ultrasonic flow theory.pdf

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Theory of Ul trasonic F low Measurem ent -Gas es Liquids

Class 3175

Don Augens tein, Vice Pres ident Engineering,

Caldon Inc. 1070 Banksville Ave . Pittsburgh, PA 15216

I n t r o d u c t i o n

Ul t rason ic trans i t -t ime f l ow m ete r techno logy is now

over 50 years o ld . Ea r l y ve rs ions o f these mete rs

were at t imes d isappoint ing in accuracy and re l iab i l i ty.

Wh i le the bas ic p r inc ip le rem a ins un changed , the

techno logy has evo lved substan t ia l ly . The ma jo r

improvem ents have been in t ransdu cer des ign , s igna l

processing and, even more important ly, in

unders tand ing the fac to rs tha t i n f l uence the

per fo rmanc e o f these mete rs . Recen t des igns o f

mu l t i-pa th t rans it t ime u l t rason ic f l ow m ete rs now

rou t ine ly ach ieve an acc u racy and re l iab i li ty

com parab le to o r be t te r than o lde r me chan ica l

technolog ies ( i .e . , turb ine, posi t ive d isp lacement

meters and or i f ice p la tes) .

U l t rason ic f l ow mete rs (U FM s) a re now beg inn ing to

d i sp lace those t rad i ti ona l f low mete rs i n hyd rocarbon

mea surem ent app l i ca ti ons. Th is t rans it ion i s be ing

dr iven by a num ber o f UFM a t t r ibu tes i nc lud ing :

• H igh Acc uracy and tu rndown ra ti o

• Ava i lab i l i ty o f large size me ters

• Non- in t rus i veness

• Low ma in tenanc e costs

• Exce l lent on- l ine d iagn ost ics

Un l i ke the mechan ica l techno logy, u l t rason ic f low

mete rs can p rov ide in fo rmat ion abo u t fl ow

character ist ics wi th in the p ipe and the proper t ies o f the

l iqu id (or gas) . I t is th is in format ion, a long wi th the

possib i l i t ies o f low uncer ta in ty, low maintenance, and

extens ive d iagnost ics , tha t make these mete rs

a t trac t ive . These fea tu res have even extended the use

o f u l t rason ic me te rs to f i sca l / custody t ransfe r

appl icat ions.

This paper 's ob ject ive is to provide potent ia l UFM

users w i th the re levan t i n fo rmat ion nec essary to

unders tand how UFMs opera te and wha t shou ld be

cons idered in the i r appl icat ion. Th is pape r reviews the

types o f UFMs used in h igh accu racy app l i ca ti ons and

the UFM operat ion pr incip les, re l iab i l ity, accu racy 1 and

repeatabi l i ty (proving meters wi th provers) .

D i s c u s s i o n

Al l UFMs be ing app l i ed i n h igh accu racy hyd rocarbon

appl icat ions are t ransi t t ime (a lso ca l led t ime-of - f l ight )

sys tem s, wh ich a re the sub jec t o f th is paper . Thes e

system s ca lcu la te f l ow us ing the t imes o f fl igh t o f

u l t rason ic energy pu lses t rave l i ng w i th and a ga ins t the

d i rec t ion o f f low. T rans i t t ime mete rs can genera l l y be

classi f ied in to two groups: wet ted me ters and

exte rna l l y moun ted mete rs .

W e t t e d M e t e r s '%~/etted m eters ge t the i r nam e f rom

the fact that the t ransducers are bu i l t in to the meter .

Thes e m ete rs requ i re tha t a me te r body w i th m u l t ip le

t ransduc er we l ls (see F igu res 1 and 4) . Thes e we l l s

a re s imi la r to the rmo we l l s used w i th RTD s ex cep t tha t

they a re ang led w i th respect to the f low and house an

u l t rason ic t ransducer . In som e we t ted mete rs , the

t ransduce rs opera te f rom beh ind a w indow in the we ll

a l l ow ing the t ransducers to be rep laced du r ing

opera t i on w i thou t spec ial ha rdware .

T rans duce rs a re a r ranged in pa i rs o r se ts tha t fo rm

acoust i c pa ths . There a re no rma l l y two o r more

acoust i c pa ths i n a we t ted mete r . The pa ths a re

spaced such tha t they can be used to numer i ca l l y

in tegrate the f low. Wet ted m eters are of ten ca l led

chorda l me te rs because the acoust i c pa ths a re o ften

arranged in para l le l chords.

F i g u r e 1 C a l d o n 2 4 C h o r d a l U F M

It is noted hat the term accuracyas used n this paper refers o the

ability of the meter o measure low with imited error.

3 8 1



E x t e r n a l M e t e rs Ex te rna l l y moun ted me te rs a re f i xed

to the ou ts ide o f the p ipe and a re comp le te ly non -

in t rus ive and non - invas ive . Ex te rna l me te r

t ransduce rs a re no rma l l y a r ranged in pa i rs as we l l .

