Modelling and Inference for Electromagnetic Flow Tomography

Electromagnetic flowmeters determine the bulk flow rate of an ohmic fluid in a pipe by measuring the voltage induced across the fluid by a transverse magnetic field. This thesis develops the theory of an electromagnetic flowmeter for groundwater aquifer applications. Electromagnetic flowmeters require slow, laminar flow for measurements of bulk flow to be accurate - even after calibration. In general, the measured voltage depends on the spatial distribution of the velocity of the fluid. Hence, determination of the velocity field is required in order to accurately measure the bulk flow rate in general flows. Accordingly, this thesis examines the inverse problem of electromagnetic flow tomography, which is the problem of determining the velocity field in a fluid from voltage measurements made at multiple locations. Electromagnetic flow tomography is a severely ill-posed linear inverse problem. The relationship between the flow and the potential induced across the fluid is described by the flowmeter equation - a boundary value problem in Poisson's equation, with the source due to the Faraday effect. A novel dipole-form of the flowmeter equation allows for analysis of spatial sensitivities. This boundary value problem is solved using Green's functions, derived by the method of images for the geometry of pipe cross-section and half-space. Computational implementation of the forward map uses a finite element method discretisation and assumes idealised point electrodes to simulate measurements. Analysis of the measurement kernel reveals extreme sensitivity to flow near the electrode locations, with low sensitivity to the majority of flow away from the electrodes. The resulting non-uniqueness in inverting the forward map implies that assumptions must be made about the spatial flow profile in order to make estimates of the bulk flow. This thesis examines a Bayesian formulation to this inverse problem, that includes a model for the forward map, and accounts for measurement noise and uncertainty in the velocity field. The Bayesian analysis of an inverse problem produces the posterior distribution, from which estimates of desired quantities may be calculated, along with uncertainties. In particular, prior modelling allows for exploring assumptions and representation of unknowns to determine potential biases. The resulting Bayesian model is a standard stochastic hierarchical model with hyperparameters to model modelling uncertainties such as the smoothness of the flow profile, or other effects. The flow is modelled as a Gaussian Markov random field and the hyperparameters are modelled using a Jefferys prior. The resulting model for the flow tomography inverse problem is a linear Gaussian model. Inference for this model is efficiently implemented using the recent marginal then conditional algorithm. That algorithm generates posterior samples by first using a Monte-Carlo Markov chain sampler for the low-dimensional marginal distribution over hyperparameters, then drawing from the full conditional distribution over the flow profile, which requires one solve of a linear equation. Posterior inference does not require the draw from the full Gaussian conditional, as moments of the Gaussian are available analytically. This method for computational Bayesian inference surpasses equivalent regularising methods in computational speed. To the best of this author's knowledge, this is the first time a Bayesian method has been used for analysing electromagnetic flow tomography. Measurements of the bulk flow in a pipe are computed using simulated data generated from physically sensible phantom flow profiles. Various geometries and electrode placements are examined, with different shapes and scales of phantom flow. The effect of using the fluid dynamics no-slip condition and changing hyperparameter values is also explored. Not surprisingly, increased number of electrodes increases the spatial flow profile resolution and accuracy of bulk flow estimates. The flow profile reconstructions and bulk flow estimates are more accurate for flow profiles which could easily be interpolated from values near electrode locations. Additionally, it is shown that there is an implicit scale in the system - the standard deviation of bulk flow correlated to the area of the pipe. The use of invasive measurements for the purpose of measuring groundwater flow is also investigated. Analysis in this thesis shows that measuring groundwater flow presents significant difficulty; the resolution of bulk flow from a realistic signal-to-noise ratio is several orders of magnitude larger than the expected bulk flow rate in unconfined aquifers

