Mechanical Performance of Fiberglass Sucker-Rod Strings

Abstract

Summary. The natural frequencies of fiberglass sucker-rod strings can be calculated by treating the rod strings as modified spring/mass vibration systems. The ratio of the pumping-unit operating speed to the rod-string natural frequency can then be used as a basis for understanding fiberglass-rod-string performance and for predicting downhole pump stroke lengths. Introduction Many oil wells with fiberglass sucker-rod strings have subsurface pump plunger stroke lengths that are longer than polished-rod strokes pump plunger stroke lengths that are longer than polished-rod strokes at the top of the rod string. In many cases, the increased fluid production represents plunger stroke lengths that are 20 to 50% greater production represents plunger stroke lengths that are 20 to 50% greater than the corresponding polished-rod stroke lengths. This phenomenon has generally been attributed to overtravel of the pump phenomenon has generally been attributed to overtravel of the pump plunger caused by acceleration forces during the rod downstroke plunger caused by acceleration forces during the rod downstroke that stretch the relatively elastic fiberglass rods. This paper shows, however, that the overtravel is caused by the dynamic amplification that results from the fiberglass rod string operating near its first longitudinal natural frequency. Little has been published on the mechanical performance of fiberglass sucker-rod strings. In limited cases where efforts have been made to calculate a fiberglass-rod-string natural frequency, the equation for calculating the natural frequency of steel rod strings has been used. Because this equation was derived for a long, thin rod with uniformly distributed mass and stiffness properties, it is not applicable to fiberglass rod strings that consist of a combination of fiberglass and steel rods. Normally, the top 50 to 90% of these rod strings consists of fiberglass rods, the lower section consists of steel sucker rods. In cases where the designer thinks additional mass is needed, sections of heavy steel sinker bars are placed at the bottom of the rod string. Most fiberglass sucker-rod strings are designed from computer programs on the basis of the wave equation described by Gibbs. programs on the basis of the wave equation described by Gibbs. Unless the program operator understands the effects of various changes on the system performance, using these programs to design a fiberglass rod string to achieve optimum crude oil production can involve a series of trial-and-error iterations. However, once the effects of the rod-string natural frequency and fluid load are understood, the design of fiberglass rods should be easier. The performance of a fiberglass/steel sucker-rod string can be modeled by a simple oscillating spring/mass mechanical system. [The natural frequency of a spring/mass system is the frequency of free vibration of the mass when no external forces are present. This is the frequency of vibration that occurs when a mass suspended on a spring is displaced and then released, allowing the mass to vibrate freely. Resonance occurs when the excitation frequency (shaking either the mass or the fixed end of the spring) equals the natural frequency of the system. As the resonant frequency of a simple spring/mass system is approached, displacements at the driven end of the spring are amplified or magnified, resulting in large displacements at the mass.] The spring represents the longitudinally elastic fiberglass rods, the mass represents the heavier steel rods suspended below the fiberglass rods, and the forcing function corresponds to the polished-rod motion at the pumping unit. As the system driving frequency (pumping-unit operating speed) approaches the rod-string first longitudinal natural frequency, the surface stroke displacement is amplified, resulting in a pump plunger stroke that is greater than the surface polished-rod stroke lengths. The sucker-rod system differs from a simple spring/mass system in that on the pump upstroke, the system includes the mass of the fluid load, which is not lifted on the downstroke. Consequently, the elastic rods stretch on the upstroke to compensate for this additional load. This results in a nonlinear vibration problem, with the plunger stroke length being reduced by an amount that is plunger stroke length being reduced by an amount that is proportional to the fluid load. proportional to the fluid load. As shown later, the rod-string natural frequency and rod stretch resulting from the fluid load are much more significant in fiberglass rod strings than in steel sucker-rod strings. Rod-String Natural Frequency The vibration of sucker-rod strings is normally analyzed with a form of the wave equation. (1) which is obtained by use of Hooke's law describing rod elasticity: For a rod such as that shown in Fig. 1a, with the mass and elasticity uniformly distributed along its length, the first longitudinal natural frequency becomes (2a) or because the speed of a stress (or sound) wave is the first natural frequency can be expressed as (2b) or in strokes per minute for a steel rod string with v= 16,333 ft/sec [4978 m/s], (2c) This is the equation used to describe the "natural frequency of a straight rod string" in API Recommended Practice for Design Calculations for Sucker Rod Pumping Systems. For all-steel rod strings, this natural frequency varies from 25 strokes/min for a 10,000-ft [3050-m] -long rod string to 80 strokes/min for a 3,000-ft [915-m] -long rod string. Although the API design curves display design data for frequencies as high as 60% of resonance, most steel sucker-rod strings operate at frequencies below 40% of resonance. SPEPE P. 346