Howeve r , p rac t i ca l acous t i c pa th a r rangemen ts a re

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

phys ics o f t ransmi t t ing th rough the p ipe wa l l requ i res

tha t acous t i c pa ths t rave l th rough the cen te r o f the

p ipe (d iame t ra l ) .

Ex te rna l me te rs tha t have two pa ths a re no t gene ra l l y

re fe r red to as mu l t i -pa th because the i r pa ths a re

d iame t ra l . In th is pape r , the te rm mu l t i -pa th me te rs

re fe rs to UFMs w i th two o r more pa ths tha t t rave l

th rough d i f fe ren t cho rds o f the p ipe c ross sec t ion (e .g . ,

we t ted me te rs ) .

Va r ia t ions o f ex te rna l me te rs do ex is t . Fo r exam p le ,

some ex te rna l me te rs inc lude a p ipe sec t ion to reduce

d imens iona l unce r ta in t ies .

Gene ra l l y , mu l t i -pa th we t ted me te rs ach ieve much

h ighe r accu rac ies than ex te rna l me te rs because they

measu re a g rea te r f rac t ion o f the p ipe c ross sec t ion

than ex te rna l me te rs .

U l t r a s o u n d B a s i c s

There a re seve ra l gene ra l p r inc ip les o f sound

p ropaga t ion tha t a re use fu l i n unde rs tand ing the

ope ra t ion o f UFMs .

S o u n d V e lo c i t y A ma te r ia l ' s sound ve loc i ty i s the

ra te a t wh ich sound t rave ls th rough i t. Sound

ve loc i t ies enco un te red in typ ica l hyd roca rbon

app l i ca t ions va ry f rom as low o f 0 .4 km/sec fo r na tu ra l

gas to 1 .6 km/sec fo r some c rude o i l s . No t on ly does

sound ve loc i ty va ry s ign i f i can t l y be tween ma te r ia ls , bu t

i t a lso var ies s ign i f icant ly in any g iven l iqu id due to

temp era tu re and p ressu re changes . Th is i s

pa r t i cu la r l y t rue fo r gases .

A c o u s t i c Im p e d a n c e A ma te r ia l ' s acous t i c

impedance i s the p roduc t o f i t s sound ve loc i ty and i t s

d e n s it y . A c o u s t i c i m p e d a n c e i s i m p o r t a n t w h e n s o u n d

t r a ve l s fr o m o n e m e d i u m t o a n o t h e r. T r a n s m i s s i o n

e f f i c iency i s a func t ion o f the acous t i c im pedan ce o f

the two med ia ; the g rea te r the d i f fe rence , the wo rse

the e f f i ciency . The mo s t no tab le compar ison o f

acous t i c impedances i s be tween o i l and na tu ra l gas .

The acous t i c impedance o f o i l i s ove r 3000 t imes

g rea te r than na tu ra l gas .

Sound t ransmiss ion e f f i c iency i s impo r tan t because

poo r s igna l s t reng th i s a common cause o f

deg rada t ion o f UFM pe r fo rmance , pa r t i cu la r l y in gas

UFM s . Con s ide r sound t rave l ing f rom s tee l in to o i l. In

th is case , 5% o f the ene rgy ac tua l l y i s t ransmi t ted in to

the o il becau se o f the d i ffe rence in acous t i c

imped ances . Wh i le th is i s no t g rea t e f f i c iency , on ly

0 .001% o f the ene rg y i s t ransmi t ted f rom s tee l in to

na tu ra l gas . Beca use o f acous t ic impedanc e , un t i l j us t

recen t l y , the re we re no ex te rna l gas UFMs on the

marke t as these losses made the i r ope ra t ion

unre l iab le .

U l t r a s o n i c B e a m W i d t h T r a n s d u c e r s a r e d e s i g n e d

so tha t the acous t i c beam is fa i r ly focused . L ike a

f lash l igh t beam, the acous t i c beam has a f in i te w id th .

Ob jec ts w i th in the beam a re i l l um ina ted by acous t i c

ene rgy and those ou ts ide a re no t . The beam w id th i s

impo r tan t when the beam i tse l f ge ts swep t

downs t ream by h igh ve loc i ty f l ow .

Ultrasonic signal attenuat ion S o u n d e n e r g y g e t s

a t tenua ted by d is tance (p ropo r t iona l to d is tance

squa red ) , v i scos i ty (p ropo r t iona l to the f requency

squa red ) , sca t te r ing (due suspens ions ) and tu rbu lence

( fo r examp le , tu rbu lence o r cav i ta t ion ) .

Princ ip les o f

O p e r a t i o n

Us ing the p rev ious u l t rason ic bas ics , we can now

d iscuss the p r inc ip les o f ope ra t ion fo r ex te rna l and

we t ted t rans i t t ime UFM s . A t rans i t t ime UFM sys tem

t r a n s m i t s a c o u s t i c e n e r g y a l o n g o n e o r m o r e p a t h s

th rough the p ipe in wh ich f low i s to be measu red (see

Figure 2) . In the f igure , a pa i r o f t ransducers is

moun ted to fo rm a d iagona l pa th th rough f low ing

l iqu id . W hi le th is figure is typ ica l o f ex terna l m eters ,

the p r inc ip les desc r ibed in the fo l low ing pa rag raphs

app ly to we t ted me te rs as we l l .

