Geothermal Well Casing Buckling

v

c ' ! b d b i A REPORT

SAND82-0863 Unlimited Release UC-66c

Printed February 1983

Euler Buckling

of

Geothermal Well Casing

SAND--82-0863 DE83 010292

Robert P. Rechard, Karl

W.

Schuler

Prepared by

Sandia National Laboratories

Albuquerque, New Mexico 87 185 and Llvermore, California 94550 for the United States Department of Energy

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3

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SAND82-0863

EULER BUCKLING OF GEOTHERMAL WELL C A S I N G

R. P. R e c h a r d K.

W.

S c h u l e r A p p l i e d M e c h a n i c s D i v i s i o n S a n d i a N a t i o n a l L a b o r a t o r i e s A l b u q u e r q u e , New M e x i c o 87185 HOTICE

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avatfability,

_-

. -. _ . . - - . A B S T R A C T G e o t h e r m a l w e l l o p e r a t o r s h a v e e x p r e s s e d c o n c e r n o v e r t h e v u l n e r a b i l i t y of u n s u p p o r t e d c a s i n g t o b u c k l i n g f r o m t h e r m a l e l o n g a t i o n . I n t h i s r e p o r t , we p r e s e n t p r e l i m i n a r y n u m e r i c a l a n d t h e o r e t i c a l c a l c u l a t i o n s , w h i c h i n d i c a t e t h e b u c k l i n g phenomenon s h o u l d n o t b e s e r i o u s i n N-80 c a s i n g i f t h e s t r i n g i s t e n s i o n p r e l o a d e d . B u c k l i n g w o u l d b e d e t r i m e n t a l f o r ' K-55 c a s i n g . The e f f e c t o f w a l l c o n t a c t was f o u n d t o b e b e n e f i c i a l f o r c l o s e l y c o n f i n e d p i p e s t r i n g s and o f n o d e t r i m e n t when h o l e gaps a r e l a r g e . The weakness o f A P I s c r e w j o i n t s

i n

b e n d i n g a p p e a r s t o b e t h e s t r u c t u r a l l i m i t a t i o n . The a n a l y s i s assumed s t r e s s e s above y i e l d c o n s t i t u t e d f a i l u r e , t h a t t h e r m a l

e x p a n s i o n was s t r a i n c o n t r o l l e d , and t h a t t h e c a s i n g was c o n t i n u o u s . E x c e s s i v e i n t e r n a l p r e s s u r e i n s t a b i l i t y was i g n o r e d . The t e m p e r a t u r e v a r i a t i o n c o n s i d e r e d was b e t w e e n c e m e n t i n g c o n d i t i o n s

o f

100-200°F

(40-95°C)

and s h u t - i n c o n d i t i o n s o f 425-450°F ( 2 2 0 - 2 3 0 ° C )

.

CONTENTS Page INTRODUCTION.

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1 G e o t h e r m a l W e l l C o n s t r u c t i o n .

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1 W e l l C a s i n g D e s i g n .

.

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.

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5 T e m p e r a t u r e E n v i r o n m e n t

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.

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6 C a s i n g I n s t a b i l i t y .

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11 ANALYSIS.

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1 7 T h e o r e t i c a l Model

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1 7 N u m e r i c a l Model

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30

A d d i t i o n o f C o n s t a n t S t r e s s

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3 3 A n a l y t i c Summary.

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3 3 RESULT IMPLICATIONS

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3 5 T h e r m a l l y I n d u c e d E u l e r B u c k l i n g .

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3 5 J o i n t B e h a v i o r . , .

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3 7

SUMMARY AND CONCLUSIONS

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3 9

REFERENCES.

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4 1 A P P E N D I X A

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N o m e n c l a t u r e

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4 3 A P P E N D I X B

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D e r i v a t i o n o f E q u a t i o n s .

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4 5

I L L U STR AT

IO

NS F i g u r e Page 1. T y p i c a l G e o t h e r m a l W e l l C o n s t r u c t i o n and C a s i n g T e m p e r a t u r e P r o f i l e .

. . .

3 2. I d e a l i z e d C o n d i t i o n s C a u s i n g C a s i n g B u c k l i n g w i t h T e m p e r a t u r e E x c u r s i o n .

. . .

7 3. P r e l i m i n a r y GEOTEMP C a l c u l a t i o n s o f T e m p e r a t u r e C o n d i t i o n s D u r i n g C e m e n t i n g

. . .

9 4. P o s t u l a t e d B u c k l i n g F a i l u r e Modes: a ) L o c a l , P l a s t i c D e f o r m a t i o n , b ) E u l e r b u c k l i n g , c ) E u l e r B u c k l i n g w i t h S u b s e q u e n t W a l l C o n t a c t , and d ) H e l i c a l B u c k l i n g

. . .

1 2 5 . Q u a l i t a t i v e P l o t o f T e m p e r a t u r e Change V e r s u s 6. D e f i n i t i o n o f Terms: a ) L i n e S k e t c h and 7 . Locus D e l i n e a t i n g E u l e r B u c k l i n g R e g i o n : ? l o t U n s u p p o r t e d L e n g t h D e p i c t i n g B u c k l i n g R e g i o n s

.

1 4

. . .

b ) F r e e Body Diagram. 1 9 o f T e m p e r a t u r e Change ( A T ) V e r s u s N o r m a l i z e d U n s u p p o r t e d L e n g t h ( L / D ) .

. . .

21 8. Maximum S t r e s s ( u ) V e r s u s T e m p e r a t u r e Change ( A T ) f o r 1 3 - 3 / 8 i n c h 54.5 p p f C a s i n g Assuming U n s u p p o r t e d L e n g t h s ( L / D ) o f 50, 100, and 200

.

2 5 9. Maximum D e f l e c t i o n V e r s u s T e m p e r a t u r e Change ( A T )

for

1 3 - 3 / 8 i n c h 54.5 p p f C a s i n g Assuming U n s u p p o r t e d L e n g t h s ( L / D ) o f 50, 100, and

200

26 10. D e f o r m e d C a s i n g Shapes w i t h W a l l C o n s t r a i n t

P r e d i c t e d b y MARC and T h e o r e t i c a l M o d e l s ,at a ) A T = 80'F,

b )

M A R C R e s u l t s a t A T = 300 F,

a n d c ) A n a l y t i c R e s u l t s a t AT = 300°F

. . .

27 11. Maximum S t r e s s ( u ) V e r s u s A T f o r 1 3 - 3 / 8 i n c h

54.5 p p f C a s i n g f o r U n s u p p o r t e d L e n g t h ( L / D ) o f 1 0 0 w i t h W a l l C o n t a c t : a ) A n a l y t i c Model, b ) MARC Computer Code, and c ) C o n s t a n t S t r e s s

c P

.

INTRODUCTION D r S l l i n g f o r g e o t h e r m a l e n e r g y b e g a n as e a r l y as t h e 1 9 2 0 ' s i n t h e G e y s e r s f i e l d i n n o r t h e r n C a l i f o r n i a , b u t a s e r i o u s e f f o r t t o h a r n e s s g e o t h e r m a l e n e r g y f o r power g e n e r a t i o n was n o t begun i n t h e U n i t e d S t a t e s u n t i l t h e 1 9 7 0 ' s . On a n a t i o n a l s c a l e , t h e r e i s t h e g e o l o g i c p o t e n t i a l t o d e v e l o p 20,000 MW o f e l e c t r i c a l e n e r g y . The g e o t h e r m a l e n e r g y i n d u s t r y p e r f o r m a n c e i n t h e l a s t 1 0 y e a r s and t h e g e o l o g i c p r o s p e c t s i n d i c a t e t h e i n d u s t r y has t h e p o t e n t i a l f o r g r o w t h and can make a

c o n t r i b u t i o n i n s u p p l y i n g t h e e n e r g y needs o f t h e n a t i o n . T h e r e a r e numerous s i m i l a r i t i e s b e t w e e n c o n v e n t i o n a l o i l and gas w e l l s and g e o t h e r m a l w e l l s i n c o n s t r u c t i o n and

