Rotary Drilling Systems Research Articles

Control strategies for mitigating torsional and axial vibrations in rotary oilwell drilling systems

Abstract This paper examines a nonlinear dynamics model to explore the significant factors influencing the coupled torsional-axial vibrations of a drill string. The primary focus lies in effectively modeling, analyzing, and controlling both torsional and axial vibrations occurring in a rotary oil well drilling system. The model employed incorporates a wave equation with a damping term (PDE) connected to an ordinary differential equation (ODE) through a nonlinear function representing the interaction between the drill bit and the rock. We proceed to establish the well-posedness of the coupled PDE-ODE in an appropriate functional space. As a PDE-ODE coupled system, we specifically investigate the stability problem concerning the velocity at the bottom extremity, considering both the presence and absence of the damping term in the wave PDE. To address this, we propose a systematic method based on a Lyapunov approach for designing feedback controllers. These controllers ensure system stability and effectively suppress harmful vibrations.

PID Control Design of Strongly Coupled Axial-Torsional Vibrations in Rotary Drilling Systems

PID Control Design of Strongly Coupled Axial-Torsional Vibrations in Rotary Drilling Systems

Dynamic Interaction Analysis of Coupled Axial-Torsional-Lateral Mechanical Vibrations in Rotary Drilling Systems

Dynamic Interaction Analysis of Coupled Axial-Torsional-Lateral Mechanical Vibrations in Rotary Drilling Systems

Development of Drilling Optimization Models for Autonomous Rotary Drilling Systems

The growing global energy demand and strict environmental policies, motivates the use of technology and performance improvement techniques in drilling operations. In the traditional drilling method, parameter optimization depends on the effectiveness of human-driller. Although existing work has identified the significance of upscaling from manual drilling to autonomous drilling system, but little has been done to support this transition. This work presents optimization models for an autonomous rotary drilling system, controlled by a self-tuning, multivariant controller that uses machine learning optimization strategy. The method determines the drilling medium from real-time measurement by estimating the unconfined compressive strength (UCS) from the latest data uploaded via the mud pulse telemetry (MPT) and adjust optimal setpoint based on model output. In the study, four machine learning algorithms were used to predict UCS including artificial neutral network (ANN), Category boast (CB), Support vector machine (SVR) and Randon Forest. Whilst Physics based empirical models with ANN were used to predict the drill rate. Results showed that machine learning (ML) application improves the prediction quality of drill rate and UCS with ANN and Catboast as best ML predictors. The coefficient of determination (R2) of 0.95 ROP prediction and (R2) for test dataset of 0.77 and 070 for UCS prediction using ANN and Catboast respectively. The Q-learning algorithm which uses the value function to search for optimal operating parameter at different Lithologies through dynamic programming, returns decisions for optimal drill rate at respective drilling states consequently improving the efficiency of rotary drilling process in terms of cost and time

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.

Dynamic Analysis of a Downhole Regulator for Drilling in Interbedded Formations

Summary In this paper, we investigate the effect of a downhole passive regulator [anti-stall tool (AST)] on the dynamics of rotary drilling systems in interbedded formations. Drilling in interbedded formations can significantly affect the vibrational signature of these systems and the associated drilling performance. Hence, models to assess the impact of drilling in such formations are needed. Here, we construct a dynamic model of the drillstring system which incorporates the bit/rock interface laws for the transitional phase of bit motion between rock layers with distinct mechanical properties. In the model, the axial and torsional dynamics of the drillstring systems are coupled by these interface laws and cast in the form of discontinuous (state-dependent) delay differential equations. Next, we include the AST in the dynamic model to enable the assessment of the influence of this downhole tool on drilling performance, in particular in terms of rate-of-penetration (ROP) and drilling efficiency. Furthermore, we also investigate the mechanical specific energy (MSE) and steady-state power losses at the bit (due to frictional torque) for different operational conditions and rock layer thicknesses. The analysis reveals that an increased drilling efficiency and lower MSE are obtained by incorporating the downhole tool in the drillstring, resulting in a higher ROP and a lower frictional contact between the bit and rock in interbedded formations.

