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8/3/2019 Seminar Vibr

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Auomatica,Vol. 23, No. 3, pp. 381 385. 1987Printed in Gre at Britain. 0005-1098/87 83.00+0.00Pergamon Journals Ltd. 1987 International Federationof AutomaticControl

B r i e f P a p e rL e a k D e t e c t io n M e t h o d s f o r P ip e li n es *

L . B I L L M A N N t a n d R . I S E R M A N N tK ey W o rd s - -Fa i l u re d e t ec ti o n ; s t a t e e s t i ma t i o n ; co r re l a ti o n m e t h o d s ; mo d e l s ; l iq u i d an d g as p i pe li n es .

A b s t ra c t - - Fo r t h e ea r l y d e t ec t i o n an d l o ca l i za ti o n o f sma l l P l P3 P , -3 Pa - tl e ak s i n p i p e l i n e s a n o n l i n ea r ad ap t i v e s t a t e o b se rv e r an d a i I I - - I I Isp ec ia l co r re l a t i o n t ech n i q u e w ere d ev e l o p ed , b a sed o n p re ssu re ~ , . . . . I Ian d f l o w measu rem en t s a t t h e p i p e l in e i n l e t an d o u t l e t. S i mu - q o q 2 q , - z Chlat ions and experim ents show the resu l t s for a gas and a l iquid ,a LR q>pipel ine . Flo . 1 . Discre te s ta te represe nta t ion of the p ipeline .IntroductionAs PIPELINES for the t rans porta t ion of l iquids or gases usual lya re o n l y i n s t ru men t ed a t t h e b eg i n n i n g an d t h e en d , t h ei n fo rma t i o n o n a l e ak a l o n g t h e p i p e l i n e d u r i n g n o rma l o p e r -a t i o n can o n l y b e b a sed o n t h e se av a i l ab l e measu remen t s .Mo s t l y j u s t t h e i n p u t an d o u t p u t f l o w s a re b a l an ced . H o w ev e r ,acco rd i n g t o t h e i n h e ren t f l o w d y n ami cs an d t h e su p e r i mp o sednoise , only leaks can be detected w i th th is s imple me thod w hicha re ab o u t >2 % fo r l i q u i d an d >1 0 % fo r g a s p ip e li n es . Th i sco n t r i b u t i o n n o w d iscusses an d p ro p o ses l e ak d e t ec t i o n me t h o d sw h i ch a re ab l e t o d e t ec t co n s i d e rab ly sma l l e r l eak s. I t su m ma-rizes research act iv i t ies durin g the last years . The im prove me ntsa re mad e b y u s i n g n o n l i n ea r ad ap t i v e s t a t e o b se rv e rs fo r t h ep i p e l in e d y n ami cs an d b y u s i n g a sp ec i al co r re l a t i o n t ech n i q u efo r t h e fau l t d e t ec ti o n . Th e o b t a i n ed re su l t s a re sh o w n fo r l e akex p e r i men t s w i t h a g a so l i n e p i pe l i n e an d s i mu l a t i o n s o f a g a spipel ine , w hich are veri f ied by m easured s ignals .Mathematical pipeline modelsA ma t h ema t i ca l d e sc r i p t i o n o f t h e p i p e l i n e d y n ami cs w asd e r i v ed b y t h eo re t i ca l mo d e l l i n g fo r g a s p i p e l i n e s (W e i man n ,1978; Bi l lmaun, 1982) and l iquid p ipel ines (Krass et a l . , 1979).S i mp l i fy in g a s su mp t i o n s su ch a s a co n s t an t d i ame t e r da (respect-i v e l y a co n s t an t sec t i o n a l a rea A ) , a t u rb u l en t f l o w an d i so t h e rmi cco n d i t i o n re su l t i n a co mm o n d esc r i p t i o n fo r t h e g a s an d l i q u i df l o w d y n ami cs .Fo r a p i p e e lemen t o f l en g t h d z t h e mass an d m o me n t u mb a l an ces a re

Op Opwo-7+-~F=oOpw Op I Opw 2

O t + ~ z + 2 0 z = - F - H (1 )w h ere p [k g m- 3 ] = d en s i ty ,w [ m s- 1 ] = v e l o c i ty o f f lo w ,p [N m - 2 ] = p ressure ,z [ m ] = l en g t h co o rd i n a t e ,t [s] = t ime coordin ate .Th e influence of the fr ic t ion i s represented by F a nd th egeom etric height influence b y H (see below).

