Patent Publication Number: US-8109127-B2

Title: Measurement of entrained and dissolved gases in process flow lines

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 12/040,385, filed 29 Feb. 2008, now U.S. Pat. No. 7,571,633, which is a divisional application of U.S. patent application Ser. No. 11/500,073, filed on Aug. 7, 2006, now abandoned, which is a continuation of U.S. patent application Ser. No. 10/762,409, filed on Jan. 21, 2004, and now U.S. Pat. No. 7,086,278, which claimed the benefit of U.S. Provisional Patent Application No. 60/482,516, filed Jun. 24, 2003; U.S. Provisional Patent Application No. 60/441,652, filed Jan. 22, 2003; U.S. Provisional Patent Application No. 60/441,395, filed Jan. 21, 2003; all of which are incorporated herein by reference in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Technical Field 
     The present invention generally relates to a device for measuring dissolved air in a fluid or process mixture flowing in a process line. 
     2. Description of Related Art 
     Monitoring levels of entrained and dissolved gases is desirable in many industrial processes. For example, entrained and dissolved gases in the approach system of paper making machines are often problematic, leading to a wide variety of problems, including flow line pulsations, pin-holes in the produced paper, reduced paper sheet strength, and excessive build-up of aerobic growths. 
     Entrained gases are gases that exist in a gaseous form, mixed in the process fluid. For many industrial applications with small, less than ±20% gas fraction by volume, the gas is typically in the form of small bubbles contained in a liquid continuous mixture. Entrained gases exist as either free bubbles moving within the stock or as bound (or residual) air that is adhered to the fiber. In either cases, entrained air can generally be detected by monitoring the compressibility of the mixture and correlating the compressibility to volumetric percentage of entrained air. 
     Dissolved gases are dissolved within the mixture on a molecular level. While in the solution, dissolved gases pose few operation problems. Typically dissolved gases have a negligible effect on the compressibility of the mixture. Thus, dissolved gases are difficult to detect via compressibility measurements. 
     Although dissolved gases are typically not problematic while dissolved, problems arise when dissolved gases come out of a solution as a result of either decreases in pressure or increases in temperature. One example of this is in pressurized head boxes on paper machines where the pressure drop associated with spraying the pulp/water mixture on to the paper machine can cause dissolved gases to come out of the solution and form entrained air. 
     Thus, to accurately monitor problems associated with entrained and dissolve gases, it is desirable to be able to measure both quantities. 
     SUMMARY OF THE INVENTION 
     In its broadest sense, the present invention provides a new and unique device having a first module arranged in relation to a process line for providing a first signal containing information about a sensed entrained air/gas in a fluid or process mixture flowing in the process line at a process line pressure. The device features a combination of a bleed line, a second module and a third module. The bleed line is coupled to the process line for bleeding a portion of the fluid or process mixture from the process line at a bleed line pressure that is lower than the process pressure. The second module is arranged in relation to the bleed line, for providing a second signal containing information about a sensed bleed line entrained air/gas in the fluid or process mixture flowing in the bleed line. The third module responds to the first signal and the second signal, for providing a third signal containing information about a dissolved air/gas flowing in the process line based on a difference between the sensed entrained air/gas and the sensed bleed line entrained air/gas. 
     In one embodiment, the first module is a primary process line entrained air measurement module that includes an array of sensors that measures the speed of sound propagating through the fluid or process mixture flowing within the process line and determines the entrained air based on a measurement using the speed of sound. The second module is a bleed line entrained air measurement module that also includes an array of sensors that measures the speed of sound propagating through the fluid or process mixture flowing within the bleed line and determines the bleed line entrained air based on a measurement using the speed of sound. The third module is a dissolved air determination processor module that processes the first and second signals and provides the third signal containing information about a dissolved air/gas flowing in the process line. 
     The device also includes a bleed line control module for controlling the bleeding off of the portion of the fluid from the process line via a bleed valve and the reinjection of said portion back to the process line via a boost pump, and also includes a controller module for controlling and coordinating the operation of the first, second and third modules, as well as a bleed line control that communicates with the bleed valve and the boost pump. 
