CA1220646A - Two phase flowmeter - Google Patents

Abstract

"TWO PHASE FLOWMETER"
ABSTRACT OF THE DISCLOSURE

The tubular flowmeter is capable of measuring two different physical parameters in a flowing mixture of liquid and gas (such as wet steam). These measurements are such that they can be used to determine the individual gas and liquid flowrates. The flowmeter comprises first means, such as an orifice plate or a twisted tape, for causing an accelerational or frictional pressure drop in the total flow. Suitable means measure such pressure drop. Downstream of the first means is positioned means for inducing rotational motion of the total flow, to cause the mixture to separate while remaining within the same conduit into discrete liquid and gas flows. Such means may comprise a rib ex-tending helically along the inner surface of the flowmeter. Means, such as a pitot-static tube assembly, measure a pressure head indicative of the velocity of the gas flow. Downstream from this velocity measure-ment device, the two phases are permitted to mix freely again, all the time remaining within the same conduit. The total flow pressure drop and gas flow velocity head measurements are used to compute or determine the individual gas and liquid flowrates.

Description

2 Field of the Invention

3 The present invention relates to a flowmeter o~ the type

4 adapted to measure two different physical phenomena or parameters per-taining to a mixed gas and liquid flow in a conduit. From the two measure-6 ments obtained, the individual flow rates for the liquid and the gas may 7 be determined by the use of suitable equations. The flowmeter was developed 8 to monitor wet steam streams, although its use is not limited to that 9 application and the flowmeter could readily be used also for the measure-ment of two phase flows containing two or more components. It could also 11 be adapted for use with gas-slurry flows which may contain more than two 12 phases 13 ~rior Art 14 The measurement of fluid flow is required in many applications -for process control and monitoring.
16 In two- or multi-phase flow, it is usually desirable to obtain 17 values of the individual phase flowrates.
18 The accurate metering of the individual phase flow rates in a lq two phase flow poses difficulties, because neither the density nor the velocity of the fluid remains constant. Thus variations in one parameter 21 are difficult to distinguish from variations in the other parameter.
22 Among the commonly employed instruments for the measuring of 23 fluid flow are the pitot-static tube meter, the ori-fice plate meter, and the 24 venturi meter. While these meters are accurate in single phase fluid metering, their accuracy in two-phase flow is limited~ because of the 26 aforementioned physical fluctuations. These meters function to create and 27 measure pressure drops due to acceleration or deceleration effects in a 28 closed conduit.

~L2~ L6 1 A number of flowmeters are known which monitor two-phase flow2 by taki~g two or more independent measurements of different physical 3 parameters of the two-phase f10w.
4 One such flowmeter is disclosed in our earlier U.S. Patent No. 4,312~234. This meter is operative to create and measure frictional 6 and accelerational pressure drops in a mixture flow. These pressure drops 7 may be correlated with flow rates by the use of theoretical two-phase 8 mathematical models. The device utilizes a twisted tape positioned in the 9 flow to create a frictional pressure drop, and a venturi, For the pro-duction of an accelerational pressure drop. Pressure transducers monitor 11 the pressure differentials across the twisted tape and the venturi.
12 A difPqrent approach for the determina-tion oF individual ~as1~ ~nsl l-iqu~ low rates in a -two-phase flowstream is exenlpliFied in U.S. Patent 1~ ~,178,801, issuecl to Cassell et al. That patent discloses a centriFugal vapour-liquid separator mounted in the vapour drum of a utility boiler.
16 Such an assembly is principally employed for the physical separation and 17 removal of the liquid phase from the vapour phase, so as to produce 18 substantially liquid-free vapour. It is advantageous in operating such a 19 separator to be apprised for the individual phase flow rates of the two-phase flowstream. Pressure and pressure drop sensors are thus provided ~1 ln ancl across the separator. The Flowrate oF the two-phase flow stream22 and the flow rates of the individual phases are computed b~ measuring the 23 pressure differential across the separator, the pressure differential 24 across the flow of the separated vapour phase, and specific absolute pressures. These pressure measurements are correlated with flow rates by 26 the use of mathematical models specific to the separator. This metering 27 technique would, however, not be applicable in the uses contemplated by the 28 flowmeter of the present invention demanding~ as it does~ the permanent 29 separation of liquid from vapour phase, and two independent flow channels.

4~
1 Other f'lowmeters are known which monitor two-phase flow by 2 taking and computing two measurements against theoretical mathematical 3 models. One such meter combines a gamma ray densitometer and a turbine 4 meter. Both of these devices are relatively expensive and not ideal for field use. A second meter proposes the use of a pair of segmental orifices 6 positioned in a conduit. However, the applicability of this meter to 7 general two-phase flow metering is restricted by the limited operating range 8 in which accurate measurements can be made. Both meters have been developed, 9 usually to meet the demands of certain specific applications.
While the two-phase flowmeter disclosed in our '234 patent 11 provided a rugged, inexpensive and accurate meter, the calculations and 12 eompu~a-tions required to arrive at the desired mass flowrates proved 13 gxseedln~ly complex.
1~ Accordingly, there was a need to provide an equa'lly rugye~, inexpensive and accurate multi-phase flowmeter which monitors parameters 16 which can more easily be correlated with flow rates, by the use of less 17 complex theoretical mathematical models.

