METHOD FOR NON-INVASIVE MEASUREMENT OF CHANGE IN THE INTERNAL PRESSURE OF A PIPE, MEASURING DEVICE AND ARRANGEMENT THEREOF.

Description

TECHNICAL FIELD

[0001] The present invention relates to a method for measuring a variation in internal pressure and / or a variation in temperature of a pipe.

[0002] The invention applies to the field of instrumentation, and more specifically to the non-intrusive measurement of a variation in hydrostatic pressure prevailing inside a pipe from its outside. PREVIOUS STATE OF THE ART

[0003] There is a need to perform a non-intrusive measurement of the hydrostatic pressure variation inside a pipe from its exterior. Such a pipe is, for example, a pipeline used for transporting hydrocarbons, a primary or secondary circuit of a nuclear reactor, a pressurized fluid (liquid or gas) supply network (industrial site, urban area, machine, etc.), or even a cylindrical pressure tank, for example used for storing a fluid (e.g., hydrogen) under high pressure.

[0004] Document FR 2 864 202 B1 describes a method for measuring a variation in the internal pressure of a pipe using sensors configured to measure a variation in the total strain of the pipe (including a mechanical component of strain and a thermal component of strain), and an additional sensor to determine the thermal component of the strain variation and thus subtract it from the measurement of the total strain variation.

[0005] Such an additional sensor is glued onto a sample made of the same material as the pipe, separate from the latter, and subjected to the same temperature as said pipe, so that the total strain variations measured by the additional sensor do not include a mechanical strain component.

[0006] The variation in internal pressure is calculated from the mechanical component of the deformation variation obtained by subtracting the thermal component from the total deformation variation.

[0007] US patent 2,420,148 A also describes such a method. To measure the pressure of a fluid in a pipe, strain gauges measure the outward deformation of the pipe in response to the internal pressure. An additional temperature sensor is provided to compensate for temperature variations.

[0008] However, such a measurement method is not entirely satisfactory.

[0009] Indeed, the implementation of such an additional sensor does not satisfactorily compensate for the thermal effects on the sensors measuring the variation of mechanical deformation of the pressurized pipe, and presents certain defects which lead to introducing a bias in the measurement of pressure variation, which is difficult to correct.

[0010] First, the state-of-the-art process requires at least three independent measurements, which multiplies the sources of uncertainty.

[0011] Furthermore, obtaining a sample of the material constituting the pipe of an existing installation proves difficult, if not impossible, in order to determine the thermal component of the total strain variation. However, it is essential that the sample have the same coefficient of thermal expansion as the pipe, so that the thermal component of the total strain variation can be subtracted from it with sufficient accuracy across the entire temperature range considered.

[0012] Furthermore, the use of such an additional sensor, due to its thermal inertia, which differs from that of the strain sensors positioned on the pipe (particularly because of the presence of pressurized fluid inside it), introduces a variable delay in the compensation of thermal effects, and therefore a systematic measurement error whenever the temperature varies, even slowly.

[0013] However, in such applications, where temperatures can vary by several tens of degrees Celsius, the mechanical component of the total deformation can be obscured by a thermally based signal which becomes dominant, and in such a case it is impossible to make a reliable measurement of pressure variation.

[0014] Thus, for example, when strain sensors are Bragg gratings glued to the surface of a 4-inch diameter austenitic steel pipe in Schedule 160 (wall thickness of 13.49 mm), with a coefficient of thermal expansion of the order of 16.4x10 -6< K -1< (per kelvin), a temperature uncertainty of one kelvin results in an error of 28 bar on the measurement of the variation of internal pressure.

[0015] One aim of the invention is therefore to propose a method for measuring the variation of the internal pressure and / or temperature of a pipe which is less affected by the effects of variations in thermal deformations (induced by temperature variations, or mechanical in the case of temperature measurement) when calculating the variation of the mechanical deformation / temperature of the pipe, resulting in a more reliable estimate of the variation of the internal pressure and / or temperature of the pipe. DESCRIPTION OF THE INVENTION

[0016] To this end, the invention relates to a method as defined in claim 1. This method for measuring a variation in the internal pressure of a pipe having a portion extending along a longitudinal axis comprises, among other things, the following steps: For each of at least two measurement zones of the pipe portion, measurement, by means of a corresponding sensor, of a tracking quantity associated with a respective measurement direction, a relative variation of the tracking quantity being representative of a variation of a corresponding local deformation of the pipe along the associated measurement direction; and calculation of the variation of the internal pressure of the pipe from at least one deformation variation, each deformation variation being obtained solely from measured tracking quantities, among which at least one first measured tracking quantity is associated with a first measurement direction and at least one second measured tracking quantity is associated with a second measurement direction, the first measurement direction defining a first angle with a plane normal to the longitudinal axis, the second measurement direction defining a second angle with a plane normal to the longitudinal axis, the first angle and the second angle having different absolute values ​​modulo π, the sensors being chosen so that the same temperature variation results in the same relative variation of their respective measured tracking quantities.

[0017] It should be noted that of course the at least two measurement zones can be distinct or coincide without departing from the scope of the invention, it being understood that, as required by the invention, the first angle and the second angle have different absolute values ​​modulo π.

[0018] Indeed, such a measurement process exploits the intrinsic property of the pipe under hydrostatic stress to exhibit two significantly different sensitivities to mechanical deformations depending on its length (longitudinal mechanical deformation) and its circumference (orthoradial mechanical deformation).

[0019] Thus, the tracking quantities measured for two different measurement angles are representative of different mechanical deformation variations.

[0020] On the other hand, the contribution of the temperature variation to its total deformation variation can be considered identical for each of the measurement zones of the pipe.

[0021] However, the sensors are chosen to exhibit identical temperature sensitivity (i.e., the same relative variation in their respective tracking values ​​for the same temperature variation). Thus, a simple subtraction using the tracking values ​​for two different measurement angles eliminates the temperature dependence of the measurement of the total deformation variation, which leads directly to a measurement of the variation in the mechanical component of deformation of the pressurized pipe.

[0022] Thus, assuming the pipe remains within its elastic range, and by applying Hooke's law, obtaining the variation of the mechanical component of deformation amounts to calculating a variation in internal pressure, completely independent of the effects of temperature variation, provided that the variation in the additional longitudinal force and the variation in external pressure are known or considered negligible. Another assumption is that the pipe is closed at each end (thus forming a pressurized reservoir), which, in practice, is always the case.