     In operation, the device according to the present invention measures dissolved gases at an operating pressure by measuring entrained gases present in a process line once the fluid or process mixture is expanded to ambient (or other known and relevant) pressure. This measurement is performed using a small amount of process mixture bled-off, either continuously or periodically, from the process. The bled-off process fluid can be recirculated or, via a boost pump, re-pressurized and reinjected. The bleed line and flow rates may be sized to minimize the amount of stock bleed off while maintained sufficiently high flow rates to maintain sufficiently homogenous flow within the bled-off liquid test section (i.e. minimize slip) such that the measured gas volume fraction within the bleed line is indeed representative of the amount of gas dissolved in the process fluid. Maintaining sufficiently high velocities avoids problems associated with stratification of the mixture and the problems associated with either the liquid of gas phases “holding up” in the process pipe. For most mixtures of liquids and gases at or near ambient pressures, flow velocities of several feet per second through the line are sufficient. 
     The process of the throttling of the process fluid to the reduced pressure provides sufficient noise to perform a sonar-based speed measurement. 
     The present invention also provides a method for measuring the entrained gas fraction at two relevant pressures, and thus provides practical measurement of the amount of both entrained and dissolved gases contained in the process fluid at the process operating conditions. 
     The foregoing and other objects, features and advantages of the present invention will become more apparent in light of the following detailed description of exemplary embodiments thereof. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
       The drawing, not drawn to scale, includes the following Figures: 
         FIG. 1  is a block diagram of a device for measurement of entrained and dissolved gases that is the subject matter of the present invention. 
         FIG. 2  is a schematic of the device shown in  FIG. 1 . 
         FIG. 3  is an overview of the system according to the present invention. 
         FIG. 4  is a graph of a gas volume fraction (GVF) between 0.00001 and 0.1 versus a mixture sound speed in meters per sec (m/s). 
         FIG. 5  is a graph of a gas volume fraction (GVF) between 0.0 and 0.1 versus a mixture sound speed in meters per sec. 
         FIG. 6  is a k−ω plot constructed according to the present invention, showing acoustic ridges, wherein the fluid flowing in the pipe is water with entrained air. 
         FIG. 7  is a block diagram of an apparatus for measuring entrained air in a fluid flowing within a pipe, such as a bleed line and primary process line, in accordance with the present invention. 
         FIG. 8  is a block diagram of another embodiment of an apparatus for measuring entrained air in a fluid flowing within a pipe, such as a bleed line and primary process line, in accordance with the present invention. 
     
    
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
       FIGS. 1 and 2  show a schematic and block diagram of a device generally indicated as  10  for measurement of entrained and dissolved gases in a fluid or process mixture generally indicated as  11  flowing in a primary process line  12  having a given process pressure. 
     In  FIG. 1 , the device  10  includes a first, or primary process line, entrained air measurement module  14 , a bleed line  16  (see also  FIG. 2 ), a second, or bleed line, entrained air measurement module  18  and a dissolved air/gas determination processor module  20 . The primary process line entrained air measurement module  14  is arranged in relation to the primary process line  12 , for sensing entrained air in the fluid or process mixture  11  and providing a first entrained air measurement module signal via line  14   a  containing information about sensed primary process line entrained air. As best shown in  FIG. 2 , the bleed line  16  is coupled to the primary process line  12  for bleeding fluid or process mixture from the primary process line  12  at a bleed line pressure that is lower than the process pressure, for example, at ambient pressure. As best shown in  FIG. 1 , the second entrained air measurement module  18  is arranged in relation to the bleed line  16 , for sensing entrained air in the fluid or process mixture in the bleed line, and providing a second entrained air measurement module signal via line  18   a  containing information about sensed bleed line entrained air. In  FIG. 1 , the dissolved air/gas determination processor module  20  responds to the first entrained air measurement module signal along line  14   a  and the second entrained air measurement module signal along line  18   a , each signal being received via a controller module  22  as shown and discussed below; determines dissolved air/gas in the fluid or process mixture flowing in the primary process line based on a difference between the sensed primary process line entrained air and the sensed bleed line entrained air; and provides a dissolved air/gas determination processor module signal containing information about the same. 
     The controller module  22  controls and coordinates the operation of the modules  14 ,  18 ,  20  and  32 . As shown, the signals along lines  14   a ,  18   a  are provided directly to the controller module  22 , although the scope of the invention is intended to include embodiments in which the signals along lines  14   a ,  18   a  are provided directly to the dissolved air/gas determination processor module  20 . The bleed line control module  32  controls the bleed valve  28  and boost pump  30  (see  FIG. 2 ) in response to a signal from the controller module  22 . 
     The primary process line entrained air measurement module  14  includes an array of sensors  24  shown in  FIG. 2  that measures the speed of sound propagating through the fluid or process mixture flowing within the process line  12  and determines the entrained air based on a measurement using the speed of sound, as will be described in greater detail hereinafter. 