Stick-Slip Vibration Suppression in Drill String Using Observer-Based LQG Controller.

Hydrocarbon exploration and production activities are guaranteed through various operations including the drilling process, which is realized by using rotary drilling systems. The process involves crushing the rock by rotating the drill bit along a drill string to create a borehole. However, during this operation, violent vibrations can occur at the level of the drill string due to its random interaction with the rocks. According to their axes of occurrence, there are three types of vibrations: axial, lateral, and torsional, where the relentless status of the torsional vibrations is terminologically known as the stick-slip phenomenon. Such a phenomenon can lead to increased fatigue of the drill string and cause its abortive fracture, in addition to reducing the efficiency of the drilling process and consequently making the exploration and production operations relatively expensive. Thus, the main objective of this paper is to eliminate the severe stick-slip vibrations that appear along the drill string of the rotary drilling system according to the LQG observer-based controller approach. The rock–bit interaction term is highly nonlinear, and the bit rotational velocity is unmeasurable; an observer was first designed to estimate the unknown inputs of the model, and then the controller was implemented in the drill string model with 10 degrees of freedom. The estimation process was essentially based on surface measurements, namely, the current and rotational velocity of the top drive. Thereafter, the performance of the proposed observer-based LQG controller was tested for different simulation scenarios in a SimScape/Matlab environment, for which the controller demonstrated good robustness in suppressing the severe stick-slip vibrations. Furthermore, the simulation and experimental results were compared to other controllers designed for the same model; the proposed observer-based LQG controller showed better performance, and it was less sensitive to structured disturbances than H∞. Thence, it is highly recommended to use the proposed approach in smart rotary drilling systems.

A high-dimensional model to study the self-excited oscillations of rotary drilling systems

This paper analyzes the self-excited axial and torsional vibrations of rotary drilling systems with a model that combines a multi-degrees of freedom representation of the drilling structure with a rate-independent bit-rock interface law. The state-dependent delay introduced by the bit-rock interaction is captured by a bit trajectory function, which leads to the formulation of a nonlinear system of coupled partial differential equation (PDE) and ordinary differential equations (ODEs). This paper describes an algorithm that utilizes the Chebyshev spectral method to convert the system of PDE–ODEs into a system of coupled ODEs. The use of Chebyshev polynomials rather than Fourier series leads to a computationally more efficient algorithm, in view of the non-periodic nature of the bit trajectory function. By linearizing the system of coupled PDE–ODEs, this algorithm is further extended to assess numerically the stability of the high-dimensional model. The predictions of the linear stability analysis are validated with published results as well as with time-domain simulations. It is shown, as anticipated by Liu et al. (2014), that the stable region in the space of the operating parameters shrinks with increasing spatial resolution of the high-dimensional model, suggesting that the effects of damping on the stability of drilling system is generally negligible in the range of practical drilling parameters. Extensive parametric studies have been carried out using the high-dimensional model to analyze the influence of various factors on the torsional stick–slip oscillations. The bit wearflats are shown to play an important role in delaying or even suppressing the occurrence of torsional stick–slip oscillations. Finally, the axial vibrations propagating along the drillstring are revealed in the form of traveling waves, whereas the torsional vibrations take the form of standing waves, whose frequency is the same as the torsional resonance of the drillstring excited by the bit-rock interaction.

Observer-Based H∞ Controller Design for High Frequency Stick-Slip Vibrations Mitigation in Drill-String of Rotary Drilling Systems

