## Abstrict This invention is related to flow meter instrumentation. More particularly,
the invention is related to obstruction flow meters which are used
in series in a flow conduit to determine the volume flow rate of
liquid and gas phases of fluid flowing within the conduit. Multiple
flow meters including at least one obstruction type flow meter are
positioned serially within a flow conduit such as a pipe. Mathematical
equations are developed for each flow meter based upon measured
quantities and phase flow rates within the liquid stream. These
equations are then solved simultaneously to obtain the desired phase
flow rates. Two flow meters are used to determine the gas and liquid
flow rates. Alternately three flow meters are used to determine
the flow rates of a gas and two liquid phases.
## Claims What is claimed is:
1. A multiple-phase flow meter for measuring a multiple-phase flow
in a conduit, comprising: at least two flow meters including at
least one obstruction flow meter serially disposed in the conduit
so that the at least two flow meters each having an upstream side
and a downstream side, and any two adjacent flow meters have an
intermediate region therebetween, the at least two flow meters being
spaced at a minimum such that the downstream flow meter encounters
little of the flow profile distortion caused by the upstream flow
meter so that the performance of the downstream flow meter is not
substantially degraded, and spaced at a maximum such that a percentage
of flow constituents remains substantially the game from the upstream
flow meter to the downstream flow meter; a plurality of sensors
located upstream, downstream, and in the intermediate region of
the at least N flow meters, the plurality of sensors measuring predetermined
characteristics of the multi-phase flow; and a processor coupled
to the plurality of sensors and capable of computing a total mass
flow rate of the multiple-phase flow by computing a quality of the
multiple-phase flow based on the measured predetermined characteristics.
2. The multiple-phase flow meter of claim 1 wherein the processor
is capable of computing quality and total mass flow rate of the
multiple-phase flow by:
such as: ##EQU7##
where, m=total mass flow rate, ##EQU8## K=flow coefficient, Y=expansion
factor, d=orifice diameter=.beta.D, D=pipe diameter, .rho.=density
of gas, liquid, or mixture, .DELTA.P=pressure drop across orifice
plate, P1 P4=pressure differential measured across the two plates,
3. The multiple-phase flow meter of claim wherein the processor
is capable of computing quality and total mass flow rate of the
multiple-phase flow by:
such as: ##EQU10##
where, m=total mass flow rate, ##EQU11## K=flow coefficient, Y=expansion
factor, d=orifice diameter=.beta.D, D=pipe diameter, .rho.=density
of gas, liquid, or mixture, .DELTA.P=pressure drop across orifice
plate, P.sub.1 P.sub.4 =pressure differential measured across the
two plates,
4. The multiple-phase flow meter of claim 1 wherein the at least
one obstruction flow meter comprises a plate with a plurality of
openings defined therein, the plurality of openings arranged in
a predetermined pattern.
5. The multiple-phase flow meter of claim 4 wherein the plurality
of openings on the plate comprise: a first series of openings positioned
in an inner circle, the first series of openings having a combined
area, the inner circle having a surface area; at least one second
series of openings positioned in a ring concentric to the inner
circle, the at least one second series of openings having a combined
area, the ring having a surface area; and a first ratio of the combined
area of the first series of openings to the inner circle surface
area being substantially the same as at least one second ratios
of the combined area of the subsequent series of openings to the
ring surface area.
6. The multiple-phase flow meter of claim 4 wherein the plurality
of openings on the plate comprise: at least two concentric series
of openings positioned in at least two concentric circular areas
on the plate, the openings of each of the at least two concentric
series of openings having a combined area, the at least two concentric
circular areas each having a surface area; and ratios of the combined
area of each of the at least two concentric series of openings to
its respective circular area surface area being substantially the
same.
7. The multiple-phase flow meter of claim 1 wherein the at least
two flow meters comprises a first obstruction flow meter and a second
obstruction flow meter, wherein the plurality of sensors comprise
a first pressure sensor disposed in the upstream side of the first
obstruction flow meter, second and third pressure sensors disposed
in the intermediate region between the first and second obstruction
flow meters, a fourth pressure sensor disposed in the downstream
side of the second obstruction flow meter, and a temperature sensor
disposed in the conduit.
8. The multiple-phase flow meter of claim 1 wherein the at least
two flow meters comprises a first obstruction flow meter and a second
obstruction flow meter, wherein the plurality of sensors comprises
a first pressure sensor disposed in the upstream side of the first
obstruction flow meter, a second pressure sensor disposed in the
intermediate region between the first and second obstruction flow
meters, a third pressure sensor disposed in the downstream side
of the second obstruction flow meter, and a temperature sensor disposed
in the conduit.
9. The multiple-phase flow meter of claim 1 wherein the at least
two flow meters comprises first, second and third obstruction flow
meters, wherein the plurality of sensors comprises a first pressure
sensor disposed in the upstream side of the first obstruction flow
meter, second and third pressure sensors disposed in the intermediate
region between the first and second obstruction flow meters, fourth
and fifth pressure sensors disposed in the intermediate region of
the second and third obstruction flow meters, a sixth pressure sensor
disposed in the downstream side of the third obstruction flow meter,
and a temperature sensor disposed in the conduit.
10. The multiple-phase flow meter of claim 1 wherein the at least
two flow meters comprises first, second and third obstruction flow
meters, wherein the plurality of sensors comprises a first pressure
sensor disposed in the upstream side of the first obstruction flow
meter, a second pressure sensor disposed in the intermediate region
between the first and second obstruction flow meters, a third pressure
sensor disposed in the intermediate region of the second and third
obstruction flow meters, a fourth pressure sensor disposed in the
downstream side of the third obstruction flow meter, and a temperature
sensor disposed in the conduit.
11. The multiple-phase flow meter of claim 1 wherein the at least
two flow meters comprises an obstruction flow meter and at least
one non-obstruction flow meter, wherein the plurality of sensors
comprise a first pressure sensor disposed in the upstream side of
the obstruction flow meter, second and third pressure sensors disposed
in the intermediate region between the obstruction flow meter and
the at least one non-obstruction flow meter, a fourth pressure sensor
disposed in the downstream side of the at least one non-obstruction
flow meter, and a temperature sensor disposed in the conduit.
12. The multiple-phase flow meter of claim 11 wherein the at least
one non-obstruction flow meter is a vortex meter.
