## Abstrict An apparatus and method for measuring the flow rates of each component
of two-phase flow consisting of a gas and a liquid or three-phase
flow consisting of water, oil and gas, including a first volumetric
flow meter stage, and second and third momentum flow meter stages
coupled in a series flow path with the volumetric flow meter stage
and in which a velocity ratio between the gas and the liquid in
the series flow path is maintained to be one. A processor calculates
flow rates of the components of flow by solving volumetric flow
and momentum or energy equations defining flow through the first
through third stages utilizing a volumetric flow output from the
first stage and momentum flux outputs from said second and third
stages, and an indicator displays flow of liquid and gas or oil,
water and gas components of the flow. To measure three-phase flow,
a water-cut meter is provided to determine the amount of water flow,
which is then used by the processor to determine the flow of the
rest of the liquid. The second and third momentum flow meter stages
can be implemented by two separate momentum flow meters or by a
single momentum flow meter, such as a venturi flow meter having
a venturi nozzle including pressure taps for obtaining at least
two differential pressure measurements. In the event that the density
of the liquid component is known, a single momentum flow meter stage
is sufficient.
## Claims What is claimed as new and desired to be secured by Letters Patent
of the United States is:
1. An apparatus for measuring flow rates of gas and liquid components
in a fluid flowing in a flow path, comprising:
.Iadd.a. .Iaddend.volumetric flow meter .[.means for.]. .Iadd.capable
of .Iaddend.measuring a total flow rate for .[.said.]. .Iadd.a .Iaddend.fluid
and .Iadd.further capable of .Iaddend.outputting a corresponding
total flow rate signal;
.Iadd.b. .Iaddend.first and second momentum flow .[.meter means.].
.Iadd.meters .Iaddend.coupled in series in said flow path with said
volumetric flow meter .[.means.]. for measuring the momentum flux
of .[.said.]. .Iadd.a .Iaddend.fluid and outputting respective first
and second .[.momentum.]. signals .Iadd.indicative of fluid momentum.Iaddend.;
.Iadd.and
c. a .Iaddend.processor .[.means.]. coupled to .Iadd.receive signals
output by .Iaddend.said volumetric flow meter .[.means.]. and said
first and second momentum flow .[.meter means for.]. .Iadd.meters,
said processor capable of .Iaddend.determining the flow rate of
a gas component and the flow rate of a liquid component .[.by solving
predetermined equations for total flow and momentum or energy utilizing
said total flow rate signal and said first and second momentum signals;
and
indicator means for displaying the determined flow rates of said
liquid and gas components.]..
2. An apparatus according to claim 1 further comprising:
.[.means.]. .Iadd.device .Iaddend.for forcing a known velocity
ratio between said gas component and said liquid component in said
flow path.
3. An apparatus according to claim 2 wherein said forcing .[.means.].
.Iadd.device .Iaddend.comprises:
at least one of a static mixer or a dynamic mixer.
4. An apparatus according to claim 3 wherein said forcing .[.means.].
.Iadd.device .Iaddend.comprises:
first and second mixers respectively coupled in series at an input
and an output of said volumetric flow meter.
5. An apparatus according to claim 2 wherein said volumetric flow
meter .[.means and said flow shaping means.]. comprise.Iadd.s.Iaddend.:
a positive displacement flow meter.
6. An apparatus according to .[.claims 1 2 3 4 or 5.]. .Iadd.claim
1.Iaddend., wherein said first and second momentum flow .[.meter
means.]. .Iadd.meters .Iaddend.comprise:
first and second venturi flow meters having different throat dimensions.
7. An apparatus according to claim.[.s.]. 1 .[., 2 3 4 or 5.].
wherein said first and second momentum flow meter means comprise:
a venturi flow meter having a .Iadd.single .Iaddend.venturi nozzle
including plural pressure measuring taps .Iadd.connected to two
or more pressure measuring devices.Iaddend..
8. An apparatus according to claim 1 wherein said first and second
momentum flow .[.meter means.]. .Iadd.meters .Iaddend.comprise:
a drag-disk flow meter having different paddle dimensions.
