CA2013586A1

CA2013586A1 - Method and apparatus for measuring multi-phase flows, in particular in hydrocarbon wells

Info

Publication number: CA2013586A1
Application number: CA002013586A
Authority: CA
Inventors: Pierre Vigneaux
Original assignee: Schlumberger Canada Ltd
Current assignee: Schlumberger Canada Ltd
Priority date: 1989-04-17
Filing date: 1990-04-02
Publication date: 1990-10-17
Also published as: BR9001736A; AU5320790A; NO901612L; FR2645901A1; EP0394085A1; NO901612D0; FR2645901B1; OA09169A

Abstract

A B S T R A C T

A method of measuring the flow of a multi-phase fluid having a continuous phase and a dispersed phase in the form of bubbles, comprising the step of producing, by means of a local sensor whose dimension in the flow direction is substantially smaller than the bubble dimension, a signal having different levels depending on which fluid phase is in contact with the sensor. The transitions between the levels of the signal carry information related to the flow parameters.

Fig. 2

Description

2~ 3~

METHOD AND APPA~ATUS FOR MEASU~ING MULTI-PHAS~ FLOWS, IN PARTICULAR IN HYDROCAR~ON WELLS

The invention relates to a method for investigating the flow para-meters of a multi-phase fluid, in particular the fluid produced in a hydrocarbon well. The invention also relates to apparatus for implemen-ting the method.
In the production of hydrocarbons, a common situation is that the fluid produced by a well is a mixture of two phases : oil and water. The oil is generally constituted by the dispersed phase in the form of bubbles within the continuous phase, which is then constituted by the water.
Conventionally, the oil flow profile as a function of depth is determined from the total flow rate, the volume fraction of each phase, also referred to as the static fraction or "hold-up", and the slippage velocity of the lighter phase (oil) over the other phase (water). The formula conventionally used for determining the oil flow rate QO is:

Qo = Vo Ho S [1]
QO (1 - Hw)(Qt + VS-HW-S) [2]
in which formulae:
- Ho and Hw are the static fractions respectively of oil and water in the section of the well;
~ Qt is the total flow rate;
- VO is the velocity of the oil phase;
- Vs is the sliding velocity between the phases; and - S is the section of the well at the depth under consideration.
The total flow rate Qt is commonly measured by means of a spinner flowmeter (see French patent 2 034 272), the water fraction is commonly measured, for example, by means of an apparatus for measuring mean density such as a differential pressure apparatus referred to as a .

' , - ~ ' .
: , , - 2 - ~3~

gradiomanometer (see French patent 1 467 151), and the slippage velocity is provided by tables on the basis of the values of the static fraction and of the density.
The above-described conventional method relies on the assumption that effects related to variations in velocity and in static fraction within the section under consideration cancel out overall. However this is merely an approximation, and is justified under certain conditions ta well with little deviation), but it is less justified for wells having significant deviation and/or when the total flow rate is low.
The invention seeks to provide a method enabling the parameters of a multi-phase fluid flow to be determined with improved accuracy.
The invention also aims at achieving such determination in a manner which is less dependent on the deviation of a well and on the flow rate.
Broadly speaking, the invention uses a local sensor of small size placed in the flow and producing a signal which has different levels depending on whether the sensor is in the presence of the dispersed phase or of the continuous phase, and relies on the discovery that the transitions between levels in the signal convey information about the flow parameters of the dispersed phase.
According to a characteristic of the invention, a signal is produced representative of the gradient in the sensor signal during a transition, said gradient being proportional to bubble velocity.
Advantageously, the gradient signal is obtained as the reciprocal of a signal representative of the time interval during a transition between crossing a lower threshold and crossing an upper threshold, with said thresholds being related respectively to said levels in the signal from the sensor, and with said time interval being referred to as the "rise time".
According to another characteristic, a signal is produced represen-tative of the time a bubble is present at the sensor, and this signal is combined with said gradient signal representative of bubble velocity, in order to obtain a signal representative of bubble diameter.
According to still another characteristic, the bubble diameter sig-nals obtained over a unit of time are summed, and the resulting sum constitutes a signal representative of the superficial velocity of the dispersed phase, which quantity corresponds to the local velocity of the .

