This D.Sc. thesis proposes new perspectives for modeling drill string torsional dynamics under uncertainties. This work develops a novel stochastic hysteretic (nonreversible) bit-rock interaction model. Firstly, a new nominal interaction model, which depends not only on the bit speed, but also on the bit acceleration is developed. Then, a new stochastic model for the bit-rock interaction, taking into account the inherent fluctuations during the drilling, is also proposed. Furthermore, here a new test-rig is proposed to analyze drill string dynamics and bit-rock interaction, which is able to reproduce stick-slip phenomena while drilling a rock sample using standard masonry bits, as well as to validate bit-rock interaction models. An original strategy for modeling uncertainties globally, based on terms of the nonparametric probabilistic approach, considering a simple torsional model for a drill string, is also proposed herein. This strategy allows to control the dispersion level of each interior and interface DOFs of each drill string substructure independently, which can provide more information to improve the operational safety. / This D.Sc. thesis proposes new perspectives for modeling drill string torsional dynamics under uncertainties. This work develops a novel stochastic hysteretic (nonreversible) bit-rock interaction model. Firstly, a new nominal interaction model, which depends not only on the bit speed, but also on the bit acceleration is developed. Then, a new stochastic model for the bit-rock interaction, taking into account the inherent fluctuations during the drilling, is also proposed. Furthermore, here a new test-rig is proposed to analyze drill string dynamics and bit-rock interaction, which is able to reproduce stick-slip phenomena while drilling a rock sample using standard masonry bits, as well as to validate bit-rock interaction models. An original strategy for modeling uncertainties globally, based on terms of the nonparametric probabilistic approach, considering a simple torsional model for a drill string, is also proposed herein. This strategy allows to control the dispersion level of each interior and interface DOFs of each drill string substructure independently, which can provide more information to improve the operational safety

This thesis analyzes the nonlinear dynamics of a drill-string including uncertainty modeling. A drill-string is a slender flexible structure that rotates and digs into the rock in search of oil. A mathematical-mechanical model is developed for this structure including fluid-structure interaction, impact, geometrical nonlinearities and bit-rock interaction. After the derivation of the equations of motion, the system is discretized by means of the finite element method and a computer code is developed for the numerical computations using the software MATLAB. The normal modes of the dynamical system in the prestressed configuration are used to construct a reduced order model for the system. To take into account uncertainties, the nonparametric probabilistic approach, which is able to take into account both system-parameter and model uncertainties, is used. The probability density functions related to the random variables are constructed using the maximum entropy principle and the stochastic response of the system is calculated using the Monte Carlo method. A novel approach to take into account model uncertainties in a nonlinear constitutive equation (bit-rock interaction model) is developed using the nonparametric probabilistic approach. To identify the probabilistic model of the bit-rock interaction model, the maximum likelihood method together with a statistical reduction in the frequency domain (using the Principal Component Analysis) is applied. Finally, a robust optimization problem is performed to find the operational parameters of the system that maximizes its performance, respecting the integrity limits of the system, such as fatigue and instability

The work presented is a master’s thesis at the track Machine Design at KTH Royal Institute ofTechnology. The project was commissioned by Epiroc AB through Svea Teknik AB. Epiroc’s Easer L is a highly versatile and flexible mobile raise boring machine used to drill opening holes and media holes. A drill string handling system is used to construct and deconstruct the drill string during a raise. Currently, the Easer utilizes a lifting arm to move the drill string components between a pipe rack and the derrick. A pipe loader, which is a second arm mounted on the derrick, is used to align the components with the drill string. This work aims to examinethe possibility to replace this system with a more compact and preferably automatable solution. The work had its main focus on a concept generation and evaluation process, where a wide range of possible means of handling the drill string handling system’s sub functions were methodically mapped in function means trees. Several concepts were synthesized using a morphological method and brain storming in a diverging process and their variants were explored and mapped. An iterative screening process utilizing a Pugh Matrix and GATEs converged the ideas until a final concept selection was performed. The resulting conceptual drill string handling system consist of a new crane and gripper solution and a new pipe loader, all modified to lift pipes horizontally instead of vertically. The pipe racks were modified to enable better interaction with the gripper module, even if racks are inclined. A sliding mechanism was integrated in the crane mounting bracket to eliminate the need for remounting the crane, reducing down times. The resulting conceptual