* Received 24 Ju ly 1984; rev ised 14 Apri l 1986; rev ised 2N o v emb er 1 9 86 . Th e o r i g i n a l v e rs io n o f t h is p ap e r w as p re sen t eda t t h e 9 t h IFA C W o r l d Co n g re ss w h i ch w as h e l d i n Bu d ap es t ,H u n g a ry d u r i n g Ju l y 1 9 84 . Th e p u b f i shed p ro ceed i n g s o f t h isI F A C M e e t i n g m a y b e o r d e r e d f r om : P e r g a m o n B o o k s L i m i t e d,H ead i n g t o n H i l l H a l l, O x fo rd O X 3 0 BW , En g l an d . Th i s p ap e rw as reco mmen d ed fo r p u b l i ca t i o n i n rev i sed fo rm b y A sso c i -a t e Ed i t o r A . v an Cau w en b e rg h e u n d e r t h e d i rec t io n o f Ed i t o rH . A u s t i n Sp an g , I I I .t l n s t i t u t f i ir Reg e l u n g s t ech n i k , Tech n i sch e H o ch sch u l eD arm s t ad t , Sch l o ssg rab en 1 , D -6 1 0 0 D arms t ad t , F .R .G .

38 1

In t ro d u c i n g t h e f l o w ra t eq = A p w (2 )

an d t h e i so t h e rmi c sp eed o f so u n db = x / ~ ( 3)

the p ipel ine model can now be s impl i f ied by assuming- - t h e i so t h e rmi c sp eed o f so u n d i s co n s t an t ,- - t h e v e l o c i ty o f f lo w i s sma l l i n co mp ar i so n t o t h e sp eed o fsound--e last ic effects of the p ipe wal l can be neglected .Th en t h e " l o n g p i p e l i n e mo d e l " re su l t s i n

A 8p 0qb 2 a t + ~ z = 0

1 8q Op gb2 q lq l g s i n aA at + az 2daA 2 p b' - ' - ~ p ( 4 )

with , l [ - ] ffi fr ic t ion coeffic ien t ,a [ o ] = angle of incl inat ion ,g [In s- 2] = gravi ty .This p ipel ine model i s a part ia l d i fferent ia l equat ion systemo f h y p e rb o l i c t y p e .If the usual ly used s impl i f icat ion that th e speed of sound i sco n s t an t i s n o t a ccep t ab le , b u t ch an g es acco rd i n g t o

Ob~-pfficonst., (5)t h i s c an b e t ak en i n t o acco u n t , a s sh o w n b y B i l l man n (1 9 8 2 ) ,b y en l a rg i n g t h e mass b a l an ce w i t h t h e co r rec t i o n fac t o r e :

a ap 0qe b--]~" + ~z = 0. (6)To so lve th is equat ion system (4) numerical ly (so lu t ion ford iscre te t ime t = k At wi th the t ime in terva l At) , the p ip l ine i sd i v i d ed i n t o N sec t io n s o f t h e l en g t h

A r f L z~ - ( 7 )as sh o w n i n F i g . 1.Bil iman n (1982} in t rodu ced a centere d d i fference sch eme

a x] 3 ~ 1 - ~ + ~ - 1Ot,~ ffi 2A t

O ' z l , ~ 4 A z (8 )


2/5

382 Brief Pap erwith k = d i s c re te t im e ,A t = t im e in te rva l ,Az = l e ng th in te rva l .T he n the fo l lowing " l ine a r " e qua t ion s ys te m re s u l t s