13. The multiple-phase flow meter of claim 11 wherein the at least
one non-obstruction flow meter is a Venturi meter.
14. The multiple-phase flow meter of claim 11 wherein the at least
one non-obstruction flow meter is a densitometer.
15. The multiple-phase flow meter of claim 1 further comprising
a memory device coupled to the processor.
16. The multiple-phase flow meter of claim 1 wherein the spacing
between adjacent flow meters is equal to at least one diameter of
the conduit.
17. The multiple-phase flow meter of claim 1 wherein the spacing
between adjacent flow meters is between one and 12 diameters of
the conduit.
18. The multiple-phase flow meter of claim 2 wherein a thickness
of the upstream obstruction flow meter is equal to between four
and eight widths of an opening in the plate.
19. A method for measuring a multiple-phase flow of a fluid in
a conduit, comprising steps of: measuring at least one pressure
and a temperature of the fluid; measuring at least one pressure
differential of the fluid across each of at least two flow meters
including at least one obstruction flow meter serially disposed
in the conduit, the spacing between the at least two flow meters
being such that a percentage of flow constituents remains the same
between the at least two flow meters; and generating a flow rate
of each phase of the fluid from the at least one pressure, the temperature,
and the at least one pressure differential by calculating a quality
of the multiple-phase flow.
20. The method, as set forth in claim 19 wherein flow rate generating
comprises computing quality and total mass flow rate of the multiple-phase
flow by:
such as: ##EQU13##
where, m=total mass flow rate, ##EQU14## K=flow coefficient, Y=expansion
factor, d=orifice diameter=.beta.D, D=pipe diameter, .rho.=density
of gas, liquid, or mixture, .DELTA.P=pressure drop across orifice
plate, P.sub.1 P.sub.4 =pressure differential measured across the
two plates,
21. The method, as set forth in claim 19 wherein flow rate generating
comprises computing quality and total mass flow rate of the multiple-phase
flow by:
##EQU16##
where, m=total mass flow rate, ##EQU17## K=flow coefficient, Y=expansion
factor, d=orifice diameter=.beta.D, D=pipe diameter, .rho.=density
of gas, liquid, or mixture, .DELTA.P=pressure drop across orifice
plate, P.sub.1 P.sub.4 =pressure differential measured across the
two plates,
22. The method, as set forth in claim 19 wherein flow rate generating
comprises: calculating at least one discharge coefficient; calculating
at least one Reynolds number (Re) and at least one quality (x);
and calculating at least one flow rate.
23. The method, as set forth in claim 22 wherein the at least
one discharge coefficient calculating step comprises solving an
equation wherein each of the at least one discharge coefficients
is a function of the at least one pressure, the temperature, and
the at least one pressure differential.
24. The method, as set forth in claim 22 wherein the at least
one Reynolds number and at least one quality calculating step comprises
solving two equations with two unknowns from the generalized equation:
wherein i is the index number of the obstruction flow meters considered.
25. The method, as set forth in claim 19 further comprising spacing
adjacent flow meters such that the downstream flow meter encounters
little of the flow profile distortion introduced by the upstream
flow meter, so that the performance of the downstream flow meter
is not significantly degraded.
26. The method, as set forth in claim 19 further comprising spacing
adjacent flow meters between one and 12 diameters of the conduit
apart.
27. The method, as set forth in claim 19 further comprising using
an obstruction flow meter with openings of a predetermined width,
and a thickness of four to eight widths of the opening with the
thickness increasing with increasing amounts of swirl in the conduit
upstream of the flow meter.
28. A method for measuring a multiple-phase flow of a fluid in
a conduit, comprising steps of: measuring at least one pressure
and a temperature of the fluid; measuring at least one pressure
differential of the fluid across each of at least two flow meters
including at least one obstruction flow meter and one densitometer
operable to be serially disposed in the conduit; measuring a density
of the fluid, .rho..sub.mixture, such that
29. A multiple-phase flow meter for measuring a mixture of offshore
petroleum products flowing in a conduit, comprising: three flow
meters including at least two obstruction flow meters serially disposed
in the conduit so that each of the three obstruction flow meters
have an upstream side and a downstream side, and any two adjacent
flow meters have an intermediate region therebetween, the at least
two flow meters being an upstream flow meter and a downstream flow
meter and being spaced at a minimum such that downstream flow meter
encounters little of the flow profile distortion caused by the upstream
flow meter as to degrade its performance, and spaced at a maximum
such that the percentage of flow constituents remains substantially
the same from the upstream flow meter to the downstream flowmeter;
a plurality of sensors operable to be located upstream, downstream,
and in the intermediate region of the three flow meters, the plurality
of sensors measuring predetermined characteristics of the multiple-phase
flow; and a computer coupled to the plurality of sensors and capable
of computing the total mass flow rate of the multiple phase flow
by calculating a quality of the multiple-phase flow based on the
measured predetermined characteristics.
30. The multiple-phase flow meter of claim 29 wherein the computer
is operable to plot and curve fit flow quality, x, as a function
of pressure differential across the three flow meters, P1 P2 and
P3:
where: ##EQU22##
and plotting total mass flow rate as a function of P1 P2 and
P3 and performing a curve fit of the total mass flow rate plot
to compute a total mass flow rate, and determining the mass flow
rates of each flow component using the total mass flow rate by plotting
and curve fitting density of the flow liquid mixture as a function
of x, P1 P2 and P3 and calculating the fraction of the liquid
that is composed of liquid1 where: ##EQU23## m.sub.total =m.sub.gas
+m.sub.liquid =m.sub.gas +m.sub.liquid1 +m.sub.liquid2
31. The multiple-phase flow meter of claim 29 wherein each of the
three flow meters comprises a plate with a plurality of openings
defined therein, the plurality of openings arranged in a predetermined
pattern.
32. The multiple-phase flow meter of claim 31 wherein the plurality
of openings on the plate comprise: at least two concentric series
of openings positioned in at least two concentric circular areas
on the plate, the openings of each of the at least two concentric
series of openings having a combined area, the at least two concentric
circular areas each having a surface area; and ratios of the combined
area of each of the at least two concentric series of openings to
its respective circular area surface area being substantially the
same.
33. The multiple-phase flow meter of claim 29 wherein at least
one flow meter is a vortex meter.
34. The multiple-phase flow meter of claim 29 wherein at least
one flow meter is a Venturi meter.