drill string handling solves many of the challenges of the existing system and increases the flexibility, automation and productivity of the Easer L. / Detta är ett examensarbete på masterspåret Maskinkonstruktion på Kungliga Tekniska Högskolan. Arbetet utfördes på uppdrag av Epiroc AB genom Svea Teknik AB. Epirocs Easer L är en mångsidig och flexibel mobil stigortsmaskin som används till öppningshål och mediehål. Borrsträngskomponenternas hanteringssystem används för att gradvis montera och demontera borrsträngen under drift. Dagens hanteringssystem inkluderar en kran med en gripanordning som flyttar borrsträngskomponenter mellan deras förvaringsställning och borrtornet. En borrörsladdare, vilken är en ytterligare arm monterad på borrtornet, används för att placera borrsträngskomponenter i linje med borrsträngen. Arbetet syftar till att undersöka möjligheteratt byta ut detta hanteringssystem mot ett mer kompakt och automatiserbart alternativ. Arbetets huvudfokus låg på konceptutveckling, där ett brett utbud av lösningar på hanteringsystemets delfunktioner kartlades metodiskt i funktions­medelträd. Detta följdes av en divergerande process där syntes av en bred mängd koncept utfördes genom morfologisk metod och idéspåning och konceptens variationer kartlades noggrant. En iterativ gallringsprocess kovergerade antalet koncept med hjälp av en Pughmatris och GATEr tills ett konceptval kunde utföras. Slutresultatet är ett konceptuellt hanteringssystem för borrsträngskomponenter beståendes av en kran och gripenhet med tillhörande borrörsladdare, vilka anpassades för att hantera borrsträngskomponenter i horisontellt läge. Detta möjliggör en mer kompakt arbetsvolym. Förvaringsställningarna modifierades för bättre interaktion med gripenheten, även vid ojämn mark. En linjärenhet integrerades i kranens fästpunkt, vilket gör att kranen inte behöver monteras om vilket tidigare orsakade ställtider. Det nya alternativet löser flertalet problem med det nuvarande hanteringssystemet, vilket gör Easer L mer flexibel och automatiserad och ökar därmed produktiviteten.

On fait l'analyse de la dynamique nonlinéaire d'une colonne de forage avec modélisation d'incertitudes. Une colonne de forage est une structure flexible mince qui tourne et fore des roches en cherchant du pétrole. Un modèle mathématique-mécanique est développeé pour cette structure en incluant de l'interaction fluide-structure, des impact, des nonlinéarités géométriques, et de l'interaction tête de la colonne-roche. Les équations de mouvement sont déduites, puis le système est discretisé par la méthode des éléments finis, et un code numérique est développeé pour les simulations numériques avec le logiciel MATLAB. Les modes normaux de la dynamique à la configuration précontrainte sont utilisés pour construire un modèle reduit pour le système. L'approche probabiliste nonparamétrique, qui est capable de prendre en compte les incertitude des paramètres du système et aussi les incertitude de modèle, est utilisée. Les fonctions densités de probabilité liées aux variables aléatoire sont construites par la méthode du Maximum d'Entropie et la réponse stochastique du système est calculée en utilisant la méthode de Monte Carlo. Une nouvelle approche pour prendre en compte des incertitudes de modèle dans une équation constitutive nonlinéaire (interaction tête de la colonne-roche) est développeé avec l'approche probabiliste nonparamétrique. La méthode du maximum de vraisemblance et la réduction statistique dans le domaine de la fréquence (Analyse de composantes principales) sont utilisés pour identifier le modèle probabiliste de l'interaction tête de la colonne-roche. Finalement, un problème d'optimisation robuste est analysé de façon à trouver les paramètres opérationnels du système qui maximise sa performance et respectent les limites d'intégrités du système, comme fatigue et instabilitée / This thesis analyzes the nonlinear dynamics of a drill-string including uncertainty modeling. A drill-string is a slender flexible structure that rotates and digs into the rock in search of oil. A mathematical-mechanical model is developed for this structure including fluid-structure interaction, impact, geometrical nonlinearities and bit-rock interaction. After the derivation of the equations of motion, the system is discretized by means of the finite element method and a computer code is developed for the numerical computations using the software MATLAB. The normal modes of the dynamical system in the prestressed configuration are used to construct a reduced order model for the system. To take into account uncertainties, the nonparametric probabilistic approach, which is able to take into account both system-parameter and model uncertainties, is used. The probability density functions related to the random variables are constructed using the maximum entropy principle and the stochastic response of the system is calculated using the Monte Carlo method. A novel approach to take into account model uncertainties in a nonlinear constitutive equation (bit-rock interaction model) is developed using the nonparametric probabilistic approach. To identify the probabilistic model of the bit-rock interaction model, the maximum likelihood method together with a statistical reduction in the frequency domain (using the Principal Component Analysis) is applied. Finally, a robust optimization problem is performed to find the operational parameters of the system that maximizes its performance, respecting the integrity limits of the system, such as fatigue and instability