[0023] Thus, thanks to the measurement method of the invention, the problem of the temperature dependence of the measurement of the variation of the pipe deformation (and that of the dependence on the pipe deformation of the measurement of the temperature variation) is intrinsically solved, providing dual information on the variation of contact temperature independently of the variation of pressure, and moreover, this method can be implemented using only two sensors.

[0024] More generally, given the principle on which thermal effect compensation is based, any external effect other than temperature, which also disturbs the measurement of each sensor in the same way, is eliminated by this means, or at a minimumvery strongly attenuated, in a completely intrinsic way. As a result, such a process can also be implemented for measuring the variation of internal pressure of a pipe arranged in radiative environments, that is to say when the pipe is subjected to ionizing radiation, and more generally, in environments where any disturbing effect on the measurement of the mechanical deformation of the pipe has an identical effect on the measurement of each of the sensors.

[0025] According to the invention, the measurement method comprises the following characteristics ▪ The measurement step is preceded by the attachment of the corresponding sensor to each measurement zone. The sensors are attached to their respective measurement zones using the same method and are chosen so that the same variation in a mechanical deformation applied to them results in the same relative variation in their respective measured tracking quantities. ▪ The process measures a variation in the internal pressure of the pipe. The pipe section has the shape of a cylinder of revolution. Each measurement zone belongs to a section of the pipe portion, the pipe being closed at its ends. The variation in internal pressure is calculated according to: ΔP int = ΔP ext + r 1 2 r 2 2 r 0 , int 2 r 0 , ext 2 E ΔΨ 2 − ΔΨ 1 r 0 , ext 2 − r 0 , int 2 K ε 1 + v r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + cos 2 ϕ 2 − cos 2 ϕ 1 π r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF where ΔPint is the variation of the internal pressure; ΔΨ1 and ΔΨ2 are respectively a relative variation of the first tracking quantity and a relative variation of the second tracking quantity; r0,ext is an external radius of the pipe portion; r0,int is an internal radius of the pipe portion; r1 is a radius at which the measurement associated with the first measurement direction is taken; r2 is a radius at which the measurement associated with the second measurement direction is taken; E is the Young's modulus of the material in which the pipe portion (12) (4) is made; v is the Poisson's ratio of the material in which the pipe portion is made; ϕ1 and ϕ2 are respectively the first angle and the second angle; ΔPext a variation of an external pressure applied to the pipe portion;δF is a variation of an additional longitudinal force applied to the portion of the pipe and distinct from a variation of a longitudinal force exerted on the portion of the pipe by the variation of internal pressure and the variation of external pressure; and κ ε is a mechanical sensitivity of the sensors, equal to a coefficient of proportionality between a relative variation of the tracking quantity and a variation of mechanical deformation applied to them.

[0026] According to other advantageous aspects of the invention, the measurement method comprises one or more of the following characteristics, taken individually or in all technically possible combinations: ▪ The corresponding sensor is a segment of optical fiber in which a Bragg grating is inscribed, the optical fiber segment being fixed to the measurement area such that the corresponding Bragg grating extends along the measurement direction associated with said measurement area, the mechanical sensitivity κ ε being expressed as: K ε = 1 n eff ∂ n eff ∂ ε mec + 1 where n eff is an effective index of the optical guide of the optical fiber; and ε mec is a longitudinal mechanical deformation of the optical fiber, the tracking quantity being a reflection wavelength of each Bragg grating; ▪ for at least two measurement zones, the corresponding optical fiber segments belong to the same optical fiber; ▪ the measurement axes associated with at least two optical fiber segments of the same optical fiber form distinct angles with the longitudinal axis of the portion of the pipe, in absolute values, modulo π; ▪ the measurement zones on which at least two optical fiber segments of the same optical fiber are fixed are arranged along a generatrix of the portion of the pipe;▪ For at least one measurement zone, the sensor is selected from the group comprising distance sensors such as a sensor implementing an acoustic method between an acoustic emitter and an acoustic receiver, sensors implementing a reflectometry method on an electrical cable, sensors implementing an optical reflectometry method, strain gauges, such as electrical strain gauges, and stereo-correlation strain sensors; ▪ the first angle is 0 modulo π, and the second angle is π / 2 modulo π; the method allows the measurement of a temperature variation of the pipe and the portion of the pipe has the shape of a cylinder of revolution, each measurement zone belonging to a section of the portion of the pipe, the pipe being closed at its ends, the temperature variation of the pipe being calculated according to: ; ΔT = r 1 2 r 2 2 ΔΨ 1 − ΔΨ 2 K ε 1 − 2 v − K P E K ⊤ K ε 1 + v r 0 , ext 2 r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + ΔΨ 1 r 1 2 cos 2 ϕ 2 − ΔΨ 2 r 2 2 cos 2 ϕ 1 K ⊤ r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + 1 K ⊤ 1 − 2 v E K ε − K P ΔP ext + K ε r 2 2 − r 1 2 cos 2 ϕ 1 + cos 2 ϕ 2 − 2 1 + v cos 2 ϕ 1 cos 2 ϕ 2 + r 1 2 + r 2 2 cos 2 ϕ 1 − cos 2 ϕ 2 2 K ⊤ πE r 0 , ext 2 − r 0 , int 2 r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF − 1 K ⊤ 1 − 2 v E K ε − K P r 1 2 r 2 2 cos 2 ϕ 2 − cos 2 ϕ 1 πr 0 , ext 2 r 0 , ext 2 − r 0 , int 2 r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF + ϵ surf 1 K ⊤ K P π r 0 , ext 2 − r 0 , int 2 δF − ΔΨ 1 − ΔΨ 2 K P E K ε 1 + v cos 2 ϕ 2 − cos 2 ϕ 1 where ΔT is the temperature variation of the pipe; ΔΨ₁ and ΔΨ₂ are respectively a relative variation of the first tracking quantity and a relative variation of the second tracking quantity; r₀,ext is an external radius of the pipe portion; r₀,int is an internal radius of the pipe portion; r₁ is a radius at which the measurement associated with the first measurement direction is taken; r₂ is a radius at which the measurement associated with the second measurement direction is taken; εₙ₊₁ is a parameter that takes the value 1 when r₁ and r₂ are both equal to r₀,int or both equal to r₀,ext and the value 0 in other cases; E is the Young's modulus of the material in which the pipe portion is made; v is the Poisson's ratio of the material in which the pipe portion is made; ϕ₁ and ϕ₂ are respectively the first angle and the second angle; ΔP ext is a variation of an external pressure applied to the portion of the pipe;δF is a variation of an additional longitudinal force applied to the portion of the pipe and distinct from a variation of a longitudinal force exerted on the portion of the pipe by the variation of the internal pressure and the variation of the external pressure; κ ε is a mechanical sensitivity of the sensors, equal to a coefficient of proportionality between a relative variation of the tracking quantity and a variation of mechanical deformation; κ T is a thermal sensitivity of the sensors, equal to a coefficient of proportionality between a relative variation of the tracking quantity and a variation of their temperature; and κ P is an intrinsic sensitivity to the hydrostatic pressure of the sensor alone, said sensitivity being equal to a coefficient of proportionality between a relative variation of the tracking quantity and a variation of the hydrostatic pressure directly applied to it;N measurement zones are circumferentially distributed every 2π / N around the longitudinal axis, N being an integer strictly greater than 1 and, preferably, N being an even number greater than 2, for at least two distinct measurement zones, the corresponding tracking quantities are associated with measurement directions defining, with a plane normal to the longitudinal axis, angles of opposite sign modulo π; the measurement associated with the first measurement direction and the measurement associated with the second measurement direction are carried out at the level of the same surface of the portion selected from an internal surface and an external surface of said portion of pipe; the method further comprising the steps: measuring, by means of a pressure sensor arranged in the pipe, a pressure of a fluid present in the pipe, forming a reference pressure;and calculation of a damage parameter from a difference between the variation of the calculated internal pressure and a concomitant variation of the measured reference pressure, the measurement method advantageously including the generation of an alert signal if the determined damage parameter is outside a predetermined tolerance range.