18 _MMARY OF THE INVENTION
19 In accordance with the present invention, we provide a flow-~ me-ter comprising a tubular body or member which incorporates two measuring 21 devices operating in series. One such device induces or causes a frictional 22 or accelerational pressure drop in the total flow of liquid-gas mixture 23 and allows this drop to be measured producing a signal indicative of the 24 magnitude thereof. The other device separates the mixture into distinct 25 liquid and gas phase flows within the same conduit and allows a measure-26 ment to be made of the velocity of the gas flow. These measurements or 27 signals can then be used to calculate the individual liquid and gas flow-28 rates or, alternatively, they can be compared against calibrated results, 29 to yield the desired individual rates.

~Ir l The one device may comprise a means for causing a frictional 2 pressure drop, such as a twisted tape insert, operatively coupled with a 3 means for measuring such drop and producing a signa1 indicative thereof.
4 Alternatively, the device may comprise a means for causing an accelerational pressure drop, such as an orifice plate, a venturi, or a flow nb~zle, 6 operatively coupled with a means for measuring the drop and producing a 7 signal indicative thereof.
8 The other device may comprise means for inducing rotational 9 motion in the total flow, to separate it within the same conduit into an outer liquid flow and an inner gas flow, coupled with means for measuring ll a pressure head indicative of gas flow velocity and producing a signal 12 indicative thereof. Preferably, a helical rib, extending along the inner 13 surface o-f the tub~lar member, is usecl to impart rotational motion. A pitot l~ tube, most preferably a shielded pitot-static tube, is preferably providedat or near the central ax;s of the tubular member to make the velocity-16 oriented measurement. Suitable means are coupled with the pitot tube to 17 produce the signal indicative of the gas flow velocity.
l~ The invention lies in the combination of devices used. Th-isl9 combination permits one to:
l. measure one physical parameter, frictional or accelerational 21 pressure drop of the total flow of mixture;
22 2. induce separation within the same conduit of the mixture 23 into separate gas and liquid flowsi and 24 3. measure a different parameter, a pressure difference indicative of velocity, which is characteristic of the 26 gas flow.
27 The two pressure difference measurements obtained can be made28 to yield the individual gas and liquid flowrates of the mixture (or other 29 derivable quantity such as total mass flowrate or quality), by either:
(a) comparison against calibrated results, or 31 (b) calculations, using theoretical relationships combined with 32 empirical factors dependent on the particular devices used.

6~
l DESCRIPTION OF THE~.DRA~INGS
2 Figure 1 is illustrative of a preferred embodiment of the 3 device in which an orifice meter is utilized as the means for creating and 4 measuring the upstream pressure differential, a helical rib separator is used to separate liquid and gas, and a shielded pitot-static tube is used 6 to measure the gas flow pressure head;
7 Figure 2 is a more detailed sectional-side view of a.preferred 8 shielded pitot-static tube positioned within the rib separator assembly;
9 Figure 3 is a plot showing the Effective Quality xe of thetotal flow versus the Actual Quality x, of the total flow as measured at ll the orifice meter which plot is utilized in the computation of meter 12 constants;
13 Figure 4 is a plot showing the relationship between the l~ me~sured velocity head at the pitot tube versus the actual Single Phase 1~ StQam Mass Flowra-te M9 , which plot is utilized in the specific meter l~ calibrations as exemplified with wet steam flowi 17 Figure 5 graphically depicts the relationship between the 18 ratio of Apparent to Actual Gas Mass Flowrate versus the Liquid to Gas Mass19 Fraction, which graph is employed in the calaculation of meter parameters; and Figure 6 is a schematic of the experimental set-up used to 21 test the flowmeter.

~ ;~

l DESCRIPTION OF TI-IE:PREFERRED EMBODIMENT
2 The f10wllleter in accordance with th~ invention has been 3 ~eveloped and tested in connection with moni-toring we-t stearn and also 4 air-water flows. It is believed that it can also be applied to other -Flo~ing two-phase mix-tures, such as g~s with oil, and other gas-liquid 6 flows. It rnay also be use~ul with three-phase flow, in which solid 7 par-ticles are carried in solution or suspension. In any case, it is 8 described hereafter in connection with a model used ~ith wet steam.
9 With re-Ference to the Figures, the flowmeter l is shown in its preFerred embodiD1ent in Figures l and 2 ll More particularly, the Flown1eter l comprises a tubular 12 member 2, adapted to be connected into the flow conduit (not shown).
l3 The tubular member 2 has a conventional orifice plate meter l~ 3 l~lounted in its inlet end. The meter 3 comprises an orifice plate 4 u~stre~nl ~nd downstrealll Flange taps 5, 6,a pressure transducer 7 16 (V~lidyne* Moclel DP-7) opera~ive to measure the pre~sure diF~ererlce between 17 the taps 5, G an~ produce a siynal indicative or proportional of such pressure di-fference, and a pressure transducer lO (Validyne Model ~P-7) 19 having one side at atn1ospheric pressure, operative to measure the staticpressure a-t tap 5, and produce a signal proportional to the said static 21 pressure. These signals are transmitted through the line 8 and ll to a 22 microprocessor 9.
23 Downstream o-f the oriFice plate 4, there is provided a 24 helically ex-tending rib 12 protruding inwardly from the inner surFace of the meIllber 2. Preferably, the rib depth should be equal to l/4 to l/lO
26 of the pipe diame-ter and have a pitch of 0.5 to 3 diameters.

