api-55-165 use of stabilizers in controlling hole deviation

8/10/2019 API-55-165 Use of Stabilizers in Controlling Hole Deviation

1/18

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 .


2/18

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.


3/18

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 .


4/18

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


5/18

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.


6/18

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


7/18

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


8/18

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.


9/18

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.


10/18

XG

S

PO

I

S

G

SN

PO

I

S

G

S

PO

I

S

XG

S

PO

-

4

5

4

s

f

C

m

U

I

S


11/18

xWG

S

PO

I

S

XG

S

PO

I

S

.

S

PO

I

S

G

S

PO


12/18

O

S

PO

O

S

PO

.

I

-

,O

r

I

S

xD

S

PO

I

S

O

S

PO


13/18

MG

S

PO

-

XWG

S

PO

I

S

C

S

PO

G

S

PO

I

S

I

S

3NH


14/18

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.


15/18

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 .


16/18

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


17/18

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.


18/18

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.

REFERENCES

Lubinski, Arthur:

A

Study of the B u c k l i n g of Rotary

Drilling Strings, Drilling and Production Practice, 178

1950).

Willers, Fr. A: T he Bu ckli ng of Heavy Ro ds (i n German),

Zeitschrift fur Angewandte Mathematik und Mechanik,

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).

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