9. An apparatus according to .[.claims 1 2 3 4 or 5.]. .Iadd.claim
1.Iaddend., further comprising:
.Iadd.a. a .Iaddend.water-cut meter .[.means.]. for measuring an
amount of water in said liquid component and outputting a corresponding
water-cut signal;
.Iadd.b. .Iaddend.said processor .[.means comprising means for.].
.Iadd.coupled to receive a signal output by said water-cut meter
and capable of .Iaddend.determining flow rates of a gas constituent,
a water constituent, and a further constituent of said liquid component
based on said water-cut signal and the determined liquid and gas
flow rates; and
.Iadd.c. .Iaddend..[.said.]. .Iadd.an .Iaddend.indicator .[.means
comprising means for.]. .Iadd.capable of .Iaddend.displaying the
determining flow rates of said water constituent and said further
constituent.
10. An apparatus according to claim 6 further comprising:
.Iadd.a. a .Iaddend.water-cut meter .[.means.]. for measuring an
amount of water in said liquid component and outputting a corresponding
water-cut signal;
.Iadd.b. .Iaddend.said processor .[.means comprising means for.].
.Iadd.coupled to receive a signal output by said water-cut meter
and capable of .Iaddend.determining flow rates of a gas constituent,
a water constituent, and a further constituent of said liquid component
in said fluid based on said water-cut signal and the determined
liquid and gas flow rates; and
.Iadd.c. .Iaddend..[.said.]. .Iadd.an .Iaddend.indicator .[.means
comprising means for.]. .Iadd.capable of .Iaddend.displaying the
determined flow rates of said water constituent and said further
constituent.
11. An apparatus according to claim 7 further comprising:
.Iadd.a. a .Iaddend.water-cut meter .[.means.]. for measuring an
amount of water in said liquid component and outputting a corresponding
water-cut signal;
.Iadd.b. .Iaddend.said processor .[.means comprising means for.].
.Iadd.coupled to receive a signal output by said water-cut meter
and capable of .Iaddend.determining flow rates of a gas constituent,
a water constituent, and a further constituent of said liquid component
in said fluid based on said water-cut signal and the determined
liquid and gas flow rates; and
.Iadd.c. .Iaddend..[.said.]. .Iadd.an .Iaddend.indicator .[.means
comprising means for.]. .Iadd.capable of .Iaddend.displaying the
determined flow rates of said water constituent and said further
constituent.
12. An apparatus according to claim 1 further comprising:
.Iadd.a. .Iaddend..[.means for.]. .Iadd.a device capable of .Iaddend.measuring
a pressure drop across the series flow path of said volumetric flow
meter .[.means.]. and said first and second momentum flow .[.meter
means.]. .Iadd.meters .Iaddend.and producing a corresponding pressure
drop signal;
.Iadd.b. .Iaddend.memory .[.means.]. for storing a table of differential
pressure drops as a function of plural values of air flow rate and
water flow rate through said series flow path;
.Iadd.c. .Iaddend..[.means.]. .Iadd.device .Iaddend.for selecting
from said table stored in said memory .[.means.]. a corresponding
differential pressure drop based on the measured gas and liquid
flow rates;
.Iadd.d. .Iaddend..[.means.]. .Iadd.device .Iaddend.for calculating
a pressure drop ratio of said pressure drop signal and the selected
differential pressure drop and outputting a corresponding pressure
drop ratio signal; and
.Iadd.e. .Iaddend..[.means.]. .Iadd.device .Iaddend.for multiplying
said pressure drop ratio signal with a predetermined signal indicative
of a pressure drop of an air/water mixture through a different flow
path to determine a pressure drop of said fluid in said different
flow path.
13. An apparatus for measuring flow rates of a gas component and
a liquid component having a known density in a fluid flowing in
a series flow path, comprising:
.Iadd.a. .Iaddend.volumetric flow meter .[.means.]. for measuring
a total flow rate for said fluid and outputting a corresponding
total flow rate signal;
.Iadd.b. a .Iaddend.momentum flow meter .[.means.]. coupled in
series in said flow path with said volumetric flow meter .[.means.].
for measuring the momentum flux of said fluid and outputting a corresponding
momentum signal;
.Iadd.c. .Iaddend.processor .[.means.]. coupled to said volumetric
flow meter .[.means.]. and said momentum flow meter .[.means.].
