The present invention provides a flowmeter for measuring pressure drops indicative of the flowrates of the individual phases in a gas and liquid containing two-phase stream. Elements are provided for creating and measuring a frictional pressure drop in the two-phase flow. Elements are also provided for creating and measuring an acceleration pressure drop in the two-phase flow. Mathematical models are known in two-phase theory for correlating these pressure drop measurements with the flowrates of the individual phases. In a preferred mode of the invention the frictional pressure drop is measured across a twisted tape; the accelerational pressure drop is measured across a venturi downstream of the twisted tape, and the pressure drops are measured by pressure transducers. The meter also preferably measures the static pressure of the two-phase flow.

BACKGROUND OF THE INVENTION 
The present invention relates to flowmeters for measuring pressure drops 
indicative of flowrates in a two-phase flowing stream. 
By two-phase flow is meant a flowing stream containing gaseous and liquid 
phases of one or more components. Exemplary streams include wet steam, oil 
and gas, and air and water. 
The flowmeters used to meter single-phase flow usually include a device for 
measuring a pressure drop in the flowing stream, which pressure drop can 
be correlated with the flow rate of the stream through theoretical 
mathematical models. 
In two-phase flow however it is usually desirable to obtain values of the 
individual gas and liquid flowrates, W.sub.g and W.sub.f respectively. 
These flowrates are usually expressed in terms of total mass flow (W) and 
quality of flow (x), which terms are defined as: 
EQU W=W.sub.g +W.sub.f ; and 
EQU x=W.sub.g /(W.sub.g +W.sub.f) 
A number of two-phase flowmeters are known in this art. Two such meters, 
which correlate one of the above flowrate parameters with a pressure 
differential measurement, are the Orifice Plate Meter and the Venturi 
Meter. The Orifice Plate Meter comprises an orifice mounted across the 
conduit carrying a two-phase flow. An accelerational pressure drop is 
measured across the orifice plate. A mathematical model is then used to 
correlate the stream's total mass flow with the accelerational pressure 
differential measured. 
The Venturi Meter comprises a venturi placed in the conduit carrying the 
two-phase flow. An accelerational pressure drop across the venturi is 
measured and correlated by mathematical models either to the quality and 
total mass flow of the stream or to the quality and a dimensionless 
modified Collins parameter F.sub.p, which parameter will be later 
explained. 
Both of the above two meters rely on one pressure differential measurement 
to evaluate parameters of two-phase flow. 
Other two-phase flow meters are known, which monitor two-phase flow with 
two or more measurements. One such meter employs a gamma ray densitometer 
to make void fraction measurements and a turbine meter or drag disc to 
obtain a second measurement. The two measurements are correlated 
mathematically to indicate the individual phase mass flowrates. This 
metering technique is limited to a very small quality range. It is also 
expensive, employing a delicate gamma ray densitometer instrument. In such 
two-phase streams as high pressure wet steam, such instruments would not 
be practical. 
Very recently an Orifice-Couple Flowmeter has been proposed for two-phase 
flow, see K. Sekoguchi et al., "Two-Phase Flow Measurements with 
Orifice-Couple in Horizontal Pipe Line," Bulletin of the ISME, Vol. 21, 
No. 162, December, 1978. The meter includes two segmental orifices or 
baffles in the conduit carrying the two-phase flow. Three pressure drop 
measurements are taken, two across the segmental orifices and the third 
across two of the orifices. The two individual pressure drops and the sum 
pressure drop are then correlated, by a model specific to this system, to 
the gas and liquid flowrates. This metering system appears to give very 
good results. A minor disadvantage to the system is that the data is not 
presented in a dimensionless form. Consequently, performances for 
different systems are difficult to predict. 
