Fluid parameter measurement for industrial sensing applications using acoustic pressures

• US 6,988,411 B2
• Filed: 05/10/2004
• Issued: 01/24/2006
• Est. Priority Date: 06/26/1998
• Status: Expired due to Term

• Current Assignee: Expro Meters, Inc. (Umbrellastream LP, Inc.)
• Original Assignee: Cidra Sarl (Nordic Cultural & Educational Foundation)
• Inventors: Kersey, Alan D., Gysling, Daniel L., Paduano, James D.
• Primary Examiner(s): LARKIN, DANIEL SEAN
• Application Number:
  US10/842,068
• Publication Number:
  US 20050000289A1
• Time in Patent Office: 624 Days
• Field of Search: 73/614.1, 73/614.7, 73/614.9, 73/617.9, 735/97, 736/43, 736/55, 736/56, 736/57, 736/45, 736/46
• US Class Current: 73/645
• CPC Class Codes: G01H 5/00 Measuring propagation velocity of ultrasonic, sonic or infrasonic waves , e.g. of pressure waves
• CPC Class Codes: G01N 2291/0217 Smoke, combustion gases
• CPC Class Codes: G01N 2291/0222 Binary liquids
• CPC Class Codes: G01N 2291/0224 Mixtures of three or more liquids
• CPC Class Codes: G01N 2291/02836 Flow rate, liquid level
• CPC Class Codes: G01N 2291/02845 Humidity, wetness
• CPC Class Codes: G01N 2291/02872 Pressure
• CPC Class Codes: G01N 2291/106 one or more transducer arrays
• CPC Class Codes: G01N 29/024 by measuring propagation velocity or propagation time of acoustic waves
• CPC Class Codes: G01N 29/42 by frequency filtering or by tuning to resonant frequency
• CPC Class Codes: G01N 29/46 by spectral analysis, e.g. Fourier analysis or wavelet analysis spectral signal processing per se G06F17/14

Abstract

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 a_mix 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 a_mix. The speed of sound a_mix 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 a_mix. 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.

Claims

1. An apparatus for industrial sensing applications for measuring at least one parameter of a mixture of at least one fluid in a pipe in an industrial fluid process, comprising:

a spatial array of at least three pressure sensors, disposed at different axial locations along the pipe, and each measuring an acoustic pressure associated with a background acoustic noise source within the pipe at a corresponding axial location, each of said sensors providing an acoustic pressure signal indicative of the background acoustic noise 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.

2. The apparatus of claim 1 wherein said signal processor comprises logic which calculates a frequency based signal for each of said acoustic pressure signals.

3. The apparatus of claim 1 wherein said acoustic pressure signals each comprise a frequency based signal and wherein said signal processor comprises logic which calculates a ratio of two of said frequency based signals.

4. The apparatus of claim 1 wherein said signal processor comprises logic which simultaneously solves the following equations for said speed of sound:

P(x₁,t)=(Ae<sup>−

ikrx1</sup>+Be^+iklx1)e<sup>iω

t</sup>

P(x₂,t)=(Ae<sup>−

ikrx2</sup>+Be^+iklx2)e<sup>iω

t</sup>

P(x₃,t)=(Ae<sup>−

ikrx3</sup>+Be^+iklx3)e<sup>iω

t</sup>

where A,B are amplitudes of the frequency based signals, x is the axial location of the pressure sensor along the, t is time, ω

is frequency, and k_r,k₁ are wave numbers.

5. The apparatus of claim 1 wherein said signal processor calculates said speed of sound of said mixture using the following relation:

$\begin{array}{c}\frac{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_1}+{\mathrm{Re}}^{{\mathrm{ik}}_l<br><br>x_1}}{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_3}+{\mathrm{Re}}^{\mathrm{i<br><br>}<br><br><br><br>k_l<br><br>x_3}}-\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_3<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]=<br><br>0\\ \mathrm{where}<br><br><br><br><br><br>R\equiv <br><br>\frac{B}{A}=<br><br>\frac{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r,x_1}-\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_2}}{\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]<br><br>{\mathrm{e<br><br>}}^{\mathrm{i<br><br>}<br><br><br><br>k_1<br><br>x_2}-{\mathrm{e<br><br>}}^{\mathrm{i<br><br>}<br><br><br><br>k_1<br><br>x_1}}\\ \mathrm{where}<br><br><br><br>k_r\equiv <br><br><br><br>\left(\frac{\mathrm{\omega <br><br>}}{a_{\mathrm{mix}}}\right)<br><br>\frac{1}{1+M_x}<br><br><br><br>\mathrm{and}<br><br><br><br><br><br>k_l\equiv <br><br>\left(\frac{\mathrm{\omega <br><br>}}{a_{\mathrm{mix}}}\right)<br><br>\frac{1}{1-M_x}\end{array}$

where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), and M_x is the axial Mach number of the flow of the mixture within the pipe, where;

