Valve Selection Handbook - Sizing Pressure Relief Devices

8/17/2019 Valve Selection Handbook - Sizing Pressure Relief Devices

1/23

7

S I Z I N G P R E S S U R E

R E L I E F D E V I C E S

T h e o p t i m u m s i z in g o f p r e s s u r e r e l i e f d e v ic e s i s e s s e n t i a l to s a f e l y p r o t e c t

a p i p i n g s y s t e m f r o m o v e r p r e s s u r i z a t i o n . A n u n d e r s i z e d s y s t e m w o u l d n o t

b e i n a p o s i t i o n t o re l i e v e t h e s y s t e m e f f e c t iv e l y a n d a n o v e r s i z e d s y s t e m

w i l l r e s u l t i n u n n eces s a r y ma t e r i a l an d l ab o r co s t s .

F l o w - t h r o u g h p r e s s u r e r e l i e f d e v i c e s m a y b e o f e i t h e r o n e o f t h e

f o l l o w i n g c a t e g o r ie s . T w o o f t h e s e h a v e s u b c a te g o r ie s "

9 G as , o r v ap o r , f l o w

9 S u b s o n i c o r n o n - c h o k e d f lo w

9 S o n i c o r c h o k e d f lo w

9 L i q u i d f l o w

9 M i x e d - p h a s e f lo w ( v a p o r p lu s l iq u i d )

9 G as co n t a i n i n g l i q u i d d r o p l e t s

9 L i q u i d c o n t a i n i n g g a s b u b b l e s

9 L i q u i d f l a sh i n g to v a p o r t h r o u g h v a l v e

E a c h o f t h e s e h as a n a p p r o p r i a t e f o r m u l a o r p r o c e d u r e f o r d e t e r m i n i n g t h e

r e q u i r e d n o z z l e s i ze o r f lo w r a te . I n t h e c a s e o f m i x e d - p h a s e f lo w , h o w e v e r ,

f ir m r e c o m m e n d a t i o n s f r o m s t a tu t o r y b o d i e s a n d s t a n d a r d o r g a n i z a ti o n s o n

ap p r o p r i a t e s i z i n g eq u a t i o n s a r e n o t y e t av a i lab l e . 1

T h e s i z i n g e q u a t i o n s a r e p r e s e n t e d i n S I a n d i m p e r i a l u n i t s . F o r

n o m e n c l a t u r e r e f e r to T a b l e 7 -1 a n d F i g u r e 7 - 1 .

1 Com pi l a t i on o f d ra f t docum en t ISO "Des ign o f sa fe ty va lves and conn ec t ed ven t l i nes

fo r gas / l i qu id two-phase f l ow" in p repa ra t i on a t t ime o f pub l i ca ti on o f t h i s book .

2 6 9


2/23

2 7 0

Valve Selection Handbook

F i g u re 7 - 1 .

Typ ica l Pressure Re l ie f Va lve Ins ta lla tion . Su bscr ip ts Used in F low

Equ at ion fo r C ond i t ions a t Ind ica ted Po in ts .

T a b le 7 -1

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

M i x e d S I M i x e d U .S .

Units Units

A F l o w a r e a m m 2 i n. 2

C G a s f l ow c o n s t a n t f o r s o n i c n o z z l e

f l o w , b a s e d o n i s e n t r o p i c c o e f f i c i e n t

k a t s t a n d a r d c o n d i t i o n s ( S e e T a b l e

7 - 2 . I f k is u n k n o w n , u s e C = 3 1 5

f o r a c o n s e r v a t i v e r e s u l t )

I n t e r n a l p i p e d i a m e t e r m m i n.

table continued on next page


3/23

S i z ing Pressure Re l i e f D ev ices

2 7 1

T a b l e 7 - 1 . c o n t i n u e d )


M i x e d S I

Uni ts

M i x e d U . S .

Uni ts

d

g

gc

G

k

K

Kb

K~

KN

KS

K R

Kv

I

M

P

P1

P2

P3

Pipe f r i c ti on f ac to r - num ber o f

ve loc i t y heads l o s t i n l eng th o f p ipe

e q u a l t o d i a m e t e r

Gas f l ow cons t an t f o r subson i c

nozz l e f low , ba sed o n i s en t rop i c

coe f f i c i en t k a t s t anda rd c ond i t i ons

and t he abso lu t e p r e s su re r a t i o

ac ros s t he va lve

D i s c h a r g e r e a c t iv e f o r c e

Grav i t a t i ona l a cce l e r a t i on

Propor t i ona l i t y cons t an t

Spec i f i c g r av i t y o f t he l i qu id r e f e r r ed

to w a t e r = 1 .00 a t 70~ (20~

I sen t rop i c co e f f i c ien t

D era t ed o r c e r t if i ed coe f f i c i en t o f

d i s cha rge 1

C apac i t y co r r ec t i on f ac to r a ccoun t -

i ng fo r t he e f f ec t o f bu i l t - up and

s u p e r i m p o s e d b a c k p r e s s u r e o n

va lve l i f t o f be l l ows ba l anced p r e s -

su r e r e l i e f va lve s

Ac tua l coe f f i c i en t o f d i s cha rge 2

N ap ie r c apac i t y co r r ec t i on f ac to r f o r

p r e s su re

N ap ie r c apac i t y co r r ec t i on f ac to r fo r

s u p e r h e a t

V e loc i t y head l o s s o f r up tu r e d ev i ce s

V i scos i t y co r r ec t i on f ac to r

L e n g t h o f p i p e l in e

M o l e c u l ar w e i g h t

Se t p r e s su re (gauge )

Re l i ev ing p r e s su re (gauge ) - - s e t

p r e s su re p lu s ove rp re s su re p lu s

a t m o s p h e r i c p r e s s u r e

Pre s su re a t va lve ou t l e t

P r e s s u r e i n s p a c e b e t w e e n v a l v e s e a t

and va lve ou t l e t

A tmosphe r i c p r e s su re ( abs . )

N

9.807 rn / sec 2

1 .0 k g m / N s 2

m m

k g / k m o l

b a r g

b a r a

b a r a

b a r a

b a r a

lb

32.17 4 f t / sec 2

32.174 lbm /f t /lb f s 2

in .

l b / l b m o l

lb / in2g

l b / i n 2 a

lb / in .2a

lb/ in. 2 a

l b / i n . 2 a

( con t inued on nex t page)

1ASM E (1992) Sect ion VIII D ivision, UG-131(e)(3) .