* Trade Mark .. ~ >

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1 At the downstream end of the rib section, a shielded pitot-2 static tube 13 is mounted in the tubular member 2, so that its axis and 3 entrance 14 coincide with the longitudinal axis of said member 2. The 4 pressure lines 15, 16 of the pitot-static tube 13 measure the static and total pressures of the gas flow. They are connected to a canventional 6 differential pressure transducer 18~(e.g. Validyne Model DP-7), which 7 is operative to produce a signal indicative of or proportional to the 8 dynamic pressure of the gas flow (which is related to the velocity of the 9 gas flow). This signal is transmitted through the line 17 to the micro-processor 9.
1l This assembly is operative to carry out the following functions.
12 The orifice plate 4 provides means for inducing an accelerational pressure 3 drop in the total flow of mixture passing through the member 2. The 1~ taps 5, 6 and -transducer 7 provide means ~or measuring the pressure charlge 1~ an~l pr~ducin~ a signal proportional to such change. The rib 12 is 1~ operative to induce rotational motion in the mixture flow, to cause it to 17 separate into an outer liquid,flow and an inner gas flow. This separation 18 is limited to a short portion of the conduit , so that the component 19 flows are only temporarily separated for the purpose of effe,cting certain measurements on the flow. On leaving the meter the flow components are 21 free to re-combine. The pitot-static tube 13 is operative to measure the 22 differential pressure head of the gas flow , in conventional fashion.
23 The signals produced are transmitted to the microprocessor 9 which is 24 governed by a data reduction program comprising correlating calibrations for the orifice signal and the pitot tube signal. The mass flow rates of 26 liquid and gas, the quality and the total mass flow rate may be computed 27 and displayed by the computer 9.

~ 2~20~L6 1 Usually, in the metering of two-phase flow, it is necessary 2 to measure additional parameters, such as the static pressure of the 3 stream and/or the temperature. As will become evident from the description4 to follow, this third parameter is usually needed in order to correlate theabove two pressure drop measurements with the individual flowrates of the 6 two phases. This correlation includes physical properties such as the 7 density and viscosity of each of the two phases. In a one-component 8 two-phase stream such as wet steam, a measurement of static pressure or 9 temperature of the stream allows one to calculate the density and viscosityof each phase. With wet steam for instance, standard steam tables may be 11 used. In a two-component two-phase stream both a temperature and static 12 pressure measurement may be needed.
13 Notwithstanding the above description of the preferred 1~ embodiment of the meter and the particular arrangement shown, it is to be ~ n~l~rs~oocl that -the order of the tw~ measuring elements is immaterial~ and 1~ khe opera-tion of the meter does not depend on this order, and they may 17 be interchanged if desired.
18 Although the use of a conventional pitot-static tube for the 19 measurement of gas velocity has been demonstrated, it is to be understood that other devices for measuring g~s velocity may be equally applicable, 21 for example, turbine meters, drag discs, anenometers, or vortex meters, 22 in cases where their use might be practical.
23 The following example is included to demonstrate the operability 2~ of the preferred embodiment of the flowmeter, and to show the types of calculations involved in correlating the flowmeter measurements with the 26 individual flowrates of the two phases.

27 Example 28 A flowmeter as shown in Figures 1 and 2 was constructed in 29 accordance with Table 1.

1)6~6;
'I TABLE 1 2 Typical Dimensions and l~aterials Associated with a:
3 Particular Embodiment of the Two-Phase Flowmeter 4 Component Size Material Pipe 2" - sch 160 ASTMI A-106 6 Ll = 60"
7 L2= 8.7"
8 L3 = 20.7"
g L4 = 23.0"

Flanges Standard 2" 1500 ASTM A-105 11 lb rating design 12 per ASA B 16.5 __ . _ . __ .. ,_ __.. _~_ ._._. ._ ._ ___~._ _ ._.. _._. .__ _._. _ ~, ..
13 Pressure Taps d;am. - 3/8"

14 OriFice Designed to ASME 300 Series SS
D= 1.64"
16 d = 0.918"
17 t = 1/8"

1~ Coil Dp = 1.39" 300 Series SS
19 Ds = 0.625"
Dc = 0.25"
21 p = 1.64"
22 Lc = 30.6"