A x k i = f( xk, x k - i , i,, ) + s(p~+ , p ~ v i ) ( 9 )

with the s ta te ve c to rX k k ~ k k= [ q o , q 2 . . . . . q k N , P i ,P 3 . . . . . P % - l ] T ( 1 0 )

a nd the he igh t c o r r e c t ion ve c to r h .As the s ys te m m a t r ix i s c ons ta n t , the l ine a r e qua t ion s ys te m(9) i s s o lve d by the fo l lowing a lgo r i thm s :

_ OBSER-!LPIPELINE ror41TOR

FIG. 2. P ipe line supervis io n s truc ture .X + 1 = A - 1 f (xk, x ~ l,/t., h) + s(p~l+ l, pkn+1)]

:+, = L q ~ + , _ j = [ 1 , o . . . . . 1 , o . . . . . O ] x l < ' ' . ( l l )

T his s o lu t ion ne e ds on ly s m a l l c om p uta t io na l e f fo r t by m ul t ip ly -ing the inve r s e m a t r ix w i th a ve c to r inc lud ing a non l ine a rfunc tion of the two las t s ta tes , of the f r ic t ion coeff ic ient , of thehe igh t c o r r e c t ion ve c to r a nd o f the two inpu t p re s s u re s igna l sP o a nd p~ . T he ou tpu t s igna l s qo a nd qN a re e le m e n ts o fthe s ta te ve c to r . T e s t s w i th m ore c om ple x s o lu t ion m e thods(non l ine a r , g r e a t c om puta t io na l e f fo r t ) ga ve r a the r s im i la r r e s u l tsfo r the a c h ie ve d a pp l ic a t ion .M o d e l l i n g o f l e a k sI t i s a s s um e d tha t a s m a l l l e a k ( flowra te q L ) o c c u r s a t loc a t ionZ L . T h is e ff ec t i s t a ke n in to a c c oun t by in t rodu c ing th i s lo s s inthe m a s s ba la nc e fo r th i s s e c t ion . T h is l e a ds to a n e n la rge dp ipe l ine m ode l w i th the l e a k in f lue nc e ve c to r I (de pe nda n t onthe l e a k loc a t ion ) :

X k + i = A - i f { xt C , k - I , . , ) -I - ~ o + i , l ~ N + i ) ] + l q L . ( 1 2 )

E qu a t ion (12) c a n now be us e d a s the ba s ic r e la t ion fo r s e ve ra ll e a k de te c t ion m e thods .K n o w n l e a k d e t e c t i o n m e t h o d s

B a l a n c i n g . T h e b a l a n c i n gpre s e n t l e a k f lowra te m e thod d i r e c t ly e s t im a te s the

SBL(k) = E { q ~ - - q k N } = qL(k). (13)Howe ve r , th i s s im ple m e thod i s r a the r s e ns i tive to a ny d i s tu rb -a nc e s a nd to inhe re n t p ipe l ine dyna m ic s . T he re fo re , on ly l a rgele a ks c a n be de te c te d . A loc a l i z a t ion o f the l e a k i s no t pos s ib le .

S h o c k w a v e b a s e d m e th o d s . In the case of laxge leaks ( l iquidsqL > 5% , ga s e s qL > 12%) wh ic h oc c ur s ud de n ly , s hoc kwa v e sc ros s the p ipe up to bo th e nds . T he r e s u l t ing p re s s u re g ra d ie n t sa re the n us e d fo r l e a k de te c t ion a nd the l e a k loc a t ion i s e s t im a te db y t h e s p e e d o f p r o p a g a t i o n ( K r a s s e t a l . , 1979).F u r t h e r d e v e l o p e d m e t h o d s , u s i n g a m o d e l o f t h e p i p e l in edyna m ic s , t ry to inc re a s e the s e ns i t iv i ty to a l e a k a n d to d e c re a s ethe m e a s ure m e n t e f fo r t.

