ULTRASONIC GUIDED WAVE SYSTEM AND METHOD FOR MEASUREMENT OF FLUID PROPERTIES AND FLUID LEVELS

BACKGROUND

[0001] The subject matter of this disclosure relates generally to a ultrasonic guided wave system that employs a waveguide for measurement of multiple fluid parameters including fluid density, fluid viscosity, and fluid level by the propagation of ultrasonic wave energy along the waveguide located partially in contact with the fluid. The local temperature is measured through a novel integration of the RTD / thermocouple along with the waveguide.

[0002] Industrial process control often requires the determination of at least one parameter attributed to fluids along flow paths, for example in pipes. The parameters may include density of the fluid, fluid velocity, fluid level, temperature, fluid phase, or the like. There are a number of known sensors which are used for detection of parameters associated with the fluids.

[0003] One such sensor used for detection of parameters associated with the fluids is a ultrasonic waveguide sensor. An ultrasonic waveguide is partially inserted into a fluid whose property needs to be measured. Wave energy is guided along the sensor held partially in contact with the fluid. The flow of fluid surrounding the ultrasonic waveguide sensor influences the ultrasonic wave characteristics, specifically the time of flight of the wave mode. In other words, the interaction of the guided wave energy along the sensor with the fluid results in a lower velocity of propagation of the guided wave energy along the sensor, so that the change in flight time of the wave, as compared to a reference time with the sensor in air or vacuum, provides an indication of a parameter of the fluid in contact with the sensor. In particular circumstances, where at least one of the fluid composition, container geometry and sensor characteristics are known, a measurement of flight time of the wave energy guided along the sensor may provide an indication of a parameter of the fluid.

[0004] Fluid property measurement systems using ultrasonic waveguide sensors generally require multiple sensors to measure a plurality of fluid properties including without limitation, density, viscosity and temperature of surrounding fluid(s) in single and multiphase fluid environments. Li view of the foregoing limitations, there is a need for a waveguide system that employs a single waveguide for measurement of multiple fluid properties. The single waveguide system should further be capable of measuring such multiple fluid properties associated with both single phase and multiphase fluid flow. The single waveguide system should further be capable of enhancing a plurality of wave propagation signatures such as, without limitation, time of flight and attenuation, to improve the resolution of the measured fluid properties.

BRIEF DESCRIPTION

[0005] Briefly, in accordance with one embodiment, a method of measuring fluid properties comprises: providing an ultrasonic waveguide sensor comprising an active sensor portion, wherein the active sensor portion comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges; immersing the active sensor portion of the ultrasonic waveguide sensor in a single phase fluid, a multiphase fluid, or both; exciting an ultrasonic wave energy in the ultrasonic waveguide sensor subsequent to immersing the active sensor portion of the ultrasonic waveguide sensor; providing ultrasonic excitation to the ultrasonic waveguide sensor subsequent to exciting an ultrasonic wave energy in the ultrasonic waveguide sensor and detecting attenuation of wave energy between predetermined portions of the ultrasonic waveguide sensor in response thereto; and determining viscosity of the fluid based on the attenuation of wave energy between the predetermined portions of the ultrasonic waveguide sensor.

[0006] According to another embodiment, a sensing system for sensing at least one parameter of a fluid, the sensing system comprising: an ultrasonic waveguide sensor comprising an active sensor portion, wherein the active sensor portion comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges; an excitation device configured to excite ultrasonic wave energy in the ultrasonic waveguide sensor, wherein at least a portion of the ultrasonic waveguide sensor is mountable for immersion in the fluid and operable to propagate the wave energy that interacts with the fluid along the at least portion of the ultrasonic waveguide sensor so as to affect attenuation of the wave energy in a manner dependent on the viscosity of the fluid; a transducer device configured to provide ultrasonic wave excitation to the ultrasonic waveguide sensor and detect the attenuation of wave energy from the active sensor portion; and a processor device configured to determine viscosity of the fluid in response to attenuation of wave energy detected by the transducer device.