~2~
TABLE 1 (Continued ) 2 Component `Size Material 3 Shielded pitot-static tube Dt = 1:/16" 300 Series SS
4 tt = 0'033"
L5 = 1.125"
6 L6 = 0.625"
7 L7 ~ 0.375"
8 L8 = 0.625"
9 Lg = 0.760'' L = o 375~
1l Lll= 0.945"
12 L ~ 0 711"
13 L13' 0.060"
14 L14- 0.5~5ll L15= 0.125"
16 L16= 0.250'' 17 L~7_ 0.935"
18 L1~3= 1.142'' 19 Llg= 0.488"
L20= 1 375"
21 L21= 0.176"

-22 Mathematical`Solùtion 23 Governing Equations 24 For the meter depicted in Figure 1, and the experimental 25 apparatus depicted in Figure 6, six equations can be appl:ied to the meter 26 elements for the purpose of determining the total mass flowrate and quality.

6~L6 1 Three governing equations.are applied to the orifice plate 2 meter to de-termine the total:mass:flowrate Mt ~ quality x and ePFective 3 quality xe as follows:

4 (1) M = Cd Y Faa `'/ (1 ~ ~4)ve where Cd is the orifice discharge coeff,icient ;
6 Y is the orifice plate fluid expansion -Factor ;
7 Fa is the orifice area thermal expansion factor ;
8 a is the orifice area;
9 9c is the proportionality constant ;
~Pl is the pressure d;~fe,rence measured across the orifice plate;
11 ~ is the ratio oF oriPice to pipe d;ameter;
12 Ve is the ePPective spe'cific volume of the fluid 13 (2~ ve a vf -~ xe Vfg 14 where Vf is the saturated l;qu;d specif;c volume;
Vf9 is the specific volume difference between the saturated 1~ gas and saturated liquid ;
17 Xe is the effective mass quality of,the fluid.

2 ~L2;2~6~6 'I (3) xe = ClxC

2 where Cl and C2 are effective''quality constants dependent upon 3 specific meter geometr;es the determina-tion o~
4 which.~ill.be hereinafter detailed.
x is the true mass quality of ,the-fluid .

6 The equations governing the pitot-static tube and applied 7 thereto to determine the apparent gas mass flowrate (Mgtp) ', the gas mass 8 flowrate (Mg) , and total mass flowrate (Mt), are as fo,llows:

9 (4) M t = C3 (0.817), ~ (D2. - dc ) ~ ~ C4 where C3 and C~ are empirica1'constants for a particular Fluid and 11 speciFic meter geometry. C4 wi'll have the units of 12 mass Flow.
13 0.817 is the theoretical ratio of.average velocity to centre-4 line velocityi ~ (D2 dC2 ) is the flow.area of the fl,uid ;
16 Vgp is the speci-fi,c volume of the gas phase at the pitot ;
17 aP2 is the dynamic pressure at the shielded pitat~static tube 18 (5) Mg = Mgtp L ' - 1-X ]
C5 ~ C6 ( - ) 19 where C5 and C6 are olllpirical cons-tan~s fo.r a particular fluid and a specific geometry.

. ... .. . ._. _ . _ . . .... _ . _ . _ . _ ......... _ __ _____ _ .. _ . __ . .. ._ ... . . _ _ . . . ..
~s3 6~6 ( Ij ) Mt = 9 2 The modelling of the empiri~al constants C~,C4 , C5 and C6, 3 wtlich models relate -to the pi-tot-st~tic`tube, will be outlined hereafter.

4 Parameters Cd , Y, Fa~ a and ~ are computed in accordance wi-th established procedures, as set forth in, for example, 'Fluid Meters -6 Tileir Theory and Application', ASME Report, 6th ed. 1971.
7 Fluid proper-ties are based on static pressure measurements, 8 and, in -the case of s-team-water flows~ nulnerical examples may be obtained, 9 for example From 'ASME Steam Tables', 1967.
Parame-ters apl and ~P2 are the actual pressure difference 11 nleasllrelllents effected a-t the meter and (leternline(l-thr~ugll the use o-f 1~ conv~n~ioll~l pressure sellsillg devices.
13 ~y subst;kuting equations (2) and (3) into equation (1), the 1~ total IllaSS -flowrate (Mt) through the.orifice is modelled in the following form:

.. ~
6 (7) M = C Y F a / 2 c ~P2 t d a / A ~ ~`
J (1-~) (V~ ~ Clx ~2 Vfg 17 The total n~ass flowrate (Mt) at the pitot-static tube is ~ modelled by substitution of equation (4) and (5) into equation (6).

~ C3 [.817 ~ (D2 - dC2) ] ~ C~ l 1 19 (8) Mt = L C5 ~ C6 ( x ) ~ x 1 ~

~ .. .. _ . .. _ _ .. .. _ . __.. ._ _ _ _ .. .. _ _ .. .. .. _ . _. ___. _ ._ . _ . ...

