How Programs Present Rod Buckling Predictions

J LeaPresident

PLTechLLC

Outside forces such a pump resistance and also rod dynamic effects tend to buckle rods. It does not take much force to buckle rods as shown to the left. A force of less than 90 lbfs can buckle a 1”rod and less for smaller rods

Equations for Buckling

w is weight per foot in liquid

E, steel, = 30 x 106 psi

I = moment of inertia of cross section, πd4/64

Rourk, R. J., and Young, W. C., Formulas for Stress and Strain, McGraw-Hill, NY,NY, 1982, P. 539

t

wEIL

ftin

wEIFeffpsixE

indIftlbww air

f 31.65}144 2.5288

.04908 30x10795.0{

}/795{.lbf 80.05

}/144

2.5288 0.04908 30x10 π.795{

})(795{.1030

04908.64/64/

/5288.2)128..1(9.2)128.1(:RodsInch Onefor n Calculatio Example

3/16

2

3/12

3/122

262

3/12

6

44

==

=

−=

−

−=

=

===

=−=−=

π

π

π

ππ

γ These equations can be used to develop the

equations on the preceding chart.

145.136.741.2273.9504.5310

109.634.26.9943.2003.679

80.0631.65.7852.5282.98

56.0728.96.6011.9362.227

37.1526.1.4421.421.636

22.8223.16.307.98541.135

(-)lbfFtin2Lb/ftLb/ft

FbcLcAreaW fluidWairSize

Critical Force and Length for Rod Buckling

A summary of forces to buckle rods ,,, Fbc (critical buckling force)

Effective Force or Tension with BouyantEffects shows if buckling occurs. True Force includes buoyancy and is not indicative of buckling tendencies.

• Teff = True +PoAo at any point in string

• Newman, K., Bhalla, K., “The Effective Force”, CTES L.C., Conroe, TX. Technical Note, Jan 13, 1999

Sample Case: 60% Fill and 50 psi PIP

Program “A”: A widely used program. Shows bottom card below zero including bouyancy

effects

However there is NO pump resistance input , so there is actually NO tendency to buckle rods at pump

The plots on the left are “True” forces and show compression at and above pump: BUT the plot on the right shows “Effective load” and tendency to

buckle only above pump, not at pump

Program “A”

Max “Effective” force to buckle listed as 1191 lbf above, not at, pump

Program “A”

A summary only like this would not show buckling above pump as previously shown

Program “A shows true load on bottom hole card and may be misinterpreted as large buckling force when there is none or only a small

load. Rod loading is true force so it does not indicate buckling, but a plot of min. effective force on downstroke is indicative of buckling and shows the

user the potential for buckling depending on predictive input.

Program “B”: Bottom hole card shows no negative loads since no pump resistance input. But this plot

is Effective Load only at the pump. Thus no compression at the pump is indicated.

Program “B”: This program shows a plot of max/min Effective/True loads top to bottom. Here

min True Load is negative at pump and above pump but Effective min shows zero compression at pump and negative loading only above the pump

Conclusion: Tendency to buckle only above pump and not at pump as input

This summary shows zero effective loading at the pump and a big true compression load at the pump. This summary can completely miss the

compression above the pump: Summary: Program “B” allows you to see a continuous picture of tendency to buckle over entire rod string as does Program “A”

Plotting Dyno Cards: The top card would be when you add the true static forces to dynamic calculated forces. The bottom card is when you efffective static forces to dynamic forces form a wave equation model.

Adding true forces to dynamic forces to plot

Adding effective forces to dynamic forces to plot

0

0

PoAo at bottom of bottom rod

Adding effective static forces to dynamic forces gives the bottom plot which shows zero negative compression forces to indicate buckling unless outside forces such as pump friction appears when dynamicforces are calculated. The bottom plot makes it much easier to see compressive forces contributing to buckling if they are present and it is suggested to plot cards like this at the pump in the future.

Pump friction if any

Pump friction if any

Program “C” is another widely used program. It gives you the choice of including buoyancy or not in plot of bottomhole dynamometer pump card.

If you input pump resistance then the bottomhole effective loading without buoyancy will be below the zero line.

However this program does not plot out any tendency to buckle over the entire length of the rods as such you can miss buckling tendency as was found in the problem shown here.

Summary: • Program A presents the bottomhole dyno card in terms

of True Loads making one think compression is high at the pump but then shows a plot of tendency to buckle showing the real situation of buckling over the rod string.

• Program B shows the bottomhole card in terms of Effective Loads and if negative shows input loads tending to buckle rods at pump.

• Program C allows user to input either True or Effective loads for the bottomhole Dyno card but does not allow a plot over the entire rod string and as such, you could miss calculated rod buckling from dynamic effects uphole from the pump.

Program D: Accurate for conditions input: Shows bottom card as effective load, no input for incomplete fillage, rod

loading not presented with depth

At bottom, no external loads: Po = 100 + .433*5000 = 2266.5 psi A=.442 sq in, Ac = 1.095 PA=2266.65*.442*1.095=1097 psi Ttrue = -1097 lbfl Teff=True+PoAO= -1097 + 1097 = 0.00 lbfs

Ptb=100 psi Size 8 .7584in2

Ac= 1.0906 2.904 #/ft L=1539’ Size 7 .601 in2

Ac= 1.0902 2.223 #/ft L=1596’ Size 6 .442 in2

Ac= 1.095 1.633 #/ft L=1865’

Po = 100 + .433*3135 = 1457.5 psi Teff = True + PoAo True = 1865*.442 – 1097 = 1948.54 lbf Teff=1948.54 +1457 *.442*1.095=2654lbf

∆A=(.601*1.092-.442*1.095)=.1723 in2

PoAo=1457.5*1723 = 251.13 lbf Teff = Ttrue + PoAo Ttrue = 1948.54 -251.13 = 1697 lbf Teff = 1697 +1457.5*.601*1.0902= 2652.4 lbf

P = 100 + .433*1589 = 766.387 psi Teff = True + PoAo Ttrue=1697.4 + 1596*2.223 = 5245.3 lbf Teff= 5245.3 + 766.387*.601*1.0902=5747.4 lbf

∆A.7854*1.0906-.601*1.0902 = .201 in2

PoAo = 766.387*.211=154 lbf Teff = True + PoAo Ttrue = 5245.3-154 = 5091 lbf Teff = 5091 +766.387*.7854*1.0906=5747.4 lbf

Ttrue = 5091 + 1539*2.904 = 9560.3 lbf Teff = True + PoAo Teff = 9560 + 100*.7854*1.0906 = 9645 lbf

Wrf = Wra(1.-.128γ) - PoAo = 11062.7 ( 1.-.128) -100*.7854*1.0906 = 9646.6 -85.65 = 9560.95 lbf

If PR 1/8 larger then PRL = 9560 –100*(.994-.7854)1.09=9537 lbf Not adding wt/ft x length up to load cell

Static True/Effective Loads on Tapered Rod String

An example calculation showing true and effective forces.

True forces are actual forces but effective force have the buoyancy effects removed to see tendency to buckle in the rods.

See: “Beam Pump Rod Buckling and Pump Leakage Considerations.”By: James C. Cox, Texas Tech University, H. Nickens, BP, J. Lea, Texas Tech University2004