Influence of Bit-Rock Interaction on Stick-Slip Vibrations of PDC Bits

Abstract

This paper describes a new approach to understand the causes of stick-slip vibrations experienced by PDC bits. This new model takes into consideration not only the axial and torsional modes of vibration, but also the coupling between these two modes through bit-rock interaction laws, which are consistent with laboratory results from single cutter experiments. These interaction laws, which account for both frictional contact and cutting processes at the bit-rock interface, are formulated in terms of the depth of cut, a variable that brings into the equations the position of the bit at a previous a priori unknown time. They also account for potential loss of frictional contact between the wear-flats and the rock. The delayed and coupled nature of this interaction is ultimately responsible for the occurrence of self-excited vibrations, which can degenerate into stick-slip oscillations under certain conditions. The features of the torsional vibrations that are predicted with this model are well in accordance with field observations. Furthermore, the results reveal that the model predicts apparent rate effects as an inherent outcome of the nature of the bit-rock interface. Introduction Different types of vibrations can take place while drilling with PDC bits, namely lateral (or bending), vertical, and torsional vibrations. The research reported in this paper focuses on torsional vibrations and more precisely on their most violent extent: the so-called stick-slip vibrations. Stick-slip, as indicated by its name, is characterized by a periodic (or almost periodic) succession of sticking phases where the bit stops for a finite time interval (typically several tenths of a second) and slipping phases where its angular velocity O increases up to two or three times the imposed velocity Oo, see Figure 1. Stick-slip oscillations can last for several minutes. Downhole measurements indicate that the magnitude of vibrations (in terms of torque and angular velocity) occurring close to the bit are up to one order of magnitude larger than the vibrations recorded at the surface (Cunningham, 1968; Lesseultre and Lamine 1998). The vibrations induced in the drilling assembly while drilling with PDC bits increase bit wear, and can result in premature fatigue failure of the string or breakage of the bit itself. According to a study performed at Elf-Aquitaine by Henneuse (1992), the occurrence of stick-slip corresponds to about 50% of the on-bottom drilling time. Field and Laboratory Observations The measured frequency fo of torsional and stick-slip oscillations is found to be close to the estimated first natural frequency of the drill string assembly in torsion (Brett 1992, Pavone and Desplans 1994, Challamel 2000). However, while the angular velocity exhibits a monofrequential behavior during stick-slip oscillations, the weight-on-bit W and the torque T present a more widely spread power spectrum, see Figure 2. Stick-slip vibrations have been observed to occur mostly under large weight-on-bit and low angular velocity (Brett 1992). Thus, an increase of the applied weight-on-bit or a decrease of the angular velocity can trigger instabilities leading eventually to stick-slip vibrations, see Figure 3. Similarly, a decrease of the applied Wo or an increase of Oo can stop stick-slip vibrations as shown in Figure 4. As depicted in these figures, stick-slip oscillations are accompanied by a decrease of the mean side (or lateral) acceleration. These data have been recorded downhole using the instrumented bit developed by Security-DBS (Lesseultre and Lamine 1998). Pragmatically in the field, it is sometimes necessary to pull the bit off-bottom in order to arrest the torsional vibrations (Brett 1992).

Development of an Innovative Model-Based Stick/Slip Control System

“…Stick/slip oscillations are characterized by a repeated alternation of sticking phases, where the bit comes to a complete standstill for a limited interval of time, and slipping phases, where its angular velocity ω increases up to two or three times the rotary speed Ω applied at the surface. The stick/slip effect has been the subject of numerous studies in the past and is still under investigation (Kyllingstad and Halsay 1988, Brett 1992, Jansen and van den Steen 1995, Richard et al 2002, Detournay et al 2008, Germay et al 2009, Navarro-Lopez 2009.…”

Stochastic adaptive learning rate in an identification method: An approach for on-line drilling processes monitoring

“…However, the main drawback of these strategies results from the lack of knowledge concerning the rock to drill before drilling operations. To overcome this difficulty, bit-rock interaction model has been developed [5]. The specificity of the achieved model lies in the possibility of not involving rock properties.…”

“…In section V concluding remarks are drawn. Research activities regarding bit-rock interaction modeling have been investigated and significant contributions have been reported [5]. These models account for the cutting action of a single cutter, which is a Polycrystalline Diamond Compact (PDC).…”

“…The cutting components c T and c W correspond to the forces transmitted by the cutting face of each cutter and the friction components f T and f W correspond to others contacts generated from bit-rock interaction. The response of the bit is obtained by combining the cutting and frictional process [5]:…”

“…The specific energy which corresponds to the necessary energy to grind a given volume of rock is defined by [5]:…”