F i g u re T r a n s i t T i m e A c o u s t i c P a t h G e o m e t r y

TRANSDUCER A '~'~ ,. I. ~ ~

k ' TE RN I I ', \ I I / ~ ~ &

O____J___J_:l . . . . . . .

1 ~ TRANSDUCER B

= PATH ANGLE

Wh en the up s t ream t ransduc e r A is exc i ted by a bu rs t

o f e lec t ri ca l ene rgy , i t w i l l t ransmi t a packe t o r p u lse o f

acous t i c ene rgy . The t ransduce r i s usua l l y des igned to

be d i rec t iona l , and the re fo re , the acous t i c ene rgy w i l l

t rave l in a s t ra igh t l i ne from t ransduce r A to t ransduce r

B , whe re i t w i l l p roduce e lec t r ica l en e rgy wh ich i s used

to s top a t imer. In th is manner the e lapsed t ime tAB,

f rom the t ime o f t ransm iss ion to the t ime o f de tec t ion ,

i s measu red .

3 8 2



W h e n d o w n s t r e a m o r t r a n s d u c e r B i s e x c it e d a n d t h e

a r r i va l o f acous t i c ene rgy a t t ransduce r A i s de tec ted ,

the t rans i t t ime tBA is s im i la r l y m easu red . The

measu red t imes a re re la ted to the d imens ions ,

p rope r t ies and ve loc i ty o f the f lu id as fo l lows :

1

t A B - - [ L p a t h / ( C p a t h - I- V p a t h ) 4 - ~ n o n f lu i d d e l a y

2 ) t B A --- - [ L p a t h / ( C p a t h - V p a t h ) ] - I- [ 'n o n lu i d d e l a y ,

W h e r e

L p a t h is aco ust ic path leng th in the f lu id ,

p a t h i s the sound ve loc i ty a long the acous t i c pa th

wi th f lu id a t res t ,

V p a t h i s the f lu id ve loc i ty p ro jec ted on to the a cous t i c

pa th , and

[ 'non f lu id de lay i s to ta l e lec t ron ic and ac ous t i c de lays

exter io r to the f lu id .

T ime in f lu id , t fA B and t feA, can be ca lc u la ted as fo l lows:

3 A ) tfAB = tAB - Xnon luiddelay

3B ) tfBA = t B A - [ 'n o n l u id d e l a y

For a g iven app l i ca t ion , non - f lu id de lay , Tnon f lu id de lay,

may be ca lcu la ted o r measu red (o r bo th ) .

Def in ing, the d i f fe re nce in the t im es o f f l igh t , At , as :

4 ) A t = tBA- tAB

- - [ L p a t h / ( C p a t h V p a t h ) ] - [ L p a t h / ( C p a t h + V p a t h ) ]

and so lv ing fo r

V p a t h L p a t h

y ie lds

5 ) V p a t h L p a t h =

[At

L p a t h 2 1 ( 2 t fA B t f B A ) ]

Th is re la t ionsh ip i s fundamen ta l to the ope ra t ion t rans i t

t ime UFMs . I t says tha t the p roduc t o f pa th leng th and

mean ve loc i ty a long tha t pa th can be de te rm ined by

t r a n s it t im e m e a s u r e m e n t s w i t h a n a b s o l u te a c c u r a c y

l imi ted on ly by :

• T h e a c c u r a c y o f t r a n si t t i m e m e a s u r e m e n t s

• T h e a c c u r a c y o f m e a s u r e m e n t ( o r c a l c u la t i on ) o f

the non - f lu id t ime de lay , and

• T h e a c c u r a c y o f p a t h l e n g th m e a s u r e m e n t

I t i s f rom th is bas ic equa t ion tha t t rans i t t ime UFM s

ca lcu la te ve loc i t ies a long the i r pa ths . Pa th ve loc it i es

a re used to ca lcu la te the vo lum e t r i c f low ra te . Fo r

ex te rna l UFMs , the vo lume t r i c f l ow equa t ion i s2 :

6) Q = [~ ID2/4] (PFE)

A t C F 2 / ( 2

ID tan ~F )

W h e r e :

ID - p ipe ins ide d iame te r

P F E - e x t e rn a l U F M p r o fi le f a c to r

~ F - ang le the acous t i c pa th takes in the f luid

2 H . E s t r a d a , T h e o r y o f U l t r a s o n ic F l o w M e a s u r e m e n t - G a s e s a n d

L i q u i d s ,

ISHM Class 3175

F e b r u a r y 2 0 0 1 .