35. The multiple-phase flow meter of claim 29 wherein at least
one flow meter is a densitometer.
36. The multiple-phase flow meter of claim 29 wherein the spacing
between adjacent flow meters is equal to at least one diameter of
the conduit.
37. The multiple-phase flow meter of claim 29 wherein the spacing
between adjacent flow meters is between one and 12 diameters of
the conduit.
38. The multiple-phase flow meter of claim 30 wherein a thickness
of the upstream obstruction flow meter is variable from four to
eight widths of an opening in the plate depending upon the amount
of swirl present upstream of the flow meter, where the thickness
of the upstream obstruction flow meter increases with increasing
swirl.
39. A method for determining a multiple-phase flow of a fluid in
a conduit, comprising steps of: measuring a pressure differential
across at least two obstruction flow meters serially disposed in
the conduit, P1 and P2 respectively; plotting quality as a function
of P1 and P2; curve fitting the plot and generating a flow quality
function, determining flow quality using the flow quality function;
determining a discharge coefficient from the flow quality; and determining
a total mass flow rate using; ##EQU24##
where, m=total mass flow rate, K=flow coefficient, Y=expansion
factor, d=orifice diameter=.beta.D, D=pipe diameter, .rho.=density
of gas, liquid, or mixture, .DELTA.P =pressure drop across orifice
plate.
40. The method, as set forth in claim 39 wherein plotting quality
comprises computing:
such as: ##EQU25##
where,
##EQU26##
41. The method, as set forth in claim 39 wherein plotting quality
comprises computing:
such as: ##EQU27##
where,
##EQU28##
42. The method, as set forth in claim 39 further comprising spacing
adjacent flow meters between one and 12 diameters of the conduit
apart.
43. The method, as set forth in claim 39 further comprising using
an obstruction flow meter with openings of a predetermined width,
and a thickness of four to eight widths of the opening with the
thickness increasing with increasing amounts of swirl in the conduit
upstream of the flow meter.
44. The method, as set forth in claim 39 further comprising: measuring
a third pressure differential, P3 across a third obstruction flow
meter; plotting flow quality, x, as a function of P1 P2 and P3
which is: ##EQU29## and performing a curve fit of the flow quality
plot to compute the flow quality; plotting total mass flow rate
as a function of P1 P2 and P3 and performing a curve fit of the
plot to compute a total mass flow rate; and determining the mass
flow rates of each flow component using the total mass flow rate
by plotting and curve fitting density of the flow components as
a function of P1 P2 and P3.
45. The method, as set forth in claim 44 further comprising determining
the density of the liquid mixture in the flow, where: ##EQU30##
##EQU31## m.sub.total =m.sub.gas +m.sub.liquid =m.sub.gas +m.sub.liquid1
+m.sub.liquid2
46. The method, as set forth in claim 45 wherein flow rates of
N phases are determined by using N flow meters and measuring N pressure
differentials across the N flow meters and plotting flow quality
as a function of the N pressure differentials.
47. The multiple-phase flow meter of claim 1 wherein the processor
is further capable of computing the flow rate of the multiple-phase
flow by calculating a quality of the multiple-phase flow independent
of any phase ratio calculation.
48. The method of claim 19 wherein generating a flow rate by calculating
a gas quality of the multiple-phase flow comprises calculating a
gas quality of the multiple-phase flow independent of a phase ratio
measurement.
## Description TECHNICAL FIELD OF THE INVENTION
This invention is related to flow meter instrumentation. More particularly,
the invention is related to obstruction flow meters which are used
in series in a flow conduit to determine the volume flow rate of
liquid and gas phases of fluid flowing within the conduit.
BACKGROUND OF THE INVENTION
Fluid flow meters are used in many areas of industry and commerce.
Various nuclear, acoustic, electromagnetic and mechanical techniques
have been used to measure flow rate and volume flow rates of fluids
containing one, two, or more components or "phases".
Obstruction type flow meters are widely used to measure single
phase flow, such as fluids comprising 100% liquid or 100% gas. In
orifice flow meters, fluid is forced to flow through an orifice
in a plate within the flow conduit, creating a pressure drop across
the plate. Orifice flow meters are relatively inexpensive to fabricate
and maintain, and are reliable in many types of field operations.
In addition, the physical size of most orifice devices is relatively
small. Measurements of the differential pressure across the plate,
along with fluid pressure and temperature measurements, are used
to compute flow rate using equations well known in the art. Orifice
flow measurements can be used to measure multiple-phase flow only
if an independent measure of the ratio of the phases is made. Furthermore,
accurate measurement of the volume flow rates of each phase can
be obtained only if the linear flow velocities of the phases are
the same, or the relative velocities or "slippage" of
the linear phase flows can be determined, or all phases are forced
to flow at the same linear flow rate at the position which the phase
ratio and orifice plate measurements are made.
Positive displacement type flow meters force fluid to flow through
a positive displacement meter such as a turbine apparatus, and the
flow rate of the fluid is determined from the rate of revolution
of the flow meter turbine. Positive displacement type flow meters
may be used in multiple-phase flows. As with orifice flow meters,
independent phase ratio measurements must be made using a variety
of technologies, and assumptions must be made concerning the linear
flow velocities of each of the phases in order to obtain accurate
volume flow rates for the individual phases. Positive displacement
type flow meters are more complex, more costly to manufacture and
maintain, and are generally larger than orifice flow meters.
Separators are widely used in multiple-phase flow measurements.
As an example, in the petroleum industry, it is of interest to measure
volume flow rates of the three fluids produced: oil, gas and water.
Gravity separators are widely used to separate these three components.
The separated components are then drawn from the separator and single
phase flow measurements are made on each of the separated components.
Characteristically, separators are physically large, are expensive
to construct, require a relatively long period of time for the multiple
phases to separate by means of the force of gravity, and require
separate flow meters and flow controllers for each separated phase.
Various two and three-phase "in-line" flow meters have
been developed, especially in the petroleum industry. Relatively
accurate three-phase "partition" measurements can be made
using nuclear, acoustic, electromagnetic, and/or a combination of
these technologies. However, a problem lies in accurately determining
the flow velocities of each of the phases. Various relationships
have been developed to calculate the relative or "slippage"
velocity of two phases with respect to a measured third phase, but
the calculations are replete with assumptions. In addition, these
devices are usually quite complex both electronically and mechanically,
are expensive to fabricate, and very expensive to maintain and calibrate.
