Heterogeneous Reservoir Characterization Utilizing Efficient Geology Preserving Reservoir Parameterization through Higher Order Singular Value Decomposition (HOSVD)

Petroleum reservoir parameter inference is a challenging problem to many of the reservoir simulation work flows, especially when it comes to real reservoirs with high degree of complexity and non-linearity, and high dimensionality. In fact, the process of estimating a large number of unknowns in an inverse problem lead to a very costly computational effort. Moreover, it is very important to perform geologically consistent reservoir parameter adjustments as data is being assimilated in the history matching process, i.e., the process of adjusting the parameters of reservoir system in order to match the output of the reservoir model with the previous reservoir production data. As a matter of fact, it is of great interest to approximate reservoir petrophysical properties like permeability and porosity while reparameterizing these parameters through reduced-order models. As we will show, petroleum reservoir models are commonly described by in general complex, nonlinear, and large-scale, i.e., large number of states and unknown parameters. Thus, having a practical approach to reduce the number of reservoir parameters in order to reconstruct the reservoir model with a lower dimensionality is of high interest. Furthermore, de-correlating system parameters in all history matching and reservoir characterization problems keeping the geological description intact is paramount to control the ill-posedness of the system. In the first part of the present work, we will introduce the advantages of a novel parameterization method by means of higher order singular value decomposition analysis (HOSVD). We will show that HOSVD outperforms classical parameterization techniques with respect to computational and implementation cost. It also, provides more reliable and accurate predictions in the petroleum reservoir history matching problem due to its capability to preserve geological features of the reservoir parameter like permeability. The promising power of HOSVD is investigated through several synthetic and real petroleum reservoir benchmarks and all results are compared to that of classic SVD. In addition to the parameterization problem, we also addressed the ability of HOSVD in producing accurate production data comparing to those of original reservoir system. To generate the results of the present work, we employ a commercial reservoir simulator known as ECLIPSE. In the second part of the work, we will address the inverse modeling, i.e., the reservoir history matching problem. We employed the ensemble Kalman filter (EnKF) which is an ensemble-based characterization approach to solve the inverse problem. We also, integrate our new parameterization technique into the EnKF algorithm to study the suitability of HOSVD based parameterization for reducing the dimensionality of parameter space and for estimating geologically consistence permeability distributions. The results of the present work illustrates the characteristics of the proposed parameterization method by several numerical examples in the second part including synthetic and real reservoir benchmarks. Moreover, the HOSVD advantages are discussed by comparing its performance to the classic SVD (PCA) parameterization approach. In the first part of the present work, we will introduce the advantages of a novel parameterization method by means of higher order singular value decomposition analysis (HOSVD). We will show that HOSVD outperforms classical parameterization techniques with respect to computational and implementation cost. It also, provides more reliable and accurate predictions in the petroleum reservoir history matching problem due to its capability to preserve geological features of the reservoir parameter like permeability. The promising power of HOSVD is investigated through several synthetic and real petroleum reservoir benchmarks and all results are compared to that of classic SVD. In addition to the parameterization problem, we also addressed the ability of HOSVD in producing accurate production data comparing to those of original reservoir system. To generate the results of the present work, we employ a commercial reservoir simulator known as ECLIPSE. In the second part of the work, we will address the inverse modeling, i.e., the reservoir history matching problem. We employed the ensemble Kalman filter (EnKF) which is an ensemble-based characterization approach to solve the inverse problem. We also, integrate our new parameterization technique into the EnKF algorithm to study the suitability of HOSVD based parameterization for reducing the dimensionality of parameter space and for estimating geologically consistence permeability distributions. The results of the present work illustrate the characteristics of the proposed parameterization method by several numerical examples in the second part including synthetic and real reservoir benchmarks. Moreover, the HOSVD advantages are discussed by comparing its performance to the classic SVD (PCA) parameterization approach

Discovery of Hidden Structures in Microseismic Data Using Tensor Decompositions and Multiway Component Analysis

