SPE
SPE 21665
Dynamic Behavior of the Sucker Rod String in the Inclined Well
SA Lukasiewicz, U. of Calgary
Copyright 1991, Society of Petroleum Engineers, Inc.
This paper was prepared for presentation at the Production Operations Symposium held in Oklahoma City, Oklahoma, April 7-9, 1991.
This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of t~e paper,
as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the aut~or(s). The ma~erial. ~s presen~ed~ does no! necessanly ref!ect
any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE f!leetlngs are sUbjec.t to publication reVIew by Edltonal C0!l1mlttees of the Society
of Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. illustrations may not be COPied. The abstract should contaIn conspicuous acknowledgment
of where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836 U.S.A. Telex, 730989 SPEDAL.
ABSTRACT
2.
The paper presents a model for predicting and
analysing the behaviour of sucker rod pumping
installations in the inclined wells.
This model
incorporates the dynamics of the curved sucker rod
string, and the friction forces resulting from the
contact of the rod with the tubing through a system
of two partial differential equations. This system
of equations is solved by the finite difference
technique. The model predicts the polished rod and
pump dynamometer cards and incorporates the effects
of fluid inertia and viscosity.
The model is
capable of simulating a wide variety of pump
conditons, and geometry of the rod string.
The
examples and comparisons with the results obtained
using a program for vertical wells to analyse the
deviated well are presented.
The
information
predicted by the model is useful in the design and
operation of sucker rod pumping installations.
The application of powerful personal computers
makes possible an effective numerical representation
of the rod pumping system even for more complex
problems such as the behaviour of the sucker rod
string in the deviated well.
An accurate prediction of the performance of
the sucker rod string requires careful modelling of
the dynamic behaviour of the rod which has to
satisfy the dynamic boundary conditions at the
polished rod and at the pump.
Let us consider a deviated rod in the curved
tubing in a vertical plane (x,z) (Fig. 1).
If we
assume that the rod is supported by the tubing only
at the points where couplings are installed, then
the reaction forces between the tubing and the rod
are the concentrated forces. If the rod lies on the
tubing, the reaction forces are distributed along
the length of the rod. The radius of the curvature
of the tubing is a function of the depth, and is
defined as R. Considering the equations of equilibrium of tife forces acting on the element of the
rod, ds, in the axial direction and the perpendicular direction to the rod, we obtain the following
system of differential equations.
The equation of the motion in the direction
tangential to the rod is
1.
INTRODUCTION
Rod pumping is still the most widely used means
for artificial lift in oil wells.
At present many
wells are designed as deviated wells with the
setting angle reaching 60°.
The dynamic behaviour,
of the sucker rod string in a deviated well is
different from that in a vertical well due to
several reasons.
One of them is the friction
between the rod and the tubing.
The other is the
curvature
of
the
rod
string.
The
curvature
causes the lateral displacements of the rods.
It
also couples longitudinal vibrations with transverse
vibrations.
Due to the axial forces in the rods
(particularly compressive forces at the bottom of
the well which can produce the buckling of the rod)
the problem is nonlinear and thus difficult to
solve.
MATHEMATICAL FORMULATION
2
as
a u
as - Ay --2 + ygA cos
at
~
'I'
_
n
au _ F = 0
at
t
'
(1)
where S is the axial force in the rod,
u(t) - axial displacement,
A
rod cross-section,
y
rod material density,
g
acceleration of gravity,
ep
- angle of the inclination of the rod
string,
n
viscous damping coefficient
F
friction force acting on the rod from
t
the tubing,
s
length measured along the curved rod,
t
time.
References and illustrations at end of paper
313
DYNAMIC BEHAVIOUR OF THE SUCKER ROD STRING IN THE INCLINED WELL
2
The
second
2
EI _Cl_
2
Cls
equation
motion
of
in
the
direction
2
2
~+.!.... ] + YA~+ n +
t
2
Cls 2
Rex
Clt
n
p
+ n
THE BOUNDARY CONDITIONS
The boundary conditions for the sucker rod
string were discussed in detail in numerous papers
[2,3]. In general the following boundary conditions
must be
satisfied.
At
the polished rod the
displacements and the velocities of the moving arm
must be equal to the displacements and velocities of
the rod.
At the pump, the loads acting on the rod
must equal the forces acting on the pump.
