Leak Detection Methods for Pipelines

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LEAK DETECTION METHODS FOR PIPELINES L. Billmann and R. Isermann / llStitlit .Ilia H.l'gflllllg:~tf(ll1lik. Tnhllivlu) !l of/llc/lIllt' /)unn .\tadl, Srh/o\.wmhIJI/ I, [)- olfJfJ /)arm .\twJt.

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Abstract. Fo r the early detection and localizati on of small leaks in pipelines a nonlinear adaptive state obse rver and a special correlation technique were developed , based on pressure and flow measurements at the pipeline inlet and outlet. Simulations and experiments show the results for a gas and a l i quid pipeline .

Keywords . Pipeline; leak-detection; leak - localization; modelling; partial differential equations; observersj parameter estimation ; correlation methods.

INTRODUCTION

The influence o f the friction is represented by F and the geometric height influence by H. Introducing the flowrate

As pipelines for the transportation of liquids or gases usually are only instrumented at the beginning and the end, the information of a leak along the pipeline during normal operation by means of a digital computer can only De based on available measurements. Mostly Just the input and output fl ows are balanced. However , according to the inherent flow dynamics and the superimposed noise only leaks can be detected with simple method whi ch are about > 2 % for liquid and> 10 % fo r gas pipelines. This con tribution now discusses and proposes leak detection methods, which are able to detect consi derably smaller leaks . It summarizes research activities during the last 8 years. The recent improvements are made by using nonlinear adaptive state observers for the pipeline dynamics and by using a special correlation technique for the fault detection. The ob tained results are shown for leak experiments with a gasoline pipeline and simulations of a gas pipeline , which are verified by measured signals .

q

=

A P w

(2)

and the isothermic speed of sound b

=

IP7P

(3)

the pipeline model can be simplified by assuming -the isothermic speed of sound is constant - the velocity of flow is small in comparison to the speed of sound - elastic effects of the pipe wall can be neglected Then the 'l ong pipeline model' results

~~ + le.!. 2 at dz b _ aq + 2£. A at az

MATHEMATICAL PIPELINE MODELS

0

_£llil 2 2d A R

P

g sina --2- P b

( 4)

[- J

fr i ction co efficient angle of inclination 9 [ m/s2 ] gravity

with

a lo l A mathemati cal description of the pipeline dynamics was derived by theoretical modelling for gas pipelines Weimann, (197 8) , Billmann, (1982) and liquid pipelines Krass and o thers, (1979). Simplifying assumptions as a constant diamete r d R (respectively a constant s ectional area A), a turbulent flo w and isothermic condition result in a common description for the ga s and liquid flow dynamics.

This pipeline model is a partial differential equation system of hyperbolic type . I f the usually used simplification that the speed of sound is constant is not acceptable , but changes according to ab ap

For a pipe element o f length dz the mass and momentum balances are

aD + at

30W -

dO w 1 o::: w + 2£. + at "2 oz az

~k g / m 3:

where

w :m/s: p I N/m2 j z t

Lm ~ ~ s ~

o

( 1)

2 -F

(5 )

this can be taken into account, as shown by Billmann (1982) , by enlarging the mass balance with the correc tion factor

0

3z

const .

(6)

-H To solve this equation system Eq. (4) numerically (solution for discrete time t = k ~ t with the time interval 6 t) the pipeline is divided into N sec t ions o f the leng th L

de nsity velocity of flow pressure length coordinate time coordinate

Lz = -.B.

N as shown in Fig. 1. 1813

( 7)

L. Bi l lmann and R . Isermann

1814

However, PN-3 I

P3 I

PN-I I

Shockwave based methods: In case of large leaks (liquids qL > 5 %, gases qL > 12 %) which occur suddenly shockwaves cross the pipe up t o bo th ends. The resulting pressure gradients are then used for leak detection and the leak locat i on is estimated by the speed of pro pa gation , Krass an d others , (1979).

qo <1-- - - - - Fi g .

this si mp l e method is rather sensitive t o

any d istu rbances and to inherent pipeline dynamics . Therefore only large leaks can be detected . Furtheron a leak localization is not p o ssible.

