Abstrict A flow meter for multiphase flows, includes a holdup measuring
device having a Venturi located upstream thereof and separated therefrom
by a distance that results in flow through the holdup measuring
device being at least partially homogenized by the effect of the
Venturi on the fluids flowing therethrough.
Claims 1. A flow meter for multiphase flows, comprising a holdup measuring
device having a Venturi located upstream thereof and separated therefrom
by a distance that results in flow through the holdup measuring
device being at least partially homogenized by the effect of the
Venturi on the fluids flowing therethrough:
2. A flow meter as claimed in claim 1 wherein the holdup measuring
device includes a capacitive device which measures the dielectric
constant of the flowing fluids.
3. A flow meter as claimed in claim 1 wherein the holdup measuring
device includes a resistive device measuring the resistivity of
the flowing fluids.
4. A flow meter as claimed in claim 1 wherein the holdup measuring
device measures volume fractions in the range of 0-100% water.
5. A flow meter as claimed in claim 4 wherein the holdup measuring
device comprises a combination of capacitive and resistive measurements
on the flowing fluids.
6. A flow meter as claimed in claim 2 wherein a capacitance sensor
comprises at least one excitation electrode provided with at least
one cutout in which at least one measurement electrode is disposed,
the electrodes being applied against a pipe through which the fluids
flow.
7. A flow meter as claimed in claim 6 further comprising a system
for maintaining the electrodes at the same potential and for measuring
the current output by the measurement electrode, and a processing
system for determining the dielectric constant of the fluids from
the measured current.
8. A flow meter as claimed in claim 6 wherein all of the conductors
liable to give rise to interference that are situated in the vicinity
of the sensor are maintained at the potential of the excitation
electrode.
9. A flow meter as claimed in claim 6 wherein the excitation electrode
is connected to the general ground of a power supply.
10. A flow meter as claimed in claim 7 wherein the excitation
electrode constitutes a floating ground for the current measuring
system.
11. A flow meter as claimed in claim 10 wherein the current measuring
system comprises a first amplification stage referenced relative
to the potential of the excitation electrode, and a second amplification
stage arranged to bring the reference of the output signal to the
general ground.
12. A flow meter as claimed in claim 11 further comprising shielding,
electrically connected to the excitation electrode, around the measurement
electrode and around the first amplification stage.
13. A flow meter as claimed in claim 12 wherein the shielding
is extended by a shielded cable along which a conductor passes that
connects the measurement electrode to the amplification stage which
also is provided with shielding
14. A flow meter as claimed in claim 13 wherein the excitation
electrode overlaps the measurement electrode.
15. A flow meter as claimed in claim 3 wherein the resistivity
measuring device comprises: (i) a pipe segment of insulating material;
(ii) an electric current generator which generates a current in
the fluid flowing along the pipe; (iii) two measurement electrodes
spaced apart in the axial direction of the insulating segment and
applied to an outside of the wall of the pipe to perform measurement
by capacitive coupling so as to measure the electrical resistance
therebetween; and (iv) a measurement system for measuring the voltage
between the measurement electrodes.
16. A flow meter as claimed in claim 15 wherein the measurement
electrodes are annular electrodes placed around the insulating pipe
segment.
17. A flow meter as claimed in claim 16 wherein a guard electrode
surrounds each of the measurement electrodes.
18. A flow meter as claimed in claim 17 wherein the measurement
system maintains the voltages of the guard electrodes at the same
values as the voltages of the corresponding measurement electrodes.
19. A flow meter as claimed in claim 15 wherein the measurement
system is configured such that the current flowing between the measurement
electrodes is small enough to avoid affecting the measured voltage
so that the potential difference between the two electrodes is equal
to the potential difference between the points in the fluid facing
the electrodes.
20. A flow meter as claimed in claim 19 wherein the measurement
system comprises respective follower amplifiers associated with
each of the measurement electrodes, each amplifier having an input
connected to a measurement electrode and another input connected
to a corresponding guard electrode and having an output connected
to the guard electrode, the system further comprising means for
determining the potential difference between the outputs of the
two follower amplifiers.
21. A flow meter as claimed in claim 20 wherein each follower
amplifier is connected to a corresponding measurement electrode
by a core of a coaxial cable, and to a corresponding guard electrode
by a shield of the coaxial cable.
22. A flow meter as claimed in claim 15 wherein the electric current
generator comprises a toroidal emitter coil surrounding the tubing
and a return electrical conductor interconnecting metal portions
of the pipe situated respectively upstream and downstream from the
insulating segment.
23. A flow meter as claimed in claim 15 further comprising a toroidal
receiver coil surrounding the tubing to form a current measuring
system.
24. A flow meter as claimed in claim 23 wherein each receiver
coil is connected to an electronic circuit having low input impedance
and the output from the electronic circuit delivers a signal that
is proportional to the current flowing in the fluid.
25. A flow meter as claimed in claim 24 wherein the measurement
system determines the ratio between the output from a voltage-measurement
system that measures the voltage between the measurement electrodes
and the output from a current-measuring system, the ratio being
proportional to the resistance of the fluid.
26. A flow meter as claimed in claim 1 wherein the holdup measuring
device is located approximately 1-10 pipe diameters downstream of
the Venturi.
27. A flow meter for multiphase flows, comprising a holdup measuring
device having a Venturi located upstream thereof and separated therefrom
by a distance that results in flow through the holdup measuring
device being at least partially homogenized by the effect of the
Venturi on the fluids flowing therethrough, the holdup measuring
device comprising a capacitive sensor for determining the flow characteristics
of a multi-phase fluid in a pipe, comprising at least one excitation
electrode which part of the surface defines a cutout to allow free
space in which at least one measurement electrode is disposed, said
electrodes being arranged to be applied against said pipe.
28. A flow meter for multiphase flows, comprising a holdup measuring
device having a Venturi located upstream thereof and separated therefrom
by a distance that results in flow through the holdup measuring
device being at least partially homogenized by the effect of the
Venturi on the fluids flowing therethrough, the holdup measuring
device comprising a device for capacitively measuring the dielectric
constant of a two-phase fluid flowing along a pipe, comprising:
at least one capacitive sensor comprising at least one excitation
electrode which part of the surface defines a cutout to allow free
space in which at least one measurement electrode is disposed, said
electrodes being arranged to be applied against said pipe; power
supply means connected to the excitation electrode of said capacitive
sensor in order to apply an AC voltage to said excitation electrode;
amplification means connected to both the excitation electrode and
the measurement electrode in order to maintain said electrodes at
the same potential and capacitively measure the current (i) output
by said measurement electrode; and deducing means connected to said
amplification means in order to deduce said dielectric constant
from said current (i).