Clw
t
at
+ ~ - ygA sin ~ ~ 0
R
(2)
PaCt) + Pf(t) + Pv(t) + P
where wet) - transverse displacement of the rod,
- bending stiffness of the rod,
EI
- viscous damping coefficient in the
nt
lateral direction,
- transverse normal force resulting from
the reaction of the tubing. If the rod
is in contact with the tubing, this
force is greater than zero.
n
- transverse normal force due to the fact
p
that th~ curved rod is Burrounded by
the liquid under the pressure p.
Moreover, we have the following additional
equations.
The bending moment in th~ rod,
where
P
Actual radius of curvature,
1
(4)
The normal force n
caused by the pressure of
the fluid is:
p
11
p
Equations (2) and (6) create a system of two
coupled nonlinear differential equations of fourth
order which can be solved rigorously using only the
iterative
numerical
techniques.
Replacing
the
derivatives by the finite differences, we can solve
the above equations together with the initial
conditions reducing them to the system of algebraic
equations. The integration with respect to time can
be obtained using explicit Runge-Kutta algorithm.
As we are mainly interested in the steady-Btate
solution, the method of finite Fourier transform can
also be used.
It, however, requires iterative
solutions due to the nonlineariti~s introduced by
the relations between the times for the valve
openings and motion of the plunger.
Also the
friction forces introduce nonlinearities due to the
fact that they change the sign with the change of
the direction of the velocity.
R
ex
I'
the
The force n changes th~ sign with the curvature of
the rod (it Pis straightening the rod) and always has
a stablizing effect.
The axial force,
Ao ~ AE [ClU + ! (Clw)2]
(5)
Cls
2 Cls
'
where 0 - normal stress in the rod,
E - Young's modulus of the material of the
rod.
=
Introduction of the force S into Eq. 1 gives
2
2
2
Cl u
Clw Cl w
1
Cl u
.!L Clu +
AE Clt
+
Cls 2
a2
;;z as
+
II
E
- a force required to accelerate the
fluid above the pump,
- friction forces in the pump,
- viscous forces along the rod and
at the pump,
- a force representing the fluid
load acting on both faces of the
plunger during the pumping cycle.
£E-
where p is the pressure of the liquid and
radius of the cross~section of the rod.
S
(t),
NUMERICAL SOLUTION
2
n
P
p
All these forces can be determined as the functions
of time and also as functions of the times for which
the valves in the pump close and open. These times,
are the functions of the position of the plunger.
The
acceleration
force
P
can
be
determined
analysing the motions of theafluid column above the
plunger.
The other conditions imposed on the rod
string result from the fact that the rod moves in
the
tubing
which
prevents
its
free
lateral
displacement.
When the rod deflects in such a way
that it comes into contact with the wall of the
tubing, further deflections are constrained and the
rod changes its relative longitudinal stiffness. At
this moment the friction force resulting from the
contact appears.
(3)
R
SPE 21665
;;Z
F
t
cos ~ - AE
o
ROD CONTACTED WITH TUBING
If the rod is supported by the tubing along a
certain length, the transverse displacement of the
rod is zero in this area. Let us examine this case
first.
From the equilibrium condition (2), with w = 0,
we have
(6)
where a = Iy/g is the sound velocity of the rod. We
see that the second term in this equation is
nonlinear and pr~sents the effect of the change of
the
axial
displacement
due
to
th~
vertical
deflection.
n = ygA sin
314
~
S
- R
(7)
Assuming that the friction in the tubing
proportional to the normal force n, we have
energy and work done by the axial and lateral
forces, the following formula for the coefficient
f in Eq. (13) is obtained.
.
1
R. 2
is
(8)
F
0,
(9)
where ~ = (D-d)/2 is the space between the rod and
the tub3.ng, where D - diameter of the tubing, d the rod diameter.
When the force S,. S<O, becomes
the compressive force,
the distance R. can be
obtained calculating the deflection of the rod and
by comparing it with the allowable space in the
tubing.
The above equations can be used to define the
condition for the contact of the rod and the tubing
and also to calculate the so called "equivalent
axial stiffness".
The concept of the equivalent
Young modulus can be introduced to account for the
effect
of
the
lateral
displacements
while
calculating the axial displacements. - The equivalent
modulus of elasticity of the curved rod E can be
found from the equation
e
ROD SUPPORTED BY THE COUPLINGS
If the rod is not supported along its whole
length, but only' at certain points where coupling
are placed, the lateral deformations w of the rod
are possible. The rod vibrates transversly together
with the longitudinal vibrations.
To simplify the
calculations, we can introduce several additional
assumptions.
It can be proved that usually the
natural frequency of rod lateral vibration is lower
than the natural frequency of the longitudinal
vibration.