Microseismic data is used by companies to analyze and check numerous processes, including horizontal well performance, directional drilling and, most recently, hydraulic fracturing. The microseismic data analysis approach is important and there is a lot more to discover within microseismic technology with an application of the correct data analysis approach. For example, different visualization methods could potentially contain hidden structures, not visible by traditional methods. This work proposes a new methodology to access those hidden structures. In particular, machine learning tools, such as Tensor Decomposition (TD) and Multiway Component Analysis (MWCA), were utilized to gain more information from a previously existing pool of microseismic data. The extracted hidden structures can be used to learn more about source location, from which the information about fracture propagation could be inferred within the reservoir. This potentially gives a fast and cost-effective technique to analyze hydraulic fracturing processes. The work further illustrates applicability to a real microseismic study of the noise reduction and model reduction methods, based on the same machine learning techniques. A special case of TD, Higher-Order Singular Value Decomposition (HOSVD) is used to decompose the data, while MWCA is used to show the relationship between the decomposed structure and hidden structures within the dataset. Finally, possible steps to improve the technology are outlined. Since the applications of MWCA and TD are still emerging, future enhancements to this methodology are expected

A Study of Compression Methods and Their Applications to Large Geological Models

The promise of deep learning is to discover rich hierarchical structure of the data that allows to circumvent manual feature extraction and engineering. In this study, we explore novel applications of the deep learning, building on the representational power of the neural networks to find latent variables governing the reservoir model. In Chapter I, we first introduce the relevant petroleum engineering background and motivation. Then, we give an overview of the state-of-the-art traditional and deep learning machine learning models explored in the previous works. After extensively covering the pitfalls in the traditional modeling approaches, we propose our model to significantly improve the performance. We conclude with Chapter II where we discuss possible uses of the latent reservoir representation, e.g., decline curve prediction

Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion

A novel method for the accurate functional approximation of possibly highly concentrated probability densities is developed. It is based on the combination of several modern techniques such as transport maps and nonintrusive reconstructions of low-rank tensor representations. The central idea is to carry out computations for statistical quantities of interest such as moments with a convenient reference measure which is approximated by an numerical transport, leading to a perturbed prior. Subsequently, a coordinate transformation leads to a beneficial setting for the further function approximation. An efficient layer based transport construction is realized by using the Variational Monte Carlo (VMC) method. The convergence analysis covers all terms introduced by the different (deterministic and statistical) approximations in the Hellinger distance and the Kullback-Leibler divergence. Important applications are presented and in particular the context of Bayesian inverse problems is illuminated which is a central motivation for the developed approach. Several numerical examples illustrate the efficacy with densities of different complexity

Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion

A novel method for the accurate functional approximation of possibly highly concentrated probability densities is developed. It is based on the combination of several modern techniques such as transport maps and nonintrusive reconstructions of low-rank tensor representations. The central idea is to carry out computations for statistical quantities of interest such as moments with a convenient reference measure which is approximated by an numerical transport, leading to a perturbed prior. Subsequently, a coordinate transformation leads to a beneficial setting for the further function approximation. An efficient layer based transport construction is realized by using the Variational Monte Carlo (VMC) method. The convergence analysis covers all terms introduced by the different (deterministic and statistical) approximations in the Hellinger distance and the Kullback-Leibler divergence. Important applications are presented and in particular the context of Bayesian inverse problems is illuminated which is a central motivation for the developed approach. Several numerical examples illustrate the efficacy with densities of different complexity

