In 1993, J. F. Lea published an SPE paper (#25416) titled "Interpretation of Calculated Forces on Sucker Rods." In this paper, Lea explained that it is the "effective" and not the true forces that determine whether a sucker rod will buckle.
Jim Leaís paper references a paper by A. Lubinski who published an API paper in 1951 titled "Influence of Tension and Compression on Straightness and Buckling of Tubular Goods in Oil Well." Lea, by referring to Lubinskiís work, explains that it is the effective tension that one must look at to determine the tendency of sucker rods to buckle. For sucker rods, the effective tension is calculated as follows:
Teff = Ttrue + PoAo
Po = the external pressure
Ao = The outside cross sectional area of the sucker rod.
According to Leaís paper, the true force is the actual axial force felt by the internal structure of the steel rods. However, the effective force is the force that determines if the rod will buckle or not when the tension becomes compression. This is because when the rod is deflected, there is a restoring force from the pressure exerted by the surrounding fluid.
He further states that although the lower end of the bottom rod is in compression on the downstroke, it actually has no tendency to buckle unless additional forces are present. These additional forces are due to pump friction and rod-tubing friction. This is why we added the capability to enter pump friction in RODSTAR. Otherwise, the bottom minimum stress at the bottom of the rod string would be zero if buoyancy effects are not included.
In RODSTAR 2.33, to include or exclude buoyancy effects, click on Setup and then select Output Options. Then select or deselect the option "Include rod string buoyancy effects" as shown in Figure 1.
Figure 1 - RODSTAR Setup Window
The default pump friction force in RODSTAR is 200lbs. This should be sufficient in most cases. However, if you have a tight pump or viscous fluids, or to simulate excessive pump friction for whatever reason, you can enter a higher value in this field. Please note that the pump friction only affects the downstroke.
In other words, it has to do with the resistance force on the pump on the downstroke. Figure 2 shows the tubing and pump information window with the new pump friction input field.
Figure 2 - Pump and Tubing Information Window
Please note that if you enter a large number for pump friction, this will result in a large negative force on the bottom of the rod string, which will cause the rods above to be in compression.
Please note that since the pump friction is usually unknown, using the 200 lb. default value is more realistic than entering zero. One way to determine a better pump friction number is use a diagnostic computer program that has the ability to show the downhole pump card without buoyancy. If the rod-tubing friction is accurately modeled, then this downhole pump card that shows effective forces can be used to estimate the pump friction. Any load below zero would be pump friction. However this may be difficult to do in practice since the amount or rod-tubing friction is usually unknown. The load cell reading lower than the actual loads causes another common problem which causes the pump card to show more negative load. Dynamometer load cells are rarely in perfect calibration. Therefore, this load error problem may actually be the most critical factor in preventing the accurate determination of pump friction. However, using the XDIAG computer program should give you a better answer since XDIAG can detect and correct load cell measurement errors.
After you select to exclude buoyancy effects, the output will show a footnote indicating that the stress calculations do not include buoyancy effects as Figure 3 shows.
Figure 3 - Output Results Window
So far, only RODSTAR has been modified with this capability of including or excluding buoyancy effects. RODDIAG and XDIAG will be modified to do the same in one to two months.