api-55-165 use of stabilizers in controlling hole deviation
TRANSCRIPT
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Use of Stabilizers
in
Controlling Hole ~eviation
H
B.
WOODS
AND
RTHURL U B I N SK I ~
ABSTRACT
R e s u l t s o f a t h e o r e t i c a l i n v e s t i g a t i o n o n u s e o f
a s t a b i l i z e r i n d r i ll i n g c r o o k ed f o r m a t i o n s a r e g i v e n
in cha r t s wh ich s how:
1 How much more weight ma y b e car r ied .
2.
W he re t h e s t a b i l i z e r s h o u l d b e p l a c e d .
T h e u s e o f r e a m e r s a n d m or e t h a n o n e s t a b i l i z e r
i s q u a l i t a t iv e l y d i s c u s s e d .
INTRODUCTION
T h e e a r ly s t u d i e s o f n ~ c h a n c
s
of dr i l l ing
c rooked -ho le fo rma t ions, bo th wi thou t s t a b i l i ze r s 1 2
and wi th
stabilizer^,^
w e r e b a s e d u po n t h e a s s u m p -
t ion tha t pe r f ec t ly ve r t i ca l ho le s cou ld be d r i l l ed .
L a t e r i t has been s hown tha t d r i l l i ng o f s uch ho le s
i s n o t p o s s i b l e 4 a n d a l l h o l e s a r e a c t u a l ly i n c l i n e d
even in homogeneous fo rma t ions . The re fo re , many
o f t h e c o n c l u s i o n s of th e e a r l y s t u d i e s a r e n o t v a l i d .
I n t h e 1 a t e r t h e o re t ic a l
investigation^,^^^
t h e as
s umpt ion of ho le ve r t i ca l i ty h a s been r emoved and
t h e e f f e c t s of c o l l a r a n d h o l e s i z e i n t h e c o n tr o l of
c r o ok e d h o l e s h a v e b e e n s t u d i e d . In , t h e p r e s e n t i n -
v e s ti g a ti o n t h e e f f e c t of s t a b i li z e r s i n t h e d ri ll -
c o l la r s t r i n g i s s t u d i ed .
I n t h e p a s t , u s e of s t a b i l i z e r s h a s s o n l e ti n le s b e e n
s ~ ~ ~ e s s f ~ 1 ~ ~ ~ ~ ~ ~ ~n d so m e t i m e s d i s a p p o in t i n g . T h e
p ro b le m i s s o c o m p l ex t h a t i t s e e m s i m p o s s i b l e fr om
f ie ld e x p e r i e n c e t o e s t a b l i s h r u l e s f or t h e s u c c e s s -
f u l u s e of s t a b i l i z e r s . F o r t h i s r e a s o n , a t h e o r e t i c a l
inves t iga t ion w as conduc ted jo in t ly by the r e s ea r ch
depa r tmen t s o f Hughes Too l C ompany and S tano l ind
Oi l and G a s C ompany . T h e numer ica l work invo lved
s ol v in g 1 e n g t h y e q u a t i o n s w h i c h n e c e s s i t a t e d
a
d ig i t a l compu te r . T he IBM Prog rammed E lec t ron ic
C a l c u l a t o r a t t h e S t a n o l in d R e s e a r c h C e n t e r w a s
u s e d .
In t h i s s t u dy th e e f f e c t s of r o t a t o n a re di s -
r e g ar d ed . T h e j u s ti f i c a ti o n f o r t h i s i s t h a t t h e s a m e
a ss um p ti on m a d e i n t h e p a s t 4 1 5 ed t o r e s u l ts i n
agreement wi th f ie ld exper ience .6110
P r o g r e s s r ep o r t s o n t h i s i n v e s t i g a t i o n w e r e p re -
s e n t ed a t mee t ings of the AP I Mid -C on tinent and
Hughes Tool Co., Houston, Te xas.
Stanolind Oil and Gas Co., Tulsa, Okla.
t Presented at the spring meeting of the Mid-Continent District,
Divi sion of Production, Amarillo, Te xa s, March
1 9 5 5 .
References are
at
the end of the paper.
Sou thw es te rn Dis t r i c t S tudy C onami t t ees on S t r a igh t-
hole Dr i l l ing .
, Genera l E f f ec t o f a S t a b i l i z e r
C o n s i d e r
a
d r i l l in g s t r i n g i n
an
i n c li n e d h o le , a s
s h o w n i n F i g . 1 A . In t h e v i c i n i ty of t h e b it , t h e
s t r i n g d o e s n o t c o n t a c t t h e w a l l o f t h e h o l e. A t s o m e
d i s t a n c e a b o v e t h e b i t, t h e d r i l li n g s t r i n g c o n t a c t s
t h e w a l l . A b o v e t h e p o in t of c o n t a c t t h e s t r i n g l i e s
on the low s i de o f the ho le .
Wi th no we igh t on the b i t , t h e on ly fo r ce ac t ing
on the b i t i s t he r e s u l t o f t he we igh t o f the po r t ion
of t h e s t r i n g b e t w e e n t h e b i t a n d t h e p o i n t o f c o n -
t ac t . T h i s i s
a
b e n ef i ci a l f o r c e b e c a u s e i t t e n d s t o
b r ing the h o le toward ve r t i ca l . When we igh t i s ap -
p l i e d , t h e r e i s a n o t h e r f o r c e w h ic h
is
de t r imen ta l
b e c a u s e i t t e n d s t o d i r e c t t h e h o l e a w a y f ro m ve r ti -
c a l .
S u p p o s e a s t a b i l i z e r
is
u s e d ,
as
s h o w n i n F i g .
1 B . T h e p o i nt o f c o n t a c t i s n ow a t t h e s t a b i li z e r ,
wh ich
is
h ighe r than t he po in t o f con tac t i n F ig . lA .