Modelling and inference for electromagnetic flow tomography

Electromagnetic flowmeters determine the bulk flow rate of an ohmic fluid in a pipe by measuring the voltage induced across the fluid by a transverse magnetic field. This thesis develops the theory of an electromagnetic flowmeter for groundwater aquifer applications. Electromagnetic flowmeters require slow, laminar flow for measurements of bulk flow to be accurate - even after calibration. In general, the measured voltage depends on the spatial distribution of the velocity of the fluid. Hence, determination of the velocity field is required in order to accurately measure the bulk flow rate in general flows. Accordingly, this thesis examines the inverse problem of electromagnetic flow tomography, which is the problem of determining the velocity field in a fluid from voltage measurements made at multiple locations. Electromagnetic flow tomography is a severely ill-posed linear inverse problem. The relationship between the flow and the potential induced across the fluid is described by the flowmeter equation - a boundary value problem in Poisson's equation, with the source due to the Faraday effect. A novel dipole-form of the flowmeter equation allows for analysis of spatial sensitivities. This boundary value problem is solved using Green's functions, derived by the method of images for the geometry of pipe cross-section and half-space. Computational implementation of the forward map uses a finite element method discretisation and assumes idealised point electrodes to simulate measurements. Analysis of the measurement kernel reveals extreme sensitivity to flow near the electrode locations, with low sensitivity to the majority of flow away from the electrodes. The resulting non-uniqueness in inverting the forward map implies that assumptions must be made about the spatial flow profile in order to make estimates of the bulk flow. This thesis examines a Bayesian formulation to this inverse problem, that includes a model for the forward map, and accounts for measurement noise and uncertainty in the velocity field. The Bayesian analysis of an inverse problem produces the posterior distribution, from which estimates of desired quantities may be calculated, along with uncertainties. In particular, prior modelling allows for exploring assumptions and representation of unknowns to determine potential biases. The resulting Bayesian model is a standard stochastic hierarchical model with hyperparameters to model modelling uncertainties such as the smoothness of the flow profile, or other effects. The flow is modelled as a Gaussian Markov random field and the hyperparameters are modelled using a Jefferys prior. The resulting model for the flow tomography inverse problem is a linear Gaussian model. Inference for this model is efficiently implemented using the recent marginal then conditional algorithm. That algorithm generates posterior samples by first using a Monte-Carlo Markov chain sampler for the low-dimensional marginal distribution over hyperparameters, then drawing from the full conditional distribution over the flow profile, which requires one solve of a linear equation. Posterior inference does not require the draw from the full Gaussian conditional, as moments of the Gaussian are available analytically. This method for computational Bayesian inference surpasses equivalent regularising methods in computational speed. To the best of this author's knowledge, this is the first time a Bayesian method has been used for analysing electromagnetic flow tomography. Measurements of the bulk flow in a pipe are computed using simulated data generated from physically sensible phantom flow profiles. Various geometries and electrode placements are examined, with different shapes and scales of phantom flow. The effect of using the fluid dynamics no-slip condition and changing hyperparameter values is also explored. Not surprisingly, increased number of electrodes increases the spatial flow profile resolution and accuracy of bulk flow estimates. The flow profile reconstructions and bulk flow estimates are more accurate for flow profiles which could easily be interpolated from values near electrode locations. Additionally, it is shown that there is an implicit scale in the system - the standard deviation of bulk flow correlated to the area of the pipe. The use of invasive measurements for the purpose of measuring groundwater flow is also investigated. Analysis in this thesis shows that measuring groundwater flow presents significant difficulty; the resolution of bulk flow from a realistic signal-to-noise ratio is several orders of magnitude larger than the expected bulk flow rate in unconfined aquifers

Research and Technology 1996: Innovation in Time and Space

As the NASA Center responsible for assembly, checkout, servicing, launch, recovery, and operational support of Space Transportation System elements and payloads, the John F. Kennedy Space Center is placing increasing emphasis on its advanced technology development program. This program encompasses the efforts of the Engineering Development Directorate laboratories, most of the KSC operations contractors, academia, and selected commercial industries - all working in a team effort within their own areas of expertise. This edition of the Kennedy Space Center Research and Technology 1996 Annual Report covers efforts of all these contributors to the KSC advanced technology development program, as well as our technology transfer activities

Analysis and testing of the IPB pico-hydro emulation platform with grid connection