The drilling process is among the most crucial steps in exploration and production activities in the petroleum industry. It consists of using mechanical mechanisms to crush rocks by the drill bit to pass through the different geological layers. The drill-string continuously transforms the rotational movement from the top drive motor to the drill bit through the drill pipes. Due to the strong interactions with the rocks, aggressive vibrations can arise in the drill-string in its three dimensions, and consequently, this may create three types of synchronous vibrations: axial, lateral, and torsional. The severe status of the latter is known as the stick-slip phenomenon, and is the most common in rotary drilling systems. Based on field observations, it has been inferred that the high frequency stick-slip vibrations may lead to drill-string fatigues and even to premature rupture. In the best case, it reduces the drilling efficiency by decreasing the rate of penetration, due to which the drilling operations become proportionally expensive. The main novelties of this research work are the design of an H∞ observer-based controller to mitigate the high frequency stick-slip vibrations, and the quantitative analysis of the vibrations’ severity for ten degrees of freedom model. The observer is designed to estimate the non-measurable rotational velocity of the drill bit due to the severity of the vibrations, while the controller is dedicated to suppressing the vibrations by using the top drive inputs. Thus, many scenarios have been considered to test and analyze the observer performance and the controller robustness. Furthermore, a comparison with the LQG observer-based controller has been conducted, where H∞ has demonstrated better efficiency in suppressing the stick-slip vibrations under unstructured perturbations.

Estimation of Circular Arc Crack Depths and Locations in Rotary Drilling Pipes Subjected to Free Vibrations

Late detection of cracks can lead to serious failures and damages of drilling components, especially drill pipes and drill bits. Currently, the widely used method of repairing rotary drilling systems after a failure is corrective maintenance. Although this strategy has shown its effectiveness in many cases, waiting for a failure to occur and then performing a repair can be an expensive and time-consuming operation. Thus, the use of preventive maintenance under the aspect of periodic inspections can solve this problem and help engineers detect cracks before they reach critical sizes. In this study, modal analysis and finite element analysis (FEA) combined with artificial neural networks (ANN) were used to dynamically estimate the depth and location of a circular arc crack in the drill pipes of rotary drilling systems. To achieve this goal, a detailed analytical approach based on Euler–Bernoulli beam theory was adopted to validate the first four natural frequencies found by FEA for an undamaged pipe. Afterwards, an arc crack was assigned to the pipe already created using Abaqus, and the first four natural frequencies were obtained for each depth and location of the crack. Simulations with FEA led to the generation of a dataset with two inputs—depth and location of cracks—and four outputs: natural frequencies. Moreover, a multilayer perceptron (MLP) was designed and trained by the data collected from simulations. Finally, a comparison between the results obtained by FEA and ANN was performed, where both approaches showed a good agreement in predicting the depth and location of cracks.

Dynamic failure analysis and lifetime estimation of Tool-string in rotary drilling system under Torsional-Axial coupled vibrations

Failure analysis and lifetime assessment of drilling systems are very important to reduce maintenance costs. Of all the failure modes, coupled vibration due to the stick–slip phenomenon is the most common problem that can affect rotary drilling systems. The main objective of this study is to estimate the number of cycles before failure (useful life) of the lower part of rotary drilling system toolstring under axial and torsional vibrations. To achieve this goal, a complete procedure based on different methods and approaches, such as: finite element method (FEM), rainflow counting method (RFM), Goodman approach (GA), S-N diagram and Miner’s rule, has been proposed. To this end, the FEM has been used to determine the loading cycles (equivalent stress); whereas, the number of stress cycles in the loading cycle diagram has been counted using RFM. The GA has been used to select the main cycles that can cause failure on the toolstring and to calculate their amplitudes. Then, S-N diagram has been used to determine the number of cycles to failure of the toolstring. Finally, Miner’s rule has been applied to find the approximate time to failure of the drilling system. Regarding the estimation of the toolstring lifetime, the results obtained have shown a good agreement with real data recorded in an oil field in Algeria.

Observer-based control of vertical penetration rate in rotary drilling systems

An algorithm for regulation of the vertical penetration rate in rotary drilling systems is developed under the assumption that parameters of the rock-bit interaction as well as those of the translational dynamics are unknown. The control design utilizes a multi-step approach, where the vertical penetration velocity is regulated through an appropriate assignment of a reference rotational velocity signal, while the tracking of the latter is achieved using tracking with disturbance rejection scheme. In contrast with the existing results, the algorithm does not require real-time measurement and communication to the ground level of the downhole variables, such as angular position, rotational velocity, and torque-on-bit. This is achieved through the use of high-order sliding mode observers which estimate the required downhole variables based on measurements performed at the ground level. Simulation results are presented which confirm efficiency of the proposed control method.