3l22~
1 Ultilnately, the to~al mass,flow rate Mt ~ an~ the quali-ty x 2 are deterlnir)ed by the silllul-taneous solution of equations (7) and (8) for 3 the values t~ereoF. I-t will be apparent, therefore, that the to-tal massq flowra~e (~'lt) will be eguivalent for each device, under the measured process conditions.

6 ample Calculations 7 Actual test.results and associa-ted calculations are reproduced 8 be'low fo,r illustrative purposés.
9 The following re$ul.ts.were recorded using the system shown scllel)latically in Figure 6, and the related dimensions given in Table 1.

11 Controlled Process Conditions 12 mw = .0555 lbin/s.
1~ TW = 72.7F.
1~ mS5 = .2264 Iblll/s '15 Pss = 36.0 psia '16 TSs = 264.4F

17 where n~w is the subcooled water mass flowrate ;
18 Tw is the subcooled water temperature ;
19 mS5 is the superheated steam mass flowrate ;
Pss is the static pressure oF :the superheated steam ;
~1 'I'ss is the superheated steam temperature .

22 The.process parameters measured were as fo,llows:
23 P; = 32.33 psia 24 ~pl = 9 99 psi L;P2 3.21 psi 26 To = 221F

, ~
.. " ~ . -- .. .. . .. .. .. .........

~2~4~
1 where Pj is the static pressure upstream o-F,the orifice,plate ;2 To is the tenlperature a~ the nleter o~-tle-t (nleasured for 3 verification only) '-4 Addi-tional instrumentation Fo,r experimental verification of test results was included in the actual test loop.

6 Calculation g-ives the Actual Total Mass Flowra-te Mt and quality 7 at the meter from the controlled.process conditions as fo.llows:

(9) Mt = In + m g a = ,0555 ~ .2264 a .2~19 lblll/s 11 I-r~ entlla'lpy balance ca'lculations, considerlng any losses 12 as negliyible, we ca n calculate an actual homogeneous quality at the 13 I~ er as:
1~1ll~WhW ~ nlSs~ss = M.t (hf -~ xa hfg) Ol~, ,~lwh~ MsShss h.~
lb (10) xl - _ Mta hv hv 17 where hw is -the specific enthalpy of compressed water ;
18 hSS is the speciFic enthalpy of superheated steam ;
19 hf is the saturated liquid specific enthalpy ;
Xa is the actual quality of the two-phase mixture ;
21 hv is the specifi,c enthalpy o~ vapori~ation .

22 Fronl the ASME Steam Tables . _ .. . .. . . _ __ __. ~ ...... . . . .. _ ... . .. .. _ _. .. _ .. _ . .. ~ . _ . ... .
~, ~

'w = ~I~.87 ~t~/lb (~eF~,re nlixer) I)S5 -, 1175.0 B-lu/lb ~be-Fore nlixer)' 3 h,f = 223.4 Btu/lb (at 32.3 psia) v = 949 4 Btu/lb (a-t 32'~3 psia) ~ilhicl~ serted il~tO e(luatio~l (10) yields~

6 x = (.0S55)(40.874) +'(.2264)(1175) 223.4 a , - -(.2819)(949.~) ,949.4 7 = 0.767 0~-ifice ~leter Parameters 9 The orifice meter parameters were determined by the proce~ures ~s ou~ ed for example in ~'luicl Meters - Their Theory and Application, ASME
11 Rep(~n~, Gth ecl. 197'1.

12 Tlle experimental results are detailed as fo,llows.
13 l'he ratio o-f oriFice to pipe diameter ~ was deternlined,as 1'~ fallu~ls:

(11) ~ = d = Ø918 = 0.56 1)- 1~

16 wilere ~ is the ratio of the arifice to pipe diameter 17 d is the.orifi,ce dianleter 18 D is the pipe diame-ter.

19 The expansion factor Y was deterMined as fo,llows.
The compressibility of.the metered fluid,is given by:

21 (12) Y = 1 - (0.41 -~ 0.35 ~4)(1 - r)/~

where r is tile ratio of clownstreaal to upstream pressures across 2 lhe orifiice plate;
3 ~ is the ratio of specil~ic heats .

