Optimal Spacing For Casing Centralizer PDF
Optimal Spacing For Casing Centralizer PDF
Optimal Spacing For Casing Centralizer PDF
Casing Centralizers
H.K. Lee, SPE, Amoco Production Co.
R.C. Smith, SPE, Amoco Production Co.
R.E. Tighe, SPE, Amoco Production Co.
Introduction
Centralizing the casing in the borehole is essential to ob- The equations presented in API Specification 10D sum-
tain effective cement placement around the casing string. marize the forces that act on a centralizer as follows.
This is particularly true for deviated holes. Spring-bow
centralizers or positive-standoff devices improve the Ws j sin 0 j + Ws j+ 1 sin 0 i+ 1
cement-flow pattern for better mud displacement and pro- - - - - - - - - - - - +2T sin 0 j
2
vide better cement-sheath coverage around the casing cir- Nj=-----~----------- . (1)
cumference. Most flow calculations relating to mud cos OJ
displacement efficiency assume the casing is centered in
the wellbore. and
It is necessary for the engineer conducting casing-
Tj-l
cementing operations to integrate the axial and weight load Tj=cos OJ +WSj cos OJ
[
forces and the bending forces caused by hole curvature cos OJ-1
into a centralizer placement schedule that provides ade-
quate pipe standoff based on the restoring force exerted
by the centralizers. sjsinO ]
+W 2 (tan oj-tan OJ-I) ........... (2)
API Specification 10D 1 contains a recommended
procedure for the calculation of lateral forces exerted by
the casing on centralizers in a two-dimensional (2D) in- At 0,
clined borehole. We present an approach that permits anal-
yses for 3D borehole trajectories and provides a complete Nj=Ws sin 0+2T j sin OJ ................... (3)
design for centralizer placement. The algorithm used in
the centralizer-spacing program is based primarily on API and
Specification 10D for lateral-load calculation. 1,2 It uses
Lubinski's 3D dogleg-severity criterion for handling the Tj=Tj_ 1 +WS cos OJ ....................... (4)
curvature changes in the borehole. 3 In addition, the ef-
fect of buoyancy on casing weight and the effective lateral The equations used in API Specification 10D are based
load on centralizers are considered in the spacing al- on Ref. 2. Use of the positive or negative sign before the
gorithm. Furthermore, pipe deflection (sagging) between tension term or tensile: load depends on the direction of
the centralizers is analyzed with Timoshenko's method 4 the dogleg. The positive sign is used in the API's publi-
to arrive at the effective standoff clearance. cation to arrive at a consistently conservative figure for
the force on a centralizer because of the various unknowns
Discussion in a typical deviated hole-e.g., the degree of angle
change between two survey points.
The lateral load imposed on a casing centralizer is the
combined effect of centralizer spacing, casing weight,
Buoyancy Effect on Casing Weight
hole-inclination angle, hole curvature, and tension from
the pipe hanging below the centralizer. It is appropriate to use the effective casing weight rather
than the air weight of the casing as presented in API Spec-
Copyright 1986 Society of Petroleum Engineers ification lOD; Le., the buoyancy effect on the casing string
caused by the density of drilling mud is considered. The Referring the hole curvature to a standard length of 100
buoyancy factor and effective weight of casing can be cal- ft [30.48 m], Lubinski 3,6 introduced the term dogleg
culated as follows: severity in connection with his well-known contribution
to analysis of drill string fatigue.
Fb= (1- Pm)Ps
........................... (5) Total hole angle 20 and the radius of the hole curva-
ture r are interrelated by the following equation. Let
!lL=r20.
and
Then
We = (Fb)(Ws ), ........................... (6)
With the dogleg severity calculation, the capability of Casing Deflection Between Centralizers
the API algorithm is enhanced to handle 3D curved
The approximate sag (maximum downward deflection on
boreholes.
the casing between centralizers) of pipe is given by the
Calculated results from both 2D and 3D algorithms are
following equations, which are based on Timoshenko's4
shown in Tables 1 and 2. Results indicate that the 3D data
analysis for a tie rod under uniform lateral load with ten-
that consider the variation of the borehole azimuth will
sion force. The maximum deflection, Ymax, occurs at the
generate greater dogleg severity and accordingly require midpoint of the casing string between centralizers-Le.,
closer centralizer spacing.