[pt] Este trabalho apresenta um estudo do comportamento dinâmico de uma bancada de testes representativa do sistema real de perfuração, composta por um motor CC acoplado a um sistema físico torcional, sujeita a fontes de atrito que induzem um regime de stick-slip no sistema em duas regiões distintas. O estudo incluiu a identificação de parâmetros da bancada de testes por meio de uma série de ensaios experimentais; e a caracterização do atrito, por meio do levantamento experimental da curva do coeficiente de atrito, em função da velocidade angular dos rotores principais. O intuito inicial foi a obtenção de um modelo numérico que fosse o mais simples possível e que representasse bem a bancada de testes. Uma vez obtido o modelo numérico, prosseguiu-se com uma série de simulações que permitissem uma caracterização indireta do regime de atrito ao qual estivessem submetidos os rotores principais, partindo-se apenas de medições de parâmetros no motor. Esse estudo é de grande relevância para a compreensão qualitativa da dinâmica do sistema real de perfuração, uma vez que ainda hoje não há técnicas totalmente confiáveis para caracterização do comportamento da coluna no fundo do poço a partir de dados da superfície somente. / [en] This paper presents a study of the dynamic behavior of a representative test bench of a real rotary drilling system, comprising a DC motor coupled to a very exible torsional system subjected to sources of friction which can induce self-excitation into two distinct regions of the system. The study includes the identification of parameter settings from the test bench by means of a series of experimental tests and characterization of friction, by obtaining the experimental curve of the friction coefficient as a function of the angular speed of the main rotor. The initial aim was to obtain a numerical model as simple as possible, capable of representing the test bench. Once obtained the numerical model, a series of numerical simulations were done, which allow an indirect characterization of the friction condition to which main rotors were subjected, starting only with the parameters measured at the drive. This study is of great importance for a qualitative understanding of the dynamics of the real drilling system, since today there is no fully reliable techniques to characterize the behavior of the column in the deep from surface data only.

O fenômeno de stick-slip, no processo de perfuração de poços de petróleo, é propiciado pela interação entre broca e formação rochosa e pode dar origem a grandes oscilações na velocidade angular podendo provocar danos irreparáveis ao processo. Neste trabalho, analisa-se o desempenho de leis de controle aplicadas à mesa rotativa (responsável por movimentar a coluna de perfuração), visando à redução de stick-slip e de oscilações da velocidade angular da broca. As leis de controle implementadas são do tipo PI (Proporcional-Integral), com parcelas de torque aplicado à mesa rotativa, proporcional e integral à velocidade da mesa, podendo ser com peso na broca constante ou variável. Para a coluna de perfuração, foi proposto um modelo em elementos finitos com função de forma linear. O torque na broca foi modelado segundo atrito de Coulomb pela forma não regularizada, curva esta ajustada pelos dados empíricos conforme propostas da literatura. Diversos critérios de desempenho foram analisados e foi observado que a minimização do desvio médio da velocidade angular em relação à referência propicia melhores condições de operação. Análises paramétricas dos ganhos de controle proporcional e integral foram realizadas, dando origem a curvas de nível para o desvio médio de velocidade angular na broca. A partir destas curvas, foram definidas regiões de estabilidade nas quais o desvio é aceitável. Estas regiões foram observadas serem maiores para menores pesos na broca e maiores velocidades angulares de referência e vice-versa. A adição do controle do peso na broca permitiu uma redução global dos níveis de desvio médio de velocidade angular, dando origem a um aumento das regiões de estabilidade do processo de perfuração. / The stick-slip phenomenon, in the process of drilling oil wells, due to the interaction between drill and rock formation can lead to large fluctuations in drill-bit angular velocity and, thus, cause irreparable damage to the process. In this work, the performance of control laws applied to the rotary table (responsible for moving the drill string) is analyzed, in order to reduce stick-slip and drill-bit angular velocity oscillations. The control laws implemented are based on a PI (Proportional-Integral) controller, for which the torque applied to the rotating table has components proportional and integral to table angular velocity with constant or variable WOB (Weight On Bit). For the drillstring, a finite element model with a linear interpolation was proposed. The torque on the drill-bit was modeled by a non-regularized Coulomb friction model, with parameters that were adjusted using empirical data proposed in literature. Several performance criteria were analyzed and it was observed that the minimization of the mean deviation of the drill-bit angular velocity relative to the target one would provide the best operating condition. Parametric analyses of proportional and integral control gains were performed, yielding level curves for the mean deviation of drill-bit angular velocity. From these curves, stability regions were defined in which the deviation is acceptable. These regions were observed to be wider for smaller values of WOB and higher values of target angular velocity and vice-versa. The inclusion of a controlled dynamic WOB reduced the levels of mean deviation of angular velocity, leading to improved stability regions for the drilling process.