Although not used for the purpose of flow metering, twisted tape swirl 
generators have been used in both single and two-phase flow to enhance 
heat transfer in heat exchangers. In these systems a tape, having a width 
equal to the diameter of the conduit carrying the two-phase flow, is 
twisted into the conduit. The twisted tape induces a swirled flow, 
otherwise termed annular flow. Annular flow is a two-phase flow pattern 
characterized by an annular film of liquid travelling along the inner wall 
of the tube with the gaseous flow moving through the centre core of the 
tube at a much larger velocity. Users of these generators have noticed a 
frictional pressure drop across the twisted tape. A frictional pressure 
drop model for gas-liquid flow through a twisted tape has been developed, 
see G. S. R. Narasimhamurty et al., "Effect of Turbulence Promoters in 
Two-Phase Gas Liquid Flow in Horizontal Pipes," Chemical Engineering 
Science, Vol. 24, 1969, p. 331. 
SUMMARY OF THE INVENTION 
We postulated that, in order to meter two-phase flow, that is to evaluate 
two of the four flowrate parameters, quality, total mass flowrate, gas 
mass flowrate and liquid mass flowrate, one should use two independent 
relationships between two of these four parameters and such easily 
measured two-phase properties as pressure and temperature. In this way two 
physical aspects of two-phase flow would be used, which aspects would 
follow independent laws. 
Theoretical two-phase models are known which may be used to correlate an 
accelerational pressure differential with flowrates and to correlate a 
frictional pressure drop with flowrates. 
In accordance with the invention, we meter two-phase flow using two 
independent measurements. By independent measurements is meant 
measurements of distinct physical aspects of the two-phase flow which 
follow independent laws. More particularly, we utilize the combination of 
frictional and accelerational pressure drop measurements to meter 
two-phase flow. 
In a preferred form of the invention, the frictional pressure drop is 
measured across a twisted tape in the conduit carrying the two-phase flow 
and the accelerational pressure drop is measured across a venturi 
positioned in the conduit downstream of the twisted tape. This preferred 
combination of measurements takes advantage of a known fact that the 
venturi accepts annular flow to give an excellent correlation between the 
pressure drop measurement and total mass flow. Thus the twisted tape, 
upstream of the venturi, enhances the performance of the venturi by 
promoting annular flow. Furthermore, the independence of the twisted tape 
and the venturi measurements is inherent since the former measures a 
"frictional" pressure drop while the latter measures an "accelerational" 
pressure drop. 
In another preferred aspect of the invention a third parameter is measured 
to evaluate the physical properties of the two-phase flow. This 
measurement is most preferably a measurement of the temperature or the 
static pressure of the flow. In a two-phase one-component stream such as 
wet steam, either the temperature or static pressure measurement can be 
used as a measure of the density and viscosity of the stream. In a 
two-phase two-component stream, both a temperature and static pressure 
measurement may be needed. These physical properties are used in the 
mathematical models used to correlate the pressure drop measurements with 
the individual mass flowrates. 
Broadly stated the invention comprises: a flowmeter for measuring 
differential pressures indicative of flowrates in a conduit carrying a gas 
and liquid flowing stream, comprising: first means for creating a 
frictional pressure drop in the conduit; means for measuring the 
frictional pressure drop; second means for creating an accelerational 
pressure drop in the conduit; and means for measuring the accelerational 
pressure drop. 
The invention also broadly contemplates a method for measuring differential 
pressures indicative of flowrates in a conduit carrying a gas and liquid 
flowing stream. The method comprises: creating a frictional pressure drop 
in the conduit; measuring the frictional pressure drop; creating an 
accelerational pressure drop in the conduit; measuring the accelerational 
pressure drop; and determining by mathematical relationships the flowrates 
of the individual phases of the stream.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
The flowmeter 1 of the present invention is functional to create and 
measure pressure drops in the two-phase flow stream, which pressure drops 
can be correlated to the individual flowrates of the two phases. 
The flowmeter 1 is shown in its preferred embodiment in FIGS. 1 and 2. The 
flowmeter 1 includes a twisted tape swirl generator 2 and a venturi 3 
mounted in a horizontal conduit 6 carrying a two-phase flow stream. 
Pressure transducer means 4 and 5 respectively are provided to measure the 
pressure differential across the twisted tape 2 and the venturi 3. 
