As discussed previously, the tubing string is subjected to a varying load during the pumping cycle. On the upstroke, it is not loaded since the plunger carries the weight of the liquid in the tubing, but this load is transferred to the tubing at the start of the downstroke. Owing to this variable load, a freely suspended tubing string periodically stretches and unstretches during the pumping cycle. It is quite easy to see that tubing stretch reduces the plunger stroke length available for lifting of fluids, resulting in a reduction of pump displacement. This phenomenon has been recognized for many years, and the anchoring of the tubing string to the casing became standard practice.

The above effects do not completely describe the behavior of the tubing string in a pumping well. It was found by Lubinski, based on his investigations of rotary drill pipe, that the lower portion of a freely suspended tubing string is subject to helical buckling. ^[11] Buckling is present during the upstroke only and causes the tubing to wrap around the rod string below a certain depth, called the neutral point. The shape of the buckled tubing is a helical surface, which is constrained on the inside by the rod string and on the outside by the casing. Figure 2-20 shows a cross section of the tubing in a pumping well during the up- and downstroke. On the upstroke, the rod string is fully under tension and straight, due to the fluid load...