Rock Interaction Model Research Articles

A high-fidelity model for nonlinear self-excited oscillations in rotary drilling systems

This paper presents an integrated model to analyze self-excited axial and torsional vibrations in rotary drilling systems using realistic PDC bits. The model combines a multi-degree-of-freedom (MDOF) drillstring representation with a detailed PDC bit–rock interaction model, accounting for cutter layouts and rock properties. The bit–rock interaction is described by rate-independent laws for reactive force and torque, encompassing cutting and frictional contact at the cutter face and wear flat. The regenerative rock cutting introduces state-dependent delays (up to 100) due to complex cutter layout of the bit, while the unilateral nature of frictional contact is formulated as a nonlinear boundary condition. The state-dependent delays are transformed into constant angular offsets prescribed by the bit design by introducing a bit trajectory function whose evolution is governed by a partial differential equation (PDE), which is coupled with the drillstring dynamics described by ordinary differential equations (ODEs). The Galerkin method with Chebyshev polynomials transforms the set of coupled PDE–ODEs into a system of ODEs. This approach bypasses the need to search for multiple delays at each time step, allowing implementation of this integrated rock-bit-drillstring model. Simulation results replicate field observed torque-on-bit (TOB) effects including velocity-weakening and hysteresis due to torsional stick–slips, attributing them to cutting depth variation rather than downhole friction. Preliminary findings regarding the influence of bit design on torsional stick–slips align with field drilling practices. The results of parametric study correspond to field test observations, enabling analysis of bit design, drillstring configuration, and drilling parameters on self-excited torsional stick–slips.

Experimental investigation of the rock cutting process and derivation of the 3D spatial distribution of the formation strength using in-cutter sensing

Recent advances in downhole measurements allow to accurately measure drilling forces at the drill bit, and estimate the evolution of the rock strength along the well profile. This paper presents an experimental methodology that allows to measure drilling forces, at the cutter scale, with a sensor embedded behind a polycrystalline diamond compact (PDC) cutter, and to infer the 3D spatial distribution of the rock strength. Two experimental campaigns have been performed on a laboratory-scaled drilling rig and complemented with standard mechanical tests to validate rock strength estimations. In the first campaign, homogeneous synthetic rock samples have been prepared. The average rock strength of each sample derived from cutter force measurements and a cutter–rock interaction model, compares well with the one derived from mechanical tests. In the second campaign, heterogeneous synthetic rock samples have been prepared. They are made of two layers of gypsum mixtures of different strengths, separated by a slanted bedding plane. Based on the instrumented cutter measurements, the 3D spatial distribution of the rock strength has been reconstructed along its path. Rock strength estimations are consistent with results obtained from mechanical tests, and the reconstructed geometry of the bedding plane matches well its actual geometry. The experimental methodology and technology presented in this paper lay the foundations for estimating rock properties in 3D, at the drilling stage. It has the potential to provide geoscientists information about complex lithological structures at an early stage, reducing the need for expensive and time-consuming coring and logging operations.

Real time prediction and detection of drilling bit issues during drilling with the focus on bit status evaluation using along string measurement (ASM)

Real-time drilling optimization requires online knowledge about drilling bit status, and a novel bit–rock interaction model coupled with extensive drilling data lays the groundwork for bit evaluation. Furthermore, as part of the dynamic modeling of drill strings, forces at the bit must also be calculated. At present, the bit selection protocol is based on the post-drilling bit assessment, although some drilling penetration rate models that are calibrated for a specific field can also be used to estimate bit condition in some cases. This research presents a bit status simulator that overcomes the limitations of existing techniques by making use of a delicate and intelligent application of along-string measurement (ASM) data to predict issues related to drilling bits and mitigate them in real time. This research follows two main lines. The polycrystalline compact (PDC) bit is first reshaped into an equivalent blade bit that incorporates all the design criteria of the PDC bit. Each equivalent blade, however, is composed of some equivalent cutters. Utilizing the ASM data, a novel cutter–rock interaction model is used to estimate normal and contact forces on cutters. Cutter–rock interaction equations and the mechanical specific energy of the bit cutters are used to assess the condition of the bit in real time. Two bits are evaluated in a section of a well on the Norwegian continental shelf using the proposed algorithm. The drilling data, including weight and torque on the bit, are reformulated into normal and cutting forces utilizing a cutter–rock interaction model and recursive least squares method. Consequently, the final simulated values are well in line with the final dull grading reports.