- 3 ~ 3 ~ ~ ~

dispersed phase assuming it to be the only phase in the section under measurement.
The flow parameter values obtained in this way are true representa-tions of real phenomena by virtue of their local nature. They consequen-tly provide a reliable basis for determining the flow rate of the dis-persed phase. By providing a plurality of local sensors of the above-specified type in different positions, a set of values can be obtained at each depth serving both to determine the flow rate of the dispersed phase accurately, and also to analyze the scale of flow phenomena. In particular, it is possible to observe backflow which may result from segregation of the water and oil phases in a highly deviated well.
A distinct advantage of the invention is that the same local sensor can be used both for determining the static fraction and also for deter-mining the superficial velocity of the dispersed phase.
The invention will be well understood from reading the following description made with reference to the accompanying drawings. In the drawings:
Figure 1 shows a radiofrequency type local sensor in a two-phase flow;
Figure 2 shows the signal produced by a bubble of the dispersed phase going past the sensor;
Figures 3A to 3D show the positions of the interface between the dispersed phase and the continuous phase relative to the sensor and in relation with various points of the signal shown in Figure 2;
Figure 4 shows a logging installation for performing measurements in an oil well;
Figure 5 shows one embodiment of a downhole apparatus including such a local sensor; and Figure 6 is a circuit diagram of an acquisition and processing circuit associated with the radiofrequency sensor.
Figure 1 shows a pipe T having a two-phase fluid flowing therein.
In the description below, reference is made to the example of an oil well, in which case the pipe T is constituted by the casing which constitutes the wall of an oil well. The fluid flowing along the well in the direction of the arrow is a two-phase mixture of water and oil. The continuous phase E is constituted by water, while the oil is in the form of bubbles B.

As mentioned in the introduction, the conventional approach for de-termining flow rates relies on measuring the total flow Qt over a sec-tion S by means of a flowmeter, and by measuring the static fraction of the water Hw by means of a pressure gradiometer, with the sliding velo-city Vs of the oil over the water being obtained from tables. In fact, the flow velocities of the two phases and the static fractions vary over any given section. The total oil flow rate Q is thus given rigorously by the following integral:
1 ~t+t~
Q T J JsV h ds dt 13]
where:
- vO is the velocity of the oil phase over an element of section ds;
- ho is the static fraction of oil in said element of section ds;
- t is the variable time; and - T is the time interval over which the measurement is performed.

The local terms vO and ho may be written:
~t+T
v = V + w I w .dt = O
o o o )t o with h = H + k ~ h .dt = O
o o o Jt where VO and Ho are respectively the mean velocity and the mean static fraction over the section, and wO and ko are fluctuation terms.

Substituting gives:
~t+T ~
QO Vo.Ho.S + - J J ko.wo.ds.dt 14]

For this expression to be identical to relationship ~1], we must assume:
r~
J J ko wo ds d t = o This assumption is an approximation which is justified, particularly in vertical wells. But the assumption becomes doubtful in deviated wells, :, ~

2 ~ r, in which substantial variations in static fraction and in velocity occur across a given section.
The approach proposed by the present invention consists in de~ermi-ning the flow pararneters locally on the basis of a signal frorn a small size sensor placed in the flow, said signal having different levels de-pending on whether the sensor is in the presence of oil or of water.
The local sensor is represented diagrammatically in Figure 1. An example of a sensor suitable for the goals of the invention is a sensor of the radiofrequency type. This comprises a probe constituted by a co-axial cable 1 having one end 2 (referred to below as the "sensor") which is placed in the flow and whose other end is connected to a high fre-quency electromagnetic wave generator (with the frequency being of the order of gigahertz). The sensor 2 is small relative to the size of the bubbles B. A typical diameter for the sensor 12 is about 1 mm, and this is much smaller than bubbles, which typically have a diameter of about 6 mm. The sensor operates on the principle that the electromagnetic wave is reflected differently depending on the impedance of the fluid in con-tact with the sensor 12. The amplitude and the phase of the wave thus vary depending on whether the sensor is immersed in water or in an oil bubble. The advantage of using high frequencies is that the variations in impedance can be considered as being variations in capacitance, in other words, the sensor 12 is sensitive essentially to the dielectric constant of the fluid, thereby enabling excellent contrast to be obtai-ned between water and oil. An embodiment of a circuit associated with such a sensor is described below.
Reference is made to Figures 2 and 3A to 3D for explaining the measurement concepts of the invention.
Figure 2 shows the signal obtained from the local sensor 2. This signal is sensitive to the phase in which the sensor is immersed and has a first level Vw when the sensor is in water, and a second level VO, lower than Vw when the sensor is immersed in an oil bubble. It can thus be noted that the portion of the signal shown in Figure 2 reveals the passage of an oil bubble.
If the signal is analyzed in greater detail relative to phenomena in the flow, it is necessary to describe the succession of situations that from the point of view of the contacts which occur between the sensor and the interface between the phases, as shown in Figures 3A to 3~, and :