Significant progress has been made recently in the area of single
plate obstruction flow meters. U.S. Pat. No. 5295397 issued to
Hall et al. on Mar. 22 1994 and entitled "Slotted Orifice
Flowmeter" ('397) discloses an orifice flow meter. The orifice
plate is designed such that measurements are relatively insensitive
to upstream and downstream flow conditions. In addition, this orifice
plate is less disruptive in the manner in which it is used to impede
flow. Therefore, fluid pressure recovers more readily within a shorter
distance from the flow meter, and incurs less unrecoverable pressure
drop than prior art orifice flow meters. Independent phase ratio
measurements must be made, or assumptions directed toward the multiple
phases must be made, in order to use the '397 device to measure
volume flow rates in multiple-phase fluid flows. This patent is
incorporated herein by reference.
U.S. Pat. No. 5461932 issued to Hall et al. on Oct. 31 1995
and entitled "Slotted Orifice Flowmeter" ('932) discloses
an orifice flow meter. A phase ratio sensor is used upstream from
the orifice plate to allow two-phase flow measurements to be made
without necessitating separation of the fluid. However, the phase
ratio measurement is completely separate from the orifice flow meter
measurement. This patent is incorporated herein by reference.
SUMMARY OF THE INVENTION
In one aspect of the present invention, a flow meter is provided
for measuring the flow rate of each phase of a multiple-phase fluid
in a conduit. Obstruction flow meters are serially positioned in
a conduit and spaced a predetermined distance apart based upon the
configuration of the orifice flow plate used in the obstruction
flow meters. Sensors are also positioned in the conduit to measure
the pressure and temperature of the multiple-phase fluid at various
locations relative to the obstruction flow meters. The measurements
are fed to a computer which calculates the flow rate of each phase
of the multiple-phase fluid.
In another aspect of the present invention, a method is provided
for measuring the flow rate of each phase of a multiple-phase fluid
in a conduit. Obstruction flow meters are serially positioned in
a conduit to create flow impedances. Pressures and the temperature
of the multiple-phase fluid are measured at various locations relative
to the obstruction flow meters. The measurements are then used to
generate the flow rates of each phase of the multiple-phase fluid.
In another aspect of the present invention, a flow meter is provided
for measuring a mixture of offshore petroleum products flowing in
a conduit. Three obstruction flow meters are serially positioned
in a conduit and spaced a predetermined distance apart based upon
the configuration of the orifice flow plate used in the three obstruction
flow meters. Sensors are also positioned in the conduit to measure
the pressure and temperature of the mixture at various locations
relative to the three obstruction flow meters. The measurements
are fed to a computer which calculates the flow rate of each phase
of the mixture. The flow rates are then stored in a memory device
for future reference when determining royalty payments.
A primary technical advantage of the present invention is to provide
multiple-phase flow measurements without the use of an independent
phase ratio measurement.
Another primary technical advantage of the present invention is
to provide a flow meter and a method for calculating more accurate
values of the Reynolds number of the fluid and the "quality"
of the gas from pressure, temperature and differential temperature
measurements made in the vicinity of the obstruction flow meters.
An additional technical advantage of the present invention is to
provide a reliable, relatively inexpensive, compact means for measuring
multiple-phase flow which is compatible with instrumentation of
single-phase orifice flow meters, thereby eliminating the necessity
to employ exotic and/or expensive technologies such as sonic, nuclear,
electromagnetic imaging, phase separation and the like to obtain
multiple-phase measurements.
A still further technical advantage of the present invention is
to provide a multiple-phase flow meter for offshore petroleum production
operations where space on drilling and production platforms is at
a premium, and reliability is of paramount importance.
Further advantages of the present invention may be appreciated
upon examining the specification and claims below.
BRIEF DESCRIPTION OF THE DRAWINGS
For a better understanding of the present invention, reference
may be made to the accompanying drawings, in which:
FIG. 1 is a schematic diagram of an embodiment of the present invention
utilizing two obstruction flow meters serially disposed in a flow
conduit;
FIG. 2 is a schematic diagram of an embodiment of the present invention
utilizing three obstruction flow meters serially disposed in a flow
conduit;
FIG. 3 is a frontal view of a slotted orifice plate used in obstruction
flow meters incorporated into the present invention;
FIG. 4 is an exemplary plot of slotted orifice discharge coefficient
variation with quality, 289 kPa line pressure, .beta.=0.50 pressure
tap 1 mixture flow rate, air density;
FIG. 5 is an exemplary plot of slotted orifice discharge coefficient
variation with quality, 289 kPa line pressure, .beta.=0.43 pressure
tap 4 mixture flow rate, air density;
FIG. 6A is a flowchart of an embodiment of a method to determine
the total mass flow rate and quality according to the teachings
of the present invention;
FIG. 6B is an exemplary quality contour plot as a function of P1
and P4;
FIG. 7 is an exemplary quality contour plot as a function of P1
and P1/P4;
FIG. 8 is an exemplary quality contour plot as a function of P1
and (P4-P1)/(P4+P1);
FIG. 9 is an exemplary three dimensional curve fit of flow quality
as a function of the .beta.=0.50 slotted orifice pressure differential
and the ratio of the .beta.=0.50 to 0.43 slotted orifice pressure
differential;
FIG. 10 is an exemplary slotted orifice discharge coefficient curve
fit for mixture mass flow rate, air density, and all air Reynolds
numbers with slotted orifice .DELTA.Ps larger than 5 kPa as a function
of flow quality,
FIG. 11 is an exemplary slotted orifice discharge coefficient curve
fit for mixture mass flow rate, water density, and all air Reynolds
numbers with slotted orifice .DELTA.Ps larger than 5 kPa as a function
of flow quality;
FIG. 12 is an exemplary plot of comparison and calculated and measured
quality, 289 kPa line pressure; and
FIG. 13 is an exemplary plot of comparison and calculated and measured
mixture mass flow rate, 289 kPa line pressure.
DETAILED DESCRIPTION OF THE INVENTION
The preferred embodiment of the present invention and its advantages
are best understood by referring to FIGS. 1-13 of the drawings,
like numerals being used for like and corresponding parts of the
various drawings. Various parameters associated with the obstruction
flow meters will be identified with the subscripts i=1 2 etc.