The twisted tape swirl generator 2 provides a means for creating a 
frictional pressure drop in the horizontal conduit 6. Alternatively a 
linear length of tubing could be used to create a frictional pressure 
drop, however this would necessitate a long length of tubing. Twisted tape 
swirl generators are known in the prior art, see for example E. Smithberg 
et al., "Friction and Forced Convection Heat-Transfer Characteristics in 
Tubes with Twisted Tape Swirl Generators," Journal of Heat Transfer, 
February, 1964, p. 39, and G. S. R. Narasimhamurty et al., "Effect of 
Turbulence Promoters in Two-Phase Gas Liquid Flow in Horizontal Pipes," 
Chemical Engineering Science, Vol. 24, 1969, p. 331. Briefly, the twisted 
tape 2 includes a length of steel tape 7 having a width equal to the 
diameter of the conduit 6. The tape 7 is twisted into the conduit 6 to a 
desired pitch and the ends 8 secured into notches 9 in the conduit 6. 
Preferably the upstream edge 10 of the tape is aligned vertically to split 
the entering liquid phase evenly. 
To measure the frictional pressure drop across the twisted tape 2, two 
pressure taps 11 are provided leadig into the conduit 6, preferably at 
points spaced slightly inwardly from the ends 8 of the tape 7. This 
spacing allows the annular flow pattern, known to be created in the 
twisted tape 2, to develop and also avoids the possible entrance and exit 
pressure losses. Each pressure tap 11 consists of a piezometric ring 12 
sealed around the conduit 6 enclosing an annulus 13 between the ring 12 
and the conduit 6. A plurality of holes 14 through the walls of the 
conduit 6 open into the annulus 13. Through a connecting hole 15 in the 
piezometric ring 12, is connected a pressure line 16 leading to one side 
of a diaphragm magnetic-reluctance transducer 17. The transducer 17 is 
well known in the art and functions to convert a pressure differential 
into an electric signal. 
The venturi 3 is shown in detail in FIG. 2. The venturi 3 provides a means 
for creating an accelerational pressure drop in the conduit 6. 
Alternatively, a nozzle, orifice, segmental baffle or other device, known 
to create an accelerational pressure drop in two-phase flow, can be 
substituted for the venturi. The venturi 3 however is preferred, since it 
is known to accept the annular two-phase flow from the twisted tape 2 and 
also to give a good correlation between the accelerational pressure drop 
measured across the venturi and the total mass flowrate (W). The venturi 3 
is placed downstream of the twisted tape 2 for the above reason. A venturi 
is well known in the prior art and includes a constricted throat section 
18 in which the velocity of the two-phase flow increases while the 
pressure across the throat 18 decreases. 
To measure the accelerational pressure drop across the venturi 3, two 
pressure taps 19 are provided leading into the venturi. As shown in FIG. 
2, the taps 19 are spaced inwardly from the ends of the venturi 3. The 
pressure taps 19 are identical to the pressure taps 11 previously 
disclosed and like reference numerals have been used to indicate like 
parts. A pressure line 20 interconnects the pressure taps 19 to opposite 
sides of a diaphragm magnetic-reluctance transducer 21. 
Since pressure fluctuations in two-phase flow metering are usually high, 
pressure snubbers 22 are preferably included in the pressure lines 16, 20 
between each of the pressure taps 11, 19 and the transducers 17, 21. These 
pressure snubbers 22 are widely used in two-phase flow metering to dampen 
the pressure fluctuations. The snubbers 22 comprise a moveable weighted 
piston (not shown) inserted in a thin capillary tube (not shown). To 
further limit pressure fluctions, the pressure lines 16, 20 are 
periodically purged with either a gas or liquid. The gas or liquid filling 
the lines 16 and 20 acts as a means for transmitting the pressure from the 
pressure taps 11, 19 to the transducers 17, 20. This purging technique is 
standard in two-phase flow metering. 
To protect the electronic transducers 17, 21, isolation valves 25 are 
included in the pressure lines 16, 20 on each side of the transducers 17, 
21. Equalization valves 26 are also included to further protect the 
transducers. 