A t - pa th t ime d i f fe ren t ia l , see Equa t ion 4

The ex te rna l m e te r p ro f i l e fac to r , PFE, re la tes the p ipe

cen te r l i ne ve loc i ty measu re d by the ex te rna l UFM to

the ave rage ve loc i ty ove r the p ipe c ross sec t ion and

can range f rom 0 .90 to ove r 1 .00 (as low as 0 .75 fo r

lam ina r f l ow) . (I)F s a func t ion o f the speeds o f sound

and d im ens ions o f al l ma te r ia ls in the acous t i c pa th . In

an ex te rna l me te r the re a re usua l l y a t leas t th ree

m a t e r ia l s : t h e t r a n s d u c e r w a v e g u i d e o r w e d g e , t h e

p ipe wal l a nd th e f lu id . In order to ca lcu la te ( l)F, the

sound ve loc i t i es and d imen s ions o f these ma te r ia ls

mu s t be known p rec ise ly . Th is can be cha l leng ing i f

the tempera tu re o f the p ipe va r ies s ign i fi can t ly . As a

prac t ica l ma tter , (l)F s phy s ica l ly l imi ted to less than 20 °

in mos t app l i ca t ions ( lower sound ve loc i t i es have

sma l le r va lues ) .

The we t ted UFM vo lume t r i c f l ow equa t ion i s :

ID ~ WiLpa~_i ti

7 ) Q = P F w - ~ - i l t a n ~ i ) t f ~ t ~ A

Where the va r iab les a re as de f ined above and :

i - p a th n u m b e r

w - n u m e r i c i n te g r a ti o n w e i g h t in g f a ct o r

P F w - w e t t e d U F M p r o f i l e f a c t o r

The we t ted p ro f i le fac to r , PFw, co r rec ts fo r l im i ta t ions

in the accu racy o f the numer ic in teg ra t ion o f the

hyd rau l i c p ro fi le . Fo r Ca ldon mu l t i -pa th we t ted me te rs ,

th is w i l l range f rom 0 .995 to 1 .005 ove r a b road range

o f hyd rau l i c geom e t r ies . Th is i s a + / -0 .5 range as

com pared w i th the + / -5 range fo r ex te rna l UFM s ( fo r

typ ica l app l i ca t ions bu t may va ry by as much as + / -

10 fo r a l l cond i t ions inc lud ing lam ina r cond it ions ) .

Compar ing th is co r rec t ion fac to r o f less than +0 .005 o f

un i ty , re f lec ts the d i f fe rence be tween we t ted UFM

ve loc i ty p ro f i l e in teg ra t ion and the ex te rna l me te r

d i a m e t r a l m e a s u r e m e n t . T h e a c tu a l p e r fo r m a n c e o f

t h e w e t t e d U F M c l o s e l y r e s e m b l e s t h e p e r f o r m a n c e

pred ic ted by s im ple phys ica l p r inc ip les , w i th l it t le

co r rec t ion .

(I) fo r we t ted UFM s is typ ica l l y a rou nd 45 ° to ma x im ize

the A t wh i le l im i t ing the leng th o f the spoo l and can be

d i rec t l y me asu re d (no te : manu fac tu re rs ma y va ry th is

ang le ) . The resu l t i s tha t the A t is usua l l y la rge r fo r a

we t ted me te r than an ex te rna l me te r fo r a g iven p ipe

d iam e te r and me te r leng th . Th is leads to sma l le r

t im ing e r ro rs because , the la rge r the A t , the sma l le r

the t im ing e r ro rs .

Bo th ex te rna l and we t ted UFMs d i rec t l y measu re a

va r iab le , A t , tha t has a l i nea r dependence on f low

ve loc i ty . Th is resu l ts in the w ide range o f accu ra te

p e r f o r m a n c e ( t u r n- d o w n r a t io ) o f U F M s a s c o m p a r e d

3 8 3



wi th d i f fe ren t ia l p roduce rs tha t d i rec t l y measu re

p ressu res tha t inc rease w i th the squa re o f the f low

ve loc i ty .

T h e p r i m a r y d i f f e re n c e s b e t w e e n e x t e r n a l a n d w e t t e d

U F M s a r e :

1 Ex te rna l UFMs a re sens i t i ve to more va r iab les

t h a n w e t te d U F M s b e c a u s e t h e a co u s t ic p a t h

t r a ve l s t h r o u g h m o r e m e d i a w h o s e p r o p e r ti e s

mus t be p rec ise ly known and i t s pa th i s no t

s t ra igh t (see F igu res 3 and 4 fo r ex te rna l and

we t ted UFMs respec t i ve ly ) .

2 . E x t e r n a l U F M s n e e d p r e c i s e f i e l d m e a s u r e m e n t s

o f d imens ions , pa r t i cu la r l y wa l l th i ckness and

d iame te r .

3 . M u l t i- p a t h w e t t e d U F M s m e a s u r e t h e ve l o c i t y o v e r

a g rea te r f rac t ion o f the p ipe .

4 .The A ts fo r ex te rna l me te rs a re gene ra l l y sma l le r

than fo r we t ted me te rs because the i r pa th ang les ,

( I D F ,

a re sha l lower , lead ing to h ighe r unce r ta in ty .