With reference to the drawings, FIG. 1 is a schematic diagram of
an embodiment of a multiple-phase flow meter 10 of the present invention.
A fluid comprising a liquid phase and a gas phase flows through
a cylindrical conduit 12 such as a pipe, in the direction indicated
by arrows 14. The inside diameter of conduit 12 is denoted as the
dimension d. Multiple-phase flow meter 10 includes a first flow
meter 20 disposed in conduit 12 and is spaced a distance, 1 from
a second flow meter 22 also disposed in conduit 12. The spacing,
1 is preferably several conduit diameters, d. At least one of the
flow meters is an obstruction flow meter such as the type disclosed
in U.S. Pat. Nos. 5295397 and 5461932 and may include a flow
plate 30 of the type shown in FIG. 3.
Flow plate 30 is generally circular and contains a solid region
32. A series of spaced slots 34 are arranged on flow plate 30 to
allow fluid to pass through. The ratio of the area of solid region
32 and the area of slots 34 is relatively constant over the entire
flow plate 30. This ratio of areas is quantified by the term .beta..sup.2
Flow plate 30 is positioned within conduit 12 such that the plane
of flow plate 30 is substantially perpendicular to the major axis
of conduit 12. The values, .beta., of obstruction flow meters 20
and 22 differ preferably by approximately 0.03 or more. As an example,
typical beta values are .beta..sub.1 =0.50 for first obstruction
flow meter 20 and .beta..sub.2 =0.43 for second obstruction flow
meter 22 yielding a P difference of 0.07.
Still referring to FIG. 1 multiple-phase flow meter 10 further
includes pressure sensors 40 and 42 which measure pressure upstream
(P.sub.11) and downstream (P.sub.12), respectively, with respect
to first obstruction flow meter 20. These pressure measurements
are provided as input into a computer 60. In a similar fashion,
pressure sensors 44 and 46 are disposed on either side of second
obstruction flow meter 22 and measure pressure upstream (P.sub.21)
and downstream (P.sub.22), respectively, with respect to second
obstruction flow meter 22. These measured pressures are also input
into computer 60. In addition, a temperature sensor 26 measures
fluid temperature, T, which is also input into computer 60. Temperature
sensor 26 may be positioned anywhere in the fluid flow.
Other parameters which are either known or obtained from independent
measurements are symbolically shown in box 50 of FIG. 1. These include
quantities .rho., .mu., k, D, R, .beta..sub.1 .beta..sub.2 and
are defined below. These parameters are also input into computer
60. Once all measured and known parameters have been input into
computer 60 the Reynolds number, Re, and the gas quality, x, are
computed. Likewise, the flow rate of the gas and liquid phases are
determined from the Reynolds number by computer 60. The details
of the computation are set forth below. The calculated values may
be output to a memory storage device 62 which may be a chart recorder
or a digital recording device.
In an alternate embodiment of the present invention, with reference
to FIG. 1 second obstruction flow meter 22 is omitted and replaced
with a densitometer. The density measurement of a mixture of liquid
and gas (of known density in the pure condition) enables solution
of the term x. If that term is known, then the Reynolds number is
extracted from a single set of data from first obstruction flow
meter 20.
The present invention is not limited to the measurement of the
flow of two phases within a fluid. As an example, the present invention
can be embodied to measure the phases of two liquids and a gas phase
in the fluid, provided that the physical properties such as density
and viscosity differ. With reference to the drawings, FIG. 2 is
a schematic diagram of this embodiment of the present invention.
A fluid comprising two liquid phases and a gas phase flows through
cylindrical conduit 12 with inside diameter, d, in the direction
indicated by arrows 14. Multiple-phase flow meter 100 includes a
first obstruction flow meter 120 disposed in conduit 12 and is
spaced a distance, l, from a second obstruction flow meter 122 also
disposed in conduit 12. Second obstruction flow meter 122 is spaced
a distance, l', from a third obstruction flow meter 124. The spacings,
l and l', are preferably several conduit diameters, d. Obstruction
flow meters 120 122 and 124 may be of the type disclosed in U.S.
Pat. Nos. 5295397 and 5461932 as discussed above.
In a preferred embodiment of the present invention, the spacing
between the obstruction flow meters is equal to at least one diameter
of the flow conduit, d. In a preferred embodiment of the present
invention, the spacing between successive obstruction flow meters
is between one pipe diameter and 12 pipe diameters. The spacing
may be greater than 12 pipe diameters, however, the resultant size
of the flow meter would render the device impracticable or impractical.
In general, the spacing between the flow meters is such that, at
a minimum, the upstream flow meter does not substantially alter
the flow profile of the flow encountered by the downstream flow
meter enough to degrade its performance, When the slotted obstruction
flow meter shown in FIG. 3 is used, this spacing may be as small
as one pipe diameter. In general, the maximum spacing between the
flow meters is such that the percentage of flow constituents or
components remains substantially the same from the upstream flow
meter to the downstream flow meter.
Still referring to FIG. 2 multiple-phase flow meter 100 further
includes pressure sensors 140 and 142 which measure pressure upstream
(P.sub.11) and downstream (P.sub.12), respectively, with respect
to first obstruction flow meter 120. These pressure measurements
are provided as input into computer 60. Similarly, pressure sensors
144 and 146 are disposed on either side of second obstruction flow
meter 122 and measure pressure upstream (P.sub.21) and downstream
(P.sub.22), respectively, with respect to second obstruction flow
meter 122. These measured pressures are also input into computer
60. In addition, pressure sensors 148 and 150 are disposed on either
side of third obstruction flow meter 124 and measure pressure upstream
(P.sub.31) and downstream (P.sub.32), respectively, with respect
to third obstruction flow meter 124. These measured pressures are
also input into computer 60. Also, a temperature sensor 26 measures
fluid temperature, T, which is also input into computer 60.
Other parameters which are either known or obtained from independent
measurements are symbolically shown in the box 50 of FIG. 2. These
include quantities .rho., .mu., k, D, R, .beta..sub.1 .beta..sub.2
.beta..sub.3 and are defined below. These parameters are also input
into computer 60. Once all measured and known parameters have been
input into computer 60 the Reynolds number, Re, and the gas quality,
x, are computed for each phase. Likewise, the flow rate of the gas
phase and two liquid phases are determined from the Reynolds number
by computer 60.