2 ASM E (1992) Sec t ion VIII Division, UG-131(e)(2).


4/23

2 7 2

Valve Selection Handbook

T a b l e 7 - 1 . c o n t i n u e d )


PC

89

PN

PR

PT

Ro

R1 =

R o / M

Q

T1

T c

TR

V

v1

W

Z

U

P

Cr i t i ca l v ap o r p ressu re , t h e

p ressu re o f sa tu ra t ed v ap o r a t t h e

c r i t i ca l t emp era tu re T c

Pressu re a t v a lv e en t ry d u g ing

p ressu re r e l i e f

P ressu re a t v a lv e n o zz le f ace

d u r in g p ressu re r e l i e f

R ed u ced p ressu re , PR = P1 /Pc

Pressu re a t f ace o f d i sch a rg e

p ip e o u t l e t d u r in g p ressu re r e l i e f

G en era l g as co n s t an t

In d iv id u a l g as co n s t an t

R a te o f f low o f l i q u id

T em p era tu re ab so lu te o f g as o r

v ap o r a t r e l i ev in g p ressu re

Cr i t ica l t em p era tu re ab so lu te ,

t h e m a x i m u m t e m p e r a t u r e a t w h i c h

th e v ap o r an d l i q u id p h ases e x i s t in

eq u i l ib r iu m

R ed u ced t emp era tu re , T R = T 1 /T c

V o lu met r i c f low ra t e o f g as o r v ap o r

a t s tan d ard p ressu re an d t emp era tu re

Speci f ic vo lume at in le t cond i t ions

M ass r a t e o f f low

Co mp ress ib i l i t y f ac to r a t ac tu a l

r e l i ev in g p ressu re an d t emp era tu re ,

co r rec t io n fo r d ev ia t io n s f ro m th e

id ea l g as l aw s

V isco s i ty S ay b o l t u n iv e r sa l seco n d s

D y n amic v i sco s i ty cen t ip o i se

D en s i ty o f l i q u id s

M i x e d SI M i x e d U .S .

Uni ts Uni ts

ba ra lb/ in . 2 a

ba ra lb/ in . 2 a

ba ra lb/ in . 2 a

8314.3 1545 ft

J / k m o l ~ l b f / l b m o l ~

8314.3 1545 ft

J / k g ~ lb f / lb ~

U S g a l /m in .

K = ~ ~ 1 7 6

N m 3 / h s c f m

m3/kg ft3/ lb

kg /h lb /h

S U

m P a l s

kg /m 3 lb / f t 3

S I Z I N G O F P R E S S U R E R E L IE F V A L V E S , G A S ,

V A P O R , S T E A M

T h e e q u a t i o n s f o r th e s i z i n g o f p r e s s u r e r e l i e f v a l v e s f o r g a s o r v a p o r a r e

b a s e d o n t h e i de a l g a s l a w s i n w h i c h i t i s a s s u m e d t h a t fl o w t h r o u g h t h e


5/23

Sizing Pressure Re lief Devices

2 7 3

T a b l e 7 - 2

Va lues o f Cr i t ica l Pressure Rat ios and Coef f ic ien ts C

k PcF/P1 C k PcF/P1 C

1.01 0.60 317 1.45 0.52 360

1.02 0.60 318 1.50 0.51 365

1.04 0.60 320 1.55 0.50 369

1.06 0.59 322 1.60 0.50 373

1.08 0.59 325 1.65 0.49 376

1.10 0.58 327 1.70 0.48 380

1.15 0.57 332 1.75 0.48 384

1.20 0.56 337 1.80 0.47 387

1.25 0.55 342 1.85 0.46 391

1.30 0.55 347 1.90 0.46 394

1.35 0.54 352 1.95 0.45 397

1.40 0.53 356 2.00 0.44 400

va l ve i s i s e n t r op i c . D e v i a t i ons f r o m t he i de a l ga s la w s a r e c o r r e c t e d b y t he

c om pr e s s i b i l i t y f a c t o r Z .

W h e n t h e r a t i o o f t h e a b s o l u t e d o w n s t r e a m t o t h e u p s t r e a m p r e s s u r e

a c r os s t he noz z l e i s h i gh e r t ha n a bou t 0 .5 , f low t h r ou gh t he va l ve no z z l e i s

s ubs on i c . A t a p r e s s u r e r a t i o o f a bou t 0 .5 a nd l ow e r , f l ow t h r ough t he va l ve

noz z l e i s s on i c . T he a c t ua l p r e s s u r e r a t i o a t w h i c h f l ow t h r ough t he va l ve

noz z l e t u r n s s on i c i s a f unc t i on o f t he i s e n t r op i c c oe f f i c i e n t a s e xp r e s s e d

b y t h e e q u a t i o n

P C F _ ( 2 ) k /( k -1 )

P l - - K + I ( 7 - 1 )

P C F i s r e f e r r e d t o a s t he c r i t i c a l noz z l e f l ow p r e s s u r e a nd t he p r e s s u r e

r a t io a s t he c r i ti c a l p r e s s u r e r a t io . F l o w p r e s s u r e a t a p r e s s u r e r a t i o be l o w

the c r i t i ca l p res sure ra t io i s re fe r red to a s subcr i t i ca l .

Va lues o f the c r i t i ca l p res sure ra t io for i s en t rop ic coe f f i c i en t s 1 .01

t h r o u g h 2 . 00 m a y b e t a k e n f r o m T a b l e 7 - 2.

Siz ing Equat ions fo r Gas and Vapor Other Than

S team

C u s t o m a r y M i x e d I m p e r i a l U n i t s, S o n i c N o z z l e F l ow

W e i gh t f lo w ~ l b / h

1

A - - C K P 1 K b - - ~ ( 7 - 2 )


6/23

9 . 7 4 V a lv e S e l ec t io n H a n d b o o k

Volumet r i c f low~scfm

g 1

A = (MT1

Z)

6.32CKP1 Kb

C ust omar y Mixe d SI U n i t s , Son ic N oz z le F low

W e i g ht f l o w ~ k g / h

A ~

1

131.6W (_~Z)'__

CKP1Kb

Volumetr ic f low ~N m 3/h

5.87V 1

A = (MTZ )~

CKP1 Kb

where

C - 5 2 0 k k + 1

For values o f C, refer to Table 7-2.

