this study, a unique non-gridded MPS analysis and pattern simulation algorithms are developed to infer statistics from modern cave networks and simulate distribution of cave structures in paleokarst reservoirs. Non-gridded MPS technique is practical by eliminating use of grids and gridding procedure, which is challenging to apply on cave network due to its complex structure. Statistics are calculated using commonly available cave networks, which are only represented by central line coordinates sampled along the accessible cave passages. Once the statistics are calibrated, a cave network is simulated by using a pattern simulation algorithm in which the simulation is conditioned to sparse data in the form of locations with cave facies or coordinates of cave structures. To get an accurate model for the spatial extent of the cave facies, an algorithm is also developed to simulate cave zone thickness while simulating the network. The proposed techniques are first implemented to represent connectivity statistics for synthetic data sets, which are used as point-set training images and are analogous to the data typically available for a cave network. Once the applicability of the algorithms is verified, non-gridded MPS analysis and pattern simulation are conducted for the Wind Cave located in South Dakota. The developed algorithms successfully characterize and model cave networks that can only be described by point sets. Subsequently, a cave network system is simulated for the Yates Field in West Texas which is a paleokarst reservoir. Well locations with cave facies and identified cave zone thickness values are used for conditioning the pattern simulation that utilizes the MP-histograms calibrated for Wind Cave. Then, the simulated cave network is implemented into flow simulation models to understand the effects of cave structures on fluid flow. Calibration of flow model against the primary production data is attempted to demonstrate that the pattern simulation algorithm yields detailed description of spatial distribution of cave facies. Moreover, impact of accurately representing network connectivity on flow responses is explored by a water injection case. Fluid flow responses are compared for models with cave networks that are constructed by non-gridded MPS and a traditional modeling workflow using sequential indicator simulation. Applications on the Yates Field show that the cave network and corresponding cave facies are successfully modeled by using the non-gridded MPS. Detailed description of cave facies in the reservoir yields accurate flow simulation results and better future predictions. / text

One of the most challenging issues in reservoir modeling is to integrate information coming from different sources at disparate scales and precision. The primary data are borehole measurements, but in most cases, these are too sparse to construct accurate reservoir models. Therefore, in most cases, the information from borehole measurements has to be supplemented with other secondary data. The secondary data for reservoir modeling could be static data such as seismic data or dynamic data such as production history, well test data or time-lapse seismic data. Several algorithms for integrating different types of data have been developed. A novel method for data integration based on the permanence of ratio hypothesis was proposed by Journel in 2002. The premise of the permanence of ratio hypothesis is to assess the information from each data source separately and then merge the information accounting for the redundancy between the information sources. The redundancy between the information from different sources is accounted for using parameters (tau or nu parameters, Krishnan, 2004). The primary goal of this thesis is to derive a practical expression for the tau parameters and demonstrate the procedure for calibrating these parameters using the available data. This thesis presents two new algorithms for data integration in reservoir modeling. The algorithms proposed in this thesis overcome some of the limitations of the current methods for data integration. We present an extension to the direct sampling based multiple-point statistics method. We present a methodology for integrating secondary soft data in that framwork. The algorithm is based on direct pattern search through an ensemble of realizations. We show that the proposed methodology is sutiable for modeling complex channelized reservoirs and reduces the uncertainty associated with production performance due to integration of secondary data. We subsequently present the permanence of ratio hypothesis for data integration in great detail. We present analytical equations for calculating the redundancy factor for discrete or continuous variable modeling. Then, we show how this factor can be infered using available data for different scenarios. We implement the method to model a carbonate reservoir in the Gulf of Mexico. We show that the method has a better performance than when primary hard and secondary soft data are used within the traditional geostatistical framework. / text

Well testing has long been used to determine the dynamic characteristics of a reservoir. However due to the increase in interest in exploring deep offshore reservoirs and the expense associated with performing well tests of sufficient duration, alternative methods for retrieving reservoir specific information from tests of limited duration are necessary. This thesis presents analysis of derivative plots from well tests in different locations along a heterogeneous channelized environment and the information that can be derived the shape of these plots. The viability of calibrating a multiple point proxy that captures the reservoir flow connectivity information contained in well test data is explored. Such a proxy can provide useful insight into the nature of reservoir heterogeneity in the vicinity of the well. The behavior of the log-log derivative plot gives invaluable information about the nature of the reservoir surrounding the penetrating wells. Based on the change in slope of the derivative plot one can tell if a flow conduit or a low permeability zone is close to the well. Proximity to these features is also indicated in the curvature of the derivative plot with the test plot showing increasing symmetry as flow boundaries are approached. This was found to be true in both systematic simulations as well as in real build up test data. The calibration of the multiple point permeability proxy also provides information about the connectivity of the reservoir. Single point statistics provide the best estimate for wells either inside a channel or very close to the channel boundary. This is because of the relative homogeneity of permeability values within the spatial template used for averaging. The further the well gets from the channel fewer high permeability blocks will be picked up by the template and thus multiple point models provide the best estimate for effective permeability, Keff. Three point models were found to be the most accurate when the template exhibited complex permeability transition from the mudstone to the channel facies. / text

