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Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: In this study, tool forces from rock cutting tests were numerically simulated through a discrete element method (DEM) in association with PFC3D™. Tribological interactions such as contact, shearing, fracturing, friction and wear were presented during these cutting simulations. Particle assemblies, representing Paarl granite and Sandstone-2, were created in PFC3D™ through a material-genesis procedure. The macro-properties of these particle assemblies, namely Young’s modulus, Poisson’s ratio, uniaxial and triaxial compressive strength and Brazilian tensile strength, were calibrated by modelling the uniaxial and triaxial compressive strength test and the Brazilian tensile strength test. The calibration was done through adjustment of the micro-properties of the assembly, namely the stiffness and strength parameters of the particles and bonds. The influence of particle size on the calibration was also investigated. These assemblies were used in the rock cutting tests. Results suggested that DEM can reproduce the damage formation during calibration tests successfully. From the results obtained from the calibration tests, it was also concluded that particle size is not a free parameter but influences the macro-properties greatly. Different rock cutting tools were simulated, namely point-attack (conical) picks, chisel-shaped tools and button-shaped tools. The numerical cutting tools were treated as rigid walls to simplify the simulation and the tool forces were not influenced by wear. In each simulation the cutting tools advanced at a constant velocity. The tool forces acting on the cutting tool, in three orthogonal directions, were recorded during the numerical simulations and the peak cutting forces were predicted by theoretical equations. The damage to the Paarl granite and Sandstone-2 assemblies was revealed as broken bonds, which merge into microscopic fractures. The mean peak cutting forces of sharp cutting tools obtained from numerical, theoretical and experimental models (from the literature) were compared. Finally the influence of factors, including wear on the tool and depth of cut, on the value of tool forces was also investigated. The results from the rock cutting tests revealed that the correlation between the numerical and the experimental models as well as the theoretical and experimental models was not strong when using sharp point-attack and chisel-shaped picks. It was concluded that the influence of wear plays a substantial part in the cutting process and it has to be included during the numerical simulation for the results to be accurate and verifiable. This study also found that there is a non-linear increase in tool forces with an increase in depth of cut, since the contact area increases. At larger cutting depths, chip formation also generally increased and therefore damage to the sample as well as wear on the cutting tool will be minimized at shallow cutting depths. Overall this study concludes that DEM are capable of simulating calibration methods and rock cutting processes with different cutting tools and producing results which are verifiable with experimental data. Therefore numerical prediction of tool forces will allow the design of efficient cutting systems and the operational parameters as well as the performance prediction of excavation machines. / AFRIKAANSE OPSOMMING: In hierdie studie is die kragte wat tydens rotssny-toetse op die sny gereedskap inwerk, numeries gesimuleer met behulp van ‘n diskrete element metode (DEM) in samewerking met PFC3D™. Tribologiese interaksies soos kontak, skeer, breking, wrywing en slytasie is gedurende hiersie snytoetse voorgestel. Partikel versamelings, wat Paarl graniet en Sandsteen-2 verteenwoordig, is in PFC3D™ geskep deur middel van ‘n materiaal-skeppings prosedure. Die makro-eienskappe van die partikel versamelings, naamlik Young se modulus, Poisson se verhouding, eenassige en drie-assige druksterkte en Brasiliaanse treksterkte, is gekalibreer deur modellering van die eenassige en drie-assige druksterkte toets en die Brasiliaanse treksterkte toets. Die kalibrasie is gedoen deur aanpassing van die mikro-eienskappe, naamlik die styfheid en die sterkte parameters van die partikels en bindings. Die invloed van partikelgrootte is ook ondersoek. Daarna is hierdie versamelings in die rotssny-toetse gebruik. Resultate het daarop gedui dat DEM die kraakvorming gedurende kalibrasie toetse suksesvol kan reproduseer. Vanuit die kalibrasie is ook gevind dat die partikelgrootte nie ‘n vrye parameter is nie, maar die makro-eienskappe grotendeels beïnvloed. Verskillende rotssny gereedskap is gesimuleer, naamlik koniese, beitel-vormige