O fenômeno de stick-slip, no processo de perfuração de poços de petróleo, é propiciado pela interação entre broca e formação rochosa e pode dar origem a grandes oscilações na velocidade angular podendo provocar danos irreparáveis ao processo. Neste trabalho, analisa-se o desempenho de leis de controle aplicadas à mesa rotativa (responsável por movimentar a coluna de perfuração), visando à redução de stick-slip e de oscilações da velocidade angular da broca. As leis de controle implementadas são do tipo PI (Proporcional-Integral), com parcelas de torque aplicado à mesa rotativa, proporcional e integral à velocidade da mesa, podendo ser com peso na broca constante ou variável. Para a coluna de perfuração, foi proposto um modelo em elementos finitos com função de forma linear. O torque na broca foi modelado segundo atrito de Coulomb pela forma não regularizada, curva esta ajustada pelos dados empíricos conforme propostas da literatura. Diversos critérios de desempenho foram analisados e foi observado que a minimização do desvio médio da velocidade angular em relação à referência propicia melhores condições de operação. Análises paramétricas dos ganhos de controle proporcional e integral foram realizadas, dando origem a curvas de nível para o desvio médio de velocidade angular na broca. A partir destas curvas, foram definidas regiões de estabilidade nas quais o desvio é aceitável. Estas regiões foram observadas serem maiores para menores pesos na broca e maiores velocidades angulares de referência e vice-versa. A adição do controle do peso na broca permitiu uma redução global dos níveis de desvio médio de velocidade angular, dando origem a um aumento das regiões de estabilidade do processo de perfuração. / The stick-slip phenomenon, in the process of drilling oil wells, due to the interaction between drill and rock formation can lead to large fluctuations in drill-bit angular velocity and, thus, cause irreparable damage to the process. In this work, the performance of control laws applied to the rotary table (responsible for moving the drill string) is analyzed, in order to reduce stick-slip and drill-bit angular velocity oscillations. The control laws implemented are based on a PI (Proportional-Integral) controller, for which the torque applied to the rotating table has components proportional and integral to table angular velocity with constant or variable WOB (Weight On Bit). For the drillstring, a finite element model with a linear interpolation was proposed. The torque on the drill-bit was modeled by a non-regularized Coulomb friction model, with parameters that were adjusted using empirical data proposed in literature. Several performance criteria were analyzed and it was observed that the minimization of the mean deviation of the drill-bit angular velocity relative to the target one would provide the best operating condition. Parametric analyses of proportional and integral control gains were performed, yielding level curves for the mean deviation of drill-bit angular velocity. From these curves, stability regions were defined in which the deviation is acceptable. These regions were observed to be wider for smaller values of WOB and higher values of target angular velocity and vice-versa. The inclusion of a controlled dynamic WOB reduced the levels of mean deviation of angular velocity, leading to improved stability regions for the drilling process.