29. A device according to claim 28 in which said excitation electrode
is connected to the general ground of said power supply means.
30. A device according to claim 28 in which an electrode is connected
to the general ground of said power supply means, a floating ground
being provided for said amplifying means for measuring the current.
31. A device according to claim 30 in which said amplifying means
for measuring the current comprise a first amplification stage referenced
relative to the potential of the excitation electrode, and a second
amplification stage organized to bring the reference of the output
signal to the general ground.
32. A device according to claim 31 including shielding electrically
connected to the excitation electrode, around the measurement electrode
and around said first amplification stage.
33. A device according to claim 28 in which said excitation electrode
covers the measurement electrode.
34. A flow meter for multiphase flows, comprising a holdup measuring
device having a Venturi located upstream thereof and separated therefrom
by a distance that results in flow through the holdup measuring
device being at least partially homogenized by the effect of the
Venturi on the fluids flowing therethrough, the holdup measuring
device comprising a device for capacitively measuring the volume
fraction of a first fluid in a two-phase fluid flowing along a pipe,
comprising: at least one device for capacitively measuring the dielectric
constant of said fluid, said device comprising: at least one capacitive
sensor comprising at least one excitation electrode which part of
the surface defines a cutout to allow free space in which at least
one measurement electrode is disposed, said electrodes being arranged
to be applied against said pipe; power supply means connected to
the excitation electrode of said capacitive sensor in order to apply
an AC voltage to said excitation electrode; amplification means
connected to both the excitation electrode and the measurement electrode
in order to maintain said electrodes at the same potential and capacitively
measure the current (i) output by said measurement electrode; calculating
means connected to said amplification means in order to deduce said
dielectric constant from said current (i) and calculate said volume
fraction from said dielectric constant.
35. A device according to claim 34 comprising a plurality of devices
for capacitively measuring the dielectric constant of said fluid,
said plurality of devices being distributed over the periphery of
a cross-section of said pipe.
36. A flow meter for multiphase flows, comprising a holdup measuring
device having a Venturi located upstream thereof and separated therefrom
by a distance that results in flow through the holdup measuring
device being at least partially homogenized by the effect of the
Venturi on the fluids flowing therethrough, the holdup measuring
device comprising a capacitive device for measuring the speed of
a two-phase fluid flowing along a pipe, comprising: at least two
devices that are disposed in different cross-sections of said pipe,
said devices comprising: at least one capacitive sensor comprising
at least one excitation electrode which part of the surface defines
a cutout to allow free space in which at least one measurement electrode
is disposed, said electrodes being arranged to be applied against
said pipe; power supply means connected to the excitation electrode
of said capacitive sensor in order to apply an AC voltage to said
excitation electrode; amplification means connected to both the
excitation electrode and the measurement electrode in order to maintain
said electrodes at the same potential and capacitively measure the
current (i) output by said measurement electrode; and deducing means
connected to said amplification means in order to deduce said dielectric
constant from said current (i); and correlating means connected
to both of said two devices in order to establish a cross-correlation
between the measurements delivered by said two devices and for deducing
said speed therefrom.
37. A device according to claim 36 in which said at least two
devices are disposed substantially along the same generator line
of said pipe, and have a common excitation electrode.
38. A flow meter for multiphase flows, comprising a holdup measuring
device having a Venturi located upstream thereof and separated therefrom
by a distance that results in flow through the holdup measuring
device being at least partially homogenized by the effect of the
Venturi on the fluids flowing therethrough, the holdup measuring
device comprising a device for capacitively measuring the flow rate
of a fluid in a two-phase fluid flowing along a pipe, comprising
at least one device for capacitively measuring the volume fraction
of a said fluid, comprising: at least one device for capacitively
measuring the dielectric constant of said fluid, said device including
at least one capacitive sensor comprising at least one excitation
electrode which part of the surface defines a cutout to allow free
space in which at least one measurement electrode is disposed, said
electrodes being arranged to be applied against said pipe; power
supply means connected to the excitation electrode of said capacitive
sensor in order to apply an AC voltage to said excitation electrode;
amplification means connected to both the excitation electrode and
the measurement electrode in order to maintain said electrodes at
the same potential and capacitively measure the current (i) output
by said measurement electrode; and calculating means connected to
said amplification means in order to deduce said dielectric constant
from said current (i) and calculate said volume fraction from said
dielectric constant. at least one capacitive device for measuring
the speed of a two-phase fluid flowing along a pipe, comprising:
at least two devices that are disposed in different cross-sections
of said pipe, said two devices including at least one capacitive
sensor comprising at least one excitation electrode which part of
the surface defines a cutout to allow free space in which at least
one measurement electrode is disposed, said electrodes being arranged
to be applied against said pipe; power supply means connected to
the excitation electrode of said capacitive sensor in order to apply
an AC voltage to said excitation electrode; amplification means
connected to both the excitation electrode and the measurement electrode
in order to maintain said electrodes at the same potential and capacitively
measure the current (i) output by said measurement electrode; deducing
means connected to said amplification means in order to deduce said
dielectric constant from said current (i); and correlating means
connected to said capacitive device for measuring the speed, in
order to establish a cross-correlation between the measurements
delivered by capacitive device and to deduce said speed and thus
said flow rate therefrom.
39. A method of measuring multiphase flows in a well, comprising
measuring holdup in the flowing fluids downstream from a Venturi
at a distance that results in flow being at least partially homogenized
by the effect of the Venturi at the point at which holdup is measured.
Description RELATED APPLICATIONS
[0001] The present application is a continuation in part of co-pending
application Ser. No. 09/335069 and is related to pending PCT application
number PCT/EP01/02762 and pending PCT application number PCT/GB00/01758
both of which designates, inter alia, the United States and the
disclosures of which are incorporated herein by reference.
FIELD OF THE INVENTION
[0002] The present invention relates to the field of flow meters
for multiphase mixtures. In particular, the invention relates to
flow meters for oil and water mixtures in hydrocarbon wells.
BACKGROUND OF THE INVENTION
[0003] The measurement of oil and water flow rate in each producing
zone of an oil well is important to the monitoring and control of
fluid movement in the well and reservoir. In addition to a flow
meter, each zone may have a valve to control the fluid inlet from
that zone. By monitoring flow rates of oil and water from each zone
and reducing flow from those zones producing the highest water cut
(i.e., ratio of water flow rate to total flow rate), the water production
of the entire well can be controlled. This, in addition, allows
the reservoir oil to be swept more completely during the life of
the well.