The preferred obstruction flow meters are disclosed in the previously
referenced U.S. Pat. Nos. 5295397 and 5461932. Among other attributes,
the design of flow plate 30 generates flow characteristics of a
fluid such that, after passing through a first obstruction flow
meter, rapidly recover prior to passing through a second obstruction
flow meter, with the exception of minimal nonrecoverable pressure
drop. The flow characteristics are also very insensitive to upstream
flow conditions. Because the obstruction flow meters of the present
invention are disposed in series in conduit 12 the flow plates
30 with their superior fluid flow recovery properties and insensitivities
to upstream flow conditions, can be spaced relatively close to minimize
the overall dimensions of the multiple-phase flow meter of the present
invention. Spacing of the obstruction flow meters is generally a
few conduit diameters, d, apart.
Alternatively, other types of flow meters may be employed in the
present invention so that only one or more flow meter is an obstruction-type
flow meter. For example, vortex meters, Venturi meters, Coriolis
meters and the like could replace the second and/or third flow meters
in the series.
In a specific embodiment of the present invention, it will be observed
that only N+1 pressure measurements are required, where N equals
the number of obstruction flow meters. Using the two obstruction
flow meter embodiment as an example, absolute pressure measurements
may be made upstream of first obstruction flow meter 20 between
first and second obstruction flow meters 20 and 22 and downstream
of second obstruction flow meter 22. In an alternative approach,
only one absolute pressure measurement need be made at any of the
location of pressure sensors 40 42 44 or 46. Assume for purposes
of discussion that pressure sensor 40 is the absolute pressure gauge.
Then, two other pressure measurements are made and they can either
be absolute measurements or can be differential pressure measurements.
In either instance, the pressure drop is measured across first and
second obstruction flow meters 20 and 22.
Recall that multiple-phase flow meter 10 of the present invention
uses the response of obstruction flow meters operating in series
to obtain the flow rate of a multiple-phase fluid. In the following
mathematical description of the present invention, the subscript
where i=1 and 2 will be used to identify various parameters associated
with first obstruction flow meter 20 and second obstruction flow
meter 22 respectively. These calculations are equally applicable
to multiple-phase flow meter 100.
The Reynolds number, Re, of the gas portion of the fluid flowing
through an obstruction type flow meter can be expressed as:
where x=the gas quality; C.sub.d,i =the discharge function; D=the
diameter of the conduit 12; .beta..sub.i =square root of the ratio
of the total open area of all openings divided by the cross-sectional
area of the flow plate 30; .mu.=the viscosity of the gas; .DELTA.P.sub.i
=the differential pressure drop across the ith obstruction flow
meter; .rho..sub.i =P.sub.i /(R T); and Y.sub.i =expansion factor
where P.sub.i =the absolute pressure in the flow stream in the
vicinity of the obstruction flow meter i; T=the temperature of the
fluid; R=the specific gas constant; and k=C.sub.p /C.sub.v =the
ratio of specific heats for the gas.
It has been determined that generalized functions Cd,.sub.1 and
Cd,.sub.2 which are dependent upon Re and x, can be expressed as
functions of selected constants with Re and x.
where the empirical constants are determined under known flow conditions
for a particular configuration of flow plates 30. The quantities
.beta..sub.i are known from the design parameters of the flow plates
30 of first and second obstruction flow meters 20 and 22. The quantities
Yi are derived from metered calibrations. The quantities .beta..sub.i
are calculated from measured quantities P.sub.i,i, T, and from a
known quantity R defined above. The quantity .mu. is also known
as defined above. Therefore, the terms in Equation (1) are known
with the exception of the Reynolds number of the fluid, Re, and
the quality of the gas, x.
Equation (1) with i=12 may be solved iteratively for Re and x
by starting with an initial guess of these quantities, as will be
illustrated in a following example. The solution yields the Reynolds
number of the gas and the quality of the gas/liquid mixture. A mass
flow rate, m, of the gas can be calculated from the expression
Volume flow rates of the liquid and gas phases can then be obtained
from m, x, and the densities of each phase.
The following known and measured parameters will be used to illustrate
the determination of Re and x using the previously described methodology.
f.sub.1 (Re,x) and f.sub.2 (Re,x) will represent discharge functions
C.sub.d,i (Re,x) through series orifice plates i=12. This example
was performed under known conditions in which the true values of
Re and x were known. The measured and known parameters were: .rho.H.sub.2
O=62.4 lb ft/sec.sup.2 .mu.=3.875 10.sup.-7 lbf sec/ft.sup.2 k=1.4
R=53.35 ft lbf/lb deg .beta..sub.1 =0.50 P.sub.i =24.2 psi .DELTA.P.sub.1
=9.83 in of H.sub.2 O .rho..sub.i =0.123 lb/ft.sup.3 Y.sub.1 =0.995
a.sub.1 =2.3712846 b.sub.1 =-4.9048095 10.sup.-7 c.sub.1 =2.4594207
d.sub.1 =0.887817 D=2.067 in. .beta..sub.2 =0.43 P.sub.2 =14.5 psi
.DELTA.P.sub.2 =19.21 in. of H.sub.2 O .rho..sub.2 =0103 lb/ft.sup.3
Y.sub.2 =0.991 a.sub.2 =1.6272073 b.sub.2 =-3.6012949 10.sup.-6
c.sub.2 =1.1792148 10.sup.-11 d.sub.2 =-0.68470117
Starting with initial values of Re=50000 and x=0.5 the solution
of Equation (1) converges at Re=5.46 10.sup.4 and x=0.881. This
compares quite favorably with the true values of Re=5.47 10.sup.4
and x=0.8987 illustrating the accuracy and robustness of the present
invention.
As a further illustration of the robustness and consistency of
the present invention, the solutions Re and x are substituted into
generalized Equations (2) and (3), expressed as discharge functions,
to yield calculated discharge function values of:
C.sub.d,1 =a.sub.1 +b.sub.1 Re+c.sub.1 x+d.sub.1 x.sup.2 =0.869
(5)
These calculated values compare favorably with experimental data
of C.sub.d,1 =0.8498 and C.sub.d,2 =0.8441. Note the two equations
are application specific and represent one type of analysis. Other
constants can be developed for alternate specific forms of equations.