en knopie-vormige instrumente. Die numeriese sny gereedskap is gesimuleer as rigiede mure om simulasies te vereenvoudig en die gereedskap-kragte is dus nie deur slytasie beïnvloed nie. Tydens elke simulasie is die sny gereedskap vorentoe beweeg teen ‘n konstante snelheid. Die gereedskap-kragte, in drie ortogonale rigtings, is aangeteken gedurende die numeriese simulasies en die piek snykragte is ook voorspel deur teoretiese vergelykings. Die skade aan die Paarl graniet en Sandsteen-2 versamelings, is voorgestel as gebreekte bindings, wat saamsmelt tot mikroskopiese frakture. Die gemiddelde piek snykragte van skerp sny gereedskap van numeriese, teoretiese en eksperimentele modelle (uit die literatuur) is vergelyk. Ten slotte is die invloed wat faktore, onder andere die slytasie van gereedskap en die snydiepte, op die grootte van die kragte het ondersoek. Die resultate van die rotssny-toetse het aan die lig gebring dat die korrelasie tussen die numeriese en eksperimentale modelle sowel as die teoretiese en eksperimentele modelle nie sterk is tydens die gebruik van skerp koniese en beitel-vormige instrumente nie. Die gevolgtrekking is gemaak dat die invloed van slytasie van sny gereedskap ‘n wesenlike rol speel in die snyproses en dat dit in die numeriese simulasie ingesluit moet word sodat die resultate akkuraat en virifieerbaar is. Hierdie studie het ook gevind dat daar ‘n nie-lineêre toename in die gereedskap-kragte is met ‘n toename in snydiepte aangesien die kontak-area toeneem met ‘n toename in die snydiepte. By groter snydieptes, het die formasie van afsplinterings verhoog en dus sal skade aan die partikel versamelings en die slytasie van die gereedskap geminimeer word by vlakker snydieptes. Algeheel het die studie tot die gevolgtrekking gekom dat DEM in staat is om kalibrasie metodes en rotssny-toetse met verskillende sny gereedskap te simuleer asook om resultate te produseer wat verifieerbaar is met eksperimentele data. Numeriese voorspellings van die gereedskap-kragte sal dus toelaat om doeltreffende sny prosesse en operasionele parameters te ontwerp sowel as om die werkverrigting van uitgrawings masjiene te voorspel.

[pt] A mecânica do corte de rochas vem sendo estudada a fim de proporcionar um melhor entendimento do processo de perfuração. A energia de corte é principalmente dependente da orientação do cortador e das propriedades da rocha. Foi previamente relatado na literatura que a energia específica de corte é fortemente dependente dos ângulos de inclinação posterior (backrake) e lateral (siderake) da broca. Embora existam boas tentativas de desenvolver uma solução analítica para descrever o processo de corte da rocha, os efeitos do ângulo de inclinação lateral não são levados em conta na maioria dos modelos. Esta dissertação propõe uma solução analítica para o corte de rocha considerando ambos os ângulos de inclinação relevantes, tanto o backrake quanto o siderake. Um modelo de corte é proposto considerado cortadores afiados e desgastados, e as soluções obtidas são corroboradas através de uma investigação experimental com base no corte de argilas. Um estudo paramétrico para duas rochas hipotéticas é realizado empregando o novo modelo proposto, mostrando que backrakes e/ou siderakes maiores tendem a aumentar exponencialmente a energia específica de corte. Todavia, a influência do backrake é fortemente dependente do ângulo de atrito interno da rocha. Os efeitos da profundidade de corte e pressão de confinamento também são investigados. Além disso, os efeitos do desgaste do cortador são apresentados através do diagrama de E-S. / [en] Rock cutting mechanics has been studied in order to better understand drilling process in cutter scale. The cutting energy is mainly dependent of cutter orientation and rock properties. It was previously reported in the literature that specific energy is strongly dependent of backrake and siderake. Although there have been good attempts to develop an analytical solution to describe the cutting process, the siderake effects are not taken into account. This Thesis proposes an analytical solution for the rock cutting considering both backrake and siderake. The proposed model is considered for sharp and blunt cutters and the solution agrees with preliminary experimental investigation based on the cutting action of clays. With the new model, a parametric study for two hypothetical rocks is made, showing that higher backrakes and/or siderakes increase the specific energy in an exponential-like trend. The backrake effect is strongly dependent of the rock internal friction angle though. The effects depth of cut and confining pressure were also investigated. Moreover, the effects of cutter bluntness are presented through the E-S diagram.