F a u l t m o d e l f i l t e r s . I f a m ode l o f the c om ple te p ipe l ine (12 )inc lud ing the l e a k in f lue nc e i s u s e d , one c a n t ry to e s t im a te thele a k in f lue nc e ve c to r I by s ta te r e c ons t ruc t ion o r by d i s c re tes ta te va r ia b le f i l t e r s . T o e x t r a c t th i s in fo rm a t ion unde r no i s yc ond i t ions , a " ba nk o f f i l t e r s " c a n be us e d , a s s um ing d i f f e r e n tloc a t ions fo r a l e a k (D ige rne s , 198 0) . Howe ve r , the c om put -a t iona l e f fo r t s e e m s to b e ve ry l a rge .F a u l t s e n s i t iv e f i l t e r s. Dif fe re n t f rom the f a u l t m ode l f i l t e r s ,f a u l t s e ns i t ive f il t e r s m o n i to r the r e s idua l s (d if f e re nc e be twe e nm e a s u re d a nd e s t im a te d f lowra te s) qo - ~o a nd qN - - ~N ( I s e r-m a n n , 1982) . I f a l e a k oc c ur s , the r e s idua l s c ha nge in p re de te r -

m ine d d i r e c t ions . Howe ve r , the a la rm i s lo s t a f t e r a wh i le ,be c a us e the s ta te va r ia b le f i l t er c om pe ns a te s th e l e a k in f lue nc e .

A n a d d i t i o n a l d r a w b a c k o f t h e t w o l a s t s t a t e v a r ia b l e m e t h o d si s tha t the p ipe l ine m ode l (12 ) ha s to be l ine a r iz e d . T he re fo rethe y a re s u i t a b le on ly fo r c ons ta n t ope ra t ing c ond i t ions .I m p r o v e d l e a k d e t e c t i o n m e t h o d sIn o rde r to de te c t l e a ks a l s o fo r w ide r a nge s o f ope ra t ingc ond i t ions , non l ine a r p ipe l ine m ode ls ha ve to b e us ed . T h isle a ds to non l ine a r s t a te obs e rve r s . An a dd i t iona l r e qu i r e m e n t i st h a t t h e i n f o r m a t i o n o n t h e l e a k s h o u l d n o t v a n i s h w i t h ti m e .L ook in g a t the p ipe l ine m o de l (11 ), m os t o f the c oe f f ic ie n ts a r eknown wi th good a c c ura c y , e xc e p t the f r i c t ion c oe f f i c ie n t ,~ ,wh ic h m a y a l s o c ha nge w i th t im e . T he re fo re th i s c oe ff ic ie n t w i llbe e s t im a te d (on - l ine ) by the l e a s t - s qua re s m e thod . T h is l e a dsto a n a d a p t ive (non l ine a r ) s t a te obs e rve r . An a dva n ta ge o f th i sa pproa c h i s fu r the rm ore tha t the e s t im a te d f r i c t ion c oe f f i c ie n td o e s n o t c h a n g e t h e s t e a d y s t a t e s o l u t io n o f t h e m a s s b a l a n c ein (4 ) , s o tha t l e a k e f f e c t s w i l l no t be c om pe ns a te d by theobs e rve r .F igu re 2 s hows th e r e s u l t ing l e ak s upe rv i s ion s t ruc tu reinc lud ing the p ipe l ine obs e rve r a nd the l e a k m on i to r , whe rebo t h d i f f e r enc e s x a nd y a c t a s r e s idua l s .T h e c o r r e s p o n d i n g e q u a t i o n s a r epipe line :

x i+ l - - A - l [ l lx i , x t - 1 ,2 ,h ) + S ( fo+l,P~N+l) ] + IqLf+ 1 _ I -1,0 . . . . 1 ,0 , . . . . 0]Xk+ 1; (14)

obs e rve r :f < + ' = A - ' r f o i " . f ' - ' . L i , ) + , @ o + ' . ~ + ' ) 7~ + 1 = [ 1 , 0 . . . . . 1 , 0 . . . . 0 ]~ k + l ; (15)

r e s i d u a l s :