Advanced signal processing concepts for multi-dimensional communication systems

Die weit verbreitete Nutzung von mobilem Internet und intelligenten Anwendungen hat zu einem explosionsartigen Anstieg des mobilen Datenverkehrs geführt. Mit dem Aufstieg von intelligenten Häusern, intelligenten Gebäuden und intelligenten Städten wächst diese Nachfrage ständig, da zukünftige Kommunikationssysteme die Integration mehrerer Netzwerke erfordern, die verschiedene Sektoren, Domänen und Anwendungen bedienen, wie Multimedia, virtuelle oder erweiterte Realität, Machine-to-Machine (M2M) -Kommunikation / Internet of Things (IoT), Automobilanwendungen und vieles mehr. Daher werden die Kommunikationssysteme zukünftig nicht nur eine drahtlose Verbindung über Gbps bereitstellen müssen, sondern auch andere Anforderungen erfüllen müssen, wie z. B. eine niedrige Latenzzeit und eine massive Maschinentyp-Konnektivität, während die Dienstqualität sichergestellt wird. Ohne bedeutende technologische Fortschritte zur Erhöhung der Systemkapazität wird die bestehende Telekommunikationsinfrastruktur diese mehrdimensionalen Anforderungen nicht unterstützen können. Dies stellt eine wichtige Forderung nach geeigneten Wellenformen und Signalverarbeitungslösungen mit verbesserten spektralen Eigenschaften und erhöhter Flexibilität dar. Aus der Spektrumsperspektive werden zukünftige drahtlose Netzwerke erforderlich sein, um mehrere Funkbänder auszunutzen, wie zum Beispiel niedrigere Frequenzbänder (typischerweise mit Frequenzen unter 10 GHz), mm-Wellenbänder (einige hundert GHz höchstens) und THz-Bänder. Viele alternative Technologien wie Optical Wireless Communication (OWC), dynamische Funksysteme und zellulares Radar sollten ebenfalls untersucht werden, um ihr wahres Potenzial abzuschätzen. Insbesondere bietet OWC ein großes, aber noch nicht genutztes optisches Band im sichtbaren Spektrum, das Licht als Mittel zur Informationsübertragung nutzt. Daher können zukünftige Kommunikationssysteme als zusammengesetzte Hybridnetzwerke angesehen werden, die aus einer Anzahl von verschiedenen drahtlosen Netzwerken bestehen, die auf Funk und optischem Zugang basieren. Auf der anderen Seite ist es eine große Herausforderung, fortschrittliche Signalverarbeitungslösungen für mehrere Bereiche von Kommunikationssystemen zu entwickeln. Diese Arbeit trägt zu diesem Ziel bei, indem sie Methoden für die Suche nach effizienten algebraischen Lösungen für verschiedene Anwendungen der digitalen Mehrkanal-Signalverarbeitung demonstriert. Insbesondere tragen wir zu drei verschiedenen Anwendungsgebieten bei, d.h. Wellenformen, optischen drahtlosen Systemen und mehrdimensionaler Signalverarbeitung. Gegenwärtig ist das Cyclic Prefix Orthogonal Frequency Division Multiplexing (CP-OFDM) die weit verbreitete Multitragetechnik für die meisten Kommunikationssysteme. Um jedoch die CP-OFDM-Nachteile in Bezug auf eine schlechte spektrale Eingrenzung, Robustheit in hoch asynchronen Umgebungen und Unflexibilität der Parameterwahl zu überwinden, wurden viele alternative Wellenformen vorgeschlagen. Solche Mehrfachträgerwellenformen umfassen einen Filter bank Multicarrier (FBMC), ein Generalized Frequency Division Multiplexing (GFDM), einen Universal Filter Multicarrier (UFMC) und ein Unique Word Orthogonal Orthogonal Frequency Division Multiplexing (UW-OFDM). Diese neuen Luftschnittstellenschemata verwenden verschiedene Ansätze, um einige der inhärenten Mängel bei CP-OFDM zu überwinden. Einige dieser Wellenformen wurden gut untersucht, während andere sich noch in den Kinderschuhen befinden. Insbesondere die Integration von Multiple-Input-Multiple-Output (MIMO) -Konzepten mit UW-OFDM und UFMC befindet sich noch in einem frühen Forschungsstadium. Daher schlagen wir im ersten Teil dieser Arbeit neuartige lineare und sukzessive Interferenzunterdrückungstechniken für MIMO UW-OFDM-Systeme vor. Das Design dieser Techniken zielt darauf ab, Empfänger mit einer geringen Rechenkomplexität zu erhalten. Ein weiterer Schwerpunkt ist die Anwendbarkeit von Space-Time Block Codes (STBCs) auf UW-OFDM und UFMC-Wellenformen. Zu diesem Zweck stellen wir neue Techniken zusammen mit Detektionsverfahren vor. Wir vergleichen auch die Leistung dieser Wellenformen mit unseren vorgeschlagenen Techniken mit den anderen Wellenformen des Standes der Technik, die in der Literatur vorgeschlagen wurden. Wir zeigen, dass raumzeitblockierte UW-OFDM-Systeme mit den vorgeschlagenen Methoden nicht nur andere Wellenformen signifikant übertreffen, sondern auch zu Empfängern mit geringer Rechnerkomplexität führen. Der zweite Anwendungsbereich umfasst optische Systeme im sichtbaren Band (390-700 nm), die in Plastic Optical Fibers (POFs), Multimode-Fasern oder OWC-Systemen wie der Kommunikation über Visible Light Communication (VLC) verwendet werden können. VLC kann Lösungen für eine Reihe von Anwendungen anbieten, einschließlich drahtloser lokaler, persönlicher und Körperbereichsnetzwerke (WLAN, WPAN und WBANs), Innenlokalisierung und -navigation, Fahrzeugnetze, U-Bahn- und Unterwassernetze und bietet eine Reihe von Datenraten von wenigen Mbps zu 10 Gbps. VLC nutzt voll sichtbare Light Emitting Diodes (LEDs) für den doppelten Zweck der Beleuchtung und Datenkommunikation bei sehr hohen Geschwindigkeiten. Daher verwenden solche Systeme Intensitätsmodulation und Direct Detection (IM / DD), wodurch gefordert wird, dass das Sendesignal reellwertig