The global context in which there is a need to reduce environmental impacts intensifies the search for new technologies for renewable sources. In addition to environmental issues, access to basic rights and social inclusion are also motivation for electricity generation, in a context including distributed generation (DG). Currently, the pico hydro power plant is an attractive application because of its resource availability; also, it is an interesting solution for a microgrid (on-grid or off-grid). On the other hand, usually, the conversion system is not "plug and play". This project presents the tests of convertion system for a "plug and play" solution, using different turbines and water wheel, permanent magnet synchronous generators (PMSG) and photovoltaic (PV) inverters. In this approach, generators can work at variable speed, having an overvoltage protection circuit. The prerequisites for device integration must be considered: power compatibility, minimum and maximum limit voltage, and the maximum current of PV inverter. The tests were done in the pico-hydro emulation platform, in the Superior School of Technology and Management (ESTiG). The low head propeller, Turgo, and Pelton turbines are tested in the emulation platform; as well as the vertical axis water wheel. The turbines were connected to the grid using SOLAX inverters (up to 1650 W) and OMNIK (up to 2300 W), presenting satisfactory results in both. The water wheel tests used five microinverters (up to 300 W), showing grid connection with three: BEON, GWL, and INVOLAR.O contexto global em que há necessidade de redução dos impactos ambientais intensifica a busca por novas tecnologias para fontes renováveis. Além das questões ambientais, o acesso a direitos básicos e inclusão social também são estímulos à geração de energia elétrica em áreas remotas, incluindo o contexto de geração distribuída (GD). Atualmente, as plantas pico-hídricas têm sua aplicação interessante pela disponibilidade do recurso primário; e interessante solução para microrredes (on-grid ou off-grid). Por outro ponto de vista, geralmente o sistema de conversão não é "plug and play". Este projeto apresenta o teste dos sistemas de conversão com uma solução "plug and play", uttilizando diferentes turbinas, geradores síncronos de ímã permanente (GSIP) e inversores fotovoltaicos. Utilizou-se a abordagem em que os geradores podem trabalhar em velocidade variável, tendo um circuito de proteção contra sobre-tensão. Devem ser considerados os pré-requisitos para integração dos componentes: compatibilidade de potência, tensões limites e corrente máxima do inversor fotovoltaico. Os testes foram feitos na plataforma de emulação de sistemas pico-hídricos na Escola Superior de Tecnologia e Gestão (ESTiG). Testaram-se turbinas para baixa queda do tipo hélice, Turgo e Pelton; e também a roda d’água de eixo vertical. A conexão das turbinas com a rede foi feita com os inversores SOLAX (até 1650 W) e OMNIK (até 2300 W), apresentando resultados satisfatórios em ambos. Com a roda d’água foram testados cinco microinversores (até 300 W), apresentando conexão com três: BEON, GWL e INVOLAR

Hydrogeologic Controls on Bioactive Zone Development in Biostimulated Aquifers

This study investigates the hydrogeological factors that control the feedback between bioactive zone formation and groundwater flow, as well as developing and assessing tools useful for making these investigations. The interaction between groundwater flow and bioactive zone development was investigated in both a subsurface biostimulation study and a laboratory experiments. Prior to the investigation, necessary advances were made in point velocity probe (PVP) technology to ensure successful observation in the field. Advances in these areas allowed for high resolution site characterization of an aquifer to undergo biostimulation for the removal of nitrate contamination. Heterotrophic denitrification was stimulated through daily pulses of acetate into the aquifer. With the onset of acetate delivery, decreases in groundwater velocity magnitude and flow redirection were correlated with permeable zones of relatively finer grain-size and poorer-sorting. In contrast, adjacent well-sorted and relatively coarse zones with initially high groundwater velocities indicated relatively little or no change in groundwater velocity after biostimulation. Superimposed onto these results, greater changes in groundwater velocity were noted where individual acetate pulses mixed through dispersive processes. In contrast, locations up-gradient of acetate pulse mixing indicated a higher variability in measured groundwater velocity. In total, changes in groundwater velocity in the biostimulated zone were in excess of those anticipated by analysis of the hydraulic gradient. Sediment-attached viable cell populations were interpreted to be partially responsible for the measured changes in velocity. Variables of grain-size and initial groundwater velocity were tested in controlled laboratory column experiments to evaluate the most favorable conditions for a bioactive zone to develop, subsequently leading to preferential bioclogging. Results from these experiments supported field observations that transition zones where relatively fine-grained, permeable sediments that lie adjacent to discontinuous coarser sediments - where the high velocities would lead to the highest flux of injected nutrients - represents the likely starting place for bioactive zone development, but may also be at greater risk for bioclogging. Further work was conducted to show that ground penetrating radar could noninvasively detect zones of relatively high bioactivity in granular material

Nonintrusive Flowmeter

The results of analytical and experimental work performed in the design, fabrication, and test of a prototype nonintrusive gaging system for use in monitoring the consumption of earth-storable fuels and oxidants in either a one-g or a zero-g environment are explained. The design specifications were those applicable to the reaction control system and to the orbital maneuvering system (OMS) fuel and oxidant on the space shuttle while in orbit. The major requirement was for the measurement of flow pulses with sufficient accuracy to provide a continuous knowledge of the fuel and oxidant remaining in the OMS system to within 1% or better. An ultrasonic frequency chirp technique was used having a high inherent rejection for signals traversing stray paths, and for random noise generated by the flowing liquid. A detailed analysis of the frequency chirp approach for two modes of operation (period and phase changes), including an error analysis are reported