L y ~ k ) _ l (16)T o s how the e ff ec ts o f a s udde n ly a ppe a r in g l e a k , a ga s p ipe l inewa s s im ula te d w i th qL = 0 .35 kg s - t a nd Z L /L R = 0 .5 (s om e da taa re g ive n l a te r ) .T he f lowra tvs a t the be g inn in g a nd the e nd o f the p ipe l inec h a n g e i n p r e d e t e r m i n e d d i r e c t i o n s d e p e n d i n g o n t h e l e a kf lowra te a nd the l e a k loc a t ion , s e e F igs 3 a nd 4 .A s e ns i t ive de c i s ion a lgo r i thm fo r " le a k" o r " no l e a k" wa sfound b y the c ros s -c o r re la t ion - func t ion (S ie be r t a nd I s e rm a nn ,1977 ; I s e rm a nn a nd S ie be r t , 1976)

d p x y ( = E { x ( k ) ' y ( k + z)} (17)w h i c h r c s u l t s ( t h e o r e t i c a l ) i n

IO no l e a k~ y ( t ) - - - - - f ( q L , Z L ) w i t h l e a k ( 1 8 )


3/5

Brief Pa per 383flow k f / s )

3 " 9 1 I teaJk3 . 7 II3 . 5 . ~I3 . 3 . II3 . 1 ! Is 1o

~ c t ,

t;mo! ! I I1 5 20 25 30 (h i

F ]o . 3. React io n a t the begin ning of the p ipel ine after a leakoccurs (simulation).f l o w I k g / s ]

3 "~ I (~ - ~ l e a U3 . 7I

3 . 11 t t t I : :0 5 10 15 20 2S 30 (hl

F 1O . 4 . R e a c t io n a t t h e e n d o f t h e p i p e f i n e a f te r a l e a k o c c u r s(simulation).

w h i ch mean s i t ch an g es i n a p red e t e rmi n ed d i rec t i o n . Th ecom puta t ion i s real ized by a recursive f i lter of f i rs t orde r~x,(r ,k) = r ~ x , ( z , k - 1) + (1 - r ) x ( k ) y ( k + O . (19)

To reduce noise effects the a larm cri terion i s taken as the sumover several t ime sh i ft s z :M~y,z (k)= ~ ~x ,(z ,k). (20)

This cross -corre la t ion sum reacts sensit ively even to s mal l leaks.A n a l a rm i s g i v en w h en t h e su m c ro sse s a p red e f i n ed a l a rm-threshold .A f t e r a l e ak i s d e tec t ed , t h e p a ram e t e r e s t i m a t i o n o f ) . i s f ro zenan d t h e e s t i ma t i o n o f t h e l e ak l o ca t i o n s ta r ts . In t ro d u c i n g t h eau t o -co r re l a t i o n -su msM

dp~ x z(k )= ~ Sx~(z,k) (21)3= -- .~an d

M~by,E(k)= ~ ~ , y ( z , k ) (22)t = - - Mt h e l e ak l o ca t i o n i s e s t i ma t ed b y

S L ( k ) L R ( 2 3 )1 - Cxxdk___J , , d k )

w h e re L a i s t h e l en g t h o f t h e p i p e l in e (S i eb e rt an d I se rman n ,1 9 7 7 ) . Th e l eak f l o w ra t e i s e s t i ma t ed b y t h e d y n ami c b a l an ceeq u a t i o n~ L ( k ) = E { x ( k ) - - y(k)}. (24)

h (m l450

300

150

0 I C ~ z ( k m l15 0FIG. 5 . Approximat ion for the geographic height profi le .

pressure (bgr]

3 3 -

3 1

2 g ~ t l m o270 10 2o 30 40 So 60 Ih l

F IG. 6 . Mea sured n pu t and ou tpu t p ressu re o r a gas p ipe l ine .