[0007] According to yet another embodiment, a method of measuring fluid levels comprises: providing one or more ultrasonic waveguide sensors, each ultrasonic waveguide sensor comprising an active sensor portion, wherein each active sensor portion comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges; immersing the active sensor portion of each ultrasonic waveguide sensor in a single phase fluid common to the one or more ultrasonic waveguide sensors, a multiphase fluid common to the one or more ultrasonic waveguide sensors, or both; exciting ultrasonic wave energy in the one or more ultrasonic waveguide sensors subsequent to immersing the active sensor portion of the one or more ultrasonic waveguide sensors; providing ultrasonic wave excitation to the one or more ultrasonic waveguide sensors subsequent to exciting ultrasonic wave energy in the one or more ultrasonic waveguide sensors and detecting velocity of an ultrasonic wave in predetermined segments of the one or more ultrasonic waveguide sensors in response thereto; and determining fluid levels of each fluid based on the detected ultrasonic wave velocities.

DRAWINGS

[0008] These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:

[0009] Figure 1 is a simplified system diagram illustrating an ultrasonic waveguide sensor system for sensing density, viscosity and level of a fluid according to one embodiment;

[0010] Figure 2 is a perspective view of an exemplary ultrasonic waveguide sensor suitable for use in the ultrasonic waveguide sensor system depicted in Figure 1 according to one embodiment;

[0011] Figure 3 is a cross-sectional view of an exemplary active sensor portion of an ultrasonic waveguide sensor according to one embodiment;

[0012] Figure 4 is a graph illustrating the effect of fluid viscosity on an ultrasonic wave at different portions of an ultrasonic waveguide sensor according to one embodiment;

[0013] Figure 5 is a graph illustrating a relationship between fluid viscosity and normalized amplitude of a corresponding ultrasonic wave according to one embodiment;

[0014] Figure 6 illustrates a single ultrasonic waveguide sensor fluid level sensor according to one embodiment;

[0015] Figure 7 illustrates a dual ultrasonic waveguide sensor fluid level sensor according to one embodiment; and

[0016] Figure 8 illustrates a single ultrasonic waveguide sensor fluid temperature sensor according to one embodiment.

[0017] While the above-identified drawing figures set forth alternative embodiments, other embodiments of the present invention are also contemplated, as noted in the discussion. In all cases, this disclosure presents illustrated embodiments of the present invention by way of representation and not limitation. Numerous other modifications and embodiments can be devised by those skilled in the art which fall within the scope and spirit of the principles of this invention.

DETAILED DESCRIPTION

[0018] Figure 1 is a simplified system diagram illustrating an ultrasonic waveguide sensor system 10 for sensing viscosity of a fluid 12 flowing through a conduit 14 according to one embodiment. In the illustrated embodiment and subsequent embodiments, the conduit may be a vertical arrangement or a horizontal arrangement. Numerous other embodiments can just as easily be employed using the principles described herein, including without limitation, any circular/spring shape or some other shape. It should be noted that even though a conduit is disclosed, the sensing system 10 is applicable to any device containing a fluid for sensing at least one parameter attributed to the fluid in both static and flowing conditions. The system 10 includes an ultrasonic waveguide sensor 16 partially immersed in the fluid 12 flowing through the conduit 14.

The ultrasonic waveguide sensor 16 includes a reference portion 18 and a active sensor portion 20. In a specific embodiment, the reference portion 18 is a cylindrical-shaped reference portion. The depth of the ultrasonic waveguide sensor 16 immersed in the fluid 12 may be varied. The present invention is not so limited however, and it shall be understood that an ultrasonic waveguide sensor without a reference portion can just as easily be employed to implement an ultrasonic waveguide sensor system according to the principles described herein.

[0019] The system 10 further includes an excitation device 21 having a wave generator 22 configured to transmit shear wave energy via an amplifier 24 to the ultrasonic waveguide sensor 16. A transducer device 26 is configured to provide ultrasonic wave excitation to the ultrasonic waveguide sensor 16. The ultrasonic guided wave, which propagates along the ultrasonic waveguide sensor 16, detects the presence and nature of the surrounding fluid 12. When the ultrasonic waveguide sensor 16 is partially immersed in the fluid 12, the propagation of wave is affected by at least one parameter of the fluid 12. Hence at least one parameter of the fluid 12 can be measured by detecting the propagation of wave energy along the sensor 16. At least one parameter includes absolute density, density profile, fluid level, absolute temperature, temperature profile, absolute viscosity, viscosity profile, absolute flow velocity, flow velocity profile, absolute fluid phase fraction, fluid phase fraction profile, or combinations thereof of the fluid 12. The fluid 12 may include a single-phase fluid, or a multi-phase fluid mixture. It should be noted herein that a multi-phase fluid mixture might include two or more fluids having different densities. For example, a multi-phase fluid mixture may include oil, water, and gas. The excitation source and receiver may be, piezoelectric, curved piezoelectric, phased array magneto-strictive, laser-based electromagnetic acoustic transducer (EMAT), phased EMAT and Membrane. The application of the exemplary sensor 16 to all such types of fluid is envisaged.