4 and QPl 9 . 9908.
( 13) 1 -r = -- = = 0.30905 pl 32 . 327 6 (~ = Cp/Cv = 1.329 (steam) Y ~ 1 _ (0.41 ~ 0.35 (o.56)4) (_~30905) 1 . 329 ~3 ~a 0.~67 9 where Cp is t:he specific heat a-t constant pressure, Cv i s Lhe spec -i F i c hea t a t constant vol ume 11 The -thermal expansion factor Fa was calculated by considering 12 Lhe saturat-ioll t~nlperature which corresponds to pressure pj, that is:

13 rsat ~ 25~1-6F (For pj = 32.327) 1~ an(l 15 Fa = 1.0035 (for a stainless steel orifice plate) 16 The ori fice area a is given by:

177,d2 7r (0.918) (15) a = ~ = ~ 4 18= 0.6619 jn2 ~ir ` ~ ~ __ ,___,_ _,_.. ____.. _ ...... __.. _ .. _.. _.. , .. _._.- - - --- - - - --- -~L2~
1 The gravitâtionâl constant gc is giYen by:
lb - ft 2 9c = 32.174 -lb s2 3 The orifice discharge coefficient, Cd , accounts for the 4 differerce betweer, the theoretical and actual mass flowrate through the orifice, as follows:

,_ 6 (16) Cd = K J 1 -7 where 8 (17) K = Ko (1 ~ A/Red) 9 (18) Ko = Ke ~(106d)/(:106d ~ 15A) ]

(19) Ke ' 0 5993 ~ ~-b-- ~ (0.364 + ~ 6) ~4 11 ~ 0.4 (1.6 - ~)5 [~0.07 ~ ]5/2 12 ~ (0 009 + --~r-4~)~ 5 ~ ~)3/2 + (65 + 3)(~ _ 0.7) 5/2 ~22~6~6 1 wl~ere K ;s -the flow coefficient 2 i~`O is the limitill~ value oF K ~or speci~ic pipe dianleter D and 3 ratio of ori~-ice to pipe diame-ter 4 ard Ke is the par-ticular value of K
wilen Red = 1 o6 ~/15 6 (20) A = d(830 - 5000 f~ -~ 9000 ~ - 4200 ~ + ~

7 ~here ~ is the parameter in flow coefficient equation -8 (21) l~ed = ReD/f~

9 ~j1Qne Re~; jS ~he uriFice Reyllolci's nu~nber;
1~ Re;) is the pipe Reynold's nulllber.

I1 (22) ReD

12 where ~J is compu-teci as the homogeneous viscosity for the mixture 13 and ~iven as :

4 (2~
x 9 ~f ~ is the absolute holllogeneous ~iscosity of the two-phase 16 mixture ;

312;~
r i s t~le absolute.viscosity o f,,the saturated 1iquid;
~1~ is the absolut~ viscosity of the saturated gas;
3 C'learly since ~, or Red are unknown, it is necessary to iter~t~. 'Ihererore, as a first approxilllation, let Cd ='0.615.

The specific volunles vf and Vfg are determined as follows:

6 V,f = 0.01715 ft3/lblll 7 Vfg = 12.~22 -ft3/lbnl (at p = 32.327 psi~) ~3 The e-ffective quali-ty constants Cl and C2 as determined 9 ~lereinafter are found to be as follows:

1~ Cl = 1.0263 Il C~ ~ 1.7362 12 l'lle Pitot-Sta tic Tube'Parame ters 13 The en~pirical constants C3, C4, C5, C6 as de-termined 14 heleillafter are given as:

C3= .004018 lG C~ = .04127 lbi~l/s 7 C5 = 1.01598 18 C6= .3836 19 Solution For Total'Mass'Flowra-te'~nd'Quality:-Conlbining the to-tal nlass fl,owrate equations fo,r the orifice 21 and pitot-static -tube, equations (7) ancl'(8) ~'respecti~ely, allows:

22 M-t = Mt orifice pitot . _ . ... _ . .. .. . ..... . . ..

6~
_ 1 (24)CdY Fa a / 29cQPl C3 H + C4 12 ~ 4) (Vf ~ Clx C2 Vfg ) C5 + C6 ( x- ) 2 where 3 (25) Hw =(0.817) 4- (D2 _ dC2 ~ ¦ V 2 c 4 Vgp =16.41 ft3/lbm for P2 = 24.83 psia the pressure at the pitot static tube (P2) is estimated by 6 P2 = Pl - 0-75 (~P1) 7 since -for an ori~ice where ~ = 0.56 the overall pressure loss is 8 75~ o-f ~he measured diF-Ferential pressure (source: Fluid Meters - Their Theory an(l Application , ASME Report, 6th ed. 1971).

To obtain an accurate value for Cd iteration was necessary.
11 The only unknown in the ahove equation is x, so we substitute numerical 12 values for all invariant terms~ for this particular set o-f measurements, 13 and simplify; viz:

y Fa a 2 ~0.8967)(1.0035~(0.6619)]2 _ 0 3 14 ~ ] [ ~ 1 - (.56)~

2gc = 64.348 16 ~pl = 9.9908 i -- -7 Hw = .817 x ~ x ~1.642 - .252) ~ 2 x 3.2116 x 32.174 x 144 18 which, after substitution into equation (24), and following algebraic 19 manipulation yields, ~L~2~
/ 713,01 0.2471 . 1 _ 1 (26) C~ (.0496) /- , 7~ 1 ~ - -u ~ (.01715 ~ 13.142 x ' '~') 1.0159~ + .3836 ,-xI x 2 This equation (for a given Cd) , can now be solved iteratively 3 for x, which in turn will yield Mt through either equation (7) or (8). The 4 computed total mass flowrate Mt is then used to correct the discharge co-efficient Cd , and subsequent iterations can be performed untll satisfactory 6 accuracy has been achieved. Results of the iterations are given in Table 2.