Hybrid Backstepping Sliding Mode Controller for Stick–slip Vibrations Mitigation in Rotary Drilling Systems

The main objective of this paper is to suppress the stick–slip vibrations in the drilling system so that the drill bit can follow the desired nominal angular velocity of the Top Drive in an optimal time. Hence to protect drilling equipment from hazards and increase drilling performances by decreasing the non-productive time (NPT). Three control systems have been proposed to achieve this objective, a sliding controller is firstly designed and then a backstepping approach is discussed secondly. Furthermore, a hybridization of sliding mode control with a backstepping approach has been proposed on the so-called hybrid backstepping sliding mode controller. The latter has not been proposed before in the literature for rotary drilling systems. Moreover, two torsion models of the system have been discussed for different degrees of freedom. Based on the comparison between controllers’ responses, the effectiveness and the robustness of the hybrid controller have been demonstrated and highlighted, whose fast response can protect the drilling equipment from hazards that may be caused by the slip phase of the vibrations. Hence, it is recommended to implement the proposed controller in smart rotary drilling systems for petroleum industry.

Hybrid sliding PID controller for torsional vibrations mitigation in rotary drilling systems

During the drilling process, the drilling system devices can be exposed to several types of phenomena incited by lateral, axial, and torsional vibrations. The latter can lead to severe damages if they are not efficiently controlled and quickly mitigated. This research work is focused on the torsional vibrations, which are stimulated by the nonlinear dynamical interaction between the geological rocks and the drill bit. Wherein, a model with three degrees of freedom was designed to demonstrate the severity of the stick-slip phenomenon as consequence of torsional vibrations. The main objective of this study was to design a robust controller based on hybridizing a conventional PID controller with sliding mode approach in order to mitigate rapidly the torsional vibrations. Moreover, a comparative study between PI, PID and sliding mode controllers allowed us to emphasize the effectiveness of the new hybrid controller and improve the drilling system performances. Furthermore, the chattering phenomenon in the sliding surface was overcome by using the saturation function rather than the sign function. The obtained results proved the usefulness of the proposed controller in suppressing the stick-slip phenomenon for smart industrial drilling systems.

Decentralized Overlapping Control Design with Application to Rotary Drilling System

The main objective of this paper is the development of overlapping decomposition strategy for controller design of rotary drilling systems based on the state feedback technique. The lamped model of the system has been considered, Graph-based representation has been used to rearrange the states of the model, and then a new model has been decomposed into subsystems after analyzing the interconnection terms. The expansion–contraction principle, combined with Lyapunov theory, is used to investigate the global stability of the decomposed system so that controllability of the designed controller is guaranteed and its robustness is improved. Moreover, the designed strategy has been validated with high-frequency mode stick-slip vibrations data measured in an operational rotary drilling system of an exploration well drilled in an Algerian hydrocarbon field.

Drill Bit Deformations in Rotary Drilling Systems under Large-Amplitude Stick-Slip Vibrations

In oil and gas industry, rotary drilling systems are used for energy exploration and productions. These types of systems are composed of two main parts: mechanical and electrical parts. The electrical part is represented by rotating motor called top drive; however, the mechanical part of the system is composed of tool string with many pipes, at the bottom end of these pipes the bit is attached to cut the rock during their contact. Since the bit is in a direct contact with rock characteristic variations, it can be under risk for heavy damage. The latter is principally caused by the fact that the rock–bit interaction term is highly nonlinear and unpredictable. In literature, many mathematical models have been proposed for rock–bit interaction, but they do not reflect the dynamic of the bit under vibrations since torsional and axial vibrations are strongly coupled and synchronized with it. In industrial development, the design of drill bit has faced many improvements in order to overcome these vibrations and mitigate unpredictable phenomena. Even though, the practical use of these drill bits confirmed that there are still many failures and damages for the new designs; moreover, bits’ virtual life become shorter than before. The objective of this study is to analyze the drill bit deformations caused by the stick-slip vibration phenomenon which is characterized by high-frequency high-amplitude in rotary drilling systems. The obtained results were validated through a case study of MWD (measurement while drilling) data of well located in a Southern Algerian oil field.