[0004] To evaluate the water and hydrocarbon flow rates in homogeneous
flows in a well, three quantities must be estimated, namely, the
mean water volume fraction H.sub.w, the mean water velocity v.sub.w,
and the mean hydrocarbon velocity v.sub.o. The flow rates are then
as follows:
q.sub.w=AH.sub.wv.sub.w [1]
[0005] for the water; and
q.sub.o=A(1-H.sub.w)v.sub.o [2]
[0006] for the hydrocarbon, where A is the section of the well.
[0007] When the flow is not homogeneous, which is possible in deviated
wells, flow-rate evaluations based on the above equations are invalid.
It is then necessary to take account of the effective distribution
of the velocities and of the volume fractions across the section
of the well. In order to adopt such an approach, it is necessary
that a plurality of devices are placed across a given cross-section
of the well.
[0008] It is also known that the velocity of a flow in a well can
be determined by measuring a magnitude that varies over time s.sub.1(t)
and s.sub.2(t) at two different locations in the well separated
in the direction of flow, and then by calculating a cross-correlation
function:
C=<s.sub.1(t)*s.sub.2(t+T)> [3]
[0009] In a two-phase fluid, the fluctuations in the magnitude
s(t) may, for example, be due to inhomogeneous structures propagating
along the pipe at the mean speed of the flow.
[0010] If T is the value of t found for which C is a maximum, the
speed v of the flow is given by:
v=L/T [4]
[0011] where L is the axial distance between the two measurement
sections.
[0012] Ideally, a flow meter for making such measurement in a well
should satisfy several criteria: 1) it should be extremely reliable
and operate for long periods at downhole temperature and pressure;
2) it should operate in both stratified (near-horizontal) and dispersed
flow regimes over a wide range of total flow rate and cut; 3) it
should not require that the well completion be oriented azimuthally
in any particular way during installation; 4) it should not require
the use of radioactive sources: and 5) the flow meter should allow
small changes in water cut and flow rate to be detected.
[0013] Typically, downhole flow meters determine the holdup (volume
fraction of oil or water) and the velocity of the oil phase, the
water phase, or both. The flow rate of water is then determined
from the product of water holdup .alpha..sub.w, the pipe area A,
and the velocity of water U.sub.W. An analogous relation holds for
oil flow rate. In general, the velocities of water and oil are different.
The slip velocity (difference in oil and water velocities) depends
on many parameters, such as the inclination angle of the flow pipe
(i.e. deviation), roughness of the pipe wall, and flow rates of
the two phases. In general, one must measure the holdup and velocities
of both oil and water to determine oil and water flow rate uniquely.
In practice, sometimes one measures the velocity of only one phase
and uses a theoretical or empirically determined slip law to obtain
the other. This has a number drawbacks including inaccuracies due
to differences conditions used as inputs to the model and the actual
conditions downhole.
[0014] A common method to determine the velocity of a fluid is
to measure the rotation rate of a spinner in the flow stream. In
single phase flow, the rotational velocity of the spinner is simply
related to the velocity of the flow. However, in mixed oil and water
flow the response of the spinner can be so complicated as to be
impossible to interpret.
[0015] Another method of velocity measurement uses tracers. A tracer
is injected into the phase of choice (oil or water) and, at a known
distance downstream, a sensor detects the time of passage of the
tracer. The velocity is computed from the known distance and time
of travel. One disadvantage of the tracer method for permanent downhole
use is the need for a reservoir of tracer material and a mechanical
tracer injector. The reservoir limits the number of measurements
and the injector, being a mechanical device, is prone to sticking
and failure.
[0016] Another method of velocity measurement uses a Venturi. In
single phase flow, a Venturi generally obeys the Bernoulli equation
which relates volumetric flow rate Q to fluid density .rho. and
pressure drop from the inlet to the throat of the Venturi: 1 Q =
C 2 p / ( 1 A throat 2 - 1 A inlet 2 ) [ 5 ]
[0017] where C is the discharge coefficient which is approximately
unity but depends on the geometry of the Venturi, .DELTA.p is the
pressure drop from Venturi inlet to throat, and A.sub.throat and
A.sub.inlet are the throat and inlet cross sectional areas, respectively.
The same equation can be used to determine the combined oil and
water flow rate where the density in this case is the average mixture
density in the throat of the Venturi. In practice, the square root
in the equation makes it relatively insensitive to errors in both
the density and pressure determinations.
[0018] A common method to determine the holdup in a flow of oil
and water is to measure the average density of the fluid. Since
oil at downhole pressure and temperature typically has a density
which is smaller than that of water (around 0.7 g/cm.sup.3 compared
to 1.0 g/cm.sup.3), the oil and water holdups .alpha..sub.o and
.alpha..sub.w can be determined proportionately from the mixture
density by the relations 2 o = w - m i x w - o [ 6 ] w = m i x -
o w - o [ 7 ]
[0019] A common method to determine the mixture density is to measure
the hydrostatic pressure of a column of fluid with a gradiomanometer.
This device relies on having a component of the gravitational force
vector along the axis of the flow pipe. This type of device, however,
fails when the flow pipe is horizontal because the gravitational
force vector is perpendicular to the pipe axis.
[0020] It is also known, e.g. from U.S. Pat. NO. 5017879 or FR
2 780 499 that capacitive devices can be used to determine the
characteristics of multi-phase flows. The dielectric constant of
a mixture of fluids depends on the respective fraction of each of
its components and on their individual dielectric constants. It
has thus been proposed to estimate the composition of a two-phase
fluid on the basis of its dielectric constant.
[0021] The dielectric constant is itself obtained by exciting the
fluid by means of electrodes separated by the fluid, in particular
electrodes placed on the pipe, and across which an AC voltage is
applied. The measured magnitude is the resulting current. Guard
electrodes have also been added to maintain the electrostatic field
between the active electrodes. It is thus easier to interpret the
measurements by limiting the edge effects due to the finite length
of the active electrodes, or by focusing the electric field in a
particular zone of the flow.
[0022] In both of the above-mentioned cases, namely when the flow
is not homogeneous, or when the velocity is measured, it is thus
necessary to dispose a plurality of devices, in particular capacitive
devices, close together on the pipe. Contradictory requirements
then have to be faced.
[0023] It is desirable to use devices that are of small size. In
a non-homogeneous flow, better resolution in space is thus obtained,
thereby considerably improving the speed and the accuracy of the
interpretation algorithm. When velocity is to be measured, the small
size of the devices makes it possible to position them closer together,
and thus to obtain a correlation peak that is clearer for the resulting
measurements, because the inhomogeneous structures deform to a lesser
extent between the two devices. Unfortunately, such a small size
generally makes the measurements much more sensitive to electromagnetic
noise. When the measurements are capacitive measurements, the measured
capacitance values are low. Typically, the currents induced by the
stray capacitance may be greater by several orders of magnitude
than the current resulting from the capacitance to be measured.