     Similarly, the bleed line entrained air measurement module  18  includes a corresponding array of sensors  26  that measures the speed of sound propagating through the fluid or process mixture  11  flowing within the bleed line  16  and determines the bleed line entrained air based on a measurement using the speed of sound. 
     The bleed line  16  has a bleed valve  28  for bleeding the fluid or process mixture  11  into the bleed line  16 . The bleed line  16  is re-coupled to the primary process line  12  via a boost pump  30  to recirculate the fluid or process mixture bled therefrom. The scope of the invention is not intended to be limited to the type or kind of bleed valve or boost pump used. The invention is shown and described in relation to a closed loop system; however, the scope of the invention is intended to include an open loop system in which the media from the bleed line is not returned to the process line. 
     The device  10  also includes a bleed line control module  32  for controlling the bleeding off of the portion of the fluid or process mixture from the process line via the bleed valve  28  and the reinjection of the same back to the process line  12  via the boost pump  30 . 
     The modules  14 ,  18 ,  20 ,  22 ,  32  may be implemented using hardware, software, or a combination thereof. The scope of the invention is not intended to be limited to any particular implementation thereof. For example, a typical software implementation may include using a microprocessor architecture having a microprocessor, a random access memory (RAM), a read only memory (ROM), input/output devices and a control, address and databus for connecting the same. 
     Although the invention is described in relation to measuring or sensing entrained air in a fluid or process mixture using an array of sensors, the scope of the invention is intended to include other ways of measuring or sensing entrained air either known now or developed in the future. Moreover, although the invention is described in relation to using an array of sensors to determine the speed of sound, the scope of the invention is intended to include other ways of measuring the speed of sound either known now or developed in the future. 
     Entrained Gas Measurement 
     The present invention uses the speed at which sound propagates within a conduit to measure entrained air in slurries. This approach may be used with any technique that measures the sound speed of a fluid or process mixture. However, it is particularly synergistic with sonar based volumetric flow meters such as described in aforementioned U.S. patent application Ser. No. 10/007,736, now U.S. Pat. No. 6,889,562, in that the sound speed measurement, and thus gas volume fraction measurement, can be accomplished using the same hardware as that required for the volumetric flow measurement. It should be noted, however, that the gas volume fraction (GVF) measurement could be performed independently of a volumetric flow measurement, and would have utility as an important process measurement in isolation or in conjunction with other process measurements. 
     Firstly, the sound speed may be measured as described in aforementioned U.S. patent application Ser. No. 09/344,094, now U.S. Pat. No. 6,354,147, Ser. No. 10/007,749, now U.S. Pat. No. 6,732,575, U.S. patent application Ser. No. 10/349,716 filed Jan. 23, 2003 and/or U.S. patent application Ser. No. 10/376,427 filed Feb. 26, 2003, now U.S. Pat. No. 7,032,432 all incorporated herein by reference, using an array of unsteady pressure transducers. For a two component mixture, utilizing relations described in U.S. patent application Ser. No. 09/344,094, now U.S. Pat. No. 6,354,147, and/or Ser. No. 10/007,749, now U.S. Pat. No. 6,732,575, knowledge of the density and sound speed of the two components and the compliance properties of the conduit or pipe, the measured sound speed can be used to determine the volumetric phase fraction of the two components. 
     The sound speed of a mixture can be related to volumetric phase fraction (φ i ) of the components and the sound speed (a) and densities (ρ) of the component through the Wood equation, where 
     
       
         
           
             
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     One dimensional compression waves propagating within a fluid contained within a conduit exert an unsteady internal pressure loading on the conduit. The degree to which the conduit displaces as a result of the unsteady pressure loading influences the speed of propagation of the compression wave. The relationship among the infinite domain speed of sound and density of a fluid; the elastic modulus (E), thickness (t), and radius (R) of a vacuum-backed cylindrical conduit; and the effective propagation velocity (a eff ) for one dimensional compression is given by the following expression: 
     
       
         
           
             
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     Note: “vacuum backed” as used herein refers to a situation in which the fluid surrounding the conduit externally has negligible acoustic impedance compared to that of the fluid internal to the pipe. For example, meter containing a typical water and pulp slurry immersed in air at standard atmospheric conditions satisfies this condition and can be considered “vacuum-backed”. 