T h u s , t h e p r e v i o u s ly m e n t io n e d b e n e fi c ia l f o r c e i s
g r ea te r. I n add i t ion , a l though i t i s d if f icu l t t o v i s u -
a l i z e , t h e d e t r i m e n t a l f o r c e i s n or ni a ll y
s
ni a l 1 e r
T h i s e x p l a i n s t h e u s e f u l n e s s of a s t a b i l i z e r .
F i g .
1 B
s u g g e s t s t h a t t h e b e s t p o s i t i o n of
a
s t a -
b i l i z e r i s as h ig h a s p o s s i b l e , p r o vi d e d t h e c o l l a r
d o e s n o t c o n t a c t t h e w a l l o f t h e h o l e , as s hown in
F i g .
1C.
I n f a c t , t h e m a t h e m a t i c a l s t u d y h a s s h o w n
tha t i n mos t cas es the op t imum pos i t ion o f a s t a -
b i l i z e r
is
as i n F i g .
1C.
I n s o m e c a s e s , h o w e v e r ,
the op tinlun l pos i t ion i s s omewh a t lower , as s h o w n
in F ig . 1B .
Th e o p t i nl u n~ pos i t ion of the s t ab i l i z e r in the
s t r i n g d e p e n d s u p on t h e s i z e of c o l l a r s , s i z e of
ho le , ho le inc l ina t ion , and we igh t on b i t. I t . do es
no t d i r ec t ly depend upon fo rma t ion c rookednes s and
fo rma t ion d ip ; bu t i t i nd i r ec t ly de pen ds upon them,
i n a s m u c h as t h e s e a r e fa c to r s wh ic h g ov ern t h e
we igh t tha t n lay be ca r r i ed .
B enefi t Der ived f rom Us ing a S tab i l i ze r
S t a b i l i z e r s a r e u s e d i n d i f f e r e n tconib inat ions wi th
o r wi thou t r eamer s . In t h i s s ec t ion , t he benef i t wh ich
m a y b e e x p e c t e d f ro m a s i n g l e s t a b i l i z e r w i l l b e
cons ide red .
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66
H. B . WOODS AND ARTHUR LUBIN SKI
F ig 1A F i g 1B
Assume. first that there i s no cl earanc e between
the stabilizer and the hole. The influence of clear-
ance will be investigated further in this paper.
Assume furthermore that, for given hole and col-
lar s ize s, it i s known how much weight nlay be ca r-
ried without a stabilizer for a given hole deviation.
Such knowledge may
be
directly provided by previ-
ous drilling experience in the field, or niay be cal-
culated with pract ical ch ar ts 5 if the field experi-
ence i s for some other combination of collar si ze ,
hole size, etc. Let us investigate how much more
weight could be carried if a stabilizer were placed
at the ideal position. The answer is given by the
lower diagrams in Fig. 10 to 25.*
Example
Assuming that the formation i s such that: Drilling
an 8'4-in. hole with 8-in. col lar s and no st ab il izer
and 50,000 lb on bit, the hole deviation i s 1 0 deg.
Then, Fig. 27 shows that, using a stabilizer
at the ideal position, 9 percent more weight could
be carried without incr easing hole deviation. T hi s
percentage of additional weight which may be car-
ried w i t h o u t increasing angle will be referred to
hereafter
as
percentage in~~rovement.
Charts
s
i mi
1
a r to F'ig. for most popular hole
sizes and various collars are included in this paper
*Se e p. 174 to
1 7 7
incl .
p i g .
2
and
3
illustrate examp les i n the te xt. They ere the same
as F ig . 15 and 16, resp ectiv ely.
(Fig. 10 to 25). Th e following general conclusions
may be drawn from these charts.
1 In very severe crooked-hole formations, where
very light weights are carried, the percentage
improvenlent i s of the order of 23 to 26 percent.
Examples
Fig. %Point
B
(packed holes).
Fig. %Point C (conventional clearances)?
2. In very mild crooked-hole formations, w h e r e
heavy weights are carried, the percentage im-
provement depends upon hole clearance:
a. For packed holes-in most ca se s,
30 to 40 percent.
Examples
Fig. 2, points and D.
b. F'or conventional clearances-40 to 80
percent.
Examples
Fig. 3, points
E
and F
Stabilizer
v s .
Collar Size
How much benefit may be gained by increasing
collar si ze i s g i v e n in a pa st publication.5 How
much benefit may be gained by use of a stabilizer
was discussed in the preceding section. The two
benefits will now be compared.
Arbitrarily a hole i s ca lled '#packed if the diarnetral clear-
ance between collara
and hole i s in. or le s s. A clearance of
2 in. or more i s cal led conventiona l.
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USE OE STABILIZERS IN CONTROLLING HOL>EDEVIATION
167
Example for a Very Severe Crooked-hole Formation
Assuming that the format ion i s such that : Dri l l ing
an 8 - in . hole with 6-in. co l lars and no s ta bi l ize r
and 3 ,700 lb on b i t, t he ho l e d e v i a t i o n i s 3 deg .
l ' h e n , u s i n g p r a c t i c a1 charts , ' one may find the
weight which could be carr ied i f o ther col lar s izes
were used . l 'hen , wi th F 'ig. 10 to 25 in th is paper,
one may f ind the weight for each col lar s ize i f a
s t a b i l i z e r w e re u s e d. l ' h u s T a b l e 1 wa s p repared .
Table
Weight to Rlain~ain Ueg, LJb
Co llar Siz e, ithout With St ab ili ze r at'
In. Stab il izer Optimum Po sit i on
Example for Moderate Crooked-hole Formations
Assu ming that the formation i s suc h that : Dri l l ing
an 83/ ,- in. hole wi th 6-in. co l la rs and no s ta bi l ize r
and 19,000 lb on b i t , the hole devia t ion i s 3 deg.
l ' h e n , by t he s a m e m e a n s a s f or T a b l e 1 , l ' a b l e 2
was prepared .