8 Solution for Total Mass Flowrate and Quality Discharge EQ (26) Total Mass Reynold's 9 Ite_ation CoefficientQuality Residue Flowrate Number Cd X Mt Re 1l ~ 0.615 .5 0.056 1~ 7 0.007 13 .8 -0.006 14 .75 0.000 .288 406572 1 0.609 .75 -0.003 16 .72 0.001 17 .73 0.000 .292 18 Xmetered 0 73 Mt = .292 lbm/s 19 Comparison of the metered total mass flowrate and quality with the actual expected values as computed yields:
21 M = 0.2819 lbm/s texpected 22 Mt = 0.292 lbm/s nletered 23 error = 3.6%

3L~2~ 6 Xexpected = 0.767 Xnletered 0 73 3 error = -4.8%

4 The Deter~ ation of Calibration Constants . _ .

S The cons-tants C.l -to C6 are obtained by the calibration of the 6 f1Owllletel against the known inle-t conditions through the operating range of 7 the nleter. Known inlet conditions would be defined as the known total mass ~ flowrate and ~uality of the flow stream. Quaiity o-f flow (x) is defined 9 by the following terms (27) x = 9 ll where W9 is the individual yas Flowrate;and 12 Wf is the individual liquid flowrate .

3 Such a calibration would be performed a single time for a 14 particular fluid and meter geonletry.

Tlle determination of the calibratiôn constants gi~en and IG illustrated hereirl3-ftPr is described. for clari~.y with respect to wet 17 stcalll rlow alld a part-icular embodinlent of the meter.

l8 The calculations assume steam water flow through a two-phase l9 flowmeter as depicted in Figure l.

'1:'-' ~

~ 36 ~
1 Orifice Plate Calibration Constants C ',and C2 2 The total mass;flowra~e Mt in two phase flow is modelled by 3 rep'lacing the single phase specific volume v by the effective specific 4 volume ve in the orifice plate mass flow equation as shown in equation (1).By measuring the pressure diffe,rence ~Pl across the orifice plate and knowing 6 the total mass flowrate from the inlet conditions, the effective specific 7 volume ve can be readily computed.
8 The effective quality xe at the orifice plate is determined 9 by substituting the effective specific volume ve into equation (2).
Saturated Fluid properties vf and Vfg are modelled from the 11 static pressure measurements preferably, on the upstream side of the orifice 12 plate.
13 It is assumed that the liquid and gas phases are saturated 14 ancl in ~hermal equilibrium with one another.
1~ The ac~ual experimental quality x can be determined from 16 the known water and steam inputs and temperature measurements, and, for '17 example, a pressure measurement before the meter. This actual quality, x, 18 is then modelled with the effective quality, xe using equation (3). The 19 correlation constants, Cl and C2 , for the orifi,ce meter are found using regression analysis.
21 Figure 3 exemplifies this analysis in showing a log-log 22 plot of xe versus x for a series of two-phase flows at pressures ranging 23 fr,om 20 to 40 psia and qualities ranging between'50% - 95%.
24 A least squares fit on this data yielded the fo,llowing results:

26 Xe = Cl.0263 x 1-7362~

27 or, in terms of constants Cl and C2 :

28 Cl ='1.0263 and C2 - 1.7362.

i4~

~ l I'ilol;-St:atic Tube Calibr~tion Constants C3 , C~ , C5 ~
. , . .. ...., _ . . __ . ___ . . .. _ 2 Un(ler conditions of s-lngle-phase steam -flow, the dynamic 3 prc~ssune measu~ ent from the shielded p-itot-static tube can be correlated 4 witll t~le total mass flowrate through the meter. Therefore, by passing several kno~.m s-ingle-phase steam Flowrates Mg' through the meter and 6 measllrillg the resultant dynamic pressures ~p2 , the equivalent-head of 7 water ll~ is derived as follows:

8 Hw = tO.817j ~ (D2 - dc ) ~

9 The results for the calibration constants were modelled by Following linear leas-t squares equations on the data as indica-ted in 11 Fi~llr~ ~ to give:

12 M~' = 0.004018 I-lW -.. 04127 3 Under two-phase flow conditions, the dynamic pressure 14 measulelllent provided by the pito-t-static tube is not an accurate measure Or tile true gas mass -flowrate flowing through the meter. The -term 16 apparellt gas mass flowrate Mgtp is in-troduced and replaces Mg' in l7 single l~hase steam flow as apparen-~ an~ actual gas mass flowrates are 18 eqtlivalerlt -to give:

19 Mgtp = C3 HW ~ C4 where C3 = .004108 and C4 - -0.04127 21 A~ addi-tional nla-thellla-tical model is required -to correlate 22 the apparent gas mass flowrate Mgtp with the actual gas mass flowrate Mg 23 in meterillg two-phase flow as, with decreasing quali-ty, the area occupied 24 by ~he liquid Flow increases rela-tive to the area available for gas flow.