The stray capacitance thus gives rise to a systematic error or bias
whose variations can exceed the amplitude of the signal itself.
[0024] Flow measurement devices are also known that comprise a
segment of insulating pipe and means for generating an electric
current in the fluid flowing in said pipe. These devices thus complement
the preceding devices since they apply to multiphase fluids having
a continuous conductive phase, i.e. fluids that are not insulating.
[0025] The difficulty with such devices lies in measuring the potential
difference between two points of the fluid to deduce the electrical
resistance between those two points, given knowledge of the current.
Thereafter, the resistance is used to deduce the mean resistivity
given that the shape of the pipe is known.
[0026] Mixers of various types have been used to mix the oil and
water, so as to effectively reduce the slip and allow for more accurate
determination of the flow rates. Some mixers are simply small orifices
in plates of suitable material. Others comprise more elaborate fins
having certain twists or curled shapes. There are a number of disadvantages,
however, in using conventional mixers when trying to measure the
flow rates of oil and water downhole. For example, the mixer often
obstructs the borehole, such that it may be difficult to pass certain
equipment such as production logging tools, etc. Mixers also can
produce unacceptable amounts of pressure loss. Additionally, mixers
are prone to excessive wear with age.
[0027] It is possible to measure the pressure differential upstream
and downstream of a conventional mixer in an attempt to determine
the total flow rate of oil and water. This technique, however, has
a number of drawbacks. For example, the accuracy of the flow rate
determined by this method is likely to be much lower than using
a Venturi, and, in general, greatly dependent upon the flow rates.
Using a mixer to measure pressure differential can also lead to
inaccuracy due to sensitivity to the exact location of pressure
measurement. Using a conventional mixer in this fashion would also
be prone to problems associated with wear. For example, in an orifice
mixer, the relationship between the pressure differential and the
velocity could change significantly over time due to slight changes
in shape and size of the orifice caused by wear.
[0028] U.S. Pat. No. 4856344 issued to Hunt, discloses using
a Venturi for obtaining a pressure differential and using a gradiomanometer
upstream and through the Venturi to measure density. Hunt discloses
using an iterative process to estimate the relative flow velocities.
Hunt also discloses using a separate upstream step discontinuity
to mix the fluids upstream of the gradiomanometer. However, the
method disclosed in Hunt is prone to problems associated with relying
on estimates of the flow velocities (i.e. a slip model), using separate
additional mixers upstream, and using a gradiomanometer (e.g. nonfunctional
when pipe is horizontal, and low accuracy when near-horizontal).
[0029] U.S. Pat. No. 5361632 issued to Magnani, discusses a
holdup measurement using a combination of gradiomanometer and gamma-ray
densitometer. Thus, the method of Magnani is prone to problems associated
with using a gradiomanometer which is not suitable for measurements
in near-horizontal pipes. Furthermore, the method obstructs the
borehole and would not be suitable for permanent installation.
[0030] U.S. Pat. No. 5661237 issued to Dussan et al. discusses
a holdup measurement using local probes. There is no mention of
a Venturi, however. The method obstructs the borehole and would
not be suitable for permanent installation.
[0031] U.S. Pat. Nos. 5893642 and 5822390 issued to Hewitt
et al. disclose a method of using a mixer to measure flow rates.
However, this method suffers from the disadvantages of using a mixer
as described above. For example, the mixer obstructs borehole and
is not suitable for permanent installation due to problems of wear.
SUMMARY OF THE INVENTION
[0032] The present invention provides a flow meter for multiphase
flows, comprising a holdup measuring device having a Venturi located
upstream thereof and separated therefrom by a distance that results
in flow through the holdup measuring device being at least partially
homogenized by the effect of the Venturi on the fluids flowing therethrough.
[0033] Preferably, the holdup measuring device is a capacitive
device and/or a resistive device. It is particularly preferred that
the holdup measuring device measures volume fractions in the range
of 0-100% water. Such a device can be provided by a combination
of capacitive and resistive measurements on the flowing fluids.
[0034] Preferred capacitive sensors for determining the characteristics
of multi-phase flows are of small size and substantially insensitive
to noise and thus substantially free from systematic error. A particularly
preferred sensor comprises at least one excitation electrode provided
with at least one cutout in which at least one measurement electrode
is disposed, the electrodes being applied against the pipe.
[0035] A device for measuring the dielectric constant of a multi-phase
fluid flowing along a pipe comprises at least one sensor as described
above, means for maintaining the electrodes at the same potential
and for measuring the current output by the measurement electrode,
and means for deducing the dielectric constant from the current.
[0036] This configuration then makes it possible for all of the
conductors liable to give rise to interference that are situated
in the vicinity of the device in the detection system to be maintained
at the potential of the excitation electrode. As the conductors
are at the same potential as the measurement electrode, the load
thereon thus depends only on the potentials applied to the active
electrodes.
[0037] In a first embodiment, the excitation electrode is connected
to the general ground of power supply means. This approach is relatively
simple.
[0038] In another embodiment, the excitation electrode constitutes
a floating ground for the current measuring means. The advantage
of this embodiment is that the signal can be amplified to a level
at which it dominates the common mode rejection voltage of the amplifier.
In this embodiment, the current measuring may comprise a first amplification
stage referenced relative to the potential of the excitation electrode,
and a second amplification stage arranged to bring the i5 reference
of the output signal to the general ground. More particularly, the
device may include shielding electrically connected to the excitation
electrode, around the measurement electrode and around said first
amplification stage. Such a configuration does not require the first
amplification stage to be located in the immediate vicinity of the
measurement electrode. The shielding of the measurement electrode
may be extended by a shielded cable along which a conductor passes
that connects the measurement electrode to the amplification means
which are themselves provided with shielding forming the following
portion of the shielded cable. The excitation electrode may overlap
the measurement electrode.
[0039] The resistivity measuring device preferably comprises a
pipe segment of insulating material and means for generating an
electric current in the fluid flowing along the pipe, the device
being characterized by the fact that it comprises two measurement
electrodes spaced apart in the axial direction of the insulating
segment to determine the electrical resistance of the fluid between
the two electrodes, the measurement electrodes being applied to
the outside of the wall of the segment to perform measurement by
capacitive coupling, and by the fact that it further comprise measurement
means for measuring the voltage between the measurement electrodes.
[0040] The measurement can thus be treated as a "4-point"
resistance measurement.