Mechanical vibrations are inevitable in drilling operations. Torsional stick-slip vibrations are vibrations that occur in drilling columns, which are produced by periodic variations of torque and characterized by large fluctuations in the speed of the drill bit. These vibrations are dangerous, primarily by the cyclical characteristic of the phenomenon that by the amplitude of the same, which can cause fatigue of the pipe, failures in the components of the drill string, deformations in the walls of the well, excessive wear of the drill, low rate of penetration, and collapse of the drilling process. The frequency of these unwanted oscillations can be reduced by the application of automatic control techniques. The objective of this study is to evaluate through numerical simulations, the application of conventional control techniques, such as proportional-integral control (PI), and nonlinear, as the sliding mode control (SMC) and the input-output linearization control (IOLC), to eliminate the presence of stick-slip oscillation in drilling columns. The controllers are designed primarily to maintain a constant speed of rotation system, by manipulating engine torque, thereby inferentially control the speed of the drill, thus providing optimum operation conditions, beyond preserving system stability. Results of simulations using drill string torsional models of two degrees of freedom (2-DOF) and four degrees of freedom (4-DOF) show the performance of the proposed control systems, which are analyzed and qualitatively compared. / Vibrações mecânicas são inevitáveis nas operações de perfuração. Vibrações torcionais stick-slip são vibrações que ocorrem em colunas de perfuração, as quais são produzidas pelas variações periódicas de torque e caracterizadas por grandes oscilações da velocidade da broca. Estas vibrações são prejudiciais, mais pela característica cíclica do fenômeno que pela amplitude da mesma, podendo originar fadiga da tubulação, falhas nos componentes da coluna de perfuração, deformações nas paredes do poço, desgaste excessivo da broca, baixa taxa de penetração e, inclusive, colapso do processo de perfuração. A frequência destas oscilações indesejadas pode ser reduzida pela aplicação de técnicas de controle automático. O objetivo deste trabalho é avaliar, mediante simulações numéricas, a aplicação de técnicas de controle convencional, como o controle proporcional-integral (PI), e não linear, como o controle por modos deslizantes (SMC) e o controle por linearização entrada-saída (IOLC) para eliminar a presença de oscilações stick-slip em colunas de perfuração. Os controladores são desenvolvidos principalmente para manter constante a velocidade do sistema de rotação, mediante a manipulação do torque do motor, para assim controlar inferencialmente a velocidade da broca, fornecendo desta maneira condições ótimas de operação, além de preservar a estabilidade do sistema. Resultados das simulações, usando modelos torcionais de uma coluna de perfuração de dois graus de liberdade (2-DOF) e de quatro graus de liberdade (4-DOF), mostram o desempenho dos sistemas de controle propostos, os quais são analisados e comparados qualitativamente.

For developing the available hydrocarbon reserves and for exploring new reservoirs, deeper and more complex wells are drilled. Drilling such deeper and complex wells requires a constant monitoring and controlling of the well paths. Therefore, the bottom hole assembly, the lower section of the drill string above the drill bit, is equipped with numerous measuring sensors for collecting geological and directional data while drilling. The collected data have to be transmitted to the surface in real time. Prior to transmit the data measured downhole to the surface, they are processed and translated into a binary code. Accordingly, the data will be represented as a series of zeroes and ones. The most common method for data transmission in boreholes is the so called mud pulse telemetry which sends the information through the drilling mud inside the drill string by means of coded pressure pulses. There are two types of devices available for downhole pressure pulses generation. The first type is the (positive or negative) pressure pulser which transmits the data by quasi-static variations of the pressure level inside the drill string. The second type is the (rotating or oscillating) mud siren which transmits the data by generating continuous pressure waves at specific frequencies. The main disadvantage of the mud pulse telemetry is its low data transmission rate which is about 10 bps. This data rate is very low compared to the measured amount of raw data. Therefore, the efficiency of the mud pulse telemetry must be improved, so that the data could be transmitted at higher rates. The present research work presents different developed and tested concepts for increasing