o p e r a t i o n . However, i m p o r t a n t d i f f e r e n c e s do e x i s t ( w h e t h e r f r o m d r y steam, d r y h o t r o c k , h o t w a t e r , o r g e o p r e s s u r i t e d f l u i d r e s e r v o i r s ) . F l u i d f l o w r a t e s a r e an o r d e r o f m a g n i t u d e l a r g e r t h a n i n t h e p e t r o l e u m i n d u s t r y . The h i g h t e m p e r a t u r e s e n c o u n t e r e d a f f e c t t h e d r i l l b i t , d r i l l i n g mud and t h e cement p e r f o r m a n c e . R e s e r v o i r c a l c u l a t i o n s m u s t i n c l u d e an e n e r g y b a l a n c e as w e l l as a mass b a l a n c e . F i n a l l y , d i f f i c u l t g e o l o g y , c o r r o s i v e e n v i r o n m e n t s , and t h e r m a l s t r e s s e s i n d u c e d i n t h e w e l l c a s i n g p r e s e n t t h e c a s i n g d e s i g n e r w i t h a new s e t o f f a i l u r e modes t o c o n s i d e r . G e o t h e r m a l W e l l C o n s t r u c t i o n T h i s i n t r o d u c t i o n i s i n t e n d e d t o p r o v i d e t h e r e a d e r u n f a m i l i a r w i t h g e o t h e r m a l w e l l c a s i n g d e s i g n a n d c o n s t r u c t i o n n e c e s s a r y b a c k g r o u n d i n f o r m a t i o n . However, i t a l s o s e r v e s t o r e m i n d t h e r e a d e r t h a t a l t h o u g h t h e c a s i n g s e l e c t i o n i s b a s e d o n t h e w o r s t c a s e d e s i g n c r i t e r i a f r o m b u r s t , c o l l a p s e , t e n s i o n , e t c . , s t r e s s e s f r o m many d i f f e r e n t l o a d s c a n b e

p r e s e n t s i m u l t a n e o u s l y -and c o n t r i b u t e t o c a s i n g f a i l u r e . More c o m p r e h e n s i v e d i s c u s s i o n s o f t h e v a r i o u s f a c t s o f G e o t h e r m a l w e l l s a r e a v a i l a b l e (e.g. Edwards e t a l . , 1 9 8 2 ) . b e u s e d f o r d i s c u s s i o n . T e m p e r a t u r e p r o f i l e s o f t h e c a s i n g and u n d i s t u r b e d f o r m a t i o n a r e a l s o shown. F i g u r e 1 c o n t a i n s w e l l f e a t u r e s f r o m s e v e r a l t y p e s o f g e o t h e r m a l f i e l d s and t h u s c a n n o t t r u l y b e c l a s s i f i e d as l l t y p i c a l . l l a r e d i r e c t i o n a l l y d r i l l e d . A p p r o p r i a t e d r i l l s i t e s a r e d i f f i c u l t t o l o c a t e i n t h e r o u g h t e r r a i n o f t e n f o u n d a b o v e g e o t h e r m a l f i e l d s . I t i s a l s o d e s i r a b l e t o d r i l l a t an a n g l e t o i n t e r s e c t m o r e f r a c t u r e s

.

G e o t h e r m a l r e s e r v o i r s f r e q u e n t l y o c c u r i n f r a c t u r e d r e s e r v o i r s b e l o w 3000 f t ( 9 0 0 m ) ; h e n c e f r a c t u r e s a r e p r i m a r i l y v e r t i c a l .

Most

g e o t h e r m a l r e s e r v o i r s a r e b e l o w t h e d r i l l mud h y d r o s t a t i c p r e s s u r e w h i c h c a u s e s l o s t c i r c u l a t i o n p r o b l e m s d u r i n g d r i l l i n g and c e m e n t i n g . A l s o , l o w g e o t h e r m a l r e s e r v o i r p r e s s u r e s make d e t e c t i o n o f s t e a m

or

h o t w a t e r b e a r i n g f r a c t u r e s d i f f i c u l t . The u s e o f a i r r e d u c e s t h e d r P l l f l u i d d e n s i t y and g r e a t l y s p e e d s u p d r i l l i n g . However, t h e d r i l l b i t l i f e i s g r e a t l y r e d u c e d b e c a u s e o f t h e h i g h t e m p e r a t u r e s e n c o u n t e r e d . The n e a r s o n i c v e l o c i t i e s p r o d u c e d w h i l e c a r r y i n g t h e c u t t i n g s u p t h e o u t s i d e o f t h e d r i l l p i p e a l s o c a u s e s e x c e s s i v e e r o s i o n o f t h e d r i l l p i p e . c o n d u c t o r p i p e , s u r f a c e c a s i n g , i n t e r m e d i a t e c a s i n g a n d p r o d u c t i o n c a s i n g . The p r o d u c t i o n c a s i n g i s o f t e n s e t as a p r o d u c t i o n l i n e r w i t h a t i e b a c k . P r o d u c t i o n c a s i n g a n d p r o d u c t i o n l i n e r s a r e d e s i g n e d w i t h t h e same c r i t e r i o n as i n t e r m e d i a t e c a s i n g and d r i l l i n g l i n e r s e x c e p t t h a t c o n s i d e r a t i o n o f d r i l l i n g wear i s n o t r e q u i r e d . The w e l l c o n s t r u c t i o n d i f f e r s s l i g h t l y f r o m c o n v e n t i o n a l o i l w e l l s i n t h a t each c a s i n g i s cemented t o t h e s u r f a c e . i n s t a l l e d . I t a i d s i n p r e v e n t i n g w a s h o u t s a r o u n d t h e d r i l l F i g u r e 1 shows a s c h e m a t i c o f a g e o t h e r m a l w e l l w h i c h w i l l The w e l l i s shown v e r t i c a l , b u t f r e q u e n t l y g e o t h e r m a l w e l l s The s t a n d a r d c o m p o n e n t s o f t h e w e l l c a s i n g p r o g r a m a r e C o n d u c t o r p i p e i s t h e f i r s t s t r i n g o f p i p e t o b e

GEOTHERMAL WELL SCHEMATIC

AND CASING TEMPERATURE

F i g u r e

1.

THE SURFACE INTERMEDIATE 13-3/8 INCH BUTTRESS JOINTS 8001 100 200c 5001 Q526'F

I

I

-

350°F- TEMPERATURE PROFILES 0 -UNDISTURBED FORMATION -CEMENT-SET

I'

TEMPERATURE 0 -0PERATINa CASING TEMPERATURE -SHUT-IN CASING TEMPERATURE

L

100 200 300 400 50°F L l 5 0 0

J

TEMPERATUREOF T y p i c a l G e o t h e r m a l We1 1 C o n s t r u c t T e m p e r a t u r e P r o f i l e .

on

and C a s i n g

.

z r i g s , p r o v i d e s a c o n d u i t f o r d r i l l i n g f l u i d s t o s u r f a c e p i t s , and h e l p s s u p p o r t w e l l h e a d e q u i p m e n t . C o n d u c t o r p i p e i s s e t s h a l l o w and i s n o t u s u a l l y c o n s i d e r e d a p r e s s u r e s t r i n g . The s u r f a c e c a s i n g i s t h e f i r s t t r u e c a s i n g s t r i n g . As a p r i m a r y s t r u c t u r a l member i t p r o v i d e s s u p p o r t f o r s u b s e q u e n t c a s i n g s t r i n g s . To a v o i d b u c k l i n g p r o b l e m s f r o m t h e c o m p r e s s i v e l o a d s a p p l i e d , i t i s o f t e n c e m e n t e d t o t h e s u r f a c e even i n c o n v e n t i o n a l w e l l s . S u r f a c e c a s i n g m u s t a l s o p r o v i d e s u f f i c i e n t h o l e s t a b i l i t y , p r o t e c t i o n t o a q u i f e r s , s o l i d s u p p o r t f o r t h e r e s e r v o i r p r e s s u r e , and p r e s s u r e i n t e g r i t y i n t h e e v e n t o f a b r u p t p r e s s u r e i n c r e a s e s ( b l o w o u t s and k i c k s ) . S u r f a c e c a s i n g i s s u b j e c t e d t o d r i l l i n g wear w h i c h r e q u i r e s h e a v y c a s i n g . Common s e t t i n g d e p t h s a r e b e t w e e n 1000 a n d 2500 f t ( 3 0 0 t o 760

m).