[0027] Furthermore, the invention relates to a device as defined in claim 12. This device for measuring a variation in the internal pressure of a pipe comprises, among other things, a portion extending along a longitudinal axis, the measuring device comprising at least two sensors and a computer, each sensor being configured to deliver, for a corresponding measurement zone of the pipe portion, a measurement signal indicative of a predetermined tracking quantity associated with a respective measurement direction, a relative variation of the tracking quantity being representative of a variation of a local deformation, along the associated measurement direction, of the measurement zone, the sensors being chosen so that the same temperature variation results in the same relative variation of their respective measured tracking quantities, the computer being configured to measure, from each measurement signal, the corresponding tracking quantity, the computer being, furthermore, configured to calculate the variation of the internal pressure of the pipe from at least one variation of deformation, each variation of deformation being obtained solely from measured tracking quantities,among which at least one first measured tracking quantity is associated with a first measurement direction and at least one second measured tracking quantity is associated with a second measurement direction, the first measurement direction defining a first angle with a plane normal to the longitudinal axis, the second measurement direction defining a second angle with a plane normal to the longitudinal axis, the first and second angles having different absolute values ​​modulo π. The invention also relates to an assembly comprising a pipe and a measuring device according to the invention, the pipe having a portion extending along a longitudinal axis, each sensor of the measuring device being associated with a respective measurement area of ​​an external surface of the portion of the pipe, and being arranged to provide a tracking quantity associated with a respective measurement direction.a relative variation of the tracking quantity being representative of a variation of a corresponding local deformation of the pipe along the measurement direction associated with at least a first measurement direction defining a first angle with a plane normal to the longitudinal axis, and at least a second measurement direction defining a second angle with the plane normal to the longitudinal axis, the first angle and the second angle having different absolute values ​​modulo π. , BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The invention will be better understood with the aid of the following description, given solely by way of non-limiting example and made with reference to the accompanying drawings in which: there figure 1 is a schematic representation of an installation comprising a pipe and a measuring device according to the invention, the sensors of the measuring device being arranged in a helix around the pipe; the figure 2 is similar to the figure 1 the sensors of the measuring device being arranged in a ring around the pipe; and the figure 3 is similar to the figure 1 the sensors of the measuring device being arranged along a generator of the pipe. DETAILED DESCRIPTION

[0029] A measuring device 2 according to the invention is illustrated by the figure 1 The measuring device 2 is intended for measuring the change in internal pressure ΔPint of a pipe 4, that is, for measuring the change in pressure of a fluid present in said pipe 4 and / or the change in temperature ΔT of said pipe 4. The pressure of the fluid present in said pipe 4 is also called "hydrostatic pressure". Such a measuring device 2 is fitted to an installation 1 comprising, in addition to the measuring device 2, the pipe 4.

[0030] This disclosure focuses on measuring the internal pressure variation. The possibility of measuring the temperature variation of pipe 4 is described subsequently, as a complement to the internal pressure measurement. Of course, while this disclosure describes the temperature variation measurement as a complement to the internal pressure variation measurement, it is perfectly conceivable, without departing from the scope of the invention, to use this temperature variation measurement alone and independently of the internal pressure variation measurement.

[0031] Such a pipe 4 has a wall 5 with a closed contour cross-section, defining an external surface 20 and an internal surface 21 of the pipe 4, a portion 12 of which extends along a longitudinal axis XX.

[0032] As illustrated by the figure 1 , the measuring device 2 comprises at least two sensors 6 and a computer 8.

[0033] Each sensor 6 is associated with a measuring zone 10 of the portion 12 of the pipe 4, and is intended to deliver a measuring signal corresponding to said measuring zone 10. Such a measuring zone 10 is a part of the external surface 20 of the pipe 4, of its internal surface 21, or is located within the thickness of its wall 5. In addition, the computer 8 is configured to determine the variation ΔP int of the internal pressure of the pipe 4 from the measuring signals received from the sensors 6.

[0034] For each measuring zone 10, the corresponding sensor 6 is associated with a respective measuring direction, bearing, for example, the reference A1-A1 or A2-A2 on the figure 1For sensor 6, the corresponding measurement signal is indicative of a predetermined tracking quantity. Furthermore, for each sensor 6, the corresponding tracking quantity is such that a relative variation of said tracking quantity is representative of a variation of a local deformation, along the associated measurement direction, of the measurement area 10 associated with said sensor 6.

[0035] Among the sensors 6 of the measuring device 2, at least a first sensor 6A is associated with a first measurement direction A 1 -A 1 defining a first angle ϕ 1 with a plane normal to the longitudinal axis XX, and at least a second sensor 6B is associated with a second measurement direction A 2 -A 2 defining a second angle ϕ 2 with a plane normal to the longitudinal axis XX.