Application of Digitalization in Real-Time Analysis of Drilling Dynamics Using Along-String Measurement (ASM) Data along Wired Pipes

An automated drilling system requires a real-time evaluation of the drilling bit during drilling to optimize operation and determine when to stop drilling and switch bits. Furthermore, in the dynamic modeling of drill strings, it is necessary to take into account the interactions between drilling bits and rock. To address this challenge, a hybrid approach that combines physics-based models with data analytics has been developed to handle downhole drilling measurements in real time. First, experimental findings were used to formulate mathematical models of cutter–rock interaction in accordance with their geometrical characteristics, rock properties, and drilling parameters. Specifically, these models represent the normal and contact forces of polycrystalline diamond compact cutters (PDCs). Experimental data are analyzed utilizing deep learning, nonlinear regression, and genetic algorithms to fit nonlinear equations to data points. Following this, the recursive least square was implemented as a data analytic method to integrate real-time drilling data, drilling bit models, and mathematical models. Drilling data captured by the along-string measurement system (ASM) is implemented to estimate cutting and normal forces, torque, and specific energy at the bit. The unique aspect of this research is our approach in developing a detailed cutter–rock interaction model that takes all design and operation parameters into account. In addition, the applicability of the algorithm is demonstrated by real-time assessments of drilling dynamics, utilizing downhole digital data, that enable the prediction of drilling events and problems related to drilling bits.

Prediction-Based Control for Mitigation of Axial–Torsional Vibrations in a Distributed Drill-String System

This article proposes a control strategy to stabilize the axial–torsional dynamics of a distributed drill-string system. An infinite-dimensional model for the vibrational dynamics of the drill string is used as a basis for controller design. In this article, both the cutting process and frictional contact effects are considered in the bit–rock interaction model. Moreover, models for the top-side boundary conditions regarding axial and torsional actuation are considered. The resulting model is formulated in terms of neutral-type delay differential equations that involve constant state delays, state-dependent state delays, and constant input delays arising from the distributed nature of the drill-string dynamics and the cutting process at the bit. Using a spectral approach, the stability and stabilizability of the associated linearized dynamics are analyzed to support controller design. An optimization-based continuous pole-placement technique has been employed to design a stabilizing controller. Since the designed state-feedback control law needs state prediction, a predictor with observer structure is proposed. Both the controller and the predictor only employ top-side measurements. The effectiveness of the control strategy, in the presence of measurement noise, is shown in a representative case study. It is also shown that the controller is robust to parametric uncertainty in the bit–rock interaction.

A Powerful Build-Up Rate (BUR) Prediction Method for the Static Push-the-Bit Rotary Steerable System (RSS)

The RSS has been widely used in directional drilling. In order to enhance wellpath control accuracy and efficiency of the static push-the-bit RSS, a powerful BUR prediction method is reconstructed by coupling a rotary steerable bottom-hole assembly (RSBHA) mechanical model and a drill bit–rock interaction model. This article showed that when establishing the RSBHA mechanical model by using the continuous beam column method, the steering rib should be treated as an eccentric stabilizer to consider the contact effect between the steering rib and wellbore wall. For the beam column containing the flexible sub and between two stabilizers, it should be rearranged into three beam columns, and the lower and upper steps of the flexible sub should be considered as virtual supports. The equilibrium tendency method (ETM) to predict the BUR can enhance wellpath prediction accuracy than those of traditional methods. Under 3D conditions, the total drilling tendency angle should be denoted by inclination tendency angle and azimuth tendency angle to enhance the solution efficiency. Case analyses have verified that the average forecast error of the BUR prediction model in this article is less than 1°/30 m.

