Fluid parameter measurement for industrial sensing applications using acoustic pressures

In industrial sensing applications at least one parameter of at least one fluid in a pipe 12 is measured using a spatial array of acoustic pressure sensors 14,16,18 placed at predetermined axial locations x1, x2, x3 along the pipe 12. The pressure sensors 14,16,18 provide acoustic pressure signals P1(t), P2(t), P3(t) on lines 20,22,24 which are provided to signal processing logic 60 which determines the speed of sound amix of the fluid (or mixture) in the pipe 12 using acoustic spatial array signal processing techniques with the direction of propagation of the acoustic signals along the longitudinal axis of the pipe 12. Numerous spatial array-processing techniques may be employed to determine the speed of sound amix. The speed of sound amix is provided to logic 48, which calculates the percent composition of the mixture, e.g., water fraction, or any other parameter of the mixture, or fluid, which is related to the sound speed amix. The logic 60 may also determine the Mach number Mx of the fluid. The acoustic pressure signals P1(t), P2(t), P3(t) measured are lower frequency (and longer wavelength) signals than those used for ultrasonic flow meters, and thus is more tolerant to inhomogeneities in the flow. No external source is required and thus may operate using passive listening. The invention will work with arbitrary sensor spacing and with as few as two sensors if certain information is known about the acoustic properties of the system. The sensor may also be combined with an instrument, an opto-electronic converter and a controller in an industrial process control system.

TECHNICAL FIELD

This invention relates to fluid parameter measurement in pipes and more particularly to measuring speed of sound and parameters related thereto of fluids in pipes using acoustic pressures for use in industrial sensing applications.

BACKGROUND ART

An industrial process sensor is typically a transducer that responds to a measurand with a sensing element and converts the variable to a standardized transmission signal, e.g., an electrical or optical signal, that is a function of the measurand. Industrial process sensors utilize transducers that include flow measurements of an industrial process such as that derived from slurries, liquids, vapors and gasses in refinery, chemical, paper, pulp, petroleum, gas, pharmaceutical, food, mining, minerals and other fluid processing plants. Industrial process sensors are often placed in or near the process fluids, or in field applications. Often, these field applications are subject to harsh and varying environmental conditions that provide challenges for designers of such sensors. Flow measurement is one of the largest segments of the industrial sensing and instrumentation market. Industries in which flow measurement is prevalent includes petroleum, chemical, pulp, paper, food, and mining and minerals.

Typical electronic, or other, transducers of the prior art often cannot be placed in industrial process environments due to sensitivity to electromagnetic interference, radiation, heat, corrosion, fire, explosion or other environmental factors. It is for these reasons that fiber optic based sensors are being incorporated into industrial process control environments in increasing number.

Further, it is known that the speed of sound amixof fluids in pipes may be used to determine various parameters of the fluid, such as is described in U.S. Pat. No. 4,080,837, entitled “Sonic Measurement of Flow Rate and Water Content of Oil-Water Streams”, to Alexander et al., U.S. Pat. No. 5,115,670, entitled “Measurement of Fluid Properties of Two-Phase Fluids Using an Ultrasonic Meter”, to Shen, and U.S. Pat. No. 4,114,439, entitled “Apparatus for Ultrasonically Measuring Physical Parameters of Flowing Media”, to Fick. Such techniques have a pair of acoustic transmitters/receivers (transceivers) that generate a sound signal and measure the time it takes for the sound signal to travel between the transceivers. This is also known as a “sing-around” or “transit time” method. However, such techniques require precise control of the acoustic source and are costly and/or complex to implement in electronics.

Also, these techniques use ultrasonic acoustic signals as the sound signal measured, which are high frequency, short wavelength signals (i.e., wavelengths that are short compared to the diameter of the pipe). Typical ultrasonic devices operate near 200 k Hz, which corresponds to a wavelength of about 0.3 inches in water. In general, to allow for signal propagation through the fluid in an unimpeded and thus interpretable manner, the fluid should be homogeneous down to length scales of several times smaller than the acoustic signal wavelength. Thus, the criteria for homogeneity of the fluid becomes increasingly stricter with shorter wavelength signals. Consequently, inhomogeneities in the fluid, such as bubbles, gas, dirt, sand, slugs, stratification, globules of liquid, and the like, will reflect or scatter the transmitted ultrasonic signal. Such reflection and scattering inhibit the ability of the instrument to determine the propagation velocity. For this reason, the application of ultrasonic flowmeters have been limited primarily to well-mixed flows.

SUMMARY OF THE INVENTION

Objects of the present invention include provision of a system for measuring the speed of sound of fluids in pipes in industrial fluid processes.

According to the present invention, an apparatus for industrial sensing applications for measuring at least one parameter of a mixture of at least one fluid in a pipe, comprising a spatial array of at least two pressure sensors, disposed at different axial locations along the pipe, and each measuring an acoustic pressure within the pipe at a corresponding axial location, each of said sensors providing an acoustic pressure signal indicative of the acoustic pressure within the pipe at said axial location of a corresponding one of said sensors; and a signal processor, responsive to said pressure signals, which provides a signal indicative of a speed of sound of the mixture in the pipe.

According further to the present invention, the signal processor comprises logic that calculates a speed at which sound propagates along the spatial array.

According further to the present invention, the signal processor comprises logic that calculates a frequency domain representation of (or frequency based signal for) each of the acoustic pressures signals. According still further to the present invention, the signal processor comprises logic that calculates a ratio of two of the frequency signals. In still further accord to the present invention, the sensors comprise at least three sensors.

According still further to the present invention, the pressure sensors are fiber optic Bragg grating-based pressure sensors. Still further accord to the present invention, at least one of the pressure sensors measures a circumferential-averaged pressure at a given axial location of the sensor. Further according to the present invention, at least one of the pressure sensors measures pressure at more than one point around a circumference of the pipe at a given axial location of the sensor.

The present invention provides a significant improvement over the prior art by providing a measurement of the speed of sound amixof a mixture of one or more fluids within a pipe (where a fluid is defined as a liquid or a gas) by using an axial array of acoustic (or ac, dynamic, unsteady, or time varying) pressure measurements along the pipe. An explicit acoustic noise source is not required, as the background acoustic noises within the pipe (or fluid therein) will likely provide sufficient excitation to enable characterization of the speed of sound of the mixture by merely passive acoustic listening.

The invention works with acoustic signals having lower frequencies (and thus longer wavelengths) than those used for ultrasonic meters, such as below about 20 k Hz (depending on pipe diameter). As such, the invention is more tolerant to the introduction of gas, sand, slugs, or other inhomogeneities in the flow.

The invention will work with arbitrary sensor spacing and arbitrary flow Mach numbers Mx; however, if the sensors are equally spaced and the axial velocity of the flow is small and therefore negligible compared to the speed of sound in the mixture (i.e., Mach number of the mixture Mx is small compared to one), the speed of sound amixmay be determined as an explicit function of the frequency domain representation (frequency based signal) for the acoustic pressure signals at a given evaluation frequency ω.

Since the speed of sound is an intrinsic property of mixtures, the present invention can be used to measure any parameter (or characteristic) of any mixture of one or more fluids in a pipe in which such parameter is related to the speed of sound of the mixture amix, e.g., fluid fraction, temperature, salinity, sand particles, slugs, pipe properties, etc. or any other parameter of the mixture that is related to the speed of sound of the mixture. For example, the present invention may be used to measure fluid volume fractions (or composition or cut or content) of a mixture of any number of fluids in which the speed of sound of the mixture amixis related to (or is substantially determined by), the volume fractions of two constituents of the mixture, e.g., oil/water, oil/gas, water/gas. Also, the present invention can be used to measure the speed of sound of any mixture and can then be used in combination with other known quantities to derive phase content of mixtures with multiple (more than two) constituents.

The present invention allows the speed of sound to be determined in a pipe independent of pipe orientation, i.e., vertical, horizontal, or any orientation therebetween. Also, the invention does not require any disruption to the flow within the pipe (e.g., an orifice or venturi). Further, the invention uses ac (or unsteady or dynamic) pressure measurements as opposed to static (dc) pressure measurements and is therefore less sensitive to static shifts (or errors) in sensing. Furthermore, if harsh environment fiber optic pressure sensors are used to obtain the pressure measurements, such sensors eliminate the need for any electronic components down-hole, thereby improving reliability of the measurement.

Also, a strain gauge (optical, electrical, etc.) that measures hoop strain on the pipe may be used to measure the ac pressure. Fiber optic wrapped sensors may be used as optical strain gauges to provide circumferentially averaged pressure. Thus, the present invention provides non-intrusive measurements of the speed of sound (and other corresponding parameters), which enables real time monitoring and optimization for oil and gas exploration and production, or for other applications.