Opposite ends 23, 24 of the conduit 6 are threaded to connect the flowmeter 
1 with the pipeline (not shown) carrying the two-phase flow. Preferably 
the diameter of the conduit 6 is the same as the diameter of the pipeline 
so as not to further interrupt the two-phase flow. 
In most two-phase flow metering situations, it is desirable to measure a 
third parameter, such as the static pressure of the stream. As will become 
evident from the description to follow, this third parameter is usually 
needed in order to correlate the above two pressure drop measurements with 
the individual flowrates of the two phases. This correlation includes 
physical properties such as the density and viscosity of each of the two 
phases. In a one-component two-phase stream such as wet steam, a 
measurement, of either the static pressure or the temperature of the 
stream, allows one to calculate the density and viscosity of each phase. 
With wet stream for instance,standard steam tables may be used. In a 
two-component two-phase stream both a temperature and static pressure 
measurement may be needed. If however, the flowmeter 1 is to be used in a 
two-phase flow stream having known physical properties, the third 
parameter would not be needed. 
In general, the third parameter can be measured anywhere in proximity to 
the twisted tape 2 and venturi 3. In FIG. 2, means 30 are shown for 
measuring the static pressure of the two-phase flow downstream of the 
venturi. The means 30, includes a pressure tap 27, identical to the 
pressure tap 11, is provided in the conduit 6. A pressure line 28 leading 
from the tap 27 is connected to a pressure sensing device 29, such as an 
open ended mercury manometer or an electronic pressure transducer. If it 
is desirable to measure the temperature of the stream, a suitable 
temperature sensing device (not shown) may be provided in the flowmeter. 
The following example is included to demonstrate the operability of the 
preferred embodiment of the flowmeter, and to show the type of 
calculations involved in correlating the flowmeter measurements with the 
individual flowrates of the two phases. 
EXAMPLE 
A flowmeter as shown in FIGS. 1 and 2 was constructed and inserted into a 
1" diameter pipeline carrying an air-water two-phase flow stream. The 
twisted tape swirl generator consisted of a 1/16".times.1".times.12" 
length of stainless steel tape twisted in an anticlockwise direction (as 
viewed from the upstream end of the flowmeter) to a pitch of 4 inches. The 
venturi consisted of a 33/4" length venturi section having an entrance and 
exit diameter of 1" and a throat diameter of 5/8". The static pressure of 
the two phase flow was measured downstream of the venturi with an open 
ended mercury manometer. 
The D.C. signals from the transducers 17 and 21 were routed to a digital 
readout, chart recorder and mini-computer (not shown). The differential 
pressure signals recorded on the chart recorder were time averaged over 
2-3 minutes. 
To initially calibrate the flowmeter, the air-water stream was injected 
through the flowmeter at known air and water flowrates, W.sub.g and 
W.sub.f respectively, in a quality (x) range of 0.25 to 0.90. 
Ultimately, the measurements from the venturi, twisted tape and static 
pressure sensor are to be combined to define any two of the parameters 
total mass flowrate (W), liquid mass flowrate (W.sub.f), gas mass flowrate 
(W.sub.g) and quality (x). Of course volumetric flowrates can also be 
calculated. 
Theoretical models are known to correlate these pressure drop measurements 
with the above parameters. In this example the twisted tape results were 
modelled by the Lockart-Martinelli parameters X.sup.2 and .phi..sup.2 in 
their following form: 
##EQU1## 
where Re.sub.gt and Re.sub.ft are Reynold's numbers for the gas and liquid 
phases respectively; 
.rho..sub.g and .rho..sub.f are the densities of gas and liquid phases 
respectively; 
##EQU2## 
where (.DELTA.P/.DELTA.L).sub.tpt is the pressure drop across the twisted 
tape 
D.sub.H is the hydraulic diameter of the conduit; 
g.sub.c is a conversion factor=32.17 lb. ft/lb.sub.f s.sup.2 ; 
A is the cross sectional area of the conduit; and 
f is Fannings friction factor. 