for determining the flow rate of said gas component and the flow
rate of said liquid component by solving predetermined equations
for total flow and momentum or energy utilizing said total flow
rate signal and said momentum signal;
.Iadd.d. .Iaddend..[.means.]. .Iadd.device .Iaddend.for measuring
a pressure drop across the series flow path of said volumetric flow
meter .[.means.]. and said momentum flow meter .[.means.]. and producing
a corresponding pressure drop signal;
.Iadd.e. .Iaddend.memory .[.means.]. for storing a table of differential
pressure drops as a function of plural values of air flow rate and
water flow rate through said series flow path;
.Iadd.f. .Iaddend..[.means.]..Iadd.device .Iaddend.for selecting
from said table stored in said memory means a corresponding differential
pressure drop based on the measured gas and liquid flow rates;
.Iadd.g. .Iaddend..[.means.]. .Iadd.device .Iaddend.for calculating
a pressure drop ratio of said pressure drop signal and the selected
differential pressure drop and outputting a corresponding pressure
drop ratio signal; and
.Iadd.h. .Iaddend..[.means.]. .Iadd.device .Iaddend.for multiplying
said pressure drop ratio signal with a predetermined signal indicative
of a pressure drop of a known mixture through a different flow path
to determine a pressure drop of said fluid in said different flow
path.
14. An apparatus according to claim 13 further comprising:
.[.means.]. .Iadd.device .Iaddend.for forcing a known velocity
ratio between said gas component and said liquid component in said
flow path.
15. An apparatus according to claim 14 wherein said forcing .[.means.].
.Iadd.device .Iaddend.comprises:
first and second mixes respectively coupled in series at an input
and an output of said volumetric flow meter.
16. An apparatus according to claim 14 wherein said volumetric
flow meter .[.means.]. and said forcing .[.means.]. .Iadd.device
.Iaddend.comprise:
a positive displacement flow meter.
17. An apparatus according to claim 13 wherein said momentum flow
meter .[.means.]. comprises:
a venturi flow meter.
18. An apparatus according to .[.claims 13 14 15 or 16.]. .Iadd.claim
13.Iaddend., further comprising:
.Iadd.a. a .Iaddend.water-cut meter .[.means.]. for measuring an
amount of water in said liquid component and outputting a corresponding
water-cut signal;
.Iadd.b. .Iaddend.said processor .[.means.]. comprising .[.means.].
.Iadd.device .Iaddend.for determining flow rates of a gas constituent,
a water constituent, and a further constituent of said liquid component
based on said water-cut signal and the determined liquid and gas
flow rates; and
.Iadd.c. .Iaddend..[.means.]. .Iadd.device .Iaddend.for displaying
the determined flow rates of said water constituent and said further
constituent.
19. A method for measuring flow rates of gas and liquid components
in a fluid flowing in a series flow path, comprising:
.Iadd.a. .Iaddend.measuring a total flow rate in said flow path
and outputting a corresponding total flow rate signal;
.Iadd.b. .Iaddend.measuring the momentum flux of said fluid at
first and second points in said series flow path and outputting
respective first and second .[.momentum.]. signals .Iadd.indicative
of fluid momentum.Iaddend.;
.Iadd.c. .Iaddend.determining the flow rate of said gas component
and the flow rate of said liquid component .[.by solving predetermined
equations for total flow and momentum or energy.]. utilizing said
total flow rate signal and said first and second .[.momentum.].
signals.[.; and.]. .Iadd.indicative of fluid momentum; .Iaddend.
.[.displaying the determined flow rates of said liquid and gas
components.]..
20. A method according to claim 19 further comprising:
forcing a known velocity ratio between said gas component and said
liquid component in said flow path.
21. A method according to .[.claims.]. .Iadd.claim .Iaddend.19
.[.or 20.]., further comprising:
.Iadd.a. .Iaddend.measuring an amount of water in said liquid component
and outputting a corresponding water-cut signal;
.Iadd.b. .Iaddend.determining flow rates of a gas constituent,
a water constituent, and a further constituent of said liquid component
in said fluid based on said water-cut signal and the determined
liquid and gas flow rates.[.; and
displaying the determined flow rates of said water constituent
and said further constituent.]..
