Dynamic Stability of Drillstrings Under Fluctuating Weight on Bit
- V.A. Dunayevsky (BP Research) | Fereldoun Abbassian (BP Research) | Arnis Judzis (BP Research)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- June 1993
- Document Type
- Journal Paper
- 84 - 92
- 1993. Society of Petroleum Engineers
- 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 1.6 Drilling Operations, 4.1.5 Processing Equipment, 1.6.1 Drilling Operation Management, 1.14.1 Casing Design, 1.10 Drilling Equipment, 5.3.1 Flow in Porous Media, 4.3.4 Scale, 1.4.4 Drill string dynamics, 1.11.2 Drilling Fluid Selection and Formulation (Chemistry, Properties), 1.2.5 Drilling vibration management, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 1.12.6 Drilling Data Management and Standards
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This paper describes the theory and the underlying formulation behind thedevelopment of a drillstring-dynamics simulator that predicts rapidly growinglateral vibrations triggered by axially induced bit excitations. The analysescenter on calculations of stable rotary speed ranges for a given set ofdrillstring parameters and are presented in vibration "severity" vs.rotary speed plots. The critical rotary speeds, which correspond to the rapidlygrowing lateral vibrations, are pinpointed by spikes on the severity plots.Some application, of pinpointed by spikes on the severity plots. Someapplication, of the drillstring-dynamics simulator are presented, andlimitations and further model development are discussed.
Field observations, in the form of downhole and surface vibrationmeasurements, have clearly indicated that drillstrings, particularly bottomholeassemblies (BHA's), generally are subjected to severe vibrations. Thesevibrations are induced primarily from two excitation sources: bit/formation anddrillstring/borehole interactions. As a result of these excitations, thedrillstring can vibrate in several ways: axially, laterally, torsionally, ormore often, as combinations of these three basic modes (e.g., whirling). Thismakes the drillstring vibration problem fairly complex to investigate and makesfull simulation of the dynamic events impractical. A more practical approach,therefore, would be to identify and investigate particulardrillstring-vibration mechanisms individually. One such mechanism frequentlyobserved in field vibration measurements is severe lateral vibrations inducedas a result of axial excitations caused by bit/formation excitations, thesubject matter of this paper. This drillstring-vibration mechanism is ofparticular significance because severe lateral vibration can induce acceleratedfatigue failure in the drillstring and also can cause borehole enlargement andpoor directional control. In addition, axial excitations also can be beneficialbecause they increase the rate of penetration (ROP) and reduce drag, soidentification of damaging axial excitations becomes even more important.Drillstrings are subjected to axial loads with static and time-dependentcomponents. The classic static-stability (buckling) theory of axially loadeddrillstrings determines the critical value of static component of axial load,the maximum allowable static weight on bit (WOB) above which buckling willoccur. The dynamic component of axial load is primarily caused by bit/formationinteraction, which results in fluctuations in the WOB. When these fluctuationsare taken into account, the loss of mechanical stability becomes evident asrapidly growing lateral drillstring vibrations (the dynamic counterpart ofbuckling). This occurs in much the same way as inducing a snaked motion in avertically hanging rope by moving its end up and down at a particularfrequency. This phenomenon, which is associated with particular frequency. Thisphenomenon, which is associated with specific axial fluctuations, is calledparametric resonance. It can occur for much smaller WOB values than thecritical WOB obtained from a static-stability (buckling) analysis.(Theoretically, dynamic instability may even occur at no WOB.) Therefore, underthese circumstances, the static-stability analysis must be complemented by adynamic-stability analysis that accounts for WOB fluctuations. Considerablework has been carried out on various aspects of drillstring vibrations. Thesehave been mainly concerned either with the transient vibration modeling or withaxial, lateral, and torsional natural excitation studies. The purpose of thispaper is to complement these studies by establishing the conditions paper is tocomplement these studies by establishing the conditions under which thedrillstring becomes laterally unstable as a result of axially inducedvibrations (i.e., by establishing dynamic stability conditions). As outlined inthis paper, such an analysis can be carried out by coupling axial and lateralvibration modes. The lateral vibration triggered by axial excitations causesthe drillstring to precess around the wellbore. The complex problem ofdrillstring dynamics therefore is reduced to the determination of the onset ofthis drillstring precessional motion as a function of relevant drillingparameters (e.g., drillstring configuration, borehole inclination, rotaryspeed, WOB, and mud weight). Such an approach is mathematically andcomputationally attractive compared with more conventional transient vibrationanalysis. Lubkin and Stoker first studied dynamic instability for simplysupported rods. Their work established the influence of axial vibration on thevalue of the static buckling load. Other researchers then carried out furtherwork. Application of dynamic instability to the drillstring vibration problemwas considered first in Refs. 16 through 18. This paper outlines the mechanismof the dynamic stability of drillstrings. The underlying formulation of adrillstring-dynamics model and its numerical implementation is presented. Anumber of model applications then are considered, and finally limitations andfurther developments are discussed.
Dynamic Instability Mechanism
The main aim of drillstring-dynamic-stability analysis is to determine underwhat conditions the axial vibrations (induced by WOB fluctuations) may triggerlateral vibrations that increase in amplitude. These conditions may occur whenthe energy associated with axial vibrations is diverted to lateral vibrations.This instability may occur when the frequency of WOB fluctuations is equal totwice a natural lateral frequency, w. This can be illustrated as follows. Fig.1a represents the motion of a point on the midspan of a simply supported columnvibrating laterally in its lowest natural frequency. At a reference time t=t ,the column is assumed to have an initial deflection w (which can beinfinitesimally small). Let us now examine what would happen if the column weresubjected to a fluctuating axial force, Ff = (F f0 sin 2wt) (Fig. 1c), whichhas a frequency 2w, twice that of the column lateral natural frequency. Fig. 1bshows the resulting lateral column deflection at various times. At time t1, theaxial load, Ff, reaches its maximum, F f0 (and starts decreasing in magnitude),while the lateral column deflection continues to increase and Point A moves tothe right to its maximum position. At time t2, when the lateral deflectionreaches maximum, the value of Ff changes its sign, prompting Point A to move tothe left. By time t4, Ff has completed one cycle, while the lateral motion hascompletes only one semicycle. At this moment, Ff reverses its sign again,prompting movement to the left after the column passes through the promptingmovement to the left after the column passes through the neutral position. Byt8, Ff has completed two cycles while the lateral displacement has completedone cycle. Now, during periods t0 to t4, the axial load pumps the amount ofenergy U into the lateral vibration mode, which at t4 (when the column ispassing its neutral position) manifests itself as excess kinetic energy.Likewise, during the next load cycle (periods t4 to t8), the axial loadcontributes a further amount of energy U that, when combined with the kineticenergy imparted during the previous load cycle (at t4), results in a lateraldeflection with an amplitude greater than the previous half-cycle (i.e., thelateral vibration amplitude grows in magnitude during each load cycle). Withfurther energy "packs," U, being pumped into lateral vibrations overeach successive load cycle, the lateral motion amplitude grows infinitely.
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