[pt] Perfuração em rochas é analisada através de métodos empíricos não havendo uma metodologia racional aceita para analisar todos os parâmetros que controlam a destruição das rochas. Esta dissertação tem como objetivo analisar a perfuração de rochas do ponto de vista de modelagem numérica, utilizando o método dos elementos distintos. Inicialmente será discutida a modelagem de rochas, um meio quase-contínuo, por um conjunto de partículas cimentadas. Em seguida, a destruição da rocha por brocas de perfuração será simulada analisando o processo de corte em rocha usando um único cortador. O produto final desta dissertação é comparar resultados de energia mecânica especifica obtidos em ensaios em laboratório com os resultados da modelagem e concluir a eficiência desta metodologia. Além disto, será possível propor estudos paramétricos para avaliar a importância de alguns elementos geométricos no ambiente de corte para melhorar a eficiência da operação. / [en] Drilling in rock is analyzed through empirical methods and there is none accepted rational methodology to analyze all the parameters that control the destruction of rocks. This dissertation aims to analyze the drilling of rocks from the standpoint of numerical modeling, using the Distinct Elements Method. Initially we discuss the modeling of rocks, a quasi-continuous medium, by a set of bonded particles. Then, the destruction of rock by drill bits will be simulated by analyzing the rock cutting process using a single cutter. The final product of this work is to compare results of specific mechanical energy obtained in laboratory tests with modeling results and conclude the method s efficiency. Moreover it is possible to propose parametric studies to evaluate the importance of some geometric elements in the cut environment to improve efficiency of the operation.

L'optimisation des systèmes de forage nécessite une meilleure compréhension des vibrations indésirables comme le stick-slip. Ce phénomène vibratoire, qui affecte principalement les outils PDC (Polycristalline Diamond Compact), met en péril l'intégrité des équipements de forage et réduit considérablement la vitesse de pénétration de l'outil. Plusieurs travaux ont été menés ces dernières années pour déterminer ses origines. Les observations réalisées en fond de puits montrent que ces oscillations s'accompagnent systématiquement d'une baisse du couple à l'outil en fonction de sa vitesse de rotation. De nombreux groupes de recherche attribuent cette baisse de performance à l'occurrence du stick-slip.L'objectif de ce travail est de développer un modèle élémentaire de coupe qui permet d'analyser l'effet de la vitesse de coupe sur la forabilité des roches dans des conditions opératoires réalistes. Dans le cadre de cette thèse, nous avons réalisé une série d'essais de coupe en utilisant des taillants et des outils à échelle réelle dans trois roches de propriétés hydromécaniques différentes, et ceci à pression atmosphérique et sous pression de fluide. Les essais réalisés à pression atmosphérique montrent que les efforts élémentaires de forage augmentent avec la vitesse de coupe. Sous pression de boue, cet effet dépend largement de la perméabilité de la roche. En effet, nous avons observé que l'effet de la vitesse est relativement faible dans les formations de faible et de moyenne perméabilité sous pression de boue de 20 MPa. En revanche, cet effet augmente d'un ordre de grandeur dans les roches très perméables.Afin de comprendre ces observations, nous avons développé un modèle hydromécanique d'interaction taillant-roche construit à partir de la théorie de la poroélastoplasticité. D'abord, le problème est résolu analytiquement en s'inspirant des travaux existants. Par la suite, nous avons apporté une résolution numérique aux éléments finis des équations de la promécanique appliquées à la coupe des roches sous pression de boue. Les deux modèles montrent que le phénomène de dilatance génère une baisse de la pression de pore qui augmente la résistance de la roche au forage. Cette chute de pression dépend de la vitesse de coupe ainsi que des caractéristiques hydrodynamiques de la roche. Les résultats théoriques ont été comparés aux nombreux résultats expérimentaux obtenus dans le cadre de ce travail. / The optimization of the drilling practice requires a better understanding of drillstring harmful vibrations such as stick-slip. This form of torsional vibrations is a typical problem of PDC (Polycristalline Diamond Compact) drillbits. It can reduce the rate of penetration drastically and can raise fatigue of the drilling devices. Many attempts were carried out in the last years in order to determine the causes of stick-slip phenomenon. Field observations show that torque on bit decreases as a function of bit velocity during stick-slip oscillations. Hence, it is widely believed that this decreasing relationship is the root cause of stick-slip.The purpose of this work is to examine cutting speed influence on rock drillability as a function of operating conditions and hydromechanical properties of the drilled formation. For this, a set of drilling tests was performed in three sedimentary rocks of different permeability using a full scale PDC drillbit and a single PDC cutter. In the first step, dry tests were carried out at atmospheric pressure. As previously observed in literature, single-cutter tests showed that drilling forces increase with cutting velocity. In a second step, we performed the same experiments at 20 MPa bottom-hole pressure. It appears that rate effect on cutting forces in the medium and low-permeability rocks is relatively low. By contrast, rate effect in the highly permeable rock increases by one order of magnitude in comparison with dry experiments.In order to understand this phenomenon, a steady state solution of the cutting model is derived in the framework of the theory of poroelastoplasticity. The problem is firstly solved analytically using some assumptions derived from previous works. Then, a numerical resolution based on finite element method is presented to solve the fully coupled problem ensuring the satisfaction of poro-material physics basic equations. Using these two different approaches, we show that pore pressure in shear-dilatant rocks decreases as a function of cutting velocity depending on rock permeability and interstitial fluid properties. This change has a hardening effect resulting in an increase of rock drilling resistance. Comparison between theory and experience shows good agreements.