[0020] In the illustrated embodiment, the transducer device 26 is also configured to detect the wave energy from the active sensor portion 20 of the ultrasonic waveguide sensor 16. A corresponding output signal from the transducer device 26 is fed via a digital oscilloscope 28 to a processor device 30, such as, without limitation, a computer. The processor device 30 is configured to determine at least one parameter of the fluid 12 in response to the output signal from the transducer device 30. It should be noted herein that the configuration of the sensing system 10 is an exemplary embodiment and should not construed in any way as limiting the scope of the embodiments described herein. The exemplary sensor 16 is applicable to any application requiring detection of at least one parameter attributed to the fluid 12 in which the fluid is contained in a vessel or flowing through a conduit. Typical examples include petroleum industry, oil & gas, or the like. The exemplary sensor design and arrangement of sensors are explained in greater detail with reference to subsequent embodiments.

[0021] Referring to Figure 2, a perspective view of an exemplary ultrasonic waveguide sensor 32 is illustrated. The ultrasonic waveguide sensor 32 includes a reference portion 34 and an active sensor portion 36. In the illustrated embodiment, the reference portion 34 is a cylindrical-shaped reference portion and the active sensor portion 36 is an X-shaped sensor portion. The present invention is not so limited however, and it shall be understood that any ultrasonic waveguide sensor shape can be employed using the principles described herein. The active sensor portion 36 includes a plurality of projections 38 extending outward and spaced apart from each other. More specifically, the active sensor portion 36 comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges when viewed into the tip 40. The active sensor portion 36 is coupled to the reference portion 34 to form an interface 35 between the reference portion 34 and the active sensor portion 36.

[0022] According to one embodiment, the ultrasonic waveguide sensor 32 utilizes change in speed of wave energy propagating along the active sensor portion 36 due to the presence of surrounding fluid medium to detect at least one parameter of the fluid medium. As the ultrasonic wave propagates through the active sensor portion 36 of the sensor 32, acceleration and deceleration of fluid surrounding the active sensor portion 36 occurs. Normal forces are exerted on the surface of the active sensor portion 36, which in turn act on the surrounding fluid. The fluid motion surrounding the active sensor portion 36 is induced by the normal velocity component of velocity at a fluid-solid interface and also by the viscous drag of the surrounding fluid. As a result, the fluid is trapped at corners of the active sensor portion 36 affecting the propagation of the wave energy. In other words, the propagation of the wave energy is attributed to the inertial of the surrounding fluid. At least one parameter of the surrounding fluid medium can be detected by determining speed of propagating wave energy.

[0023] Referring to Figure 3, a cross-sectional view of an exemplary active sensor portion 42 is illustrated. The active sensor portion 42 is an X-shaped portion. The active sensor portion 42 includes a plurality of projections 44 extending outward from a common inner section 46 and spaced apart from each other. More specifically, the active sensor portion 42 comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges. The polygon shape cross section can be symmetric or non-symmetric and is only limited in its requirement for vertices that alternate between joining outward and inward pointing pairs of edges. The present invention is not so limited however, and it shall be understood that numerous active sensor portion shapes including an X-shaped sensor portion can be employed to implement an ultrasonic waveguide using the principles described herein.