Table
Weight to hlaintain 3 L)eg, L,b
Co llar Siz e, i thout With Sta bil ize r a3
In . S tab i l izer Opt imum Pos i t ion
6 19,000 (A) 27,500 (U)
7 30 ,000 ( c ) 41 ,800 (D)
8 42,500 E) 56,500 (E )
S ev er al si m il ar e x a n ~ ~ l e sere worked out for for-
mat ions of various degrees of crookedness and for
va r ious ho l e s i zes , and the fo l l owing genera l con -
c lus ions d rawn :
1 A s indicated by a comparison of s i tuat ions (U)
and (E) , about the same weight may be carr ied:
a . w i th no s t ab i l i z e r and ove rs i zed co l l a rs .
L with
a
s t a b i l i z e r a n d t h e l a r g e s t c o l l a r s i z e
that can be washed over.
2. A s indic ated by a comparison of s i tu at i on s
E)
and (E ), if ove rs i zed co l l a rs a re u sed , t hen s t i l l
add i t i ona l advan tage s may be ga ined by us ing a
s t ab i l i ze r .
3 . As indicated by a conlparison of s i tuat ions (13)
and (U), the use of col la rs any sm al ler than the
maximum size which may be washed over should
be avoided in crooked-hole dri l l ing .
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68
H B
WOODS AND ARTHUH LUBINSKI
Ideal Position of Stabilizer
A s in the previous section, assunie for the tinie
being that there is no clearance between the st a-
bilizer and the hole. The ideal position of a stabi-
lizer may be obtained from the upper diagrams in
F'ig. 10 to
25.
Exaniple
Assuniing that the formation i s such tha t: Drill-
ing an 83/,-in. hole with 8-in. drill collars and one
stabilizer and 20,000
Ib on bit, the hole deviation
i s 4 deg. Then, pointG Fig. 2, shows that the ideal
position of a stabil izer i s 69 ft above the bit.
Most of the curves are limited to the right by a
dashed line, in which case any curve
nu st
be con-
sidered to f o l l o w the dashed line downward, a s
shown in the following example.
Example
Assuniing that the formation i s such that: Drilling
an 83/,-in. hole with 6-in. drill coll ars and one s tabi -
lizer and 40,000 lb on bit, the hole deviation is 3
deg. Then, point H Fig. 3, shows that the ideal po-
sition of a stabilize r i s 56 ft above the bit.
The following general conclusions may be drawn
froni Fig. 2 and 3, or, more generally, from F'ig. 10
to 25.
1 The ideal position of a stabil izer is displac ed
downward by an inc rease of weight.
2. The i d e a position of a stab ili zer is , in niost
cases, displaced downward by an increase of
hole inclination.
Example
Drilling a n 834-in. hol with 6-in. drill collars
and 10,000 lb on bit:
Fig. 3-Point I: inclination
2
deg; ideal
position 93 ft.
Fig. 3-Point J : inclination 3 deg; ideal
position 85 ft.
3.
For some conditions the previous conclusion
does not hold true and the ideal position i s in-
dependent of hole angle.
Example
Drilling an 8?/,-in.hole with 6-in. drill collars
and 40,000 lb on bit:
Fig. 3-Point H: inclination 2 deg; ideal
position 56 ft.
Fig. 3-Point H (same point): inclination 3 deg;
ideal position 56 ft.
Influence of Clearance on Benefit Derived from
Using a Stabilizer
So far, s ituat ions in which the s tabi lize r com-
pletely fills the hole have been analyzed. The in-
fluence of stabili zer c learance will now be investi-
gated.
l'he lower charts of Fig. 4 and 5 show how clear-
ance aflects the percentage improvement. They are
representative of packed hole and non-packed hole
conditions, respectively. For both figures, the left-
hand and right-hand charts are for hole deviations
of 2 and 1 0 deg, respec tively.
The following conclusions may be reached from
the inspection of these charts:
1 A s
clearance inc reas es, the percentage improve-
ment decreases.
2. The lo ss in p e r c e n t a g e improvenient for the
same clearance i s much greater for packed h oles
than non-packed holes.
Examples
a. For 8-in. collars in 8 -in . hole, and for light
weight, a b o u t one third of the percentage ini-
provement i s l os t when c 1e a r a n c e increases
froni zero to in. The lo ss is greater than one
third for heavy weight.
b. Fo r +in. col lars in 83/,-in. hole , for both light
and heavy weight, only about one tenth of the
percentage improvement i s lo st when clear ance
incre ases from zero to in.
W E I G H T
WlTH
S T AB I L I Z E R - T HOUS AND P OUNDS
WE I GH T WlTH NO STABILIZER-THOUSAND
POUNDS
Fig. 4-Influence of Stabili zer Clearan ce
Example for Packed Holes
Ho l e s =
834 In
o l l a r s
= 8 In
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USE OF STAB ILIZE RS IN CONTROLLING HOLE DEVIATION
169
1
so
a0
T O
6
10
O
10
1
1 40
SO ID 1
1 4 0
1
WEIGHT WIT H STABILIZER THOUSAND POUNDS
WEIGHT W IT H NO STABILIZER THOUSAND POUNDS
Fig. 5 Influence of Stabi lizer Clearance
Example for Non packed Holes
Holes 8?/, In. Collars
= 6
In.
Influence of Clearance on Ideal Position
of Stabilizer
The upper charts of Fig. 4 and 5 show how clear-
ance affects the ideal stabilizer position. The fol-
lowing conclusions may be reached from the inspec-
tion of these charts:,
1 In p a c e d holes, a s clearance increases, the
ideal st abilizer position i s di splaced downward.