[0041] Since this arrangement is not dependent on the contact impedance
between the fluid and the upstream and downstream metal portions
of the pipe, the surface state of the pipe has no effect on the
measurement. Furthermore, no measurement electrode comes into contact
with the fluid. There is thus no risk of corrosion. This characteristic
makes the device of the invention particularly suitable for continuous,
long term measurements. It is thus possible to fit a production
tube with measurement segments of the invention at the levels of
the fluid inlets, and thus monitor the actual production of each
production zone in a hydrocarbon well. The device is also suitable
for performing continuous measurements on the surface, in particular
at a well head.
[0042] In a particular embodiment, the measurement electrodes are
annular electrodes placed around the insulating pipe segment. Also,
a guard electrode may surround each of the measurement electrodes.
[0043] More particularly, the measurement means for measuring the
voltage between the measurement electrodes may be arranged to maintain
the voltages of the guard electrodes at the same values as the voltages
of the corresponding measurement electrodes.
[0044] The measurement means for measuring the voltage between
the measurement electrodes may also be arranged so that the current
flowing between the measurement electrodes is small enough to avoid
affecting the measured voltage. Thus, the potential difference between
the two electrodes is equal to the potential difference between
the points in the fluid facing the electrodes.
[0045] In this case, the measurement means for measuring the voltage
between the measurement electrodes may comprise respective follower
amplifiers associated with each of the measurement electrodes, each
amplifier having one of its inputs connected to a measurement electrode
and its other input connected to the corresponding guard electrode
and having its output connected to the guard electrode, the device
further comprising means for determining the potential difference
between the outputs of the two follower amplifiers. Such a follower
amplifier possesses high input impedance which avoids the potential
drop due to current passing through the insulation by the capacitive
effect. Its output voltage is equal to the input voltage, but current
is available at its output. More particularly, each follower amplifier
may be connected to the corresponding measurement electrode by the
core of a coaxial cable, and to the corresponding guard electrode
by the shield of the cable.
[0046] In a particular embodiment, the means for generating an
electric current in the fluid flowing in the pipe comprise a toroidal
emitter coil surrounding the tubing and a return electrical conductor
interconnecting metal portions of the pipe situated respectively
upstream and downstream from the insulating segment. Such a coil
has the advantage of not coming into contact with the fluid, and
thus of being unaffected by corrosion problems. The emitter coil,
connected to an AC voltage generator, generates an electric field
in the fluid and thus behaves like a primary winding of a transformer
whose secondary winding is constituted by the fluid and the return
conductor. This electric field generates the above-specified current,
which depends on the resistance of the fluid.
[0047] It is also preferred that the device of the invention comprises
a toroidal receiver coil surrounding the tubing to form a current
measuring system. Each receiver coil is connected to an electronic
circuit having low input impedance. The output from the electronic
circuit delivers a signal that is proportional to the current flowing
in the fluid. In this case, the device may comprise means for determining
the ratio between the output from the voltage-measurement means
for measuring the voltage between said measurement electrodes and
the output from the current-measuring system. This ratio is proportional
to the resistance of the fluid, ignoring contact impedance.
[0048] The invention therefore provides a device for determining
the volume fraction (or "holdup") of the conductive fluid
in a multiphase fluid having a continuous conductive phase comprising
a device of the type described above to measure the mean resistivity
of the multiphase fluid, and means for deducing the volume fraction
from the resistivity.
[0049] Determining the volume fraction requires not only knowledge
of the mean resistivity, but also knowledge of the resistivity of
the conductive phase and of the flow conditions. The resistivity
of the conductive phase can be determined by other means, and it
is possible to make various assumptions about the flow conditions
or again, they can be measured directly.
[0050] In a particular embodiment of the invention, a Venturi total
volumetric flow rate measurement is provided with a holdup measurement
approximately 1-10 pipe diameters downstream of the Venturi. The
invention makes use of a flow instability downstream of the Venturi
throat. When the oil and water flow accelerates into the throat
of the Venturi, the streamlines converge from their upstream value
and the pressure drops as the hydrostatic head is converted into
kinetic energy. Conversely, as the flow enters the diffuser section
the pressure recovers as the flow decelerates. This adverse pressure
gradient can lead to separation of the flow within the boundary
layer at some position downstream of the throat of the Venturi.
That position depends on the geometry of the Venturi, the individual
oil and water flow rates, the deviation angle of the pipe to the
horizontal, and the densities of the two fluids. The main flow expands
beyond the Venturi as a jet of approximately uniform velocity bounded
by a free shear layer, and such shear layers are prone to Kelvin-Helmholtz
type instabilities that grow and are convected downstream. In the
diffuser of the Venturi, an instability such as this grows and perturbs
the interface between the two fluids. The amplitude of the instability
depends on the geometry of the Venturi, the deviation of the pipe,
the densities of the fluids, and the flow rates. An instability
of sufficient strength causes the interface to roll up and break
with a resulting mixing of the two layers completely across the
pipe.
[0051] According to the invention, a method of determining the
flow rate of a first fluid phase in a pipe containing at least two
fluid phases is provided. The fluid phases flow through an upstream
pipe, a constriction, which is preferably a Venturi, and a downstream
pipe. The differential pressure of the fluid phases is measured
such that it can be related to the total flow rate of the fluid
phases through the section of pipe. The differential pressure is
preferably measured between the upstream pipe and the throat of
the Venturi. The volume fraction of the first fluid phase (preferably
water) is determined by making a measurement at a location downstream
of the constriction where a substantial amount of mixing of the
at least two fluid phases is present, which results from the fluid
passing through the Venturi. The flow rate of the first fluid (preferably
water) is determined by assuming its velocity is substantially the
same as that of the other fluid phases.
[0052] The present invention can provide a flow meter suitable
for downhole placement that is extremely reliable and capable of
operating for years at downhole temperatures and pressures. It can
be capable of operating in both stratified (near-horizontal) and
dispersed flow regimes over a wide range of total flow rate and
cut. The flow meter may not require that the wellbore be oriented
azimuthally in any particular way during installation. The invention
also provides a flow meter that avoids the use of relatively strong
radioactive sources. It can be capable of detecting small changes
in water cut and flow rate and providing a measurement of a phase
transition pressure. The invention can also be used to alleviate
the problems associated with the use of conventional mixers, including
the possible problems associated with measuring the pressure differential
upstream and downstream of a conventional mixer.