A simulação geoestatística por múltiplos pontos é um campo de pesquisa bastante ativo e tem sido aplicada com sucesso na indústria petrolífera. Entretanto, poucos estudos foram direcionados para o seu emprego em depósitos minerais. A simulação multipontual é um método promissor que supera as principais desvantagens dos métodos tradicionais. Por ser um método estocástico, ela gera diversas realizações equiprováveis que permitem a inferência de incertezas. E a integração de mapas de probabilidade local como dados secundários permite que a deficiência das simulações em precisão local seja superada. Além de tudo, diferentemente da krigagem e da simulação clássica, que são baseadas em estatísticas de segunda ordem (bipontuais), a simulação multipontual é capaz de representar estruturas geológicas complexas, ao extrair de training images padrões estatísticos de alta ordem. Nesta dissertação, os contatos litológicos dos envelopes de minério de três depósitos minerais reais e de um depósito sintético foram estimados por krigagem e simulados por um método de simulação tradicional e por um método de simulação multipontual. Constatou-se que a simulação multipontual pode ser facilmente aplicada a depósitos minerais e o desempenho dos três métodos foi comparado em situações de diferentes densidades amostrais. Apesar da melhor adequação teórica da simulação multipontual para a representação de geologias complexas, os resultados obtidos para um depósito complexo foram insatisfatórios. A solução para esse caso pode estar entre os diversos algoritmos de simulação multipontual que têm sido recentemente desenvolvidos. Por outro lado, a aplicação da simulação multipontual nos três depósitos de geologia mais simples foi muito exitosa. Os resultados mostraram contornos geologicamente plausíveis e muito mais definidos do que com os métodos tradicionais. Os modelos gerados foram tão precisos quanto os oriundos de métodos determinísticos e possibilitaram a avaliação de incertezas por meio de uma média de realizações, como qualquer método estocástico. Outra vantagem do método multipontual foi a incorporação de mapas de probabilidade local como dados secundários que permitiram definir a zona de incerteza desejada nos modelos. Todo o procedimento empregado foi descrito e justificado detalhadamente. / Geostatistical multiple-point simulation (MPS) is a very active field of research that has been applied successfully in the oil industry. However, few studies about its application in mineral deposits have been conducted. MPS is a promising method that overcomes the main drawbacks of traditional methods. Because it is a stochastic method, it generates several equiprobable realizations that allow uncertainties inference. And the integration of local probability maps as secondary data allows the lack of local precision in simulations to be overcome. Furthermore, unlike kriging and classical simulation, which are based on second-order (two-point) statistics, a MPS is able to reproduce complex geological features by high-order statistical patterns extraction from training images. In this thesis, ore envelopes lithological contacts of three real mineral deposits and of a synthetic deposit were estimated by kriging and simulated by a traditional simulation method and by a MPS method. It was verified that the MPS can be easily applied to mineral deposits and the performances of the three methods were compared in situations of different sample densities. Despite the theoretical suitability of the MPS for the representation of complex geological structures, the results obtained for a complex deposit were unsatisfactory. The solution for this case may be among the several MPS algorithms that have been recently developed. On the other hand, the application of MPS in the three simple geology deposits was very successful. The results showed geologically plausible contours much more defined than those obtained through the traditional methods. The models created were as accurate as those derived from the deterministic methods and enabled the evaluation of uncertainties by means of a mean of realizations, like any stochastic method. Another advantage of the multiple-point method was the incorporation of local probability maps as secondary data that allowed setting the zone of uncertainty desired in the models. The entire procedure was described and explained in detail.

Spinning the Plan Sideways is the story of Clara Gantz, a thirty-eight year old architect who spent her twenties getting her plans—and sections and elevations—just right. She built buildings in lieu of a family and has considered these buildings her children, but lately she’s been finding a void in wood, marble, and steel. Encouraged, with methods bordering on coercion, by Greta, her “sister” from the Gantz Home for Girls, Clara agrees to mentor Julien, a troubled twelve-year-old. Years ago, when Julien was five, his mother split their house apart, lifting it to make three-stories from one, and moved into the top level with her new husband and daughter, leaving Julien and his father, Michel on the levels below. The separation drove Michel to attempt suicide on Julien’s ninth birthday leaving him with violent aversions to homes over one-story tall. As Clara works with Julien, she discovers her life had been focused on developing the wrong types of plans and she invests in creating new plans for herself, Julien, and Michel. The story unfolds through the parallel viewpoints of Clara and Michel, with Julien’s Grim Fairytale tucked in the middle.