To put the foregoing into context, consider several oil wells which
are drilled in a particular field. The wells usually flow a mixture
of water, oil and gas. For purposes of discussion, assume the fluid
flow consists only of oil and gas. It is not uncommon for the pressure
in the producing formation to be sufficiently high so that the gas
is dissolved in the oil. Therefore, the oil itself tends to carry
the dissolved gas along as an adequate pressure is maintained, but
the gas will come out of the oil depending on agitation, prevailing
temperatures, pressure and other terms which are less significant
than those. Moreover, as the field produces over a long interval
of time, the ratio can change markedly. In other words, the amount
of natural gas produced may change significantly over months or
years. The total volumetric production will also change. For these
reasons, it is important to know the relative mix of the two fluids
(oil and natural gas).
Assume, therefore, that several wells are producing into a 6"
diameter gathering line. Assume further that the production from
the field must be measured and measurements transferred once each
month for determination of royalties to be paid to the land owners.
The royalties typically are given by a formula which provides different
royalty rates for the produced natural gas and the oil, To accomplish
this, memory storage device 62 is connected to computer 60 so that
measurements can be output and stored for the month. These measurements
will be distinctly more accurate than those that have been accepted
in the industry in the past. It has been common in the industry
to use a circular paper disk connected with a clock so that the
line marked on the disk represents the flow for one revolution of
the disk. The disk is normally rotated once per day, once per week,
or once per month. The disk must be serviced to avoid marking a
second line over the first line; this requires disk removal at the
end of one disk interval of time (i.e., one disk is assigned to
each day, week or month). That requires the difficulty of servicing
in the field. The old disk is removed and taken to a measuring facility
where the area under the curve is measured, thereby representing
the integrated flow through that particular measuring device for
that time interval. That is represented as so many barrels of oil
in a week, or so many standard cubic feet of natural gas in a time
interval such as a week.
As will be seen, an easily implemented set of measurements (only
pressure and temperature) may be used in determining the flow of
the oil and gas. This flow through the gathering line can be output
to memory storage device 62 and that memory can be interrogated
daily, weekly or monthly as required.
The present invention operates most efficiently when the percent
of liquid in the fluid is in the 0-80% range. For liquid content
above 80%, "slugs" of 100% liquid tend to flow within
the pipeline, especially if the pipeline undulates with terrain.
Low points in the pipeline can act as liquid traps and thereby create
the liquid slugs. Liquid slugs can damage flow meters, especially
if the linear flow velocity of the slugs is large. Such slugging
derives from the fluid context and does not indicate any defect
of the present system. When the liquid content is sufficiently large
that slugging no longer occurs (such a bubbly flow), the present
invention will operate properly and with high accuracy.
Referring to the two obstruction flow meter embodiment, relationships
can be developed which are dependent on four variables: T, P, .DELTA.P.sub.1
and .DELTA.P.sub.2. More specifically in observing only first obstruction
flow meter 20 it will be understood that an equation of the generalized
form can be developed. Two such equations are given because there
are two obstruction flow meters; these are generally set forth in
the form of equations (7) and (8):
These functional equations can then be viewed simply as two equations
dealing with two unknowns and are solved to obtain solutions which
are robust and consistent over a reasonable range of product flow
through the two obstruction flow meters. As a practical matter,
the two obstruction flow meters can thus provide measurements based
upon four measured variables (T, P, and .DELTA.P.sub.1 and .DELTA.P.sub.2).
As will be understood, the development shown in equations (7) and
(8) represents a more generalized case than that of equations (2)
and (3). This suggests significant benefits and advantages in viewing
the system in this manner. The precise nature of the functional
relationship given in equations (7) and (8) can be that which was
developed earlier but other empirical relationships can likewise
be developed for use as equations (7) and (8).
Referring to the three obstruction flow meter embodiment, relationships
can be developed which are dependent on five variables: T, P, .DELTA.P.sub.1
.DELTA.P.sub.2 and .DELTA.P.sub.3. The system can be generalized
mathematically as three equations of the form
where the subscripts i=123 represent first, second and third
obstruction flow meters 120 122 and 124. These equations, and the
simultaneous solutions for three unknowns (e.g., oil, water and
gas flow) are analogous to the two obstruction flow meter embodiments
discussed previously and expressed mathematically in generalized
equations (7) and (8). Solutions for the oil, water and gas phases
are possible because the physical properties of each phase, such
as the density and viscosity, differ, and therefore result in distinctive
responses in each of obstruction flow meters 120 122 and 124. The
simultaneous solution of Equations (9) through (11) is obtained
using computer 60. These equations are effective for volumetric
quantification and are also effective for mass flow rate.
The flow calculation algorithm for the slotted orifice flow meter
was investigated to determine how accurate two-phase flow meter
calibration curves can be obtained. These techniques can be extended
to multiphase applications using similar approaches. The first technique
uses the standard orifice flow meter flow equation. This standard
orifice flow meter flow equation is given by: ##EQU1## where, m=total
mass flow rate, K=flow coefficient, Y=expansion factor, d=orifice
diameter=.beta.D, D=pipe diameter, .rho.=density of gas, liquid,
or mixture, .DELTA.P=pressure drop across orifice plate.
Data obtained for an air-water flow was analyzed to determine values
of slotted orifice discharge coefficients (KY). For this analysis,
the previous equation was rearranged and the product KY was calculated
by using either the density of the gas, liquid, or a mixture, and
the total mass flow rate observed in the flow. The air density was
calculated using the pressure and temperature in the pipe. The flow
quality (X) based upon mass and the total flow rate (M) are defined
by:
and
##EQU2##
Exemplary KY values computed using the mixture flow rate and the
air density are shown in the FIGS. 4 and 5 for two different slotted
orifice plates, .beta.=0.50 and .beta.=0.43 respectively. The .beta.=0.50
slotted orifice plate responded very well to the two-phase flow.
It may be noted that the KY values are independent of air Reynolds
numbers. Only the Re=18400 data does not collapse to the common
curve. This is due to the very small pressure differentials produced
at this low Reynolds number resulting in very large uncertainties
in the measurements. The .beta.=0.43 slotted orifice plate follows
the same trends but there is an air Reynolds number dependence,
where discharge coefficient, KY, decreases with increasing air Reynolds
number. This variation is consistent with a compressibility effect
where expansion factor, Y, decreases as with increasing pressure
drop across the slotted orifice plate. This is the same type of
variation in Y as observed in standard orifice flow meters. By fitting
curves for these discharge coefficients, it is possible to solve
for the mixture flow rate and quality by solving the two orifice
flow equations (one for each orifice plate) simultaneously.