Ymax =(Y)x=tl2, where is the centralizer spacing.
Effective Lateral Force on Centralizers 1 u2
---1+-
(3845D ' [COSh 2]
If the 3D effect of the borehole curvature change is ig- 4
nored, a decrease in the calculated lateral load caused by N eS ) u
... (13)
the method used in Ref. 2 for dogleg-severity calculation Ymax = (5/24)4
results. This can make a significant difference in the num-
ber of centralizers required in the upper part of the hole. and
With the 3D dogleg-severity calculation, the algorithm
gives a better approximation of the curvature effect on S2
borehole. The effective load is defined as the root mean U= (Te )Ih, .......................... (14)
square of the gravitational, hole-curvature, and axial-load 4EI
forces.
where E=30x 10 6 psi [206.8 x 10 3 MPa].
N e =[(We )2+(Te )2J'h, ................... (10)
...
0.9125 3.3 NI7E
584'.0 0.50" '.0 NIt E
1 Centralizer/Jt (40'):3000'-TD 5937.0
e030.0
8122.0
0.5C35
0.0000 '.0
NICE
NnE
0.0000 '.0 NnE
5214.0
.....
0.2274 '.0 NnE
e30M 0.5882 '.0 N 71e
8399.0 1.1505 NnE
6491.0 14144 N'3E
8583.0 1.4288 e. N 75
8675.0 0.&307 7. NilE
6788.0
68110.0
6952.0
0.7924
0.827' 7'
'.0
NeH
N5IE
15816 7.3 NICE
7065.0
1151.0
72....0
18722
29650
3.2625
,.7e
9.3
N 73
N'H
snE
73410 21206 10.3 SUE
7433.0 11735 11.3 SOlE
75250 '."22 12.3 551 E
76110 1.2073 13.5 5 ..1
77090 15039 14.5 547
7801.0 0.1677 15.5 S43E
78930 03042 '8.3 S44E
79650 0._ 16.3 S43E
10780 008119 18.0 S43E
81100 0392e 15.0 S43E
e... o 0.3928 15.3 S44E
113540
.,..60
0.2717
0.2717
'.0
14.8
545
S45E
85380 0.0000 14.5 5.5
eeoso 0.0000 '4.5 S45E
5000
5500
6000
-
-~-=
~
po-.
~--.
~
-==--:-
~. r===,. ))
_6500'
:s
:$7000
a.
Q)
Cl
c= ~c
-<
"l
'k--
~
~.
--~
~
.5
~
-
r
I-'"
7500
-
~
8000
t--
8500 I~
~
9000
0 200 400 600 8000 100 0 0.2 0.4 0.6 0:.
Lateral Load per Joint (Ib) MiIIvoIts Stand-Off (fraction)
the dogleg severity and lateral and axial loads on the cen- values of restoring force for various casing/hole size com-
tralizer. It also computes the standoff in the annulus, the binations are listed in Ref. 1.
spacing, and the number of centralizers required for each The variation of the lateral load generally reflects the
borehole section. The program generates lateral load as dogleg severity effects in the borehole (see Fig. 3). The
well as a standoff diagram when constant spacing is re-. lateral load tends to deflect the pipe, whereas the tensile
quested. If the variable-spacing option is exercised, a spac- force tends to straighten the pipe and counter the sag
ing diagram instead of standoff diagram will be generated deflection. Therefore, with a slant hole that has constant
by the program because standoff is the predetermined pa- dogleg severity-Le., both inclination and azimuth angle
rameter specified by the user. are constant-the casing near the bottomhole requires
closer centralizer spacing than that in the upper hole be-
The restoring force is the force exerted by a centraliz-
cause of the lower tensile effect near the bottom.
er against the borehole to keep the pipe away from the The sagging (deflection) prediction is based on the com-
borehole wall. API assumes that bow centralizers will bination of lateral load and tensile force from the pipe
deflect one-third of the theoretical radial clearance while hanging below the centralizer. In the determination of
the specified restoring force is developed. The actual minimum standoff, the sag deflection is additive to any
restoring force should be provided by the manufacturer lateral deflection in the centralizer that occurs in the de-
through a standard testing procedure. The API minimum velopment of the centralizer restoring force.