the efficiency and the data transmission rate of the mud pulse telemetry. Both, the transmitter and the receiver end, were taken into consideration by developing the new concepts. Different hardware and software tools were used for performing the present research work. The available flow loop test facility and the experimental prototypes of the mud siren and positive pulser were used. The test facility was extended in order to enable the investigation of the new concepts. The available 3D numerical model (ANSYS CFX) was modified and extended in order to study the new concepts. At the transmitter end, a novel concept for a hybrid mud pulse telemetry system was developed and successfully tested. Here, two different types of mud pulse telemetry could be used in a combination, such as a mud siren and a pressure pulser. The developed concept was registered at the German Patent and Trade Mark Office for a patent in 2018. Two concepts for a multi-frequency mud siren were developed for simultaneous generation of two frequencies. In the first approach, two sets of stator/rotor were installed in a row connection, while they were installed in a parallel connection in the second approach. The two concepts were registered at the German Patent and Trade Mark Office for patents in 2015. An experimental multi-frequency generator was built and used for testing of several new ideas, such as transmitting the data using several carrier frequencies at the same time, transmitting the data with different wave forms (sine, sawtooth, triangle and rectangle), or transmitting the data using the chirp modulation. The innovative design of the experimental multi-frequency generator was registered at the German Patent and Trade Mark Office for patents in 2016. At the receiver end, two different methods for processing and analyzing the received multi-frequency signals using the Wavelet and Fourier analysis were drafted and tested. A novel concept for the use of a multi-sensor receiver was developed and successfully tested. The use of a multi-sensor receiver could strongly improve the detection of the received signals.:Table of Contents Declaration ii Abstract iii Acknowledgements v Table of Contents vi List of Abbreviations x List of Symbols xii CHAPTER 1 Introduction 1 CHAPTER 2 Modern Drilling Technology and Low Data Transmission Rate as a Limitation 5 2.1 Introduction to the modern drilling technology 5 2.1.1 Directional drilling technology 5 2.1.2 Steering technology 6 2.1.3 Measuring technology 8 2.1.4 Technology of data transmission in boreholes 9 2.2 Low data transmission rate as a problem with respect to the whole drilling process 13 CHAPTER 3 Fundamentals of Communication Technology 16 3.1 Modulation techniques for data transmission in baseband 16 3.2 Modulation techniques for data transmission in passband 17 3.3 Multiple frequency and chirp spread spectrum modulation techniques 19 3.4 Digital signal processing 21 3.4.1 Fourier transformation 21 3.4.2 Continuous wavelet transformation 23 3.4.3 Filtering 24 CHAPTER 4 State of the Art for Mud Pulse Telemetry Systems 26 4.1 Historical development of mud pulse telemetry including latest improvements applied for increasing its data transmission rate 26 4.2 Available types of mud pulse telemetry devices 30 4.2.1 Negative pulser 31 4.2.2 Positive pulser 32 4.2.3 Mud siren 32 4.2.4 Oscillating shear valve 33 4.3 Limitations of data transmission via mud pulse telemetry 34 4.3.1 Effect of noise sources in the mud channel on the transmission signal 34 4.3.2 Effect of attenuation in the mud channel on the transmission signal 36 4.3.3 Effect of reflections and their interference with the main transmission signal 37 4.3.4 Pass and stop bands 38 4.4.5 Minimum transmission time slot 38 CHAPTER 5 Novel Concepts and Tools for Increased Data Transmission Rates of Mud Pulse Telemetry 40 5.1 Transmitter end 41 5.1.1 Hybrid mud pulse telemetry (HMPT) 41 5.1.2 Multi-frequency generator 43 5.2 Receiver end 45 5.2.1 Investigation of the Wavelet analysis suitability for multi-frequency signal detection 45 5.2.2 Flexible placement of multi-sensor receiver 46 CHAPTER 6 Laboratory Test Facility and Used Hard and Soft Tools 49 6.1 Laboratory test facility for hydraulic data transmission in boreholes 49 6.2 Experimental prototypes of the pressure pulsers and mud siren 53 6.3 3D numerical simulation model for the test facility and mud siren 55 6.4 MATLAB software 58 CHAPTER 7 Hybrid Mud Pulse Telemetry (HMPT) System 59 7.1 Combination of mud siren and negative pressure pulser 60 7.2 Combination of mud siren and positive pressure pulser 63 7.3 Evaluating the laboratory investigations of the hybrid mud pulse telemetry (HMPT) system 66 CHAPTER 8 Mathematical and Numerical Investigation of the Concept of the Multi-Frequency Mud Siren 68 8.1 Preliminary considerations for the concept of the