This
effect
makes
possible
the
separation of the two fundamental Eqs (1) and (2)
and application of the assumption that the period of
forced lateral vibrations corresponds to the pumping
frequency. Then Eq.(I) can be solved independently
from Eq. (2) . However, due to the curvature of the
rod and its lateral displacements, its effective
longitudinal stiffness changes and becomes smaller
as compared to the stiffness of the straight rod.
The solution of the second equation of motion,
Eq.(2), can be achieved approximately applying, for
example, the Galerkin method or by using the
Hamilton principle. If the curved rod is supported
by the wheeled couplings it will laterally deform as
presented
in
Fig. (2) .
For
example,
we
can
approximate the deflection of the rod by the series
k
E
n-l
~s
f + f sin ~ + f sin
2
1
o
2~s
-r+
cr
where S
=
4~2EI/R.2 + 2~r2p is the critical
bucklingcYorce for the rod submerged in the liquid
and S is the axial force in the rod.
If the rod segment is under a tensile force,
S>O, the rod straightens and comes in to contact
with the curved tubing. To prevent that contact the
guide or wheeled coupling should be installed there.
The minimal distance between the guides can be
,obtained for this case from a simple geometric
relation (the weight of the rod is not here
included),
R. < 8Rt:.
min
c
which can be solved with respect to u. The solution
of Eq. (9) for the case when we can assume that the
rod is in contact with the tubing along its length,
can be obtained using finite Fourier transform.
In
this case Eq. (9) becomes a quasilinear, partial,
differential equation.
Imposing the boundary conditions for the ends
of each rod segment, we can create the solution for
the tapered rod string. This solution together with
the boundary conditions for the top and the bottom
of the rod can be used to model the behaviour of the
tapered rod string in the zones where the rod
contacts tubing in a deviated well which is of
rather a smooth and small curvature.
=
(14)
8R
Introducing this relation into Eq.(I) and using Eqs.
(4 and 5), we obtain the following equation
a2u 1 a2u
as 2 - a 2 at 2
w(s)
3
S. Lukasiewicz
SPE 21665
E
= E/(1
e
+
~un/~u),
(15)
where ~un is the elongation of the rod due to the
change of the curvature and ~u is the axial
elongation corresponding to the same force level.
~u
1 JR.
n
2
'2
(16)
0 (w) ds.
Then E can be used to linearize Eq. (6) from
which we cag remove the second nonlinear term. The
above set of equations (14 and 15) can be used to
model the behaviour of the rod string when it is not
in contact with the tubing.
The solution can be
obtained using iterative technique.
Equations Eq.
(13) and Eq. (14) make it possible to find the
maximum
distance
between
rod
couplings
which
prevents the contact of the rod with the tubing.
(13)
MODEL IMPLEMENTATION AND RESULTS
A computer program SRPUMP based on the above
discussed equations was developed and used to model
the behaviour of the sucker rod string in the
deviated wells. The results were compared with the
results obtained from the program for vertical wells
applied for the same case.
where R. is the distance between guides or wheeled
couplings; In the case when the rod has no guides R.
is a certain characteristic length of the wave of
lateral deflection of the rod in the tubing, f
is
the
parameter which
defines
the
initial 0 rod
deformation.
f l ' f , _ are the unknown parameters
defining the lateral aeflections.
The equilibrium of the rod is given by the
equation CU = 0 where U is the total potential
energy of the system.
Calculating the bending
Evaluation of ,Existing Well
Fig.
315
3
presents
the
geometry
of
the
well
DYNAMIC BEHAVIOUR OF THE SUCKER ROD STRING IN THE INCLINED WELL
4
obtained from measurements. The rod is not exactly
straight. It is slightly curved. The corresponding
data are collected in Table 1.
In this table, the
radius of curvature of the rod string and the
recommended distance between wheeled rod couplings
obtained from Eq.(13) and (14) are presented.
Fig. 4 presents the distribution of the friction
between the rod and the tubing which is the function
of the weight of the rod and its curvature.
Fig. 5 presents a polished rod displacement
diagram obtained from measurements.
Fig. 6 shows
the calculated bottom-hole load displacement diagram
(continuous line) calculated using the developed
program and load displacement diagram predicted by
the program for the vertical well (asterisk).
The comparison shows that the developed model
is able to create a more precise bottom-hole
load-displacement diagram.
In the examined example
the pump is in a hitting up condition. Applying the
program for the vertical well to analyze the
behaviour of deviated wells (a common practice
nowadays), incorrectly indicates that total friction
concentrates
at
the
plunger
whereas,
it
is
distributed along the rod.