L e a k d e t e c t i o n f o r g a s p i p e l i n e sTests wi l l be described , which are based on mea sured s ignalsof a gas p ipel ine . In orde r to s imu late leaks, the obse rver i senlarged by the leak influence vector I wi th a negat ive leakflowrate. T his rea lizatio n (also useful for self test) respects thed y n ami cs o f t h e l e ak in f lu ence an d i s a g o o d ap p ro x i m a t i o n fo ra real suddenly-appearing leak in the p ipel ine according to theresultin g residu als (Billmann, 1983).Th e p i p e l in e i s 1 5 0 k m l o n g w i t h a d i ame t e r o f 0.2 6 m an d av a ry i n g sp eed o f so u n d (d ep en d i n g o n t h e p re ssu re ) . T h e fo u rmea sured s ignals (q0 , Po , qN, PN) were sam pled every 3 ra in . Th eobserv er uses a t ime in terval of 30 s, so that the me asured s ignalsh av e t o b e i n t e rp o la t ed . W i t h t h e l en g t h i n t e rv a l o f ab o u t 9 k mt h e sy s tem o rd e r i s 17 . Fu r t h e rmo re , an ap p ro x i ma t i o n o f th egeographic height profi le i s included, see Fig . 5 .The decis ion a lgori thm is modified , subst i tu t ing x ( k ) and ~(k)in (19) by~ k ) = x (k ) - E{ y(k )}y ( k ) = y ( k ) - E { x ( k ) } . (25)

This y ie lds a bet ter sen si t iv i ty and i s independe nt o f the leaklocat ion .F i g u re 6 sh o w s t h e measu red i n p u t an d o u t p u t p re s su re o fthe described p ipel ine during a test period of 65 h .As i l lust ra ted in Figs 7 and 8 , the p ipel ine observer describest h e d y n ami c b eh av i o u r o f t h e p i p e l i n e q u i t e w e l l , so t h a t asensi t ive leak detect ion s hould be possib le . R esul t s from severalleak s imulat ions wi th d i fferent leak ra t ios ( leak ra t io g ivenrela t ive to a me an flow ra te) are g iven in Fig . 9 . Figur e 10 showsan ex am p l e o f t h e l e ak l o ca t i o n e s t i ma t i o n fo r a l e ak ra t i o o f5 % .Fu r t h e rm o re t h e t i me fo r co mp u t a t i o n ( l e ss t h an 2 s fo r aPD P 1 1 /3 4 ) i s ra t h e r sma l l in co m p ar i so n t o t h e samp l i n g t i meof 3 rain.

L e a k d e t e c t i o n f o r l i q u i d p i p e l i n e sSince the dynamics of a l iquid p ipel ine are very fast incomparison to gas p ipel ines, the sampl ing t ime and the lengthin terval decrease and the com putat io nal effort increases, w hichcan b e a h an d i cap fo r t h e ap p l i ca t i o n w i t h mi c ro -co mp u t e rs .Therefo re , a s impl i fied m ode l can be used by ta k ing thes t a t i o n a ry so l u t i o n o f (4 ) , d u e t o t h e a s su mp t i o n o f s t a t i o n a ry(o r q u as i - s t a t io n a ry ) p u mp i n g co n d i t io n s .


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~ o = ~ / ~ o + p g ho ) - ~ + p g h , , ) f, ( ~ o )= x / (~ o + p g h o ) - ~ + p g h N)f2 ( '~s)" (29)