Abrasivity is a characteristic property of rocks. Rock abrasivity has influence on tool wear, energy consumption and construction time and is therefore an important parameter in rock engineering. Over the years, a number of testing methods have been developed to define and quantify the abrasive potential of rocks. Due to simple design and convenient handling, Cerchar abrasivity test and its index, Cerchar abrasivity index, are most commonly used to assess the rock abrasivity. Besides the abrasivity index, various parameters can be derived from the Cerchar test thanks to the development of a special designed testing device. Diverse parameters like scratching force, applied work and specific energy can be used to estimate the cutting efficiency. Moreover, a new composite parameter named Cerchar abrasion ratio is proposed, which considers both, the wear on the stylus tip and the material removal on the rock surface and can be regarded as an indicator to evaluate the cutting effectivity. Since the development of Cerchar abrasivity test, major attentions are focused on the abrasion of the stylus, but minor attentions are paid to investigate the mechanical behavior of rocks against the action of the stylus during the scratching process. The scratch groove produced on the rock surface is observed under a scanning electron microscope. The Cerchar wear mechanism can be explained as follows: mineral grains are detached from damaged surface by fracturing after plastic deformation on stressed surface. Transition from plastic deformation-induced to cracking-induced wear are related to the rock microstructure. For the Cerchar test, various factors affecting the Cerchar abrasivity index have been studied, which can be divided into testing condition-based and geotechnical-based factors. The influence of some dominant testing condition-based factors including surface condition, testing distance and velocity on the test result is investigated by using the new designed testing device, in which the sliding distance and scratching velocity can be exactly controlled during the test. Results show that the surface condition can affect the result of Cerchar index, especially for hard and inhomogeneous rocks, while the testing distance and velocity have no obvious influence on the Cerchar index. As far as it is known, in rock mechanics, anisotropic features of rocks can affect the experimental results significantly. In the original Cerchar specification, testing procedure for stratified or foliated rocks is not specially discussed. Due to this, the influence of rock anisotropy on the Cerchar abrasivity index is investigated based on two intact metamorphic rocks of slate and gneiss. However, no significant dependency is found. Cerchar scratch test is simulated based on a quasi-homogeneous model made of sandstone with respect to its mineralogical-mechanical properties. The numerical simulation is conducted by using the discrete element method-based particle flow code of PFC3D. As a result, the simulated scratching force shows a good agreement with the experimental result. A gap between numerical and experimental studies can be attributed to the testing condition-based factors, such as rock mineralogy and microstructure, scratching velocity and depth of scratch, tool abrasion and temperature. Based on the calibrated sandstone model, numerical simulations of rock cutting are conducted under different testing conditions. The influence of tool geometry like tip shape, tip angle and tip wear, and cutting parameters including cutting velocity, depth of cut and rake angle on the cutting force and crack pattern is studied.