2. n
non-packed holes, this e f f e c t i s much le s s
pronounced and even nil for heavy weight.
Practical Position of Stabilizer
In actual drilling it would be very impractical to
keep displacing the stabilizer as the ideal position
varies. It i s therefore relevent to investigate how
much i s l os t by p 1a c i n g the stabilizer somewhat
away froni the ideal position.
Fig. 6 sh ows how placing the stabil izer 10 per-
cent off the i d e a1 position affects the percentage
improvement. It covers examples for:
1. Packed holes (8-in. collars , 834-in. hole) and
non-packed holes (6-in. col lars , B3/,-in. hole).
2. Small and large s t a b i 1 z e r clearanc es (zero
clearance and 4 in.).
3
Small and large hole inclina tions (2 and 10 deg).
l hree curves are drawn in each diagram, viz.:
a. Curve for the stabili zer at the ideal position.
b. Curve
L
for the sta bili zer 1 0 percent too low.
c. Curve
H
for the stabilizer 10 percent too high.
The following conclusions may be reached froni
the inspection of these diagrams:
1 If the stabil izer i s located 10 p e r c e n
t
off the
ideal position, either too low or too high, then,
for light weight, over half of the percentage ini-
provement i s lost.
2. A s the weight increases, it becomes progres-
sively b e t t e r to place the stabilizer too low
rather than too high.
3. In non-packed holes, this i s extremely signifi-
can t in a frequently used range of weights.
4 In packed holes, it is significant for very heavy
weights only.
From
a
conibination of infomiation such a s that
presented in Fig. 4, 5, and 6, one could establish
a practical range of stabili zer locatio ns rather than
the ideal location only. Such work i s confusing and
not very practical. After h a v i n g worked many nu-
merical examples, it was found that the following
general rule, although far from p e r f e c t , may be
adopted for reasons of i t s simplicity.
Place the s tabi l izer between the ideal pos i t ion
according t o Fig.
10 t 25
and
a
position
10
percent
closer to the bit .
This makes allowance for the following:
1 In packed holes, stabilizer clearance appreci-
ably lowers the ideal stabilizer position and
there is bound to be some clearance either be-
cause the hole is oversized or because the sta-
bilizer i s worn.
2. In non-packed holes:
a. Clearance has some effect, a1 h o u g h l es s
than in packed holes.
b. Rluch of the dr illing may be in a weight range
where it
i s
much worse to have the stabilizer
too far than too close.
3. There is always a section of reduced diameter
at the stabilizer. This lowers the ideal stabi-
lize r position.*
The foregoing rule does not a 1
1
ow for the fact
that, .with very light weight in,n~n-~ackedoles,
where effect of cl ear ance i s minor, most of the in-
dicated improvement is 1o s t if the stabilizer i s
placed 10 percent too clo se to the bit. Under such
conditions, it might be desirab le to put the s tab ilizer
no more than
5
percent closer than the ideal posi-
tion a s indicated by Fig. 10 to
25.
Because the magnitudes of some of the factors
affecting the ideal position of the s tab iliz er are not
Any reduction of diameter in a drill-collar string decreases
its quality as a straight-hole tool. Both the diameter reduc-
tion end the
length of the reduced section should be kept to
a minimum.
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170
H. B. WOODS AND ARTHUR LUBINSKI
WEIGHT WlTH NO STABILIZER-THOUSAND POUNDS
WEIGHT WlT H NO STABILIZER -THOUS AND POUNDS
C U R V E S ID E A L P O S IT IO N
C U R V E S
L 10 T O O
OW
C U R V E S H - 10 TO O H I G H
F i g .
6 Influence of Stabi lizer Located Off Ideal Position
Hole
8=
In.
k no wn , i t i s i m p o s s i b l e t o s t a t e e x a c t l y h o w m uc h
i m p ro v em en t m ay ex p ec t e d if t h e fo reg o i n g r ec -
o m m e n d a t io n s a r e f o l l o w e d . T h e a u t h o r s e s t i m a t e
t h a t t h e w e i g h t c o u l d b e i n c r e a s e d b y a b o u t 2 0 p e r-
c e n t i n v e r y crooked f o r n la t i on s a n d 5 0 p e r c e n t i n
m i l d ly c r o o k e d f o r n ~ a t i o n s .
? h e w e i g h t i n c r e a s e of 2 0 p e r c e n t o b t a i n a b l e i n
v e ry c ro o k ed fo rm a t i o n s s h o u l d n o t b e m i n im i zed .
E v e n t h o u gh i t m a y , a m o u n t t o a n i n c r e a s e i n w e i g h t
of o n l y I,O OO o r 2 , 0 0 0 l b , i t s h o u l d a l w a y s r e s u l t i n
a n i n c r e a s e i n d r i l l i n g r a t e o f
at
l e a s t 2 0 p e r c e n t
w i t h s o m e i n c r e a s e i n b i t f o o t a g e .
l h e c o n c l u s i o n s r e a c h e d i n t h e f o r e g o i n g h a v e
b e e n p a r t l y co nf ir m ed b y f i e ld e x p e r i e n c e a s f o l l o w s :
1 U s e of s t a b i l i z e r s in v e ry c r o o k e d fo r m a t i o n s
i
( l ig h t w e i g h t ) h a s o f t e n r e s u l t e d i n n o i m p r ov e -
m e nt . T h i s i s u n d e r s t a n d a b l e i n v ie w of t h e f a c t
t h a t n o t o n l y t h e m ax im um p o s s i b l e b e n e fi t i s
r a t h e r l i m i t e d , b u t a l s o b e c a u s e s u c h b e n e f it d e -
p e n d s r a t h e r c r i t i c a l l y u po n p r o p e rl y l o c a t i n g
t h e s t a b i l i z e r . I t i s b e l i e v e d t h a t p r o pe r a p p l i-
c a t i o n o f t h i s p a p e r w o u l d l e a d t o n o t i c e a b l e r e -
s u l t s .