I n a c o n v e n t i o n a l w e l l , i n t e r m e d i a t e c a s i n g c a n b e e x p o s e d t o h i g h b o t t o m h o l e p r e s s u r e s w h i c h r e q u i r e s s u b s t a n t i a l b u r s t r e s i s t a n c e . H i g h c o l l a p s e r e s i s t a n c e i s a l s o r e q u i r e d f o r t h e

d e e p e r c a s i n g . Heavy muds and cement s l u r r i e s r e q u i r e d f o r d e e p d r i l l i n g c a n c r e a t e h i g h c o l l a p s e l o a d s s h o u l d l o s t c i r c u l a t i o n z o n e s e m p t y t h e p i p e . T h e s e c o n d i t i o n s d i c t a t e h e a v y c a s i n g . As w i t h s u r f a c e s t r i n g s , i n t e r m e d i a t e c a s i n g and d r ill i n g 1 i n e r s a r e s u b j e c t e d t o m e c h a n i c a l damage f r o m d r i l l i n g wear. v a l u e s i n many g e o t h e r m a l f i e l d s . However, a s t a n d a r d c a s i n g p r o g r a m i n t h e p r o m i n e n t G e y s e r s g e o t h e r m a l f i e l d c o n s i s t s o f 26 a n d / o r 20 i n c h ( 6 6 0 o r 508 mm) d i a m e t e r c o n d u c t o r p i p e , 1 3 - 3 / 8 i n c h ( 3 4 0 mm) s u r f a c e c a s i n g , and 9 - 5 / 8 i n c h ( 2 4 4 mm) i n t e r m e d i a t e c a s i n g

or

l i n e r ( w i t h o r w i t h o u t a t i e b a c k s t r i n g o f e i t h e r 9 - 5 / 8 o r 1 0 - 3 / 4 i n c h ( 2 4 4 o r 273 mm) c a s i n g ) (Capuano, 1 9 7 9 ) . Because s u p e r h e a t e d s t e a m i s p r o d u c e d , a p r o d u c t i o n c a s i n g i s n o t needed. An open h o l e i n t h e r e s e r v o i r i s u s u a l l y s t a b l e . T h e c a s i n g s i z e s shown i n F i g u r e 1 a r e commonly s e l e c t e d

W e l l C a s i n g Des&

_--

-

The p r o p e r s e l e c t i o n o f t h e t y p e , s i z e , and s e t t i n g d e p t h o f t h e w e l l c a s i n g i s b a s e d on t h e e x p e c t e d w e l l o p e r a t i o n c o n d i t i o n s and t h e d r i l l i n g s i t e g e o l o g y . The u s u a l p r a c t i c e i s t o c o n s i d e r t h e w o r s t c a s e o r maximum l o a d i n d e t e r m i n i n g t h e r e q u i r e d c a s i n g c o n f i g u r a t i o n . n e s t i n g a r e u s u a l l y i g n o r e d . A l i s t o f c a s i n g f a i l u r e modes i n c l u d e s ( S n y d e r , 1 9 7 9 ) : C o m p l i c a t i o n s due t o c a s i n g * M e t a l f a i l u r e : b u r s t , c o l l a p s e , t e n s i o n , o r c o r r o s i o n , * M e c h a n i c a l damage: d r i l l p i p e wear, w e l d i n g p r o b l e m s , t h r e a t damage, o r l e a k a g e and p e r f o r a t i o n , . C a s i n g i n s t a b i l i t y : l a t e r a l d e f l e c t i o n ( b u c k l i n g ) f r o m e x c e s s i v e c o m p r e s s i v e l o a d s ( e . g t h e r m a l e x p a n s i o n ) o r i n t e r n a l p r e s s u r e , *Cement f a i l u r e s : v o i d s f r o m l o s t c i r c u l a t i o n zones' o r cement t o o l p r o b l e m s , cement d i s s o l u t i o n and c o r r o s i o n p e r m i t t i n g f l u i d movement b e t w e e n c a s i n g and f o r m a t i o n , o r p o o r h i g h - t e m p e r a t u r e s l u r r y b e h a v i o r , f a i l u r e s ( t e l e s c o p i n g ) , l e a k a g e i n c o u p l i n g s f r o m c y c l i c l o a d i n g , e x c e s s i v e b e n d i n g l o a d s

i n

dog l e g s , s t r a i n b e y o n d u l t i m a t e . T h i s t a b u l a t i o n p r e s e n t s p o s s i b l e f a i l u r e modes. * T h e r m a l s t r e s s f a i l u r e s : c o m p r e s s i o n a n d / o r t e n s i o n U n f o r t u n a t e l y l i t t l e d e t a i l e d p u b l i c i n f o r m a t i o n e x i s t s on g e o t h e r m a l w e l l c a s i n g f a i l u r e s . The a n a l y s t can o n l y p o s t u l a t e t y p e s and f a i l u r e mechanisms and t h u s t h e d a n g e r e x i s t s t h a t an i m p o r t a n t o r more l i k e l y f a i l u r e mechanism has b e e n o v e r l o o k e d . i n d e p e n d e n t . For--example, a cement f a i l u r e c o u l d c a u s e i n s u f f i c i e n t l a t e r a l s u p p o r t and r e s u l t i n c a s i n g i n s t a b i l i t y when h i g h i n t e r n a l p r e s s u r e s o c c u r r e d . The r e s u l t i n g l a t e r a l d e f l e c t i o n c o u l d i n t u r n r e s u l t i n e x c e s s i v e d r i l l p i p e wear d u r i n g t h e d r i l l i n g o p e r a t i o n and s u b s e q u e n t b u r s t o f t h e c a s i n g d u r i n g t h e p r o d u c t i o n o p e r a t i o n . I t s h o u l d b e n o t e d t h a t t h e f a i l u r e modes l i s t e d a r e n o t

I n o i l o r gas w e l l c a s i n g d e s i g n , t h e m a j o r c o n c e r n a d d r e s s e d i s m e t a l f a i l u r e f r o m b u r s t , c o l l a p s e , o r t e n s i o n . However, t h e p r e s e n c e o f t h e r m a l l o a d s i n g e o t h e r m a l w e l l c a s i n g g r e a t l y i n c r e a s e s t h e o p p o r t u n i t y f o r c a s i n g i n s t a b i l i t y . C a s i n g s t a b i l i t y can b e i m p r o v e d by: 1 ) c e m e n t i n g t h e e n t i r e s t r i n g t o p r o v i d e l a t e r a l s u p p o r t o r 2 ) a p p l y i n g a t e n s i o n l o a d i n t h e u n c e m e n t e d s e c t i o n s . F u l l y c e m e n t i n g t h e c a s i n g s t r i n g i s t h e u s u a l c h o i c e . U n f o r t u n a t e l y , p o o r f o r m a t i o n c o n d i t i o n s f r e q u e n t l y e x i s t i n g e o t h e r m a l a r e a s . The r e s e r v o i r i s u s u a l l y b e l o w h y d r o s t a t i c p r e s s u r e a n d can b e h i g h l y f r a c t u r e d . C o n s e q u e n t l y , l o s t c i r c u l a t i o n w h i l e d r i l l i n g w i t h mud o r c e m e n t i n g c a s i n g i s common. I t i s t h u s i m p o s s i b l e t o e n s u r e a c o m p l e t e cement j o b i n many i n s t a n c e s . F a i l u r e o f s t a g e c e m e n t i n g t o o l s i n g e o t h e r m a l w e l l s i s f r e q u e n t and a l s o c r e a t e s u n s u p p o r t e d t u b u l a r s e c t i o n s ( S n y d e r , 1979). B u c k l i n g f a i l u r e s o f t h e c a s i n g f r o m t h e r m a l e x p a n s i o n w h e r e cement f a i l u r e s h a v e o c c u r r e d i s t h e s u b j e c t o f t h i s r e p o r t ( F i g u r e 2 ) . T e m D e r a t u r e E n v i r o n m e n t The t e m p e r a t u r e e n v i r o n m e n t i s i m p o r t a n t i n f o r m a t i o n f o r t h e t h e r m a l a n a l y s i s . f i g u r e 1 p r e s e n t s a h y p o t h e t i c a l t e m p e r a t u r e e n v i r o n m e n t . The s u r f a c e and b o t t o m h o l e t e m p e r a t u r e s a r e as s u r m i s e d b y t h e w e l l o p e r a t o r s i n The G e y s e r s f i e l d (Pye, 1980; J e n k i n s and S n y d e r , 1 9 7 9 ) , b u t t h e a c t u a l t e m p e r a t u r e p r o f i l e s t h r o u g h o u t t h e s t r a t i g r a p h y and c a s i n g a r e unknown. I n F i g u r e 1 c a s i n g t e m p e r a t u r e s a r e assumed t o v a r y l i n e a r l y . The u n d i s t u r b e d f o r m a t i o n p r o f i l e i s shown w i t h one e l b o w . A f e w p r o f i l e s a v a i l a b l e f r o m The

G e y s e r s f i e l d c o n t a i n t w o k i n k s : t h e s e c o n d e l b o w o c c u r s w i t h i n t h e f i r s t 500 f t ( 1 5 0 m ) .