multi-frequency mud siren 69 8.2 Mathematical model investigation of different approaches for the multi-frequency mud siren concept 71 8.2.1 Multi-frequency mud siren with stators and rotors in a row 72 8.2.2 Multi-frequency mud siren with parallel connection of stators and rotors 74 8.3 Numerical model investigation of multi-frequency mud siren with two sets of stator/rotor in a row 77 8.3.1 Numerical simulations for data transmission with a multi-frequency mud siren using two carrier frequencies 79 8.3.2 Evaluation of the simulation results 81 8.3.3 Increasing the transmission reach of the mud siren for deep drilling operations 83 CHAPTER 9 Laboratory Investigations of Multi-Carrier Hydraulic Data Transmission Using an Experimental Multi-Frequency Generator 85 9.1 Laboratory multi-carrier frequency transmission tests 87 9.2 Investigation of the Wavelet analysis suitability for the detection of multi-frequency signal transmitted in boreholes 95 9.3 Initial investigations of hydraulic data transmission using chirp modulation and different pressure wave forms 100 9.3.1 Data transmission using chirp modulation (Chirp Spread Spectrum, CSS) 100 9.3.2 Data transmission using different wave forms 101 CHAPTER 10 Investigation of the Use of a Multi-Sensor Receiver for Improving the Hydraulic Data Transmission in Boreholes 104 10.1 Numerical model investigation of the use of a multi-sensor receiver 104 10.1.1 Data transmission using single-input and multiple-output (SIMO) 104 10.1.2 Data transmission using multiple-input and multiple-output (MIMO) 107 10.2 Laboratory investigations of the use of a multi-sensor receiver 108 10.3 Evaluating the use of a multi-sensor receiver for improving the hydraulic data transmission in boreholes 112 CHAPTER 11 Conclusion and Outlook 116 11.1 Conclusion 116 11.2 Outlook 120 References 122 List of Figures 129 List of Tables 136 List of Publications 137 List of Patents 138 Appendix- Chapter 7 139 Appendix- Chapter 8 141 Appendix- Chapter 9 142 Appendix- Chapter 10 146

[pt] Nesta tese, a teoria das hastes de Cosserat é revisitada e aplicada à dinâmica de coluna de perfuração. O objetivo é estudar o comportamento dessas estruturas dentro de poços de petróleo curvos. Para atingir este objetivo, um modelo estrutural determinístico é construído onde as tubos de perfuração (drill-pipes) e o conjunto de fundo (bottom hole assembly) são considerados como uma estrutura unidimensional de Cosserat. Em seguida, é desenvolvida uma estratégia para tratar o contato lateral em poços com configuração curvilínea. Depois disso, o problema de contorno livre é tratado mediante uma estratégia que considera como a condição de borda evolui à medida que a estrutura de perfuração avança. Isto é feito mediante uma formulação de interação broca-rocha que deve considerar a dinâmica de corte. Para isso, uma equação extra, de advecção, é resolvida junto com as equações de movimento de Cosserat. Em seguida, alguns casos de aplicação são apresentados. Numa primeira instancia, alguns elementos do problema são avaliados separadamente. Seguidamente, eles são integrados e analisados de forma conjunta. Por exemplo, primeiramente uma coluna de perfuração sem contato de fundo (off-bottom) é simulada, ou seja, sem contato broca-rocha, para estudar o comportamento e a implementação da estratégia para o contato lateral. Aqui também são calibrados alguns dos parâmetros do modelo de atrito. Em seguida, a estratégia para contabilizar o corte na rocha é implementada em um modelo 2-DOF de baixa dimensão e em um semi-discreto onde a dinâmica de torção é modelada como uma equação de onda. Os resultados mostram que o uso de abordagens contínuas resulta mais apropriade que aquelas onde se utilizam modelos de baixa dimensãom, particularmente quando são consideradas colunas longas, e quando há interesse em analisar não apenas o comportamento da broca, mas também o comportamento do sistema mecânico ao longo dos tubos de perfuração. Isso é reforçado por outro exemplo onde a dinâmica de corte é combinada com a formulação de Cosserat. Observações semelhantes do ponto de vista qualitativo são encontradas. Resumindo os resultados obtidos, as diferenças nas previsões dadas pelos modelos de baixa dimensão e o de unidimensional de Cosserat justificam o desenvolvimento e aplicação da abordagem com esta formulação em estruturas de perfuração. Finalmente, a modo de introduzir outro aspecto importante em colunas de perfuração e que pode ser uma linha de pesquisa para continuar o trabalho, a variabilidades presente em elementos como rocha, inclui-se um caso de aplicação considerando um poço horizontal e um campo estocástico de atrito. / [en] In this thesis, the theory of Cosserat rods is applied to the dynamics of drill-strings. The main objective is to evaluate the behaviour of these strings when they move within curved wells. To