Rod Loads in Deviated Wells
Chris Norris, Theta Enterprises
Overview
Interpreting the output from a computer simulation of a deviated beam pumper adds a few new
considerations to an already complicated vertical case. This paper present some of the pencil and
paper calculations the user can do to make more sense of the output. Hopefully, better
understanding of these deviated forces will allow more intelligent designs on both existing and
future wells.
The calculations on the output numbers are fairly easy. But for practical decisions you will need
access to a deviated wave equation simulator to crunch the mass of numbers and predict the
forces in the first place, summing hundreds of rod force elements over hundreds of time steps.
Dogleg & Axial Force
Interactions
In deviated sections of the
wellbore, axial tension in the rod
string forces the rod against the
tubing as a function of (Tension *
Dogleg Severity).
The chosen example (final page
shows graphical profile) is an
Austin Chalk well with “medium”
radius, relatively smooth build, and
a small pump.
Our sample
calculation is at the point of highest
side loading, just below the kickoff
point. Here the weight of the rods,
the pump load, and drag all add up
to maximize the normal force
between rods and tubing.
Figure 2 illustrates the calculations
a simulator makes on an individual
rod at this point.
At small angles, the sine function
within the Normal Force formula is
linear. So triple the dogleg severity
in deg/100’ means triple the side
force. And double the axial force
also means double the side force.
At each contact point there is an
additional drag load in the axial
direction equal to the Coefficient of Friction time the Normal Force. This coefficient ranges from
0.2 for steel-on-steel up to 0.35 for certain rod guide materials (simulators let you adjust this
friction factor for each taper).
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Solution of the wave equation takes noticeably longer because of the additions of all these point
drag loads. The rod string must be divided into as many as 10X the number of length increments
as required for an accurate vertical solution, with a proportional increase in time steps. The rods
still behave like a Slinky toy as in vertical solutions, but with drag loads also happening at
different times and directions all along the rod string.
A simulation that ran in 2 seconds for a vertical well mights take 30 seconds now. Have a cup of
coffee and write down what you were doing so you don’t forget.
Gravity Force
Usually of lesser magnitude is support of the
rod string by the tubing against gravity. Figure
3 shows an example calculation for a single 1”
rod at various inclinations. The combined
forces “A” and “f”, the axial rod load and
frictional drag, must equal the gravity force
pulling on the rod in the direction tangent to the
tubing just to keep it from sliding downhole.
The problem is similar to the “70 degree rule”
in wireline tools. Above this inclination,
almost the entire weight of the tool string is
supported by the tubing and will only move by
applying axial force “A”. Fortunately, sucker rods apply a compressive load “-A” much better
than a slickline unit.
In many instances, the gravity force and axial/dogleg force act to push the rod to opposite sides of
the tubing. At certain depths and inclinations, the contact point between rod and tubing could
alternate between the high and low sides of the tubing during different parts of the stroke.
Wear Tracks in the Tubing
Most of us are familiar with the position-load plot obtained at
surface when a beam pumping well is “weighed.” This basic
card shape applies (changing gradually) all the way down the rod
string with diminishing magnitude in deeper sections as there is
less hanging rod weight below. The closer to the pump, the more
the card looks like the downhole pump card.
The output of a simulator usually plots just the maximum and
minimum loads of this card at all depths. But the rod coupling is
tracing a vertical wear pattern in the tubing analagous to the
vertical track that a phonograph machine lays down in a record
master (I remember this, it is easier than burning a CD in
Windows…). Transforming the axes, the track laid down at
different depths of contact during the downhole stroke would
look something like the diagram at left.
Not only is the tubing wear constrained to an exact given vertical
plane, the high loads may occur during only a portion of the
stroke. So a trick like adding a few feet of pony rods at the
bottom of the string during a pump change moves this wear to a
completely “virgin” spot in the tubing. Rod and tubing rotators
spread it out almost continuously, and rod guides can sacrificially prevent it almost completely
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(for a while). If it were not for aggressive produced saltwater that adds the “corrosion” to
“corrosion-erosion”, we would probably never run short of effective solutions to rod coupling and
tubing wear.
Existing Well Design Suggestions
If you already have a crooked well you want to pump, there is not much you can do about the
magnitude and location of the doglegs. But you can reduce the loads and work with the wear
points:
1. Run smaller and lighter high strength rods.
2. Employ rod and tubing rotators to move the wear around.
3. Respace the rod string during pulling jobs using pony rods on bottom.
4. Use a smaller pump (load = pressure * area). If you are really desperate, a higher
pumping fluid level will reduce the pressure half of this equation.
Only add rod guides where the simulator and actual experience (worn couplings, tubing holes)
say you need them. Note that rod guides always add drag compared to steel, so PRHP and maxmin loads will increase. Consult the suppliers’ experts on best placement and materials.
Try continuous or batch corrosion inhibition. “Fresh steel” being exposed during each stroke at
the rub points needs an inhibitor film on it to slow down the corrosion half of corrosion-erosion.
Spray metal couplings are likely to reduce coupling wear both from less corrosion and a harder
surface. Tubing wear probably decreases because dissimilar materials slide more easily against
each other.
There is a lot more material to erode away to the failure point if you use rod and tubing rotators.
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Future Wellbore Planning
If you can hit the target by kicking off deeper, do it. Ideally, an ultra-short radius allows a very
low pumping bottomhole pressure with the pump still set in the vertical part of the well.
In the attached example well, note that a 9,000 pound axial load and 10deg/100’ dogleg yields the
same side load as 27,000 pounds and only 3.3deg/100’ dogleg. Those shallow sidetracks around
a fish, or uncontrolled uphole “vertical” wells that are not really can cause huge pumping
problems later because there could be so much rod weight hanging below. It might be cheaper in
the long run to skid the rig and start a new hole.
More gradual direction changes certainly decrease side loads on each rod. Each rod guide is only
designed to handle about 50 pounds of side force; it is difficult to spread the load evenly between
multiple guides. If the projected combination of dogleg and axial load will results in 500 pounds
of side force per rod, they will not keep the rod coupling away from the tubing for very long
before they wear out. The resulting drag from 10 guides on each rod with 0.35 friction
coefficient will be high.
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