Cross-scale hydraulic characterization of a major karst and alluvial aquifer system for drinking water supply

Grundwasser ist die wichtigste Ressource für die Trinkwasserversorgung in Deutschland sowie in zahlreichen Ländern weltweit. Dürren, Starkregen und steigende Evapotranspiration, Phänomene die durch den Klimawandel verstärkt werden, reduzieren die verfügbare Menge an Grundwasser. In Kombination mit einem steigenden Bedarf aufgrund höherer Temperaturen, ist die Aufrechterhaltung einer funktionierenden und nachhaltigen Wasserversorgung eine der wichtigsten und dringendsten Aufgaben denen sich Wasserversorger aktuell stellen müssen. Zur Entwicklung und Umsetzung notwendiger Anpassungsmaßnahmen sind gute Kenntnisse der Grundwasserressourcen notwendig, welche lediglich durch detaillierte Untersuchungen der Einzugsgebiete und Grundwasserleiter erreicht werden können. In dieser Thesis wird das komplexe System eines Karstaquifers in Kombination mit einem alluvialen Grundwasserleiter im Grundwasserschutzgebiet Donauried-Hürbe untersucht. Es umfasst einen großen Teil der östlichen Schwäbischen Alb sowie des baden-württembergischen Donautals und wurde für die über 200 Entnahmebrunnen im Donauried ausgewiesen, die durch den Zweckverband Landeswasserversorgung betrieben werden. Das dort entnommene Wasser trägt zur Trinkwasserversorgung von ca. 3 Millionen Menschen in Süddeutschland bei, inklusive der Metropolregion Stuttgart. Ziel dieser Thesis ist eine skalenübergreifende Charakterisierung des Einzugsgebiets der Entnahmebrunnen, insbesondere im Hinblick auf den Zustrom zum Donautal. Während Einzel-Bohrloch-Verdünnungsversuche (single-borehole dilution tests, SBDTs) für die kleinskaligen Untersuchungen eingesetzt werden, erfolgt die großmaßstäbliche Betrachtung mittels eines kombinierten Markierungsversuchs. SBDTs sind eine Markierungsmethode zur Charakterisierung von Grundwassermessstellen sowie Bohrlöchern. Sie können in allen Aquifertypen angewendet werden – besonders interessant sind heterogene Karst- und Kluftaquifere – und können mittels uniformer Eingabe oder Punkteingabe durchgeführt werden. Uniforme Eingaben streben eine homogene Konzentration des Markierungsmittels über die gesamte gesättigte Länge eines Bohrlochs an und liefern Informationen über maßgebliche Zu- und Abflusshorizonte. Wenn keine vertikalen Strömungen auftreten, können zudem horizontale Filtergeschwindigkeiten berechnet werden. Bei der geläufigsten Methode für uniforme Eingaben wird ein Schlauch zur Injektion gelöster Markierungsstoffe eingesetzt. In der ersten Studie wird eine vereinfachte Methode für uniforme Eingaben unter natürlichen Fließbedingungen entwickelt, geprüft und mit der gängigen Schlauchmethode verglichen. Die neue Methode nutzt einen permeablen Injektionsbeutel (PIB), um eine möglichst gleichmäßige Verteilung des Markierungsstoffs in der gesättigten Zone zu erreichen. Die PIB-Methode wird für eine Vielzahl an Tests im Labor und in mehreren Grundwassermessstellen im Untersuchungsgebiet eingesetzt, um eine fundierte Beurteilung zu ermöglichen. Wiederholte Tests in ausgewählten Messstellen werden durchgeführt, um die Reproduzierbarkeit der Methode zu untersuchen. Darüber hinaus werden zwei unterschiedliche Berechnungsmethoden basierend auf linearer Regression sowie der eindimensionalen Advektions-Dispersions-Gleichung genutzt, um scheinbare horizontale Filtergeschwindigkeiten zu berechnen. Die Ergebnisse belegen, dass die PIB-Methode für die untersuchten Grundwassermessstellen wertvolle und reproduzierbare Daten generiert. Außerdem ist sie äußerst flexibel im Hinblick auf die Tiefe der Messstellen, benötigt weniger Ausrüstung als vergleichbare Methoden und kann von einer einzelnen Person durchgeführt werden. In der zweiten Studie wird eine Sonde für SBDTs mit Punktinjektion vorgestellt, die im Rahmen dieser Thesis entwickelt und getestet wird. Mit der Injektion eines