Using Surface Motion Profiling to Manage Sucker-Rod Dynamics
by Ron Peterson
One aspect of sucker-rod-pumped wells that has vexed engineers for decades is rod dynamicsthe overshoots and oscillations in rod loads that occur from acceleration forces associated with reciprocating the rod-string mass. Sucker-rod dynamics often contribute to problems such as premature rod breaks, rod fatigue, and tubing wear caused by rod buckling.
Developments over the years have adapted equipment to better tolerate rod dynamics, including more sophisticated rod string design and better rod and coupler materials. Little work has been done, however, to address the major contributor of excessive rod dynamicsthe motion profile of the surface pumping equipment.
The motion profile of a conventional pumping unit is forever fixed by its geometry and speed, irrespective of rod characteristics such as stiffness, natural oscillation frequency, and natural damping. Consequently, the default conventional surface motion profile may or may not be well suited for adequate control of a given rod string. Typically it is not, as it is indifferent to the rod and pump motion, exciting rod string resonances, and undesirable dynamic loads.
The application of servo motion profiling and closed-loop damping algorithms to manage resonant loads in various machine operations has been well accepted in industrial processes for decades. The same technology can be applied to sucker rod pumping.
To demonstrate the effect, a newer style surface linear rod pumping unit mechanism has been simulated, such as that shown in Figure 1. The linear rod pump is fitted with a variable-speed drive. As a comparison, a conventional Class I pumping unit of identical stroke length and average pumping speed has also been simulated. The simulation models reservoir inflow, pump action, rod string behavior, surface pumping equipment, and motor/drive response using industry-accepted predictive software modeling techniques.
In both cases, the pump stroke is 100 inches. The examples are both running an average speed of 6 spm. The well is 5,000 feet deep with a 1.5 inch pump. The rod string is tapered with a diameter of 0.875 inches at 4,000 feet and 0.75 inches at 2,000 feet.
Figures 2 and 3 illustrate the results from a conventional pumping unit running clockwise rotation with a relatively constant crank speed. Figure 2 illustrates the polished rod and pump linear velocities. The rod speed peaks at 30 inches/sec (blue trace). The downhole pump speed peaks at 45 inches/sec (green trace). Figure 3 illustrates the corresponding surface and downhole dynamometer plots.
Figures 4 and 5 illustrate the results from the linear rod pump with surface motion profiling, specifically deadbeat rod damping control. The polished rod motion profile is manipulated very calculatingly so as to almost completely eliminate rod string dynamics. Peak velocities are limited. Whereas time was previously wasted by inauspiciously low acceleration rates during certain parts of the cycle, the velocity is now continuously manipulated in a more favorable way, improving overall response while maintaining the same average pumping speed. Figure 4 illustrates the polished rod and pump linear velocities, both peaking at 20 inches/sec. Figure 3 illustrates the corresponding surface and down-hole dynamometer plots. The rod damping control reduced the peak down-hole pump velocity to half its original value. Rod load dynamics (overshoot and oscillation) have been eliminated, reducing the peak rod differential loading by over 2,000 pounds.
To demonstrate the rod damping effect along the entire rod string, Figure 6 and 7 illustrate rod string loads from surface to pump (at various points down the length of the rod) without and with rod damping control. For simplification, buoyancy effects have been ignored. The rod damping case shows a considerable reduction in rod dynamics along the entire string, reducing rod fatigue and rod buckling potential. Generally speaking, the rod string is much better behaved. (To specifically evaluate rod buckling tendency, one would include buoyancy effects, which would shift the load lines down correspondingly; if the minimum rod load drops below a critical compressive value, the risk of rod buckling exists.)
There are other advantages to surface motion profiling beyond controlling rod dynamics. For example, a “soft landing” feature can reduce the speed of the downhole pump just prior to fluid impact, reducing the impact force. In a similar fashion, peak upstroke pump speeds can be limited to reduce viscous flow pressure drop across the pump intake. Look for future articles on these topics and more.