A multiple-point Arnoldi method is derived for model reduction of computational fluid dynamic systems. By choosing the number of frequency interpolation points and the number of Arnoldi vectors at each frequency point, the user can select the accuracy and range of validity of the resulting reduced-order model while balancing computational expense. The multiple-point Arnoldi approach is combined with a singular value decomposition approach similar to that used in the proper orthogonal decomposition method. This additional processing of the basis allows a further reduction in the number of states to be obtained, while retaining a significant computational cost advantage over the proper orthogonal decomposition. Results are presented for a supersonic diffuser subject to mass flow bleed at the wall and perturbations in the incoming flow. The resulting reduced-order models capture the required dynamics accurately while providing a significant reduction in the number of states. The reduced-order models are used to generate transfer function data, which are then used to design a simple feedforward controller. The controller is shown to work effectively at maintaining the average diffuser throat Mach number. / Singapore-MIT Alliance (SMA)

A distribuição espacial e o volume dos domínios litológicos são freqüentemente as maiores fontes de incerteza na modelagem geológica. Geralmente, a interpretação destas características é baseada em critérios subjetivos de observações, sem levar em consideração a incerteza inerente a este processo. Existem métodos de simulação geoestatísticos capazes de quantificar esta incerteza tipológica das unidades geológicas. A maioria desses métodos utiliza como medida de continuidade geológica os modelos de covariância. Entretanto, estas ferramentas de estatística de dois-pontos, raramente, conseguem capturar os padrões de geometrias complexas. Uma alternativa para esta limitação é utilizar métodos de estatística de múltiplos pontos para reproduzir os padrões espaciais de heterogeneidade que são informados por uma imagem de treinamento. Nessa dissertação, será aplicada a geoestatística de múltiplos pontos (SNESIM) para simular os litotipos de um depósito de minério de ferro. A imagem de treinamento foi baseada em seções interpretadas. Os furos de sondagem são utilizados como amostras primárias. As informações geológicas são acessadas por mapas de probabilidade utilizados como informações secundárias. A metodologia é testada na simulação de um depósito de ferro brasileiro com três diferentes litotipos. Os resultados das simulações são comparados contra um modelo de referência e novos furos de sondagens. As geometrias e distribuição espacial das tipologias foram reproduzidas de forma consistente. A incerteza das distribuições e dos volumes dos domínios tipológicos foi quantificada. O algoritmo de múltiplos pontos e a metodologia proposta mostraram grande potencial de aplicação na simulação de depósitos minerais. / The spatial distribution and volumes of lithological domains are often the biggest sources of uncertainty in geological modeling. Usually, the interpretation of these characteristics is based on subjective criteria of observations, without taking into account the uncertainty inherent in this process. There geostatistical simulation methods capable of quantifying this uncertainty typological geological units. Most of these methods uses as a measure of continuity in geological models covariance. However, these two-point statistical is rarely sufficient to capture the patterns of complex geometries. An alternative to this limitation is to use statistical methods of multiple points to reproduce the spatial patterns of heterogeneity that are informed by a training image. In this dissertation, will be applied to multi-point geostatistics (SNESIM) to simulate lithotypes a deposit of iron ore. The training image was based on sections interpreted. The drillholes are used as primary samples. Geologic information is accessed by probability maps used as secondary information. The methodology is tested in the simulation of a deposit of Brazilian iron with three different rock types. The simulation results are compared against a reference model and new drillholes. The geometries and spatial typologies were reproduced consistently. The uncertainty distributions and volumes of typological domains were quantified. The algorithm of multiple points and the proposed methodology showed great potential for application in the simulation of mineral deposits.

