Case Studies of the Bending Vibration and whirling Motion of Drill Collars

Abstract

Summary. This paper describes two principal sources of bottomhole-assembly (BHA) bending vibration:drill-collar whirling andlinear coupling between weight-on-bit (WOB) fluctuations and bending vibration of an initially curved BHA. It also evaluates the consequences of bending vibration in terms of drill-collar wear and connection fatigue. Equations are given for forward and backward whirl rate and for tangential velocity at the borehole wall. Downhole measurements of bending moment are used to detect and to identify bending-vibration events, and data taken with a downhole vibration-measurement system are used to illustrate cases of linearly coupled bending vibration, forward and backward whirl, and bit bounce. Introduction Because of the lack of adequate downhole-vibration data, very little has been known about the actual bending dynamics experienced by the drillstring during rotary drilling and about the contributions of bending vibration to drillstring deterioration and failure. Recent use of downhole-vibration recorders and systems with hard wires to the surface has provided much needed data and insight to events downhole. At first glance, the data appear to be extremely complex, even to the experienced vibration analyst. Many different vibration phenomena occur simultaneously, malting it difficult to isolate, evaluate, and explain any one of them. To varying degrees, axial, torsional, and bending vibrations are all present and at times infinitely coupled. Bit bounce, stick slip, forward and backward whirl, and linear and parametric coupling between axial and bending vibrations all occur. Several authors have made recent contributions particularly relevant to the measurement of bending vibration of BHA'S. Wolf et al. present downhole-vibration data acquired in the same well as the data presented here. Included in the paper are several suspected cases of whirling. Besaisow and Payne also show suspected examples of bending vibration and whirling. Burgess et al. conclude specifically that transverse vibration is a source of downhole measurement-while-drilling (MWD) tool failure and cite a method for reducing downhole failures. Dunayevsky et al. make an important contribution in identifying a mechanism for parametric excitation of drillstring bending vibration by means of coupling parametric excitation of drillstring bending vibration by means of coupling between axial and lateral vibrations. Close et al. present downhole recordings of large-amplitude bending vibrations. This paper discusses two sources of inverse or bending vibration of the BHA:linear coupling of axial and transverse vibrations owing to initial curvature of the BHA anddrill-collar whirling. This paper goes beyond earlier works; it presents a detailed analysis of these two phenomena verified by downhole measurements. The mechanisms are first described; then means of identifying each event m downhole data are developed. Case studies based on downhole measurements are presented that illustrate several important types of vibration, including forward and backward whirl, linear coupling between WOB and lateral vibration, and bit bounce. Coupling of Axial and Transverse Vibrations Two types of bending vibration result from coupling with axial forces: "linear" and "parametric" coupling. Dunayevsky et al. describe parametric coupling between axial forces m the drillstring and bending vibrations. Although this mechanism is likely to be important in some circumstances, it is not covered here because of space restrictions and lack of a good example from field measurements. Linear coupling between the axial forces on the bit and bending vibration occurs frequently in real drilling assemblies and is often superposed on other bending-vibration phenomena. The source of linear coupling is initial curvature of the BHA (see Fig. 1). Linear coupling is easy to visualize by taking a thin or a piece of paper, giving it a slight curve, and then pressing axially on the ends. paper, giving it a slight curve, and then pressing axially on the ends. The object responds by additional bending in the plane of the initial curvature. The frequency of the bending and axial vibrations is the same. Linear coupling will not occur on a perfectly straight beam excited by an axial load that is less than the critical buckling load. If any initial curvature exists, however, an axial load will cause a lateral deflection. For small amounts of curvature, the greater the initial curvature, the greater the lateral deflection. Curvature is of course very common in BHA's because of the combined effects of gravity and axial force in inclined holes. Whirling also results in curvature of the BHA and therefore leads to coupling. Dynamic variations in the WOB then cause bending vibration to occur about the mean statically deflected shape. Drill-Collar Whirling Whirling is simply the centrifugally induced bowing of the drill collar resulting from rotation. Consider the drill collar shown in Fig. 1. It is centered in the hole at the bit and at the stabilizer. If the center of gravity of the drill collar is not initially located pre-cisely on the centerline of the hole, then as the collar rotates, pre-cisely on the centerline of the hole, then as the collar rotates, centrifugal force acts at the center of gravity, causing the collar to bend. The magnitude of the force is proportional to the mass of the collar, the square of the rotation rate, and the initial eccen-tricity (the distance from the center of gravity to the axis formeby a line drawn from the center of the bit to the center of the stabilizer). The initial eccentricity of the drill-collar can result from several causes, including an initially ben drill collar or the combination of drill-collar sag owing to gravity and high compressive loads owing to WOB, and causes a dynamic imbalance. Destructive whirling has long been known to occur in rotating machinery when the rotation rate of the shaft is equal to the natural frequency of that shaft in bending. When this happens, the machine is known to be operating at a critical speed. An enormous amount of established literature exists on the subject of whirling of such machines as turbine engines, axial flow compressors, and generators. Ref. 6, an excellent tutorial on the subject, presents a mathe-matical formulation of whirling of rotating shafts and machinery. Also, Shyu presents an in-depth analysis of drill-collar whirling. A great deal of effort and money is spent on balancing shafts and on developing operating guidelines for machinery to prevent serious whirling. This is generally not done with drillstrings. One reason is that drillstrings operate within the borehole. Whirling generally does not result m precipitous drill-collar failures because deflection amplitudes are limited by wall contact. There are, however, undesirable consequences of drill-collar whirling-e.g., surface abrasion of drill collar by rubbing on the wall. Abrasion is most serious during "'forward synchronous whirl," in which the same side of the collar is in continuous contact with the side of the hole. This type of whirl is the probable cause of a flat worn in one place when a collar comes out of the hole. place when a collar comes out of the hole. Another potentially damaging form of whirl is "backward whirl". SPEDE P. 282