[0024] According to another embodiment, viscosity of the surrounding fluid is determined by correlating the attenuation of an ultrasonic wave in the ultrasonic waveguide sensor 32. Figure 4 is a graph 48 illustrating the effect of fluid viscosity on an ultrasonic wave at different portions of the ultrasonic waveguide sensor 42 according to one embodiment. The first reflection signal 52 and second reflection signal 54 are measured at the ultrasonic waveguide sensor interface 35 depicted in Figure 2 in response to a sensor input signal 50. Further, the first reflection signal 56 and second reflection signal 58 are measured at the sensor tip 40 depicted in Figure 2. The present inventors discovered that the amplitude of the reflected signal 52, 54, 56, 58 decreases measurably between the first and second reflections in each case and recognized this feature could be used to measure the viscosity of the surrounding fluid by correlating the attenuation of the ultrasonic wave in the sensing portion of the ultrasonic waveguide sensor 42.

[0025] Figure 5 is a graph illustrating a relationship between fluid viscosity and normalized amplitude of a corresponding ultrasonic wave according to one embodiment. It was discovered that a linear trend in decay of ultrasonic wave amplitude occurs in response to a decrease in ultrasonic wave input amplitude. The attenuation can be measured, for example, as a difference between the first and second reflected signals at the ultrasonic waveguide sensor interface 35 or as a difference between the first and second reflected signals at the ultrasonic waveguide sensor tip 40. A table can then be easily created for a particular ultrasonic waveguide sensor 42 that identifies the surrounding fluid using the principles described herein.

[0026] Figure 6 illustrates application of a single ultrasonic waveguide sensor 42 to measure fluid level 62 according to one embodiment. The portion of the ultrasonic waveguide sensor 42 above the fluid level 62 is represented as segment XI. The portion of the ultrasonic waveguide sensor 42 below the fluid level 62 is represented as segment X2. The velocity of the ultrasonic wave measured in segment XI is then represented as V1. The velocity of the ultrasonic wave measured in segment X2 is represented as V'2. A set of simultaneous equations can then be formulated and solved to determine the actual fluid level. The set of simultaneous equations using XI, X2, V1 and V'2 can be represented as

[0027] Figure 7 illustrates application of a pair of ultrasonic waveguide sensors 42 to measure multiple fluid levels 64, 66 according to one embodiment. The portion of the ultrasonic waveguide sensors 42 above the upper fluid level 64 is represented as segment XI. The portion of the ultrasonic waveguide sensors 42 below the bottom fluid level 66 is represented as segment X3. The portion of the ultrasonic waveguide sensors 42 between the upper fluid level 64 and the lower fluid level 66 is represented as segment X2. The velocity of the ultrasonic wave measured in segment XI of the first ultrasonic waveguide sensor R1 is then represented as V1. The velocity of the ultrasonic wave measured in segment X2 of the first ultrasonic waveguide sensor R1 is represented as V'2. The velocity of the ultrasonic wave measured in segment X3 of the first ultrasonic waveguide sensor R1 is represented as V'3. The velocity of the ultrasonic wave measured in segment XI of the second ultrasonic waveguide sensor R2 is then represented as V" 1. The velocity of the ultrasonic wave measured in segment X2 of the second ultrasonic waveguide sensor R2 is represented as V"2. The velocity of the ultrasonic wave measured in segment X3 of the second ultrasonic waveguide sensor R2 is represented as V"3. A set of simultaneous equations can then be formulated and solved to determine the actual fluid levels. The fluid levels depicted in the illustrated embodiment include a water fluid level, an oil fluid level, and an emulsion fluid level between the water fluid level and the oil fluid level. One set of simultaneous equations using XI, X2, X3, V1, V'2, V'3, V" 1, V"2 and V"3 can be represented as It can be appreciated that in each case, a combination of time-of-flight (TOF) and attenuation of wave mode measurement data is used to measure the surrounding fluid viscosity, which in turn enhances the estimation of surrounding fluid density. Measurement of fluid properties at two locations with a known separation, combined with a correlation algorithm helps to obtain the individual phase velocity.

[0028] Figure 8 illustrates a single ultrasonic waveguide sensor 42 mat includes a temperature RTD 72 integrated therein and that is suitable to measure the temperature of the surrounding fluid according to one embodiment. According to one aspect, the integration of RTD 72 provides a means for accurately measuring the fluid temperature to allow compensating for density, viscosity and level measurements to standard temperature and pressure (STP) conditions. More specifically, the placement of RTD 72 for fluid temperature measurement enables online calculation of fluid properties at STP conditions.