$M_x\equiv <br><br>\frac{V_{\mathrm{mix}}}{a_{\mathrm{mix}}}$

and where Vmix is the axial velocity of the mixture, and where P₁(ω

),P₂(ω

),P₃(ω

) are said frequency based signals for each of said acoustic pressure signals.

6. The apparatus of claim 1 wherein said sensors are equally spaced, a Mach number of the mixture is small compared to one, and said signal processor calculates the speed of sound of the mixture using the following relation:

$a_{\mathrm{mix}}=\frac{\mathrm{\omega <br><br>}}{\left[\frac{1}{\mathrm{\Delta <br><br>}<br><br><br><br>x}\right]<br><br>i<br><br><br><br>\log <br><br>\left[\frac{P_{12}+P_{13}<br><br>P_{12}+{\left(P_{12}^2+2<br><br>P_{13}<br><br>P_{12}^2+P_{13}^2<br><br>P_{12}^2-4<br><br>P_{13}^2\right)}^{1/2}}{2<br><br>P_{13}}\right]}$

where P₁₂=P₁(ω

)/P₂(ω

), P₁₃=P₁(ω

)/P₃(ω

), i is the square root of −

1, Δ

x is the axial spacing between sensors, where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), and where P₁(ω

),P₂(ω

),P₃(ω

) are said frequency based signals for each of said acoustic pressure signals.

7. The apparatus of claim 1 wherein said sensors are equally axially spaced, a Mach number of the mixture is small compared to one, and said signal processor calculates the speed of sound of the mixture using the following relation:

$\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)+P_3<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}=2<br><br>\cos <br><br>\left(\frac{\mathrm{\omega <br><br>\Delta <br><br>}<br><br><br><br>x}{a_{\mathrm{mix}}}\right)$

where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), Δ

x is the axial spacing between said sensors, and where P₁(ω

),P₂(ω

),P₃(ω

) are said frequency based signals for each of said acoustic pressure signals.

8. The apparatus of claim 1 wherein the signal processor comprises logic which calculates a fluid composition of the mixture in the pipe.

9. The apparatus of claim 1 wherein said signal processor comprises logic which calculates a fluid composition of the mixture having two fluids using the following relation:

$a_{\mathrm{mix}}=\sqrt{\frac{1+\frac{{\mathrm{\rho <br><br>}}_1}{{\mathrm{\rho <br><br>}}_2}<br><br>\frac{h_2}{h_1}}{\frac{1}{a_1^2}+\frac{{\mathrm{\rho <br><br>}}_1}{{\mathrm{\rho <br><br>}}_2}<br><br><br><br>\frac{h_2}{h_1}<br><br><br><br>\frac{1}{a_2^2}}}$

where a₁,a₂ are known speeds of sound, ρ

₁,ρ

₂ are known densities, and h₁,h₂ are volume fractions of the two respective fluids, and a_mix is the speed of sound of the mixture.

10. The apparatus of claim 1 wherein said speed of sound is substantially determined by two fluids within the mixture.

11. The apparatus of claim 1 wherein at least one of said pressure sensors is at least one of a fiber optic pressure sensor, accelerometer, velocity sensor, displacement sensor, hydrophone, and strain sensor.

12. The apparatus of claim 1 wherein at least one of said pressure sensors measures a circumference-averaged pressure at said axial location of said sensor.

13. The apparatus of claim 1 wherein at least one of said pressure sensors measures pressure at more than one point around a circumference of the pipe at said given axial location of said sensor.