Chemical and boron isotope composition of tourmaline from the Kiaka orogenic gold deposit (Burkina Faso, West African Craton) as a proxy for ore-forming processes

The Kiaka orogenic gold deposit (Burkina Faso), located in the Paleoproterozoic domain of the West African Craton, is characterized by a two-stage gold mineralization hosted in volcano-sedimentary metamorphic rocks that was formed during the Eoeburnean (2.20–2.13 Ga) and Eburnean (2.13–2.05 Ga) orogenic cycles. These two stages include an early disseminated low-grade gold mineralization and a late vein-hosted high-grade gold mineralization. Paragenetic studies indicate that the first gold stage was coeval with the deposition of hydrothermal tourmaline. The aim of this paper is twofold: (i) to determine the processes responsible for deposition of the economic disseminated gold mineralization and (ii) to identify the source of the mineralizing fluids. For this purpose, we performed an in situ study on tourmaline by combining electron probe microanalysis and secondary ion mass spectrometry measurements of boron isotopes. Hydrothermal tourmaline hosted in metamafic volcanic rocks and metagreywackes has a dravite composition but shows different δ11B values falling within the two intervals of − 25.1 to − 22.0‰ and − 19.6 to − 15.1‰, respectively. Our results suggest that tourmaline formed from a distal, high-temperature (ca. 400 °C), reduced, and low-salinity hydrothermal fluid that interacted with the local host rocks. Based on the modeling of tourmaline–fluid boron isotope fractionation, we propose a metamorphic fluid origin derived from devolatilization of deeply buried muscovite schists during the regional prograde to peak metamorphism prior ca. 2.13 Ga. This metamorphic fluid–rock interaction model may possibly extend to other orogenic gold deposits in the West African Craton.

Modification of the Infinite-Dimensional Neutral-Type Time-Delay Dynamic Model for the Coupled Axial–Torsional Vibrations in Drill Strings With a Drag Bit

Abstract Drill strings are subjected to complex coupled dynamics. Therefore, accurate dynamic modeling, which can represent the physical behavior of real drill strings, is of great importance for system analysis and control. The most widely used dynamic models for such systems are the lumped element models, which neglect the system distributed feature. In this paper, a dynamic model called neutral-type time delay model is modified to investigate the coupled axial–torsional vibrations in drill strings. This model is derived directly from the distributed parameter model by employing the d'Alembert method. Coupling of axial and torsional vibration modes occurs in the bit–rock interface. For the first time, the neutral-type time delay model is combined with a bit–rock interaction model that regards cutting process in addition to frictional contact. Moreover, mistakes made in some of the related previous studies are corrected. The resulting equations of motion are in terms of neutral-type delay differential equations with two constant delays, related to the oscillatory behavior of the system, and a state-dependent delay, induced by the bit–rock interaction. Illustrative simulation results are presented for a representative drill string, which demonstrates intense axial and torsional vibrations that may lead to system failure without a controller.

Numerical Research on Cutting Force and Fracture Morphology of Rock Plate with Two Sides Fixed and Two Sides Free

Conical pick is a diffusely applied cutting tool in rock excavation in the coal-mining industry. In order to enhance the capability of conical pick, a new rock cutting method based on increased free surface is proposed. To research the peak cutting force and fracture morphology, ANSYS/LS-DYNA is used to establish the conical pick and rock interaction model. To obtain the fracture morphology of rock plate, eroding contact, erosion element failure, and damage constitutive are considered in the numerical model. Mechanical properties test and rock plate cutting experiment are carried out to guarantee and verify the correctness of the numerical model. The width and height of rock plate influencing peak cutting force and fracture morphology are studied, and the stable peak cutting force is defined. Lower width and height contribute to more fragments in smaller dimension produced during the rock plate cutting process. Besides, higher skew angle leads to more fragments. The peak cutting force decreases with the increasing width and height of rock plate while reaching stable peak cutting force, and it reduces and then remains stable with the increasing cutting position and symmetrical with skew angle of zero degree.

