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Transcript of ultrasonic flow theory.pdf
8/11/2019 ultrasonic flow theory.pdf
http://slidepdf.com/reader/full/ultrasonic-flow-theorypdf 1/7
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.
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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 .
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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
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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 .
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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
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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.
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