3 ~

to identify corresponding points A, B, C, and D in the signal situated at the end or at the beginning of a step in the signal.
In Figures 3A to 3D, the sensor 2 is shown diagrammatically in the form of a cylinder of diameter D . The diameter Dc is a "characteristic dimension" of the sensor. This dimension is a function, above all, of the diameter of the sensor 2 (or of its dimension in the flow direction, if its shape is other than cylindrical), however it may not be identical to the diameter. It may be considered as a known parameter for a sensor 2 of given dimensions and geometry.
Reference is made initially to Figure 3A which shows an oil bubble B
coming into contact with the sensor 2. Prior to this contact, the sen-sor 2 was immersed entirely in water, so the level of the electrical signal was Vw. As soon as the bubble B makes contact with the sensor 2, the signal level drops until the sensor 2 is fully immersed in the oil bubble, at which stage the signal reaches value VO. Point A on the sig-nal (time tA) corresponds to the bubble beginning to make contact with the sensor 2, and point B (time tB) corresponds to the sensor losing contact with the water. Similarly, point C in the signal (at time tc) marks the beginning of a new contact between the sensor and the water phase, as shown in Figure 3C, and point D (time tD) marks the end of contact between the sensor and the oil bubble, as shown in Figure 3D.
The signal is then back at value V~.
If the transitions As or CD in the signal are analyzed, it can be seen that the time taken by the signal to go from level Vw to VO (or vice versa) is the time taken by the bubble to travel the "characteris-tic dimension" Dc of the sensor 12. As a result, the faster the velocity of the bubble, the shorter the time taken by transitions. This observa-tion leads to ~he conclusion that transitions in the signal convey in-formation about the flow characteristics of the oil phase.
The above observation can be expressed mathematically.
; Let vb be the displacement velocity of the bubble B, let x be thedistance travelled, let t be time, and let V be signal level. The following equation can be written:
dx dx dV QV
Vb = = - = -.grad V
dt dV dt ~V
The term x is the distance travelled during a transition, i.e. Dc, and ;
~ "
.

: .

the term ~V is the difference between the levels of the signal level.
~hence:

Vb = ~ . grad V [5]
w o The term "grad V" is the slope of the signal during a transition.
In order to determine this slope, it is advantageous to use the linear portion of the transition (normally the middle portion thereof), thereby avoiding interference from changes in the dynamic range Vw to VO of the signal. The slope is thus determined between lower and upper thresholds Vi and Vs equidistant from the mean level Vm = 1/2(Vo + Vw) and such that:

Vs ~ Vi = a(Vw - VO) where a is a coefficient lying in the range O to 1.
With the thresholds Vi and Vs being reached respectively at times ti and ts, a rise time Tm can be defined as being the interval :
Tm ts Thus:
~V a(Vw - VO) grad V = - =
~t Tm and consequently Dc.a Vb = - [6]
The value obtained in this way is an instantaneous value obtained from the slope of one transition. It is naturally possible to determine an average value over a given time interval by calculating the average of a plurality of instantaneous values.
Other flow parameters of great significance can be obtained from the signal from the sensor 12. These are the local oil flow rate qO and the superficial velocity VS of the oil phase, where VS is defined as being tke ratio of the local oil flow rate qO to the section sb of the bubble.
The superficial velocity VS represents the local velocity which the oil 'V'.J~.3 phase would have, assuming that the local section contained the oil phase only.
The local oil flow rate q is equal to the total volume of oil bubbles going past the sensor per unit time:

q = T(~ Wb) where:
~ Wb is the volume of a bubble;
- T is the measurement time interval; and - ~Wb is the sum of the volumes Wb as determined in succession over time interval T.
; The superficial velocity VS is thus:

Vs T ~(Wb/Sb) 17]
Assuming that the bubbles of oil are spheres of diameter Db, as shown in Figures 3A to 3D, then the ratio Wb/sb is:
~Db :6 2 Wb/sb = 2 4 = 3-Db and the expression for the superficial velocity becomes:

Vs = ~ Db~ [8, The coefficient 2/3 corresponds to the assumption that the bubbles are perfectly spherical. It is likely that the real shape of the bubbles is close to that of a sphere but is not exactly spherical. That being the case, the coefficient expressing the ratio of the volume to the cross-section of the bubbles will have a value k that differs a little from 2/3. The appropriate correction is defined in an experimental installation by comparing the results obtained with the results of measurements performed in a different manner. Thus, a more exact .
: ', ~ , :
'`
.