Research on the Stress Distribution Law of Fully Anchored Bolt and Analysis of Influencing Factors under the Condition of Surrounding Rock Deformation

As the mining depth increases, the deformation of the roadway becomes more difficult to control. As a main supporting structure for maintaining the stability of roadway, the fully anchored bolt is widely used to reinforce deep mine. At the same time, the analysis of the stress distribution law of fully anchored bolt is the basic work to optimize anchor design. Therefore, this paper establishes a fully anchored bolt‐surrounding rock interaction model based on the law of surrounding rock deformation and derives the analytical expressions for the axial force and shear stress of the fully anchored bolt during normal support and critical failure. At the same time, the effects of surrounding rock properties, support resistance, and bolt length on the stress distribution of fully anchored bolt are analyzed. The results show that the stress distribution of fully anchored bolt is consistent with the “neutral point” theory and the most important is the fact that the conditions of surrounding rock, the supporting resistance, and the length of bolt affect the actual stress distribution of the fully anchored bolt. It provides a certain theoretical basis for the design and development of anchoring and supporting technology.

Efficient and high-fidelity steering ability prediction of a slender drilling assembly

In drilling engineering, it is extremely challenging to drill a prescribed wellbore over several thousand meters. One of the main difficulties arises from accurately predicting and controlling the directional drilling performance, caused by the complex nonlinear dynamics of the slender drilling assembly and its interactions with the surrounding rocks. Nowadays, the simplified analytical geometry method, which has been adopted as the industry standard, can merely offer a rough estimation of the drilling direction, while the high-accuracy finite element method is computationally inefficient. This study is intended to provide a straightforward prediction of the drilling direction for a long drilling distance accurately and efficiently by proposing a dynamical simulation method based on the flexible multibody approach. Three techniques were adopted to achieve the critical objective of the paper. First, an Arbitrary Lagrangian–Eulerian formulation was used to provide a new approach to balance the efficiency and accuracy. Additionally, it can perfectly simulate the realistic drilling operation that drill pipes are continuously added to the drill string one by one through dynamically inserting new beam elements into the existing model. Second, the whole drill string and its interaction with the wellbore were all considered to carry out a high-fidelity simulation. Finally, the bit–rock interaction model was introduced to offer a straightforward way of evaluating the steerability of drilling assemblies. The presented method and model were validated by the consistency between the simulated wellbore trajectory and the in-field experimental data and are ready to be applied in drilling tools design, real-time drilling simulation, and drilling direction control.

Design and simulation of a lab-scale down-hole drilling system

As global energy demand rises, so does the need for resources and the means to extract them safely and efficiently by means of, for example, down-hole drilling. These large mechanical rigs often encounter lateral, axial, and torsional vibrations which can cause serious equipment damage and possibly failure. To minimize malignant effects, control algorithms are developed and tested on lab-scale models before implementation on large-scale rig systems. Many previous lab-scale systems artificially reproduce vibrations via inertial masses, shakers, braking systems, etc. However, they do not attempt to match the physical properties or natural response of the drill string. The goal of this research is to naturally reproduce a drilling system’s physical behaviors at lab scale through systematic analysis and design. First, a lumped parameter model is used to model the system dynamics. Through nondimensional stiffness ratios, which dictate the drill string material and geometric selection, the drill string’s elastic nature is reproduced. From this selection, the system parameters are further defined by the maximum allowable forces, derived from a bit–rock interaction model and chosen failure criteria. After development of a dynamics model and outline of design constraints, a systematic method of design and simulation of a customizable lab-scale drilling system is proposed.

Trajectory Tracking and Rate of Penetration Control of Downhole Vertical Drilling System

This paper investigates a nonlinear control design for trajectory tracking and rate of penetration (ROP) control of the vertical downhole drilling process. The drilling system dynamics are first built incorporating the coupled axial and torsional dynamics together with a velocity-independent drill bit–rock interaction model. Given the underactuated, nonlinear, and nonsmooth feature of the drilling dynamics, we propose a control design that can prevent significant downhole vibrations, enable accurate tracking, and achieve desired rate of penetration. It can also ensure robustness against modeling uncertainties and external disturbances. The controller is designed using a sequence of hyperplanes given in a cascade structure. The tracking control is achieved in two phases, where in the first phase the drilling system states converge to a high-speed drilling regime free of stick–slip behavior, and in the second phase, the error dynamics can asymptotically converge. Finally, we provide simulation results considering different case studies to evaluate the efficacy and the robustness of the proposed control approach.