22. A method according to claim 20 further comprising:
.Iadd.a. .Iaddend.measuring a pressure drop across said series
flow path and producing a corresponding pressure drop signal;
.Iadd.b. .Iaddend.storing .[.a table of.]. differential pressure
.[.drops.]. .Iadd.drop data .Iaddend.as a function of plural values
of said flow rate and water flow rate through said series flow path;
.Iadd.c. .Iaddend.selecting from the stored .[.table.]. .Iadd.data
.Iaddend.a corresponding differential pressure drop based on the
measured gas and liquid flow rates;
.Iadd.d. .Iaddend.calculating a pressure drop ratio of said pressure
drop signal and the selected differential pressure drop and outputting
a corresponding pressure drop ratio signal; and
.Iadd.e. .Iaddend.multiplying said pressure drop ratio signal with
a predetermined signal indicative of a pressure drop of an air/water
mixture through a different flow path to determine a pressure drop
of said fluid in said different flow path.
23. A method of measuring flow rates of a gas component and a liquid
component having a known density in a fluid flowing in a series
flow path, comprising:
.Iadd.a. .Iaddend.measuring a total flow rate in said flow path
and outputting a corresponding total flow rate signal;
.Iadd.b. .Iaddend.measuring the momentum flux of said fluid in
said series flow path and outputting a corresponding .[.momentum.].
signal .Iadd.indicative of fluid momentum.Iaddend.;
.Iadd.c. .Iaddend.determining the flow rate of said gas component
and the flow rate of said liquid component by solving predetermined
equations for total flow and momentum or energy utilizing said total
flow rate signal and said .[.momentum signals.]. .Iadd.signal.Iaddend.;
.Iadd.d. .Iaddend.measuring a pressure drop across said series
flow path and producing a corresponding pressure drop signal;
.Iadd.e. .Iaddend.storing .[.a table of.]. differential pressure
.[.drops.]. .Iadd.drop data .Iaddend.as a function of plural values
of said flow rate and water flow rate through said series flow path;
.Iadd.f. .Iaddend.selecting from the stored .[.table.]. .Iadd.data
.Iaddend.a corresponding differential pressure drop based on the
measured gas and liquid flow rates;
.Iadd.g. .Iaddend.calculating a pressure drop ratio of said pressure
drop signal and the selected differential pressure drop and outputting
a corresponding pressure drop ratio signal; and
.Iadd.h. .Iaddend.multiplying said pressure drop signal with a
predetermined signal indicative of a pressure drop of a known mixture
through a different flow path to determine a pressure drop of said
fluid in said different flow path.
24. A method according to claim 23 further comprising:
forcing a known velocity ratio between said gas component and said
liquid component in said flow path to be one.
25. A method according to .[.claims.]. .Iadd.claim .Iaddend.23
.[.or 22.]., further comprising:
.Iadd.a. .Iaddend.measuring an amount of water in said liquid component
and outputting a corresponding water-cut signal;
.Iadd.b. .Iaddend.determining flow rates of a gas constituent,
a water constituent, and a further constituent of said liquid component
in said fluid based on said water-cut signal and the determined
liquid and gas flow rates; and
.Iadd.c. .Iaddend.displaying the determined flow rates of said
water constituent and said further constituent.
## Description BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to-an apparatus and method for measuring
two-phase flow (liquid/gas) or three-phase flow (liquid/liquid/gas)
of fluids.
2. Discussion of Background
The measurement of oil, water and gas flow finds application in
various fields. In oil production, it is required for reservoir
control and fiscal reasons. High accuracy of measurement is necessary
as well as small instrumentation space requirements. Additional
applications exist in petrochemical, nuclear and other industries.
In the past, three principal methods have been utilized for flow
measurements.
As disclosed in U.S. Pat. No. 4760742 the gas in a liquid is
physically separated from the liquid, and each fluid is measured
separately. A water-cut monitor is used to measure the amount of
the water and the oil in the liquid phase. Two conventional single-phase
flow meters are used to measure the gas and the liquid flow rates.
This method can yield high accuracy, but require gas-separating
devices which are either very large or are very sensitive to flow
rates and the liquid's viscosity, surface tension, etc.
