When designing a new rod pump-ing system, it is wise to design it to handle the worse loading conditions for the well. To most people this means designing the system for a full pump with the fluid level at the pump intake. The reason for this is because when the fluid level is at the pump, this creates the maximum pressure difference across the pump plunger which results in the highest fluid load on the plunger. Using a full pump maximizes the work done by the pump. Most people think that when you design a system for full pump with fluid level at the pump, the system will be able to handle any other fluid level or pump condition without being over-loaded. This is true in most cases but not in all cases. Which brings up the question: “How do I design my rod pumping system for the worst case to avoid overloading the pumping unit, the rods and the motor?” To answer this question we need to discuss what factors contribute to the loading and power requirements of the rod pumping system.
Dynamometer Card Area
The area of the surface dynamometer card represents the work done by the system for one cycle. This area along with the pumping speed of the system allows us to calculate the power required at the polished rod which in turn is used to calculate the minimum required motor size. This means that the more area the surface dynamometer card has and the faster the unit is running, the bigger the motor we need. Also, the area of the dynamometer card affects the gearbox loading. The closer the dynamometer card gets to the permissible diagram, the closer we get to overloading the gearbox. Therefore, when the area of the dynamometer card increases, this does not only affect the motor size we need, but also the gearbox and rod loading. The reason the rod loading is affected is because the load range is the biggest factor in the rod loading fatigue calculations.
Factors Affecting the Area of the Surface Dynamometer Card
The main factors that contribute to the shape and area of the surface dynamometer card are:
Fluid load also affects rod stretch which in turn affects stroke length. The complex nature of the relationships between these variables is why we need to use sophisticated wave equation simulators such as RODSTAR to model what happens in rod pumping systems. However, it does help to be aware of the relationships between these variable to understand why in some cases, a certain fluid level over the pump can result in higher gearbox loading than when the fluid level is at the pump.
This rarely if ever happens with steel rod strings. However, it can occur if you use fiberglass & steel rod strings that have overtravel (stroke at the pump is longer than the stroke at the surface). The explanation for this is as follows: For a fixed SPM, the area of the dynamometer card is a function of both stroke length and plunger load (fluid load). When the fluid level over the pump rises, this reduces the fluid load. This in turn reduces the stretch on the rods and the pump stroke increases. If the pump stroke increase is larger than the fluid load reduction, the overtravel increases (stroke at the pump gets longer). This means the system is doing more work than before and the area of the surface dynamometer card increases. However, Since the surface stroke is fixed, the dynamometer card area can only increase if the dynamometer gets fatter in the vertical direction only. This brings the dynamometer card closer to the permissible load diagram which increases the gearbox loading.
To illustrate this phenomenon, I ran an 8000 foot deep case with fiberglass and steel rods and varied the fluid level from 8000 to 2000 feet from surface to see what happens to the loads on the system.
Figure 1 shows the surface and downhole dynamometer cards with a fluid level of 7000 feet from surface. The gearbox loading for this condition was 68%.
Figure 1. Example Dyno Plots for Fluid level of 7000 feet from Surface
Figure 2 shows the surface and dowhole dynamometer cards when the fluid level is 3000 feet from surface. The gearbox loading for this condition was 125%.
Figure 2. Example Dyno Plots for Fluid level of 3000 feet from Surface
Notice that the reason the surface dynamometer card has a much larger area as compared to figure 1 is because of pump plunger overtravel. This more than makes up for the smaller fluid load on the plunger.
The maximum rod loading was higher when the fluid level was 7000 from surface
(93% vs. 87%) but the required motor size was significantly different for the
two fluid levels. For the 7000 ft fluid level run, the required motor size was
30 hp. For the 3000 ft fluid level run, the required motor size was 50 hp. This
means that if you work on this type of well and the fluid level rises above
the pump, when you put the well back on production, the gearbox and the motor
will be overloaded until the fluid level goes back to 7000 feet from surface
and the system reaches a stabilized condition.
In the above comparisons, it was assumed that the unit would be perfectly balanced
for each of these conditions (ran RODSTAR with unknown Max. CB Moment). However,
if this was a real well that we designed to normally operate with a fluid level
of 7000 ft from surface and the unit was balanced for this condition, if the
fluid level is 3000 ft from surface after the well is worked on, then when you
restart the unit, the gearbox loading will be 160% and the required motor size
will be 60 hp. This indicates that sever overloading can occur when you least
expect it (when the fluid level is much higher than what most people think is
worse case condition.)
Full Pump versus Fluid Pound
Another common belief is that new rod pumping systems must be designed for a
full pump. Of course this is true in most cases since a full pump requires more
work and is the pump condition that must be used to correctly size the motor
you need. However, a full pump may not give you worse case loading or the correct
number of sinker bars needed.
For example, I ran a RODSTAR design for an 8000 ft deep system. Using the traditional
approach, I selected a full pump condition and fluid level at the pump. Then,
I compared my results with a second run for the same system but with a fluid
pound condition with a 50% pump fillage.
The results were interesting. The rod and gearbox loadings were higher with
the full pump condition. The structural loading was slightly higher with fluid
pound (97% vs. 96% for full pump) but not enough to worry about. When I designed
the case with a full pump, I used a 76 rod string with 300 feet of 1 ½
inch sinker bars on the bot-tom to keep the ¾ inch rods in tension (with
buoyancy effects not included). Then, I fixed the rod string design after running
RODSTAR by selecting “Manual rod string entry” from the Rod string
entry option list. This brings in the rod string that RODSTAR designed and enters
it as if it was entered manually. Then, I ran the case with fluid pound with
50% fillage. Even though most loads were worse for the full pump condition,
the ¾ inch rods were now in compression. To avoid compression I had to
add another 50 feet of sinker bars for a total of 350 feet of 1 ½ inch
sinker bars. Then, I reran this case with a full pump using the longer sinker
bar section.
I hope that the above examples help you improve your designs with RODSTAR and
help avoid unnecessary failures by designing your rod pumping systems for worse
case conditions that take in consideration other transient or steady state conditions
your systems may experience such as fluid pound or a high fluid level over the
pump.
If you found this article useful and have more questions about it please email
me your questions and I will be happy to further clarify some of these concepts
for you. Also, I would appreciate any suggestions for items of interest to discuss
in this newsletter in the future.