Vibration analysis of horizontal rotating beam in pipe

Horizontal well drill string is simplified into a horizontal rotating beam, the beam–borehole interaction model and the bit–rock interaction model of horizontal well drilling string system are also analyzed. Based on the above analysis, the equations which describe the nonlinear dynamics of the mechanical system are derived by Timoshenko's beam model and extended Hamilton's principle. The system are analyzed in nonlinear dynamics based on the equations, the results show that: in the process of movement, horizontal beam is always in the lower right location of the wellbore; with the increase of weight on bit, radial amplitude of beam rises slightly, longitudinal amplitude of beam declines; with the increase of rotating speed, radial amplitude of beam rises, longitudinal amplitude of beam also rises.

Study of DTH Bit–Rock Interaction Numerical Simulation Method and DTH Bit Properties Evaluation

A systematic bit–rock interaction model was built by analyzing the borehole bottom lithomechanics of air hammer drilling. Moreover, based on the balance laws from mechanics of continuum, a damage evolution equation was constructed which considers the strength deterioration of rock elements caused by original cracks, a rock damage model for strength reduction and damage accumulation was constructed. By using static tester and split Hopkinson pressure bar, the constitutive parameters for the sampled rocks were acquired by coupling the “strain-softening” damage evolution equation with dynamic HJC constitutive and then embedding them into LS-DYNA. By simulating the rock breakage performance by Down the Hole bit, the well-distinguishable fluctuation zones and stable zones were found in the curve of impact energy and crushing work ratio, and then the concepts of critical impact energy and critical WOB for air percussive drilling were put forward. From the aspects of rock breakage efficiency, durability and safety, the concepts were proposed about equivalent rock breakage volume and bit energy efficiency coefficient. With the simulation model, the rock breakage performances were compared among the four regular bits. Rock breakage effects by air percussion drilling are distinctive under different structures, with levels of difficulty as follows: reverse fault > strike-slip fault > normal fault. Various types of bits have specific rock breakage performance under different structures, and even the same types of bits inconsistently resulted in different formations.

Nonlinear output‐feedback control of torsional vibrations in drilling systems

SummaryThis paper considers the design of a nonlinear observer‐based output‐feedback controller for oil‐field drill‐string systems aiming to eliminate (torsional) stick–slip oscillations. Such vibrations decrease the performance and reliability of drilling systems and can ultimately lead to system failure. Current industrial controllers regularly fail to eliminate stick–slip vibrations under increasingly challenging operating conditions caused by the tendency towards drilling deeper and inclined wells, where multiple vibrational modes play a role in the occurrence of stick–slip vibrations. As a basis for controller synthesis, a multi‐modal model of the torsional drill‐string dynamics for a real rig is employed, and a bit–rock interaction model with severe velocity‐weakening effect is used. The proposed model‐based controller design methodology consists of a state‐feedback controller and a (nonlinear) observer. Conditions, guaranteeing asymptotic stability of the desired equilibrium, corresponding to nominal drilling operation, are presented. The proposed control strategy has a significant advantage over existing vibration control systems as it can effectively cope with multiple modes of torsional vibration. Case study results using the proposed control strategy show that stick–slip oscillations can indeed be eliminated in realistic drilling scenarios in which industrial controllers fail to do so. Moreover, key robustness aspects of the control system involving the robustness against uncertainties in the bit–rock interaction and changing operational conditions are evidenced. Copyright © 2017 John Wiley & Sons, Ltd.

Global axial–torsional dynamics during rotary drilling

We have studied the global dynamics of the bottom hole assembly (BHA) during rotary drilling with a lumped parameter axial–torsional model for the drill-string and a linear cutting force model. Our approach accounts for bit-bounce and stick-slip along with the regenerative effect and is independent of the drill-string and the bit–rock interaction model. Regenerative axial dynamics due to variable depth of cut is incorporated through a functional description of the cut surface profile instead of a delay differential equation with a state-dependent delay. The evolution of the cut surface is governed by a nonlinear partial differential equation (PDE) which is coupled with the ordinary differential equations (ODEs) governing the longitudinal and angular dynamics of the BHA. The boundary condition for the PDE captures multiple regeneration in the event of bit-bounce. Interruption in the torsional dynamics is included by considering separate evolution equations for the various states during the stick period. Finite-dimensional approximation for our coupled PDE-ODE model has been obtained and validated by comparing our results against existing results. Bifurcation analysis of our system reveals a supercritical Hopf bifurcation leading to periodic vibrations without bit-bounce and stick-slip which is followed by solutions involving bit-bounce or stick-slip depending on the operating parameters. Further inroads into the unstable regime leads to a variety of complex behavior including co-existence of periodic and chaotic solutions involving both bit-bounce and stick-slip.