A second approach is described in U.S. Pat. Nos. 4168624 and
4050896 wherein the total flow is measured at two different flow
conditions (for example: different temperatures and different pressures
along the pipeline). The changing of the gas volume during the change
of this condition makes it possible to calculate the flow rates
of the gas and the liquid. To achieve high accuracy in this method,
a large difference in flow conditions between the two flow meters
is required. This requires a large pressure drop, which is costly
in terms of pumping energy.
A third technique as described by Baker, "Measuring Multi-Phase
Flow", Chemical Engineer, No 453 pp 39-45 October 1988 and
Reimann et al, "Measurement of Two-Phase Mass Flow Rate: A
Comparison of Different Techniques", Int J. of Multi-Phase
Flows, Vol. 8 No. 1 pp. 33-46 1982 measures the total momentum
flux, total density, total volumetric flow rate, and the water cut.
All are required to calculate the amount of gas, oil and water.
One such device uses the combination of a turbine flow meter, a
venturi flow meter, a gamma ray densitometer or void fraction meter
and a water-cut monitor. The advantage of this method is that it
enables the use of venturies which have low pressure drops. The
weak link in this technique is the densitometer, which is sensitive
to the flow characteristics and the fluid's contaminants (heavy
metals, etc.).
In many multi-phase flow applications it is desirable to predict
the pressure drops which will occur in various piping apparata with
different combinations of multi-phase fluids. This information is
critical to piping design, pump sizing, etc. While information has
been compiled on the pressure drops of a two-phase fluid comprising
of water and air, it has not been possible to predict the pressure
drops for other, more unique multi-phase fluids.
SUMMARY OF THE INVENTION
Accordingly, one object of the invention is to provide a new and
improved apparatus and method for measuring multiphase flow by means
of simple, low cost, compact equipment which has high flow rate
measuring accuracy.
Another object is to provide a novel apparatus and method for measuring
multi-phase flow and which entails small pressure drops and therefore
requires little pumping energy.
Yet a further object is to provide a novel apparatus and method
as above noted, which does not need gas separating devices or densitometers
or measurement of a void fraction to perform the flow measurement.
Still a further object of this invention is to provide a novel
apparatus and method capable of developing a table predicting the
pressure drops which will occur in piping apparata for different
multi-phase fluids.
These and other objects are achieved according to the present invention
by providing a novel apparatus for measuring the flow rates of each
component of two-phase flow consisting of a gas and a liquid, including
a first volumetric flow meter stage, second and third momentum flow
meter stages coupled in a series flow path with the volumetric flow
meter stage, wherein a velocity ratio between the gas and the liquid
in the series flow path is maintained at a known value, e.g., one,
and a processor for calculating flow rates of the components of
flow by solving volumetric flow and momentum or energy equations
defining flow through the first through third stages utilizing a
volumetric flow output from the first stage and momentum flux outputs
from said second and third stages, and an indicator for displaying
flow rates of the liquid and gas components of the two-phase flow.
The second and third momentum flow meter stages can be implemented
by two separate momentum flow meters or by a single momentum flow
meter having a venturi nozzle including at least three pressure
taps for obtaining at least two differential pressure measurements.
In the event that the density of the liquid component is known,
a single momentum flux measurement from a single momentum flow meter
stage is sufficient to measure two-phase flow.
To measure three-phase (oil, water, gas) flow a water-cut meter
is provided to determine the amount of water flow, which is then
used by the processor to determine the amount of oil flow. The flow
rates of oil, water and gas are then displayed.
To enable prediction of multi-phase fluid pressure drops in various
flow apparata, a differential pressure measurement is taken across
the first through third (and optionally fourth) stages, and means
are provided to calculate and display ratios of the pressure drops
of multi-phase fluids relative to the known pressure drops of fluids
comprising water and air.