This leads to further
errors in the calculations of the stresses along the
rod string. It also may cause erroneous conclusions
related to the stability of the bottom rods.
We
see that the program for the vertical well is not
able to detect the peak of the load when the plunger
hits the pump. However, it is clearly seen from the
results obtained from the developed program that the
pump works in hitting up conditions.
Fig. 7 presents the comparison of balanced
torques.
We see a substantial difference between
the distribution of the torques obtained from both
programs. We see that the angle of inclination of
the rod string has an important effect on the
calculated value of torques. It is clear that these
calculations can not be simplified, assuming that
the rod is vertical.
Fig. 8 shows the geometry of the deviated rod
string with the local deviation from the straight
line. The results for this configuration are given
in Table 2.
Corresponding friction forces are
presented in Fig. 9. We observe that these forces
change rapidly in the area of strong curvatures.
This is the result of the fact that the rod string
comes into contact with the tubing there.
The
contact forces are larger in certain zones along the
length of the rod. That has an important effect on
the
stresses in the rod
string and on its
elongation.
SPE 21665
Analysis of Inclined Wells
The program was used to analyze the effect of
several factors on the performance of the inclined
well. The results of the calculations are presented
in Figs. 11-16. The geometry of the wells is shown
in Fig. 11.
Several different types of wells are
examined.
Fig.
12
shows
the
change
in
the
production rate for two straight wells with the
inclination angle. In the case of the small depth,
little change is observed with the change of the
angle.
Fig. 13 shows the relations between the
safety factors and the polished rod horsepower and
the angle of inclination.
We see the stresses in
the rod decrease with the angle, however, the power
requirements do not change much.
Fig. 14 presents
the relation of the production rate for different
inclination angles and
the different
friction
coefficiellts.
Fig. 15 presents the effect of the
viscosity on the production rate.
Figs. 16-18 show the comparison of the results for
different
shapes
of
the wells.
The
general
conclusions which can be obtained from the above
analysis are that the safety of the rod increases
and the production rate decreases with the increase
of the deviation angle.
The effects of the
deviation of the well are more important for deep
wells.
REFERENCES
1.
2.
3.
4.
DESIGN AND PREDICTION
The developed model was applied to the design
of the new wells and to predict the behaviour of the
existing wells.
A number of wells were examined.
The results were compared with the data obtained
from the measurements in the oil fields in Alberta.
Some of these results are shown in Table 3.
Also
shown in these tables are comparisons of computer
predictions and actual results for rod loading and
fluid production on the surveyed wells.
These
comparisons show that the computer program was able
to predict surface rod loadings and production note
with a high degree of accuracy of no less th~n 10%.
The program predicts also the polished rod diagram
with good accuracy. (see Fig. 10)
316
Gibbs, S.G. "A Review of Methods for Design and
Analysis of Rod Pumping Installations", Journal
of Petroleum Technology, pp. 2931-2940, Dec.
(1982).
Doty, D.R. and Schmidt, Z. "An Improved Model
for Sucker Rod Analysis", Society of Petroleum
Engineers Journal, pp. 33-41, Feb. (1983).
Everitt, T.A., and Jenning, J .W •• "An Improved
Finite Difference
Calculation of
Downhole
Dynamometer Cards for
Sucker Rod Pumps",
Transactions of
the
Society of Petroleum
Engineers SPE 18189, pp. 83-94.
Jacobs, G.H., "Cost Effective Methods for
Designing and Operating Fibeglass Sucker Rod
Strings",
Transactions of
the
Society of
Petroleum Ellgineers, SPE 15427, pp. 1-8.
SPE
21665
x
y
wheeled coupling
q :: }'g A ds
t: ." :t
U
F
Fig. 1
ds +np.ds
(m)
0.0
-185. f
(N/m)
~
-370.3
~
'~
-555.4
-740.6
0.0
Fig. 3
Normal Deflections of the Rod in the Tubing
Fig. 2
Geometry of the Rod String and Equilibrium
of the Forces Acting on the Element of the
Rod
186.7
213.5
~
320.2
( Ib/ft)
1.62
O.H
1.28
0.09
0:93
0.06
0.58
0.04
0.24 ~-_...l-_ _----L_ _-L.L-_ _..J 0.02
0.0
2t3.8
427.6
64..3
855. f (m)
427.0 (m)
Geometry of the Rod String, Example 1
Fig. 4
317
Friction Forces Along the Rod, Example 1
( Ib)
(Ib)
5968.0.---......---.,-----,----....------,
Hitting up
1500r--.,------,---,-----.,---.,.,
5223.0 1-I--..L--I-----=-+-~-___=l>o.L..-~_..!Ljf
500~-+---_+---1_--+_-____a
4478.0 H-----+----+----+------H
/
~
0 iX
jl
3733.01------+----+-----+----+--1
i~
I?'