und positiv sein sollte. Dies impliziert auch, dass die herkömmlichen Wellenformen, die für die Radio Frequency (RF) Kommunikation ausgelegt sind, nicht direkt verwendet werden können. Zum Beispiel muss eine hermetische Symmetrie auf das CP-OFDM angewendet werden, um ein reellwertiges Signal zu erhalten (oft als Discrete Multitone Transmission (DMT) bezeichnet), das im Gegenzug die Bandbreiteneffizienz verringert. Darüber hinaus begrenzt die LED / LED-Treiberkombination die elektrische Bandbreite. Alle diese Faktoren erfordern die Verwendung spektral effizienter Übertragungsverfahren zusammen mit robusten Entzerrungsschemata, um hohe Datenraten zu erzielen. Deshalb schlagen wir im zweiten Teil der Arbeit Übertragungsverfahren vor, die für solche optischen Systeme am besten geeignet sind. Insbesondere demonstrieren wir die Leistung der PAM-Blockübertragung mit Frequenzbereichsausgleich. Wir zeigen, dass dieses Schema nicht nur leistungsstärker ist, sondern auch alle modernen Verfahren wie CP-DMT-Schemata übertrifft. Wir schlagen auch neue UW-DMT-Schemata vor, die vom UW-OFDM-Konzept abgeleitet sind. Diese Schemata zeigen auch ein sehr überlegenes Bitfehlerverhältnis (BER) -Performance gegenüber den herkömmlichen CP-DMT-Schemata. Der dritte Anwendungsbereich konzentriert sich auf mehrdimensionale Signalverarbeitungstechniken. Bei der Verwendung von MIMO, STBCs, Mehrbenutzerverarbeitung und Mehrträgerwellenformen bei der drahtlosen Kommunikation ist das empfangene Signal mehrdimensional und kann eine multilineare Struktur aufweisen. In diesem Zusammenhang können Signalverarbeitungstechniken, die auf einem Tensor-Modell basieren, gleichzeitig von mehreren Formen von Diversität profitieren, um Mehrbenutzer-Signaltrennung / -entzerrung und Kanalschätzung durchzuführen. Dieser Vorteil ist eine direkte Konsequenz der Eigenschaft der wesentlichen Eindeutigkeit, die für matrixbasierte Ansätze nicht verfügbar ist. Tensor-Zerlegung wie die Higher Order Singular Value Decomposition (HOSVD) und die Canonical Polyadic Decomposition (CPD) werden weithin zur Durchführung dieser Aufgaben empfohlen. Die Leistung dieser Techniken wird oft mit zeitraubenden Monte-Carlo-Versuchen bewertet. Im letzten Teil der Arbeit führen wir eine Störungsanalyse erster Ordnung dieser Tensor-Zerlegungsmethoden durch. Insbesondere führen wir eine analytische Performanceanalyse des Semi-algebraischen Frameworks für approximative Canonical polyadic decompositions Simultaneous matrix diagonalizations (SECSI) durch. Das SECSI-Framework ist ein effizientes Werkzeug zur Berechnung der CPD eines rauscharmen Tensor mit niedrigem Rang. Darüber hinaus werden die erhaltenen analytischen Ausdrücke in Bezug auf die Momente zweiter Ordnung des Rauschens formuliert, so dass abgesehen von einem Mittelwert von Null keine Annahmen über die Rauschstatistik erforderlich sind. Wir zeigen, dass die abgeleiteten analytischen Ergebnisse eine ausgezeichnete Übereinstimmung mit den Monte-Carlo-Simulationen zeigen.The widespread use of mobile internet and smart applications has led to an explosive growth in mobile data traffic. With the rise of smart homes, smart buildings, and smart cities, this demand is ever growing since future communication systems will require the integration of multiple networks serving diverse sectors, domains and applications, such as multimedia, virtual or augmented reality, machine-to-machine (M2M) communication / the Internet of things (IoT), automotive applications, and many more. Therefore, in the future, the communication systems will not only be required to provide Gbps wireless connectivity but also fulfil other requirements such as low latency and massive machine type connectivity while ensuring the quality of service. Without significant technological advances to increase the system capacity, the existing telecommunications infrastructure will be unable to support these multi-dimensional requirements. This poses an important demand for suitable waveforms with improved spectral characteristics and signal processing solutions with an increased flexibility. Moreover, future wireless networks will be required to exploit several frequency bands, such as lower frequency bands (typically with frequencies below 10 GHz), mm-wave bands (few hundred GHz at the most), and THz bands. Many alternative technologies such as optical wireless communication (OWC), dynamic radio systems, and cellular radar should also be investigated to assess their true potential. Especially, OWC offers large but yet unexploited optical band in the visible spectrum that uses light as a means to carry information. Therefore, future communication systems can be seen as composite hybrid networks that consist of a number of different wireless networks based on radio and optical access. On the other hand, it poses a significant challenge to come up with advanced signal processing solutions in multiple areas of communication systems. This thesis contributes to this goal by demonstrating methods for finding efficient algebraic solutions to various applications of multi-channel digital signal processing. In particular, we contribute to three different scientific fields, i.e., waveforms, optical wireless systems, and multi-dimensional signal processing. Currently, cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) is the widely adopted multicarrier technique for most of the communication