Also, the invention may be combined with a controller and other devices and used in an industrial process control system.

BEST MODE FOR CARRYING OUT THE INVENTION

Referring toFIG. 1, a pipe (or conduit)12has three acoustic pressure sensors14,16,18, located at three locations x1,x2,x3along the pipe12. The pressure may be measured through holes in the pipe12ported to external pressure sensors or by other techniques discussed hereinafter. The pressure sensors14,16,18provide pressure time-varying signals P1(t),P2(t),P3(t) on lines20,22,24, to known Fast Fourier Transform (FFT) logics26,28,30, respectively. The FFT logics26,28,30calculate the Fourier transform of the time-based input signals P1(t),P2(t), P3(t) and provide complex frequency domain (or frequency based) signals P1(ω),P2(ω),P3(ω) on lines32,34,36indicative of the frequency content of the input signals. Instead of FFT's, any other technique for obtaining the frequency domain characteristics of the signals P1(t),P2(t),P3(t), may be used. For example, the cross-spectral density and the power spectral density may be used to form a frequency domain transfer functions (or frequency response or ratios) discussed hereinafter.

Also, some or all of the functions within the logic60may be implemented in software (using a microprocessor or computer) and/or firmware, or may be implemented using analog and/or digital hardware, having sufficient memory, interfaces, and capacity to perform the functions described herein.

Acoustic pressure sensors14,16,18sense acoustic pressure signals that, as measured, are lower frequency (and longer wavelength) signals than those used for ultrasonic flow meters of the prior art, and thus the current invention is more tolerant to inhomogeneities in the flow. In addition, the present invention differs from prior art fluid parameter measurement devices in that the present invention incorporates the compliance of the pipe to determine the effective speed of sound of the pipe/fluid system. The typical frequency range for acoustic pressure signals of the present invention is from about 10 Hz to about 10,000 Hz. The acoustic pressure signals are generated within the fluid of the pipe12by a variety of non-discrete sources such as remote machinery, pumps, valves, elbows, as well as the fluid flow itself. It is this last source, the fluid flowing within the pipe, that is a generic source of acoustic noise that assures a minimum level of acoustics for any fluid piping systems for which the present invention takes unique advantage. The flow generated acoustics increase with mean flow velocity and the overall noise levels (acoustic pressure levels) are a function of the generating mechanism and the damping mechanism. Experience indicates that pipe systems typically have sufficient ambient noise levels of 100 to 180 dbA. As such, no external discrete noise source is required within the present invention and thus may operate using passive listening. It is within the scope of the present that the pressure sensor spacing may be known or arbitrary and that as few as two sensors are required if certain information is known about the acoustic properties of the system as will be more fully described herein below.

The frequency signals P1(ω),P2(ω),P3(ω) are fed to amix-Mx Calculation Logic40which provides a signal on a line46indicative of the speed of sound of the mixture amix(discussed more hereinafter). The amixsignal is provided to map (or equation) logic48, which converts amixto a percent composition of the fluid and provides a % Comp signal on a line50indicative thereof (as discussed hereinafter). Also, if the Mach number Mx is not negligible and is desired to be known, the calculation logic40may also provide a signal Mx on a line59indicative of the Mach number Mx (as discussed hereinafter).

More specifically, for planar one-dimensional acoustic waves in a homogenous mixture, it is known that the acoustic pressure field P(x,t) at a location x along a pipe, where the wavelength λ of the acoustic waves to be measured is long compared to the diameter d of the pipe12(i.e., λ/d>>1), may be expressed as a superposition of a right traveling wave and a left traveling wave, as follows:
P(x,t)=(Ae−ikrx+Be+iklx)eiωtEq. 1
where A,B are the frequency-based complex amplitudes of the right and left traveling waves, respectively, x is the pressure measurement location along a pipe, ω is frequency (in rad/sec, where ω=2πf), and kr,klare wave numbers for the right and left travelling waves, respectively, which are defined as:kr≡(ωamix)⁢11+Mx⁢⁢and⁢⁢kl≡(ωamix)⁢11-MxEq.⁢2
where amixis the speed of sound of the mixture in the pipe, ω is frequency (in rad/sec), and Mxis the axial Mach number of the flow of the mixture within the pipe, where:Mx≡Vmixamix⁢⁢where⁢⁢Vmix⁢⁢is⁢⁢the⁢⁢axialEq.⁢3
velocity of the mixture. For non-homogenous mixtures, the axial Mach number represents the average velocity of the mixture and the low frequency acoustic field description remains substantially unaltered.

The frequency domain representation P(x,ω) of the time-based acoustic pressure field P(x,t) within a pipe, is the coefficient of the eiωtterm of Eq. 1, as follows:
P(x,ω)=Ae−ikrx+Be+iklxEq. 4

Referring toFIG. 1, we have found that using Eq. 4 for P(x,ω) at three axially distributed pressure measurement locations x1,x2,x3along the pipe12leads to an equation for amixas a function of the ratio of frequency based pressure measurements, which allows the coefficients A,B to be eliminated. For optimal results, A and B are substantially constant over the measurement time and substantially no sound (or acoustic energy) is created or destroyed in the measurement section. The acoustic excitation enters the test section only through the ends of the test section51and, thus, the speed of sound within the test section51can be measured independent of the acoustic environment outside of the test section. In particular, the frequency domain pressure measurements P1(ω),P2(ω),P3(ω) at the three locations x1,x2,x3, respectively, along the pipe12using Eq. 1 for right and left traveling waves are as follows:
P1(ω)=P(x=x1,ω)=Ae−ikrx1+Be+iklx1Eq. 5
P2(ω)=P(x=x2,ω)=Ae−ikrx2+Be+iklx2Eq. 6
P3(ω)=P(x=x3,ω)=Ae−ikrx3+Be+iklx3Eq. 7
where, for a given frequency, A and B are arbitrary constants describing the acoustic field between the sensors14,16,18. Forming the ratio of P1(ω)/P2(ω) from Eqns. 6,7, and solving for B/A, gives the following expression:R≡BA=ⅇ-ⅈ⁢⁢kr⁢x1-[P1⁡(ω)P2⁡(ω)]⁢ⅇ-ⅈ⁢⁢kr⁢x2[P1⁡(ω)P2⁡(ω)]⁢ⅇⅈ⁢⁢kl⁢x2-ⅇⅈ⁢⁢kl⁢x1Eq.⁢8
where R is defined as the reflection coefficient.

Forming the ratio of P1(ω)/P3(ω) from Eqs. 5 and 7 and solving for zero gives:ⅇ-ⅈ⁢⁢kr⁢x1+R⁢eⅈ⁢⁢kl⁢x1ⅇ-ⅈ⁢⁢kr⁢x3+Reⅈ⁢⁢kl⁢x3-[P1⁡(ω)P3⁡(ω)]=0Eq.⁢9
where R=B/A is defined by Eq. 8 and kr and kl are related to amixas defined by Eq. 2. Eq. 9 may be solved numerically, for example, by defining an “error” or residual term as the magnitude of the left side of Eq.9, and iterating to minimize the error term.mag⁢[ⅇ-ⅈ⁢⁢kr⁢x1+Reⅈ⁢⁢kl⁢x1ⅇ-ⅈ⁢⁢kr⁢x3+Reiⅈkl⁢x3-[P1⁡(ω)P3⁡(ω)]]≡ErrorEq.⁢10

For many applications in the oil industry, the axial velocity of the flow in the pipe is small compared to the speed of sound in the mixture (i.e., the axial Mach number Mxis small compared to one). For example, the axial velocity of the oil Voilin a typical oil well is about 10 ft/sec and the speed of sound of oil aoilis about 4,000 ft/sec. Thus, the Mach number Mx of a pure oil mixture is 0.0025 (Voil/aoil=10/4,000), and Eq. 2 reduces to approximately:kr=kl=ωamixEq.⁢11
and the distinction between the wave numbers for the right and left traveling waves is eliminated. In that case (where Mx is negligible), since all of the variables in Eq. 10 are known except for amix, the value for amixcan be iteratively determined by evaluating the error term at a given frequency ω and varying amixuntil the error term goes to zero. The value of amixat which the magnitude of the error term equals zero (or is a minimum), corresponds to the correct value of the speed of sound of the mixture amix. As Eq. 10 is a function of frequency ω, the speed of sound amixat which the error goes to zero is the same for each frequency ω evaluated (discussed more hereinafter). However, in practice, there may be some variation over certain frequencies due to other effects, e.g., pipe modes, non-acoustical pressure perturbation, discretization errors, etc., which may be filtered, windowed, averaged, etc. if desired (discussed more hereinafter). Furthermore, since each frequency is an independent measurement of the same parameter, the multiple measurements may be weighted averaged or filtered to provide a single more robust measurement of the speed of sound.