[0036] In other words, the first sensor 6A is associated with a first tracking quantity whose relative variation is representative of the local deformation variation of the corresponding measurement zone 10 along the first measurement direction A1 -A1, which defines the first angle ϕ1 with a plane normal to the longitudinal axis XX. Furthermore, the second sensor 6B is associated with the second measurement direction A2 -A2, whose relative variation is representative of the local deformation variation of the corresponding measurement zone 10 along the second measurement direction A2 -A2, which defines the second angle ϕ2 with a plane normal to the longitudinal axis XX.

[0037] The first angle ϕ 1 and the second angle ϕ 2 have, in absolute value, different values ​​modulo π.

[0038] Advantageously, the first angle ϕ1 is equal to 0 modulo π, and the second angle ϕ2 is equal to π / 2 modulo π. These values ​​are those leading to the greatest measurement sensitivity within the scope of the invention.

[0039] In addition, the 6 sensors are chosen so that the same temperature variation results in the same relative variation of their respective tracking quantities.

[0040] In this way, since the variation of the thermal component of deformation is reflected in the same way on the measured monitoring quantities, the suppression of the effects of thermal variations on the variations of the measured deformations of the pipe is made possible, by a simple compensation between the sensors 6.

[0041] Preferably, each sensor 6 is intended to perform such a measurement by being fixed to the corresponding measurement zone 10.

[0042] In this case, the sensors 6 are advantageously fixed to their respective measuring zones 10 using the same fixing method. Furthermore, the sensors 6 are chosen so that the same variation in mechanical deformation results in the same relative variation in their respective tracking quantities.

[0043] In this way, the sensors 6 exhibit similar behaviors with respect to variations in deformation; disparities between the variations of the measured tracking quantities, which would lead to a poor estimation of the variation of the internal pressure ΔP int, are thus avoided.

[0044] Such a fixing is, for example, achieved by gluing the sensors 6 to their respective measuring areas.

[0045] Preferably, each sensor 6 is an optical fiber segment 14 in which a Bragg grating 16 is inscribed. In this case, each optical fiber segment 14 is fixed to the corresponding measurement area 10, so that its Bragg grating 16 extends along the measurement direction associated with said sensor 6, i.e. to said measurement area 10. In addition, for each fiber segment 14, the associated tracking quantity is the reflection wavelength of the corresponding Bragg grating 16.

[0046] Furthermore, to satisfy the requirements regarding the relative variation of the tracking quantity with temperature and mechanical deformation, the optical fiber segments 14 advantageously originate from the same preform. Even more preferably, the segments 14 belong to the same optical fiber 18 and are distributed along this optical fiber 18.

[0047] Advantageously, the measurement axes associated with at least two optical fiber segments 14 of the same optical fiber 18 form, with a plane normal to the longitudinal axis XX of the portion 12 of the pipe 4, angles, in absolute value, distinct modulo π. In this way, a measurement of the variation in internal pressure of the pipe 4 is likely to be obtained by means of a single optical fiber 18.

[0048] For example, as shown on the figure 2The optical fiber 18 is wound in a ring around the longitudinal axis of the portion 12. In this case, as well as in the case where the measurement zones 10 are arranged helically around the longitudinal axis, it is advantageous for N measurement zones 10 (N being an integer strictly greater than 1) to be circumferentially distributed every 2π / N around the longitudinal axis XX, the pressure variation measurement being the result of the arithmetic mean of the pressure variation measurements taken for each of these zones. In this way, the effects of bending of the portion 12 of the pipe 4 are likely to be compensated.

[0049] Preferably, with N being an even number greater than 2, the tracking quantities corresponding to said measurement zones are respectively associated with measurement directions defining, with a plane normal to the longitudinal axis, angles of opposite sign modulo π. In this way, in addition to compensating for the effects of pipe 4 bending on the measurement, the effects of its torsion are also likely to be compensated.

[0050] In a particularly advantageous way, to allow good compensation for torsion, N can be an even integer, each measurement zone can have an even corresponding measurement zone whose measurement directions are of opposite signs, the pressure variation measurement can then be the result of the arithmetic mean of the pressure variation measurements made for each of these zones, and thus be compensated against the effects of torsion.

[0051] According to a variant illustrated by the figure 3The measurement zones 10, to which at least two optical fiber segments 14 of the same optical fiber 18 are attached, are arranged along a generatrix of the portion 12 of the pipe 4. This is advantageous, since only a part of the pipe 4 is accessible, making it difficult, if not impossible, to wind the optical fiber 18 around its circumference. The optical fiber segments 14 are thus arranged in contact with and mechanically secured to the accessible part of the pipe 4.

[0052] In another example, for at least one measurement zone 10, the corresponding sensor 6 is a distance sensor, such as a sensor implementing a method for measuring the acoustic distance between an acoustic emitter and an acoustic receiver. In this case, the tracking quantity is the distance measured by the sensor 6.

[0053] Alternatively, sensor 6 is a sensor implementing an electrical cable reflectometry method, a sensor implementing an optical reflectometry method, an electrical strain gauge.

[0054] Alternatively, the sensor 6 is capable of measuring the tracking quantity without being fixed to the corresponding measuring zone 10. This is, for example, the case of a stereo-correlation strain sensor.

[0055] As previously stated, the calculator 8 is configured to determine the variation ΔP int of the internal pressure of pipe 4 from the measurement signals received from sensors 6.

[0056] More specifically, for each sensor 6, the computer 8 is configured to measure, from the measurement signal it delivers, the corresponding tracking quantity.

[0057] In addition, calculator 8 is configured to calculate the variation ΔP int of the internal pressure of pipe 4 from at least one variation of strain, each variation of strain being obtained solely from measured tracking quantities obtained directly from pipe 4 itself.

[0058] Preferably, in addition to deformation variations, calculator 8 is configured to implement a variation ΔP ext of an external pressure P ext and a variation of an additional longitudinal force δF applied to portion 12 of pipe 4 for the calculation of the variation ΔP int of the internal pressure of pipe 4.

[0059] The measured tracking quantities implemented by the computer 8 include at least one first measured tracking quantity associated with sensor 6A (i.e., for which the respective first measurement direction defines the first angle ϕ1 with the plane normal to the longitudinal axis) and a second measured tracking quantity associated with sensor 6B (i.e., for which the second measurement direction defines the second angle ϕ2 with the plane normal to the longitudinal axis XX).