F o r w e l l s c o m p l e t e d i n l o w - p r e s s u r e h o t - w a t e r o r s t e a m r e s e r v o i r s , t h e c a s i n g s a r e t h o u g h t t o b e cemented a t a t e m p e r a t u r e b e t w e e n 100-2OO'F (40-95°C). T h i s assumes t h e

i

.

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HOT WATER, STEAM

CEMENT SHEATH

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ure 2 .

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Temperature Excursion.

c a s i n g i s n o t p u r p o s e l y a l l o w e d t o h e a t u p b e f o r e c e m e n t i n g . Upon c o m p l e t i o n , t h e w e l l i s t e m p e r a t u r e c y c l e d b e t w e e n p r o d u c i n g c o n d i t i o n s o f a p p r o x i m a t e l y 325-400°F (160-205°C) and s h u t i n c o n d i t i o n s o f 425-450°F ( 2 2 0 - 2 3 5 ° C ) . The c y c l i n g i s due t o a i r p o l l u t i o n s t a n d a r d s w h i c h l i m i t t h e v e n t i n g o f g e o t h e r m a l w e l l s . C y c l i n g c a n o c c u r 2 t o 3 t i m e s p e r week i f t h e s t e a m c o n t a i n s a p o l l u t a n t s u c h as h y d r o g e n s u l f i d e ( H 2 S ) . When t h e w e l l r e q u i r e s r e m e d i a l w o r k , t h e c a s i n g t e m p e r a t u r e i s r e d u c e d t o a r o u n d 100°F ( 4 0 ° C ) w i t h c o o l w a t e r . These a r e a p p r o x i m a t e v a l u e s o n l y . A t e m p e r a t u r e p r o f i l e i s v e r y u s e f u l i n v i s u a l i z i n g t h e t e m p e r a t u r e change t o w h i c h each t y p e o f c a s i n g i s s u b j e c t e d . A c c u r a t e i n f o r m a t i o n o f t h i s t y p e w o u l d g r e a t l y a i d t h e d e s i g n and a n a l y s i s o f t h e c a s i n g i n t e g r i t y . As seen i n F i g u r e 1, t h e c a s i n g can b e s u b j e c t e d t o l a r g e t e m p e r a t u r e changes. C o n s e q u e n t l y l a r g e t h e r m a l s t r e s s e s m u s t b e a n t i c i p a t e d . I t i s seen t h a t t h e more s e v e r e t e m p e r a t u r e changes o c c u r n e a r t h e s u r f a c e d u r i n g t h e c y c l i n g b e t w e e n p r o d u c t i o n and s h u t - i n . However, t h e w h o l e c a s i n g s t r i n g can b e s u b j e c t e d t o l a r g e t e m p e r a t u r e changes a f t e r c e m e n t i n g and whenever t h e w e l l m u s t b e quenched. An a c c u r a t e c e m e n t - s e t t e m p e r a t u r e i s e s s e n t i a l t o t h e t h e r m a l s t r e s s a n a l y s i s b e c a u s e t h i s i s t h e t e m p e r a t u r e t h e c a s i n g becomes c o n s t r a i n e d . The G E O T E M P c o m p u t e r p r o g r a m ( W o o l e y , 1980; M i t c h e l l , 1 9 8 2 ) b e i n g d e v e l o p e d u n d e r c o n t r a c t t o S a n d i a w i l l be h e l p f u l i n more c a r e f u l l y d e f i n i n g t h e t e m p e r a t u r e r e g i m e o f t h e w e l l c a s i n g . P r e l i m i n a r y GEOTEMP t e m p e r a t u r e c a l c u l a t i o n s a r e shown i n F i g u r e 3. R a d i a l t e m p e r a t u r e s a t 200 f t ( 6 0 m ) d e p t h u n d e r t h r e e g e o t h e r m a l f l u i d f l o w c o n d i t i o n s a r e d e p i c t e d f o r a G e y s e r s w e l l . The c e m e n t i n g c o n d i t i o n s a r e l o w e r t h a n g e n e r a l l y assumed b y o p e r a t o r s . V e r i f i c a t i o n o f t h e GEOTEMP p r o g r a m i s n o t c o m p l e t e , b u t t h e t e m p e r a t u r e d i f f e r e n c e shown c o u l d b e s i g n i f i c a n t and needs t o b e more c a r e f u l l y e x a m i n e d .

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.

c a s i n g i s n o t p u r p o s e l y a l l o w e d t o h e a t u p b e f o r e c e m e n t i n g . Upon c o m p l e t i o n , t h e w e l l i s t e m p e r a t u r e c y c l e d b e t w e e n p r o d u c i n g c o n d i t i o n s o f a p p r o x i m a t e l y 325-400°F ( 1 6 0 - 2 0 5 ° C ) and s h u t i n c o n d i t i o n s o f 425-450°F ( 2 2 0 - 2 3 5 ° C ) . The c y c l i n g i s due t o a i r p o l l u t i o n s t a n d a r d s w h i c h l i m i t t h e v e n t i n g o f g e o t h e r m a l w e l l s . C y c l i n g c a n o c c u r 2 t o 3 t i m e s p e r week i f t h e s t e a m c o n t a i n s a p o l l u t a n t s u c h as h y d r o g e n s u l f i d e

(H2S).

When t h e w e l l r e q u i r e s r e m e d i a l w o r k , t h e c a s i n g t e m p e r a t u r e i s r e d u c e d t o a r o u n d 100°F (40'C) w i t h c o o l w a t e r . These a r e a p p r o x i m a t e v a l u e s o n l y . A t e m p e r a t u r e p r o f i l e i s v e r y u s e f u l i n v i s u a l i z i n g t h e t e m p e r a t u r e change t o w h i c h each t y p e o f c a s i n g

i s

s u b j e c t e d . A c c u r a t e i n f o r m a t i o n o f t h i s t y p e w o u l d g r e a t l y a i d t h e d e s i g n and a n a l y s i s o f t h e c a s i n g i n t e g r i t y . As seen i n F i g u r e 1, t h e c a s i n g c a n b e s u b j e c t e d t o l a r g e t e m p e r a t u r e c h a n g e s . C o n s e q u e n t l y l a r g e t h e r m a l s t r e s s e s m u s t b e a n t i c i p a t e d . I t i s seen t h a t t h e m o r e s e v e r e t e m p e r a t u r e c h a n g e s o c c u r n e a r t h e s u r f a c e d u r i n g t h e c y c l i n g b e t w e e n p r o d u c t i o n and s h u t - i n . However, t h e w h o l e c a s i n g s t r i n g c a n b e s u b j e c t e d t o l a r g e t e m p e r a t u r e c h a n g e s a f t e r c e m e n t i n g and whenever t h e w e l l m u s t b e quenched. An a c c u r a t e c e m e n t - s e t t e m p e r a t u r e i s e s s e n t i a l t o t h e t h e r m a l s t r e s s a n a l y s i s b e c a u s e t h i s i s t h e t e m p e r a t u r e t h e c a s i n g becomes c o n s t r a i n e d . The GEOTEMP c o m p u t e r p r o g r a m ( W o o l e y , 1980; M i t c h e l l , 1 9 8 2 ) b e i n g d e v e l o p e d u n d e r c o n t r a c t t o S a n d i a w i l l b e h e l p f u l i n more c a r e f u l l y d e f i n i n g t h e t e m p e r a t u r e r e g i m e o f t h e w e l l c a s i n g . P r e l i m i n a r y GEOTEMP t e m p e r a t u r e c a l c u l a t i o n s a r e shown i n F i g u r e 3. R a d i a l t e m p e r a t u r e s a t 200 f t . ( 6 0 m ) d e p t h u n d e r t h r e e g e o t h e r m a l f l u i d f l o w c o n d i t i o n s a r e d e p i c t e d f o r a G e y s e r s w e l l . The c e m e n t i n g c o n d i t i o n s a r e l o w e r t h a n g e n e r a l l y assumed b y o p e r a t o r s . V e r i f i c a t i o n o f t h e GEOTEMP p r o g r a m i s n o t c o m p l e t e , b u t t h e t e m p e r a t u r e d i f f e r e n c e shown c o u l d b e s i g n i f i c a n t a n d n e e d s t o b e more c a r e f u l l y e x a m i n e d .