One example of how the speed of sound of the mixture amixin the pipe12may be used is to determine the volume fraction of the mixture. In particular, the speed of sound of a mixture amixof two fluids (where a fluid is defined herein as a liquid or a gas) in a pipe is in general related to the volume fraction of the two fluids. This relationship may be determined experimentally or analytically. For example, the speed of sound of a mixture may be expressed as follows:amix=1+ρ1ρ2⁢h2h11a12+ρ1ρ2⁢h2h1⁢1a22Eq.⁢12
where a1,a2are the known speeds of sound, ρ1,ρ2are the known densities, and h1,h2are the volume fractions of the two respective fluids, amixis the speed of sound of the mixture, and the densities ρ1,ρ2of the two fluids are within about an order of magnitude (10:1) of each other. Other expressions relating the phase fraction to speed of sound may be used, being derived experimentally, analytically, or computationally.

Referring toFIG. 2, where the fluid is an oil/water mixture, a curve10shows the speed of sound of the mixture amixplotted as a function of water volume fraction using Eq. 12. For this illustrative example, the values used for density (ρ) and speed of sound (a) of oil and water are as follows:
Density (ρ): ρwater=1,000 kg/m3; ρoil=700 kg/m3
Speed of sound (a): awater=5,000 ft/sec; aoil=4,000 ft/sec.
The subscripts 1,2 of Eq. 12 assigned to the parameters for each fluid is arbitrary provided the notation used is consistent. Thus, if the speed of sound of the mixture amixis measured, the oil/water fraction may be determined.

Referring toFIG. 3, to illustrate the concept by example, a transmission matrix model for the acoustics of an example pipe having 9 sections (or elements or segments) 1–9, an acoustic source64, a radiation (or transmission) impedance ζrad(ζrad=P/ρmixamixμmix) where μmixis an acoustic perturbation; Mx=0, and where the pressures P1,P2,P3are measured across test sections 5–6 and 6–7. For this example, each element is 1 meter long.

Depending on the application, an explicit acoustic noise source may or may not be required, as the background acoustic noises within the pipe may provide sufficient excitation to enable a speed of sound measurement from existing ambient acoustic pressures. In an oil or gas well application, if the background acoustic noises are not sufficient, an acoustic noise source (not shown) may be placed at the surface of the well or within the well, provided the source is acoustically coupled to the test section51over which the speed of sound is measured.

Referring toFIG. 4, illustrations (a)–(c), an example of the axial properties of the mixture in the segments 1–9 of the pipe12is shown. The volume fraction of water h, the speed of sound of the mixture amix, and the density of the mixture ρmixvary over the length of the pipe12and the test segments 5,6 (from 4–6 meters) between the pressure measurements P1-P3have constant properties. In particular, the values for ρmix, amix, hwaterfor sections 1–9, respectively, are shown graphically inFIG. 4and are as follows:
hwater=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9;
ρmix=730, 760, 790, 820, 850, 850, 910, 940, 970 (kg/m3);
amix=4053, 4111, 4177, 4251, 4334, 4334, 4539, 4667, 4818 (ft/sec);

Referring to FIGS.5,6, the magnitude and phase of the ratio of the frequency based pressure signals P1(ω)/P2(ω) and P1(ω)/P3(ω) is shown for the model ofFIG. 3with the properties ofFIG. 4with 50% water in the test section and a radiation impedance of ζrad=1.0 corresponding to an infinitely long pipe with constant properties of ρmixand amixfor section 9 and beyond.

Referring toFIG. 7, the error term of Eq. 10 using the frequency responses of FIGS.5,6, is a family of curves, one curve for each frequency ω, where the value of the error is evaluated for values of amixvaried from awater(5,000 ft/sec) to aoil(4,000 ft/sec) at each frequency and the frequency is varied from 5 to 200 Hz in 5 Hz increments. Other frequencies may be used if desired. The speed of sound amixwhere the error goes to zero (or is minimized) is the same for each frequency ω evaluated. In this case, the error is minimized at a point70when amixis 4335 ft/sec. FromFIG. 2, for an oil/water mixture, an amixof 4335 ft/sec corresponds to a 50% water volume ratio in the test section that matches the water fraction of the model. Also, the sensitivity of a change in amixto a change in error varies based on the evaluation frequency. Thus, the performance may be optimized by evaluating amixat specific low sensitivity frequencies, such frequencies to be determined depending on the specific application and configuration.

Referring to FIGS.8,9, for an radiation impedance ζrad=0.5, the magnitude and phase of the frequency responses (i.e., the ratio of frequency based pressure signals) P1(ω)/P2(ω) and P1(ω)/P3(ω) is shown for the model ofFIG. 3with constant properties across all sections 1–9 of 50% water fraction (h=0.5), density of mixture ρmix=850 kg/mr and speed of sound of mixture amix=4334 ft/sec.

Referring toFIG. 12, for a 50% water fraction, the magnitude of the error term of Eq. 10 using the frequency responses of FIGS.8,9, is a family of curves, one curve for each frequency ω, where the value of amixis varied from awater(5,000 ft/sec) to aoil(4,000 ft/sec) at each frequency and is shown at four frequencies 50, 100, 150, 200 Hz. As discussed hereinbefore, the speed of sound amixwhere the error goes to zero (or is minimized) is the same for each frequency ω evaluated. In this case, the error is minimized at a point72where amix=4334 ft/sec, which matches the value of amixshown inFIG. 7for the same water fraction and different ζrad. FromFIG. 2(or Eq. 2), for an oil/water mixture, an amixof 4334 ft/sec corresponds to a 50% water volume ratio in the test section which corresponds to the water fraction of the model. This shows that the invention will accurately determine amixindependent of the acoustic properties of the mixture outside the test sections and/or the termination impedances.

Referring to FIGS.10,11, the magnitude and phase of the frequency responses (i.e., the ratio of the frequency based pressure signals) P1(ω)/P2(ω) and P1(ω)/P3(ω) is shown for the model ofFIG. 3with constant properties across all sections 1–9 of 5% water fraction (h=0.05), density of mixture ρmix=715 kg/m3, and speed of sound of mixture amix=4026 ft/sec, and a radiation impedance ζrad=0.5.

Referring toFIG. 12, for a 5% water fraction, the magnitude of the error term of Eq. 10 using the frequency responses of FIGS.10,11, is a family of dashed curves, one curve for each frequency ω, where the value of amixis varied from awater(5,000 ft/sec) to aoil(4,000 ft/sec) at each frequency and is shown at four frequencies 50, 100, 150, 200 Hz. As discussed hereinbefore, the speed of sound amixwhere the error goes to zero (or is minimized) is the same for each frequency ω evaluated. In this case, the error is minimized at a point74when amix=4026 ft/sec. FromFIG. 1(or Eq. 1), for an oil/water mixture, an amixof 4026 ft/sec corresponds to a 5% water volume ratio in the test section which corresponds to the water fraction of the model and, thus, verifies the results of the model.

Referring toFIG. 12, for both 5% and 50% water fraction, the sensitivity of a change in amixto a change in error varies based on the evaluation frequency. In particular, for this example, of the four frequencies shown, the error approaches zero with the largest slope (ΔError/Δamix) for the 200 Hz curve, thereby making it easier to detect the value where the error goes to zero, and thus the value of amix. Thus, 200 Hz would likely be a robust frequency to use to determine the speed of sound in this example.

If the pressure sensors are equally spaced (i.e., x1−x2=x3−x2=Δx; or Δx1=Δx2=Δx) and the axial Mach number Mx is small compared to one (and thus, kr=kl=k), Eq. 10 may be solved for k (and thus amix) in a closed-form solution as a function of the pressure frequency responses (or frequency based signal ratios) as follows:k=ωamix=⁢[1Δ⁢⁢x]⁢i⁢⁢log[P12+P13⁢P12+(P122+2⁢P13⁢P122+P132⁢P122-4⁢P132)1/22⁢P13]Eq.⁢13
Solving for amix, gives:amix=ω[1Δ⁢⁢x]⁢⁢i⁢⁢log[P12+P13⁢P12+(P122+2⁢P13⁢P122+P132⁢P122-4⁢P132)1/22⁢P13]Eq.⁢14
where P12=P1(ω)/P2(ω), P13=P1(ω)/P3(ω), i is the square root of −1Log[ ] function is an imaginary number, yielding a real number for the speed of sound amix.

The analytical solution to the Eq. 10 shown in Eqs. 13 and 14 is valid primarily for the frequencies for which the length of the test section51along the pipe12(i.e., x3−x1 or 2Δx for equally spaced sensors) is shorter than the wavelength x of the acoustic waves to be measured. This restriction is due to multiple possible solutions to the Eq. 10. Alternative solutions to Eq. 10 for other frequency ranges may be derived using a variety of known techniques.