BRIEF DESCRIPTION OF THE DRAWINGS
[0053] FIG. 1 is a perspective view of a section of pipe including
a Venturi used to measure velocity and to mix oil and water according
to a preferred embodiment of the invention;
[0054] FIG. 2 is a detailed cross sectional view of a Venturi used
to measure velocity and to mix oil and water according to a preferred
embodiment of the invention;
[0055] FIG. 3 is a perspective view of a section of pipe including
a Venturi and other equipment used to measure velocity and to mix
oil and water according to a preferred embodiment of the invention;
[0056] FIG. 4 is a graph illustrating the relationship between
water holdup compared to the water cut as experimentally measured
at a Venturi throat section;
[0057] FIG. 5 is a graph illustrating the relationship between
water holdup compared to the water cut as experimentally measured
at a location upstream from a Venturi;
[0058] FIG. 6 is a graph illustrating the relationship between
water holdup compared to the water cut as experimentally measured
at a location downstream from a Venturi, according to a preferred
embodiment of the invention;
[0059] FIG. 7 shows an installation according to one embodiment
of the invention;
[0060] FIG. 8 is an electric circuit diagram of a device of the
invention for measuring the dielectric constant of a two-phase fluid;
[0061] FIG. 9 shows a variant of the device shown in FIG. 8;
[0062] FIG. 10 shows how devices of the type shown in FIG. 8 are
used to obtain cross-sections, e.g. of volume fraction distribution;
[0063] FIG. 11 shows another embodiment of the arrangement shown
in FIG. 10;
[0064] FIG. 12 shows how devices of the type shown in FIG. 8 are
used to perform flow-rate measurements.
[0065] FIG. 13 is an overall view of a device for measuring resistivity
of flowing fluids according to an embodiment of the invention; and
[0066] FIG. 14 is an electrical circuit diagram for use with the
device of FIG. 14.
DETAILED DESCRIPTION OF THE INVENTION
[0067] FIG. 1 is a perspective view of a section of pipe 100 including
a Venturi 110 used to measure velocity and to mix oil and water
according to a preferred embodiment of the invention. The direction
of flow is shown by arrow 102. Pipe section 112 is upstream of the
Venturi 110. Venturi 110 comprises a tapered inlet section 114
a Venturi throat 116 and a Venturi diffuser 118. Pipe section 120
is downstream of the Venturi 110 and has diameter 124. According
to the invention, it has been found that significant mixing of oil
and water takes place downstream of Venturi 110 and therefore it
is a good place to make a holdup measurement. In FIG. 1 downstream
location 122 is shown to be a suitable location for measuring the
holdup.
[0068] FIG. 2 is a detailed cross sectional view of a Venturi used
to measure velocity and to mix oil and water according to a preferred
embodiment of the invention. The direction of flow is shown by arrow
102. Inlet 114 is smoothly tapered from the diameter of the upstream
section 112 to the diameter of the Venturi throat 116. As shown
in FIG. 2 the Venturi throat 116 has a diameter narrower than upstream
section 112. The walls of the Venturi throat 116 are preferably
approximately parallel along the direction of flow 102. The Venturi
diffuser 118 is gradually tapered from the diameter of the Venturi
throat 116 to approximately the diameter 124 of the downstream section
120. Upstream section 112 inlet 114 throat 116 diffuser 118
and downstream section 120 all have approximately circular cross-sections,
and the diameter of the throat 116 is preferably about half that
of the upstream pipe section (i.e. 0316<.beta.<07751). For,
example if the upstream pipe section diameter is 15 cm, then the
throat is preferably about 7.5 cm. Preferably, Venturi 110 is designed
to meet the ISO standard and is designed so as to allow for relatively
accurate measurements of differential pressure, while impeding the
flow as little as possible. However, it is contemplated that other
Venturi dimensions and geometries could also facilitate an accurate
differential pressure measurement and provide sufficient mixing
for an accurate holdup measurement, according to the invention.
The location with respect to the Venturi where the holdup measurements
were taken is shown at downstream location 120. As will be described
in greater detail below, measuring the holdup at locations downstream
as shown advantageously allows for much more accurate determinations
of flow rates. As shown in FIG. 2 a port 134 is provided to measure
the pressure at a location within Venturi throat 116. Another port,
not shown in FIG. 2 is provided upstream which in combination with
port 134 allows for measurement of pressure differential.
[0069] FIG. 3 is a perspective view of a section of pipe including
a Venturi and other equipment used to measure velocity and to mix
oil and water according to a preferred embodiment of the invention.
[0070] In a preferred embodiment shown in FIG. 3 the invention
combines a Venturi 110 with a combined resistivity and dielectric
measurement-based flow meter that is described in more detail below.
A differential pressure sensor 130 measures the pressure drop between
the inlet 112 (at port 132) and the Venturi throat 116 (at port
134). (Note that although the pressure sensor 130 is shown to measure
the differential pressure between the locations of ports 132 and
134 other locations could be chosen. For example, although unconventional,
one of the measurements could be taken downstream of the Venturi.)
A flow instability develops as the flow exits from the Venturi diffuser
118. The holdup meter is preferably placed at a particular location
which is a distance 1-10 times the downstream pipe diameter 124.
However, a substantial improvement in the accuracy of determining
the relative flow rates of water and oil can be obtained under some
circumstances by measuring the holdup at any location from just
downstream of the Venturi to about 20 pipe diameters. For example,
it may be sufficiently accurate to measure the holdup at locations
where the stratification has been significantly perturbed.
[0071] It is presently believed that measuring the holdup in a
region approximately 1-5 diameters from the Venturi can provide
even greater accuracy over a wider range of flow rates. In certain
conditions, it is believed that measuring the holdup at approximately
5 diameters from end of the diffuser will provide the greatest accuracy
in relative flow rate measurement.
[0072] In general, the distance from the Venturi at which a suitable
amount of mixing occurs will depend on many factors. First the amount
of mixing needed to substantially improve flow rate determination
depends on the method of holdup measurement. Second, the distance
from the Venturi at which suitable mixing occurs depends on the
particular geometry and anticipated flow rates of the fluids in
the Venturi. Furthermore, the density and viscosity of the fluids,
and the deviation can influence the amount and location of mixing
caused by the Venturi.
[0073] FIG. 4 is a graph illustrating the relationship between
water holdup compared to the water cut as experimentally measured
at a Venturi throat when flowing various mixtures of oil and water.
The vertical axis is the water holdup, or the volume fraction of
water. The horizontal axis is water cut, or the ratio of water flow
rate to the total volumetric flow rate. The measurements were taken
at different total volumetric flow rates ranging from 40 cubic meters
per hour to 100 cubic meters per hour. As can be seen in FIG. 4
the water holdup varies significantly from the water cut at all
measured flow rates.
[0074] Similarly, FIG. 5 is a graph illustrating the relationship
between water holdup compared to the water cut, but the holdup measurements
were made at a location upstream from a Venturi. As in FIG. 4 the
holdup measurements do not accurately reflect the water cut values
for most of the flow rates measured.