W h i l e f a i l u r e s i n cemented s t r i n g s s u c h as c o m p r e s s i o n a n d / o r t e n s i o n f a i l u r e s and c o n n e c t i o n f a i l u r e s a r e o f c o n c e r n , o p e r a t o r s h a v e e x p r e s s e d g r e a t e r c o n c e r n o v e r c a s i n g b u c k 1 i n g i n p a r t i a l l y c e m e n t e d s t r i n g s ( P y e , 1980; Kumataka, 1981, S n y d e r , 1 9 7 9 ) . As r e g a r d s p a r t i a l l y c e m e n t e d s t r i n g s , w o r k i n t h e a r c t i c o i l f i e l d s h a s shown t h a t t h e cement a n d l o r f o r m a t i o n s u p p o r t needed t o a v o i d b u c k l i n g f r o m s u b s i d e n c e i s q u i t e s m a l l ( W i l s o n e t a l . , 1 9 8 0 ) . ( B o t h s u b s ' i d e n c e and t h e r m a l s t r e s s l o a d s a r e s t r a i n c o n t r o l l e d . ) , Because l i t t l e l a t e r a l s u p p o r t i s n e c e s s a r y , b u c k l i n g i s l i m i t e d t o a r e a s w h e r e f o r m a t i o n c o n d i t i o n s c a u s e e n l a r g e d h o l e s t o f o r m w i t h s u b s e q u e n t v o i d s i n t h e cement s h e a t h s u c h t h a t a c o m p l e t e l y u n s u p p o r t e d s e c t i o n o c c u r s ( F i g u r e 2 ) . p a r t i a l l y c e m e n t e d s t r i n g s can b e d i v i d e d i n t o f o u r c a t e g o r i e s . The f a i l u r e t y p e i s d e p e n d e n t on t h e u n s u p p o r t e d c a s i n g l e n g t h and i n t e r n a l - e x t e r n a l p r e s s u r e i n t e r a c t i o n ( F i g u r e 4 ) . The c a t e g o r i e s a r e : C a s i n g i n s t a b i l i t y f a i l u r e s f r o m a t h e r m a l l o a d i n % . L o c a l p l a s t i c d e f o r m a t i o n , ~ E u l e r b u c k 1 i n g , C o n s t r a i n e d E u l e r b u c k l i n g f o l l o w e d b y p l a s . t i c d e f o r m a t i o n *He1 i c a l b u c k l i n g . o r c o l l a p s e due t o o v a l a t i o n , ' . I t i s i m p o r t a n t t o e m p h a s i z e t h e d i f f e r e n c e b e t w e e n s t a n d a r d c o l u m n b u c k l i n g u n d e r an a p p l i e d . l o a d a b u c k l i n g f r o m t h e r m a l f a r c e s w h e r e s u p p o r t o f - a f o l l o w e r a x i a l l o a d i s n o t r e q u i r e d . R a t h e r t h a n c a t a s t r o p h i c .f a i l u v e f r o m a 5 c r i t i c a l t e m p e r a t u r e change, t h e c a s i n g s l o w l y d e f o r m s e l a s t i c a l l y i n t o t h e d e f o r m e d shape f o r l a r g e + u n s u p p o r t e d l e n g t h s . Thus c o l u m n " b e n d i n g " i s a more a p p r o p r i a t e d e s c r i p t i o n o f t h e phenomenon. The p i p e s t r i n g i n s t a b i l i t y m a n i f e s t s i t s e l f as a l a t e r a l d e f l e c t i o n .

7

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The r e s u l t i n g d e f o r m a t i o n may n o t impede o p e r a t i o n s i f t h e d e f o r m a t i o n i s s l i g h t . The l a r g e s t t h e r m a l s t r e s s e s a r e i n t r o d u c e d d u r i n g s h u t - i n a f t e r t h e w e l l i s c o m p l e t e d , t h u s

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d a n g e r o f e x c e s s i v e p i p e wear d u r i n g d r i l l i n g h a s p a s s e d . However, e v e n s l i g h t b e n d i n g a t c o n n e c t i o n s can r e s u l t i n j o i n t f a f l u r e b e c a u s e s t a n d a r d A m e r i c a n P e t r o l e u m I n s t i t u t e ( A P I ) j o i n t s a r e n o t d e s i g n e d t o w i t h s t a n d b e n d i n g s t r e s s e s . F i g u r e 5 q u a l i t a t i v e l y i n d i c a t e s w h e r e v a r i o u s b u c k 1 i n g modes o c c u r . I t i s i m p o r t a n t

t o

n o t e t h a t i n t e r n a l - e x t e r n a l p r e s s u r e i n t e r a c t i o n h a s b e e n i g n o r e d . O n l y u n s u p p o r t e d l e n g t h a n d t e m p e r a t u r e was c o n s i d e r e d . d e f o r m a t i o n a n d / o r c o l l a p s e w o u l d b e e x p e c t e d . A t l o n g e r u n s u p p o r t e d l e n g t h s , E u l e r b u c k l i n g w o u l d o c c u r . W i t h c o n t i n u e d t e m p e r a t u r e i n c r e a s e , t h e c a s i n g c o u l d d e f l e c t enough t o c o n t a c t t h e d r i l l h o l e s i d e s . P l a s t i c d e f o r m a t i o n o r p i p e c o l l a p s e f r o m t h e w e a k e n i n g e f f e c t s o f c r o s s - s e c t i o n o v a l a t i o n c o u l d f o l l o w . t h e o i l w e l l i n d u s t r y , t h e c o r k s c r e w i n g i s due p r i m a r i l y t o e x c e s s i v e , d e s t a b i l i z i n g , i n t e r n a l p r e s s u r e s ( L u b i n s k i e t a1

.,

1 9 6 2 ) . F r e q u e n t l y , t h e d e f o r m a t i o n i s n o t s e v e r e enough t o c a u s e p e r m a n e n t d e f o r m a t i o n ( T e x t e r , 1955).. Because l o n g u n s u p p o r t e d l e n g t h s a r e much l e s s l i k e l y and t h e u l t i m a t e f a i l u r e mechanism i s s i m i l a r t o t h a t e n c o u n t e r e d w i t h s i n g l e o r d e r E u l e r b u c k l i n g , t h i s r e g i o n i s o f l e s s i n t e r e s t . t h e r m a l b u c k l i n g and l o c a l i z e d p l a s t i c d e f o r m a t i o n o f g e o t h e r m a l c a s i n g . F i r s t , a n a l y s i s o f t h e E u l e r b u c k l i n g r e g i m e a s s u m i n g b u i l t - i n ends and s u b s e q u e n t e l a s t i c - p l a s t i c b e n d i n g n e e d s t o b e e x a m i n e d . A n a l y s i s o f n e s t e d c a s i n g b e h a v i o r when c o n s t r a i n e d b y cement a n d / o r f o r m a t i o n s c o u l d a l s o b e i n v e s t i g a t e d m o r e t h o r o u g h l y . Second, a n a l y s i s o f l o c a l i z e d p l a s t i c d e f o r m a t i o n s s u c h as s y m m e t r i c a l b u c k l i n g and w r i n k l i n g i n s t a b i l i t i e s needs t o b e e x a m i n e d . S m a l l s c a l e F o r s h o r t u n s u p p o r t e d l e n g t h s o n l y l o c a l i z e d p l a s t i c H e l i c a l b u c k l i n g o c c u r s i n l o n g u n s u p p o r t e d l e n g t h s . I n Two b a s i c s u b j e c t a r e a s need t o b e i n v e s t i g a t e d c o n c e r n i n g

QUALITATIVE DESCRIPTION OF

VARIOUS BUCKLING MODES

1

I-

<I _{FAILURE ZONE}

FAILURE WITH WALL CONTACT

FAILURE WITHOUT

BUCKLING ZONE WALL CONTACT

HELICAL I- BUCKLING ZONE NO ADVERSE DEFORMATION UNSUPPORTED LENGTH, L F i g u r e 5 . Q u a l i t a t i v e P l o t o f T e m p e r a t u r e Change V e r s u s U n s u p p o r t e d L e n g t h D e p i c t i n g Buck1 i n g R e g i o n s .

laboratory

t e s t s

of thermally-induced buckling should a l s o

be

conducted t o enhance t h e understanding

o f

the phenomenon.