14. An industrial process control system for controlling at least one parameter of an industrial fluid process, said system comprising:

an apparatus for measuring at least one parameter of a mixture of said at least one fluid, said apparatus comprising;

a spatial array of at least two pressure sensors, disposed at different axial locations along said pipe, and each measuring an acoustic pressure associated with a background acoustic noise source within said pipe at a corresponding axial location, each of said sensors providing an acoustic pressure signal indicative of the background acoustic noise within said pipe at said axial location of a corresponding one of said sensors; and

a signal processor, responsive to said pressure signals, which provides an output signal indicative of a speed of sound of the mixture in the pipe; and

a control device receiving said output signal and capable of controlling said process parameter to a predetermined level.

15. The control system of claim 14 wherein said signal processor comprises logic which calculates a frequency based signal for each of said acoustic pressure signals.

16. The control system of claim 14 wherein said acoustic pressure signals each comprise a frequency based signal and wherein said signal processor comprises logic which calculates a ratio of two of said frequency based signals.

17. The apparatus of claim 14 comprising at least three of said sensors.

18. The control system of claim 17 wherein said signal processor comprises logic which simultaneously solves the following equations for said speed of sound:

P(x₁,t)=(Ae<sup>−

ikrx1</sup>+Be^+iklx1)e<sup>iω

t</sup>

P(x₂,t)=(Ae<sup>−

ikrx2</sup>+Be^+iklx2)e<sup>iω

t</sup>

P(x₃,t)=(Ae<sup>−

ikrx3</sup>+Be^+iklx3)e<sup>iω

t</sup>

where A,B are amplitudes of the frequency based signals, x is the axial location of the pressure sensor along the, t is time, ω

is frequency, and k_r,k_l are wave numbers.

19. The control system of claim 17 wherein said signal processor calculates said speed of sound of said mixture using the following relation:

$\frac{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_1}+{\mathrm{Re}}^{{\mathrm{i<br><br>k}}_l<br><br>x_1}}{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_3}+{\mathrm{Re}}^{{\mathrm{i<br><br>k}}_l<br><br>x_3}}-\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_3<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]=0<br><br><br><br>\mathrm{where}$$R\equiv <br><br>\frac{B}{A}=\frac{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_1}-\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_2}}{\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_l<br><br>x_2}-{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_l<br><br>x_1}}<br><br><br><br>\mathrm{where}$$k_r\equiv <br><br>\left(\frac{\mathrm{\omega <br><br>}}{a_{\mathrm{mix}}}\right)<br><br>\frac{1}{1+M_x}<br><br><br><br>\mathrm{and}<br><br><br><br>k_l\equiv <br><br>\left(\frac{\mathrm{\omega <br><br>}}{a_{\mathrm{mix}}}\right)<br><br>\frac{1}{1-M_x}$

where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), and M_x is the axial Mach number of the flow of the mixture within the pipe, where;

$M_x\equiv <br><br>\frac{V_{\mathrm{mix}}}{a_{\mathrm{mix}}}$

and where Vmix is the axial velocity of the mixture, and where P₁(ω

),P₂(ω

),P₃(ω

) are said frequency based signals for each of said acoustic pressure signals.

20. The control system of claim 17 wherein said sensors are equally spaced, a Mach number of the mixture is small compared to one, and said signal processor calculates the speed of sound of the mixture using the following relation:

$a_{\mathrm{mix}}=\frac{\mathrm{\omega <br><br>}}{\left[\frac{1}{\mathrm{\Delta <br><br>}<br><br><br><br>x}\right]<br><br>i<br><br><br><br>\log \left[\frac{\begin{array}{c}{P}_{12}+P_{13}<br><br>P_{12}+\\ {\left(P_{12}^2+2<br><br>P_{13}<br><br>P_{12}^2+P_{13}^2<br><br>P_{12}^2-4<br><br>P_{13}^2\right)}^{1/2}\end{array}}{2<br><br>P_{13}}\right]}$

where P₁₂=P₁(ω

)/P₂(ω

), P₁₃=P₁(ω

)/P₃(ω

), i is the square root of −

1, Δ

x is the axial spacing between sensors, where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), and where P₁(ω

),P₂(ω

),P₃(ω

) are said frequency based signals for each of said acoustic pressure signals.