For v alues o f Kb, refer to Figure 7-3.

C u s t o m a r y M i x e d I m p e r i a l U n i t s, S u b s o n i c N o z z l e F lo w

W e ig h t f l o w ~ l b / h

A ___

1

w

735FK d P1

Volumet r i c f low~scfm

g 1

A = (MTZ)~

4645FKdP1

C u s t o m a r y M i x e d S I U n i t s, S u b s o n i c N o z z l e F lo w

Weigh t f low--kg /h

m ___

1

w

5.58FKd P1

( 7 - 3 )

(7 - 4 )

( 7 - 5 )

(7 - 6 )

( 7 - 7 )

( 7 - 8 )

( 7 - 9 )


7/23

Sizing Pressure Relie f Devices 2 7 5

V o l u m e t r i c f l o w ~ s c f m

W 1

A = ( M T Z ) ~

125 .1FKd P1

w h e r e

2

i

- / I k - l t I l 1 /

F o r va l ue s o f F , r e f e r t o F i gu r e 7 - 2 .

Note :

(7 - 10)

( 7 - 1 1 )

1 . T he c oe f f i c ie n t o f d i s c ha r ge a s de t e r m i ne d a t s on i c noz z l e f l ow c ond i -

t i ons a pp l i e s a l s o t o s ubs on i c no z z l e f low , p r ov i de d t he ba c k p r e s s u r e

f o r de t e r m i n i ng t he va l ue o f t he f a c t o r F i s t a ke n a s t he p r e s s u r e F 2 i n

t h e c h a m b e r b e t w e e n n o z z l e a n d v a l v e o u t l e t . V a l v e m a n u f a c t u r e r s

m a y p r ov i de e qua t i ons t ha t pe r m i t t he v a l ue o f F 2 t o be c a l c u l a t e d

f r om t he ba c k p r e s s u r e P2 a t t he ou t l e t f l a nge o f the va l ve .

2 . I f the ba c k p r e s s u r e P'2 c a nn o t be d e t e r m i ne d , a c oe f f ic i e n t o f d is -

c h a r g e s h o u l d b e a p p l ie d a s d e t e r m i n e d i n a c c o r d a n c e w i t h A P I

S t a nda r d 2 0 0 0 .

C o m p r e s s i b i l i ty f a c t o r Z = P 1V 1 /R 1 T 1 . T h e f a c t o r Z c o m p e n s a t e s f o r

de v i a t i ons o f r e a l ga s e s f r om t he i de a l ga s l a w s . I t s va l ue i s e va l ua t e d a t

i n l e t c ond i t i ons . A ny c o r r e c t i on f o r Z how e ve r i s e m p i r i c a l , a s t he e n t i r e

de r i va t i on o f t he e qua t i ons i s ba s e d on t he i de a l ga s l a w s .

W he n c r i t ic a l p r e s s u r e P c a nd c r it i c a l t e m pe r a t u r e T c o f t he ga s a r e

k n o w n , t h e r e d u c e d p r e s s u r e P 1 /P c a n d t h e r e d u c e d t e m p e r a t u r e T 1 / T c c a n

b e c a l c u l a t e d a n d u s e d t o o b t a in t h e v a l u e o f Z f r o m F i g u r e s B - 1 t h r o u g h

F i g u r e B - 3 i n A p p e n d i x B . V a lu e s o f P c a n d T c f o r a n u m b e r o f g a s e s m a y

be ob t a i ne d f r o m T a b l e B - 1 i n A pp e nd i x B . P l e a s e no t e t ha t t he c r it i c a l

p r e s s u r e i n T a b l e B - 1 i s s t a te d i n t e r m s o f M P a a nd l b / in 2.

I f t he c om pr e s s i b i l i t y f a c t o r c a nn o t be de t e r m i ne d , a va l ue o f 1 . 0 i s

c o m m o n l y u s e d . T h i s v a l u e g i v e s c o n s e r v a t i v e r e su l ts a s lo n g a s p r e s s u r e

a n d t e m p e r a t u r e a r e n o t to o h i g h .

Sizing Equations for Dry S aturated Steam

H i s t o r ic a l l y , p r e s s u r e r e l i e f va l ve s f o r d r y s a t u r a t e d s t e a m a r e s i z e d i n t he

U . S . o n N a p i e r ' s s t e a m f l o w e q u a t i o n . T h e e q u a t i o n h a s b e e n f o r m u l a t e d


8/23

2 7 6 Va lve Selec t i on H andboo k

o o t /

095

.090

.005

.080

/

.075

.O7O

. 0 6 5 . - -

.060

.035

F .030

.040 i

.035

.030 /

P = P =

P r e s s u r e R a t i o ~ o r

P l P l

f ~

~ - - 7 ' , 1 .2o

j ~ i o o

9 .90

~ , 1 . 7 0

9 1.60

1.50

- , 5 . ~ o

.550

.525

.500

.475

.450

.425

.400

.375

.350

.325

300

.275

.250

.225

.200

.175

.150

.125

.100

Fi gu re 7 -2 . Flow Correction Factor F. ( C o u r t e s y f A n d e r s o n , G r e e n w o o d Co.,

S o u r c e C a t a l o g 9 0 / 9 0 0 0 - U S . 9 6 . )

emp i r i ca l l y f or cond i t i ons o f choked f l ow. In the l ower p ressu re range

u p to 105 bara (1515 p s i a ) , Nap i er ' s equ at i on g i ves s i mi l ar resu l ts to

s i z i n g e q u a t i o n s a p p l i c a b l e f o r a n y g a s , u s i n g a n i s e n t r o p i c e x p o n e n t o f

k = 1 . 3 . A t h i gher p ressu res, ho wev er , Na p i er ' s equ at i on can l ead to

g r o s s o v e r s i z i n g . T h i s l e d L . T h o m p s o n a n d O . B . B u x t o n , J r . t o d e v e l o p

a cap ac i ty correc t i on f ac tor (K N) f or u se i n conj u nct i on wi th Nap i er ' s

equ at i on . 5~

C u s t o m a r y M i x e d I m p e r i a l U n i t s

W

A - ( 7 - 1 2 )

5 1 . 5 K P 1 K N K S H

K N - - 1 00 wh ere P1 < 1515 p s i a


9/23

Sizing Pressure R elie f Devices

2 7 7

1 . 0 0

0 . 9 0

0 . 8 0

0 . 7 0

0 . 6 0

0 . 5 0 i

0

\

5 1 0 1 5 2 0 2 S 3 0 3 5 / , 0 / , 5 5 0

PERCENT BAC K PRESSURE

F i g u r e

7 -3 . Bac k P r ess u re C o r r ec ti on F ac t o r Kb, Account ing fo r t he E f fec t o f Bu i l t-Up

an d Sup er impose d Ba ck Pressure on Va lve L i ft o f Be l lows Ba lanced-Pressure Re l ie f

Va l v es in G as o r Va po r Se r v ic e . (Repr in ted f rom AP I RP 52 0 Par t I, D ecem ber 1976,

Cou rtesy of A m erican Petroleum Inst itute.)