BRIEF DESCRIPTION OF THE DRAWINGS
A more complete appreciation of the invention and many of the attendant
advantages thereof will be readily obtained as the same becomes
better understood by reference to the following detailed description
when considered in connection with the accompanying drawings, wherein:
FIG. 1 is a block diagram of an apparatus for two-phase flow measurement
according to the present invention;
FIG. 2 is a schematic diagram of an apparatus for two-phase flow
measurement according to the present invention, utilizing two venturi
tubes and an ultra-sonic flow meter;
FIG. 3 is a schematic of a preferred embodiment for measuring two-phase
flow, using a combination of a single modified venturi meter with
a positive displacement flow meter;
FIG. 4 is a schematic diagram of an embodiment of the present invention
for three-phase flow with the flow meter shown in FIG. 3 and a water-cut
monitor;
FIG. 5 is a schematic diagram illustrating how the flow meter shown
in FIG. 4 can be used to measure the relative pressure drop of a
three-phase fluid; and
FIG. 6 is a flow chart of the overall process of the present invention
for measuring three-phase flow and determining pressure drop ratios,
according to the apparata described in relation to FIGS. 2-5.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring now to the drawings, wherein like reference numerals
designate identical or corresponding parts throughout the several
views, and more particularly to FIG. 1 thereof, there is shown schematically
an embodiment of the apparatus of the invention, including a volumetric
flowmeter 10 serving as a first stage in which a mixture of gas
and liquid flows through the volumetric flow meter 10. This flow
meter 10 measures the total flow rate for the mixture. The mixture
then flows through second and third stages, consisting of two momentum
flow meters 12 and 14 with different dimensions (for example, two
venturi flow meters with different throat diameters). Momentum flow
meters are flow meters that measure the momentum flux of the fluid
(M=mv). In order to avoid using a void fraction meter, the present
invention forces the velocity ratio between the gas and the liquid
(slip ratio) inside the apparatus to be a known value, a slip ratio
of one being conveniently enforced. This is achieved through using
either static or dynamic mixers or a positive displacement meter.
In each stage the absolute pressure and temperature are measured
by means of temperature transducers 16 and pressure transducers
18. One momentum flow meter can also be used by itself, in the instance
that the liquid component's density is known. The data from Stages
1 2 and 3 is transferred to a computer 20 that calculates the flow
rates of the liquid and the gas components by solving equations
presented hereinafter.
FIG. 2 shows an example of a more concrete embodiment of the invention
for two-phase flow measurement. Stage 1 is an ultra-sonic flow meter
10.sub.1 installed between two static mixers 22 and 24. The ultrasonic
flow meter measures volumetric flow. Other volumetric flow meters
can also be used, such as turbine, vortex shedding, magnetic, heat
transfer, variable area, paddle and Coriolis volumetric flow meter.
In this modification the static mixers 22 24 are used to force
a unitary velocity ratio between the phases. Instead of measuring
the absolute pressure independently in each stage, the absolute
pressure is measured with a pressure transducer 18 in stage 1 and
is calculated using differential pressure transducers 26 and 28
in stages 2 and 3.
The two momentum flow meters shown in FIGS. 1 and 2 can be reduced
to one, by drilling one more pressure tap along the venturi nozzle,
as shown in FIG. 3. Such a modified venturi flowmeter is designated
by numeral 31 in FIG. 3. Here the volumetric flow meter 10.sub.2
is a positive displacement (P.D.) type. The advantage of using a
P.D. flow meter is that it provides an exact measurement of the
sum of the liquid and gas flow rates, will no slip between the gas
and liquid phases inside the meter or immediately after the meter.
Thus, the P.D. flow meter forces the slip ratio to a known amount,
i.e., unity, and permits dispensing with the static mixers of the
FIG. 2 embodiment.
The embodiments shown in FIG. 1-3 are above-described using one
or two venturi-type momentum flow meters. However, it should be
understood that other momentum flow meters can be used to practice
the present invention. For example, a target or drag-disk-type flow
meter having different paddle dimensions can also be utilized to
obtain sufficient parametric data to solve the energy and momentum
equations of the fluids. For more detail about particular instrumentation
described herein, see Hewitt, G. F., "Measurement of Two Phase
Flow Parameters", Whitstable, Litho Ltd , Whitstable, Kent,
Great Britain, 1978 and Holman, J. P., "Experimental Methods
for Engineers", McGraw-Hill Book Company, 1978.
The differential pressure transducers 26 and 28 measure the pressure
difference along the venturi nozzle. A three-phase flowmeter in
which a mixture of oil, water and gas can be measured is constructed
with the addition of a fourth stage water-cut meter. FIG. 4 shows
a water-cut meter 32 (such as described in U.S. Pat. Nos. 4503383
and 4771680) that measures the water concentration c of the mixture.