T h i s f o r m u l a i n c l u d e s t w o e s t i m a t e d f r i c t i o n c o e f f ic i e n ts t oc o m p e n s a t e m e a s u r e m e n t e r r o r s f o r t h e i n l e t a n d o u t l e t f l o w .T h i s m e t h o d m a k e s i t p o s s i b l e t o m o n i t o r t h e p i p e l i n e d u r i n gs l o w c h a n g e s o f o p e r a t i o n c o n d i t i o n s . T h e f r e q u e n t l y m e a s u r e dv o l u m e t r i c f l o w ' c a n a l s o b e a c c e p t e d b e c a u s e o f t h e c o n s t a n td e n s i t y .T h e m e t h o d w a s t e s t e d b y S i e b e r t a n d K l a i b e r ( 1 9 8 0 ) a t a6 8 k m g a s o l i n e p i p e l in e w i t h a d i a m e t e r o f 0. 2 73 m . T h e t h r e em e a s u r e d s i g n a l s ~ ' o, P o a n d ~ ' , w e r e s a m p l e d e a c h 1 . 7 s ( th eo u t p u t p r e s s u r e w a s a t m o s p h e r i c p r e s s u r e a n d t h e r e f o r e i t w a sn o t n e c e s s a ry t o m e a s u re i t ). L e a k s c o u l d b e g e n e ra t e d a r t i f i ci a l l ya t t h e b r a n c h e s t o i n t e r m e d i a t e d e p o t s . F i g u r e s 1 1 , 1 2 a n d1 3 s h o w t h e m e a s u r e d s i g n a l s d u r i n g o n e e x p e r i m e n t . T h ec o r r e s p o n d i n g l e a k a l a r m c r i t e ri a ( c r o s s - c o r r e l a t io n - s u m ) i ss h o w n i n F i g . 1 4 a n d t h e e s t i m a t e d l e a k l o c a t i o n i n F i g . 1 5. T h er e s u l t s s h o w t h a t i t w a s p o s s i b l e t o d e t e c t s u d d e n l y a p p e a r i n gl e a k s w i t h a s i z e o f 0 . 2 % (1 11 m i n - 1 ) i n 9 0 s a n d t o e s t i m a t e t h el e a k l o c a t i o n w i t h a n a c c u r a c y o f 0 . 9 % .


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ConclusionSimulations, measurements and leak experiments have showntha t the ea r ly de tec t ion and loca l iza tion o f sm al l leaks in l iqu idand gas pipelines can be considerab ly improved. The leakde tec t ion m ethods a re based on m athem at ica l dynam ic m odels,non l inear adap t ive s ta te observers and a cor re la t ion de tect iontechnique. The measured signals are one flowrate and onepressure at eac h end of a pipeline (section). As the requ iredcomputational effort is relatively small, micro-computers canbe used.

ReferencesBillmann, L. (1982). Studies on im proved leak de tection me thodsfor gas pipelines. Interna l Report. Institu t f 'ur Regelungstech-n i l T H - D a r m s t a d t ( in G e rm a n ).Billmann, L. (1983). A m ethod for le ak detection and localizationin gnspipelines. Conf. on "Appl. Control & Ident.", Copen-hagen, Denmark (Proc. publ. by IAESTED).Billmann, L. (1985). M ethode n zur Leck/iberwachung undRegelung von Gasfemleitungen. VD I-Forts chr. Bet., Reihe 8,Nr. 85.Digem es, T. (1980). Real-time failure dete ction an d identificationapplie d to supervision o f oil transp ort in pipelines. Modeling,ldent. Control 1, 39--49.Isermann, R. (1982). Process fault detection bas ed on modellingand es t im at ion m ethods- -a su rvey 6th IFAC Syrup. ldent .Syst. Para. Est. , W ashington D.C. , U.S.A. (Proc. publ. byPergam on Press, Oxford; (1984). Automatica, 20, 387-404).Isermann, R. and H. Siebert (1976). Verfahren zur Lecker-kennung u nd L eckortung bei Rohffernleitungen. PatentP2603 715.0. (F. R. G.)Krass, W ., A. Kittel and A. Uhde (1979). Pipelinetechnik. T U E VRheinland, K61n.Siebert, H. and R . Isermann (1977). Leckerkenn ung und-Iokalisierung bei Pipelines durch O n-line -Kor relation miteinem Prozessrechner. Regelungstechnik, 25, 69-74.Siebert, H. an d Th. Klaib er (1980). Testing a m ethod for leakagemo nitoring of a gasoline pipeline. In Process Automation, pp .91-96. Olden bourg, Miinchen, F.R.G.Weimann, A . (1978). Modellierung und Simu lation der D ynam ikyon Gasverteilnetzen im Hinblick au f Gasnetzfiihrung undGasnetziiberwachung. Dissertat ion an der TU Manchen,Fachbereich ET.

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