1. Discrete state representation of the

pipeline. Billmann (1982) introduced a centered di ffer ence

Further developed methods us in g a model o f the

scheme

Jx

OX! 3t

j

z,k

k+ 1 k k- I - 4x + x z z z nt

pipeline dynamic s try to increase the sensitivity to a leak and to decrease th e measuremen t effort.

(8) k+1 x z+1

ox' ozlz,k with

k 6t ~z

-

k+1 k + x x z- I z+1 46 z

-

k x z-I

Fault model filters : I f a model of the complete pipel ine Eq.

discrete time time i nterval length interval

ent locations f or a leak (Digernes , 1980) . Howeve r ,

Then the follo wi ng linear equation system results (9)

with the state vector (10)

and the height correc tion vector h . As the system matrix is constant the line ar equa -

tion system Eq. algorithms .

x

k+1

k+1

"L

~

-I .

(9) is solved by the follo wing k

k-I

l !(~ , ~

[

k+1

, \ , ~) + ~(PO

-

0,

.. . 0 , 1 , 0 , ...

the computational effort seems t o be very

large. Fault senstitive filters : Differen t to the fault model filte r s fault sensitive filters monitor the residuals (difference between measured and estimated flo wrates) ~ - qo and qN - qN Iser mann , (1982) . If then a leak occ urs the residuals change in predetermined direc tions. Ho wever , th e alarm is lost af ter a whil e , because the state variable filter compen sates the

leak influence.

k+1 , PN ) J

k+l] - l1.0 - '.. .......... . °J

qo k+1 qN

(12) inc l-

uding th e leak in fluence is used, one can try t o estimate the leak influence vector ~ by state rec onstru c tion or by discrete state variable filters . To extract this in formation under noisy conditions a ' bank of filters' can be used , assu ming differ-

(11) k+1

An addi t ional drawback of the two last state variable methods is , that the pipeline model Eq . ( 12) has t o be l inearized . Therefore they a r e suitable only for constant ope rating conditions.

° -x

IMPROVED LEAK DETECTION METHODS This solution needs only small compu tational eff ort by multiplying the inverse matrix with a vec -

In order to detect leaks also for wi de ra nges of

t or including a nonlinear func t ion of the two last

ope rating conditions nonlinear pipeline models

states , of the friction coeff icient, of the height

have to be used. This leads to nonlinear state ob -

correction vecto r and the t wo input pressure

servers . An additional requirement is that th e

signals PO and PN' The output signals qo and q N

formation on the leak should not vanish with time. Looking at the pipeline model Eq . (11) , most of

a r e ele ments of the state vector. Tests with more complex solution methods (non1 inear , grea t computat i onal effort) gave rather

similar results for the achieved application.

MODELLING OF LEAKS It is assumed that a small leak ( f lowrate qL) occurs at location zL o This effect is taken into

account by introducing this loss in the mass ba l ance for th is section . This leads t o an enlarged pipeline model with the l ea k influence vec t or 1 (dependent on the lea k location) . x

k+1

-I ·

~

k

k-I

.i(~ , ~

, )' , h)

k+1

+ .§.(Po

k+1

,PN

1

)" +

13L

Eq. ( 12) can now be used as the basic relation ( 12) for several leak detection methods .

the coeff icients are known with good accuracy ,

excep t the frict i on coefficient \ , which may also change with time. Therefore this coeff i cien t will be estima ted (on - line) by a least squa r es method. This leads t o an adaptive (no nlinear ) state o bser ver . An advantage of this app r oach is fur theron that the estimated friction coeffic i ent does not c hange the steady state solution of the mass bal ance in Eq. (4) , s o that leak effects will not be compensated by the o bserver. Fig. 2. sho ws the r esulting leak supervision structure including the pipeline o bserver and the leak moni t o r , wher e the both differe nces x and y act a s r e siduals . The corre spondin g equations are

pipeline : x

k+1 k+1

KNOWN LEAK DETECTION METHODS

"L

Balancing : The balancing method directly estimates the pres ent leak flowrate ( 13)

in -

. k+1

1 , 0 , ... , I , 0 , .. .