2. U s e o f s t a b i l i z e r s i n m il d ly c r o o k e d f o r n ~ a t i o n s
( h ea v y w ei gh t) h a s b e en s u c c e s s f u l . 6 ~ 7 h i s i s
a l s o u n d e r s t a n d a b l e b e c a u s e u n d e r t h e s e c o n di -
t i o n s t h e b e n e f it s w h i c h m a y b e g a i n e d b y s t a -
b i l i z e r a r e l a r g e a n d i t s p r o p er p o s i t io n i n g i s
n o t v e r y c r i t ic a l . I t i s b e l i e v e d t h a t p r o p e r a p -
p l i ca t i o n o f t h e f i n d i n g s o f t h i s p ap e r w o u l d co n -
s i s t e n t l y l e a d t o still b e t t e r r e s u l t s .
I n a c u a 1 d r il li n g, h o l e d e v i a t i o n a n d w e i gh t
c h a n g e a s d r il l in g p r o g r e s s e s . T h e r e f or e , t h e i d e a l
p o s i ti o n o f t h e s t a b i l i z e r a l s o c h a n g e s a n d s u b s
m u s t b e u s e d t o d i s p l a c e t h e s t a b i l i z e r a s n ee d e d.
A f te r h a v i n g c o n s i d e r e d s e v e r a l s i t u a t i o n s , t h e f o l -
l o w i n g g e n e r a l c o n c l u s i o n s w e r e r e a c h e d .
1 W hen d r i l l i n g w it h a n e a r l y c o n s t a n t d e v i a t i o n
( i n t h e v i c i n i t y o f t h e co n t r ac t an g l e ) , n i ax i -
m um o f t w o s u b s o n t h e r i g , o n l y o n e o f w h i ch
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I
USE OF STABI LIZE RS IN CONTROLLING HOLE DEVIATION
i s used a t a time, is sufficient to keep the sta-
bilizer within the reconlmended range.
2
When, in order to decrease drilling costs, the
contract permits a gradual buildup of angle, say
1
deg per 1,000 ft, then
3
or 4 subs on the rig,
only one of which i s u s e d at a time, may be
needed.
Example
An 8'4-in. hole i s to be dri lled with 8-in. drill
collars and a stabili zer.The contract angle i s
5
deg,
but an attempt will be made to keep the angle with-
in 4 deg. Previous experience indicates that weight
will vary between 10,000 and 40,000 lb.
Fi.g.
15
indicates that for a 4-deg hole and 8-in.
collars, the i d e a1 stabi lizer position i s 70 ft for
10,000 lb and 67 ft for 40,000 lb. One sub, posi-
tioning the stabilizer at 67 ft from the bit, would
suffice because, for both w e i g h t s , the stabilizer
would be located within the recommended range.
Use of hlore Than One Stabilizer
So far we have analyzed the effect of stabilizing
the str ing at one point. Consider now the effect of a
continuous stabilization. Continuous stabilization
has been tried in the past, for example, by welding
long st rip s on the drill collars. In the c as e of con'-
tinuous stabilization, the equilibrium angle may be
calculate d with our previous stu dies 4 simply by
considering a s hole cl earance the diametral clear-
ance between hole and strips and not between hole
and collars. Thus i t nlay be shown that, in crooked
fornlations, such a small clearance r e s u t
s
in a
larger equilibrium angle than with one stabilizer at
the ideal position. l'his, however, does not neces-
sarily mean that continuous stabi lization i s always
detrimental, because such a stabilization results in
less severe dog-legs and in a much smaller rate of
buildup angle. Therefore, continuous stabilization
could be useful in the following two cases.
1.
Drilling
s
h o r t sect ions of extremely crooked-
-
hole formations.
Thus, although continuous stabilization would re-
su lt in an equilibrium angle that i s all out of rea-
son, and if the s e c t i o n were thick enough, this
would eventually be reac hed , the rat e of buildup of
angle may be s p lob that the s e c t i o n i s drilled
through before the angle becomes excessive.
2 Drilling when building up angle until the maxi-
mum acceptable angle i s reached.
l' he slow ia te of buildup of an gle permits one to
carry more weight. After the niaximunl accept abl e
angle is reached, con~ple testabilization becomes
detrimental and drilling should either proceed with-
out any stabilization or with a stabilizer close to
the ideal position.
Our i
n
t e r e
s
t in continuous stabilization stems
from the fact that sever al closely spaced stabiliz ers
in the lower portion of the str ing, with the lowermost
just above the bit, result in a condition approaching
continuous stabilization, and that the f o r e go i n g
sta teme nts approximately hold true.
If
more than one st abil izer i s used and the lower-
most i s a t the i de al position, then we believe that
the additional st abi li zer s have little , if any, effect,
on hole deviation. Opinions have been expressed
that they ar e useful insofar a s that they may both
decrease the overall stabilizer wear and reduce the
frequency of drill-collar connection fail ures ,788 he
anal ysi s of which i s out side the sco pe of t his .p'aper.
Use of Reamers
A
reamer above the bit i s commonly used when
drilling through certain abrasive formations in the
Permian Basin. l 'h e e
f f
e c t of a reamer was not
n la then la t i~a l l~nvestigated, but we believe that
its presence greatly increases the equilibrium an-
gle. Po ssi bly the common practice of us in g- a sta-
bilizer 30 ft above the reamer reduces part of its
detrimental effect. It would be useful to investigate
the optimum posit ion of a sta bil iz er when a reamer
i s used.
A s
in the case of continuous stabilization pre-
viously a naly zed, the conibination of a reamer and
stabilizer may be u
s
e
f
u in reducing the rate of
buildup angle.