An alternative closed form solution for amix(in a trigonometric form) from the three pressure Eqs. 5–7, where the pressure sensors are equally spaced and Mx is negligible (i.e, kl=kr), is as follows. Forming the ratio [P1(ω)+P3(ω)]/P2(ω) from Eqs. 5–7, gives the following expression:P1⁡(ω)+P3⁡(ω)P2⁡(ω)=A⁢⁢ⅇ-ⅈ⁢⁢kx1+B⁢⁢ⅇ+ⅈ⁢⁢kx1+A⁢⁢ⅇ-ⅈ⁢⁢kx3+B⁢⁢ⅇ+ⅈ⁢⁢ikx3A⁢⁢ⅇ-ⅈ⁢⁢k⁢⁢x2+B⁢⁢ⅇ+ⅈ⁢⁢k⁢⁢x2Eq.⁢15

Dividing the numerator and denominator by A, gives:P1⁡(ω)+P3⁡(ω)P2⁡(ω)=1+R+⁢ⅇ-2⁢ⅈ⁢⁢k⁢⁢Δ⁢⁢x+R⁢⁢e+2⁢ⅈ⁢⁢k⁢⁢Δ⁢⁢x⁢ⅇ-ⅈ⁢⁢k⁢⁢Δ⁢⁢x+Re+ⅈ⁢⁢k⁢⁢Δ⁢⁢xEq.⁢17
where R=B/A is defined by Eq. 8 with x1=0, x2=Δx, which gives:R≡BA=1-[P1⁡(ω)P2⁡(ω)]⁢ⅇ-ⅈ⁢⁢k⁢⁢Δ⁢⁢x[P1⁡(ω)P2⁡(ω)]⁢ⅇⅈ⁢⁢k⁢⁢Δ⁢⁢x-1Eq.⁢18
Plugging R into Eq. 17, gives:P1⁡(ω)+P3⁡(ω)P2⁡(ω)=1+ⅇ-2⁢ⅈ⁢⁢k⁢⁢Δ⁢⁢x+[1-[P1⁡(ω)P2⁡(ω)]⁢ⅇ-ⅈ⁢⁢k⁢⁢Δ⁢⁢x[P1⁡(ω)P2⁡(ω)]⁢ⅇⅈ⁢⁢k⁢⁢Δ⁢⁢x-1]+(1+ⅇ+2⁢ⅈ⁢⁢k⁢⁢Δ⁢⁢x)ⅇ-ⅈ⁢⁢k⁢⁢Δ⁢⁢x+[1-[P1⁡(ω)P2⁡(ω)]⁢ⅇ-ⅈ⁢⁢k⁢⁢Δ⁢⁢x[P1⁡(ω)P2⁡(ω)]⁢ⅇⅈ⁢⁢k⁢⁢Δ⁢⁢x-1]⁢ⅇ+ⅈ⁢⁢k⁢⁢Δ⁢⁢xEq.⁢19
Simplifying Eq. 19, gives:P1⁡(ω)+P3⁡(ω)P2⁡(ω)=(P1P2⁢ⅇ-2⁢ⅈ⁢⁢k⁢⁢Δ⁢⁢x-1)⁢(1+ⅇ-2⁢ⅈ⁢⁢k⁢⁢Δ⁢⁢x)+(1-P1P2⁢ⅇ-ⅈ⁢⁢kx)⁢(1+ⅇ+2⁢ⅈ⁢⁢k⁢⁢Δ⁢⁢x)(P1P2⁢ⅇ+ⅈ⁢⁢k⁢⁢Δ⁢⁢x-1)⁢(ⅇ-ⅈ⁢⁢k⁢⁢Δ⁢⁢x)+(1-P1P2⁢ⅇ-ⅈ⁢⁢kx)⁢(ⅇ+ⅈ⁢⁢k⁢⁢Δ⁢⁢x)Eq.⁢20
Distributing terms and simplifying, gives:P1⁡(ω)+P3⁡(ω)P2⁡(ω)=-ⅇ-2⁢ⅈ⁢⁢k⁢⁢Δ⁢⁢x+ⅇ+2⁢ⅈ⁢⁢k⁢⁢Δ⁢⁢x-ⅇ-ⅈ⁢⁢k⁢⁢Δ⁢⁢x+ⅇ+ⅈ⁢⁢k⁢⁢Δ⁢⁢xEq.⁢21
Using the relation between exponents and the sine function, gives:P1⁡(ω)+P3⁡(ω)P2⁡(ω)=2⁢i⁢⁢sin⁡(2⁢k⁢⁢Δ⁢⁢x)2⁢i⁢⁢sin⁡(kx)=2⁢⁢sin⁡(kx)⁢cos⁡(kx)sin⁡(kx)Eq.⁢22
Simplifying and substituting k=ω/amix, gives:P1⁡(ω)+P3⁡(ω)P2⁡(ω)=2⁢⁢cos⁡(k⁢⁢Δ⁢⁢x)=2⁢⁢cos⁡(ω⁢⁢Δ⁢⁢xamix)Eq.⁢23

Eq. 23 is particularly useful due to its simple geometric form, from which amixcan be easily interpreted. In particular, amixcan be determined directly by inspection from a digital signal analyzer (or other similar instrument) set up to provide a display indicative of the left side of Eq. 23, which will be a cosine curve from which amixmay be readily obtained. For example, at the zero crossing of the cosine wave, Eq. 23 will be equal to zero and amixwill be equal to 2ωΔX/π. Alternatively, Eq. 23 may be used to determine amixusing an iterative approach where a measured function is calculated from the left side of Eq. 23 (using the measured pressures) and compared to a cosine curve of the right side of Eq. 23 where amixis varied until it substantially matches the measured function. Various other curve fitting, parameter identification, and/or minimum error or solution techniques may be used to determine the value of amixthat provides the best fit to satisfy Eq. 23.

Referring toFIG. 41, a graph of speed of sound (amix) versus water cut is shown where amixis calculated using Eq. 23 as described hereinbefore.FIG. 41is for a Schedule 160 steel pipe having a 2 inch ID, ΔX=2 ft even spacing between three axial sensing locations, each sensor being a piezo-electric ac pressure sensor, there being four evenly circumferentially spaced sensors at each axial sensing location. The line452shows the theoretical value for water cut based on Eq. 12 andFIG. 2discussed hereinbefore, and the circles are the calculated values for amix.

Alternatively, Eq. 9 may be written in trigonometric form for arbitrary spacing between the pressure sensors and where Mx is negligible (kl=kr), as follows:sin⁡(ωamix⁢(x3-x1))-P32⁢sin⁡(ωamix⁢(x2-x1))-P12⁢sin⁡(ωamix⁢(x3-x2))=0Eq.⁢25
where P32=P3(ω)/P2(ω) and P12=P1(ω)/P2(ω).

Referring to FIGS.13,14, if Mach number Mx is not negligible and/or is desired to be calculated, the value of Mx and amixwhere the error term of Eq. 10 is zero can be uniquely determined from Eq. 10 for a given water fraction. In particular, for a given % water fraction, there is a unique value indicated by points90,92for 5% and 50% water cut, respectively. Known software search algorithms may be used to vary amixand Mx over predetermined ranges to find the value of Mx and amixwhere the error=0 (discussed more hereinafter).

Referring toFIG. 15, the calculation logic40begins at a step100where P12is calculated as the ratio of P1(ω)/P2(ω), and a step102where P13is calculated as the ratio of P1(ω)/P3(ω). Next a step103determines whether the Mach number Mx of the mixture is negligible (or whether it is desirable to calculate Mx, i.e. for cases where Mx is not negligible, as set forth herein below with reference to “A” andFIG. 16). If Mx is negligible, a step104determines if the sensors14,16,18are equally spaced (i.e., x1−x2=x2−x3=Δx). If equally spaced sensors, steps106set initial values for ω=ω1 (e.g., 100 Hz) and a counter n=1. Next, a step108calculates amix(n) from the closed form solution of Eq. 14. Then, a step110checks whether the logic40has calculated amixat a predetermined number of frequencies, e.g., 10. If n is not greater than 10, steps112,114, increments the counter n by one and increases the frequency ω by a predetermined amount (e.g., 10 Hz) and the step108is repeated. If the logic40has calculated amixat 10 frequencies, the result of the step116would be yes and the logic40goes to a step116which determines an average value for amixusing the values of amix(n) over the 10 frequencies, and the logic40exits.

If the sensors are not equally spaced, a series of steps150are performed starting with steps120set x1,x2,x3 to the current pressure sensor spacing, and set initial values for ω=ω1 (e.g., 100 Hz) and the counter n=1. Next, a step122sets amix=amix−min(e.g., aoil=4000 ft/sec) and a step124calculates the error term from Eq. 10. Then, a step126checks whether error=0. If the error does not equal zero, amixis incremented by a predetermined amount in step128and the logic40goes back to step124.