-500 i-r
~
i~
ill:
298S.0 L -_ _
0.0
45.0
---l.._~_-IoL_~_J.....JL
_
90.0
135.0
I:
____I
IS0.0 (em)
-1000
-1500
If-
1--0. _ _
-
rr
I ~~1\
0
polished Rod Load - Displacement Diagram
Fig. 5
.J
40
~
~
V
~
SO
160 (em)
120
Plunger Load - Displacement Diagram, solid
line - results from the model,
Results
from th~ program for v~rtical well
used to evaluate the inclined well,
Example 1.
Fig. 6
*
EXMPLE 2 - IIELL GElJIETRY
( in/lb)
[ft)
,"".,.,
500001--+......,....~----1'rF~.y-+-----1
I
!
250001---~~+-----+------\-r----j
-617
J
!
"
"--
' ' -..
1""
',,--
I
,
I
Ol-~-+----f--+---tt\----j
---+----1
!
I
-1852.1;-'
J
-2469 ...
--.l.____
.8
183.8
1116.1
S1aiftlPrtSc=Pri.t Scree.
Enter=Contillle
-750000L---.!J9.!O------I1S-0---2...J7'-0--....3....60 (deg)
Fig. 7
Gearbox Balanced Torque, solid line
presents results from the model,
results
obtained from the program for vertical
*
Fig. 8
318
1',,",,
I """, I
I
'.",1 [ft)
12ll'J.1
1612.1
Xthen Enter=Escape
Geometry of the Inclined Well Intentionally
Distorted, Example 2
SPE
Well a
EIltiIIPLI 2 - RICTllIIlIJID IE1IlEIII D ".. 1IJIE
.
1•
mAt)
£!hj
21665
- FORCE us. DISI'I.ACmEIlT DIAGIIAI1S
S635.~--..,...-~---.----.,-------.
PREDICTED
~
I
-
I
_\.
j\}J IV l
---743.6
.8
SIliftJfrtSc=Print Screen
Fig. 9
1487.1
Enter=Conti_
~
22311.7
1ft)
-78Z.~=~=.b~ _ _.L--==="""'===-------.J(in.l
2974.2
-2.1
11.9
Xthen Enter=Escape
25.9
48.8
54.8
SlIIFACE DYIWiRllPIl FROM MEASUREMENTS
Distribution of Friction Forces Along the
Rod, Example 2
18
Fig. 10
78
28
Predicted and Measured Polished Rod
Diagram, Comparison for the Inclined Well.
6500 ft
_----------+-----,~x
I
200ft
I
constant
I
two parabolic curves
in connection ( 45° P. Rod)
Liquid Level
2000 ft
-"
I
I
I
I
45° Straight
0.875
0.750
Three
Sections
in Equal
Lenoth
0.625
I
I
30° Straight
I
I
Parabolic
(0° P. Rod)
I
Fig. 11
Geometry of the Examined Wells, Depth of
all Wells 6500 ft.
319
0.500
SPE
,
.8.0
7.0
400
>.
.g
,
(J)
-
6.0
Q)
/f
c
-
1.2
b
U
~
0
300
5.0
( ,)
If
.2
•
( ,)
::t
£
C
3000ft well depth
6500 ft well depth
~
CI
(It
200
0
Fig. 12
1.00
50
10
20
30
Angle of Inclination of Straight
10
20
40
30
50
Angle of Inclination
(Straight Well only)
Fig. 13
Production Rate versus Angle of Inclination
for Straight Wells for Two Different
Depths.
Relation Between Safety Factors and Angle
of Inclination.
Co)
I\)
o
500.
.10.0
Q.
-
~
~
400
~
lD
_---0- ___ -- _______
.c
-0
--- ------
8.0
L-
I
0
200
0
0
;:
(,)
0
~
6.0 a:
.ea
::t
0Q)
a:
~
i
'3
.. 300
c
~
f
100
L-
a.