This r e p o r t q u a n t i t a t i v e l y d e f i n e s t h e Euler buckling

regime f o r a

c a s i n g

with f i x e d

ends

with a n d without subsequent

h o l e wall c o n t a c t .

,

ANALY

S IS

T h e o r e t i c a l Model

-4

-

--

-

6

---

A S s u m p t i o n s . The down h o l e e f f e c t s o f i m p r o p e r c e m e n t i n g may be m a n i f e s t e d i n many ways. However, w i t h o u t d e t a i l e d f i e l d o r l a b o r a t o r y d a t a on g e o t h e r m a l c a s i n g b e h a v i o r o r c a s i n g f a i l u r e s , t h e r e i s l i t t l e need t o s h a r p l y f o c u s on one s u b j e c t a r e a . T h e r e f o r e a s i m p l e a n a l y t i c and n u m e r i c a l model i s p r e s e n t e d i n o r d e r t o g a i n i n s i g h t i n t o t h e p r o b l e m . The a n a l y s i s assumed: 1 ) t h e c a s i n g was i n i t i a l l y v e r t i c a l ( b o d y f o r c e s

i g n o r e d ) and c e m e n t i n g above and b e l o w t h e u n s u p p o r t e d c a s i n g p r o v i d e d f i x e d - e n d c o n d i t i o n s , 2 ) c o m p l i c a t i o n s f r o m c o u p l i n g s s u c h as c h a n g e s i n moment o f i n e r t i a

( I )

a n d weakness i n b e n d i n g w e r e un i m p o r t a n t , 3 ) c a s i n g s t r e s s e s r e m a i n e d i n t h e e l a s t i c r e g i o n and t h e m o d u l u s o f e l a s t i c i t y

( E )

was i n d e p e n d e n t of t e m p e r a t u r e a n d e q u a l t o 2 9 x

l o 6

p s i ( 2 0 0 GPa), 4 ) t h e l i n e a r t h e r m a l e x p a n s i o n c o e f f i c i e n t ( a ) was c o n s t a n t a n d e q u a l t o 6.5 x 10-6'F ( 1 . 2 x lO-5'C), 5 ) c o m p l i c a t i o n s due t o c a s i n g n e s t i n g w e r e n e g l i g i b l e , 6 ) t h e i n t e r n a l and e x t e r n a l t i t b u l a r p r e s s u r e s w e r e e q u a l , 7 ) c r o s s - s e c t i o n a l shape c h a n g e s ( o v a l a t i o n ) due t o l a t e r a l and b e n d i n g f o r c e s w e r e u n i m p o r t a n t . A s s u m p t i o n s 5,

6,

and 7 w e r e j u s t i f i e d b y t h e f o l l o w i n g f a c t s : F i r s t , c a s i n g n e s t i n g i s r a r e l y c o n s i d e r e d i n a c t u a l d e s i g n a p p l i c a t i o n s . Second, c a s i n g o v a l a t i o n p r o b l e m s a t t h e w a l l c o n t a c t w e r e t h o u g h t m i n o r i f s t r e s s e s r e m a i n e d b e l o w y i e l d . The n u c l e a r r e a c t o r i n d u s t r y h a s been a d d r e s s i n g t h i s

p r o b l e m t o some e x t e n t . F i n a l l y f o r l o w p r e s s u r e , h o t w a t e r , o r s t e a m r e s e r v o i r s , t h e c a s i n g i n t e r n a l p r e s s u r e i s l i k e l y t o b e l e s s t h a n e x t e r n a l f o r m a t i o n p r e s s u r e s ; hence n e g l e c t i n g i n t e r n a l - e x t e r n a l p r e s s u r e i n t e r a c t i o n was f e l t j u s t i f i e d * ( L u b i n s k i e t a1

.,

1962; H a m m e r l i n d l , 1978; J e n k i n s and Snyder, 1 9 7 9 ) . These a s s u m p t i o n s p e r m i t t e d t h e a p p l i c a t i o n o f E u l e r beam t h e o r y . The o u t l i n e o f t h e e q u a t i o n d e v e l o p m e n t i s p r e s e n t e d i n t h e f o l l o w i n g s e c t i o n . More d e t a i l e d d e r i v a t i o n s a r e p r e s e n t e d i n A p p e n d i x B. C r i t i c a l T e m p e r a t u r e . A f r e e b o d y d i a g r a m f o r a d e f o r m e d beam i s shown i n F i g u r e 6. The d i f f e r e n t i a l e q u a t i o n t h a t d e s c r i b e s t h e beam i s as f o l l o w s : (Terms a r e d e f i n e d i n F i g u r e 6 and i n A p p e n d i x A ) . M = MR

-

Py + V X = E I y " T h e r e a r e f o u r b o u n d a r y c o n d i t i o n s : x = o , y = o x = 0, y ' = 0 x =

R,

y ' = 0 x = R , y = e The f i r s t t w o b o u n d a r y c o n d i t i o n s e s t a b l i s h t h e e q u a t i o n : where

*

A s

a c h e c k on t h i s a s s u m p t i o n , one can compare t h e m a g n i t u d e o f t h e t h e r m a l a x i a l l o a d w i t h t h e l o a d c a l c u l a t e d f r o m t h e

i n t e r n a l - e x t e r n a l p r e s s u r e d i f f e r e n c e t i m e s t h e p i p e

c r o s s - s e c t i o n a l a r e a . The l a t t e r l o a d s h o u l d be much s m a l l e r i n c o m p a r i s o n t o t h e t h e r m a l l o a d .

DEFINITION OF TERMS

HOLE WALL

~ 4 4

ENDS

a)

F i g u r e 6. D e f i n i t i o n of Terms: a ) L i n e S k e t c h and

b )

F u l l

Body

D i a g r a m .

The f o u r t h b o u n d a r y c o n d i t i o n e s t a b l i s h e s a r e l a t i o n s h i p b e t w e e n MR, V, and

P

( o r K ) . as seen f r o m t h e f o l l o w i n g e q u a t i o n : T h e r e a r e t h r e e s p e c i a l c a s e s MR V y ' =

p

( K s i n K R )

-

( 1

-

c o s K R ) The t h r e e c a s e s a r e : 2 ) 1

-

C O S

K R

= 0 and s i n K R = 0

3 )

M = 0 a..d 1

-

c o s K R = 0

R

Case 1 i s t h e s i t u a t i o n b e f o r e w a l l c o n t a c t ( y < e ) . c a s i n g t a k e s t h e shape o f a c o s i n e f u n c t i o n : MR y =

p

( 1

-

C O S K X ) where K = 2 n / L T h e c r i t i c a l l o a d

(Per)

i s t h e r m a l l y i n d u c e d and ( 3 ) The t h u s ( 4 ) e q u a l t o AEaAT. The r e s u l t i n g e x p r e s s i o n f o r t h e c r i t i c a l t e m p e r a t u r e change

AT^,)

w h i c h i n i t i a t e s b u c k l i n g i s : 2

4 n

1

AT^^

=

-2

L Aa ( 5 ) F i g u r e 7 p l o t s e q u a t i o n ( 5 ) . The u n s u p p o r t e d l e n g t h ( L ) i s n o r m a l i z e d b y t h e o u t s i d e c a s i n g d i a m e t e r

(D).

A l t e r n a t e l y o n e can u s e t h e r a d i u s o f g y r a t i o n ( r ) ( N e l s o n , 1 9 7 5 ) . 9

!

1300

c1200

!

13 3/8 tNCH 54.5ppf

-

ACTUAL \ A 9 5 / 8 INCH 36.OPPf

-

BEHAVIOR

-

\ rn 9 5/8 INCH 40.0PPf

-

\ \ ~EFORMATION 100

%ooo

g

900-

z

2

8 0 0 - 7 0 0 - W

2

6 0 0 -

2

5 0 0 - 400-

E

3 0 0 - 200 100 0

Figure

7 .