If the error=0 (or a minimum) in step126, a step130sets amix(n)=amix. Next, a step132checks whether n is greater than or equal to 10. If not, a step134increments n by one and a step136increases the frequency ω by a predetermined amount (e.g., 10 Hz) and continues at step122as shown inFIG. 15. If n is greater than or equal to 10, a step138calculates an average value for amixover the 10 frequencies, and the logic40ends.

If the result of step210is no, a step212increases amixby a predetermined amount (e.g., 1 ft/sec) and the logic goes back to step206. If the result of step210is yes, a step214increases Mx by a predetermined amount (e.g., 1) and the logic goes back to step204.

When step208indicates error=0 (or a minimum), a step216sets amix(n)=amixand Mx(n)=Mx, and a step218checks whether the values of amixand Mx have been calculated at 10 different frequencies. If not, a step220increments the counter n by one and a step222increases the value of the frequency o) by a predetermined amount (e.g., 10 Hz), and the logic goes back to step202. If the values of amixand Mx have been calculated at 10 different frequencies (i.e., n is equal to 10), a step224calculates a average values for amix(n) and Mx(n) at the 10 different frequencies to calculate amixand Mx, and the logic exists. The value for a mix above is similar to that shown in FIGS.13,14, discussed hereinbefore, where the final value of amixare the points90,92where the error equals zero.

Instead of calculating an average value for amixin steps116,138,224, amixmay be calculated by filtering or windowing amix(n), from predetermined frequencies. The number of frequencies and the frequencies evaluated may be any desired number and values. Also, instead of calculating amixand/or Mx at more than one frequency, it may be calculated at only one frequency. Further, the logic shown in FIGS.15,16is one of many possible algorithms to calculate amixusing the teachings herein.

Referring toFIGS. 1 and 18, the compliance (or flexibility) of the pipe12(or conduit) in the sensing region may influence the accuracy or interpretation of the measured speed of sound amixof the mixture in two primary ways.

Regarding the first way, referring toFIG. 18, flexing of the pipe12in the sensing region reduces the measured speed of sound amixfrom the sound in an unbounded domain. The sound speed in an unbounded domain (infinite media) is a property that is closely linked with the fluid properties. In particular, the influence of pipe wall thickness (or compliance of the pipe) on measured speed of sound due reduction in the speed of sound for a pipe having a 2 inch nominal diameter and having 100% water (ρw=1,000 kg/m3; aw=5,000 ft/sec) inside the pipe and a vacuum (or air) outside the pipe diameter, is shown. The speed of sound of water in an infinitely rigid pipe (i.e., infinite modulus) is indicated by a flat curve350, and the speed of sound of water in a steel pipe is indicated by a curve352. A point354on the curve352indicates the value of the speed of sound of about 4768 ft/sec for a Schedule80steel pipe. Accordingly, the thicker the pipe wall, the closer the speed of sound approaches the value of 5,000 ft/sec for an infinitely rigid pipe.

The errors (or boundary effects) shown inFIG. 18introduced into the measurements by a non-rigid (or compliant) pipe12can be calibrated and corrected for to accurately determine the speed of sound in the fluid in an unbounded media. Thus, in this case, while the system (pipe) does modify the propagation velocity, such velocity can be mapped to the propagation velocity in an infinite media in a predictable fashion.

In particular, for fluids contained in a compliant pipe, the propagation velocity of compression waves is influenced by the structural properties of the pipe. For a fluid contained in the pipe12surrounded with a fluid of negligible acoustic impedance (ρa), the propagation velocity is related to the infinite fluid domain speed of sound and the structural properties via the following relation:1ρmix⁢ameasured2=1ρmix⁢amix2+σ⁢⁢where⁢⁢σ≡2⁢REtEq.⁢26

where R=the pipe radius, t is the pipe wall thickness, ρmixis the density of the mixture (or fluid), amixis the actual speed of sound of the mixture, ameasuredis the measured speed of sound of the mixture contained in the pipe12, and E is the Young's modulus for the pipe material. Eq. 26 holds primarily for frequencies where the wavelength of the acoustics is long (e.g., greater than about 2 to 1) compared to the diameter of the pipe and for frequencies which are low compared to the natural frequency of the breathing mode of the pipe. Eq. 26 also applies primarily to wavelengths which are long enough such that hoop stiffness dominates the radial deflections of the pipe.

ForFIG. 18, the curve352(for 100% water) would be one of a family of curves for various different oil/water mixtures. For Eq. 26, the terms may be defined in terms of the density of each constituent, and the volumetric phase fraction as follows:1ρmix⁢amix2=∑i=1N⁢⁢ϕiρi⁢ai2⁢⁢where:ρmix=∑i=1N⁢⁢ϕi⁢ρi⁢⁢and⁢⁢∑i=1N⁢⁢ϕi=1

where ρiis the density of the ithconstituent of a multi-component mixture, aiis the sound speed of the ithconstituent of the mixture, φiis the volumetric phase fraction of the ithconstituent of the mixture, and N is the number of components of the mixture. Knowing the pipe properties, the densities and the sound speed (in an infinite domain) of the individual constituents, and the measured sound speed of the mixture, Eq. 26 can be solved for amix. Thus, amixcan be determined for a compliant pipe. The calibration of the pipe can be derived from other equations or from a variety of other means, such as analytical, experimental, or computational.

For certain types of pressure sensors, e.g., pipe strain sensors, accelerometers, velocity sensors or displacement sensors, discussed hereinafter, it may be desirable for the pipe12to exhibit a certain amount of pipe compliance.

Alternatively, to minimize these error effects (and the need for the corresponding calibration) caused by pipe compliance, the axial test section51of the pipe12along where the sensors14,16,18are located may be made as rigid as possible. To achieve the desired rigidity, the thickness of the wall53of the test section51may be made to have a predetermined thickness, or the test section51may be made of a very rigid material, e.g., steel, titanium, Kevlar®, ceramic, or other material with a high modulus.

Regarding the second way, if the pipe12is compliant and acoustically coupled to fluids and materials outside the pipe12in the sensing region, such as the annulus fluid, casing, rock formations, etc., the acoustic properties of these fluids and materials outside the pipe12diameter may influence the measured speed of sound. Because the acoustic properties of such fluids and materials are variable and unknown, their affect on measured speed of sound cannot be robustly corrected by calibration (nor mapped to the propagation velocity in an infinite media in a predictable fashion).

Referring toFIG. 20, to alleviate this effect, an outer isolation sleeve410(or sheath, shell, housing, or cover) which is attached to the outer surface of pipe12over where the pressure sensors14,16,18are located on the pipe12. The sleeve410forms a closed chamber412between the pipe12and the sleeve410. We have found that when the chamber412is filled with a gas such as air, the acoustic energy in the pipe is not acoustically coupled to fluids and materials outside the pipe12in the sensing region. As such, for a compliant pipe the speed of sound can be calibrated to the actual speed of sound in the fluid in the pipe12as discussed hereinbefore. The sleeve410is similar to that U.S. application Ser. No. 09/344,070, entitled “Measurement of Propagating Acoustic Waves in Compliant Pipes”, filed Jun. 25, 1999, which is incorporated herein by reference.

Referring toFIG. 19, instead of single point pressure sensors14,16,18, at the axial locations x1,x2,x3along the pipe12, two or more pressure sensors, e.g., four sensors400,402,404,406, may be used around the circumference of the pipe12at each of the axial locations x1,x2,x3. The signals from the pressure sensors,400,402,404,406around the circumference at a given axial location may be averaged to provide a cross-sectional (or circumference) averaged unsteady acoustic pressure measurement. Other numbers of acoustic pressure sensors and annular spacing may be used. Averaging multiple annular pressure sensors reduces noises from disturbances and pipe vibrations and other sources of noise not related to the one-dimensional acoustic pressure waves in the pipe12, thereby creating a spatial array of pressure sensors to help characterize the one-dimensional sound field within the pipe12.

The pressure sensors14,16,18described herein may be any type of pressure sensor, capable of measuring the unsteady (or ac or dynamic) pressures within a pipe, such as piezoelectric, optical, capacitive, resistive (e.g., Wheatstone bridge), accelerometers (or geophones), velocity measuring devices, displacement measuring devices, etc. If optical pressure sensors are used, the sensors14,16,18may be Bragg grating based pressure sensors, such as that described in U.S. patent application Ser. No. 08/925,598, entitled “High Sensitivity Fiber Optic Pressure Sensor For Use In Harsh Environments”, filed Sep. 8, 1997, now U.S. Pat. No. 6,016,702. Alternatively, the sensors14,16,18may be electrical or optical strain gages attached to or embedded in the outer or inner wall of the pipe which measure pipe wall strain, including microphones, hydrophones, or any other sensor capable of measuring the unsteady pressures within the pipe12. In an embodiment of the present invention that utilizes fiber optics as the pressure sensors14,16,18, they may be connected individually or may be multiplexed along one or more optical fibers using wavelength division multiplexing (WDM), time division multiplexing (TDM), or any other optical multiplexing techniques (discussed more hereinafter).