achieve this goal, a deterministic structural model is constructed, where the drill-pipes and the bottom hole assembly are taken as a Cosserat rod. Next, a strategy to deal with the lateral contact in curved well configurations is developed. After that, the free boundary problem is assessed: while drilling, the boundary changes due to cutting, modifying the position of the soil and, consequently, changing the bit-rock interaction forces. For this reason, a bit-rock model that can account for the cutting dynamics is adopted, in which an extra advection equation is solved together with the equations of motion of the Cosserat rod. Next, application cases are provided. First, some effects included in the model are tested in isolation, such as the lateral friction, the lateral contact, and the cutting. After that, they are all combined. In the first analysis, an off-bottom string is simulated, i.e. without contact at the bit. This allows testing the formulation associated with the lateral contact. Also, the calibration of the lateral friction parameters is made. Following that, the strategy to account for the cutting at the bit is implemented in a low-dimensional 2-DOF model, and in a semi-discrete model with a continuous wave equation for the torsional dynamics. The results show that the use of continuous approaches is more appropriate than low-dimensional models. Especially when long columns are considered, and when there is interest in understanding not only the behaviour at the bit but also along drill-pipes. This finding is reinforced by another application where the cutting dynamics are combined with the Cosserat rod formulation. Again, similar observations from a qualitative point of view are found. Overall, the differences in the results between the lumped low-dimensional models and the continuous Cosserat rod justify the development and application of the Cosserat approach to drilling structures. Finally, an introductory stochastic analysis concerning the variability of the rock is presented as an introduction to a future line of research, where stochasticity is included. / [es] En esta tesis, la teoria de Cosserat para elementos unidimensionales es revisitada y aplicada a la simulación de columnas de perforación. El objetivo es estudiar el comportamiento de estas estructuras en pozos de geometría curva. Para alcanzar este objetivo se construye un modelo determinístico. En este modelo, los caños de perforación (drill-pipes) y el conjunto de fondo (bottom hole assembly) son modelados como una estructura unidimensional de Cosserat. Seguidamente, una estrategia para tratar con el contacto lateral en pozos curvos es desarrollada. Luego, el problema de frontera libre es estudiado: durante la perforación, la condición de borde cambia debido al cambio del perfil altimétrico del terreno, alterando su posición y consecuentemente las fuerzas asociadas a la interacción broca-roca. Por esta razón, se decide utilizar un modelo de interacción broca-roca que tiene en cuenta la dinámica del corte. En este abordaje una ecuación extra, la ecuación de advección, es resuelta en forma acoplada con las ecuaciones del movimiento de la estructura de Cosserat. Algunos ejemplos de aplicación son presentados. En una primera instancia, algunos de los elementos del problema son estudiados en forma aislada. Luego combinados en un modelo completo. Por ejemplo, el caso de una columna sin contacto de fondo (off-bottom) es tratado para evaluar el comportamiento y la implementación de la estrategia mencionada para detectar el contacto lateral. Además, se efectúa la calibración de alguno de los parámetros relacionados con la fricción lateral. Luego, la estrategia para considerar el corte en la punta es implementada en un modelo de 2-DOF, y en otro semi-discreto donde se considera un modelo de ecuación de onda para la dinámica torsional. Los resultados muestran que el uso de formulaciones continuas es más apropiado que aquellas formulaciones donde se utilizan modelos de dimensiones reducidas, particularmente cuando se estudia columnas largas donde el interés se centra en entender no solo el comportamiento de la broca sino también a lo largo de la tubería. Este resultado es reforzado por otro caso de aplicación en donde se combina la dinámica de corte con un modelo de Cosserat. Observaciones similares son vistas en el comportamiento cualitativo de la solución. En resumen, las diferencias observadas en los diferentes ejemplos de aplicación entre los modelos de dimensiones reducidas y el modelo continuo de Cosserat justifican el desarrollo y la aplicación de la teoría de Cosserat a estructuras de perforación. Finalmente, dado que uno de los objetivos planteados también es considerar la variabilidad en algunos elementos como ser las propiedades de la roca, un caso de aplicación considerando un pozo horizontal es mostrado.