[0060] Here, the variation of the additional longitudinal force δF is defined as the variation of a longitudinal force exerted on portion 12 of pipe 4, and which is distinct from the variation of a longitudinal force exerted on said portion 12 by the only variations of the internal pressures P int and external P ext.

[0061] In the specific case where portion 12 of pipe 4 has the shape of a cylinder of revolution, each measuring zone 10 belonging to an external surface 20 of portion 12 of the pipe, the pipe being closed at its ends, the calculator 8 is configured to calculate the variation of the internal pressure ΔP int according to: ΔP int = ΔP ext + r 0 , ext 2 E ΔΨ 2 − ΔΨ 1 K ε 1 + v cos 2 ϕ 2 − cos 2 ϕ 1 1 r 0 , int 2 − 1 r 0 , ext 2 + δF πr 0 , int 2 where ΔΨ 1 and ΔΨ 2 are respectively a relative variation of the first tracking quantity and a relative variation of the second tracking quantity; r 0,ext is an external radius of portion 12 of pipe 4; r 0,int is an internal radius of portion 12 of pipe 4; E and v are respectively the Young's modulus and Poisson's ratio of the material in which portion 12 of pipe 4 is made; κ ε is a mechanical sensitivity of the sensors, equal to a proportionality coefficient between a relative variation of the tracking quantity and a variation of mechanical deformation; and δF is a variation of an additional longitudinal force applied to the portion of the pipe and distinct from a variation of a longitudinal force exerted on the portion of the pipe by the variation of the internal pressure and the variation of the external pressure.

[0062] In the case where the sensors 6 are positioned within the thickness of the pipe at the same radius r: ΔP int = ΔP ext + r 2 E ΔΨ 2 − ΔΨ 1 K ε 1 + v cos 2 ϕ 2 − cos 2 ϕ 1 1 r 0 , int 2 − 1 r 0 , ext 2 + r 2 πr 0 , int 2 r 0 , ext 2 δF where r is a radius at which the first and second sensors 6 are positioned, and which is therefore associated with the first and second measurement zone 10, in other words with the first and second measurement.

[0063] And in the most general case where the first and second sensors 6 are positioned within the thickness or on the surface of the pipe, respectively at a radius r1 and a radius r2: ΔP int = ΔP ext + r 1 2 r 2 2 r 0 , int 2 r 0 , ext 2 E ΔΨ 2 − ΔΨ 1 r 0 , ext 2 − r 0 , int 2 K ε 1 + v r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + cos 2 ϕ 2 − cos 2 ϕ 1 π r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF where r 1 is a radius at which the first sensor 6 is positioned, which is therefore associated with the first measurement zone 10 and the first measurement; r 2 is a radius at which the second sensor 6 is positioned, which is therefore associated with the second measurement zone 10 and the second measurement.

[0064] It should be noted, of course, that the values ​​of the radii r 0,int , r 0,ext , r, r 1 , and r 2 are reference values ​​determined at a reference instant, like an initial instant, since these values, taking into account the forces exerted on pipe 4, are bound to evolve.

[0065] In particular, for a sensor 6 formed by a segment of optical fiber 14 in which a Bragg grating 16 is inscribed, the mechanical sensitivity κ ε is expressed as: K ε = 1 n eff ∂ n eff ∂ ε mec + 1 where n eff is an effective index of the optical guide of optical fiber 18; and ε mec is a longitudinal mechanical deformation of the optical fiber.

[0066] In the advantageous case where, at the predetermined reference time, the internal pressure P int,0 of the pipe 4 is known and recorded in a memory of the computer 8, said computer 8 is configured to calculate the internal pressure P int at any final time later than the initial time by integrating, in time, the variation of the internal pressure ΔP int between the reference time and the final time.

[0067] Preferably, the calculator 8 is also configured to calculate a temperature variation in pipe 4 from the measured monitoring variables, including at least the first and second measured monitoring variables. This indicator measurement of contact temperature variation can advantageously be used in conjunction with the measurement of internal pressure variation to prevent the formation of hydrate plugs in pipelines used for transporting hydrocarbons.

[0068] It should be noted that, more precisely and as indicated below, the calculated or determined temperature variation of pipe 4 is a contact temperature between the pipe (or more precisely its portion 12) and the sensors 6 corresponding to the measurement zones

[0069] More specifically, in the case where portion 12 of pipe 4 has the shape of a cylinder of revolution, each measuring zone 10 belonging to an external surface 20 of portion 12 of the pipe, pipe 4 being closed at its ends, the calculator 8 is configured to calculate said temperature variation according to: ΔT = 1 K ⊤ 1 − 2 v 1 + v ΔΨ 1 − ΔΨ 2 cos 2 ϕ 2 − cos 2 ϕ 1 + ΔΨ 1 cos 2 ϕ 2 − ΔΨ 2 cos 2 ϕ 1 cos 2 ϕ 2 − cos 2 ϕ 1 + 1 − 2 v E K ε − K P ΔP ext − 2 K ε 1 − v πE r 0 , ext 2 − r 0 , int 2 δF where ΔT is the variation in the temperature of pipe 4; and κ T is a thermal sensitivity of the sensors, equal to a coefficient of proportionality between a relative variation in the tracking quantity and a variation in their temperature.

[0070] In such a configuration, the temperature variation ΔT of the pipe determined is a contact temperature of the external surface of the pipe 4.

[0071] In the case where the sensors are positioned on the internal surface of the pipe at the same radius r 0,int: ΔT = 1 K ⊤ ΔΨ 1 − ΔΨ 2 K P E r 0 , ext 2 − r 0 , int 2 + K ε 1 − 2 v r 0 , int 2 K ε 1 + v r 0 , ext 2 cos 2 ϕ 2 − cos 2 ϕ 1 + ΔΨ 1 cos 2 ϕ 2 − ΔΨ 2 cos 2 ϕ 1 cos 2 ϕ 2 − cos 2 ϕ 1 + 1 − 2 v E K ε − K P ΔP ext − 1 πE K P E − K ε 1 − 2 v r 0 , ext 2 + 2 K ε 1 − v r 0 , ext 2 − r 0 , int 2 δF

[0072] In such a configuration, the temperature variation ΔT of pipe 4 determined is a contact temperature of the internal surface of pipe 4.