This dissertation evaluates the possibilities and limitations of rock type identification in rock cutting with conical picks. For this, machine learning in conjunction with features derived from high frequency cutting force measurements is used. On the basis of linear cutting experiments, it is shown that boundary layers can be identified with a precision of less than 3.7 cm when using the developed programme routine. It is further shown that rocks weakened by cracks can be well identified and that anisotropic rock behaviour may be problematic to the classification success. In a case study, it is shown that the supervised algorithms artificial neural network and distributed random forest perform relatively well while unsupervised k-means clustering provides limited accuracies for complex situations. The 3d-results are visualised in a web app. The results suggest that a possible rock classification system can achieve good results—that are robust to changes in the cutting parameters when using the proposed evaluation methods.:1 Introduction...1 2 Cutting Excavation with Conical Picks...5 2.1 Cutting Process...8 2.1.2 Cutting Parameters...11 2.1.3 Influences of Rock Mechanical Properties...17 2.1.4 Influences of the Rock Mass...23 2.2 Ratios of Cutting Force Components...24 3 State of the Art...29 3.1 Data Analysis in Rock Cutting Research...29 3.2 Rock Classification Systems...32 3.2.1 MWC – Measure-While-Cutting...32 3.2.2 MWD – Measuring-While-Drilling...34 3.2.3 Automated Profiling During Cutting...35 3.2.4 Wear Monitoring...36 3.3 Machine learning for Rock Classification...36 4 Problem Statement and Justification of Topic...38 5 Material and Methods...40 5.1 Rock Cutting Equipment...40 5.2 Software & PC...42 5.3 Samples and Rock Cutting Parameters...43 5.3.1 Sample Sites...43 5.3.2 Experiment CO – Zoned Concrete...45 5.3.3 Experiment GN – Anisotropic Rock Gneiss...47 5.3.4 Experiment GR – Uncracked and Cracked Granite...49 5.3.5 Case Study PB and FBA – Lead-Zinc and Fluorite-Barite Ores...50 5.4 Data Processing...53 5.5 Force Component Ratio Calculation...54 5.6 Procedural Selection of Features...57 5.7 Image-Based Referencing and Rock Boundary Modelling...60 5.8 Block Modelling and Gridding...61 5.9 Correlation Analysis...63 5.10 Regression Analysis of Effect...64 5.11 Machine Learning...65 5.11.2 K-Means Algorithm...66 5.11.3 Artificial Neural Networks...67 5.11.4 Distributed Random Forest...70 5.11.5 Classification Success...72 5.11.6 Boundary Layer Recognition Precision...73 5.12 Machine Learning Case Study...74 6 Results...75 6.1 CO – Zoned Concrete...75 6.1.1 Descriptive Statistics...75 6.1.2 Procedural Evaluation...76 6.1.3 Correlation of the Covariates...78 6.1.4 K-Means Cluster Analysis...79 6.2 GN – Foliated Gneiss...85 6.2.1 Cutting Forces...86 6.2.2 Regression Analysis of Effect...88 6.2.3 Details Irregular Behaviour...90 6.2.4 Interpretation of Anisotropic Behaviour...92 6.2.5 Force Component Ratios...92 6.2.6 Summary and Interpretations of Results...93 6.3 CR – Cracked Granite...94 6.3.1 Force Component Results...94 6.3.2 Spatial Analysis...97 6.3.3 Error Analysis...99 6.3.4 Summary...100 6.4 Case Study...100 6.4.1 Feature Distribution in Block Models...101 6.4.2 Distributed Random Forest...105 6.4.3 Artificial Neural Network...107 6.4.4 K-Means...110 6.4.5 Training Data Required...112 7 Discussion...114 7.1 Critical Discussion of Experimental Results...114 7.1.1 Experiment CO...114 7.1.2 Experiment GN...115 7.1.3 Experiment GR...116 7.1.4 Case Study...116 7.1.5 Additional Outcomes...117 7.2 Comparison of Machine Learning Algorithms...118 7.2.1 K-Means...118 7.2.2 Artificial Neural Networks and Distributed Random Forest...119 7.2.3 Summary...120 7.3 Considerations Towards Sensor System...121 7.3.1 Force Vectors and Data Acquisition Rate...121 7.3.2 Sensor Types...122 7.3.3 Computation Speed...123 8 Summary and Outlook...125 References...128 Annex A Fields of Application of Conical Tools...145 Annex B Supplements Cutting and Rock Parameters...149 Annex C Details Topic-Analysis Rock Cutting Publications...155 Annex D Details Patent Analysis...157 Annex E Details Rock Cutting Unit HSX-1000-50...161 Annex F Details Used Pick...162 Annex G Error Analysis Cutting Experiments...163 Annex H Details Photographic Modelling...166 Annex I Laser Offset...168 Annex J