2~3~

equation is:

s T ~(k Db) [9]
with k = 2/3 + ~ (for small ~).
A ~irst way of determining bubble diameter Db is theoretical.
Bubble diameter can be predicted as a function of the surface tension a at the water-oil interface and of the difference in density ~p between the phases at the depth under consideration. The theoretical bubble diameter Dth is given by:
Dth = ~(2a/g~p) (where g is acceleration due to gravity) This approach is based on the assumption of constant bubble diameter over the time interval under consideration. Assuming that this is satisfied, then the equivalent velocity simply becomes:
V = k-Dth-Nb [10]
where Nb is the number of bubbles going past the sensor per unit time.
This number is easily obtained since it is the same as the number of rising (or falling) transitions in the signal during one time unit.
Another approach does not assume that bubble diameter is constant, and makes use of information taken from the sensor signal in order to determine the diameter of each individual bubble passing the sensor.
This approach relies on the observation that the distance travelled by the bubble during the time Tp it is present at the sensor is indeed the diameter of the bubble. Since the bubble is travelling at velocity Vb which is determined as described above, the diameter of the bubble Db is given by:
Db = vb.Tp i.e., replacing vb by the expression derived earlier:
Db = DC.~(Tp/Tm) [11]
The time Tp a bubble is present at the sensor can be determined, for example, as shown in Figure 2: taking the halfway points L and M at the mean level Vm of the signal as being representative of the beginning and the end of contact between the bubble and the sensor, and noting the : , ' . ' .

2 ~ ~ 3 ~ ~ ,3 times corresponding to points L and M as tL and tM~ then the time Tp that a bubble is present is determined as follows:
Tp = tM ~ tL
Using this method, a diameter value Db is calculated for each indi-vidual bubble on the basis of the measurement signal. The equivalent velocity VS is then proportional to the sum of all of the diameter values Db determined during one unit of time, which sum is itself proportional to the sum of the ratios of bubble present time to rise time as determined for each transition from a falling sequence to a rising sequence. Thus :
k T k T
v = ~ Db) = --Dc-~- ~(Tp/Tm) [12]

The above description relates to using a local sensor sensitive to phase in accordance with the invention to determine parameters represen-tative of local flow. Such a sensor can also be used, as described by the present Applicant's French patent application number 88 12729 filed 29 September 1988 for determining the local static fraction ho of the oil phase. The fraction h may be obtained by the ratio of the time Tp a bubble is present at the sensor to the total time of a sequence, i.e.
the time between two consecutive falling transitions. In Figure 2, the point N indicates the falling transition following the rising transition referenced M. The total time of one sequence is then:

Tt N L
and the local static fraction over one sequence is given by:
h = Tp/Tt = (tM - tL)~(tN ~ tL) For a time interval T including a plurality of sequences, the static fraction ho is given by:

h = - ~T [13]
T

The flow parameters determined from the signal from the sensor 2 as described above are local parameters. If several sensors 2 are disposed in the flow section at suitably chosen points, different values are -, .