Such harsh environments are typically found in the industrial process area and include sensor exposure to acids, caustics, nuclear energy, electromagnetic interference and exposure to explosive vapors among other hazards. Because the sensor is glass based it is chemically impervious to most industrial process related chemicals. Further because the sensor of the present invention uses light for signal transmission it does not require any electrical power and as such is not influenced by electromagnetic fields and cannot create arcing or explosions when used in the presence of flammable vapors. In addition the sensor of the present invention has no moving parts, such as a bellows, which makes the device more reliable and less susceptible to system hysteresis found in other mechanical pressure sensors that utilize diaphragms bellows or other displacement type devices.

Referring toFIG. 21, if a strain gage is used as one or more of the pressure sensors14,16,18, it may measure the unsteady (or dynamic or ac) pressure variations Pin inside the pipe12by measuring the elastic expansion and contraction, as represented by arrows350, of the diameter (and thus the circumference as represented by arrows351) of the pipe12. In general, the strain gages would measure the pipe wall deflection in any direction in response to unsteady pressure signals inside the pipe12. The elastic expansion and contraction of pipe12is measured at the location of the strain gage as the internal pressure Pinchanges, and thus measures the local strain (axial strain, hoop strain or off axis strain), caused by deflections in the directions indicated by arrows351, on the pipe12. The amount of change in the circumference is variously determined by the hoop strength of the pipe12, the internal pressure Pinthe external pressure Poutoutside the pipe12, the thickness Twof the pipe wall352, and the rigidity or modulus of the pipe material. Thus, the thickness of the pipe wall352and the pipe material in the sensor sections51(FIG. 1) may be set based on the desired sensitivity of sensors14,16,18, and other factors and may be different from the wall thickness or material of the pipe12outside the sensing region51.

Still with reference toFIG. 21andFIG. 1, if an accelerometer is used as one or more of the pressure sensors14,16,18, it may measure the unsteady (or dynamic or ac) pressure variations Pininside the pipe12by measuring the acceleration of the surface of pipe12in a radial direction, as represented by arrows350. The acceleration of the surface of pipe12is measured at the location of the accelerometer as the internal pressure Pinchanges and thus measures the local elastic dynamic radial response of the wall352of the pipe. The magnitude of the acceleration is variously determined by the hoop strength of the pipe12, the internal pressure Pin, the external pressure Poutoutside the pipe12, the thickness Twof the pipe wall352, and the rigidity or modulus of the pipe material. Thus, the thickness of the pipe wall352and the pipe material in the sensing section51(FIG. 1) may be set based on the desired sensitivity of sensors14,16,18and other factors and may be different from the wall thickness or material of the pipe12outside the sensing region14. Alternatively, the pressure sensors14,16,18may comprise a radial velocity or displacement measurement device capable of measuring the radial displacement characteristics of wall352of pipe12in response to pressure changes caused by unsteady pressure signals in the pipe12. The accelerometer, velocity or displacement sensors may be similar to those described in commonly-owned copending U.S. patent application Ser. No. 09/344,069, entitled “Displacement Based Pressure Sensor Measuring Unsteady Pressure in a Pipe”, filed Jun. 25, 1999 and U.S. patent application Ser. No. 09/344,093 entitled “Non-Intrusive Fiber Optic Pressure Sensor for Measuring Unsteady Pressures within a Pipe”, filed Jun. 25, 1999 and incorporated herein by reference.

Referring to FIGS.22,23,24, if an optical strain gage is used, the ac pressure sensors14,16,18may be configured using an optical fiber300that is coiled or wrapped around and attached to the pipe12at each of the pressure sensor locations as indicated by the coils or wraps302,304,306for the pressures P1,P2,P3, respectively. The fiber wraps302,304,306are wrapped around the pipe12such that the length of each of the fiber wraps302,304,306changes with changes in the pipe hoop strain in response to unsteady pressure variations within the pipe12and thus internal pipe pressure is measured at the respective axial location. Such fiber length changes are measured using known optical measurement techniques as discussed hereinafter. Each of the wraps measure substantially the circumferentially averaged pressure within the pipe12at a corresponding axial location on the pipe12. Also, the wraps provide axially averaged pressure over the axial length of a given wrap. While the structure of the pipe12provides some spatial filtering of short wavelength disturbances, we have found that the basic principle of operation of the invention remains substantially the same as that for the point sensors described hereinbefore.

Referring toFIG. 22, for embodiments of the present invention where the wraps302,304,306are connected in series, pairs of Bragg gratings (310,312),(314,316), (318,320) may be located along the fiber300at opposite ends of each of the wraps302,304,306, respectively. The grating pairs are used to multiplex the pressure signals P1,P2,P3to identify the individual wraps from optical return signals. The first pair of gratings310,312around the wrap302may have a common reflection wavelength λ1, and the second pair of gratings314,316around the wrap304may have a common reflection wavelength λ2, but different from that of the first pair of gratings310,312. Similarly, the third pair of gratings318,320around the wrap306have a common reflection wavelength λ3, which is different from λ1,λ2.

Referring toFIG. 23, instead of having a different pair of reflection wavelengths associated with each wrap, a series of Bragg gratings360,362,364,366with only one grating between each of the wraps302,304,306may be used each having a common reflection wavelength λ1.

Referring toFIGS. 22 and 23the wraps302,304,306with the gratings310,312,314,316,318,320(FIG. 22) or with the gratings360,362,364,366(FIG. 23) may be configured in numerous known ways to precisely measure the fiber length or change in fiber length, such as an interferometric, Fabry Perot, time-of-flight, or other known arrangements. One example of time-of-flight (or Time-Division-Multiplexing; TDM) would be where an optical pulse having a wavelength is launched down the fiber300and a series of optical pulses are reflected back along the fiber300. The length of each wrap can then be determined by the time delay between each return pulse.

While the gratings310,312,314,316,318,320are shown oriented axially with respect to pipe12, in FIGS.22,23, they may be oriented along the pipe12axially, circumferentially, or in any other orientations. Depending on the orientation, the grating may measure deformations in the pipe wall352with varying levels of sensitivity. If the grating reflection wavelength varies with internal pressure changes, such variation may be desired for certain configurations (e.g., fiber lasers) or may be compensated for in the optical instrumentation for other configurations, e.g., by allowing for a predetermined range in reflection wavelength shift for each pair of gratings. Alternatively, instead of each of the wraps being connected in series, they may be connected in parallel, e.g., by using optical couplers (not shown) prior to each of the wraps, each coupled to the common fiber300.

Referring toFIG. 24, alternatively, the sensors14,16,18may also be formed as a purely interferometric sensor by wrapping the pipe12with the wraps302,304,306without using Bragg gratings where separate fibers330,332,334may be fed to the separate wraps302,304,306, respectively. In this particular embodiment, known interferometric techniques may be used to determine the length or change in length of the fiber10around the pipe12due to pressure changes, such as Mach Zehnder or Michaelson Interferometric techniques, such as those set forth in U.S. patent application Ser. No. 09/726,059, titled “Method and Apparatus for Interrogating Fiber Optic Sensors” filed Nov. 29, 2000. The inteferometric wraps may be multiplexed such as is described in Dandridge, et al, “Fiber Optic Sensors for Navy Applications”, IEEE, February 1991, or Dandridge, et al, “Multiplexed Intereferometric Fiber Sensor Arrays”, SPIE, Vol. 1586, 1991, pp 176–183. Other techniques to determine the change in fiber length may be used. Also, reference optical coils (not shown) may be used for certain interferometric approaches and may also be located on or around the pipe12but may be designed to be insensitive to pressure variations.

Referring toFIGS. 25 and 26, instead of the wraps302,304,306being optical fiber coils wrapped completely around the pipe12, the wraps302,304,306may have alternative geometries, such as a “radiator coil” geometry (FIG. 25) or a “race-track” geometry (FIG. 26), which are shown in a side view as if the pipe12is cut axially and laid flat. In this particular embodiment, the wraps302-206are not necessarily wrapped 360 degrees around the pipe, but may be disposed over a predetermined portion of the circumference of the pipe12, and have a length long enough to optically detect the changes to the pipe circumference. Other geometries for the wraps may be used if desired. Also, for any geometry of the wraps described herein, more than one layer of fiber may be used depending on the overall fiber length desired. The desired axial length of any particular wrap is set depending on the characteristics of the ac pressure desired to be measured, for example the axial length of the pressure disturbance caused by a vortex to be measured.