K N - -

0 . 1 9 0 6 P 1 - 1 0 0 0

0 . 2 2 9 2 P 1 - 1 0 6 1

w h e r e P 1 < 1 5 1 5 p s i a a n d u p t o 3 2 1 5 p s i a

K S H - - s u p e r h e a t c o r r e c t i o n f a c t o r T a b l e 7 - 3.

V a l u e s o f t h e c o r r e c t i o n f a c t o r f o r h i g h - p r e s s u r e s a t u r a t e d s t e a m , K N ,

m a y b e o b t a i n e d f r o m F i g u r e 7 - 4 .

C u s t o m a r y M i x e d S I U n i t s

W

A - ( 7 - 1 3 )

0 . 5 2 5 K P 1 K N K S H

K N - - 1 . 0 0 w h e r e P 1 < 1 0 5 b a r a

K N - -

2 . 7 6 4 P 1 1 0 0 0

3 . 3 2 3 P 1 - 1 0 6 1

w h e r e P1 > 1 0 5 b a r a a n d u p t o 2 2 1 . 7 b a r a

K S H - - s u p e r h e a t c o r r e c t i o n f a c t o r T a b l e 7 - 3 .

V a l u es o f c o r r e c t io n f a c t o r fo r h i g h - p r e s s u r e s a t u r a te d s t e am , K N , m a y

b e o b t a i n e d f r o m F i g u r e 7 - 4 .


10/23

s

L

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11/23

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12/23

2 8 0

Va l ve Selec t i on H and book

p s i a

3 2 o 0

3 1 0 o 9

3 0 0 0 "

29 0 0 "

2 8 0 0

. . . .

270O

2600

2500

2 4 0 0 ~

23OO ~

2 2 0 0

2 1 0 0 9

2 0 0 0 i

19 0 0 !

1 8 0 0 ~ - -

F

1 7 0 0

1 6 0 0

15O0

. 9 5

! /

/

_/

r

J

/

/

/

/

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/

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r

k P a a

2 2 0 6 0

2 1 3 7 0

2 0 6 9 0

2 0 0 0 0

1 9 3 1 0

1 8 6 2 0

179 3 0

1724 0

1 6 5 5 0

1 5 8 6 0

1 5 1 7 0

1 4 4 8 0

1 3 7 9 0

1 3 1 0 0

1 2 4 1 0

1 1 7 2 0

1 1 0 3 0

1 0 3 4 0

bara

2 2 0 . 6

2 1 3 . 7

2 0 6 . 9

2 0 0 . 0

19 3 .1

1 8 6 . 2

179 .3

172.4

1 6 5 . 5

1 5 8 . 6

15 1 .7

14 4 .8

13 7,9

1 3 1 . 0

124 .1

117.2

1 1 0 . 3

10 3 .4

1 . 0 0 1 . 0 5 1 . 1 0 1 . 1 5 1 . 2 0

Correction Factor,

K N

F i gu re 7 -4 . Co r rec ti on F ac to r fo r H i gh P ressure Sa tu ra ted S team , KN.

(Courtesyo f

Crosby Engineering Ha ndb ook, TechnicalDocumentNo . TP-V300, Septem ber 1995 ,

Crosby Valve & Ga ge Com pany, Wrentham , MA .)

S i z i n g E q u a t i o n s f o r L i q u i d F l o w

C u s t o m a r y M i x ed I m p e r i a l U n i ts

V o l u m e t r i c f l o w ~ U S g p m

1

~ ( ~ t

- 3 8 K K p K v K w P1 - P----~

C u s t o m a r y M i x e d S I U n i ts

W e i gh t f l o w ~ k g / h

A m

0 . 6 2 1 W

1

KK p Kv K w [ (P1 - P2) P] ~

( 7 - 1 4 )

(7-15)


13/23


281

C

0

8

1.10 ....

1.00

09o /

0.80 / ,

0.70 /

0.60 =

0.50

0.40

j l

/ -

: I I

I

1

0.20

0.10

0

10 15 20 25 30 35 40 45 50

Percent overpressure

Figure

7-5 . Ca pac i ty C or rec t ion Facto r Kp fo r Pressure Re l ie f Va lves in L iqu id

Serv ice tha t Requ i res an Overpressure o f 25% to Open Fu l ly . A t an Overpressure

Low er than 10% , There Is a He igh tened Poss ib il it y o f Va lve C haf fe r.

(Repr inted f rom

AP I RP 52 0 Pa rt I , 6th Edi t ion, March 199 3, Co urtesy o f Am er ican Petro leum

Institute.)

N o t e :

K - C o e f f i c i e n t o f d i s c h a r g e :

1 . F o r p r e s s u r e r e l i e f v a l v es t h a t o p en f u l l y o n l i q u i d w i t h i n an o v e r -

p r e s s u r e o f 1 0 % , o b t a i n t h e c e rt if ie d v a l u e o f K f r o m m a n u f a c t u r e r.