Absolute pressure and temperature are measured in this stage by
transducers 16 and 34 respectively. Reference numeral 31 designates
the modified venturi flowmeter having the pressure taps 1-3 and
associated transducers shown in FIG. 3 in correspondence with stages
2 and 3 shown in FIG. 1. Because of the change in the specific volume
of the gas (v=p/RT), measurement of the absolute pressure and temperature
at all stages is necessary.
Next described is the analytical basis by which the present invention
performs flow measurements utilizing momentum equations. In the
following analysis, the following English and Greek letters and
subscripts are used and have the noted meanings:
English letters
A--cross section
c--percent of water
d--longitude differential
g--gravity constant
m--total mass flux
M--momentum flux
p--pressure
P--circumference
Q--volumetric flow rate
R--gas constant
s--velocity ratio between the gas and the liquid ("slip")
T--absolute temperature
v--specific volume
x--quality
Greek letters
.alpha.--void fraction
B--slope of the instrumentation
.rho.--density
.tau.--wall shear
Subscripts
G--gas
O--oil
PD--pointer displacement
TOTAL--sum of all the fluid components
TP--two-phase
W--water
In performing a two-phase flow measurement, Q.sub.L and Q.sub.G
are unknowns, but not the only unknowns.
The density of the liquid is also unknown (other unknown properties
of the liquid and the gas have only a minor effect on the present
method, and are therefore ignored here). The three equations that
need to be solved for three unknowns are the following:
1) The volumetric flow meter equation for stage 1:
Q.sub.PD is derived from the volumetric flow meter output.
2) The momentum equation for stage 2 (for example the venturi meter
shown in FIG. 3 from tap 1 to tap 2):
where .rho..sub.1 -.rho..sub.2 is the differential pressure derived
from transducer 28 in FIG. 3.
3) The momentum equation for stage 3 (for example the venturi meter
shown in FIG. 3 from tap 1 to tap 3):
where .rho..sub.1 -.rho..sub.3 is the differential pressure derived
from transducer 30 in FIG. 3.
Certain assumptions must be made for the equations to be solvable:
1) The expansion of the gas along the venturi nozzle is isothermal.
2) Evaporation and dissolution of vapor and gas are negligible.
3) The ideal gas equation holds, and the liquid is incompressible.
4) The velocity ratio between the gas and the liquid=1 or can
be found experimentally as a function of the liquid and the gas
flow rates.
Equations 2 and 3 shown here in general form, are in fact integral
equations derived from the full expression of the momentum equation
(see Hetsroni, G., "Handbook of Multi-Phase Systems",
Chaps 1.2 2.1 2.3 Hemisphere Publishing Corporation, U.S.A.,
1982).
The momentum equation can be simplified to a model for one-dimensional,
steady-state flow based on the Separated Two-Phase Flow model (see
Hetsroni, G., supra) and can integrate from the first tap of the
venturi to the second tap: ##EQU1## and from the first tap of the
venturi to the third tap: ##EQU2##
In equations 4 and 5 .rho..sub.TP, m, x and .alpha. are functions
of Q.sub.G, Q.sub.L and .rho..sub.L : ##EQU3##
Substituting equations 6 7 8 and 9 into equations 4 and 5 and
then solving with equation 1 provides solutions for Q.sub.L, Q.sub.G
and .rho.L since we have three equations and three unknowns.
Equations 4 and 5 are solved using known numerical analysis techniques.
The selection of a particular numerical analysis technique is based
on a trade-off between accuracy and speed of execution, and is a
function also of the availability of fast and economic computation
devices. The relative merits of some techniques are discussed in
Scheid, "Theory and Problems of Numerical Analysis", Schaum's
Outline Series, McGraw-Hill Book Co., 1968. The technique most appropriate
for equations 4 and 5 today, is the Runge-Kutta method described
in Chapter 19 of Scheid, supra. It is anticipated, however, that
the development of cheaper and faster computation devices, or more
efficient or more accurate methods of solving integral equations,
will suggest other techniques to be utilized in the future. Similarly,
a method well suited for solving the set of equations 1 4 and 5
is the Newton method described in Chapter 25 of Scheid.