-

-

APPROXIMATE LIMIT

-

OF EULER BUCKING

-

FORMULATION

-

-

-

1580 CASING

-

-

I I I I I I I I I

Locus D e l i n e a t i n g Euler Buckling Region:

P l o t

o f

Temperature Change ( A T ) Versus Normal i t e d

T h r e e t y p i c a l c a s i n g s w e r e examined: 9 - 5 / 8 i n c h 36 p p f , 9 - 5 / 8 i n c h 40 p p f , and 1 3 - 3 / 8 i n c h 54.5 p p f ( 2 4 4

mm

5 4 kg/m, 244

mm

6 0 kg/m, and 340

mm

8 0 k g l m ) . L i t t l e d i f f e r e n c e b e t w e e n t h e c a s i n g s e x i s t s . The moment o f i n e r t i a

( I )

d e c r e a s e s s l i g h t l y f o r t h e 9 - 5 / 8 i n c h 40 p p f ( 2 4 4

mm

60 k g / m ) p i p e b e c a u s e t h e o u t s i d e d i a m e t e r r e m a i n s c o n s t a n t . T h i s e x p l a i n s t h e s l i g h t d e c r e a s e i n

AT^^

f o r t h i s s u p p o s e d l y s t r o n g e r p i p e . i m p o r t a n t t o n o t e f r o m e q u a t i o n ( 5 ) t h a t l a r g e r d i a m e t e r p i p e w i l l i n c r e a s e t h e c r i t i c a l b u c k l i n g t e m p e r a t u r e w h e t h e r o r n o t t h e p i p e s t r e n g t h i n c r e a s e s . b y n o t i n g t h a t A I S C ( 1 9 8 0 ) recommends t h e s l e n d e r n e s s r a t i o ( K L / r ) r e m a i n above r ( 2 E / a )ll2. 9 Y e s t a b l i s h e d b e c a u s e c o l u m n f a i l u r e modes s u c h as l o c a l i z e d p l a s t i c d e f o r m a t i o n o r k i n k i n g became i m p o r t a n t f o r s m a l l e r v a l u e s . The above c r i t e r i o n e s t a b l i s h e s a minimum l e n g t h o f 22 f t ( 6 . 8

m )

o r 27.5 D f o r E u l e r b u c k l i n g o f N-80 9 - 5 / 8 i n c h 40 p p f ( 2 4 4

mm

6 0 k g l m ) c a s i n g . when E u l e r b u c k l i n g w i l l i n i t i a t e . Whether t h e b u c k l i n g r e s u l t s i n p l a s t i c d e f o r m a t i o n s m u s t b e e x a m i n e d f r o m t h e s t r e s s s t a n d p o i n t . The t o t a l s t r e s s ( a t ) a f t e r b e n d i n g a t a maximum f i b e r i s e q u a l t o t h e a x i a l s t r e s s (a,) p l u s t h e maximum b e n d i n g s t r e s s ( a b ) m a x ( o v a l a t i o n s t r e s s e s n e g l e c t e d ) : I t i s The r a n g e o f a p p l i c a b i l i t y o f e q u a t i o n ( 5 ) c a n be e s t i m a t e d T h i s c r i t e r i o n was Maximum s t r e s s b e f o r e w a l l c o n t a c t . F i g u r e 7 i n d i c a t e s ‘t = lT a + (‘b)max where u = P c r / A = E ~ A T= c o n s t a n t ~ ~ a = M r /I ( ‘b )max R o

The end moment r e a c t i o n ( I d R ) i n t h e e x p r e s s i o n f o r ( a b ) m a x i s f o u n d f r o m t h e c o n d i t i o n e s t a b l i s h e d b y t h e f i x e d ends; t h e

t h e r m a l d i s p l a c e m e n t ( s ( T ) ) m u s t e q u a l t h e sum o f t h e a x i a l l o a d d i s p l a c e m e n t

( s ( P ) )

and t h e c a s i n g d e f l e c t i o n d i s p l a c e m e n t ( s ( y ) ) ( B o l e y a n d W e i n e r , 1 9 6 0 ) : The d i s p l a c e m e n t s a r e e x p r e s s e d as: ( 1 1 ) 6 ( P ) = PcrL/AE = c o n s t a n t a ( y )

=

( y l ) ' d x ( T i m o s h e n k o , 1 9 6 1 ) ( 1 2 ) 2

=($)

L

Once b u c k l i n g has o c c u r r e d t h e t h e r m a l l y i n d u c e d l e n g t h change

s ( T ) i s e n t i r e l y a b s o r b e d b y t h e c o l u m n d e f l e c t i o n t e r m s ( y ) ; h e n c e , s ( P ) r e m a i n s c o n s t a n t . C o n s e q u e n t l y u a r e m a i n s a t t h e c r i t i c a l b u c k l i n g s t r e s s as n o t e d above. I n s e r t i n g t h e d i s p l a c e m e n t e x p r e s s i o n s i n t o e q u a t i o n ( 9 ) a n d s o l v i n g f o r MR r e s u l t s i n ( A T

>

AT^,):

( 1 4 ) 1 / 2 MR = [ a ( A T

-

AT^^)]

lr A s s e m b l i n g t h e e x p r e s s i o n s f o r u a and ( a b ) m a x and i n s e r t i n g i n t o ( 6 ) y i e l d s : 4 L r 0 1 +

--51--T-'

[ a ( AT-AT,, )

3

I2

1

( 1 5 )

f

~ ( r o

+ r i ) a t = EaATcr

E q u a t i o n ( 1 5 ) i s p l o t t e d f o r 1 3 - 3 / 8 i n c h 54.5 p p f ( 3 4 0 mm 80 k g / m ) c a s i n g w i t h

L / D

= 50, 100, 200 i n F i g u r e 8. The u p p e r r a n g e o f a p p l i c a b i l i t y f o r f i g u r e 8 i s when t h e s t e e l r e a c h e s i t s y i e l d p o i n t ( 8 0 k s i ( 5 5 0 MPa) f o r

N-80

c a s i n g ) o r t h e c a s i n g d e f l e c t s enough t o c o n t a c t t h e h o l e s i d e s . The l a t t e r c o n d i t i o n i s a d d r e s s e d b e l o w . F i g u r e 9 p l o t s maximum d e f l e c t i o n ( y m a x ) v e r s u s t e m p e r a t u r e change ( A T ) and e n a b l e s one t o p r e d i c t when w a l l c o n t a c t w o u l d o c c u r . c o n d i t i o n s l e a d s t o t h e r e s u l t t h a t

M R

= -Mb ( F i g u r e 6 ) . The d e f o r m e d c a s i n g shape i s n o t c o m p a t i b l e w i t h t h e s e end

moments. Hence c a s e 3, a c o n c e n t r a t e d s h e a r l o a d ( V ) a c t i n g a t t h e p o i n t o f c o n t a c t , was u s e d t o m a t h e m a t i c a l l y d e s c r i b e t h e c a s i n g a t w a l l c o n t a c t . * The shape o f t h e c a s i n g b e t w e e n p o i n t s and " b t l i n F i g u r e 6 i s : Maximum s t r e s s a f t e r w a l l c o n t a c t . Case 2 o f t h e b o u n d a r y

---

---

----

s i n 2 K x ) V Y = p ( X - Z i i ; N o t e t h a t t h e e n d moment ( M R ) i s r e p l a c e d w i t h t h e s h e a r f o r c e ( V ) . U n t i l w a l l c o n t a c t , t h e c o l u m n shape i s d e s c r i b e d b y a c o s i n e f u n c t i o n ( e q u a t i o n 2 ) . An i n s t a n t a n e o u s change i n c a s i n g shape i s r e q u i r e d . An i m p o r t a n t c o n s e q u e n c e i s t h a t s t r e s s v a l u e s a r e n o t c o m p a t i b l e when w a l l c o n t a c t o c c u r s u s i n g t h e t w o d i f f e r e n t shapes. E q u a t i o n s ( 4 ) and ( 1 6 ) a l o n g w i t h c o m p u t e r r e s u l t s t o b e d i s c u s s e d l a t e r a r e p l o t t e d i n F i g u r e l o a . A s o l u t i o n t o t h e p r e d i c a m e n t ( s u b j e c t t o c o n f i r m a t i o n b y n u m e r i c a l a n a l y s i s ) was t o assume t h e c o l u m n shape a f t e r

c o n t a c t was t h e same as b e f o r e . The o n l y d i f f e r e n c e was t h a t i t was " s p l i t . " T h i s a s s u m p t i o n r e q u i r e d i m a g i n a r y end moments

. i T X m o s h E o

( 1 9 5 9 ) d i s c u s s e s t h e c a s e o f a f i x e d e n d beam u n i f o r m l y l o a d e d w i t h f o u n d a t i o n c o n t a c t b u t n o r e f e r e n c e was f o u n d d i s c u s s i n g a x i a l l y - l o a d e d members w i t h w a l l c o n t a c t .