The resu l t o f these d i f fe rences i s tha t we t ted UFMs

gene ra l l y have much be t te r accu racy and repea tab i l i t y

than ex te rna l UFM s in the sam e app l ica t ion . Typ ica l l y

ex te rna l UFMs have abso lu te accu rac ies o f

a p p r o x i m a t e l y 1 - 5 w h i l e w e t t e d U F M s h a v e

abso lu te accu rac ies f rom 0 .25 -0 .5 (assum ing no in

se rv ice ca l ib ra t ion ) .

F i g u re 3 E x t e r n a ll y M o u n t e d U F M A c o u s t i c P a t h

A N S 0 U C E . A

7 , ,

TRANSDUCER B

~F= FLUID PATH ANGLE

~p= PIPE ANGLE

~ ~ = WEDGEANGLE

F i g u re 4 W e t te d U F M A c o u s t i c P a t h

F L o ~

• , . . : , - . : , . - ~ - . . , . - . ~, , - - :, - - . .~ . - . -~. - - - , .- . . . . r ; , - . - 7 - , ~ , , , , ~ . ; . . . . . . . ~ : ~ - z

. . . . . . . . .. . . . . . . . . . .. . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . .. . . . . . . . . . .. . . . . . . . . .. . . . . . . ~ :~ ;7~ T . . . . . . . . . . . . . . . . . . . . . . . . . . .

' ~ & ~

~ , ~

F a c to r s A f f e c t in g U F M P e r f o r m a n c e

T h r e e a s p e c t s o f U F M p e r f o r m a n c e m e r i t d i sc u s s io n :

re l iab i li t y, accu rac y and repea tab i li t y . Thes e fac to rs

a re in te r re la ted in tha t acous t i c deg rada t ion can lead

to deg rada t ion in accu racy and repea tab i l i t y .

R e l i a b il it y A c o u s t i c P e r f o r m a n c e

One o f the p r imary bene f i t s tha t can be ach ieved w i th

the app l i ca t ion o f UFMs is reduced ma in tenance cos ts .

UFMs have no mov ing pa r ts and a re no t p rone to f low

induced wea r . Fu r the r , they do no t requ i re f reque n t

ca l ib ra t ion . Th e re l iab i l ity o f the e lec tron ics is

comparab le to tha t o f o the r me te rs .

Q u e s t io n : S o w h a t d o e s g o w r o n g ( a s id e f r o m

e lec t ron ics )? Mos t comm on ly i t 's a poo r app l ica t ion

where the acous t i c ene rgy i s too weak (due to s igna l

a t tenua t ion ) . The a t tenua t ion o f acous t i c ene rgy in

f lu ids encoun te red in typ ica l hyd roca rbon UFM

appl ica t ions is a func t ion o f the f lu id v iscos i ty , f lu id

type and flu id homo gene i ty . The g rea te r the

at tenuat ion , the lower the s igna l to no ise ra t io wi l l be

and th is resu l ts in g rea te r da ta sca t te r and e r ro rs in

t iming.

Viscosi ty At tenuat ion

The a t tenua t ion in a g iven

f lu id inc reases w i th v iscos i ty . Gene ra l l y , fo r v i scos i t ies

less than 5cS , v i scous losses a re no t s ign i fi can t .

Howeve r , h ighe r v i scos i t ies a t tenua te s ign i f i can t l y

h ighe r (by o rde rs o f mag n i tude ) . I t i s the re fo re

impor tan t tha t the range o f v i scos i ties be p rov ided to

t h e U F M v e n d o r t o a s s u r e t h e b e s t p e r f o r m a n c e o f th e

me te r . UFM s can be des igned to ope ra te in f l u ids w i th

v iscos i t ies ove r 1000cS .

G a s A t t e n u a t io n :

In gases , the a t tenua t ion o f the

acous t i c ene rgy i s a func t ion o f mo lecu la r abso rp t ion

and re laxat ion , as we l l as v iscos i ty . As a resu l t , the

acous t i c losses in gases a re usua l l y much h ighe r than

in l iqu ids and, un l ike l iqu ids , the acoust ic losses are a

s t rong func t ion o f the f lu id tem pera tu re and p ressu re .

Consequen t l y , i t i s even more impo r tan t fo r gas

app l i ca t ions to in fo rm U FM m anu fac tu re rs o f the range

o f tempera tu res and p ressu res fo r an app l i ca t ion .

N o n h o m o g e n o u s F lu id s ~ G as e s :

Signa l a t tenua t ion

w i l l occu r whe n re f lec tions o f f d iscon t inu i t ies / re f lec to rs

ex is ts in the f lu id (e .g . , scat ter ing ). Th e mor e

sca t te r ing tha t occu rs ( fo r examp le , due to gas

bubb les in the l iqu id or l iqu id in the gas), the greater

the losses w i l l be . A pa r t i cu la r l y bad comb ina t ion i s

en t ra ined gas in l iqu id sys tem s . Even a few pe rcen t

b y v o lu m e o f e nt r a in e d g a s c a n r e n d e r m o s t U F M s

inope rab le . The re fo re , i t i s c r i ti ca l tha t UFM vendo rs

know i f the re i s go ing to be en t ra ined g as in an

app l ica t ion .