0
Fig. 14
a:
2.0
~
Ql
~
CIl
50
Production Rate for Different Coefficients
of Friction versus Inclination Angle.
a
+=
(,)
Production Rate
Friction Coeff. =0.05
---- Friction Coe". =0.1
10
20
30
40
Angle of Inclination for Stroight Wells
~
~
A
~
2
8.0 ~
w
"
8
6.0 0
&.
LQ)
C
a:
5
0
~
,
_ 300
200.
~
L-
a.
tOO
0
4.0
----------A...,
""" ..... ...
.....
::t
'8
--Viscosity = 10cP
---- Viscosity =100 cP
to
0
20
""''- .....
30
2.0
.....
Effect of the Viscosity
If
~
~
Q)
""' .......... ....
40
Angle of Inclination for Straight Wells
Fig. 15
Q.
~
c
"
400
4.0 a.
Polished Rod Power
10.0
~
-,,
~
~
CIl
'0
o a.
50
21665
SP.E 21665
Safety Factor
Polished Rod Power, hp
Sofe~
Factor
Polished Rod Power, hp
1.3
8.0
t.3
8.0
1.2
7.0
1.2
7.0
U
6.0
f.t
6.0
i.O-+--..IL.LC£A""""""
5.0
_,---L~ill~.5.0
t.0 -+-_~:.LJ:l~
HOOO
tl000
500
tOOoo
500
400
9000
400
300
8000
300
200
i 00 -,---,~;".a,.;......,.""
7000
200
6000
1 0u-'--'-'.4:-'~"""
B/day
ProductIon Rate
D
~ Straight
Straight
Vertical
~ 20° inclination
11Im
mY
~ Parabolic
~ 0° P. Rod
Fig. 16
Total Rod Weight,lbs
10000
Parabolic
40° P. Rod
~ Parabolic
Comparison of the Results from the Model.
The Inclined, Curved and Straight Wells
(see Fig. 11) (Small Deviation)
TABLE
1
DEPTH
ALONG
THE ROD
m
m
O.
43.
85.
137.
196.
248.
278.
322.
374.
419.
471.
523.
568.
620.
658.
718.
740.
TABL~
RADIUS
MAXIMUM
ROD
OF
SPACING
DIAMETER CURVATURE OF WHEELS
mm
O.
51.
103.
162.
231.
291.
325.
376.
436.
487.
547.
607.
658.
718.
761.
829.
855.
Comparison of the Results Obtained for the
Inclined, Curved and Straight Wells (Large
Deviation)
Fig. 17
DEVIATED HOLE VALUES
VERTICAL
DEPTH
Parabolic
45° P. Rod
~ 0° P.Rod
m
31. 750 10000000.
22.100
2254.
22.100
723.
19. 050
3545.
19.050
2021.
19.050
15056.
19.050
3412.
19.050
12837.
6269.
19.050
19.050
3149.
19.050
9994.
19.050
1267.
19.050
1372.
19.050
2416.
19.050
5230.
19.050
2311.
19.050
12771.
m
10.
21.
25.
25.
32.
22.
26.
22.
24.
26.
24.
32.
30.
26.
26.
26.
26.
DEVIATED HOLE VALUES
2
VERTICAL
DEPTH
DEPTH
ALONG
THE ROD
m
m
O.
30.
75.
121.
168.
223.
277.
321.
371.
421.
466.
510.
562.
606.
652.
706.
MAXIMUM
RADIUS
OF
SPACING
ROD
DIAMETER CURVATURE OF WHEELS
O.
36.
91.
145.
199.
263.
326.
381.
444.
517.
562.
616.
680.
734.
789.
852.
mm
m
31. 750 10000000.
2851.
19.050
2200.
19.050
1878.
19.050
26658.
19.050
19.050
5309.
19.050
395.
310.
19.050
152.
19.050
37.
19.050
40.
19.050
317.
19.050
750.
19.050
1075.
19.050
1204.
22.230
22.230
6839.
TABLE 3
Well Comparison
Number
Depth
of Strokes Vert. Horiz.
(n/min. )
(ft. )
Summar~
ProductioI
Measured
Inclined Wells
Rate
Calculatec
(B/Day)
Peak PRL
Meas. Calcul
(lb)
Max.Torque
Meas. Calcul.
(in/lb)
l.
17.33
1042
519
452
449
2792
3042
23611
21813
2.
9.5
1222
490
215
233
3056
3304
28676
28409
3.
12.68
1960
660
304
290.5
5936
5874
57872
53584
4.
14.20
1744
652
325
338
6331
5875
65038
57030
321
m
10.
31.
42.
67.
22.
26.
14.
13.
9.
4.
5.
25.
41.
30.
27.
24.