     For paper and pulp slurries, the conditions are such that for slurries with non-negligible amounts of entrained gas, say &lt;0.01%, the compliance of standard industrial piping (Schedule 10 or 40 steel pipe) is typically negligible compared to that of the entrained air. 
       FIGS. 4 and 5  show the relationship between sound speed and entrained air for slurries with pulp contents representative of the range used in the paper and pulp industry. Referring to  FIG. 4 , two slurry consistencies are shown; representing the lower limit, a pure water mixture is considered, and representing the higher end of consistencies, a 5% pulp/95% water slurry is considered. Since the effect of entrained air on the sound speed of the mixture is highly sensitive to the compressibility of the entrained air, the effect of the entrained air is examined at two pressures, one at ambient representing the lower limit of pressure, and one at four atmospheres representing a typical line pressure in a paper process. As shown, the consistency of the liquid slurry, i.e., the pulp content, has little effect on the relationship between entrained air volume fraction and mixture sound speed. This indicates that an entrained air measurement could be accurately performed, within 0.01% or so, with little or no knowledge of the consistency of the slurry. The chart does show a strong dependence on line pressure. Physically, this effect is linked to the compressibility of the air, and thus, this indicates that reasonable estimates of line pressure and temperature would be required to accurately interpret mixture sound speed in terms of entrained air gas volume fraction. 
       FIG. 4  also shows that for the region of interest, from roughly 1% entrained air to roughly 5% entrained air, mixture sound speeds (a mix ) are quite low compared to the liquid-only sound speeds. In the example shown above, the sound speed of the pure water and the 5% pulp slurry were calculated, based on reasonable estimates of the constituent densities and compressibilities, to be 1524 m/s and 1541 m/s, respectively. The sound speed of these mixtures with 1% to 5% entrained air at typical operating pressure (1 atm to 4 atms) are on the order of 100 m/sec. The implication of these low sound speeds is that the mixture sound speed could be accurately determined with an array of sensors, i.e. using the methodology described in aforementioned 
     U.S. patent application Ser. No. 09/344,094, now U.S. Pat. No. 6,354,147, and/or Ser. No. 10/007,749, now U.S. Pat. No. 6,732,575, with an aperture that is similar, or identical, to an array of sensors that would be suitable to determine the convection velocity, using the methodology described in aforementioned U.S. patent application Ser. No. 10/007,736, now U.S. Pat. No. 6,889,562, which is incorporated herein by reference. 
     A flow chart of the proposed measurement is shown in  FIG. 3 , where the inputs are the mixture of SOS, P and T are pressure and temperature, respectively, and GVT air (gas volumetric flow of air) is provided from the box “Entrained Air Volume Fraction” as an output and to the box “correct for void fraction of air” and Q mixture (volumetric flow of the mixture) is provided from the box “Total Mixture Flow Rate” as an output and to the box “correct for void fraction of air”. 
     Other information relating to the gas volume fraction in a fluid and the speed of sound (or sonic velocity) in the fluid, is described in “Fluid Mechanics and Measurements in two-phase flow Systems”, Institution of mechanical engineers, proceedings 1969-1970 Vol. 184 part 3C, Sep. 24-25, 1969, Birdcage Walk, Westminster, London S. W. 1, England. 
     Based on the above discussion, one may use a short length scale aperture to measure the sound speed. 
     The characteristic acoustic length scale is: λ=c/f; where c is the speed of sound in a mixture, f is frequency and λ is wavelength. 
     If Aperture=L and if L/λ is approx. constant. 
     Then Lwater/λwater=Lwater*f/C water ≈L GVF *f/c GVF    
     Therefore: L GVF =Lwater(C GVF /C water ); where GVF is gas volume fraction. 
     Thus for SOS of water (Cwater=5,000 ft/sec), and SOS of the Gas volume fraction (C GVF=500 ft/sec) and a length aperture of L water=5 ft (which we have shown is sufficient to accurately measure the SOS of water), the length aperture for a gas volume fraction L GVF  would be about 0.5 feet. 
     Note that this entrained air or gas volume fraction measurement GVFair may be used with any flow meter or consistency meter to correct for errors introduced into a measurement by entrained air. In particular, an electromagnetic flow meter will show an error when entrained air exists in the mixture. The present invention may be used to correct for this error. In addition, a consistency meter will show an error when entrained air exists in the mixture. The present invention may be used to correct for this error. 
     The scope of the invention is also intended to include using other models and corrections for determining entrained air in a fluid that may be used to compensate for gas volume fraction. 