2 . I f t h e p r e s s u r e r e l i e f v a l v e i s o f t h e t y p e t h a t r eq u i r e s an o v e r p r e s -

s u r e o f 2 5 % t o o p en f u l l y , a co e f f i c i en t o f d i s ch a r g e o f 0 .6 2 f o r an

o v e r p r e s su r e o f 25 % is c o m m o n l y a s s u m e d . A t l o w e r o v e r p r e ss u r e s,

a c a p a c i t y c o r r e c t i o n f a c t o r K P t o b e o b t a i n e d f r o m F i g u r e 7 - 5

m u s t b e a p p l ie d . A t a n o v e r p r e s s u r e o f l e ss t h a n 1 0 % , h o w e v e r , t h e

v a l v e w i l l d i s p l a y a h e i g h t e n e d t e n d e n c y t o c h a t t e r . F o r o v e r p r e s -

s u r e s a b o v e 2 5 % , t h e v a l v e c a p a c i t y i s a f f e c t e d o n l y b y t h e c h a n g e

i n o v e r p r e s s u r e .


14/23

2 8 2 Valve Selection Handbook

1 0

0'g

0 8

W

0'7

0.6

0.5

\

10 20 30 40 50

PERCENT BACK PRESSURE

Figure

7 -6 . Capac i t y

Co r rec tion F ac to r Kw fo r

Bel low s Balanced-Pressure

Re l ief in L iquid Se rvice tha t

Requ i res an Overpressure o f

25% to Ope n Fu l l y . For Va lues

of Kw fo r Pressure Re l ie f Va lves

tha t in L iqu id Serv ice Open

Ful ly w i th in 10% Overpressure,

Con su l t Ma nufac tu rer .

(Repr inted f rom A PI RP 52 0

Part I , Decem ber 1976,

Cour tesy o f Am er ican

Petroleum Institute.)

K w = C a p a c i t y C o r r e c t i o n F a c t o r D u e t o B a c k

P r e s s u r e

T h e co r r ec t i o n f ac t o r ap p l i e s t o b a l an ced b e l l o w s - t y p e p re s s u re r e l i e f

v a l v es . T y p i ca l v a l u es may b e o b t a i n ed f ro m F i g u re 7 -6 . Fo r p ro d u c t

app l i cab le va lues , consu l t va lve manufac tu rer .

Co n v en t i o n a l p r e s s u re r e l i e f v a lv es a r e a f f ec t ed o n l y b y b u i l t- u p b ac k

pressure , though cor rec t ion fo r capac i ty i s no t commonly a l lowed fo r .

K v = C a p a c i t y C o r r e c t io n F a c t o r D u e t o V i s c o s i t y

W h en a p r e s s u re r e l i e f v a l v e i s to b e em p l o y ed fo r v i sco u s s e rvi ce , th e

or i fi ce a rea has to be d e te rm ined th rou gh an i t e ra t ive p rocess .

1 . So lve in i ti a l ly fo r non -v i scous f low and de te rm ine the nex t ava i l ab le

s tandard or i f ice s ize.

2 . Determine the Reynolds number , RE, fo r the in i t i a l ly ca lcu la ted

or i fi ce a rea f rom e i ther one o f the Equ at ions (7 -16) th rough (7 -18) .

3 . F ind va lue o f K v f rom F igure 7 -7 and app ly to the in i t ia l ly ca lcu la ted

d i scharge a rea . I f the thus cor rec ted in i t i a l a rea exceeds the chosen

area , the above ca lcu la t ions shou ld be repea ted us ing the nex t l a rger

s tandard or i f ice s ize.


15/23

Sizin g Pr essur e R el i e f evices 2 8 3

1 . 0

O . g

I--

o

< 0 . 8 = 9

U.

z

o

h

u

ta 0 . 7 - -

I1:

117

8

>-

0 . 6 '

I -

0 . . . . .

-~

o s l

>

ii

2

0 . 4

0 . 3

IO

r

L

[/

J

|

i i

'J :i

~ [

_J_

r " - r

I L _ , i

. . . . . . . .

t : j I

~ J . L---. ,.

2 0 4 0 6 0 I 0 0 2 0 0 4 0 0 1 , 00 0 2 , 0 0 0 4 , 0 0 0 I 0 , 0 0 0 2 0 , 0 0 0 I 0 0 , 0 0 0

R = REYNOLDS NUMBER

Figure 7 - 7 . Ca pa c i ty Co rrec t ion F ac tor Kv due to V iscos i ty . (Repr inted f rom A P I RP

52 0 Pa rt I , Dece mb er 19 76 , Cou rtesy of Am er ican Petro leum Inst itute.)

R e y n o l d s N u m b e r U S U n i t s

V o l u m e f lo w Q - U S g p m

Q 2 8 0 0 G

R E - - ~ ( 7 - 1 6 )

p~(A) :

127OOQ

R E - - 1 ( 7 - 1 7 )

U ( A ) ~

R e y n o l d s N u m b e r S I U n i t s

W e i g h t f l o w W - k g / h

3 1 3 W

R E - - I ( 7 - 1 8 )

~t(A)~

w h e r e

IX - d y n a m i c v i s c o s i t y a t t h e fl o w i n g t e m p e r a t u r e , i n c e n t i p o i s e

U - v i s c o s i t y a t t h e f l o w i n g t e m p e r a t u r e , i n S a y b o l t u n i v e r s a l

s e c o n d s


16/23

284 V a lv e S el e c ti o n H a n d b o o k

N o t e : E q u a t i o n 7 - 1 7 i s n o t r e c o m m e n d e d f o r v i s c o s i t i e s l e s s t h a n 1 0 0

S a y b o l t u n i v e r s a l s e c o n d s .

In f luence of In le t Pressure L o s s o n V a l v e

D is c h a r g e C a p a c i t y

T h e f lo w c a p a c i t y o f t h e d i s c h a r g i n g v a l v e r e s p o n d s t o th e

p r e s s u r e a t t h e v a l v e i n l e t , w h i ch i s t h e s e t p r e s s u r e mi n u s i n l e t

p r e s s u r e l o s s .

I n t h e ca s e o f g a s f l o w a t s o n i c v e l o c i t y , t h e i n l e t p r e s s u r e l o s s r ed u ces

t h e m as s f lo w r a t e i n d i r ec t p r o p o r t i o n t o t h e i n l e t p r e s s u r e l o s s . I n t h e ca s e

o f s u b s o n i c g a s f l o w an d l i q u i d f l o w , t h e ch an g e i n mas s f l o w d ep en d s o n

t h e c h a n g e o f p re s s u r e d i f fe r e n c e a c r o s s t h e n o z z le .