Supplements Experiment CO...169 Annex K Supplements Experiment GN...187 Annex L Supplements Experiment GR...191 Annex M Preliminary Artificial Neural Network Training...195 Annex N Supplements Case Study (CD)...201 Annex O R-Codes (CD)...203 Annex P Supplements Rock Mechanical Tests (CD)...204 / Die Dissertation evaluiert Möglichkeiten und Grenzen der Gebirgserkennung bei der schneidenden Gewinnung von Festgesteinen mit Rundschaftmeißeln unter Nutzung maschinellen Lernens – in Verbindung mit aus hochaufgelösten Schnittkraftmessungen abgeleiteten Kennwerten. Es wird auf linearen Schneidversuchen aufbauend gezeigt, dass Schichtgrenzen mit Genauigkeiten unter 3,7 cm identifiziert werden können. Ferner wird gezeigt, dass durch Risse geschwächte Gesteine gut identifiziert werden können und dass anisotropes Gesteinsverhalten möglicherweise problematisch auf den Klassifizierungserfolg wirkt. In einer Fallstudie wird gezeigt, dass die überwachten Algorithmen Künstliches Neurales Netz und Distributed Random Forest teils sehr gute Ergebnisse erzielen und unüberwachtes k-means-Clustering begrenzte Genauigkeiten für komplexe Situationen liefert. Die Ergebnisse werden in einer Web-App visualisiert. Aus den Ergebnissen wird abgeleitet, dass ein mögliches Sensorsystem mit den vorgeschlagenen Auswerteroutinen gute Ergebnisse erzielen kann, die gleichzeitig robust gegen Änderungen der Schneidparameter sind.:1 Introduction...1 2 Cutting Excavation with Conical Picks...5 2.1 Cutting Process...8 2.1.2 Cutting Parameters...11 2.1.3 Influences of Rock Mechanical Properties...17 2.1.4 Influences of the Rock Mass...23 2.2 Ratios of Cutting Force Components...24 3 State of the Art...29 3.1 Data Analysis in Rock Cutting Research...29 3.2 Rock Classification Systems...32 3.2.1 MWC – Measure-While-Cutting...32 3.2.2 MWD – Measuring-While-Drilling...34 3.2.3 Automated Profiling During Cutting...35 3.2.4 Wear Monitoring...36 3.3 Machine learning for Rock Classification...36 4 Problem Statement and Justification of Topic...38 5 Material and Methods...40 5.1 Rock Cutting Equipment...40 5.2 Software & PC...42 5.3 Samples and Rock Cutting Parameters...43 5.3.1 Sample Sites...43 5.3.2 Experiment CO – Zoned Concrete...45 5.3.3 Experiment GN – Anisotropic Rock Gneiss...47 5.3.4 Experiment GR – Uncracked and Cracked Granite...49 5.3.5 Case Study PB and FBA – Lead-Zinc and Fluorite-Barite Ores...50 5.4 Data Processing...53 5.5 Force Component Ratio Calculation...54 5.6 Procedural Selection of Features...57 5.7 Image-Based Referencing and Rock Boundary Modelling...60 5.8 Block Modelling and Gridding...61 5.9 Correlation Analysis...63 5.10 Regression Analysis of Effect...64 5.11 Machine Learning...65 5.11.2 K-Means Algorithm...66 5.11.3 Artificial Neural Networks...67 5.11.4 Distributed Random Forest...70 5.11.5 Classification Success...72 5.11.6 Boundary Layer Recognition Precision...73 5.12 Machine Learning Case Study...74 6 Results...75 6.1 CO – Zoned Concrete...75 6.1.1 Descriptive Statistics...75 6.1.2 Procedural Evaluation...76 6.1.3 Correlation of the Covariates...78 6.1.4 K-Means Cluster Analysis...79 6.2 GN – Foliated Gneiss...85 6.2.1 Cutting Forces...86 6.2.2 Regression Analysis of Effect...88 6.2.3 Details Irregular Behaviour...90 6.2.4 Interpretation of Anisotropic Behaviour...92 6.2.5 Force Component Ratios...92 6.2.6 Summary and Interpretations of Results...93 6.3 CR – Cracked Granite...94 6.3.1 Force Component Results...94 6.3.2 Spatial Analysis...97 6.3.3 Error Analysis...99 6.3.4 Summary...100 6.4 Case Study...100 6.4.1 Feature Distribution in Block Models...101 6.4.2 Distributed Random Forest...105 6.4.3 Artificial Neural Network...107 6.4.4 K-Means...110 6.4.5 Training Data Required...112 7 Discussion...114 7.1 Critical Discussion of Experimental Results...114 7.1.1 Experiment CO...114 7.1.2 Experiment GN...115 7.1.3 Experiment GR...116 7.1.4 Case Study...116 7.1.5 Additional Outcomes...117 7.2 Comparison of Machine Learning Algorithms...118 7.2.1 K-Means...118 7.2.2 Artificial Neural Networks and Distributed Random Forest...119 7.2.3 Summary...120 7.3 Considerations Towards Sensor System...121 7.3.1 Force Vectors and Data Acquisition Rate...121 7.3.2 Sensor Types...122 7.3.3 Computation Speed...123 8 Summary and Outlook...125 References...128 Annex A Fields of Application of Conical Tools...145 