21. The control system of claim 17 wherein said sensors are equally axially spaced, a Mach number of the mixture is small compared to one, and said signal processor calculates the speed of sound of the mixture using the following relation:

$\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)+P_3<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}=2<br><br>\cos <br><br>\left(\frac{\mathrm{\omega <br><br>\Delta <br><br>}<br><br><br><br>x}{a_{\mathrm{mix}}}\right)$

where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), Δ

x is the axial spacing between said sensors, and where P₁(ω

),P₂(ω

),P₃(ω

) are said frequency based signals for each of said acoustic pressure signals.

22. The control system of claim 14 wherein the signal processor comprises logic which calculates a fluid composition of the mixture in the pipe.

23. The control system of claim 17 wherein said signal processor comprises logic which calculates a fluid composition of the mixture having two fluids using the following relation:

$a_{\mathrm{mix}}=\sqrt{\frac{1+\frac{{\mathrm{\rho <br><br>}}_1}{{\mathrm{\rho <br><br>}}_2}<br><br>\frac{h_2}{h_1}}{\frac{1}{a_1^2}+\frac{{\mathrm{\rho <br><br>}}_1}{{\mathrm{\rho <br><br>}}_2}<br><br>\frac{h_2}{h_1}<br><br>\frac{1}{a_2^2}}}$

where a₁,a₂ are known speeds of sound, ρ

₁,ρ

₂ are known densities, and h₁,h₂ are volume fractions of the two respective fluids, and a_mix is the speed of sound of the mixture.

24. The control system of claim 14 wherein said speed of sound is substantially determined by two fluids within the mixture.

25. The control system of claim 14 wherein said pressure sensors are fiber optic pressure sensors.

26. The control system of claim 14 wherein at least one of said pressure sensors measures a circumference-averaged pressure at said axial location of said sensor.

27. The control system of claim 14 wherein at least one of said pressure sensors measures pressure at more than one point around a circumference of the pipe at said given axial location of said sensor.

28. The control system of claim 14 wherein at least one of said pressure sensors measures strain on the pipe.

29. A method for measuring at least one parameter of a mixture of at least one fluid in a pipe in an industrial fluid process, comprising:

measuring an acoustic pressure associated with a background acoustic noise source within the pipe at at least three different axial locations along the pipe, each acoustic pressure signal indicative of the background acoustic noise within the pipe at said corresponding axial location; and

determining a signal indicative of a speed of sound of the mixture in response to said pressure signals.

30. The method of claim 29 wherein determining a signal indicative of the speed of sound includes simultaneously solving the following equations for said speed of sound:

P(x₁,t)=(Ae<sup>−

ikrx1</sup>+Be^+iklx1)e<sup>iω

t</sup>

P(x₂,t)=(Ae<sup>−

ikrx2</sup>+Be^+iklx2)e<sup>iω

t</sup>

P(x₃,t)=(Ae<sup>−

ikrx3</sup>+Be^+iklx3)e<sup>iω

t</sup>

where A,B are amplitudes of the frequency based signals, x is the axial location of the pressure sensor along the, t is time, ω

is frequency, and k_r,k₁ are wave numbers.

31. The method of claim 29 wherein determining a signal indicative of the speed of sound includes calculating said speed of sound of said mixture using the following relation:

$\frac{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_1}+{\mathrm{Re}}^{{\mathrm{i<br><br>k}}_l<br><br>x_1}}{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_3}+{\mathrm{Re}}^{{\mathrm{i<br><br>k}}_l<br><br>x_3}}-\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_3<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]=0<br><br><br><br>\mathrm{where}$$R\equiv <br><br>\frac{B}{A}=\frac{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_1}-\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_2}}{\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_l<br><br>x_2}-{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_l<br><br>x_1}}<br><br><br><br>\mathrm{where}$$k_r\equiv <br><br>\left(\frac{\mathrm{\omega <br><br>}}{a_{\mathrm{mix}}}\right)<br><br>\frac{1}{1+M_x}<br><br><br><br>\mathrm{and}<br><br><br><br>k_l\equiv <br><br>\left(\frac{\mathrm{\omega <br><br>}}{a_{\mathrm{mix}}}\right)<br><br>\frac{1}{1-M_x}$

where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), and M_x is the axial Mach number of the flow of the mixture within the pipe, where;

$M_x\equiv <br><br>\frac{V_{\mathrm{mix}}}{a_{\mathrm{mix}}}$

and where Vmix is the axial velocity of the mixture, and where P₁(ω

), P₂(ω

), P₃(ω

) are said frequency based signals for each of said acoustic pressure signals.