[0073] In the case where the sensors are positioned within the thickness of the pipe at the same radius r: ΔT = 1 K ⊤ r 2 ΔΨ 1 − ΔΨ 2 K ε 1 − 2 v K P E K ε 1 + v r 0 , ext 2 cos 2 ϕ 2 − cos 2 ϕ 1 + ΔΨ 1 cos 2 ϕ 2 − ΔΨ 2 cos 2 ϕ 1 cos 2 ϕ 2 − cos 2 ϕ 1 + 1 − 2 v E K ε − K P ΔP ext − K ε r 0 , ext 2 + 1 − 2 v r 2 − K P Er 2 π Er 0 , ext 2 r 0 , ext 2 − r 0 , int 2 δF where ΔT is here the variation of the temperature at radius r; and KP is an intrinsic sensitivity to the hydrostatic pressure of the sensor alone, said sensitivity being equal to a coefficient of proportionality between a relative variation of the tracking quantity and a variation of the hydrostatic pressure that is directly applied to it.

[0074] In such a configuration, the temperature variation ΔT of the pipe 4 determined is a temperature of the wall of the pipe 4 at radius r.

[0075] And in the most general case where the sensors are positioned within the thickness of section 12 of pipe 4, respectively at a radius r1 and a radius r2: ΔT = r 1 2 r 2 2 ΔΨ 1 − ΔΨ 2 κ ε 1 − 2 ν − κ P E κ T κ ε 1 + ν r 0 , ext 2 r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + ΔΨ 1 r 1 2 cos 2 ϕ 2 − ΔΨ 2 r 2 2 cos 2 ϕ 1 κ T r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + 1 κ T 1 − 2 ν E κ ε − κ P ΔP ext + κ ε r 2 2 − r 1 2 cos 2 ϕ 1 + cos 2 ϕ 2 − 2 1 + ν cos 2 ϕ 1 cos 2 ϕ 2 + r 1 2 + r 2 2 cos 2 ϕ 1 − cos 2 ϕ 2 2 κ T πE r 0 , ext 2 − r 0 , int 2 r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF − 1 κ T 1 − 2 ν E κ ε − κ P r 1 2 r 2 2 cos 2 ϕ 2 + cos 2 ϕ 1 πr 0 , ext 2 r 0 , ext 2 − r 0 , int 2 r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF where r 1 is a radius of portion 12 of pipe 4 at a predetermined reference instant associated with the angle ϕ 1 ; r 2 is a radius of portion 12 of pipe 4 at a predetermined reference instant associated with the angle ϕ 2 ; K p is an intrinsic sensitivity to hydrostatic pressure of the sensor alone, said sensitivity being equal to a coefficient of proportionality between a relative variation of the tracking quantity and a variation of the hydrostatic pressure which is directly applied to it.

[0076] In such a configuration, the temperature variation ΔT of pipe 4 determined is a temperature of the wall of pipe 4, intermediate between the radii r 1 and r 2.

[0077] Similarly, and in the same way as for the determination of the pressure variation, the values ​​of the radii r 0,int , r 0,ext , r, r 1 , and r 2 , indicated above, are reference values ​​determined at a reference instant, like an initial instant, since these values, taking into account the forces exerted on pipe 4, are bound to evolve.

[0078] Advantageously, the calculator 8 is also configured to measure, from a signal delivered by a pressure sensor 22 (included or not in the measuring device 2) arranged in the pipe 4, a pressure (called "reference pressure") of a fluid present in the pipe 4.

[0079] In this case, calculator 8 is also configured to determine a damage parameter from a difference between the calculated internal pressure variation ΔP int and a concomitant variation of the measured reference pressure.

[0080] For example, the damage factor is equal to the ratio between, on the one hand, the difference between the variation of the reference pressure and the variation of the calculated internal pressure ΔP int, and on the other hand, the variation of the reference pressure.

[0081] Preferably, calculator 8 is also configured to generate a warning signal if the determined damage parameter is outside a predetermined tolerance range.

[0082] The operation of measuring device 2 will now be described.

[0083] First, the 6 sensors are arranged so that each 6 sensor delivers an indicative measurement signal of the tracking variable associated with a respective measurement area 10 and measurement direction.

[0084] Among the set of sensors 6, at least one first sensor 6A is such that the corresponding measurement direction defines a first angle with a plane normal to the longitudinal axis, and a second sensor 6B is such that the corresponding measurement direction defines a second angle with a plane normal to the longitudinal axis XX. The first angle and the second angle have different absolute values ​​modulo π.

[0085] The calculator 8 receives, from each sensor 6, and in particular from the first sensors 6A and the second sensors 6B, the corresponding measurement signal, and measures, from each measurement signal, the corresponding tracking quantity.

[0086] More specifically, for each sensor 6, the calculator 8 calculates a relative variation of the corresponding tracking quantity.

[0087] In addition, the calculator 8 receives information representative of a value of the variation of the external pressure ΔP ext, and of the variation of the additional longitudinal force δF applied to the pipe 4, distinct from a variation of a longitudinal force by the variation of the internal pressure and the variation of the external pressure.

[0088] The calculator also calculates the variation of the internal pressure of pipe 4, from the variation of the external pressure, the variation of the additional longitudinal force and the measured tracking quantities, including at least the first measured tracking quantity associated with the first sensor 6A and the second measured tracking quantity associated with the second sensor 6B.

[0089] Preferably, calculator 8 also calculates the variation in contact temperature of portion 12 of pipe 4 from the measured tracking quantities.

[0090] In addition, calculator 8 determines the damage parameter from the calculated variation of internal pressure ΔP int, and generates an alert signal if the determined damage parameter is outside the predetermined tolerance range.