F r o m o b s e r v a t i o n , t h e i n d u s t r y c o m m o n l y n e g l e c t s t h e c a p a c i t y l o s s

d u e t o an i n l e t p r e s s u r e l o s s o f 3 % w h en s i z i n g d i r ec t - ac t i n g p r e s s u r e

r e l i e f v a l v e s , a n d a p p l ic a t i o n c o d e s d o n o t a p p e a r t o o f fe r g u i d a n c e a t

t h i s p o i n t . I n mo s t p r ac t i ca l ap p l i ca t i o n s h o w ev e r , t h e s e l ec t ed n o zz l e

s i z e i s b i g g e r t h a n t h e c a l c u l a t e d s i z e b y a n a m o u n t t h a t m a y c o m -

p en s a t e p a r t l y o r f u l l y f o r t h e cap ac i t y l o s s d u e t o f l o w r e s i s t an ce i n

the i n l e t p ipe .

T h e s a m e c a p a c i t y lo s s d u e t o in l e t p i p i n g p r e s s u r e l o s s is a ls o c o m m o n l y

n e g l e c t e d w h e n s i z i n g p i l o t - o p e r a t e d p r e s s u r e r e l i e f v a l v e s . A n y c a p a c i t y

l o s s d u e t o p r e s s u r e l o s s i n t h e i n l e t p i p i n g t o t h e ma i n v a l v e o f mo r e

t h a n 3 % h o w e v e r s h o u l d b e t a k e n i n to a c c o u n t . I n t he c a s e o f s n a p - a c t i n g

f l o w i n g - t y p e p i l o t s , t h e p r e s s u r e l o s s i n t h e p i p e l i n e f r o m t h e s o u r ce o f

p r e s s u r e t o t h e p i l o t c o n n e c t i o n s h o u l d i n n o c a s e e x c e e d 3 % o f t h e s e t

p r e s s u r e t o p e r m i t s t a b le v a l v e o p e r a t i o n a t a b l o w d o w n o f n o t l o w e r t h a n

5 % . C o n s u l t m a n u f a c t u r e r .

S I Z I N G O F IN L E T P I P I N G T O P R E S S U R E

R E L IE F V A L V E S

Co d es f o r t h e i n s t a l la t i o n o f p r e s s u r e r e l i e f v a l v es r eq u i r e t h a t th e cu m u -

l a t i v e t o t a l o f n o n - r eco v e r ab l e p r e s s u r e l o s s e s i n t h e i n l e t p i p i n g t o t h e

p r e s s u r e r e l i e f v a l v es a t r a t ed m as s f l o w , in c l u d i n g en t r y l o s s a t t h e p r e s s u r e

v es s e l co n n ec t i o n , s h a l l n o t ex ceed 3 % o f t h e s e t p r e s s u r e .


17/23


2 8 5

~P

1

0,1

1

, ,

/

r f I I I

I ' , ' , I I I

J l~ I 1

f , ~r j i i

l l l J I

j , / i j , 1 1

, / 1 7 / / . ,

I I / / Z . :

l i I l ~/

i l l f Z /

/ / ' 1 1 1 i

l l j , i ,

i / Z / / g /

10

0 . 9 , , _ . ~

NK

Figure

7-8 . D iag ram fo r t he Es t im at ion Res is tance Co ef f ic ien t For 3% Pressure Loss

in I n l e t L i ne t o P r es su r e R e l ie f Va l v e , A pp l ic ab l e t o G a s es and Vap o r s w i t h an

Isen t rop ic Coef f i c ien t o f k = 1 .3 . The Dash L ine Ap p l ies a lso to L iqu ids Reg ard less o f

Pressure R at io P 2/P1 . (ReprintedFrom A D-MerkblattA2, Courtesyof Verband der

Technischen Uberwachungs-Vereinee.V., Essen.)

T h e fo l l o w i n g p ro ced u re p e rmi t s t h e e s t i ma t i o n o f t h e r e s i s t an ce

coef f i c i en t o f the in le t p ip ing fo r 3 % in le t p ressure loss"

1 . In i t i a l ly es t imate the res i s t ance coef f i c i en t o f the p roposed in le t

p ip ing .

2 . Calcu la te the va lue o f (0.9AE/ANK). Use th i s va lue to ob ta in f rom

Figu re 7 -8 the va lue o f the res i s t ance c oef f i c i en t fo r an in le t p ressure

loss o f 3%. The i sen t rop ic coef f i c i en t fo r gases a l lowed fo r in th i s

d iagra m i s 1 .3 . The dash l ine app l i es a l so to liqu ids , i r respec t ive o f

pressure rat io Pz/P1.

3 . I f the thus ob ta ined res i s t ance c oef f i c i en t fo r 3% in le t p ressure loss

i s equa l to o r h igher than the res i s t ance coef f i c i en t o f the p roposed

in le t line , the p ropo sed ins ta l la t ion i s adequa te .


18/23

2 8 6 V alve Se l ec ti on H andb ook

S I Z I N G O F D IS C H A R G E P I P I N G O F

P R E S S U R E R E L I E F V A L V E S 1

Pr io r to s i z ing the d i scharge p ipe , ob ta in f rom the m anufa c tu rer the per -

m iss ib le back p ressure P2 a t va lve ou t l e t fo r the type o f p ressure re l i e f va lve

und er cons idera t ion . In the case o f be l low s ba lanc ed p ressure re l i e f va lves ,

t h e p e rmi s s i b le b ack p re s s u re is t he s u m o f b u il t- u p an d s u p e r i mp o s ed b ack

pressure .

In i t i a l ly ca lcu la te the res i s t ance coef f i c i en t o f the p roposed d i scharge

p ipe l ine . Then ca lcu la te f rom the equa t ions be low the res i s t ance coef -

f i c i en t fo r the permiss ib le bu i l t -up back p ressure . I f the thus ca lcu la ted

res i s t ance c oef f i c ien t i s equa l to o r low er than the res i s t ance coef f i c ien t o f

the p ropo sed d i scharge p ipe l ine , the in i ti a l ly p rop osed ins ta ll a t ion i s ade-

qua te . Otherwise , redes ign the d i scharge p ipe l ine fo r a lower res i s t ance

coeff icient .

For l iquids"

The bu i l t -up back p ressure , in t e rms o f the p ressure d i f fe ren t i a l across

the va lve (P1 - P2) , m ay be exp ressed by the Equat ion 7 -19

P 2 - P 3 . _ ~ 2 ( 7 - 1 9 )

P1 - P 2 0.9A2

where the p ressures P a re abso lu te p ressures .