f ~'~-r-
.""':'" --;:-
3~r---+---+-~+~--~~-~'---~~I----+---+---~---~
4000r--~---+-~-+---- I----+--_/~--+--+---~--I
4~0~-~2~OO---~400~--~600*---~800~0~--~----~~0~-~0.-2--0~.4--~O~.6--~O.8
Lateral Load per Joint (Ib) Millivolts Stand-Off (fraction)
1500,...------r----r------,
'~
.....,..... r--...,..--...,..--...,..--....
r---.,...........=/. ~
45OO~0----~*----~---~~---:~-'~-"~~----~I~--~-----+--_I~----~
500 1000 1500 0 100 0 0.2 0.4 0.6 0.8
Lateral Load per Joint (Ib) Millivolts Stand-Off (fraction)
predicted for the 3D trajectory. Because pipe deflection formation signals from TD to 2,600 ft [800 m], except
is a fourth-power function of the lateral load, however, for the interval between 2,750 and 3, 100ft [840 and 950
the decrease in standoff was only 10%. Generally, the m]. In this well, the hole inclination is almost constant
centralizer spacing of one per joint was adequate; in con- and the lateral load and standoff are very uniform.
junction with other cement-placement practices, a good Fig. 5 shows the centralizer-program information for
cement job was obtained. . San Andres completion in New Mexico. At 3,650 to 3,750
The example shown in Fig. 4 is an offshore well with ft [1110 to 1140 m] there is a 0.8 /100-ft [0.8/
good gauge 12%-in. [31.4--cm] hole and uniform 20 hole 30 .48--m] change in hole inclination and a 4 /1 00--ft [4 /
inclination throughout the cement--casing interval. An in-- 30.48-m] 3D dogleg. Similarly, there is a 1.5/100--ft
flatable ECP was placed between 3,360 and 3,400 ft [1020 [l.5 /30.48-m] change in hole inclination at 2,250 ft [690
and 1040 m] to cover the primary completion interval. m], while a 7.4/100-ft [7.4/30.48-m] dogleg is indi-
Centralizers were run at an interval of one per joint be-- cated for the hole trajectory. Reduced standoff is predicted
tween 2,300 and 3,448 ft [700 and 1050 m]. The wave- for both locations. Below 2,750 ft [840 m], the program
form display on the cement bond log (CBL) showed good predicts more than *-in. [1.91-cm] standoff. The effort
SPE Drilling Engineering, April 1986 127
to achieve good pipe centralization is aimed at placing a Subscripts
good sheath of gas-blocking cement around the casing. e = effective
Cement was circulated to the surface. The CBL shows i = increment
the effect of some gas cutting as well as reduced bonding s = steel
and salt and anhydrite sections in the well. Above 1,620
ft [490 m], the centralizers were not used. The CBL shows Acknowledgments
clear indications of uncemented pipe and collars above
1,700 ft [520 m]. At the dogleg locations mentioned We thank Amoco Production Co. for permission to pub-
above, there is some suggestion of poorer cement, lish this paper . We also express appreciation to Alan
although poor bond is also indicated for locations believed Pierce of Amoco for his assistance in the mathematical
analyses in this paper.
to have good standoff.
Unfortunately, there is no way to measure standoff for
casing in the well. CBL's can indicate good cement place- References
ment, but poor cementing results can be caused by con- 1. "API Specification for Casing Centralizers," API Specification
ditions other than standoff. The detailed calculation 100, second edition, API, Dallas (1973).
2. Myers, G.M. and Sutko, A.A.: "The Development and Application
procedure described here does provide more assurance of a Method for Calculating the Forces on Casing Centralizer,"
to the operator that adequate consideration is given to paper 851-42-H presented at the 1968 API Spring Meeting of the
standoff. Perhaps additional studies on a large number of Mid-Continent Dist., Amarillo, TX, April 3-5.
past and future cementing jobs could be made with the 3. Lubinski, A.: "Maximum Permissible Dog-Legs in Rotary Bore-
standoff-calculation procedure presented here to help de- holes," J. Pet. Tech. (Feb. 1961) 175-94; Trans., AIME, 222.
4. Timoshenko, S.: "Strength of Materials," Advanced Theory and
fine the minimum standoff required for successful cement- Problems, second edition, D. Van Nostrand Co. (1956) II, 43.
ing jobs. 5. von Gutsche, W., Bushati, C.M., and Weichold, U.: "Placement
of Casing Centralizer in Borehole Sections with Dog-Leg Severity,"
Nomenclature Erdoel-Erdgas Zeitschrift (May 1978) 94.