; I
Dimensionless Charts
; , ,
.
F'ig. 7, 8, and
9
are din~ensionlesscharts pre-
pared from for n~ul as erive &in the .4ppendix. Th es e
figures were used in pr e' p a r i n g all dimensional
charts in this paper and n G y be used for preparing
similar charts for other holeand collar sizes.
F'ig.
7
and 8 give the ideal position of the st abi-
lizer, and Fig.
9
the improvement.
The dimensionless quantities used are as fol-
lows:
1 n
sin
a/r
wherein:
.
r is the length, in feet, of one din~ensionless
unit, the definition of which i s given in Ref.
1
The value of
m
for any collar size may be
obtained from Fig. 3 Bef. 4.
a
is hole inclination with respect to the verti-
cal, in radians.
is the r a d i a1 clearance, in feet, between
hole and collar.
2
x2-weight w i t h stabilizer, in din~ensionless
units. The weight of one dimensionless unit
for any collar s i z e may be obtained from
F'ig. 4, Ref.
4
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172
H B WOODS AND ARTHUR LUBINSKI
3 ,-distance bit to stabilizer, in dimensionless
units.
4
-dinlensi onless clearance, i.e., ratio of st a-
bilizer clearance to collar clearance.
The dinlensionless charts of Fig. 7, 8, and
9
are
for either 0 or 0.5. Chart s for 0.25 were
also prepared. They are not presented in this paper
because it was found that linear interpolation i s
satisfactory for all practical purposes.
Some of the curves of Fig. 7 and 8 d i
s
p a y a
break, to the le ft of which the curves ar e horizontal.
Poi nts l ocat ed to the right of the break correspond
to situat ions for which, with the s tabi lize r at the
ideal position, the drill collar barely contac ts the
wall of the hole between the s tab il ize r and the bit.
On the other hand, points located to the left of the
break correspond to situations for which, with the
stabilizer at the ideal position, the collar does not
contact the wall.
Similar breaks are also present in the curves of
Fig. 9, but they are visible only when the stabilizer
i s located too high.
?'he left-hand portions of some of the cur ves of
Fig.
7, 8,
and
9
are dashed. They indicate the heli-
cal buckling range, and results obtained in the re-
gion of t hes e dashed li nes a re meaningless.
A s
for
the case of drill collars with no ~t ab i li ze r , ~he re-
gion of helical buckling was detertilined with model
experiments.
Suggestions for Future Research
l'he following theoretical investigations are sug-
gested:
1
Effect of a stabilizer used in conjunction with
a reamer.
2 Effect of the reduction of drill-collar section at
the stabilizer.
CONCLUSIONS
1.
l' he use of st abi li zer s should be considered in
conjunction with, or sep ara te ly from, one or seve ral
of the following techniques , quantitat ively evalu-
ated in previous publications:4*5
a. Deliberate ly accepting more deviation.
b. Using larger than conventional drill col lars.
c. Drilling a larger than c on v e n t i o n a1 hole and
using larger than conventional collars.
2 l'he use of one stabilizer presents the follow-
ing advantages:
a. With one stabilizer, more weight nlay be carried
without incr easi ng hole deviation . ?'he addition-
al weight is about
2
percent for very crooked
formations and up to
50
percent for other fornia-
tions.
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USE OF STA BILI ZER S IN CO NTROLLING HOLE DEVIATION
73
NOTE: x IS THE
W I G H T
WITH NO STABILIZER
IN
DIMENSIONLESS UNITS
Fig. 9 Benefit Derived from Using
a
Stabilizer
Dimensionless Charts
b. About the same advantage may be obtained by
using a s tabi liz er with the maximum si ze of col-
lar s that can be washed over a s with oversi zed
collars without a stabili zer. Thi s conclusion i s
of inter est in c as es where the us e of oversi zed
collars i s not desired.
c. More weight may be carried with oversized col-
lar s and a stabilize r than with oversized collars
alone. This conclusion is of interest in ca se s
where it is considered that oversized collars
may be used without undue risk.
3
The use of one stabilizer presents the follow-
ing disadvantages:*
a. The st abi liz er must be placed within a few feet
of a definite position, given in the cha rts of th is
Obvious disadvantag es, such as the increase of sticking and
fishing hazards, which incidentally may be greatly m inimized
by use of rubber stabilizers, are not discussed.
paper, necess ita tin g the use of a sub. Failure
to properly locate the stabilizer can explain the
f
r e qu e n t lack of su cc es s encountered in the
past.
b It may be necessary to change the stabilizer
p o i t i o
n
a
few times during the dri lling of a
well. All possible positions may be approxi-
niated closely enough with a maximum of four
subs of different lengths on the rig, only one of
which i s used at a time. In most c a s e s , how-
ever, one or two subs would suffice.
4
The use of several stabilizers closely spaced?
from the bit, or the use of a reamer and stabilizer,
will resu lt in a con tinued buildup of an gle and the
deviation niay eventually become excessive. Such
practi ces, however, may be useful a s a means of
reducing the rate of buildup a ngle before the maxi-
mum accep table angle i s reached.
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8/10/2019 API-55-165 Use of Stabilizers in Controlling Hole Deviation
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178
H . B . WOODS AND ARTHUR LUBINSKI
APPENDIX
First Case: Collars Do not Contact Wall of the Hole
between Bit and Stabilizer
The coordinate axes are as s h ow n i n Fi g.
26.
Consider a straight but inclined hole, the low side
of w h i c h i s represented by the straight line DC.
The angle of i nclination with respec t to the verti-
ca l i s
a
The c u r v e APB represents the elastic
line of the drill ing string.