2~ ,3~

obtained for the same parameter, thereby obtaining an indication of the variation profile of this parameter across the flow section. In particu-lar, it is possible to obtain a profile of the superficial velocity across the section in this way. It is then possible to determine the superficial velocity of the oil phase (i.e. the oil flow rate) for the flow section as a whole, by integrating the said velocity profile over the section.
The sensors are disposed by selecting a set of points situated at different distances from the center of the section and at different azimuth bearings relative to the central axis of the flow.
Figures 4 to 6 show an embodiment of a logging system designed to implement the techniques described above.
Figure 4 is a diagram showing a surface unit 10 including means for processing data and located in the vicinity of a drilling rig 11 itself disposed over a borehole 12 passing through hydrocarbon-producing geolo-gical strata 13. The borehole 12 includes cylindrical casing 14 within which there is a flow of multi-phase fluid. The fluid reaching the sur-face is removed via a duct 15 to a storage installation (not shown).
In order to measure the flow parameters of the fluid flowing inside the casing 14, a logging tool 16 is used which is suspended from the end of a cable 17 wound on a winch 18. Since measurements are performed at different depths, it is necessary to know the depth of the tool. To this end, the winch 18 is associated with a conventional detector member 19 which detects magnetic marks disposed at regular intervals along the cable 17.
The logging tool comprises an elongate body 20, a top electronics section 21, a bottom nose 22, and measurement and data processing means described in detail below. In the embodiment shown in Fig~lre 4, the tool 16 is disposed in the center of the casing 14 by conventional top and bottom centralizers 23 and 24.
In Figure 5, the logging tool 16 in accordance with the invention includes items already described with reference to Figure 4, and these items bear the same references. The tool is shown centered in a portion of casing 14 lining a slanting well. The body 20 has arms 25 mounted thereon, with each arm being hinged about a pivot 26 having an axis orthogonal to the longitudinal axis z-z' of the tool. Conventional ac-tuator means (e.g. hydraulic means, not shown) serve to pivot each arm ~ ;

in a diametral plane of the tool between a retracted position against the tool body, enabling the tool to be displaced between measurements, and a deployed position (as shown in Figure 5) away from the axis z-z' in a position suitable for performing a measurement. The actuator means are housed in a section 27 on which the arms Z5 are mounted.
The tool carries measurement probes 1 mounted at the ends of the arms 25. Each of these probes 1 corresponds to one of the local probes described above, and each includes an end 2 corresponding to the above--described local sensor.
The tool shown in Figure 5 has three probes 1 disposed at 120 intervals, however, it should be understood that this is merely by way of example. The tool could have more such probes, e.g. six probes disposed at 60 intervals. In addition, the actuator means could be designed to operate differently : the arms 25 could be actuated in unison, in which case all of the probes would be at the same distance from the axis z-z', or else distinct actuator means could be provided for each arm or group of arms, in which case the probes would not all be at the same distance from the axis, thereby obtaining measurements from points situated at different distances from the well axis, for the reasons explained above.
The tool also includes reference means, e.g. gravity based, for indicating the angular position of each arm 25 in the well relative to the projection of the vertical onto the right cross-section under consideration.
Inside each arm 25 there is a block 3 for processing the measurement signals. It is mentioned above that one example of a suitable local sensor is of the radiofrequency type. There follows a description with reference to Figure 6 of the circuit associated with the probe in this particular case.
It is mentioned above that the electromagnetic wave propaga~ing along the probe is reflected differently depending on the impedance of the medium (water or oil) in which the sensor 2 is bathed. For an oil--water mixture, the phase of the electromagnetic wave varies between two levels depending on whether the sensor 2 is in oil or in water. The mea-sured magnitude constituting the output signal from the sensor 2 is a voltage which is directly related to variations in phase in the electro-magnetic wave.

. . , , - 13 - 2~

The circuit shown in Figure 6 comprises a high frequency (HF) por-tion 55 received in the block 31 of each arm 25, and a low frequency portion 57 for processing the signal digitally. The portion 57 is spread over the electronics section 21 and the surface unit 10.
The HF portion comprises a generator 58 generating electromagnetic waves at a constant frequency of about 1 gigahertz, e.g. 1 GHz or 2 GHz.
The output from the generator 58 is connected to an amplifier associated with a lowpass filter (cf. amplifier and filter block 59). The output from the amplifier and filter 59 is applied across one of the diagonals of a Wheatstone bridge 60. The probe 61 constituted by a coaxial cable comprises a first measurement portion 62 whose end is placed in the flow and a second reference portion 63 which is disposed in the air inside the arm. The measurement portion 62 of the probe (impedance Z3) is placed in one branch of the bridge 60 while the reference portion 63 (impedance Z4) of the probe is placed in another branch, with the other two branches comprising respective impedances Z1 and Z2. A detector 64 connected across the other diagonal of the bridge delivers a measurement signal representative of bridge unbalance.
In principle, measurement is performed by detecting and analyzing the unbalance of the bridge, which unbalance is characteristic of the phase in contact with the end of the measurement portion 62 of the probe 61.
In operation, the output signal from the bridge is equal to the dif-ference between the two signals reflected respectively from the end of the measurement portion 62 and from the end of the reference portion 63 of the cable. The response of the measurement probe is phase shifted relative to the reference (placed in air) by a value:
QC.
= 2 Arc tan z where C is the change in capacitance, ~ the angular frequency, and Z
stands for the impedance.
Thus, the phase shift is greater when the measurement portion of the probe is in water than when it is in oil. The variation in the capacitance at the end of the measurement portion 62 of the probe gives rise to a variation in the phase of the reflected wave. The variation may be about 1.5 pF, for example, on a cable having an impedance of 50 - 14 - 2 ~ 3 ~ ~ ~