6. Lubinski, A.: "How to Spot Dog-Legs Easily," Oil and Gas J.
e = distance, in. [cm] (Feb. 4, 1957) 129-33.
C = coefficient
E = Young's modulus, psi [Pal Appendix-Detailed Deflection Anal,sis
F b = buoyancy factor for Casing String
1 = moment of inertia for casing string, in.4 Timoshenko' s 4 comprehensive analysis is used for the
[cm4] centralizer-spacing program to estimate the downward
L = length of borehole section between two deflection of a casing segment between the centralizers.
This criterion models a tie rod under uniform lateral load
survey points, ft [m]
with tension force on both ends of the rod.
N = lateral load (or force) on centralizer, Ibf/in.
[N/m] Combined Direct Compression and Lateral Load. Con-
P = force, Ibf [N] sider the simple problem of a strut with hinged ends loaded
r = radius of curvature by a single force, P, and centrally compressed by two
s = centralizer spacing or casing length equal side forces, S (Fig. A-I). Assuming that the force
between centralizers, in. [cm] P acts in one of the principal planes of the strut, we see
T = tension (or tensile load) of pipe hanging that the bending proceeds in the same plane. The differ-
below the centralizer, lbf [N] ential equations of the deflection curve for the two por-
tions of the strut are
u = strain energy
W = casing weight, Ibf/ft [N/m]
d2 y Pe
x = /2, where is the centralizer spacing, in. EI-=-Sy--x .................... (A-la)
dx 2
[cm]
y = deflection, in. [cm] and
Ymax = maximum deflection, in. [cm]
o = one-half the change in angle in borehole d2y P(-e)
(or between centralizers) EI dx
2
=- (-x) , ................ (A-lb)
ODLS = dogleg severity, degrees per 100 ft
[degrees per 30.48 m] where is the centralizer spacing and S is effective ten-
T/ = hole direction angle, degrees sile force.
ilT/ = change of hole direction (azimuth) between With the notation
two survey points, degrees S
() = hole inclination angle (at the centralizer), - =p2 .............................. (A-2a)
EI
degrees
il8 = change of hole inclination between two and
survey points, degrees
Pm = mud density, Ibm/gal [kg/m3] p24 S2
u 2 =-4-= 4EI' ...................... (A-2b)
Ps = steel density, Ibm/gal [kg/m3]
Cr- c
f
y
we represent the solutions of Eqs. A-I a and A-I b in the The corresponding expressions for the second portion
following form: of the strut are obtained by substituting (f-x) for x and
(f-c) for c in Eq. A-4. These substitutions give
Pc
y=C 1 cos Px+C z sin Px--x .......... (A-3a)
Sf P sin P(f-c) . P(f-c)
y= sm P(f-x)---(f-x) . . (A-5)
SP sin Pf Sf
and
+
sin P(f-x) ri
J q sin P(f-c)dc
SP sin Pf i-x
The remaining two constants of integration we find from
the conditions of continuity at the point of application of
the load P, which require that Eqs. A-3a and A-3b give
f-x ri
- - J q(f-c)dc,
the same deflection and the same slope for x=f-c. We Sf i-x
obtain
where q is the effective lateral load. Integrating the above
C z sin P(f-c)=C4 [sin P(f-c)-tan Pf cos P(f-c)] gives
and
COS(Pf -px)
CZP cos P(P-c) = C4 P[cos P(f-c) y =q-
SpZ
[2 Pf
-1 ] q
--x(f-x)
2S
.. (A-6)
P cos-
+tan Pf sin P(f-c)] + -,
S 2
from which and
P sin Pc
C z =-------
SP sin Pf
q
Ymax=(Y)x=i1Z=--
SpZ
(1 u
- - - - - 1 -U- )
cos 2
Z
and
1 uZ
---I--
P sin P(f-c) 5 qf4 cos u 2
C4 =- SP tan Pi .