Annex B Supplements Cutting and Rock Parameters...149 Annex C Details Topic-Analysis Rock Cutting Publications...155 Annex D Details Patent Analysis...157 Annex E Details Rock Cutting Unit HSX-1000-50...161 Annex F Details Used Pick...162 Annex G Error Analysis Cutting Experiments...163 Annex H Details Photographic Modelling...166 Annex I Laser Offset...168 Annex J Supplements Experiment CO...169 Annex K Supplements Experiment GN...187 Annex L Supplements Experiment GR...191 Annex M Preliminary Artificial Neural Network Training...195 Annex N Supplements Case Study (CD)...201 Annex O R-Codes (CD)...203 Annex P Supplements Rock Mechanical Tests (CD)...204

[pt] A perfuração de poços de petróleo em ambientes adversos requer especialistas dedicados a estuda-la a fim de garantir que ela ocorra de forma rápida, segura e com qualidade. Dentro desse contexto, há estudos experimentais e numéricos que avaliam a ação de corte feita por um cortador individual objetivando quantificar as forças de contato, propor soluções para aumentar o seu tempo de vida útil e a sua taxa de penetração, e entender o mecanismo de corte. Seguindo esta linha de pesquisa, a presente Tese visa oferecer uma melhor compreensão para o problema de interação rocha/cortador PDC (Polycrystalline Diamond Compact) ao longo da perfuração de depósitos evaporíticos de halita e de reservatórios de carbonatos. O estudo foi abordado através da modelagem numérica do ensaio de cortador único e da modelagem numérica de corte por múltiplos cortadores através do método dos elementos discretos. Resultados experimentais aferiram a calibração da amostra sintética e dos modelos numéricos de corte em rocha. Um estudo numérico paramétrico do ensaio de cortador único foi feito objetivando identificar parâmetros que controlam a ação de corte. Em seguida, foi desenvolvida uma equação analítica que quantifica a energia específica mecânica global resultante da ação de múltiplos cortadores, a fim de entender e quantificar qual a contribuição de cada cortador na eficiência global. A equação foi aplicada usando os resultados das modelagens numéricas de múltiplos cortadores. Constatou-se que o bom ajuste entre as previsões numéricas e os resultados experimentais validou o uso do método dos elementos discretos para modelar o processo de corte em diferentes tipos de rochas. A modelagem numérica desenvolvida neste estudo pode ser considerada uma ferramenta útil para projeto e otimização do desempenho de brocas de perfuração. / [en] Oil wells drilling in adverse environments requires specialists dedicated to study the drilling process to ensure a quickly, safely and quality performance. In this context, experimental and numerical studies can be find in technical literature that evaluate the cutting action done by a single cutter aiming to quantify the contact forces, proposing solutions to increase its useful life time and its rate of penetration, and to understand the cutting mechanism. Following this line of research, this Thesis aims to provide a better understanding regarding the rock / polycrystalline diamond compact cutter interaction during the halite deposits and carbonate reservoirs drilling. The study was approached through numerical modeling of the single cutter test and through numerical modeling of the cutting action by multiple cutters using the discrete element method. Experimental results were used to calibrate the synthetic sample and the rock cutting numerical models. A parametric numerical study of the single cutter test was done aiming to identify parameters that control the cutting action. Then, an analytical equation was developed that quantifies the global mechanical specific energy resulting from the cutting action of multiple cutters, in order to understand and quantify the contribution of each cutter to overall efficiency. The equation was applied using the results of numerical modeling of multiple cutters developed in this work. It was verified that the good agreement between numerical predictions and experimental results validated the use of the discrete element method to model the cutting process in different rock types. The numerical modeling developed in this study can be considered a useful tool for design and optimizing the performance of drill bits.

[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.