A
i s the point of tangen-
cy, B is the bit, and P is .t he stabilizer. Let and
I denote the conlponents in the directions of co-
ordinate a xe s of the reaction of the bottom of the
hole on the drilling string.
Following t he reasoning of Szego s dis cus sion of
the paper, Ref.
4,
the differential equation for the
section BP is:
dZYl
EI -
X
- H ,
X-WY
[ Y, - l
cos a
dX
a
0
in whic h.the meaning of the syn lbols
E, I, p, 6,
and
]
is the same as in Ref.
1
and
4.
The subscripts I in equation (1) distinguish it
from a corresponding equation for section
PA,
for
which sub scrip ts
2
will be used.
SzegoYsmethod was used in Ref. 5, in which it
was e x p
1
a i n e d that simplifying the problem by
making
cos a
=
1
res ult s in insignificant error.
Let us introduce certain dinlensionless quanti-
ties, some of which are similar to those of Ref.
1
and 4.
y 1
U l =-
m s i n a
2)
H 1
h l = -
r nps i na
(5)
wherein:
Using equations
2)
to
(6)
and making cos a =
I
equation (I), on differentiating, becomes:
Fig. 26
d3u l d u , d u ,
- -x , - x - x
h, 7)*
dx
dx
x
The differential equation
7)
was solved
by
an
iteration method. Let the function, u, be approxi-
mated by a function, uln,
as
follows:
Equation 8)wa.4 substituted into the right-hand
member of equation
(7)
and integrated three times.
Syn~bolically,he operations are a s follows:
If the quantities u
z Z
and rn were defined as follo ws,
Y l
W
U l =
X2
=
m tan ec p c o s p c o s
equation 1)
would yield equation 7 ) without making the ap
proximation cos = 1. Th e procedure followe d introduces only
insignificant errors and results in more readily usable r e l e
tions between dimensional quw titie s.
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I
USE O F STABILIZER S IN CONTROLLING HOLE DEVIATION
d2u1 x
- = -( x2- x )u I a- s X u l adx+-+hlx+K1 (9)
dx2 0 2
d u 1
X
- = -
(x2- x)J u l a dx-2
sX
X u l adxdx
dx 0
0 0
x 3 h l x 2
+-+-+Klx+Ll (10)
6 2
u I = - (x2-x)P
J ~ u ~ ~
xdx-3
sX
X u l a xdxdx
0
0
0 0 0
x4 hlx3 K lx2
- +-+-+L,x+&l
1
(11)
24 6
2
in which
K 1 , L 1 ,
and
hll
are integration constants.
l'he function
ul
thus obtained i s a better approxi-
niation of the actua l function
ul
than the f i r s t ap-
proxinlation
u
a and will be designated hereafter
u l b .
Corresponding equations for the section
P A
are
obtained by replacing the subscripts 1 by 2
in (I), (2), (5), (7),
8),
(9), (lo), and (11).
The equations .thus derived contain 17 constants
and parameters, viz.:
1.Six integration constants:
K l , L I , il l l , K 2 , L,,
and
M 2
2. Eight constants:
A l , B 1 ,
C1
D l , A 2 , B 2 , C2
and
U 2 .
3 Two l
and
h 2
present
i n
the
ential equation, but actually unknown.*
4. One parameter:
x 2 ,
defined by equation 3).
5.
F'our additional parameters
x l ,
x 3 p and
s,
defined a s follows:
A
x
=
-
in which
:YI is
the distance bit to
ni
stabilizer.
N
x ,
=-,
in which
X
is the distance stabilizer
n1
to point of tangency.
r
p =-
ni
sin
a
S
s
= -
r
*For more comple te
explanation,
see Ref. 1, p.
200.
in which
r
i s the apparent radius of the hole,
i.e., the radial clea ranc e between hole and col-
lar; and
S
is the stabil izer radial clearance.
There are nine boundary conditions, viz.:
A t x = O
u 1
O
(12)
d 2 u l '
--
-
0
(13)
dx2
A t x
=
x l
u1 = p s (14)
u 2 = p s (15)
d u , d u ,
=
(16)
dx dx
d 2 u 1 d 2 u 2
--
- -
(17)
dxz dx2
A t x = x l x g
u2 = P (18)
dl,
--
-
0
(19)
dx
d 2 u 2
--
- 0
(20)
dx2
The following i b t conditions
were
imposed on
l a
and
U l b ,
A t x = O
-
- U l b (21)
X 1
A t x = -
3
l a = ' l b
(22)
2 x 1
A t x = -
l a =
' l b (23)
At x = x I
U l a = U l b .
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180
H B . WOODS
AND ARTHUR
LUBINSKI
S~n in ia r i z in~ ,here are 17 relationships between
21 cons tan ts and paranieters. Therefore, theoreti-
cally, 1 7 of the parameters could be expr essed a s
functio ns of the other
4
which were chosen p, x
2
x l and s One such expression could be written:
Le t denote the angl e of inclina tion with re-
sp ec t to the ve rti cal of the force on bit. F rom F ig.
26 we obtain:
H I
tan qi- J
=-
or, from equations (5) and (3) and rearranging:
s in X z
Substi tut ing (30) into (29), an equation of the fol-
lowing form could be obtained:
s i n a - t a n ( a - 6 )
= ~ ( p , s , ~ ~ , x ~ )31)
s in
Substituting equation (19) and (16) similar one s
into equation (11) and into the cor respond ing equa-
tion for the section TA, the following relationships
could be obtained:
Consid er a lar ge number of se t s of valu es of
x 2
(weight on bit),
x l
(dist ance bit to stabilizer), and
s (st abil izer clearance). F or ea ch se t, the range of
values of p (essentially collar clearance) for which
u I b and u 2 b are snialler than p (collars do not con-
tact the wall of the hole between the points B and
A may be fo u n d . Equation (31) has a physical
meaning in this range only.