Referring toFIGS. 27 and 28, embodiments of the present invention include configurations wherein instead of using the wraps302,304,306, the fiber300may have shorter sections that are disposed around at least a portion of the circumference of the pipe12that can optically detect changes to the pipe circumference. It is further within the scope of the present invention that sensors may comprise an optical fiber300disposed in a helical pattern (not shown) about pipe12. As discussed herein above, the orientation of the strain sensing element will vary the sensitivity to deflections in pipe wall352deformations caused by unsteady pressure signals in the pipe12.

Referring toFIG. 27, in particular, the pairs of Bragg gratings (310,312), (314,316), (318,320) are located along the fiber300with sections380,382,384of the fiber300between each of the grating pairs, respectively. In that case, known Fabry Perot, interferometric, time-of-flight or fiber laser sensing techniques may be used to measure the strain in the pipe.

Referring toFIG. 28, alternatively, individual gratings370,372,374may be disposed on the pipe and used to sense the unsteady variations in strain in the pipe12(and thus the unsteady pressure within the pipe) at the sensing locations. When a single grating is used per sensor, the grating reflection wavelength shift will be indicative of changes in pipe diameter and thus pressure.

Any other technique or configuration for an optical strain gage may be used. The type of optical strain gage technique and optical signal analysis approach is not critical to the present invention, and the scope of the invention is not intended to be limited to any particular technique or approach.

For any of the embodiments described herein, the pressure sensors, including electrical strain gages, optical fibers and/or gratings among others as described herein, may be attached to the pipe by adhesive, glue, epoxy, tape or other suitable attachment means to ensure suitable contact between the sensor and the pipe12. The sensors may alternatively be removable or permanently attached via known mechanical techniques such as mechanical fastener, spring loaded, clamped, clam shell arrangement, strapping or other equivalents. Alternatively, the strain gages, including optical fibers and/or gratings, may be embedded in a composite pipe. If desired, for certain applications, the gratings may be detached from (or strain or acoustically isolated from) the pipe12if desired.

Referring to FIGS.29,30, it is also within the scope of the present invention that any other strain sensing technique may be used to measure the variations in strain in the pipe, such as highly sensitive piezoelectric, electronic or electric, strain gages attached to or embedded in the pipe12. Referring toFIG. 29, different known configurations of highly sensitive piezoelectric strain gages are shown and may comprise foil type gages. Referring toFIG. 30, an embodiment of the present invention is shown wherein pressure sensors14,16,18comprise strain gages340. In this particular embodiment strain gages340are disposed about a predetermined portion of the circumference of pipe12. The axial placement of and separation distance ΔX1, ΔX2between the pressure sensors14,16,18are determined as described herein above.

Referring toFIGS. 31–33, instead of measuring the unsteady pressures P1–P3on the exterior of the pipe12, the invention will also work when the unsteady pressures are measured inside the pipe12. In particular, the pressure sensors14,16,18that measure the pressures P1,P2,P3may be located anywhere within the pipe12and any technique may be used to measure the unsteady pressures inside the pipe12.

Referring toFIGS. 34–36, the invention may also measure the speed of sound of a mixture flowing outside a pipe or tube425. In that case, the tube425may be placed within the pipe12and the pressures P1–P3measured at the outside of the tube425. Any technique may be used to measure the unsteady pressures P1–P3outside the tube425. Referring toFIG. 34, for example, the tube425may have the optical wraps302,304,306wrapped around the tube425at each sensing location. Alternatively, any of the strain measurement or displacement, velocity or accelerometer sensors or techniques described herein may be used on the tube425. Referring toFIG. 35, alternatively, the pressures P1-P3may be measured using direct pressure measurement sensors or techniques described herein. Any other type of unsteady pressure sensors14,16,18may be used to measure the unsteady pressures within the pipe12.

Alternatively, referring toFIG. 36, hydrophones430,432,434may be used to sense the unsteady pressures within the pipe12. In that case, the hydrophones430,432,434may be located in the tube425for ease of deployment or for other reasons. The hydrophones430,432,434may be fiber optic, electronic, piezoelectric or other types of hydrophones. If fiber optic hydrophones are used, the hydrophones430,432,434may be connected in series or parallel along the common optical fiber300.

The tube425may be made of any material that allows the unsteady pressure sensors to measure the pressures P1-P3and may be hollow, solid, or gas filled or fluid filled. One example of a dynamic pressure sensor is described in co-pending commonly-owned U.S. patent application Ser. No. 09/326,097 entitled “Mandrel Wound Fiber Optic Pressure Sensor”, filed Jun. 4, 1999. Also, the end422of the tube425is closed and thus the flow path would be around the end422as indicated by lines424. For oil and gas well applications, the tube425may be coiled tubing or equivalent deployment tool having the pressure sensors14,16,18for sensing P1–P3inside the tubing425. Alternatively the tube425may also include a bluff or rounded shaped end as indicated by dashed line420.

Referring toFIG. 17, there is shown an embodiment of the present invention in a typical industrial processing application, the sensing section51may be connected to or part of process tubing502(analogous to the pipe12in the test section51) within an industrial process control system500. The isolation sleeve410may be located over the sensors14,16,18as discussed hereinbefore and attached to the pipe502at the axial ends to protect the sensors14,16,18(or fibers) from damage during deployment, use, or retrieval, and/or to help isolate the sensors from acoustic external pressure effects that may exist outside the pipe502, and/or to help isolate ac pressures in the pipe502from ac pressures outside the pipe502. The advantages and effect of the isolation sleeve410, as well as other isolation techniques, are described in commonly owned copending U.S. patent application Ser. No. 09/344,070, entitled “Measurement of Propagating Acoustic Waves in Compliant Pipes” incorporated herein by reference in its entirety. The sensors14,16,18are connected to a cable506which may comprise the optical fiber300(FIGS.22,23,27,28) and is connected to a transceiver/converter510of the control system500.

When optical sensors are used, the transceiver/converter510may be used to receive and transmit optical signals504to the sensors14,16,18and provides output signals indicative of the pressure P1–P3at the sensors14,16,18on the lines,20,22,24, respectively. Also, the transceiver/converter510may be part of the Fluid Parameter Logic60. The transceiver/converter510may be any device that performs the corresponding functions described herein. In particular, the transceiver/converter510together with the optical sensors described hereinbefore may use any type of optical grating-based measurement technique, e.g., scanning interferometric, scanning Fabry Perot (resonator, cavity, interferometer or other known Fabry Perot arrangement), acousto-optic-tuned filter (AOTF), optical filter, time-of-flight, and may use WDM and/or TDM, etc., having sufficient sensitivity to measure the ac pressures within the pipe.

A plurality of the sensors10of the present invention may be connected to a common cable and multiplexed together using any known multiplexing technique by connecting end511to other sensors (not shown). For instance, it is contemplated that the various embodiments of the sensor10of the present invention include the capability being multiplexed as well as capable of communication with various protocols and systems currently in use in the industrial sensing area. For instance, and with reference toFIG. 17there is shown a portion of a process control system500incorporating a sensor10in accordance with the present invention. Fluid parameter logic60communicates signals Mx, amix, and % Composition along lines59,46,50to control device70, a computer or micro-processor for example, where the information may be used to control the fluid characteristics in pipe502through known controls means such as a pump, valve, throttle, etc. (not shown). In certain embodiments of control system500and with appropriate electro-optical conversion of the sensor return signal to a conventional 4–20 mA signal the signal can be combined with other control devices and sensors at control device70via separate electrical lines. In this particular embodiment the communication from the fiber optic sensor is performed with a 4–20 mA analog signal, and the open protocol HART®. (Highway Addressable Remote Transducer) digital communications format. Similarly, communication from the fiber optic sensor10may also be performed with open and interoperable protocol FOUNDATION™ Fieldbus that provides a digital communication link among intelligent field level and control devices via electrical lines. The control device70can be configured for use with other process protocols, including Device Bus, Sensor Bus, Profibus, the ethernet, and others in use throughout the world. The use of feedthroughs511, as shown inFIG. 17, make the sensor10of the present invention uniquely qualified for industrial applications requiring multiple sensors. The use of sensors having feedthroughs in a large multi-point process enables connectivity to the multiple sensors through a single fiber optic cable. Electronic sensors of the prior art require dedicated wiring to the sensor and back to the instrumentation. For instance, a typical industrial process control system that utilizes electronic flowmeters of the prior art requires an electrical process loop to facilitate both a power signal to the transmitters and bi-directional communication, and can be constructed in accordance with a number of the aforementioned process communication protocols.