[0029] In summary explanation, a single ultrasonic waveguide sensor provides for measuring density, viscosity, level and temperature of a fluid with high sensitivity and resolution for single and multiphase fluids. The sensor provides improved resolution for fluid level sensing using a simplified algorithm solving simultaneous equations. An integrated temperature sensor (RTD) configuration enhances the accuracy of fluid property measurement.

[0030] While only certain features of the invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.

CLAIMS:

1. A method of measuring fluid properties comprising:

providing an ultrasonic waveguide sensor comprising an active sensor portion, wherein the active sensor portion comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges;

immersing the active sensor portion of the ultrasonic waveguide sensor in a single phase fluid, a multiphase fluid, or both;

exciting ultrasonic wave energy in the ultrasonice waveguide sensor subsequent to immersing the active sensor portion of the ultrasonic waveguide sensor;

providing ultrasonic wave excitation to the ultrasonice waveguide sensor subsequent to exciting ultrasonic wave energy in the ultrasonic waveguide sensor and detecting attenuation of wave energy between predetermined portions of the ultrasonic waveguide sensor in response thereto; and

determining viscosity of the surrounding fluid based on the attenuation of wave energy between the predetermined portions of the ultrasonice waveguide sensor.

2. The method according to claim 1, wherein determining viscosity of the fluid based on the attenuation of wave energy between the predetermined portions of the ultrasonic waveguide sensor comprises:

measuring the amplitude of a first reflected signal in response to an ultrasonic wave in a first immersed portion;

measuring the amplitude of a single or multiple reflected second portion signal in response to the ultrasonic wave in the immersed sensor; and

correlating a viscosity level with an amplitude difference signal based on the first reflected first portion signal and the single or multiple reflected second portion signal.

3. The method according to claim 1, further comprising:

integrating a resistance temperature device (RTD) into the ultrasonic waveguide sensor;
applying power to the RTD;

measuring the resistance of the RTD;

calculating the surrounding fluid temperature based on the resistance measurement of the RTD; and

compensating the viscosity to standard temperature and pressure conditions based on the calculated fluid temperature.

4. The method according to claim 1, further comprising:

detecting velocity of an ultrasonic wave in predetermined segments of the ultrasonic waveguide sensor in response to the ultrasonic excitation; and

determining a fluid level of the surrounding fluid based on the detected ultrasonic wave velocities.

5. The method according to claim 4, further comprising:

providing one or more additional ultrasonic waveguide sensors, each additional ultrasonic waveguide sensor comprising an active sensor portion, wherein the active sensor portion comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges;

immersing the active sensor portion of each ultrasonic waveguide sensor in a single phase fluid, a multiphase fluid, or both such that the fluid surrounds predetermined portions of
the one or more additional ultrasonic waveguide sensors;

exciting ultrasonic wave energy in the additional one or more ultrasonic waveguide sensors subsequent to immersing the active sensor portions of the one or more additional ultrasonic waveguide sensors;

providing ultrasonic excitation to each ultrasonic waveguide sensor subsequent to exciting ultrasonic wave energy in the one or more additional ultrasonic waveguide sensors and detecting attenuation of wave energy between the predetermined portions of each additional ultrasonic waveguide sensor in response thereto;

detecting velocity of an ultrasonic wave in predetermined segments of each ultrasonic waveguide sensor in response to the ultrasonic wave excitation; and

determining a fluid level of each surrounding fluid based on the detected ultrasonic wave velocities when the surrounding fluid comprises a plurality of fluids.

6. A sensing system for sensing at least one parameter of a fluid, the sensing system comprising:

an ultrasonic waveguide sensor comprising an active sensor portion, wherein the active sensor portion comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges;

an excitation device configured to excite ultrasonic wave energy in the ultrasonic waveguide sensor, wherein at least a portion of the ultrasonic waveguide sensor is mountable for immersion in the fluid and operable to propagate the wave energy that interacts with the fluid along the at least portion of the ultrasonic waveguide sensor so as to affect attenuation of the wave energy in a manner dependent on the viscosity of the fluid;

a transducer device configured to provide ultrasonic wave excitation to the ultrasonic waveguide sensor and detect the attenuation of wave energy from the active sensor portion; and

a processor device configured to determine viscosity of the fluid in response to attenuation of wave energy detected by the transducer device.