systems. However, to overcome the CP-OFDM demerits in terms of poor spectral containment, poor robustness in highly asynchronous environments, and inflexibility of parameter choice, and many alternative waveforms have been proposed. Such multicarrier waveforms include filter bank multicarrier (FBMC), generalized frequency division multiplexing (GFDM), universal filter multicarrier (UFMC), and unique word orthogonal frequency division multiplexing (UW-OFDM). These new air interface schemes take different approaches to overcome some of the inherent deficiencies in CP-OFDM. Some of these waveforms have been well investigated while others are still in its infancy. Specifically, the integration of multiple-input multiple-output (MIMO) concepts with UW-OFDM and UFMC is still at an early stage of research. Therefore, in the first part of this thesis, we propose novel linear and successive interference cancellation techniques for MIMO UW-OFDM systems. The design of these techniques is aimed to result in receivers with a low computational complexity. Another focus area is the applicability of space-time block codes (STBCs) to UW-OFDM and UFMC waveforms. For this purpose, we present novel techniques along with detection procedures. We also compare the performance of these waveforms with our proposed techniques to the other state-of-the-art waveforms that has been proposed in the literature. We demonstrate that space-time block coded UW-OFDM systems with the proposed methods not only outperform other waveforms significantly but also results in receivers with a low computational complexity. The second application area comprises of optical systems in the visible band (390-700 nm) that can be utilized in plastic optical fibers (POFs), multimode fibers or OWC systems such as visible light communication (VLC). VLC can provide solutions for a number of applications including wireless local, personal, and body area networks (WLAN, WPAN, and WBANs), indoor localization and navigation, vehicular networks, underground and underwater networks, offering a range of data rates from a few Mbps to 10 Gbps. VLC takes full advantage of visible light emitting diodes (LEDs) for the dual purpose of illumination and data communications at very high speeds. Because of the incoherent nature of the LED sources, such systems employ intensity modulation and direct detection (IM/DD), thus demanding that the transmit signal should be real-valued and positive. This also implies that the conventional waveforms designed for the radio frequency (RF) communication cannot be directly used. For example, a Hermitian symmetry has to be applied to the CP-OFDM spectrum to obtain a real-valued signal (often referred to as discrete multitone transmission (DMT)) that in return reduces the bandwidth efficiency. Moreover, the LED/LED driver combination limits the electrical bandwidth. All these factors require the use of spectrally efficient transmission schemes along with robust equalization schemes to achieve high data rates. Therefore, in the second part of the thesis, we propose transmission schemes that are best suited for such optical systems. Specifically, we demonstrate the performance of PAM block transmission with frequency domain equalization. We show that this scheme is not only more power efficient but also outperforms all of the state-of-the-art schemes such as CP-DMT schemes. We also propose novel UW-DMT schemes that are derived from the UW-OFDM concept. These schemes also show a much superior bit error ratio (BER) performance over the conventional CP-DMT schemes. The third application area focuses on multi-dimensional signal processing techniques. With the use of MIMO, STBCs, multi-user processing, and multicarrier waveforms in wireless communications, the received signal is multidimensional in nature and may exhibit a multilinear structure. In this context, signal processing techniques based on a tensor model can simultaneously benefit from multiple forms of diversity to perform multi-user signal separation/equalization and channel estimation. This advantage is a direct consequence of the essential uniqueness property that is not available for matrix based approaches. Tensor decompositions such as the higher order singular value decomposition (HOSVD) and the canonical polyadic decomposition (CPD) are widely recommended for performing these tasks. The performance of these techniques is often evaluated using time consuming Monte-Carlo trials. In the last part of the thesis, we perform a first-order perturbation analysis of the truncated HOSVD and the Semi-algebraic framework for approximate Canonical polyadic decompositions via Simultaneous matrix diagonalizations (SECSI). The SECSI framework is an efficient tool for the computation of the approximate CPD of a low-rank noise corrupted tensor. Especially, the SECSI framework shows a much improved performance and comparatively low-complexity as compared to the conventional algorithms such as alternative least squares (ALS). Moreover, it also facilitates the implementation on a parallel hardware architecture. The obtained analytical expressions for both algorithms are formulated in terms of the second-order moments of the noise, such that apart from a zero-mean, no assumptions on the noise statistics are required. We demonstrate that the derived analytical results exhibit an excellent match to the Monte-Carlo simulations

Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion

This paper presents a novel method for the accurate functional approximation of possibly highly concentrated probability densities. It is based on the combination of several modern techniques such as transport maps and low-rank approximations via a nonintrusive tensor train reconstruction. The central idea is to carry out computations for statistical quantities of interest such as moments based on a convenient representation of a reference density for which accurate numerical methods can be employed. Since the transport from target to reference can usually not be determined exactly, one has to cope with a perturbed reference density due to a numerically approximated transport map. By the introduction of a layered approximation and appropriate coordinate transformations, the problem is split into a set of independent approximations in seperately chosen orthonormal basis functions, combining the notions h- and p-refinement (i.e. “mesh size” and polynomial degree). An efficient low-rank representation of the perturbed reference density is achieved via the Variational Monte Carlo method. This nonintrusive regression technique reconstructs the map in the tensor train format. An a priori convergence analysis with respect to the error terms introduced by the different (deterministic and statistical) approximations in the Hellinger distance and the Kullback–Leibler divergence is derived. Important applications are presented and in particular the context of Bayesian inverse problems is illuminated which is a main motivation for the developed approach. Several numerical examples illustrate the efficacy with densities of different complexity and degrees of perturbation of the transport to the reference density. The (superior) convergence is demonstrated in comparison to Monte Carlo and Markov Chain Monte Carlo methods