A distribuição espacial e o volume dos domínios litológicos são freqüentemente as maiores fontes de incerteza na modelagem geológica. Geralmente, a interpretação destas características é baseada em critérios subjetivos de observações, sem levar em consideração a incerteza inerente a este processo. Existem métodos de simulação geoestatísticos capazes de quantificar esta incerteza tipológica das unidades geológicas. A maioria desses métodos utiliza como medida de continuidade geológica os modelos de covariância. Entretanto, estas ferramentas de estatística de dois-pontos, raramente, conseguem capturar os padrões de geometrias complexas. Uma alternativa para esta limitação é utilizar métodos de estatística de múltiplos pontos para reproduzir os padrões espaciais de heterogeneidade que são informados por uma imagem de treinamento. Nessa dissertação, será aplicada a geoestatística de múltiplos pontos (SNESIM) para simular os litotipos de um depósito de minério de ferro. A imagem de treinamento foi baseada em seções interpretadas. Os furos de sondagem são utilizados como amostras primárias. As informações geológicas são acessadas por mapas de probabilidade utilizados como informações secundárias. A metodologia é testada na simulação de um depósito de ferro brasileiro com três diferentes litotipos. Os resultados das simulações são comparados contra um modelo de referência e novos furos de sondagens. As geometrias e distribuição espacial das tipologias foram reproduzidas de forma consistente. A incerteza das distribuições e dos volumes dos domínios tipológicos foi quantificada. O algoritmo de múltiplos pontos e a metodologia proposta mostraram grande potencial de aplicação na simulação de depósitos minerais. / The spatial distribution and volumes of lithological domains are often the biggest sources of uncertainty in geological modeling. Usually, the interpretation of these characteristics is based on subjective criteria of observations, without taking into account the uncertainty inherent in this process. There geostatistical simulation methods capable of quantifying this uncertainty typological geological units. Most of these methods uses as a measure of continuity in geological models covariance. However, these two-point statistical is rarely sufficient to capture the patterns of complex geometries. An alternative to this limitation is to use statistical methods of multiple points to reproduce the spatial patterns of heterogeneity that are informed by a training image. In this dissertation, will be applied to multi-point geostatistics (SNESIM) to simulate lithotypes a deposit of iron ore. The training image was based on sections interpreted. The drillholes are used as primary samples. Geologic information is accessed by probability maps used as secondary information. The methodology is tested in the simulation of a deposit of Brazilian iron with three different rock types. The simulation results are compared against a reference model and new drillholes. The geometries and spatial typologies were reproduced consistently. The uncertainty distributions and volumes of typological domains were quantified. The algorithm of multiple points and the proposed methodology showed great potential for application in the simulation of mineral deposits.

A distribuição espacial e o volume dos domínios litológicos são freqüentemente as maiores fontes de incerteza na modelagem geológica. Geralmente, a interpretação destas características é baseada em critérios subjetivos de observações, sem levar em consideração a incerteza inerente a este processo. Existem métodos de simulação geoestatísticos capazes de quantificar esta incerteza tipológica das unidades geológicas. A maioria desses métodos utiliza como medida de continuidade geológica os modelos de covariância. Entretanto, estas ferramentas de estatística de dois-pontos, raramente, conseguem capturar os padrões de geometrias complexas. Uma alternativa para esta limitação é utilizar métodos de estatística de múltiplos pontos para reproduzir os padrões espaciais de heterogeneidade que são informados por uma imagem de treinamento. Nessa dissertação, será aplicada a geoestatística de múltiplos pontos (SNESIM) para simular os litotipos de um depósito de minério de ferro. A imagem de treinamento foi baseada em seções interpretadas. Os furos de sondagem são utilizados como amostras primárias. As informações geológicas são acessadas por mapas de probabilidade utilizados como informações secundárias. A metodologia é testada na simulação de um depósito de ferro brasileiro com três diferentes litotipos. Os resultados das simulações são comparados contra um modelo de referência e novos furos de sondagens. As geometrias e distribuição espacial das tipologias foram reproduzidas de forma consistente. A incerteza das distribuições e dos volumes dos domínios tipológicos foi quantificada. O algoritmo de múltiplos pontos e a metodologia proposta mostraram grande potencial de aplicação na simulação de depósitos minerais. / The spatial distribution and volumes of lithological domains are often the biggest sources of uncertainty in geological modeling. Usually, the interpretation of these characteristics is based on subjective criteria of observations, without taking into account the uncertainty inherent in this process. There geostatistical simulation methods capable of quantifying this uncertainty typological geological units. Most of these methods uses as a measure of continuity in geological models covariance. However, these two-point statistical is rarely sufficient to capture the patterns of complex geometries. An alternative to this limitation is to use statistical methods of multiple points to reproduce the spatial patterns of heterogeneity that are informed by a training image. In this dissertation, will be applied to multi-point geostatistics (SNESIM) to simulate lithotypes a deposit of iron ore. The training image was based on sections interpreted. The drillholes are used as primary samples. Geologic information is accessed by probability maps used as secondary information. The methodology is tested in the simulation of a deposit of Brazilian iron with three different rock types. The simulation results are compared against a reference model and new drillholes. The geometries and spatial typologies were reproduced consistently. The uncertainty distributions and volumes of typological domains were quantified. The algorithm of multiple points and the proposed methodology showed great potential for application in the simulation of mineral deposits.