Claims

1. A method for measuring a variation in an internal pressure of a pipe (4) including a portion (12) extending along a longitudinal axis, the measurement method comprising the steps of: - for each of at least two measurement areas (10) of the portion (12) of the pipe (4), measuring, by means of a corresponding sensor (6, 6A, 6B), a monitoring quantity associated with a respective measurement direction, a relative variation in the monitoring quantity being representative of a variation in a corresponding local deformation of the pipe (4) according to the associated measurement direction; and - calculating the variation in the internal pressure of the pipe (4) based on at least one deformation variation, each deformation variation being obtained only based on measured monitoring quantities, among which at least one first measured monitoring quantity is associated with a first measurement direction and at least one second measured monitoring quantity is associated with a second measurement direction, the first measurement direction defining a first angle (ϕ1) with a plane normal to the longitudinal axis, the second measurement direction defining a second angle (ϕ2) with a plane normal to the longitudinal axis, the first angle and the second angle having different absolute values modulo π, the sensors (6, 6A, 6B) being selected so that the same variation in their temperature results in the same relative variation in their respective measured monitoring quantities, wherein the measurement step is preceded by fastening the corresponding sensor (6, 6A, 6B) to each measurement area (10), the sensors (6, 6A, 6B) being fastened to their respective measurement areas (10) according to the same fastening method, and being selected so that the same variation in a mechanical deformation applied thereto results in the same relative variation in their respective measured monitoring quantities, wherein the method allows measuring a variation in the internal pressure of the pipe (4) and the portion (12) of the pipe (4) has an axisymmetric cylindrical shape, each measurement area (10) belonging to a section of the portion (12) of the pipe (4), the pipe (4) being closed at its ends, the variation of the internal pressure being calculated according to: ΔP int = ΔP ext + r 1 2 r 2 2 r 0 , int 2 r 0 , ext 2 E ΔΨ 2 − ΔΨ 1 r 0 , ext 2 − r 0 , int 2 κ ε 1 + ν r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + cos 2 ϕ 2 − cos 2 ϕ 1 π r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF where ΔPint is the variation of the internal pressure; ΔΨ1 and ΔΨ2 are respectively a relative variation of the first monitoring quantity and a relative variation of the second monitoring quantity; r0,ext is an outer radius of the portion (12) of the pipe (4); r0,int is an inner radius of the portion (12) of the pipe (4); r1 is a radius at which the measurement associated with the first measurement direction is performed; r2 is a radius at which the measurement associated with the second measurement direction is performed; E is the Young's modulus of the material in which the portion (12) of the pipe (4) is made; v is the Poisson's ratio of the material in which the portion of the pipe is made; ϕ1 and ϕ2 are respectively the first angle and the second angle; ΔPext a variation in an external pressure applied to the portion (12) of the pipe (4); δF is a variation in an additional longitudinal force applied to the portion of the pipe, and distinct from a variation in a longitudinal force exerted on the portion (12) of the pipe (4) by the internal pressure variation and the external pressure variation; and κε is a mechanical sensitivity of the sensors, equal to a proportionality coefficient between a relative variation in the monitoring quantity and a variation in the mechanical deformation applied thereto.

2. The measurement method according to claim 1, wherein, for at least one measurement area (10), the corresponding sensor (6, 6A, 6B) is an optical fibre segment (14) in which a Bragg grating (16) is inscribed, the optical fibre segment (14) being fastened to the measurement area (10) so that the corresponding Bragg grating (16) extends along the measurement direction associated with said measurement area (10), the mechanical sensitivity κε being expressed as: K ε = 1 n eff ∂ n eff ∂ ε mec + 1 wherein neff is an effective index of the optical guide of the optical fibre (18); and εmec is a longitudinal mechanical deformation of the optical fibre (18), the monitoring quantity being a reflection wavelength of each Bragg grating (16).

3. The measurement method according to claim 2, wherein, for at least two measurement areas (12), the corresponding optical fibre segments (14) belong to a same optical fibre (18).

4. The measurement method according to claim 3, wherein the measurement axes associated with at least two optical fibre segments (14) of the same optical fibre (18) form, with the longitudinal axis of the portion (12) of the pipe (4), angles that are distinct, in absolute values, modulo π.

5. The measurement method according to claim 3 or 4, wherein the measurement areas (10), on which at least two optical fibre segments (14) of the same optical fibre (18) are fastened, are arranged along a generatrix of the portion (12) of the pipe.

6. The measurement method according to any one of claims 1 to 5, wherein, for at least one measurement area (10), the sensor (6, 6A, 6B) is selected from the group comprising distance sensors such as a sensor implementing an acoustic method between an acoustic emitter and an acoustic receiver, the sensors implementing a reflectometry method on an electrical cable, the sensors implementing an optical reflectometry method, the deformation gauges, such as the electrical deformation gauges, and the stereo-correlation deformation sensors.

7. The measurement method according to any one of claims 1 to 6, wherein the first angle (ϕ1) amounts to 0 modulo π, and the second angle (ϕ2) amounts π / 2 modulo π.

8. The measurement method according to claim 7, wherein the method enables the measurement of a variation in the temperature of the pipe (4) and the portion (12) of the pipe (4) has an axisymmetric cylindrical shape, each measurement area (10) belonging to a section of the portion (12) of the pipe (4), the pipe (4) being closed at its ends, the variation in the temperature of the pipe being calculated according to: ΔT = r 1 2 r 2 2 Δψ 1 − Δψ 2 K ε 1 − 2 ν − K P E K T K ε 1 + ν r 0 , ext 2 r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + Δψ 1 r 1 2 cos 2 ϕ 2 − Δψ 2 r 2 2 cos 2 ϕ 1 K T r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + 1 K T 1 − 2 ν E K ε − K P ΔP ext + K ε r 2 2 − r 1 2 cos 2 ϕ 1 + cos 2 ϕ 2 − 2 1 + ν cos 2 ϕ 1 cos 2 ϕ 2 + r 1 2 + r 2 2 cos 2 ϕ 1 − cos 2 ϕ 2 2 K T πE r 0 , ext 2 − r 0 , int 2 r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF − 1 K T 1 − 2 ν E K ε − K P r 1 2 r 2 2 cos 2 ϕ 2 − cos 2 ϕ 1 πr 0 , ext 2 r 0 , ext 2 − r 0 , int 2 r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF + ϵ surf 1 K T K P π r 0 , ext 2 − r 0 , int 2 δF − Δψ 1 − Δψ 2 K P E K ε 1 + ν cos 2 ϕ 2 − cos 2 ϕ 1 where ΔT is the variation in the temperature of the pipe (4); ΔΨ1 and ΔΨ2 are respectively a relative variation of the first monitoring quantity and a relative variation of the second monitoring quantity; r0,ext is an outer radius of the portion (12) of the pipe (4); r0,int is an inner radius of the portion (12) of the pipe (4); r1 is a radius at which the measurement associated with the first measurement direction is performed; r2 is a radius at which the measurement associated with the second measurement direction is performed; εsurf is a parameter that takes the value 1 when r1 and r2 are both equal to r0,int or both equal to r0,ext and the value 0 in the other cases; E is the Young's modulus of the material in which the portion (12) of the pipe (4) is made; v is the Poisson's ratio of the material in which the portion (12) of the pipe (4) is made; ϕ1 and ϕ2 are respectively the first angle and the second angle; ΔPext is a variation in an external pressure applied to the portion (12) of the pipe (4); δF is a variation in an additional longitudinal force applied to the portion (12) of the pipe (4) and distinct from a variation in a longitudinal force exerted on the portion (12) of the pipe (4) by the internal pressure variation and the external pressure variation; κε is a mechanical sensitivity of the sensors (6, 6A, 6B), equal to a proportionality coefficient between a relative variation in the monitoring quantity and a mechanical deformation variation; κT is a thermal sensitivity of the sensors (6, 6A, 6B), equal to a proportionality coefficient between a relative variation in the monitoring quantity and a variation in their temperature; and KP is a sensitivity intrinsic to the hydrostatic pressure of the sensor (6, 6A, 6B) alone, said sensitivity being equal to a proportionality coefficient between a relative variation in the monitoring quantity and a variation in the pressure hydrostatic that is directly applied thereto.