Second Case: Collars Contact Wall of the Hole
between Bit
and
Stabilizer
Thi s c a s e i s represented in E ig. 27, which i s
simila r to E ig. 26. l he only difference i s tha t the
drill collars c o n t a c t the wall of the hole at T
X
=
nix is the distance between B and T.
l he approxinlating fu nctions use d for sec ti on s
BT, TP,
and
PA were a s follows:
X
u l a
=
psin- (34)
2 x a
F ig
27
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USE OF STAB ILIZER S IN CONT ROLLING HOLE DEVIATION
Proceeding a s for the first cas e, equations (37),
(38 ), and (39) may be derived, the first two of which
are similar to e quatio ns (29) and (31):
s i n a - t a n ( a - 4 )
= G ( p , s, x , ,x , ) (38 )
sin
a
hl -h2+x, >0 means that the collar pr es se s agains t
the wall of the hole at T It i s only in t his range
that equation (38) i s valid.
Ideal Position of Stabilizer
The left-hand member of equat ions (31) and (38)
i s the expres sion of Ref.
6.
F or sm all va lues of
a and
4
i t i s equal to /a, i.e., the ordinate of
Fig. 20f Ref.
5.
F or a gi ven s e t of va lu es of
p s ,
and x2, i.e.,
for a given hole size, collar size, weight, and sta-
stabilizer clearance, the hole deviation will be the
smallest when the inclination
4
of the force on bit
i s the smallest, i.e., when [si na- tan fa- +)I /si na
i s minimum. Therefore, the optimum dis tan ce xl ,
bit to s tabili zer, i s that for which [s in a-tun(a-+)I
/sin
a
i v e n either by equation (31) or equation
(381, i s minimum.
Percentage Improvement
Le t x2 be the dimens ionles s weight on bit when
a stabilizer i s used and x2 the d i n~ n s i o n e s
s
w e i g h t with no stabilizer for the same values of
[sin a-tan(a+)]/sin
a
and p, i.e., for the same hole
si ze , collar siz e, and hole inclination. By definition,
the percentage improvement i s 100 (x2 /x2 -1). With
a stabilizer in any position, x2 may be determined
from either equation (31) or equation (38), which-
ever i s valid. ~ ~ n ~ a ye determined from equations
(13) and (15) of Ref. 5, provided [sina-tan(a-+)I
/ s i n a and are substituted for
+/a
and arn/r,
respectively.
Accuracy of Iterations
Because of the complexity of the ex pressi ons ob-
tained in both of the iterative procedures, it would
be out of the question to check eit he r of them by a
second algebraic iteration. sec ond iteration was,
however, perfornied on a few numerical values cor-
responding to the first case. It was found that the
use of t he cu bic equatio ns a s approximating func-
tions resulted in negligible errors.
l he reason why a simil ar approxinlating function
was not used in the second case, involving three
ela sti c curves instead of two, i s because the alge-
bra would beconie altogether too complicated.
To check the iteration in the second case, it was
noted that equations (31) and (38) should give the
sanie result in the limiting case in which, physical-
ly, the collars c o n t a c t the wall of the hole with
zero force. Ageenlent was good in most c a s e s .
However, in a not too signif icant range, clo se to
helical buckling conditions, agreement was poor
and the results obtained for the second case were
slightly changed to obtain agreement.
Actual Mathematical Treatment and Comoutations
The mathematical treatment us ed in t hi s work has
been only more or less synibolically described in
this Appendix. The coordinate axes actually used
were of ten d i
f f
e r e n t from tho se indica ted and i t
would unnecessar ily conlplicate the Appendix to in-
dicate all such details.
Actually, because of the conlplexity of the equa-
tions, it was impossible to express equations (29),
(32), and (33) in an algebraic form. It was, however,
possi ble to obtain four equations a s follows:
Elimination of the parameter x3 was performed by
trial and error. In fact, it was found necessary to
resor t to trial-and-error procedure many times; and,
without the u se of the I13M Programnied E lect ronic
Calculator, this work probably would have been im-
possible.
In view of the conlplexity and length of actual
equations, their inclusion in this Appendix would
not be practical. For instance, equation (40) con-
tai ns 13 1 terms. On request, actual equ ations will
be furnished by the authors.
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182
H B WOODS AND ARTHUR LUBINSKI
CKNOWLEDGMENT
l 'he authors wish to thank both H u g h e s Tool
Conipany and Stanolind Oil and Gas Company for
perniission to publish thi s paper. They feel indebted
to the API Study Committees on Straight-hole Drill-
ing in both hlid-Continent and Southwestern Dis-
tricts for having organized meetings at which the
authors obtained useful inforniation. They als o wish
to thank the following for valuable help:
R B. hlcCloy and W R Johnston, chairmen of
the API study comn~ittees.
W 13
Rider, Jeanne Haley, and
J.
C. Stall,
Stanolind Oil and Gas Company.
R A
Cunningham,
E. A
hlorlan, F.
H.
Little,
and
S.
T.
Crews, Hughes Tool Company.
Peter A Szego, formerly with The Rice Institute.
R J. Bromell, Great Western Drilling Company;
John
W
Speer, Shell Oil Company.
H. hl
Rollins and
W B.
Bachnian, Drilco Oil
Tools, Inc.
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Lubinski, Arthur:
A
Study of the B u c k l i n g of Rotary
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1950).
Willers, Fr. A: T he Bu ckli ng of Heavy Ro ds (i n German),
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21 43 1941).
MacDonald,
G.
C. and Lubinski, Arthur: Straight-hole
Drilling in Crooked-hole Country, Drilling an d Prod uc-
tion Practice,
80 1951).
4L ub in sk i, Arthur, and Woods, H.
B:
Factors Affecting
the Angle of Inclination and Doglegging in Rotary Bore
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