32. The method of claim 29 wherein determining a signal indicative of the speed of sound includes calculating the speed of sound of the mixture using the following relation:

$a_{\mathrm{mix}}=\frac{\mathrm{\omega <br><br>}}{\left[\frac{1}{\mathrm{\Delta <br><br>}<br><br><br><br>x}\right]<br><br>i<br><br><br><br>\log \left[\frac{\begin{array}{c}{P}_{12}+P_{13}<br><br>P_{12}+\\ {\left(P_{12}^2+2<br><br>P_{13}<br><br>P_{12}^2+P_{13}^2<br><br>P_{12}^2-4<br><br>P_{13}^2\right)}^{1/2}\end{array}}{2<br><br>P_{13}}\right]}$

where P₁₂=P₁(ω

)/P₂(ω

), P₁₃=P₁(ω

)/P₃(ω

), i is the square root of −

1, Δ

x is the axial spacing between sensors, where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), and where P₁(ω

), P₂(ω

), P₃(ω

) are said frequency based signals for each of said acoustic pressure signals, wherein the axial location are equally spaced and a Mach number of the mixture is small compared to one.

33. The method of claim 29 wherein determining a signal indicative of the speed of sound includes calculating the speed of sound of the mixture using the following relation:

$\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)+P_3<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}=2<br><br>\cos <br><br>\left(\frac{\mathrm{\omega <br><br>\Delta <br><br>}<br><br><br><br>x}{a_{\mathrm{mix}}}\right)$

where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), Δ

x is the axial spacing between said sensors, and where P₁(ω

), P₂(ω

), P₃(ω

) are said frequency based signals for each of said acoustic pressure signals, wherein the axial locations are equally axially spaced and a Mach number of the mixture is small compared to one.

34. The method of claim 29 wherein determining a signal indicative of the speed of sound includes calculating a fluid composition of the mixture in the pipe.

35. The method of claim 29 wherein determining a signal indicative of the speed of sound includes calculating a fluid composition of the mixture having two fluids using the following relation:

$a_{\mathrm{mix}}=\sqrt{\frac{1+\frac{{\mathrm{\rho <br><br>}}_1}{{\mathrm{\rho <br><br>}}_2}<br><br>\frac{h_2}{h_1}}{\frac{1}{a_1^2}+\frac{{\mathrm{\rho <br><br>}}_1}{{\mathrm{\rho <br><br>}}_2}<br><br>\frac{h_2}{h_1}<br><br>\frac{1}{a_2^2}}}$

where a₁,a₂ are known speeds of sound, ρ

₁,ρ

₂ are known densities, and h₁,h₂ are volume fractions of the two respective fluids, and a_mix is the speed of sound of the mixture.

36. A method for controlling at least one parameter of an industrial fluid process, said system comprising:

measuring an acoustic pressure associated with a background acoustic noise source within the pipe at at least two different axial locations along the pipe, each acoustic pressure signal indicative of the background acoustic noise within the pipe at said corresponding axial location; and

determining an output signal indicative of a speed of sound of the mixture in response to said pressure signals,

controlling said at least one process parameter to a predetermined value in response to said output signal.

37. The method of claim 36 wherein measuring an acoustic pressure includes measuring an acoustic pressure at at least three different axial locations along the pipe.

38. The method of claim 37 wherein determining a signal indicative of the speed of sound includes simultaneously solving the following equations for said speed of sound:

P(x₁,t)=(Ae<sup>−

ikrx1</sup>+Be^+iklx1)e<sup>iω

t</sup>

P(x₂,t)=(Ae<sup>−

ikrx2</sup>+Be^+iklx2)e<sup>iω

t</sup>

P(x₃,t)=(Ae<sup>−

ikrx3</sup>+Be^+iklx3)e<sup>iω

t</sup>

where A,B are amplitudes of the frequency based signals, x is the axial location of the pressure sensor along the, t is time, ω

is frequency, and k_r,k_l are wave numbers.