,O ~~

. .1 , 0 , . .. , I , 0 , ...

, O.~

o bserver:

., k+1

( 15 )

Le ak De t ec ti o n Me thod s fo r P i pe lines residua l s: k

e

IX(k)

k

'i.

= lY(k).,

18 15

and y(k) , Siebert and Isermann ( 1977) and Isermann and Siebert, (1976) ,

~k

- 'i.


xy

= E{x(k) · y(k+') }

(,)

( 1 7)

which results (theoretical) in

-- -- --

l

q,

p,

l

P [PELlNE -

q,

q.

x

\j

o

( 18)

tha t means it changes in a predetermined direction. The computation is realized by a recursive filter of first order

-

P [PELlNE -

To furthe r reduce noise effects the alarm crite ria is taken as the sum over several time shifts.

I

MONITOR

II

no leak

q.

I

OBSERUER

-

I

I

p.

M


F ig . 2. Pipel i ne supervision structure .

To show the effects of a suddenly appea r ing leak a gas pipeline was simulated with qL = 0.35 kg /s and zL/LR = 0.5 ( s ome data are given later). The flowrates at the begin and the end of the p i peline change in predetermined directions dependent on the leak flowrate and the leak location, F ig. 3 . and Fig. 4 ..

~(k)

xy~

=

l:


,=-Mxy

(20)

("k)

This cross - corrElation-sum reacts sensitively even to small leaks. An alarm is given when the sum crosses a predefined alarm-thr eshold . Afte r a leak is detected , the parameter estimation of A is frozen and the estimation of the leak loc ation starts. Introducing the auto - cor relation-sum M

l:

, =-M


(, , k)

(2 1 )

("k)

(22)

xx

and M


flow [kg/5J

=

l:


,=-Myy

the leak location is estimated by

3.9

( 23)


~ leak

3.7

qo

(t)

-

~ yy~

where LR is the length of the pipeline , Siebert and Isermann, (1977) . The leak flo wrate is esti mated by the dynamic balance equation

3.5 '"

qo (t)

3.3

(24)

time LEAK DETECTION FOR GAS PIPELINES

3.1 F ig.

0

10

5

15

20

25

30

[hJ

3. Reac t ion at the begin of the pipeline after a leak occurs (simulation) .

flow [kg/5J 3.9 ~ leak

3.7

'" (t) qN

3.5 3.3 3.1

qN (t) 0

5

10

15

I

I

I

20

25

30

Tests will be described , which are based on mea sured signals of a gas pipline . In orde r to simu late leaks the observer is enlarged by the leak influence vector ~ with a negative leak fl o wrate. This realization (also useful for self test) res pects the dynamic of the leak influence and is a good approximation for a real suddenly appearing leak in the pipeline according to the resulting residuals , Bi llmann , (19 8 3) . The p ipeline is 150 km long with a diameter of 0 , 26 m and a pressure dependent speed of sound. The four measured Signals (qO , PO ,qN , PN) were sampled every three m~nutes . The observe r uses a time interval of 30 sec. , so that the measure d signals have to be interpolated. With the length interval of about 9 km the system order is 17. Furtheron an approximation of the geographic hei ghtprofile is included.

ti me t>

[ hJ

Fig. 4 . Reaction at the end of the pipeline after a leak occurs (simula tion) . A sensitive decision algorithm for ' leak ' o r ' no leak ' was found by the cro ss - cor relation of x(k)

z

(kM)

ISO

Fig. 5. Approximation for the geographic heightprofile .

L . Bil lma nn and R. I sermann

18 16

Fig. 6. shows the measured input and output press ure of the discribed pipeline during a test period of 65 hours .

The decision a l gorithm is modified , substituting

x(k) and y(k) in Eq.

(19) by

x(k)

x(k) - E{y(k)}

y(k)

y(k) - Eix(k) }

(25)

pressure [bar1 This yields a better sensitivity and is independ ent on t h e leak location.

35

Results from several leak simulations with differ -

ent leak ratios (leak ratio given rela t ively to a mean flowrate) are given i n F ig. 9 . . Fig. 10.