Markierungsmittels in einem spezifischen Tiefenbereich wird eine detaillierte Untersuchung der Fließprozesse in dieser Tiefe ermöglicht. Darüber hinaus produzieren uniforme Injektionen oftmals keine eindeutigen Ergebnisse hinsichtlich vertikaler Fließbewegungen, welche besonders in Karst- oder Kluftaquiferen häufig auftreten; Punktinjektionen hingegen sind explizit zur Untersuchung von Vertikalbewegungen geeignet. Die Kenntnis vertikaler Grundwasserströmungen ist essentiell für das Verständnis hydraulischer Prozesse in komplexen Aquifersystemen. Die entwickelte Injektionssonde ist darauf ausgelegt, 500 mL Markierungsstofflösung in einer beliebigen Tiefe freizusetzen, ohne den natürlichen Grundwasserfluss durch den Injektionsprozess zu verändern. Die Sonde besteht aus einem hohlen Zylinder mit einem Öffnungsmechanismus, der durch ein Fallgewicht entlang des Maßbandes ausgelöst wird, an welchem die Sonde befestigt ist. Zur Evaluierung der Injektionssonde werden zahlreiche Labor- und Feldtests durchgeführt. Besonders werden mittels mehrerer Versuche in einem Acrylglasrohr Ausdehnung und Reproduzierbarkeit des generierten Injektionsprofils untersucht. Wiederholte Eingaben zeigen jeweils eine nahezu identische Konzentrationskurve, wodurch bestätigt wird, dass die entwickelte Sonde eine reproduzierbare Tracerwolke erzeugt. Außerdem erweist sich der Öffnungsmechanismus als robust und verlässlich. Die Sonde kann von einer einzelnen Person und mit jeglichem lösbaren Markierungsmittel eingesetzt werden. Darüber hinaus ist sie für jeden Aquifertyp geeignet und äußerst flexibel bezüglich der Eingabetiefe, wodurch die Sonde im Vergleich mit gängigen Methoden zahlreiche Vorteile aufweist. Die dritte Studie fasst die Ergebnisse aller durchgeführten Markierungsversuche zusammen und wertet die Resultate bezogen auf das Grundwasserschutzgebiet Donauried-Hürbe aus, mit dem Ziel eine skalenübergreifende Charakterisierung des Aquifersystems zu erreichen. Besonderer Fokus wird dabei auf den Zustrom zum Donautal und den Entnahmebrunnen des Zweckverbands Landeswasserversorgung gelegt. Während mit den Ergebnissen von SBDTs kleinräumige Fließprozesse evaluiert werden, wird der regionale Grundwasserfluss mit einem kombinierten Markierungsversuch untersucht, der im Oktober 2017 in Zusammenarbeit mit dem regionalen Wasserversorger (Zweckverband Landeswasserversorgung) gestartet wurde. Die Untersuchungen ausgewählter Grundwassermessstellen belegen eine große Bandbreite an Ergebnissen, besonders im Hinblick auf die Abflusszeiten. Während Messstellen mit einer guten Anbindung an die Karströhren sowie Messstellen in hochdurchlässigen Bereichen des alluvialen Aquifers einen schnellen Abstrom des Markierungsmittels zeigen, werden in Messstellen geringdurchlässiger Formationen lange Abflusszeiten von bis zu mehreren Tagen festgestellt. 40 % der untersuchten Grundwassermessstellen zeigen vertikale Strömungen, die auf die komplexe Hydraulik des Aquifersystems zurückzuführen sind. Mit dem kombinierten Markierungsversuch werden hohe Fließgeschwindigkeiten von etwa 80 m/h zwischen der Schwinde im Lonetal und einer Quellgruppe in Langenau beobachtet. Jedoch werden ebenfalls äußerst verzögerte Durchgänge mit Ersteinsätzen von 250 und 370 Tagen nach der Eingabe dokumentiert, woraus maximale Fließgeschwindigkeiten von lediglich 0.44 und 0.39 m/h resultieren. In den Entnahmebrunnen des Zweckverbands Landeswasserversorgung ist bis einschließlich März 2023 kein Markierungsmittel nachweisbar. Zusammenfassend belegen die Ergebnisse der eingesetzten Markierungsmethoden die ausgeprägte und skalenübergreifende Heterogenität des Grundwasserflusses im Schutzgebiet Donauried-Hürbe. Zusätzlich zu den methodischen Weiterentwicklungen von SBDTs, trägt diese Thesis wesentlich zu einem tieferen Verständnis des für die Wasserversorgung von drei Millionen Menschen in Süddeutschland essentiellen und komplexen Aquifersystems bei