[0075] FIG. 6 is a graph illustrating the relationship between
water holdup compared to the water cut as measured at a location
downstream from a Venturi, according to a preferred embodiment of
the invention. Specifically, in FIG. 6 the water holdup was measured
at a location approximately 3 pipe diameters downstream from the
downstream end of the Venturi diffuser. As can be seen in FIG. 6
in stark contrast from the data in FIGS. 4 and 5 the measured holdup
accurately reflects the water cut at all the measured flow rates.
[0076] A significant instability exists downstream of the Venturi
regardless of the flow regime at the inlet of the Venturi as long
as the total flow rate exceeds a minimum value. For example, for
a 15 cm diameter upstream section of pipe with a Venturi throat
diameter of about 7.5 cm (i.e. 0316<.beta.<07751), approximately
20 cubic meters per hour. Because of this instability and the mixing
that it produces, oil and water are well-mixed approximately 1-10
pipe diameters downstream of the Venturi exit, although as mentioned
above, other measuring the holdup at other locations may be suitable
in certain situations.
[0077] Due to the well-mixed condition, the oil and water are nearly
homogeneously distributed throughout the pipe and the slip velocity
between oil and water is very small. In such a condition, the water
holdup is equal to the water cut Xw, or ratio of the water volumetric
flow rate to the total flow rate. Conversely, the oil holdup is
equal to the oil cut, or ratio of the oil volumetric flow rate to
the total flow rate. This is important because the oil and water
flow rates can then be obtained directly from the product of the
respective holdup and total flow rate from the Venturi:
Q.sub.o=X.sub.oQ=.alpha..sub.oQ Equation 4
Q.sub.w=X.sub.wQ=.alpha..sub.wQ Equation 5
[0078] Advantageously, no slip model is required. Even if the water
holdup is not exactly the same as the water cut, differences of
a few percent can be incorporated as empirical corrections to the
equations given above. Preferably, the holdup measurement is made
at a location downstream of the Venturi where the difference between
the water holdup and the water cut is be negligible for the particular
measurement requirements the application at hand.
[0079] In a well-mixed flow, there is little slip and the water
holdup is essentially equal to the water cut. It is important to
note that such conditions do not exist at other locations in the
pipe, such as upstream of the Venturi or in the Venturi throat.
The water holdup at the Venturi throat is compared to the water
cut in FIG. 4. Clearly, the holdup is not equal to the cut, indicating
that the mixture is not homogeneous. In FIG. 5 the water holdup
upstream is compared to the water cut. Again, the holdup is not
equal to the cut. Finally, in FIG. 6 the water holdup downstream
at a spacing of 3 pipe diameters from the Venturi exit is plotted
against water cut. In this case the holdup is very nearly equal
to the cut.
[0080] Although the present invention has thus far been principally
described in connection with measuring fluid flow rates in mixtures
of oil and water, the present invention is also applicable to facilitate
the determination of fluid flow rates in other mixtures. In general,
a Venturi could also be used to determine velocity and as a mixer
for mixtures of any fluids, including gas phases. For example, two
liquids, one liquid and one gas, or two liquids and one gas. The
geometry of the Venturi can be designed so as to facilitate a suitable
amount of mixing at the flow rates of interest, and the measurement
of the holdup should be taken at a downstream location where a sufficient
amount of mixing takes place to enable an accurate determination
of flow rate from the measured volume fraction.
[0081] As mentioned, the present invention is applicable to mixtures
of three or more phases, where a suitable Venturi can be used to
both measure velocity and mix the various phases. So long as the
velocity of the phases and the geometry of the Venturi is sufficient
to mix the various phases, the amount of slip can be reduced to
a relatively small level and accurate flow rates can be determined.
When determining flow rates in mixtures of three or more phases,
one or more additional measurements can be taken to determine the
particular holdup of interest.
[0082] FIG. 7 shows one embodiment of a system 200 according to
the invention. The system comprises a base tube 202 through which
the fluids produced by the well flow. The first part of the system
is a Venturi device 204 of the type described above which is provided
with differential pressure measuring sensors 206 which are located
outside the tubing 202. Downstream of the Venturi device 204 is
located a resistivity and dielectric flow measurement device 208
which is described in more detail below mounted on a mandrel 210.
Measurement and telemetry electronics 212 are located on the tubing
202 adjacent the flow measurement device 208 and are connected to
the flow measurement device 208 and differential pressure measuring
sensors by a leak proof cable 214.
[0083] The dielectric (capacitance) measurement part of the flow
meter 208 is shown in FIGS. 8-12. At this point, the pipe 202 comprises
a metal tube 221 designed to withstand pressure and internally lined
with an insulating material 222. A multi-phase fluid (hydrocarbons
and water) represented by arrow F, flows along the pipe 221.
[0084] Two active electrodes 223 and 224 are disposed facing each
other on the inside surface of the pipe, thereby substantially forming
two semi-cylindrical half-sleeves (as also shown in FIG. 12). The
electrode 223 is uninterrupted, whereas the "excitation"
electrode 224 is cut to allow space in contact with the tube for
a measurement electrode 225 from which the excitation electrode
is electrically insulated. The electrode 224 overlaps most of the
measurement electrode 225 and is merely provided with an orifice
226 for passing a conductor 227 connected to the measurement electrode
225.
[0085] A voltage generator 228 whose output terminals are connected
to the electrodes 223 and 224 delivers an AC voltage across said
electrodes.
[0086] The conductor 227 and a conductor 229 connected to the electrode
224 are connected to the input of an amplifier 230 fed with DC from
a power supply 231. The amplifier maintains the electrodes 224 and
225 at the same potential. The output 232 of the amplifier 230 is
connected to an input of an instrumentation amplifier 233 whose
other input receives a conductor 234 connected to the electrode
224.
[0087] The two amplifiers 230 and 233 thus form the first two stages
of an amplification system for amplifying the current i delivered
by the measurement electrode 225. The first stage has a floating
ground referenced relative to the potential of the electrode 224
whereas the second stage is referenced to the general ground 235.
The output voltage U of amplifier 233 relative to the general ground
235 is proportional to the current i.
[0088] It can be observed that shielding 236 connected to the electrode
224 covers and isolates the entire first amplification stage 230
thereby contributing to further reducing the crosstalk between the
device and the excitation, which crosstalk is already limited considerably
by the fact that all of the conductors situated in the vicinity
of the measurement electrode 225 are at the same potential as the
measurement electrode.