=-_. . ............ (A-7)
384 EI (5/24)u 4
In "Optimal Spacing for Casing Centralizers" (April 1986 SPEDE, plicable for the calculation of casing deflection between two cen-
Pages 122-130) Lee et al. present equations for the calculation of tralizers because the casing is not hinged at each centralizer. A
casing deflection between centralizers. We believe that some of their different solution is given by Timoshenk0 3 for the case of a
assumptions and equations are incorrect and can lead to significant laterally loaded tie rod with built-in ends. This equation is, in our
errors in calculating casing deflection, standoff, and, consequently, opinion, appropriate for calculating the maximum deflection of
optimal spacing for casing centralizers. These errors are of par- casing between centralizers.
ticular concern because the equations given in their paper hitve been
adopted by the API in their Spec. lOD. 1
First, we agree with the authors that "it is appropriate to use Ymax =~(24)(U2 _
4
U cosh u-u) . .......... (D-2)
the effective casing weight rather than the air weight of the 384 EI u 2 sinh U
casing.,,2 However, they recommend the use of the following
equation for calculating the buoyancy factor (Eq. 5). Eq. D-2 predicts a casing deflection that differs significantly from
the value predicted by Eq. A-7. When there is negligible tension
in the casing, the two answers differ by a factor of five.
Note that the buoyancy factor actually changes quite significantly
during the cementing operation. For example, consider the case
of lO-li:>m/gal [1198-kg/m3] mud at a particular location outside
In our opinion, this equation is generally not appropriate for use
the casing when there is 15.6-lbrn/gal [1869-kg/m3] cement inside
in cementing applications. This equation is valid only if the density
the casing. At this time, the i:>uoyancy factor is 1.33 at that par-
of the fluid inside the casing is the same as the density of the fluid
ticular location. If the fluid on the outside is an 8.4-lbm/gal [1007-
outside the casing. When calculating load on centralizer or casing
kglm 3] water flush and the cement is on the inside, the appropriate
deflection between two centralizers, a more appropriate equation
buoyancy factor is about 1.5. This factor would be used for cal-
for the buoyancy factor is culating load on centralizer and deflection between centralizers. A
different, weighted buoyancy factor would be used for calculating
i
(1- PePs )_(dde )2(1_ PPi)
the axial tension at any point in the casing.
_ s Nomenclature
F b2- ................. (D-l)
1-( dY
de
i
de = OD of casing, in. [cm]
d i = ID of casing, in. [cm]
E = Young's modulus, psi [kPa]
Is the difference significant? We believe it is. For example, con- Fb = buoyancy factor normally used for calculating
sider a string of 7-in. [18-cm] -OD, 20-lbm/ft [30-kg/m] casing effective weight of casing string
being cemented with 15.6-lbm/gal [1869-kg/m3] cement that has Fb2 = proposed buoyancy factor for calculating lateral
just been displaced by lO-lbm/gal [1198-kg/m3] mud. (Pipe force on centralizer or deflection of casing
ID=6.456 in. [16.4 cm].) between centralizers
In this case Lee et al. 's Eq. 5 gives a buoyancy factor as follows. I = moment of inertia for casing string, in. 4 [cm4]
i = centralizer opening
q = effective lateral load
U = strain energy
Ymax = maximum deflection, in. [cm]
=0.847. Pe = density of fluid on outside of casing (e.g., cement
slurry), Ibm/gal [kg/m3]
Eq. D-l gives a significantly different answer. Pi = density of fluid inside casing (e.g., drilling mud),
Ibm/gal [kg/m3]
Pm = mud density, Ibm/gal [kg/m3]
(
1_~)_(6.456)2(1_~) Ps = density of material in casing (e.g., steel), Ibm/gal
65.4 7.000 65.4 [kg/m3]
Fb= - - - - - - - - - - - -
1_(6.456 )2 Reference.
7.000 I. Spec. lOD, Specification for Casing Centralizers, third edition, API,
=0.274. Dallas (1986).
2. Lee, H.K., Smith, R.C., and Tighe, R.E.: "Optimal Spacing for Casing
Centralizers," SPEDE (April 1986) 122-130.
These answers differ by a factor of approximately 3. 3. Timoshenko, S.: "Strength of Materials," Advanced Theory and
Second, Eq. A-7 was derived by Timoshenk0 3 for the case of Problems, Robert E. Krieger Publishing Co. Inc., Malabor, FL (1983)
a laterally loaded tie rod with hinged ends and is clearly not ap- 43,45-46.