A second technique for obtaining the mass flow rate and quality
is shown in FIG. 6A and based on an exemplary plot shown in FIG.
6B. In block 200 (FIG. 6A), a contour plot of quality as a function
of the pressure differential measured across the two slotted orifice
plates, P1 and P4 is obtained. This surface contour can be curve
fit to produce a function where the measured values of the pressure
drop across two slotted orifice plates can be used to directly calculate
the quality of the flow mixture, as shown in blocks 202 and 204.
In block 206 once the quality is determined, the discharge coefficient,
KY, can be obtained from FIG. 4 which is only dependent upon the
mixture quality. Finally, given the flow quality and one of the
flow meter's discharge coefficients, the total mass flow rate can
be calculated, as shown in block 208.
The third and fourth techniques were developed due to the rapid
variation of quality with respect to P1 and P4 as shown in FIGS.
6A and 6B. Various combinations of P1 and P4 were considered and
two alternatives which greatly increase the accuracy of the flow
computation were identified. FIGS. 7 and 8 are exemplary plots that
present the graphical information. By using a function of P1 and
P4 such as the ratio of P1/P4 or a functional combination of (P4-P1)/(P4+P1),
the rapid variation of quality with the measured pressure differences
is reduced. FIG. 7 illustrates a problem with the data for P1<4
kPa with the large spike appearing in the plot. This spike is due
to large uncertainties in the measured pressures at these low values.
Full scale of the pressure transducer is 62 kPa. Therefore, pressures
below 6 kPa have unacceptably high uncertainty. The difference-sum
ratio does not exhibit this problem and may be the ultimate preferred
technique.
Using the data presentation in FIG. 7 the flow measurement calculation
can be based upon exemplary calibration curves shown in FIGS. 9
to 11. The quality is calculated directly from the two pressure
differentials, P1 and P4 measured across the .beta.=0.50 and 0.43
slotted orifice plates, respectively. The contour plots (FIG. 6)
showed that using P1 and P4 directly result in very large uncertainties
at low pressures since the contour plot shows a very large gradient
in X for very small changes in P1 and P4. FIG. 7 shows how representing
X(P1 P1/P4) spreads the contours out over a larger area which results
in a more accurate calculation of X. An exemplary curve fit of these
data is shown in FIG. 9 and has a goodness of fit of 0.99687. The
equation shown in FIG. 9 is used to calculate the quality of the
flow. The total mass flow rate is then calculated using the orifice
flow equation for the .beta.=0.50 slotted orifice plate using either
the density of the gas or liquid (FIGS. 10 and 11) since the values
of KY were independent of air Reynolds numbers for the data having
P1>6 kPa. Both the air and water density curves were fit and
are shown. Both curve fits have goodness of fit values greater than
0.999. Subsequent analysis showed there was no difference in the
accuracy of the mass flow rate calculation between the air and water
density based calculation.
The actual experimental values of P1 and P4 were used in the following
equations along with the air density calculated from the downstream
pressure and temperature to calculate the quality and total mass
flow rate: ##EQU3##
Exemplary results are shown in FIGS. 12 and 13. The calculated
values follow the measured values very well. To quantify the goodness
of the calculation, the ratio of the calculated value divided by
the measured value were computed. For the ratio Xcalc/X, the mean
is 1.001 and the standard deviation is 0.023. Therefore, on the
average, the quality is calculated to within 0.1% of the true value
with a standard deviation of 2.3%. The mixture accuracy is similar
with a mean of 1.003 and a standard deviation of 0.017 which translates
to calculated mass flow rate error of 0.3% with a standard deviation
of 1.7%. These results indicate a meter which is highly accurate.
The magnitude of the standard deviation can be reduced by decreasing
the uncertainty in the pressure measurements. The errors in the
calculations appear to be random since the mean has a very low uncertainty.
Replacing X(P1 P1/P4) with a curve fit of X(P1 {P4-P1}/{P4+P1})
may provide an increase in accuracy since the low pressure accuracy
problem is not apparent in FIG. 8 and the surface area of the graph
has increased resulting is less sensitivity of the calculated quality
to minor variations or errors in the measured values of P1 and P4.
The method above may be extended to a three-phase solution. A third
flow meter is disposed in series with the above-described two flow
meters to measure a third pressure differential, P3. Using three
pressure differentials (P1 P2 P3), a four-dimensional curve fit
is used to produce an equation for flow quality, X, as a function
of P1 P2 P3. This function may involve combination functions of
P1 P2 P3. (Note in the previous discussion the second pressure
differential is denoted as P4.) From the operating flow meter, measurements
P1 P2 and P3 are obtained and flow quality, X(P1 P2 P3) is calculated,
where quality is given by: ##EQU4##
A curve fit of the total mass flow rate as a function of P1 P2
and P3 is given by:
m.sub.total (P1 P2 P3)
Similar to the two-phase solution described above, from the flow
quality value and discharge coefficient, the total mass flow rate
of the gas and of the liquid mixture can be calculated. Next, the
mass flow rates of the two individual liquid components in the liquid
mixture are determined. Knowing the total mass flow rate of the
gas and of the sum of the two liquid components, .gamma. is defined
as the ratio: ##EQU5##
Further definitions are: ##EQU6## m.sub.total =m.sub.gas +m.sub.liquid
=m.sub.gas +m.sub.liquid1 +m.sub.liquid2
The density of the liquid mixture .rho..sub.liquid can be obtained
from a curve fit of .rho..sub.liquid as a function of P1 P2 and
P3. Once the density of the liquid mixture is known, then the value
of .gamma. tan be calculated and used to determine the mass flow
rate of the two liquid components. It is noted that the present
invention is adaptable to flow having three or more phases using
similar techniques as described above.
In an embodiment of the present invention, the preferred thickness
of the flow meter slotted orifice plate is 4 to 8 times the width
of the slots. If swirl is absent from the flow, 4 slot widths are
sufficient; if swirl is present, 8 slot widths are sufficient to
eliminate use of a flow straightener. With this preferred thickness,
upstream flow straighteners or conditioners are not needed.
While the foregoing disclosure is directed to specific embodiments
of the present invention, other and further embodiments of the invention
may be devised without departing from the basic scope thereof, and
the scope thereof is determined by the claims which follow. |