[0089] The output 237 of the amplification system is connected
to the input of a processing unit 238. The processing unit 238 shapes
the output signal, digitizes it, and deduces the capacitance of
the capacitor made up of the electrode 223 and of the measurement
electrode 225 from the AC voltage delivered by the generator and
from the resulting current i. Knowing the geometry of the capacitor,
the unit 238 can then determine the dielectric constant of the two-phase
fluid, and calculate the water volume fraction by the above-mentioned
relationship: 3 e m = e o 1 ( 1 - H w ) 3
[0090] In another embodiment, shown in FIG. 9 the amplification
and measurement electronic circuitry is no longer situated at the
measurement electrode 225 but rather it is situated a certain distance
away. In this case, the electronic circuitry 239 is disposed in
shielding 240 connected to the shielding 236 of the measurement
electrode 225 by a braid 241 of a coaxial cable 242. The conductor
227 is then brought to the electronic circuitry 239 in the cable
242.
[0091] In the case shown in FIG. 9 the excitation electrode 224
is connected to the general ground of the power supply means. If
a floating ground were provided for the current-measuring means,
the equivalent of the conductor 234 shown in FIG. 8 would also be
brought along the cable 242.
[0092] When the fluid is not homogeneous, which occurs, for example,
in a deviated well having a low flow rate, the configurations shown
in FIGS. 10 and 11 may be chosen.
[0093] The embodiment shown in FIG. 10 is similar to that shown
in FIG. 8. A semi-cylindrical electrode 243 corresponds to the electrode
223 and an excitation electrode 244 corresponds to the excitation
electrode 224. However, in this embodiment, the excitation electrode
244 is provided with three cutouts into which three measurement
electrodes 245 246 and 247 are inserted. The three measurement
electrodes are disposed in the same cross-section of the pipe, and
they are uniformly distributed over one half of the circumference
of the cross-section. Naturally, a larger number of measurement
electrodes may be provided.
[0094] In the embodiment shown in FIG. 11 four independent sensors
are provided, each of which comprises a respective excitation electrode
248a-248d provided with a cutout in which a respective measurement
electrode 249a-249d is included.
[0095] The outputs of all of the sensors are connected to the input
of a processing unit (not shown) which provides a section of the
distribution of the water volume fraction in the fluid across the
pipe.
[0096] FIG. 12 shows a device similar to the FIG. 8 device, except
that it comprises two measurement electrodes 250 and 251 disposed
on the same generator line of a pipe, and included in respective
cutouts in the same excitation electrode 252. As above, the signal
generator 253 applies an AC voltage across the electrode 252 and
an opposite electrode 254.
[0097] As indicated above, cross-correlation of the signals collected
at the measurement electrodes 250 and 251 gives the speed at which
the inhomogeneous structures are displaced between the measurement
electrodes 250 and 251 and thus the mean speed of the flow along
the pipe.
[0098] Naturally, the two embodiments shown in FIGS. 9 and 10 may
be combined to deliver as many flow characteristics as possible.
[0099] The resistivity measuring part of the flow meter 208 is
shown in FIGS. 13 and 14 and is applicable to flows in which the
aqueous phase is continuous, such that the mixture is electrically
conductive.
[0100] The pipe 202 is constituted by an upstream segment 262 and
a downstream segment 263 that are both made of metal, together with
a measurement segment 264 of a material that is electrically non-conductive.
An electrical conductor 265 interconnects the conductive segments
262 and 263 so as to form an electric circuit that is completed
by the fluid flowing along the pipe.
[0101] A toroidal emitter coil 266 is disposed around the pipe
202 inside the current loop defined by the conductor 265 e.g. in
the upstream portion of the measurement segment 264 as shown herein.
The coil 266 is powered by a generator 267 for generating an alternating
voltage. It thus generates an alternating electric field in the
fluid which in turn generates an alternating current in the fluid
and in the conductor 265.
[0102] A toroidal receiver coil 268 is disposed around the pipe
202 also within the current loop defined by the conductor 265
e.g. in the downstream portion of the measurement segment 264. The
coil 268 is connected to a measurement circuit 269 having low input
impedance. The current in the fluid induces a current in the coil
268 such that the output signal from the measurement circuit 2o
269 is proportional to the current in the fluid.
[0103] Two annular measurement electrodes 270 and 271 are disposed
on the outside surface of the pipe segment 264. They are covered
by two respective guard electrodes 272 and 273.
[0104] The output from the measurement electrode 270 takes place
via the core conductor 274 of a coaxial cable 275 which passes through
a hole in the guard electrode 272. The shield 276 of the coaxial
cable 275 is connected to said electrode 272.
[0105] Similarly, the output from the measurement electrode 271
is taken via the core conductor 277 of a coaxial cable 278 which
passes through a hole in the guard electrode 273. The shield 279
of the coaxial cable 278 is connected to the electrode 273.
[0106] The core 274 of the cable 275 is connected at one input
to a follower amplifier 280 whose other input and whose output are
connected to the shield 276. Similarly, the core 277 of the cable
278 is connected to one input of a follower amplifier 281 whose
other input and whose output are connected to the shield 279.
[0107] Thus, the electrodes in each of the pairs 270 272 and 271
273 are maintained at the same potential as each other and a very
small current flows along the conductors 274 and 277 such that
each of the electrodes 270 and 271 is at the same potential as the
fluid facing it on the other side of the wall of the pipe segment
264.
[0108] The outputs from the amplifiers 280 and 281 are applied
respectively to the inverting and to the non-inverting inputs (-
and +) of a differential amplifier 282. The output from the amplifier
282 is thus representative of the potential difference in the fluid
between the planes of the electrodes 270 and 271.
[0109] The output from the measurement circuit 269 i.e. the current
in the fluid, and the output from the amplifier 282 i.e. the above-mentioned
potential difference, are input to a circuit 283 which determines
the ratio of these two quantities. The output from the circuit 283
is thus representative of the resistance of the fluid between the
planes of the electrodes 270 and 271.
[0110] Given knowledge of the cross-section of the segment 264
and the axial distance between the electrodes 270 and 271 it is
possible in a circuit 284 to deduce the mean resistivity of the
fluid.
[0111] From the above, and by using appropriate computation means,
it is thus possible to deduce the water volume fraction or "holdup"
of the two-phase mixture, assuming that the resistivity of the water
is known, and making assumptions about the flow conditions of the
fluid.
[0112] For a flow that is well stratified, the water and the hydrocarbons
flow along the pipe in the form of two separate layers. Under such
circumstances: 4 R = W L S W
[0113] where .rho..sub.w is the resistivity of the water, S.sub.w
is the cross-section of the water layer, and L is the distance between
the measurement electrodes.
[0114] The volume fraction or "holdup" of the water H.sub.w
is then: 5 H W = S W S = W L R S
[0115] where S is the total cross-section of the pipe.
[0116] Conversely, for a flow that is entirely uniform, the resistivity
of the mixture .rho..sub.mix is given by: 6 R = m i x L S
[0117] The water volume fraction H.sub.w is then deduced from the
"Ramu Rao" formula: 7 m i x = W 3 - H W 2 H W 3 - H W
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