I f the permiss ib le back p ressure i s l imi ted , fo r example , to 10% of the

set pressure, then:

P 2 - P 3

P1 - P2

= 0 . 1 0

In t roducing the above p ressure ra t io in to Equat ion 7 -19 and rear rang ing

the va lue o f the res i s t ance coef f i c i en t o f the d i scharge p ipe l ine fo r 10%

b u i l t- u p b ack p re s s u re may b e o b t a i n ed f ro m E q u a t i o n 7 -20 :

0 .1 0 ( 0 . 9 A 2 ) 2

~ 2 - - | _ 0 . 1 0 K A N (7 - 20)

1 S i z i n g p r o c e d u r e t a k e n f r o m B o p p & R e u t e r.

Safety Valve Handbook far System Planners

and Operators. (Courtesy of Bopp Reuther.)


19/23

Sizing Pressure R elief Devices 2 8 7

5.!

4 "

J

. , .

1

0 1 2 3 4 5 6

Z e t a - V a l u e

bk= 2 , 0

J j ~ e k = l , 8

-

-k = l , '2

_ . k = l , 0 .

7 8 9 10

Bu i l t -up bac k p res s u re P ae i n t h e v a l v e ou t le t t o "c r i t ic a l " p res s u re P" a t th e p ipe end ,

d e p e n d e n t o n t h e z e t a v a l u e o f th e d i s c h a r g e p i p e

Figure

7-9 . D iag ram fo r the E s t ima t ion o f the Res is tance Co e f f ic ien t o f the

D ischarge P ipe l ine o f a P ressu re Re l ie f Va lve fo r the Permiss ib le Bu i lt -Up Back

Pressu re in Gas o r Va po r Serv ice . (Courtesyof Bop p & R euther, Safety

Va lves-Ha nd bo ok for System Planners and Op erators. )

F o r g a s o r v a p o r "

This i s the p roposed s i z ing p rocedure :

1 . Calcu la te the va lue o f the p ressure ra t io (P1 /PT) , f rom Eq uat ion 7 -21

k

PT (2) KAN

Pi k + 1 0 .9AT

( 7 - 2 1 )

where the p ressures P a re abso lu te p ressures .

2 . Calcu la te f rom the p ressure ra t io (P1 /PT) the va lue o f PT. I f the

pressure PT i s h igher than the a tmospher ic p ressure P3 , the p ressure

PT i s c r i t i ca l . I f the ca lcu la ted va lue o f PT i s lower than the a tmo-

spher ic p ressure P3 , the p ressure a t the d i scharge p ipe ou t l e t i s the

pressure P3.

3 . Calcu la te the va lue o f P2/PT and de te rm ine f rom F igure 7 -9 the res i s -

t ance coef f i c i en t o f the d i scharge p ipe l ine fo r the permiss ib le bu i l t -up

back p ressure in gas o r vapor se rv ice .


20/23

288 V a lv e S e le c t io n H a n d b o o k

Sizing o f Ru pture Discs

Ru p t u re d i s c s may b e emp l o y ed i n p r e s s u re s y s t ems s u b j ec t n o t o n l y

to nonv io len t p ressure excurs ions , as in reg imes in which p ressure re l i e f

va lves a re employed , bu t a l so in sys tems sub jec t to v io len t p ressure

excurs ion resu l t ing f rom the def l agra t ion o f f l ammable gases o r dus t s

i n l o w -s t r en g t h co n t a i n e r s . E ach p re s s u re ex cu r s i o n r eg i me r eq u i r e s a

d i f fe ren t approa ch to rup tu re d i sc s i z ing .

Rup ture Disc S iz ing for No nv io len t Pressure

Excursions

T h e A SM E Co d e (1 9 9 2) 1 an d t h e A P I RP 520 P a r t I (M arch 1 9 9 3) 2

presen t a s impl i f i ed method o f s i z ing rup tu re d i scs by neg lec t ing p res -

su re d rops in the in le t p ip ing and in the d i scharge p ip ing . Based on the

equat ions app l i cab le to p ressure re l i e f va lves fo r a l l f lu ids , an e f fec t ive

coef f i c i en t o f d i scharge o f K - - 0 .623 may be used wi th in the fo l lowing

l imi tat ions:

Co e f f i c i en t o f

discharge method.

T h e co e f fi c ien t o f d i s ch a rg e m e t h o d ,

us ing a coef f i c i en t o f d i scharge K equal to 0 .62 , may be used wi th in the

fo l lowing l imi ta tions :

1 . The rup tu re d i sc d i scharges d i rec t ly to the a tmosphere , i s ins t a l l ed

wi th in e igh t p ipe d iameters f rom the vesse l nozz le en t ry , and has a

1A SM E Code (1992) , Sec t ion VII I , Div . 1 , UG -127 (2 ) (a ).

2 A PI R P 520, Part 1 , 6 th edi t ion , 1993, c lause 4 .8 .1 .

3 ISO S tandard 6718 and the co r respond ing E uropean S t andard pe rmi t t he coe f f ic i en t o f

discharge of 0 .62 for l iquid appl icat ions only . For compressib le f lu ids , the f low ra te i s

con t ro l l ed by the noz z l e en t ry conf igu ra t ion o f t he eq u ipme n t and the rup tu re d i sc dev ice .

The s t andard l is t s a num ber o f nozz l e en t ry conf igu ra t ions and the app l i cab le coe f f i c i en t

o f d i scha rge .

In add i t i on to t he coe f f i c i en t o f d i scha rge me thod , t he ISO S tandard pe rmi t s t he f l ow

res i s t ance va lue me thod , wh ich requ i res t he rup tu re d i sc t o be s i zed by ana lys ing the

f low res i s t ance o f t he en t i re sys t em. Th i s s i z ing me thod wi l l be adop ted a l so i n t he

pend ing rev i s ions o f t he ASME Code and the API RP 520 Par t I , and in t he emerg -

ing European S t andard dea l ing wi th t he s i z ing o f rup tu re d i sc dev ices . Manufac tu re rs

wi l l have to provide the cert i f ied f low resis tance coeff ic ient of the rupture d isc device

KR, wh ich i s a d imens ion less fac to r u sed to ca l cu l a t e t he ve loc i ty head lo ss t ha t

re su l ts f rom the p resence o f t he rup tu re d i sc dev ice i n t he p ressu re re l i e f sys t em. Th i s

s i z ing me thod may requ i re t he use o f a compute r p rog ram fo r speed and accu racy

of calcula t ion .