9. The measurement method according to any one of claims 1 to 8, wherein N measurement areas (10) are circumferentially distributed every 2π / N around the longitudinal axis, N being an integer strictly greater than 1 and, preferably, N being an even number greater than 2, for at least two distinct measurement areas (10), the corresponding monitoring quantities are associated with measurement directions defining, with a plane normal to the longitudinal axis, angle having opposite signs modulo π.

10. The measurement method according to any one of claims 1 to 9, wherein the measurement associated with the first measurement direction and the measurement associated with the second measurement direction are performed at the same surface of the portion (12) of the pipe (4) selected from among an inner surface and an outer surface of said portion (12) of the pipe (4).

11. The measurement method according to any one of claims 1 to 10, further comprising the steps of: - measuring, by means of a pressure sensor arranged in the pipe (4), a pressure of a fluid present in the pipe (4), forming a reference pressure; and - calculating a damage parameter based on a discrepancy between the variation in the calculated internal pressure and a concomitant variation in the measured reference pressure, the measurement method advantageously comprising generating an alert signal if the determined damage parameter is outside a predetermined tolerance range.

12. A device (2) for measuring a variation in an internal pressure of a pipe (4) including a portion (12) extending along a longitudinal axis, the measurement device (2) comprising at least two sensors (6, 6A, 6B) and a calculator (8), each sensor (6, 6A, 6B) being configured so as to output, for a corresponding measurement area (10) of the portion (12) of the pipe (4), a measurement signal indicative of a predetermined monitoring quantity associated with a respective measurement direction, a relative variation in the monitoring quantity being representative of a variation in a local deformation, according to the associated measurement direction, of the measurement area (10), the sensors (6, 6A, 6B) being selected so that same temperature variation results in the same relative variation in their respective measured monitoring quantities, the calculator (8) being configured to measure the corresponding monitoring quantity based on each measurement signal, the calculator (8) being further configured to calculate the variation in the internal pressure of the pipe (4) based on at least one deformation variation, each deformation variation being obtained only from the measured monitoring quantities, among which at least one first measured monitoring quantity is associated with a first measurement direction and at least one second measured monitoring quantity is associated with a second measurement direction, the first measurement direction defining a first angle (ϕ1) with a plane normal to the longitudinal axis, the second measurement direction defining a second angle (ϕ2) with a plane normal to the longitudinal axis, the first angle and the second angle having different absolute values modulo π, the sensors (6, 6A, 6B) being fastened to their respective measurement areas (10) according to the same fastening method, and being selected so that the same variation in a mechanical deformation applied thereto results in the same relative variation in their respective measured monitoring quantities, wherein the calculator (8) is configured to allow measuring a variation in the internal pressure of the pipe (4) and the portion (12) of the pipe (4) has an axisymmetric cylindrical shape, each measurement area (10) belonging to a section of the portion (12) of the pipe (4), the pipe (4) being closed at its ends, the variation of the internal pressure being calculated according to: ΔP int = ΔP ext + r 1 2 r 2 2 r 0 , int 2 r 0 , ext 2 E Δψ 2 − Δψ 1 r 0 , ext 2 − r 0 , int 2 K ε 1 + ν r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 + cos 2 ϕ 2 − cos 2 ϕ 1 π r 1 2 cos 2 ϕ 2 − r 2 2 cos 2 ϕ 1 δF where ΔPint is the variation of the internal pressure; ΔΨ1 and ΔΨ2 are respectively a relative variation of the first monitoring quantity and a relative variation of the second monitoring quantity; r0,ext is an outer radius of the portion (12) of the pipe (4); r0,int is an inner radius of the portion (12) of the pipe (4); r1 is a radius at which the measurement associated with the first measurement direction is performed; r2 is a radius at which the measurement associated with the second measurement direction is performed; E is the Young's modulus of the material in which the portion (12) of the pipe (4) is made; v is the Poisson's ratio of the material in which the portion of the pipe is made; ϕ1 and ϕ2 are respectively the first angle and the second angle; ΔPext a variation in an external pressure applied to the portion (12) of the pipe (4); δF is a variation in an additional longitudinal force applied to the portion of the pipe, and distinct from a variation in a longitudinal force exerted on the portion (12) of the pipe (4) by the internal pressure variation and the external pressure variation; and κε is a mechanical sensitivity of the sensors, equal to a proportionality coefficient between a relative variation in the monitoring quantity and a variation in the mechanical deformation applied thereto.

13. An apparatus (1) comprising a pipe (4) and a measurement device (2) according to claim 12, the pipe (4) including a portion (12) extending along a longitudinal axis, each sensor (6, 6A, 6B) of the measurement device (2) being associated with a respective measuring area (10) of an outer surface of the portion (12) of the pipe (4), and being arranged so as to provide a monitoring quantity associated with a respective measurement direction, a relative variation in the monitoring quantity being representative of a variation in a corresponding local deformation of the pipe (4) according to the associated measurement direction the first measurement direction defining the first angle (ϕ1) with a plane normal to the longitudinal axis, and the second measurement direction defining the second angle (ϕ2) with the plane normal to the longitudinal axis, the first angle and the second angle having different absolute values modulo π.