3 8 4



Wax i n g A n o t h e r c a s e i s t h e a c c u m u l a t io n o f w a x e s

a long the p ipe wa l l and in the t ransduce rs we l l s o f

w e t t e d U F M s . O n c e a g a i n , th e U F M v e n d o r sh o u l d b e

a le r ted to the po ten t ia l fo r s ign i f ican t w ax bu i ldup as

des ign pa rame te rs can be op t im ized to m in im ize the

e f fec t o f these acc um u la t ions (e .g ., hea t t rac ing ) .

C o u p l i n g : For the mos t pa r t , t ransduce rs a re ve ry

re l iab le , howeve r , the coup l ing o f the t ransduce r to the

p ipe and f lu id has been a common fa i lu re mode fo r

som e ea r ly sys tem s . The so u rce o f th is p rob lem is the

ma te r ia l used to coup le the t ransduce r . Greases ,

r u b b e r s a n d o t h e r m a t e r i a ls a r e c o m m o n l y u s e d .

Fa i lu res have occu r red due to the ins tab i li t y o f these

coup lan ts ove r t ime a t the ins ta l la t ion cond i t ions . H igh

t e m p e r a t u r e a p p l i c a t io n s g e n e r a l l y h a v e m o r e

p rob lems w i th loss o f coup l ing than low tempera tu re

app l i ca t ions , and ex te rna l sys tems gene ra l l y have

more p rob lems w i th loss o f coup l ing because they

gene ra l l y have less s igna l s t reng th marg in and a more

d i f fi cu lt geom e t ry .

A c c u r a c y P r o fi le F a c t o r

The fo l low ing rev iews the b igges t fac to r a f fec t ing

UFM 's accu racy ; p ro f i le fac to r . O the r impo r tan t fac to rs

such as p ipe d imens ions (pa r t i cu la r l y fo r ex te rna l

me te rs ) and t rans i t t ime /A t measu remen t , wh i le no t

d iscussed , a re impo r tan t 3 .

The s ing le mos t s ign i f ican t sou rce o f e r ro r is the p ro f i l e

fac tor . As d iscussed , the pro f i le fac tor is used to

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

the UFM to a t rue spa t ia l ly ave rag ed ve loc i ty . Th is

co r rec t ion mus t be made because f low ve loc i t i es va ry

in bo th magn i tude and d i rec t ion ove r the p ipe c ross

sect ion .

The ve loc i ty p ro f i le w i th in a p ipe i s a func t ion o f two

sets o f fo rces : inert ia l fo rces a nd v iscous/ f r ic t ion

fo rces . Fo r examp le , a t the ou t le t o f a bend , tee o r

s im i la r p ip ing componen t tha t changes the d i rec t ion o f

the f low, the inert ia l fo rces dominate o f ten resu l t ing in

g ross ly d is to r ted ve loc i ty p ro f i le . The v iscous / f r ic t ion

f o r c e s t he n b e c o m e m o r e d o m i n a n t a s th e d i s ta n c e

f rom the e lbow/d is tu rbance inc reases . I t i s the

v iscous / f r ic t ion fo rce s a long the p ipe wa l l tha t d iss ipa te

the d is to r tion cau sed by the ine r t ia l fo rces . I f the p ipe

is long enough, the e f fec ts o f the inert ia l fo rces are

com p le te ly e l im ina ted and a fu l ly deve loped cond i t ion

is reached whe re the f low p ro f i l e does no t change .

Un fo r tuna te ly , i n p rac t i ce i t can take 50 d iam e te rs o r

mo re fo r the p ro fi l e to s top deve lop ing . Fu r the r , the

shape o f the p ro f il e whe n fu l l y deve loped i s a

3s. Corey, H. Estrada, Theory and Ap plication of U ltrasonic Flow

Meters,

ISHM Class 3175

2002

func t ion o f the v iscos ity and roug hness o f the p ipe

wa l l . In mo s t app l ica t ions , the v iscos i ty i s no t we l l

known and the e f fec t i ve roughness o f the p ipe wa l l i s

a lmo s t neve r known . As a resu l t, the ex te rna l UFM

pro f i le fac to r in fu l ly deve loped f low can range ove r

+ / -10% depend ing on the f lu id v iscos i ty and wa l l

rough ness ( f rom lamina r f l ow reg ime s up to tu rbu len t

f low reg imes ) . Co r rec t ing th is change in p ro f i le fac to r

then i s an im po r tan t task fo r the ex te rna l me te r .