7. The sensing system according to claim 6, wherein the processor is further configured to determine viscosity of the fluid based on the attenuation of wave energy between predetermined portions of the ultrasonic waveguide sensor.

8. The sensing system according to claim 7, wherein the processor is further configured to determine viscosity of the fluid based on the amplitude of a first reflected signal in response to an ultrasonic wave in a first immersed portion of the ultrasonic waveguide sensor, and further based on the amplitude of a single or multiple reflected second immersed portion signal in response to the ultrasonic wave in the immersed sensor.

9. The sensing system according to claim 8, wherein the processor is further configured to correlate a viscosity level with an amplitude difference signal based on the first reflected signal and single or multiple reflected signals.

10. The sensing system according to claim 6, further comprising a resistance temperature device (RTD) integrated into the ultrasonic waveguide sensor.

11. The sensing system according to claim 6, wherein the processor is further configured to calculate a fluid level of the surrounding fluid based on detected ultrasonic wave velocities.

12. The sensing system according to claim 6, further comprising:

one or more additional ultrasonic waveguide sensors, each additional ultrasonic waveguide sensor comprising an active sensor portion, wherein the active sensor portion comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges, wherein the active sensor portion of each ultrasonic waveguide sensor is immersed in a single phase fluid, a multiphase fluid, or both such that the fluid surrounds predetermined portions of the one or more additional ultrasonic waveguide sensors, and further wherein the processor is further configured to calculate a fluid level of each surrounding fluid based on the detected ultrasonic wave velocities when the surrounding fluid comprises a plurality of fluids.

13. A method of measuring fluid levels comprising:

providing one or more ultrasonic waveguide sensors, each ultrasonic waveguide sensor comprising an active sensor portion, wherein each active sensor portion comprises a polygon shape cross section having vertices that alternate between joining outward and inward pointing pairs of edges;

immersing the active sensor portion of each ultrasonic waveguide sensor in one or more single phase fluids common to the one or more ultrasonic waveguide sensors, one or more multiphase fluids common to the one or more ultrasonic waveguide sensors, or both;

exciting ultrasonic wave energy in the one or more ultrasonic waveguide sensors subsequent to immersing the active sensor portions of the one or more ultrasonic waveguide sensors;
providing ultrasonic excitation to the one or more ultrasonic waveguide sensors subsequent to exciting ultrasonic wave energy in the one or more ultrasonic waveguide sensors and detecting velocity of an ultrasonic wave in predetermined segments of the one or more ultrasonic waveguide sensors in response thereto; and

determining fluid levels (L) of each fluid based on the detected ultrasonic wave velocities.

14. The method according to claim 13, wherein determining fluid levels (L) comprises solving a set of simultaneous equations represented by for a single ultrasonic waveguide sensor system, wherein XI is an ultrasonic waveguide sensor segment above the fluid level L, X2 is an ultrasonic waveguide sensor segment below the fluid level L, VI is the ultrasonic wave velocity in segment XI, V'2 is the ultrasonic wave velocity in segment X2, and TOF is a time of flight of ultrasonic wave energy in the surrounding fluid.

15. The method according to claim 13, wherein determining fluid levels (L) comprises solving a set of simultaneous equations represented by for an ultrasonic waveguide sensor system comprising first and second ultrasonic waveguide sensors, wherein XI is an ultrasonic waveguide sensor segment above a first fluid level L, X2 is an ultrasonic waveguide sensor segment below the segment XI, X3 is an ultrasonic waveguide sensor segment below segment X2, V1 is the ultrasonic wave velocity in segment XI of the first ultrasonic waveguide sensor, V'2 is the ultrasonic wave velocity in segment X2 of the first ultrasonic waveguide sensor, V'3 is the ultrasonic wave velocity in segment X3 of the first ultrasonic waveguide sensor, Vl is the ultrasonic wave velocity in segment XI of the second ultrasonic waveguide sensor, V"2 is the ultrasonic wave velocity in segment X2 of the second ultrasonic waveguide sensor, V"3 is the ultrasonic wave velocity in segment X3 of the second ultrasonic waveguide sensor, TOF' is a time of flight of shear wave energy in the surrounding fluid associated with the first ultrasonic waveguide sensor, and TOF" is a time of flight of ultrasonic wave energy in the surrounding fluid associated with the second ultrasonic waveguide sensor.