     As shown in  FIG. 3 , the sonar meter measures the speed at which acoustic wave propagating in the process piping to determine the amount of entrained air in the process line. The acoustic wave can be generated by a pump or other device disposed in the piping system, or generated simply by the mixture/fluid flowing through the pipe, all of which provide a passive acoustic source. Alternatively, the sonar flow meter includes an active acoustic source that injects an acoustic wave into the flow such as by compressing, vibrating and/or tapping the pipe, to name a few examples. 
     e flow such as by compressing, vibrating and/or tapping the pipe, to name a few examples. 
     The connection between speed of sound of a two-phase mixture and phase fraction is well established for mixtures in which the wavelength of the sound is significantly larger than any inhomogenieities, i.e. bubbles, in the flow. 
     The mixing rule essentially states that the compressibility of a mixture (1/(ρa 2 )) is the volumetrically-weighted average of the compressibilities of the components. For gas/liquid mixtures at pressure and temperatures typical of paper and pulp industry, the compressibility of gas phase is orders of magnitudes greater than that of the liquid. Thus, the compressibility of the gas phase and the density of the liquid phase primarily determine mixture sound speed, and as such, it is necessary to have a good estimate of process pressure to interpret mixture sound speed in terms of volumetric fraction of entrained air. The effect of process pressure on the relationship between sound speed and entrained air volume fraction is shown in  FIG. 4 . 
     Conversely, however, detailed knowledge of the liquid/slurry is not required for entrained air measurement. Variations in liquid density and compressibility with changes in consistency have a negligible effect on mixture sound speed compared to the presence of entrained air.  FIG. 5  shows the mixture sound speed as a function of entrained air volume fraction for two slurries, one with 0% wood fiber and the other with 5% wood fiber by volume. As shown, the relationship between mixture sound speed and gas volume fraction is essentially indistinguishable for the two slurries. Furthermore, mixture sound speed is shown to an excellent indicator of gas volume fraction, especially for the trace to moderate amounts of entrained air, from 0 to 5% by volume, typically encountered in the paper and pulp industry. 
     Speed of Sound Measurement 
     As mentioned earlier, the relationship between mixture sound speed and entrained air in bubbly liquids is well established. However, as will be developed below, in bubbly flows, these relations are only applicable for the propagation of relatively low frequency, long wavelength sound. While this restriction does not present any significant obstacles for the sonar meter, it does present significant challenges to ultrasonic sound speed measurement devices. 
     Ultrasonic meters typically operate in 100 Khz to several Mhz frequency range. For these meters, entrained air bubbles have length scales on the same order as the acoustic waves generated by the ultrasonic meters. They posed several problems. Firstly, the bubbles scatter the ultrasonic waves, impairing the ability of the ultrasonic meter to perform a sound speed measurement. Also, ultrasonic meters rely on information derived from only a small fraction of the cross sectional area of the pipe to be representative of the entire cross section, an assumption that breaks down for flows with inhomogenieties on the same length scale as the ultrasonic wavelength. 
     Sonar flow meters use an approach developed and commercialized specifically for multiphase flow measurement in the oil and gas industry. Sonar meters measure the propagation velocity of operationally generated sound in the ±100 to 1000 Hz frequency range. In this frequency range, sound propagates as a one-dimensional wave using the process pipe as a waveguide. The wavelength of sound in this frequency range (&gt;1 m) is typically several orders of magnitude larger than the length scale of the any bubbles. The long wavelength acoustics propagate through the bubbles unimpeded, providing a robust and representative measure of the volumetrically averaged properties of the flow. 
     For the sound speed measurement, the sonar flow meter utilizes similar processing algorithms as those employed for the volumetric flow measurement. As with convective disturbances, the temporal and spatial frequency content of sound propagating within the process piping is related through a dispersion relationship.
 
 k=ω/a   mix  
 
As before, k is the wave number, defined as k=2π/λ, ω is the temporal frequency in rad/sec, and a mix  is the speed at which sound propagates within the process piping. Unlike disturbances which convect with the flow, however, sound generally propagates in both directions, with and against the mean flow. For these cases, the acoustic power is located along two acoustic ridges, one for the sound traveling with the flow at a speed of a mix +V mix  and one for the sound traveling against the flow at a speed of a mix −V mix .