ohms. It can be seen from the above equation that the change in phase increases with increasing frequency, whence the advantage of using high frequencies.
The purpose of the digital processing performed by the portlon 57 is to extract the various flow parameters of bubble velocity, bubble diameter, and equivalent velocity, from the sensor signal delivered by the portion 55 in analog form. The above explanations concerning the way in which these parameters are determined are sufficient for there to be no point in describing a circuit specifically for performing this processing. It also appears from the preceding explanation that in addition to the flow parameters mentioned above, the processing may also provide the local static oil fraction.
It is merely mentioned that the analog signal from the portion 55 is sampled at a frequency which may be 1 MHz, for example. The above-men-tioned levels Vi and Vs which are equidistant from the mean level Vm and chosen such that Vs ~ Vi = ~(Vw - VO) are determined by sampling the signal at a frequency of 1 kHz, for example, and updating the values from the preceding sampling, where necessary. If a new sample does not lie in the range defined by the previous extreme values, then the new sample becomes a new minimum or maximum value as the case may be. This process is continued over a time interval which may be about 10 seconds, after which the extreme values return to determined initial values.
It should also be observed that to determine the bubble-present time Tp, it is sufficient in practice to determine when the thresholds Vi and Vs are crossed rather than when the mean level Vm is crossed. The cros~
sing of the lower threshold Vi is initially detected during a falling transition (i.e. a transition which crosses the upper threshold Vs before the lower threshold Vi), and then the subsequent crossing of the upper threshold Vs is detected which takes place during the following rising transition. The first crossing occurs at time t'i and the second at time ts, so the period ts - t'i can be taken as the bubble-present time Tp.

.
- ~, ,

Claims

1. A method of measuring the flow of a multi-phase fluid comprising a continuous phase and a dispersed phase in the form of bubbles, the method comprising the step of producing by means of a local sensor whose dimension in the flow direction is substantially smaller than the bubble dimension, a signal having different levels depending on which fluid phase is in contact with the sensor, the transitions between said levels carrying information related to the flow parameters.

2. A method according to claim 1, in which a signal is produced representative of the gradient of the signal from the sensor during a transition, said gradient being proportional to bubble velocity.

3. A method according to claim 2, in which the gradient signal is obtained as the reciprocal of the rise time, said rise time being defined as the interval of time which occurs, during a transition, between the crossing of a lower threshold and the crossing of an upper threshold, which thresholds are related to respective ones of said levels in the signal from the sensor.

4. A method according to claim 2 or 3, in which a signal is produced representative of the time a bubble is present at the sensor, and in which this signal is combined with said gradient signal representative of the bubble velocity, thereby obtaining a signal representative of bubble diameter.

5. A method according to claim 4, in which the signals representative of the bubble diameter obtained over a unit of time are summed, the resulting sum constituting a signal representative of the superficial velocity of the dispersed fluid phase.

6. A method according to any one of claims 1 to 3, in which the bubble diameter is determined from a theoretical model, and the number of bubbles going past the sensor per unit time is determined, from which a signal is obtained representative of the superficial velocity of the dispersed fluid phase by multiplying said diameter by said number of bubbles.

7. A method according to any one of claims 1 to 6, in which a plurality of local sensors are placed in a section of the flow at different points within said section.

8. A logging apparatus for measuring flows in hydrocarbon wells, the well fluid possibly comprising a continuous phase and a dispersed phase in the form of bubbles, the apparatus comprising a local sensor having a dimension which is substantially smaller than the bubbles, and means for producing a signal having different levels depending on which fluid phase is in contact with the sensor.

9. An apparatus according to claim 8, wherein the dimension of the sensor in the flow direction is about 1 millimeter.

10. An apparatus according to claim 8 or 9, in which a plurality of local sensors are disposed to be placed at different points in a section of the well.

11. Apparatus according to any one of claims 8 to 10, in which the sensor is of the radiofrequency type.