In operation, industrial process uses for the present invention include reverse osmosis, coking, general refining uses, in-line pressure sensors for emissions monitoring, sensors for monitoring hydrogen, combustion control, gas composition analysis, distributed sensors in tank gauging, multi-phase computational fluid dynamics, instrumentation of multiphase flows, among others.

It should be understood that the present invention can be used to measure fluid volume fractions of a mixture of any number of fluids in which the speed of sound of the mixture amixis related to (or is substantially determined by), the volume fractions of two constituents of the mixture, e.g., oil/water, oil/gas, water/gas. The present invention can be used to measure the speed of sound of any mixture and can then be used in combination with other known quantities to derive phase content of mixtures with multiple (more than two) constituents.

Further, the present invention can be used to measure any parameter (or characteristic) of any mixture of one or more fluids in which such parameter is related to the speed of sound of the mixture amix, e.g., fluid fraction, temperature, salinity, mineral content, sand particles, slugs, pipe properties, etc. or any other parameter of the mixture that is related to the speed of sound of the mixture. Accordingly, the logic48(FIG. 1) may convert amixto such parameter(s).

Further, the invention will work independent of the direction of the flow or the amount of flow of the fluid(s) in the pipe, and whether or not there is flow in the pipe. Also, independent of the location, characteristics and/or direction(s) of propagation of the source of the acoustic pressures. Also, instead of a pipe, any conduit or duct for carrying a fluid may be used if desired.

Also, the signals on the lines20,22,24(FIG. 1) may be time signals H1(t),H2(t),H3(t), where Hn(t) has the pressure signal Pn(t) as a component thereof, such that FFT[H1(t)]=G(ω)P1(ω), FFT[H2(t)]=G(ω)P2(ω), and the ratio H2(ω)/H1(ω)=G(ω)P2(ω)/G(ω)P1(ω)=P2(ω)/P1(ω), where G(ω) is a parameter which is inherent to each pressure signal and may vary with temperature, pressure, or time, such as calibration characteristics, e.g., drift, linearity, etc.

Also, Instead of calculating the ratios P12and P13, equations similar to Eqs. 9,10 may be derived by obtaining the ratios of any other two pairs of pressures, provided the system of equations Eq.5–7 are solved for B/A or A/B and the ratio of two pairs of pressures. Also, the equations shown herein may be manipulated differently to achieve the same result as that described herein.

Still further, if, for a given application, the relationship between A and B (i.e., the relationship between the right and left travelling waves, or the reflection coefficient R) is known, or the value of A or B is known, or the value of A or B is zero, only two of the equations 5–7 are needed to determine the speed of sound. In that case, the speed of sound amixcan be measured using only two axially-spaced acoustic pressure sensors along the pipe.

Further, while the invention has been described as using a frequency domain approach, a time domain approach may be used instead. In particular, the Eqs. 5,6,7 may be written in the form of Eq. 1 in the time-domain giving time domain equations P1(x1,t), P2(x2,t),P3(x3,t), and solved for the speed of sound amixand eliminating the coefficients A,B using known time domain analytical and signal processing techniques (e.g., convolution).

Referring toFIGS. 37–40, it should be understood that although the invention has been described hereinbefore as using the one dimensional acoustic wave equation evaluated at a series of different axial locations to determine the speed of sound, any known technique to determine the speed at which sound propagates along a spatial array of acoustic pressure measurements where the direction of the source(s) is (are) known may be used to determine the speed of sound in the mixture. The term acoustic signals as used herein, as is known, refers to substantially stochastic, time stationary signals, which have average (or RMS) statistical properties that do not significantly vary over a predetermined period of time (i.e., non-transient ac signals).

For example, the procedure for determining the one dimensional speed of sound amixwithin a fluid contained in a pipe using an array of unsteady pressure measurements is similar to a problem encountered in underwater acoustics (e.g., SONAR or Sound Navigation Ranging). In underwater acoustics, axial arrays of sensors are deployed to determine the bearing (or direction) of underwater noise sources. The process is referred to as “beam forming”. In free space, i.e., in an unbounded media, such as the ocean, the speed at which a sound wave propagates along an axial array is dependent on both (1) the free-space speed of sound and (2) the incident angle of the sound wave on the axial array.

Referring toFIG. 37, the apparent sound speed axat which the wave propagates along the array is related to the angle or bearing (θ=90−γ) of the source S1and the sound speed a in the media. For a SONAR application, as is known, the speed of sound is known and the apparent sound speed axis measured, which allows the bearing to be determined by the relation: θ=cos−1(a/ax).

Conversely, referring toFIG. 38, we have found that in a pipe12where the angle or bearing on the array of the incident sound is known, i.e., θ=0 deg, the speed of sound a of the fluid in the pipe12can be determined as follows.

In particular, referring toFIG. 39, for a single distant source in two dimensional (2D) space, the pressure wave can be written as follows (such as is generally described in A. Dowling and J. Williams, “Sound and Sources of Sound”, Ch 4, pp 79–81):
P(x,y,t)=Aeiω(t−x sin γ1/a−γcos γ1/a)Eq. 27

Pressure as seen on the array at y=0 is:
P(x,y=0,t)=Aeiω(t−x sin γ1/a)Eq.28
P(x,t)=Ae−ikxrxeiωtEq. 29

A similar analysis may be done for a left travelling wave along the array from the source S2as:
P(x,t)=Be+ikxlxeiωtEq. 30

For the situation where the sound is propagating along a pipe, then γ1=γ2=90 deg. and where a=amix which is the speed of sound of the fluid mixture in the pipe, then:kxr=kxl=ωamixEq.⁢31

Thus, referring toFIG. 38, for a left and right travelling acoustic waves travelling in the pipe12, the pressure equation becomes:
P(x,t)=Ae−ikxrxeiωt+Be+ikxlxeiωtEq. 32
which is the same as Eq. 1, and which may be used to determine the speed of sound by using the sensors described herein and solving the associated equations Eq. 5–7 shown hereinbefore. The same result may also be shown from sources originating in three dimensional space using cylindrical or other coordinate systems.

The data from the array of sensors may be processed in any domain, including the frequency/spatial domain (such as Eq. 4), the temporal/spatial domain (such as Eq. 1), the temporal/wave-number domain or the wave-number/frequency (k-ω) domain. As such, any known array processing technique in any of these or other related domains may be used if desired.

For example, Eq. 5 can be represented in the k-ω domain by taking the spatial Fourier transform of Eq. 5, resulting in the following k-ω representation:P⁡(k,ω)=12⁢π⁢∫-∞+∞⁢P⁡(x,ω)⁢ⅇⅈ⁢⁢kx⁢⁢ⅆx=A⁡(ω)⁢δ⁡(k-ωa)+B⁡(ω)⁢δ⁡(k+ωa)Eq.⁢33
where k is the wave number and δ is the Dirac delta function, which shows a spatial/temporal mapping of the acoustic field in the k-ω plane.

Alternatively, instead of using the three equations Eq. 5–7, any technique known in the art for using a spatial (or phased) array of sensors to determine the direction of an acoustic source in three dimensional sound field with a known speed of sound (e.g., spatial array processing for SONAR arrays, RADAR (RAdio Detecting And Ranging) arrays or other arrays, beam forming, or other signal processing techniques), may be used to solve for the sound speed knowing the direction of travel of the acoustic waves, i.e., axially along the pipe. Some of such known techniques are described in the following references, which are incorporated herein by reference: H. Krim, M. Viberg, “Two Decades of Array Signal Processing Research—The Parametric Approach”, IEEE Signal Processing Magazine, pp 67–94, R. Nielson, “Sonar Signal Processing”, Ch. 2, pp51–59.

Referring toFIG. 40, accordingly, the fluid parameter logic60may comprise spatial array processing logic450which receives the spatial array of acoustic pressure signals P1(t), P2(t), P3(t) and performs the spatial array processing described herein to determine the speed of sound amixon the line46.

By utilizing the output of sensor10of the present invention with various fluid properties related to speed of sound, such as density, a plethora of uses are enabled. For instance, signal processing logic60may contain simple look-up tables that include values of various parameters of fluids dependant on sound speed, such as the fluid type. Once the fluid density is determined the fluid type may be ascertained and reported by signal processing logic60. Other examples of the use of the flowmeter of the present invention include determining the heating value of a fluid, the acid strength of sulfuric acid solution (or other acid or caustic mixture), the steam quality of a fluid, the salinity of fluid mixture, determining the phrase fraction for a three phase mixture and other known or contemplated uses where the sound speed and density of the fluid mixture yield powerful insight in determining other fluid values and compositions.

It should be understood that any of the features, characteristics, alternatives or modifications described regarding a particular embodiment herein may also be applied, used, or incorporated with any other embodiment described herein.