The results from the venturi were modelled by the following modified 
Collins parameter F.sub.p and quality (x): 
##EQU3## 
where D is the inside conduit diameter; 
.DELTA.P.sub.tpv is the pressure drop across the venturi; and 
##EQU4## 
The flowmeter was first calibrated with known flowrates W.sub.f and 
W.sub.g. The pressure transducers 17 and 21 were calibrated by known 
techniques using a column of water. The results for the transducer 
calibrations were modelled by the following linear least squares 
equations: 
##EQU5## 
From the measurements of .DELTA.P.sub.tpv, (.DELTA.P/.DELTA.L).sub.tpt and 
the static pressure P.sub.s at a number of known flowrates W.sub.f, 
W.sub.g, a number of values of F.sub.p, n, .phi..sup.2 and X.sup.2 were 
calculated. The values for Re.sub.gt, Re.sub.ft .rho..sub.g, and 
.rho..sub.f were calculated from the values of P.sub.s, the static 
pressure value. Using these results the venturi results were modelled by 
the linear relationship: 
EQU x=m F.sub.p +b, (7) 
and the twisted tape results were modelled by the relationship: 
EQU .phi..sub.g.sup.2 =B.sub.1 +B.sub.2 X+B.sub.3 X.sup.2. (8) 
The parameters m, b, B.sub.1, B.sub.2 and B.sub.3 were derived from a least 
squares analysis for a number of gas mass flowrate, W.sub.g, values. For 
clarification purposes these values for W.sub.g, B.sub.1, B.sub.2 and 
B.sub.3, m and b are reproduced in Table 1. 
TABLE 1 
______________________________________ 
LEAST SQUARES AMETERS FOR THE 
TWISTED TAPE AND VENTURI MODELS 
##STR1## 
W.sub.g (lb/hr) 
B.sub.1 B.sub.2 B.sub.3 mb 
______________________________________ 
64.702427 
1.75059 16.565439 
3.471168 
0.649527 -0.154006 
132.4895 
0.8729569 
35.193932 
-45.160512 
0.560633-0.151019 
159.9971 
1.108096 38.224306 
-55.09309 
0.537628-0.162189 
222.7917 
1.16932 40.792134 
-43.551016 
0.554722-0.205751 
263.138 
1.485076 39.851965 
-24.578145 
0.51217-0.178217 
______________________________________ 
A computer program was constructed to utilize these relationships (7) and 
(8) in a linear interpolation technique to evaluate values for the gas and 
liquid flowrates, W.sub.g and W.sub.f, for a given set of pressure 
readings P.sub.s, (.DELTA.P/.DELTA.L).sub.tpt and .DELTA.P.sub.tpv. The 
computer program utilized is reproduced in FIG. 3. By exploiting the 
W.sub.g level dependency shown in Table 1, values for W.sub.f were 
evaluated for each of equations (7) and (8). Subsequently, two sets of 
W.sub.f and W.sub.g values were generated from the venturi and twisted 
tape equations (7) and (8). The trend of W.sub.f with respect to W.sub.g 
for each set of values was quite different. Thus the intersection of both 
sets of data was used to represent the simultaneous solution of the 
venturi and twisted tape equations (7) and (8). This intersection was 
evaluated by applying a linear interpolation for each set of data points. 
The efficiency of this technique of metering and correlating is illustrated 
in FIGS. 4 and 5 in which the W.sub.f and W.sub.g predicted values are 
plotted against the W.sub.f and W.sub.g actual values. Accuracy was 
generally within about 3% for W.sub.g and 6% for W.sub.f. The accuracy of 
these predictions could be improved if more experimental data were used to 
decrease the size of the interval which required linear interpolation. 
Extrapolation beyond the original range used in calibrating the instrument 
is not advised. 
While the present invention has been disclosed in connection with the 
preferred embodiment thereof, it should be understood that there may be 
other embodiments which fall within the spirit and scope of the invention 
as defined by the following claims.