In p rac ti ce , the lowes t unce r ta in ty in the p ro f i l e fac to r

fo r an ex te rna l me te r i s usua l l y ach ieved be tween 10

a n d 2 0 d i a m e t e r s d o w n s t r e a m o f t h e d i s tu r b a n c e

where the ine r t ia l fo rces a re s t i l l dominan t bu t the

pro f i le is not as d is tor ted. Even in th is range, the

abso lu te accu racy o f the p ro f i l e fac to r fo r an ex te rna l

me te r i s l im i ted to app rox ima te ly 1% and in mos t

cases i s c lose r to 2% un less i t i s based on app l i ca t ion -

spec i f i c hyd rau l i c tes t ing tha t mode ls the p ip ing

geomet ry and f lu id v iscos i ty .

The accu ra cy o f a mu l t i -pa th we t ted m e te r p ro f i le

fac to r can be subs tan t ia l l y be t te r because they samp le

a g rea te r f rac t ion o f the f low p ro f il e . Typ ica l l y p ro f i l e

fac to r accu rac ies o f + / -0 .25% o r be t te r can be

ach ieved .

UFMs a re a lso sens i t i ve to ve loc i ty p ro f i l es whe re

the re i s a la rge ro ta t iona l com pon en t (sw i r l) . Sw i r l is

n o r m a l l y g e n e r a t e d b y tw o o r m o r e o u t o f p l a n e

changes in f l ow d i rec t ion (e .g . one e lbow/ tee tha t goes

f rom ve r t i ca l to ho r i zon ta l fo l lowed by an e lbow/ tee

tha t chang es the d i rec tion o f f l ow in the ho r i zon ta l

p lane ) . Sw i r l is p resen t to som e deg ree in a lmos t

eve ry app l i ca t ion . Sw i r l can gene ra te s ign i f i can t

t ransve rse ve loc i ty compo nen ts and i t takes a long

d i s t a n c e t o d i s s i p a t e .

On an ind iv idua l pa th bas is , a UFM canno t reso lve

t ransve rse ve loc i ty componen ts f rom ax ia l ve loc i ty

com pone n ts . I t i s no rma l l y assum ed tha t the ve loc ity

is pure ly ax ia l. How ever, i f the cente r o f swir l ro ta t ion

is the cen te r o f the p ipe , i t w i l l no t a f fec t U FM s

bec aus e i t is se l f cance l ing . Ho we ver, i f the swir l is

no t cen te red , i t can cause s ign i f ican t e r ro rs . In

app l i ca t ions whe re s ign i f i can t sw i r l may be p resen t ,

th is p rob lem can be e l im ina ted by ins ta l l i ng f low

cond i t ione rs tha t la rge ly e l im ina te sw i r l ups t ream o f

the UFM . Ano th e r so lu tion i s to use a UFM tha t

d i rec t l y measu res the sw i r l and can remove i t s e f fec t .

F o r e x a m p l e , C a l d o n ' s s y m m e t r i c 8 p a th m e t e r s

measu re the ax ia l and t ransve rse ve loc i t i es a t each

cho rd loca t ion a l low ing the e f fec t o f t ransve rse f lows to

b e r e m o v e d .

L ike o the r m e te rs , the p ro f il e fac to rs o f bo th ex te rna l

and we t ted UFMs a re sens i t i ve to changes in the

3 8 5



ups t ream cond i t ions wh i le in se rv ice . Fo r exam p le , i f

o n e o f m u l t i p le f e e d s t o a h e a d e r u p s t r e a m o f a U F M

is i so la ted , the p ro f i le fac to r fo r the me te r ma y change .

Ex te rna l me te rs a re much more sens i t i ve to these

changes than mu l t i -pa th we t ted UFMs due to the fac t

tha t mu l t i -pa th we t ted me te rs samp le a g rea te r f rac t ion

o f the p ipe .

UF Ms a re no t un ique in th is sens i t iv i t y . Gene ra l l y ,

changes in ve loc i ty p ro f i le w i l l cause comparab le

e r ro rs in compe t ing ins t rumen ts . Howeve r , un l i ke

c o m p e t i n g i n s tr u m e n t s , m u l t i - p a th U F M s a r e c a p a b l e

o f de tec t ing these changes .

S ign i f i cance :

1 . Pro f i le fac tors are a la rge potent ia l e rror source .

2 . UFM vend o rs shou ld be awa re o f the ins ta lla t ion

s i te hyd rau l i c cond i t ions .

3 . Mu l t i -pa th UFMs have muc h lower p ro f i le fac to r

e r ro rs and can be ve ry insens i t i ve to changes in

ve loc i ty pro f i les .

4 . Mu l t i -pa th UFM s have the capab i l i t y o f de tec t ing

change s in ve loc i ty p ro f i les .

R e p e a t a b i l i t y M e t e r P r o v i n q

Ul t rason ic f low me te rs a re samp led sys tems . Tha t i s ,

the t rans i t t ime measu red fo r a s ing le pu lse t rave l ing in

one d i rec t ion a long an acous t i c pa th samp les the f lu id

ve loc i ty and sound ve loc i ty a long tha t pa th . These

va r iab les va ry in t ime bec ause o f tu rbu lence , f low

con t ro l ope ra t ions and o the r fac to rs . A s ing le samp le

does no t es tab l i sh the mean ve loc i ty .