 
       FIG. 6  shows a k−ω plot generated for acoustic sound field recorded from water flowing at a rate of 240 gpm containing ˜2% entrained air by volume in a 3 inch, schedule  10 , stainless steel pipe. The k−ω plot was constructed using data from an array of strain-based sensors attached to the outside of the pipe. Two acoustic ridges are clearly evident. Based on the slopes of the acoustic ridges, the sound speed for this mixture was 330 ft/sec (100 m/s), consistent with that predicted by the Wood equation. Note that adding 2% air by volume reduces the sound speed of the bubbly mixture to less than 10% of the sound speed of single phase water.  FIG. 7  illustrates a schematic drawing of one embodiment of the present invention. The apparatus  210  includes a sensing device  216  comprising an array of pressure sensors (or transducers)  218 - 221  spaced axially along the outer surface  222  of a pipe  214 , having a process flow propagating therein, similar to that described hereinbefore. The pressure sensors measure the unsteady pressures produced by acoustical disturbances within the pipe, which are indicative of the SOS propagating through the mixture  212 . The output signals (P 1 −P N ) of the pressure sensors  218 - 221  are provided to the processor  224 , which processes the pressure measurement data and determines the speed of sound, gas volume fraction (GVF) and other parameters of the flow as described hereinbefore. 
     In an embodiment of the present invention shown in  FIG. 7 , the apparatus  210  has a processing unit  224  having an array processing unit  223  and a speed of sound processing unit  225 . The apparatus  210 , similar to the arrays  24 , 26  of  FIG. 2 , also has the at least two pressure sensors  218 - 221  disposed axially along the pipe  214  for measuring the unsteady pressure P 1 -P N  of the mixture  212  flowing therethrough. The speed of sound propagating through the flow  212  is derived by interpreting the unsteady pressure field within the process piping  214  (e.g., the bleed line  16  and primary process line  12 ) using multiple transducers displaced axially over ˜2 diameters in length. The flow measurements can be performed using ported pressure transducers or clamp-on, strain-based sensors. The apparatus  210  has the ability to measure the gas volume fraction and other parameters by determining the speed of sound of acoustical disturbances or sound waves propagating through the flow  212  using the array of pressure sensors  218 - 221 . 
     Generally, the apparatus  210  measures unsteady pressures created by acoustical disturbances propagating through the flow  212  to determine the speed of sound (SOS) propagating through the flow. Knowing or measuring the pressure and/or temperature of the flow by a pressure sensor  23  and a temperature sensor  25 , respectively, and the speed of sound of the acoustical disturbances, the processing unit  224  can determine the gas volume fraction of the mixture, similar to that shown in U.S. patent application Ser. No. 10/349,716, filed Jan. 21, 2003, now U.S. Publication 2003/0154036, U.S. patent application Ser. No. 10/376,427, filed Feb. 26, 2003, now U.S. Pat. No. 7,032,432, and U.S. Provisional Patent Application Ser. No. 60/528,802, filed Dec. 11, 2003 which are all incorporated herein by reference. 
     The apparatus  210  in  FIG. 7  also contemplates providing one or more acoustic sources  227  to enable the measurement of the speed of sound propagating through the flow for instances of acoustically quiet flow. The acoustic sources may be disposed at the input end or output end of the array of sensors  218 - 221 , or at both ends as shown. One should appreciate that in most instances the acoustics sources are not necessary and the apparatus passively detects the acoustic ridge provided in the flow  212 . The passive noise includes noise generated by pumps, valves, motors, and the turbulent mixture itself. 
     The apparatus  210  of the present invention may be configured and programmed to measure and process the detected unsteady pressures P 1 (t)−P N (t) created by acoustic waves propagating through the mixture to determine the SOS through the flow  212  in the pipe  214 . One such apparatus  310  is shown in  FIG. 8  that measures the speed of sound (SOS) of one-dimensional sound waves propagating through the mixture to determine the gas volume fraction of the mixture. It is known that sound propagates through various mediums at various speeds in such fields as SONAR and RADAR fields. The speed of sound propagating through the pipe and mixture  212  may be determined using a number of known techniques, such as those set forth in U.S. patent application Ser. No. 09/344,094, entitled “Fluid Parameter Measurement in Pipes Using Acoustic Pressures”, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147; U.S. patent application Ser. No. 09/729,994, filed Dec. 4, 2002, now U.S. Pat. No. 6,609,069; U.S. patent application Ser. No. 09/997,221, filed Nov. 28, 2001, now U.S. Pat. No. 6,587,798; and U.S. patent application Ser. No. 10/007,749, entitled “Fluid Parameter Measurement in Pipes Using Acoustic Pressures”, filed Nov. 7, 2001, now U.S. Pat. No. 6,732,575, each of which are incorporated herein by reference. 