33

shows an example of the leak location estimat i on for a leak ratio of 5 %.

31 P (U N

29

t.ime 27+-- -+---+---+---+--=+-- -+---t>

o

10

20

30

40

50

50

'Psum x.01

2.5~

-5

As illustrated in Fig . 7. and Fig. 8 . the pipeline observer describes the dynamic behaviour of the pipeline quite well, s o that a sensitive leak

-24

flow [kg/s 1 5

(U

N

:I:

~Leak

I I

10

~

0

5

10

t.I me -----!>

15

20

25

30

[h1

Fig. 9 . Cross - corrElation - sum during leak tests.

leak locat.ion [km1

5 4

150

3

120

~Leak I

t.ime 2

5

-12 -18

detectio n should be p o ssible.

~

0

[h 1

Fig. 6. Measured input and o utput pressure for a gas pipeline.

q

Leak rat.io

0

0

10

20

I

I

I

I

30

40

50

50

t>

slmulat.ed - --

80

est.lmat.ed

[ h1

40

Fig. 7. Measured outlet flowrate for a gas pipeline.

t.lme o+---+---+-~~--+---~--~~

o

flow [kg/s1

5

10

15

20

25

30

[h 1

Fig . 10. Estimation of the leak location.

5

Furtheron the time for computation (less than 2

sec. for a PDP 11/34) is rather small in compari SOn to the sampling time of 3 minutes.

5

LEAK DETECTION FOR LIQUID PIPELINES

4

As the dynamics of a liquid pipeline are ve r y fast in comparison t o gas pipelines ,

3

t.ime

2+---~----~--~---+----+---~---t>

o

10

20

30

40

50

Fig. 8. Estimated outle t fl o wrate by the o bserver.

50

(h 1

the sampling time

and the length interval decrease and the computa tional effort increases , which can be a handicap for the application with micro computers.

Therefore a simplified model can be used by taking the statio nary solution o f Eq. (4) (this results in the pressuredrop equation), due to the assump tion of stati ona ry (or quasi stationary) pumping conditions.

18 17

Leak De t ection Methods for P i pe l ines With a positive flowrate and a constant density Eq . (4) is reduced to

dq

o

az

(26)

325 (27)

324 (28) where h is the height of the pipeline at the beginningOand h at the end. This leads to the ' pipeline -obs~rver' algorithms

323 322

t.lme 321

(29)

1 0

I

I

I

I

I

I

40

80

120

160

200

240

I>

[s]

Fig. 12. Measured inlet volume flow of a gasoline pipeline. These equations contain two estimated friction coefficients to compensate measurement errors for each flowmeter (slow changes of the flowmeters, by faults or varying pumping conditions, are accepted by changing the corresponding friction coefficient) . This method makes it possible to monitor pipelines also during slow changes of operation conditions. The frequently measured volumetric flow V can also be accepted because of the constant density.

The method was tested by Siebert and Kla i ber ( 1980) at a 68 km gasoline pipeline with a diameter ~f 0.273 m. The three measured signals O ' Po and V were sampled each 1 . 7 seconds (the output press~re was atmospheric pressure and therefore it was not necessary to measure it). Leaks could be generated artificially at the branches to intermediate depots. Fig. 11. , 12. and 13 . show the measured signals during one experiment . The corresponding leak alarm criterium (cross correlation - sum) is shown in Fig. 14 and the estimated leak location in Fig . 15 .

flow [m 3 /h] 325 q

324

(t.)

N

323

v

322

t.ime

321+1--~1~--+1----~1--~I----~I--~I--~I>

o

40

80

120

160

200

240

[s]

Fig. 13. Measured outlet volume flow of a gasoline pipeline .

Psum x.Ol

pressure [bar]

o

67.2

Leak ratio 0.19% alarm-threshold

67.0 -10

66.8

t-i> I

-15

66.6 t.I me

66.4

0

I

I

I

I

40

80

120

160

I

I

200 240

I>

-20

[s] Fig.

Fig.

11 . Measured input pressure of a gasoline pipeline .