Mu l t ip le samp les a re necessa ry to reduce the

m e a s u r e m e n t u n c e r ta i n ty . T h e s a m p l in g c h a r a c t e r i s ti c

o f u l t rason ic f low me te rs i s fundamen ta l l y d i f fe ren t

than tha t o f tu rb ines and pos i t i ve d isp lacem en t m e te rs ,

wh ich in teg ra te the f low f ie ld mechan ica l l y and tend to

smoo th t ime-w ise f low va r ia t ions by the i r ro ta t iona l

inert ia.

Fac to rs a f fec t ing the re pea tab i l i t y o f u l t rason ic flow

mete rs a re :

• Tu rbu lence In tens i ty : Typ ica l l y , the rms va lue fo r

loca l tu rbu lence w i l l li e in the ran ge o f 3 to 7% o f the

mea n ax ia l ve loc i ty 4. The ma gn i tude w i l l depend on

u p s t r e a m h y d r a u li c s . T h e m e a n v e l o c it y m e a s u r e d

a long a pa th w i l l be be low the 3 to 7% f igu re

because o f spa t ia l ave rag ing a long the pa th

( typ ica l ly rang ing 2 to 4%) .

• Sam p le Ra te : A p rov ing run takes p lace ove r a f in ite

t ime pe r iodm fo r a ba l l p rove r , 10 to 20 seconds i s

typ ica l . The more f requen t ly an u l t rason ic f low me te r

samp les the f low du r ing the run pe r iod , the more

4 Reference Boundary Layer Theory Seventh Edi t ion ,

Sc h l i ch t ing C ha p te r X V II I ) , Mc G ra w -H i l l

p r e c i s e t h e m e a s u r e m e n t o f th e c a l ib r a ti o n

coe f f i c ien t . Th is i s pa r t i cu la r l y t rue when a compac t

p rove r i s used and f low t rans ien ts ex is t .

Assuming , tha t the p rove r i s pe r fec t o r has a neg l ig ib le

con t r ibu t ion to unce r ta in ty and repea tab i l i t y then , the

repea tab i l i t y o f a U FM w i ll be a func tion o f ce r ta in

meter and app l ica t ion charac ter is t ics . In part icu lar , i t

w i l l depend on 1 ) me te r pa th con f igu ra t ion , 2 ) samp le

ra te , 3 ) p rove r vo lume , and 4 ) tu rbu lence .

C h a r a c t e r i s t i c S t a t i s t i c s : For pu lse ou tpu t me te rs ,

the number o f pu lses requ i red to ob ta in repea tab i l i t y

com mo n ly used in p rove r ca lib ra t ions , 0 .05% f rom f i ve

runs , i s dependan t upon the pu lse - to -pu lse regu la r i t y s .

The worse the regu la r i t y , the more pu lses a re requ i red

to ob ta in a g iven repea tab i l i t y . Cons ide r the d i f fe ren t

me te rs ( tu rb ine , vo r tex and UFM) shown in F igu re 5 .

F i g u r e 5 P r e d i c t e d R e p e a t a b i li t y v s . N u m b e r o f

P u l s e s / S a m p l e s f o r V a r y i n g S t a n d a r d D e v i a t i o n s

O .7O

0.60

~ o . , t r / o

L ~ / o •

o . ~ %

o . l o % '

o . ~ %

~ mezm-(le-ls%)

10,000 IOQ

N o . o f Pul~m/SampI¢=

A good tu rb ine me te r has a pu lse - to -pu lse s tanda rd

dev ia t ion o f be t te r than 1 -2%. The tu rb ine me te r mee ts

the repea tab i l i t y requ i remen ts w i th a re la t i ve ly sma l l

number o f pu lses . Fu r the r w i th a compac t p rove r ,

pu lse in te rpo la t ion i s a va lid concep t b ecause o f it s

p red ic t i ve na tu re (e .g . , good regu la r i ty o f pu lse ou tpu t ) .

A v o r t e x m e t e r a t t h e o t h e r e x t r e m e h a s a s o m e w h a t

inde te rm ina te regu la r i ty , bu t from the au tho rs '

expe r ience has a pu lse - to -pu lse regu la r i t y s tanda rd

dev ia t ion be tween 10 -15%. I t can be seen tha t many

more pu lses a re requ i red to ob ta in good repea tab i l i t y .

Inc luded in F igu re 5 i s a s ta t is t i ca l pe r fo rm ance

typ i fy ing a UFM ( in th is case an Ca ldon LEF M 2 40C) . 6

s The Predict ions of Cal ibration Repeatabi l ity Using Com pact

Provers and Pulse Interpolat ion R. Paton

6The value assum es hat the LEFM produces one pulse per flow

measurement samp le, and that there s no pulse nterpolation

(sample rate 60-7 0 Hz). The pulse/sample output rom an ultrasonic

meter s derived rom converting each sampled low measurement

into pulses. The jitter or standard deviation s due to turbulence

and hydraulic variability h at n tum produce variability n the pulse

output.

8 6

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