.. . . . . . . . ......... .. . .. . . .. .. . . . . ... . . ...... . ..
~. ~

3~Z~ L6 1 For a fiYed yas Flowrate an increased ~ynamic pressure reading would ~ tIIcnefone resul-t. The effects of quality are predicted by use of the 3 follol~in~ models.

M t l;
M = C5 -~ C6 ( x F-igure 5 exemplifies graph;cally tl,e aforementioned linear relationship 6 bet~Ieerl apparent and actual gas mass flowrates.
7 T~e calibration constants C5 and C6 are derived by a nnode11ing 8 oF linear least squares equations upon the data expressed in Figure 5 to 9 provi~e:

gtp = ~ 015~$ ~ 0-3~3~ ~ x Il Rearrarl~ing tlle abovenIentioned equation gives My as follows:

12 M = M 1 ~ gtp C C (I )/

13 where C5 = 1.01598 and C6 - 0.3836 .

14 The operating range oF the~prcFerred embodiment of the two-phase fIowme-ter encompasses both annular flow and wavy flow. This IG techIlique oF metering and correlating proved effective and acourate in 17 flo~s haYing a qllality ranging from 50 to 100%.
18 WI)ile the present invention has been disclosed in connection 19 wit~l the preFerred embodiInent thereof it should be understood that there may be otller eIllbodilnents which fall within the spirit and scope of the 21 invention as deFined by the following claims.

;~ . .. . ...

; ~.
. ~ ....

Claims (8)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A flowmeter for measuring two different physical parameters of a gas and liquid mixture flow passing through a conduit, which measurements may be used to determine the individual gas and liquid flowrates, comprising:
means for causing a frictional or accelerational pressure change in the total flow and measuring such pressure change;
and means for separating the mixture into individual gas and liquid phase flows within the same conduit and measuring a pressure difference indicative of the velocity of the gas flow.

2. The flowmeter for measuring two different physical parameters of a gas and liquid mixture flow passing through a conduit, which measurements may be used to determine the individual gas and liquid flowrates, comprising:
means for causing a frictional or accelerational pressure change in the total flow, measuring such pressure change, and producing a signal proportional to such pressure change;
means for separating the mixture into individual gas and liquid phase flows within the same conduit, measuring a pressure dif-ference indicative of the velocity of the gas flow, and producing a signal proportional to such pressure difference.

3. The flowmeter as set forth in claim 2 comprising:
means for receiving said signals, calculating the individual liquid and gas flowrates, and displaying said flowrates.

4. A tubular flowmeter for measuring two different physical parameters of a gas and liquid mixture flow passing through a conduit, said flowmeter being adapted to form part of said conduit, which measure-ments may be used to determine the individual gas and liquid flowrates, comprising:
first means for causing an accelerational or frictional pressure change in the total flow, said means being selected from the group consisting of an orifice plate, a venturi, a flow nozzle, and a twisted tape;
second means for measuring such pressure change;
third means for producing a signal proportional to such pressure change;
fourth means, operative to induce rotational motion of the mixture, for separating said mixture into discrete gas and liquid flows within the same conduit, fifth means for measuring a pressure difference indicative of the velocity of the gas flow, said means comprising a pitot-static tube assembly having its axis substantially at the axis of the tubular flowmeter and its entrance positioned within the region of separated flows;
sixth means for producing a signal proportional to such velocity head; and seventh means for receiving said signals, calculating the individual liquid and gas flowrates, and displaying said flowrates.

5. The flowmeter as set forth in claim 4 wherein:
the fourth means comprises a rib extending helically along the inner surface of the flowmeter.

6. The flowmeter as set forth in claim 5 wherein:
the depth of said rib ranges from about one-quarter to one-tenth of the diameter of said conduit and has a pitch of about one-half to three diameters.

7. A tubular flowmeter for measuring two different physical parameters of a gas and liquid mixture flow passing through a conduit, said flowmeter being adapted to form part of said conduit, which measurements may be used to determine the individual gas and liquid flowrates, comprising:
a tubular body forming a flow passage;
an orifice plate, mounted in the body across the passage, for causing an accelerational pressure drop in the total flow;
second means associated with the body, for measuring such pressure drop;
a rib, extending helically along the inner surface of the body, downstream of the orifice plate, for inducing rotational motion of the mixture to cause it to separate into discrete gas and liquid flows within the same conduit; and a pitot-static tube assembly, associated with the body and having its axis substantially at the axis of the passage and its entrance positioned so as to be at the centre of the gas flow, for measuring a pressure head indicative of the velocity of the gas flow.

8. The flowmeter as set forth in claim 7 wherein:
the depth of said rib ranges from about one-quarter to one-tenth of the diameter of said passage and has a pitch of about one half to three diameters.