More or less detailed, and different types of models can be written
as well, depending on the required accuracy of the meter. Applying
the momentum equations provides a much more accurate solution than
the energy equations, since the momentum equations only have to
take into account the friction on the wall (easy to estimate), as
compared with the energy equations which have to take into account
the energy losses (very difficult to estimate). Generally, it is
considered that the present invention utilizes conservation equations,
which can be either momentum or energy equations (see Hetsroni,
supra).
The equation for deriving three-phase flow (oil/water/gas) by the
addition of a water-cut meter in stage 4 is: ##EQU4## The liquid
flow rate is the sum of the water and the oil flow rates:
Therefore, the equation for determining the water flow rate can
be written as:
and then Q.sub.O can be derived from equation 12 once Q.sub.W is
known.
FIG. 5 shows how the multi-phase flow meter can also be used to
predict pressure drops for different multi-phase fluids in different
piping devices. The addition of differential pressure transducer
(36) provides measurement of the pressure drop across the meter.
In the calibration process a look-up table is generated, which contains
the measured pressure drop across the meter when different proportions
and rates of water and air are flowed through it. In effect the
look-up table is a matrix of values of .DELTA.P.sub.water/air for
different values of Q.sub.air and Q.sub.water.
When a multi-phase fluid consisting of different components than
water and air flows through the meter, stages 1 2 and 3 measures
Q.sub.G and Q.sub.L, while stage 5 measures the differential pressure
across the meter (.DELTA.P.sub.fluid). The .DELTA.P.sub.water/air
that corresponds to the equivalent air and water values for the
measured Q.sub.G and Q.sub.L of the working fluid is then looked
up in the above-noted look-up table, and the pressure drop ratio
is calculated.
The equation for the pressure drop ratio of the working multi-phase
fluid relative to an equivalent water/air mixture is: ##EQU5##
Once this ratio has been calculated, it can be applied to obtain
an accurate prediction of the pressure drop of multi-phase fluids
in other devices in the line, where the pressure drop of an equivalent
water/air mixture is known.
For example, to obtain the pressure drop in a vertical pipe in
a field pipe line where crude oil, water and natural gas are flowing,
a priori knowledge of the present drop for an air/water mixture
in the same vertical pipe at the same flow rate is needed. This
can be found in field handbooks (see Perry et al, "Chemical
Engineer's Handbook", McGraw-Hill , Book Co., 1973 pp. 5.40-5.47).
Multiplication of this number with the pressure drop ratio calculated
according to the present invention provides an accurate prediction
of the pressure drop across the vertical pipe for the working fluid.
FIG. 6 shows a flow chart that summarizes the process of the present
invention.
In FIG. 6 in step 100 the output of the volumetric flow meter
10 Q.sub.PD, is measured. In step 110 differential pressure, .rho..sub.1
-.rho..sub.2 is measured. In step 120 the differential pressure
.rho..sub.1 -.rho..sub.3 is measured. In step 130 the water-cut,
c, is measured. The outputs of the steps 100 110 120 and 130 are
fed to the computer 20 which then calculates Q.sub.L, Q.sub.G and
.rho..sub.L, solving equations 1 4 and 5 and utilizing equations
6-9. In step 150 Q.sub.water and Q.sub.oil are calculated utilizing
equations 10-12 and in step 160 the results of the various calculations
performed as thus far described, Q.sub.G, Q.sub.water and Q.sub.oil
are displayed.
FIG. 6 also illustrates steps by which the ratio .DELTA.P.sub.fluid
/.DELTA.P.sub.water/air is determined. In step 170 .DELTA.P.sub.fluid
is measured by means for the sensor 36 shown in FIG. 5. In step
180 a look-up table is utilized to determine .DELTA.P.sub.water/air,
based on the values of Q.sub.L and Q.sub.G determined in step 140.
In step 190 the ratio of .DELTA.P.sub.luid, determined in step 170
and .DELTA.P.sub.water/air, determined in step 180 is determined
and likewise displayed in step 160.
Obviously, numerous modifications and variations of the present
invention are possible in light of the above teachings. It is therefore
to be understood that within the scope of the appended claims, the
invention may be practiced otherwise than as specifically described
herein. |