21/23

Sizing Pressure Relie f Devices 2 8 9

l e n g t h o f d i s c h a r g e p i p e n o t g r e a t e r th a n f i v e p i p e d i a m e t e r s f r o m t h e

r u p t u r e d i s c d e v i c e .

2 . T h e n o m i n a l d i a m e t e r s o f t h e in l e t a n d d i s c h a r g e p i p i n g a r e e q u a l to

o r g r e a t e r t h a n t h e s t a m p e d N P S ( o r N B ) d e s i g n a t o r o f t h e d e v ic e .

3 . T h e a r e a , A , t o b e u s e d i n t h e t h e o r e t ic a l f lo w e q u a t i o n i s t h e m i n i m u m

n e t f l o w a r e a 4 a s s p e c i f i e d b y t h e r u p t u r e d i s c m a n u f a c t u r e r .

W i t h i n t h e s e l i m i t a t i o n s , t h e f o l l o w i n g s i z i n g e q u a t i o n s s i m i l a r t o t h o s e

f o r p r e s su r e r e l i e f v a l v e s m a y b e a p p l i e d :

S iz in g E q u a t io n s fo r Ga s o r V a p o r O t h e r t h a n

S t e a m

C u s t o m a r y M i x e d I m p e r i a l U n i t s , S o n i c N o z z l e F l o w

W e i g h t f l o w ~ l b / h

A - C K 1 P 1

V o lu m e tr ic f l o w ~ s c f m

W 1

A = ( M T 1 Z ) ~ ( 7 - 2 3 )

6 . 3 2 C K P 1

C u s t o m a r y M i x e d S I U n i ts , S o n i c N o z z l e F l o w

W e i g h t f l o w ~ k g / h

13 1 . 6 W (~__~Z) 89

A - - ( 7 - 2 4 )

C K P 1

V o lu m e tr ic f l o w ~ N m 3 / h

5 . 8 7 V 1

A = ~ ( M T Z ) ~ ( 7 - 2 5 )

C K P 1

4 The minimum flow are a is the calculated net area af ter a complete burst of the disc w ith

appropriate allowance for any structural mem bers whic h may redu ce the net flow area

through the ruptu re disc device. The net flow ar ea for sizing purposes shall not exceed

the nom inal pip e size area of the rupture disc device.


22/23

9-9 0 Valve Se lec t ion Handb ook

w h e r e

C - 5 2 0 k k + 1

Fo r values of C , refer to Table 7-2 .

C u s t o m a r y M i x e d I m p e r i a l U n i ts , S u b so n i c N o z z l e F lo w

W e ig h t f l o w ~ l b / h

m _._

W

735FKP1

( 7 - 2 6 )

V o lu m e tr ic f l o w ~ s c f m

W 1

A = ( M T Z ) ~

4645FKP1

( 7 - 2 7 )

C u s t o m a r y M i x e d S I u n i t s - - S u b s o n i c N o z z le F l o w

W e ig h t f lo w - - k g / h

m

w

5.58FKP1

( 7 - 2 8 )

V o l u m e t r i c f l o w ~ N m 3 / h

W 1

A = (MTZ )~

125.1FKP1

( 7 - 2 9 )

where

For Values of F refer to F igure 7-1 .


23/23

Sizing Pressure Re lief Devices 9.9 |

Sizing Equations for Liquid Flow

C u s t o m a r y M i x e d I m p e r i a l U n i t s

V o lu m e tr ic f l o w m U S g p m

1

Q

( 7 - 3 0 )

A - 3 8K K v P 1 - P 2

Cu s to m a ry Mix ed S I Uni t s

W e i g h t f l o w ~ k g / h

0 . 6 2 1 W

A = ~ ( 7 - 3 1 )

KK v[(P1 - P2)9] ~

Rup ture Disc Sizing for V iolen t Pressure

E x c u r s i o n s

in Low-Strength Containers

S i z i n g d a t a o n v e n t p a n e ls f o r e x p l o s i o n v e n t i n g a r e b a s e d o n i n f o r m a t i o n

f r o m s i m p l e m o d e l s a n d d a t a o b t a i n e d f r o m v a p o r a n d d u s t e x p l o s i o n s i n

v e s s e ls f i tt ed w i t h e x p l o s i o n r e l ie f . T h e r e c o m m e n d e d s i zi n g p r o c e d u r e s

a r e c o n t a i n e d i n p u b l i c a t io n s o f n a t io n a l l y r e c o g n i z e d o r g a n i z a ti o n s . T h e

w i d e l y r e c og n i z e d p ub l i c a t i ons i n the U . S . a re the

NF P A G u i d e f o r V ent in g

o f Def lagra t ions ,

a n d in G e r m a n y

V D I-R i ch t l i n i en 367 3 (19 9 5)o n

P r e s s u r e

R e l e a s e o f D u s t E x p l o s i o n s . 1

F a c t o r s t ha t i n f l ue nc e t he r e qu i r e d s i ze o f the e xp l o s i on v e n t i nc l ude :

9 V o l um e a nd s ha pe o f e nc l o s u r e s uc h a s c ub i c o r e l onga t e d ( s i l o s ) .

9 H o m o g e n e o u s o r n o n - h o m o g e n e o u s m i x t u r e ( p n e u m a t ic f i lli ng ).

9 M a x i m u m p r e ss u r e a l lo w e d d u r i n g v e n ti n g .

9 S t a ti c bu r s t i ng p r e s s u r e o f t he ve n t i ng de v i c e .

9 E x p l o s i o n s e v e r it y o f t h e p o t en t i al h a z a r d , e x p r e s s e d i n t e r m s o f h a z a r d

c l a s s e s K S T f o r dus t o r K G f o r ga s .

9 G e n e r a ll y , th e a p p l i c a ti o n o f N o m o g r a m s .

1 VDI-Richtlinien 3673 1995 on p ressure release of du st explosions are p rinted in German

and English.

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Valve Selection Handbook - Sizing Pressure Relief Devices