Bayesian approach to identify the bit–rock interaction parameters of a drill-string dynamical model

A drill string is a slender structure used to search for oil and gas. Many works have tackled the problem of modeling the drill-string dynamics in a vertical well. One important aspect in this dynamics is the bit–rock interaction, and, therefore, an identification of the parameters of the bit–rock interaction model becomes crucial. Few works related to this identification problem have been published. The present paper applies the Bayesian approach to identify the parameters of the bit–rock interaction model considering a simplified drill-string dynamical model which takes into account only torsional vibrations. It is assumed an additive Gaussian noise model, and the Metropolis–Hasting algorithm is used to approximate the posterior distribution of the variables analyzed.

A bit–rock interaction model for rotary–percussive drilling

Rotary–percussive drilling is considered a promising approach to improve drilling performance in hard rock formations. Different from percussive drilling, it is a hybrid form of drilling, since the weight-on-bit and the angular velocity are still acting as in conventional rotary drilling. This paper deals with a bit–rock interaction model for bits under rotary and percussive actions and a methodology to evaluate rotary–percussive drilling performance. First, experimental drilling data from laboratory tests conducted with an in-house designed drilling rig are investigated. Next, a phenomenological model for the drilling action is proposed, assuming that the interface laws are rate-independent and that the state of variables are averaged over at least one revolution of the bit. Within the framework of the proposed model, quantitative information from drilling data related to rock properties, bit conditions and drilling efficiency can be extracted. Furthermore, the effectiveness of the percussive action is captured by a single number, λ = ε / ψ , which corresponds to the intrinsic specific energy ratio. The similarity between the experimental results and the theoretical predictions are encouraging in regard to the use of this model to investigate rotary–percussive drilling response. The results have also shown that rotary–percussive drilling technique has potential application as an alternative method for drilling highly deviated wells or horizontal wells, where the limitations of weight-on-bit can be compensated by percussive action.

Does burial diagenesis reset pristine isotopic compositions in paleosol carbonates?

Sedimentological study of early Oligocene continental carbonates from the fluvial Dagshai Formation of the Himalayan foreland basin, India resulted in the recognition of four different types namely, soil, palustrine, pedogenically modified palustrine and groundwater carbonates. Stable oxygen and carbon isotopic ( δ 18O and δ 13C) analyses of fabric selective carbonate microsamples show that although the pristine isotopic compositions are largely altered during deep-burial diagenesis, complete isotopic homogenization does not occur. δ 18O and δ 13C analyses of ~ 200 calcrete and palustrine carbonates from different stratigraphic horizons and comparison with δ 18O of more robust bioapatite (fossil vertebrate tooth) phase show that dense micrites (~ > 70% carbonate) invariably preserve the pristine δ 18O value (mean) of ~ − 9.8‰, while altered carbonates show much lower δ 18O value ~ − 13.8‰. Such inhomogeneity causes large intra-sample and intra-soil profile variability as high as > 5‰, suggesting that soils behave like a closed system where diagenetic overprinting occurs in local domains. A simple fluid–rock interaction model suggests active participation of clay minerals to enhance the effect of fluid–rock ratio in local domains during diagenesis. This places an upper limit of 70% micrite concentration above which the effect of diagenetic alteration is minimal. Careful sampling of dense micritic part of the soil carbonate nodules, therefore, does provide pristine isotopic composition and it is inappropriate, as proposed recently, to reject the paleoclimatic potential of all paleosol carbonates affected by burial diagenesis. Based on pristine δ 13C value of − 8.8 ± 0.2‰ in soil carbonates an atmospheric CO 2 concentration between ~ 764 and ~ 306 ppmv is estimated for the early Oligocene (~ 31 Ma) Dagshai time. These data show excellent agreement between two independent proxy records (viz. soil carbonate and marine alkenone) and support early Oligocene survival of the Antarctic ice sheet.