     In accordance with one embodiment of the present invention, the speed of sound propagating through the mixture  212  is measured by passively listening to the flow with an array of unsteady pressure sensors to determine the speed at which one-dimensional compression waves propagate through the mixture  212  contained within the pipe  214 . 
     As shown in  FIG. 8 , an apparatus  310  embodying the present invention has a sensing device  150  having an array of at least two acoustic pressure sensors  115 , 116 , located at the locations x 1 ,x 2  axially along the pipe  214 . One will appreciate that the sensor array may include more than two pressure sensors as depicted by pressure sensors  117 , 118  at locations x 3 ,x N . The pressure generated by the acoustic waves may be measured through pressure sensors  115 - 118 . The pressure sensors  115 - 118  provide pressure time-varying signals P 1 (t),P 2 (t),P 3 (t),P N (t) on lines  120 , 121 , 122 , 123  to a signal processing unit  130  to known Fast Fourier Transform (FFT) logics  126 , 127 , 128 , 129 , respectively. The FFT logics  126 - 129  calculate the Fourier transform of the time-based input signals P 1 (t)−P N (t) and provide complex frequency domain (or frequency based) signals P 1 (ω),P 2 (ω),P 3 (ω),P N (ω) on lines  132 , 133 , 134 , 135  indicative of the frequency content of the input signals. Instead of FFT&#39;s, any other technique for obtaining the frequency domain characteristics of the signals P 1 (t)−P N (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. 
     The frequency signals P 1 (ω)−P N (ω) are fed to an array processing unit  138 , similar to the array processing unit  223 , which provides a signal to line  140  indicative of the speed of sound of the mixture a mix , discussed more hereinafter. The a mix  signal, temperature signal (from temperature sensor  4 ), and pressure signal (from pressure sensor  3 ) is provided to an entrained gas processing unit  142 , similar to the processing unit  225 . The processing unit  142  converts a mix  to a percent composition of a mixture and provides a gas volume fraction or % Comp signal to line  144  indicative thereof (as discussed hereinafter). 
     The data from the array of sensors  115 - 118  may be processed in any domain, including the frequency/spatial domain, the temporal/spatial domain, 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, similar to the techniques used in the fields of SONAR and RADAR. 
     One such technique of determining the speed of sound propagating through the flow  212  is using array processing techniques to define an acoustic ridge in the k−ω plane as shown in  FIG. 6 . The slope of the acoustic ridge is indicative of the speed of sound propagating through the flow  212 . This technique is similar to that described in U.S. Pat. No. 6,587,798 filed Nov. 28, 2001, titled “Method and System for Determining The Speed of Sound in a Fluid Within a Conduit”, which is incorporated herein by reference. The speed of sound (SOS) is determined by applying sonar arraying processing techniques to determine the speed at which the one dimensional acoustic waves propagate past the axial array of unsteady pressure measurements distributed along the pipe  214 . 
     The signal processor  224  performs a Fast Fourier Transform (FFT) of the time-based pressure signals P 1 (t)−P N (t) to convert the pressure signal into the frequency domain. The power of the frequency-domain pressure signals are then determined and defined in the k−ω plane by using array processing algorithms (such as Capon and Music algorithms). The acoustic ridge in the k−ω plane, as shown in the k−ω plot of  FIG. 6 , is then determined The speed of sound (SOS) is determined by measuring slope of the acoustic ridge. The gas volume fraction is then calculated or otherwise determined, as described hereinafter. 
     The flow meter of the present invention uses known array processing techniques, in particular the Minimum Variance, Distortionless Response or other adaptive array processing techniques (MVDR, Music, or Capon technique), to identify pressure fluctuations, which convect with the materials flowing in a conduit and accurately ascertain the velocity, and thus the flow rate, of said material. These processing techniques utilize the covariance between multiple sensors  218 - 221  at a plurality of frequencies to identify signals that behave according to a given assumed model; in the case of the apparatus  310 , a model, which represents pressure variations convecting at a constant speed across the pressure sensors comprising the sensing device  216 . 
     Also, some or all of the functions within the processor  130  may 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. 
     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 pipe  214  to exhibit a certain amount of pipe compliance. 
     The pressure sensors  218 - 221  described 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 sensors  218 - 221  may 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, which are incorporated herein by reference. Alternatively, the sensors  218 - 221  may 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 pipe  214 . In an embodiment of the present invention that utilizes fiber optics as the pressure sensors  218 - 221 , 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. 