39. The method of claim 37 wherein determining a signal indicative of the speed of sound includes calculating said speed of sound of said mixture using the following relation:

$\frac{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_1}+{\mathrm{Re}}^{{\mathrm{i<br><br>k}}_l<br><br>x_1}}{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_3}+{\mathrm{Re}}^{{\mathrm{i<br><br>k}}_l<br><br>x_3}}-\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_3<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]=0<br><br><br><br>\mathrm{where}$$R\equiv <br><br>\frac{B}{A}=\frac{{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_1}-\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_r<br><br>x_2}}{\left[\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}\right]<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_1<br><br>x_2}-{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>k_1<br><br>x_1}}<br><br><br><br>\mathrm{where}$$k_r\equiv <br><br>\left(\frac{\mathrm{\omega <br><br>}}{a_{\mathrm{mix}}}\right)<br><br>\frac{1}{1+M_x}<br><br><br><br>\mathrm{and}<br><br><br><br>k_l\equiv <br><br>\left(\frac{\mathrm{\omega <br><br>}}{a_{\mathrm{mix}}}\right)<br><br>\frac{1}{1-M_x}$

where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad!sec), and M_x is the axial Mach number of the flow of the mixture within the pipe, where;

$M_x\equiv <br><br>\frac{V_{\mathrm{mix}}}{a_{\mathrm{mix}}}$

and where Vmix is the axial velocity of the mixture, and where P₁(ω

), P₂(ω

), P₃(ω

) are said frequency based signals for each of said acoustic pressure signals.

40. The method of claim 37 wherein determining a signal indicative of the speed of sound includes calculating the speed of sound of the mixture using the following relation:

$a_{\mathrm{mix}}=\frac{\mathrm{\omega <br><br>}}{\left[\frac{1}{\mathrm{\Delta <br><br>}<br><br><br><br>x}\right]<br><br>i<br><br><br><br>\log \left[\frac{\begin{array}{c}{P}_{12}+P_{13}<br><br>P_{12}+\\ {\left(P_{12}^2+2<br><br>P_{13}<br><br>P_{12}^2+P_{13}^2<br><br>P_{12}^2-4<br><br>P_{13}^2\right)}^{1/2}\end{array}}{2<br><br>P_{13}}\right]}$

where P₁₂=P₁(ω

)/P₂(ω

), P₁₃=P₁(ω

)/P₃(ω

), i is the square root of −

1, Δ

x is the axial spacing between sensors, where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), and where P₁(ω

), P₂(ω

), P₃(ω

) are said frequency based pressure signals, wherein the axial location are equally spaced and a Mach number of the mixture is small compared to one.

41. The method of claim 37 wherein determining a signal indicative of the speed of sound includes calculating the speed of sound of the mixture using the following relation:

$\frac{P_1<br><br>\left(\mathrm{\omega <br><br>}\right)+P_3<br><br>\left(\mathrm{\omega <br><br>}\right)}{P_2<br><br>\left(\mathrm{\omega <br><br>}\right)}=2<br><br>\cos <br><br>\left(\frac{\mathrm{\omega <br><br>\Delta <br><br>}<br><br><br><br>x}{a_{\mathrm{mix}}}\right)$

where a_mix is the speed of sound of the mixture in the pipe, ω

is frequency (in rad/sec), Δ

x is the axial spacing between said sensors, and where P₁(ω

), P₂(ω

), P₃(ω

) are said frequency based signals for each of said acoustic pressure signals, wherein the axial locations are equally axially spaced and a Mach number of the mixture is small compared to one.

42. The method of claim 36 wherein determining a signal indicative of the speed of sound includes calculating a fluid composition of the mixture in the pipe.

43. The method of claim 37 wherein determining a signal indicative of the speed of sound includes calculating a fluid composition of the mixture having two fluids using the following relation:

$a_{\mathrm{mix}}=\sqrt{\frac{1+\frac{{\mathrm{\rho <br><br>}}_1}{{\mathrm{\rho <br><br>}}_2}<br><br>\frac{h_2}{h_1}}{\frac{1}{a_1^2}+\frac{{\mathrm{\rho <br><br>}}_1}{{\mathrm{\rho <br><br>}}_2}<br><br>\frac{h_2}{h_1}<br><br>\frac{1}{a_2^2}}}$

where a₁,a₂ are known speeds of sound, ρ

₁, ρ

₂ are known densities, and h₁,h₂ are volume fractions of the two respective fluids, and a_mix is the speed of sound of the mixture.