Leak t.lme --(>

0

40

80

120

160

200

240

[s]

14. Cross - correlation - sum during an exper imen t.

The results show that it was possible to detect s uddenly appearing leaks with a size of 0.2 % (11 l/min) in 90 sec. and to estimate the leak locati on with an accuracy of 0 . 9 %, i.e. 500 m.

L. Billmann and R. Isermann

1818

The two program systems 'LEO-CADGEN' (liquid) and 'LEOGAP-CADGEN' (gas) are implemented o n a PDP 11/34 and a LSI 11/23, using a harddisk , a graphic display and a plotter. The shown hardware configu-

leak location [km]

ration is only used for the d es ign , whereas the resulting leak-monitoring routine can be implemented in a micro-computer based system.

80 60

estimated simulated

40

o

~~

----t

20

~I>

CONCLUSION Simulations, measurements and leak experiments have shown that the early detection and localization of

I

I

Leak

t.I me

+-----+
-----+
----~I----~1~~L-41----~1-----1>

o

40

80

120

160

200

240

[s]

Fig. 15. Estimation of the leak location.

COMPUTER AIDED DESIGN OF A LEAK MONITORING SYSTEM

small leaks in liquid and gas pipelines can be con siderably improved . The leak detection methods are based o~ mathemat ical dynamic models, nonlinear adaptive state observers and a correlation detection technique. The measured signals are one flowrate and one pressure

at each end of a pipeline (section). As the required computational effor t is r elatively small , microcompu ters can be used for leak detection including monitori ng of the inner pipeline state.

RE FERENCES

The leak supervision method discussed is rather

general applicable . However it has to be adapted t o each special pipeline configuration . TO find a suitable adjustment of several coeffi cients and the alarm-threshold a computer aided design technique is used , see Fig. 16.

Billmann, L . (1982). Studies o n improved leak detection methods for gas pipelines. Interna l Report.

Institut fuer Regelungstechnik,

TH - Darmstadt ( i n German). Billmann , L . (19 83 ) . A metho d for leak detect i on and localization in g aspipelines . Conference on ' Applied Con t rol & Identification ', Copen-

hagen, Denmark (Proc. pupl . by I AESTED) . Digernes , T. (1980) . Real-time failure detect i on and identification applied to supervision of oil transport in pipelines. Modeling , identifi -

cation and control 1, 39-49 (published by NTNF , Oslo , Norway). Isermann , R. (1982) . Process fault de t ect i on based on modelling and estimation methods.

Plenary paper at the 6th IFAC - Symposium on Identification and System Parameter Estimation,

Washington D.C ., US A, (Proc. , pupl. by Pergamon Press, Oxfo rd ) . To appear in Automatica ( 1984) . Isermann, R. and Siebert , H. ( 1976). Verfahren zur Leckerkennung und Leckortung bei Rohrfernleitungen . Patent P2603 715 . 0 . Krass, W., Kittel, A., Uhde, A. (1979) . Pipelinetechnik. Verlag TUV Rheinland, Koeln. Siebert, H. and Isermann , R. (1977) . Leckerken nung und -lokalisierung bei Pipelines durch On - line - Korrelation mit einem Prozess r echner.

Regelungstechnik 25 , 69 - 74. Siebert, H. and Isermann , R. (1980). Test i ng a Metho d f o r Leakage Monitoring of a gaso l ine Pipeline. Process Automation, 91 - 96 . (Olden bourg Verlag , Muenchen). Weimann, A. (1978). Modellierung und Simulation der Dynamik v o n Gasverteilnetzen im Hinblick auf Gasnetzfuehrung und Gasnetzueberwachung . Dissertation an de r TU Muenchen, Fachbereich

ET. Fig.

16. Computer aided design strategy.

The design starts with the definition of the p i peline configuration (length , diameter , he i ght pro fi l e , sampling time, . .. ) and finds a suitable samp l ing period for the numerical solution

(o nly f o r gas). Afterwards, a measured data base is used for testing, where leak effects can be simulated at different locat i on and with different size. The coefficients can be adjusted

step by step and the results are displayed on a graphic display . After finding a suitable set of c o efficients the

system generates the resulting leak -mo nitoring r o utine (FORTRAN IV) automaticaly .