     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 pipe  214 . 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 pipe  212  if desired. 
     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 pipe  214 . 
     In certain embodiments of the present invention a piezo-electronic pressure transducer may be used as one or more of the pressure sensors  218 - 221  and it may measure the unsteady (or dynamic or ac) pressure variations inside the pipe  214  by measuring the pressure levels inside of the pipe  214 . In an embodiment of the present invention the sensors  218 - 221  comprise pressure sensors manufactured by PCB Piezotronics. In one pressure sensor there are integrated circuit piezoelectric voltage mode-type sensors that feature built-in microelectronic amplifiers, and convert the high-impedance charge into a low-impedance voltage output. Specifically, a Model 106B manufactured by PCB Piezotronics is used which is a high sensitivity, acceleration compensated integrated circuit piezoelectric quartz pressure sensor suitable for measuring low pressure acoustic phenomena in hydraulic and pneumatic systems. It has the unique capability to measure small pressure changes of less than 0.001 psi under high static conditions. The 106B has a 300 mV/psi sensitivity and a resolution of 91 dB (0.0001 psi). 
     The pressure sensors incorporate a built-in MOSFET microelectronic amplifier to convert the high-impedance charge output into a low-impedance voltage signal. The sensor is powered from a constant-current source and can operate over long coaxial or ribbon cable without signal degradation. The low-impedance voltage signal is not affected by triboelectric cable noise or insulation resistance-degrading contaminants. Power to operate integrated circuit piezoelectric sensors generally takes the form of a low-cost, 24 to 27 VDC, 2 to 20 mA constant-current supply. A data acquisition system of the present invention may incorporate constant-current power for directly powering integrated circuit piezoelectric sensors. 
     Most piezoelectric pressure sensors are constructed with either compression mode quartz crystals preloaded in a rigid housing, or unconstrained tourmaline crystals. These designs give the sensors microsecond response times and resonant frequencies in the hundreds of kHz, with minimal overshoot or ringing. Small diaphragm diameters ensure spatial resolution of narrow shock waves. 
     The output characteristic of piezoelectric pressure sensor systems is that of an AC-coupled system, where repetitive signals decay until there is an equal area above and below the original base line. As magnitude levels of the monitored event fluctuate, the output remains stabilized around the base line with the positive and negative areas of the curve remaining equal. 
     The pressure sensors  218 - 221  described 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, thermal, capacitive, inductive, resistive (e.g., Wheatstone bridge), accelerometers (or geophones), velocity measuring devices, displacement measuring devices, etc. If optical pressure sensors are used, the sensors  218 - 221  may 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 sensors  218 - 221  may 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 pipe  214 . In an embodiment of the present invention that utilizes fiber optics as the pressure sensors  218 - 221 , 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. 
     A piezo-electronic pressure transducer may be used (or alternatively even a common strain gage may be used) as one or more of the pressure sensors  218 - 221 , and it may measure the unsteady (or dynamic or ac) pressure variations Pin inside the pipe  214  by measuring the pressure levels (or for the strain gage, the elastic expansion and contraction of the diameter of the pipe  214 . In an embodiment of the present invention the sensors  218 - 221  comprise pressure sensors manufactured by PCB Piezotronics. In one pressure sensor there are integrated circuit piezoelectric voltage mode-type sensors that feature built-in microelectronic amplifiers, and convert the high-impedance charge into a low-impedance voltage output. Specifically, a Model 106B manufactured by PCB Piezotronics is used which is a high sensitivity, acceleration compensated integrated circuit piezoelectric quartz pressure sensor suitable for measuring low pressure acoustic phenomena in hydraulic and pneumatic systems. It has the unique capability to measure small pressure changes of less than 0.001 psi under high static conditions. The 106B has a 300 mV/psi sensitivity and a resolution of 91 dB (0.0001 psi). 
     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 pipe  212 . 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 pipe  212  if desired. 
     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 pipe  212 . 
     While the sonar-based flow meter using an array of sensors to measure the speed of sound of an acoustic wave propagating through the mixture, one will appreciate that any means for measuring the speed of sound of the acoustic wave may used to determine the entrained air volume fraction of the mixture/fluid. 
     It should be understood that, unless stated otherwise herein, 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. 
     Although the invention has been described and illustrated with respect to exemplary embodiments thereof, the foregoing and various other additions and omissions may be made therein without departing from the spirit and scope of the present invention.