Unknown Resistive Torque Estimation of a Rotary Drilling System Based on Kalman Filter

ABSTRACT Rotary drilling systems are widely used in petroleum engineering to drill oil and gas wells. Control of drilling process is a very important topic because it allows industrials to optimize drilling cost, improve borehole quality, and protect equipment. Many researchers have dealt with the control of rotary drilling systems, wherein, the main difficulty is that the rock-bit interaction term is highly nonlinear, and mathematical models simulate its dynamic but with insufficient fidelity because of the lack of measurement devices for bottom torque for these systems. In order to design an efficient controller, it is mandatory to have the model highly loyal to the rotary drilling system, which can represent the dynamic of the system under the rock-bit interaction term. The objective of this study is to estimate the unknown input torque based on Kalman filter, the estimation has been validated on a test bench. Moreover, it has been noticed that Kalman estimator has better efficiency in comparison to the pole placement method. The algorithm has been implemented on CompactRio using LabView environment and applied to experimental equivalent system to rotary drilling system equipment.

An alternative formulation for modeling self-excited oscillations of rotary drilling systems

This paper describes an alternative formulation of the nonlinear equations governing the coupled axial and torsional dynamics of a discrete model of a rotary drilling system equipped with a drag bit. This model assumes a rate-independent bit/rock interface law that accounts for both cutting and frictional contact processes. The regenerative effect associated with the cutting introduces a term with delay, and thus a feedback, in the equations of motion, while the frictional contact results in set-valued contact forces and discontinuities in the boundary conditions, which are responsible for the occurrence of axial and torsional stick-slip oscillations. Inspired by P. Wahi and A. Chatterjee (Self-interrupted regenerative metal cutting in turning, International Journal of Non-Linear Mechanics 43:2, 111–123, 2008), the regenerative effect is captured by a bit trajectory function, whose evolution is governed by a first order partial differential equation. With this approach, the original state-dependent delay differential equations (SDDDEs) governing the dynamics of the discrete model are replaced by the partial differential equation of the bit trajectory function together with the axial and angular equations of motion of the two degrees-of-freedom model. The equation governing the evolution of the bit trajectory function is further approximated by a system of first order ordinary differential equations through application of the Galerkin method. The introduction of the bit trajectory function makes it possible to consider a bit with two state-dependent delays (and in principle multiple delays) without reducing the computational efficiency. The accuracy of this approximation is validated using published results, and the convergence and robustness properties of the proposed method are analyzed using three cases corresponding to different regimes of instability. Finally, we extend the discrete model to a more generic lumped-parameter model with multiple degrees-of-freedom, which captures the propagation of axial and torsional vibrations along the drillstring.

Adaptive output-feedback control of torsional vibration in off-shore rotary oil drilling systems

Motivated by an engineering application of torsional vibration suppression of off-shore oil drilling, we design an adaptive output-feedback controller for a one-dimensional wave partial differential equation (PDE) system, where an anti-damping term with an unknown coefficient and a general harmonic disturbance with unknown amplitudes exist in the bit, which is modeled as a second-order-in-time boundary. The control input anti-collocated with this boundary subject to uncertainty, is designed by using the adaptive control method and infinite-dimensional backstepping technique. The asymptotic convergence to zero of the uncontrolled boundary states, i.e., the oscillations of the angular displacement and velocity at the bit, and the boundedness of all states in the closed-loop system, are proved via Lyapunov analysis. The effectiveness of the proposed adaptive controller is verified via numerical simulation. The results also can be applied to other applications, such as vibration control of cable elevators with uncertain cage-guide friction and cage disturbances.

Exponential Stabilization of Torsional Vibrations in Rotary Drilling Systems

The paper considers oilwell drilling operations and, in particular, the problem of minimizing drilling vibrations. We develop a stabilizing controller for a one dimension wave PDE with damping term that describes the drillstring torsional system. The drillstring system stability is studied via the Lyapunov theory and the control steps are deduced from a PDE backstepping approach. As a result, exponential vibration suppression is obtained in presence of stick-slip friction due to the drill-bit and the soil interactions. The torsional vibration rejection is shown through the developed simulation results.