F

c

GEOTHERMAL WELL CASING

EULER BUCKLING

MAXIMUM STRESS

I I I I 1

1

TEMPERATURE CHANGE, AT ( O R

Figure

8 .

Maximum S t r e s s

( a )

Versus Temperature Change ( A T )

f o r 1 3 - 3 1 8 inch 5 4 . 5 ppf C a s i n g Assuming

GEOTHERMAL WELL CASING

EULER BUCKLING

MAXIMUM DEFLECTION

I I I 13 3/8 INCH S4.Sppf CASING UNSUPPORTED LENGTH 0 V D = l O O (111 ft) L/D=200 (223 ft) A u D = 6 0 ( 5 8 f f ) I OO F i g u r e 9. Maximum D e f l e c t i o n V e r s u s T e m p e r a t u r e Change ( A T ) f o r 1 3 - 3 / 8 i n c h 54.5 p p f C a s i n g Assuming U n s u p p o r t e d L e n g t h s ( L / D ) o f 50, 100, a n d 200. 100 200 300 400

COMPARISON OF DEFORMED CASING SHAPES AT AT EQUAL 80 OF* 10 l a W 6 I C H Mdppf CA6lG HOLE QAP. 010=060 (6.60 NCMS) 0 . UNSUPPORTEO L€NGTn.UD=lOO 6 - 0 NARCRESULTS

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ANALYTIC RESULTS (AT=SOO*F)

LENGTH (INCHES) COMPARISON OF DEFORMED CASING SHAPES 10, 1 b)

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15 W 6 INCH 64.5 ppf CASING UNSUPPORTED LENGTH. U D = 100 HOLE QAP. o/O=O.SO (6.60 INCHES) YARC RESULT

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LENGTH (INCHES)

F i g u r e 10. D e f o r m e d C a s i n g Shapes w i t h W a l l C o n s t r a i n t P r e d i c t e d

by MARC

and T h e o r e t i c a l M o d e l s a t a ) A T = 80°F, b ) M A R C r e s u l t s a t A T o 300°F,

( M R ) e x i s t e d e q u a l t o P e / 2 . The m a t h e m a t i c a l model was s i m i l a r t o t h a t used p r i o r t o t h e w a l l c o n t a c t w i t h t h e e x c e p t i o n o f a v a r i a b l e c o l u m n l e n g t h ( 2 ) . b e t w e e n t h e f i x e d e n d a n d t h e p o i n t o f w a l l c o n t a c t . The l e n g t h ( 2 ) s h o r t e n s as t h e c a s i n g segment a g a i n s t t h e w a l l l e n g t h e n s due t o i n c r e a s e d d e f o r m a t i o n . An e x p r e s s i o n f o r was f o u n d f r o m t h e c o n d i t i o n t h a t t h e - t h e r m a l d i s p l a c e m e n t ( 6 ( T ) ) e q u a l e d t h e sum o f t h e a x i a l l o a d d i s p l a c e m e n t ( s ( P ) )

and t h e beam d e f l e c t i o n d i s p l a c e m e n t ( a ( y ) ) . . U s i n g t h e same d i s p l a c e m e n t e x p r e s s i o n s as b e f o r e ( e q u a t i o n s ( l o ) , (ll), a n d ( 1 2 ) ) r e s u l t e d i n : F i g u r e 6 d e p i c t s t h e v a r i a b l e l e n g t h ( 2 ) . I t i s t h e l e n g t h R = {(,e)2 A + A2 + 256 L 2 2 1 I A a A T I 1 / 2 ) /16LAaAT ( 1 7 ) The t o t a l s t r e s s ( a b ) a t a maximum f i b e r i n t h e c a s i n g e q u a l s t h e a x i a l s t r e s s ( u a ) p l u s t h e maximum b e n d i n g s t r e s s ( “b )ma x ( e q u a t i o n 6 ) where: u a = E a A T c r = M r /I ( “ b ) m a x R o ( 7 ) and 2 2 MR = P e / 2 = T E I e / = 2 The e x p r e s s i o n f o r t h e maximum s t r e s s i s t h u s : ( 1 9 ) 2 2 a t = EaATcr + 1 E e r o / 2 R F i g u r e l l a p l o t s e q u a t i o n ( 1 9 ) f o r a 1 3 - 3 / 8 i n c h 54.5 p p f ( 3 4 0 mm 8 0 k g / m ) c a s i n g 1 0 0 d i a m e t e r s l o n g . W a l l c o n t a c t

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EULER BUCKLING WITH SUBSEQUENT WALL CONTACT I I i s a / 8 INCH s 4 . s p p f CASING loo - UNSUPPORTED LENGTH, L/D = 100 90

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HOLE GAP, */D 0 0.25 (5.34 INCH) m 1.00 (13.58 INCH) Q 8 0 - 0 O I O (6.69 INCH) A 0.71 (10.03 INCH) 0

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a) 0 0 400 TEMPERATURE CHANGE, AT ( O F )

MARC FE ANALYSIS USING THIN WALLED BEAM ELEMENT

I I I I

F i g u r e 11.

g e n e r a l l y l o w e r s t h e s t r e s s i f t h e d i s t a n c e t o t h e h o l e w a l l ( e / D ) i s l e s s t h a n 0.50 and t e m p e r a t u r e c h a n g e s ( A T ) a r e w i t h i n t h e n o r m a l 200-3OO'F (95-15O'C) r a n g e .

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N u m e r i c a l Model The a n a l y s i s o f c a s i n g b u c k l i n g i s d i f f i c u l t f o r a s t a t i c f i n i t e e l e m e n t code t o h a n d l e . I n a d d i t i o n , t h e n u m e r i c a l model f o r m u l a t i o n r e q u i r e s a s l i d i n g i n t e r f a c e c a p a b i l i t y t o s i m u l a t e w a l l c o n t a c t . The n u m e r i c a l model d e v e l o p e d used t h e t h in - w a l l e d beam e l emen t ( E u l e r t h e o r y ) w i t h c i r c u l a r c r o s s - s e c t i o n and t h e f r i c t i o n gap e l e m e n t f r o m t h e M A R C f i n i t e e l e m e n t p r o g r a m ( 1 9 7 9 ) . As a c h e c k , a n o t h e r model was a l s o r u n u s i n g a s t a n d a r d beam-column e l e m e n t w i t h an i d e n t i c a l m o m e n t - o f - i n e r t i a a r e a r a t i o ( I / A ) . The r e s u l t i n g s t r e s s e s were p r a c t i c a l l y i d e n t i c a l u n t i l n e a r t h e y i e l d p o i n t . t o t h o s e o f t h e a n a l y t i c model. C o m p l i c a t i o n s due t o c a s i n g n e s t i n g a n d c r o s s - s e c t i o n a l shape changes ( o v a l a t i o n ) due t o l a t e r a l and b e n d i n g f o r c e s w e r e n o t i n c l u d e d . C a s i n g i n s t a b i l i t y f r o m i n t e r n a l - e x t e r n a l p r e s s u r e i n t e r a c t i o n was n e g l e c t e d , F i n a l l y , o n l y 1 3 - 3 / 8 i n c h 54.5 p p f ( 3 4 0 mm 8 0 k g l m ) c a s i n g 100 d i a m e t e r s l o n g was e x a m i n e d . H i g h t e m p e r a t u r e c h a n g e s w e r e a n t i c i p a t e d n e a r t h e s u r f a c e i f w e l l s h u t d o w n o c c u r r e d and t h u s l a r g e d i a m e t e r p i p e was t h o u g h t a p p r o p r i a t e . The u n s u p p o r t e d l e n g t h s e l e c t e d was a r b i t r a r y . F o r t h i s i n i t i a l i n v e s t i g a t i o n , i n e l a s t i c a n a l y s i s a b o v e t h e y i e l d p o i n t was o m i t t e d ( 8 0 k s i ( 5 5 2 MPa) f o r N-80 c a s i n g ) . n u m e r i c a l l y u n s t a b l e ) a t A T e q u a l t o 58°F ( 1 4 ° C ) . ~ ~ v a l u e compares p o o r l y w i t h t h e a n a l y t i c a l l y c o m p u t e d 72°F (22'C) c r i t i c a l t e m p e r a t u r e change

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