Quantitative analysis of flow profile characteristics for ultrasonic metering systems

1. An ultrasonic flow metering system, comprising:

an ultrasonic flow meter comprising:

a spool piece defining a central passage for fluid flow;

a plurality of pairs of ultrasonic transducers disposed in the spool piece, each of the pairs of ultrasonic transducers disposed to form a chordal path across the central passage; wherein the ultrasonic flow meter comprises a plurality of chordal paths;

a condition monitor configured to:

determine a reference chordal velocity ratio for each of the plurality of chordal paths;

for each chordal path of the plurality of chordal paths:

compute, for the chordal path, a predicted chordal velocity based on the reference chordal velocity ratio for the chordal path and measured flow velocities for all other chordal paths of the plurality of chordal paths;

compute a first estimated mean flow velocity for the ultrasonic meter, the first estimated mean flow velocity based on the predicted chordal velocity for the chordal path and the measured flow velocities for all other chordal paths of the plurality of chordal paths; and

compute, for each other chordal path of the plurality of chordal paths, a predicted chordal velocity ratio based on the measured flow velocity for the other chordal path and the first estimated mean flow velocity.

2. The system of claim 1 , wherein the condition monitor is configured to, for each other chordal path of the plurality of chordal paths:

compute a difference between the predicted velocity ratio and the reference chordal velocity ratio for the other chordal path; and

identify a largest of the differences across the other chordal paths of the plurality of chordal paths.

3. The system of claim 2 , wherein the condition monitor is configured to generate, for each chordal path, a display of the largest difference.

4. The system of claim 1 , wherein the condition monitor is configured to compute, for each chordal path, a degree of measurement error attributable to the chordal path based on the predicted chordal velocity for the chordal path and the measured flow velocity for all other chordal paths.

5. The system of claim 1 , wherein the condition monitor is configured to:

compute, for a first chordal path of the plurality of chordal paths, a second estimated mean flow velocity of the ultrasonic flow meter based on the measured velocity for the first chordal path and estimated chordal velocities for all other chordal paths of the plurality of chordal paths, the estimated chordal velocities estimated based on the measured velocity for the first chordal path and calculated velocities for all other chordal paths of the plurality of chordal paths, the calculated velocities calculated based on the measured velocity for the first chordal path and the reference chordal velocity ratios for all other chordal paths of the plurality of chordal paths.

6. The system of claim 5 , wherein the condition monitor is configured to:

compute the second estimated mean flow velocity of the ultrasonic flow meter with each chordal path of the plurality of chordal paths successively being the first chordal path; and

compute, for each chordal path of the plurality of chordal paths, a difference between the second estimated mean flow velocity and a measured mean flow velocity.

7. The system of claim 6 , wherein the condition monitor is configured to generate, for each chordal path of the plurality of chordal paths, a display of the difference.

8. The system of claim 6 , wherein the condition monitor is configured to determine whether the differences are indicative of a change in site conditions.

9. A method for monitoring operation of an ultrasonic flow metering system, comprising:

in an ultrasonic flow meter comprising a spool piece defining a central passage for fluid flow; and a plurality of pairs of ultrasonic transducers disposed in the spool piece, each of the pairs of ultrasonic transducers disposed to form a chordal path across the central passage; wherein the ultrasonic flow meter comprises a plurality of chordal paths:

for each of the chordal paths:

determining, for the chordal path, a reference chordal velocity ratio;

determining, for the chordal path, a predicted chordal velocity based on the reference chordal velocity ratio for the chordal path and measured flow velocities for all other chordal paths of the plurality of chordal paths;

determining a first estimated mean flow velocity for the ultrasonic meter, the first estimated mean flow velocity based on the predicted chordal velocity for the chordal path and the measured flow velocities for all other chordal paths of the plurality of chordal paths;

determining, for each other chordal path of the plurality of chordal paths, a predicted chordal velocity ratio based on the measured flow velocity for the other chordal path and the first estimated mean flow velocity.

10. The method of claim 9 , further comprising, for each other chordal path of the plurality of chordal paths:

determining, for the other chordal path, a difference between the predicted velocity ratio for the other chordal path and the reference chordal velocity ratio for the other chordal path; and

identifying a largest of the differences across the other chordal paths.

11. The method of claim 9 , further comprising determining, for each chordal path, a degree of measurement error attributable to the chordal path based on the predicted chordal velocity for the chordal path and the measured flow velocity for all other chordal paths.

12. The method of claim 9 , further comprising determining, for a first chordal path of the plurality of chordal paths, a second estimated mean flow velocity of the ultrasonic flow meter based on the measured velocity for the first chordal path and estimated chordal velocities for each other chordal path of the plurality of chordal paths, the estimated chordal velocities estimated based on the measured velocity for the first chordal path and calculated velocities for all other chordal paths of the plurality of chordal paths the calculated velocities calculated based on the measured velocity for the first chordal path and the reference chordal velocity ratios for all other chordal paths of the plurality of chordal paths.

13. The method of claim 12 , further comprising:

determining, the second estimated mean flow velocity of the ultrasonic flow meter with each chordal path of the plurality of chordal paths successively serving as the first chordal path; and

determining, for each chordal path of the plurality of chordal paths, a difference between the second estimated mean flow velocity and a measured mean flow velocity.

14. The method of claim 13 , further comprising determining whether the differences are indicative of a change in site conditions based on relative trends in velocity change of the chordal paths.

15. An ultrasonic flow metering system, comprising:

an ultrasonic flow meter comprising:

a spool piece defining a central passage for fluid flow;

a plurality of pairs of ultrasonic transducers disposed in the spool piece, each of the pairs of ultrasonic transducers disposed to form a chordal path across the central passage; wherein the ultrasonic flow meter comprises a plurality of chordal paths; and

a condition monitor configured to:

determine a reference chordal velocity ratio for each of a plurality of chordal paths of an ultrasonic flow meter; and

compute, for a first chordal path of the plurality of chordal paths, a first estimated mean flow velocity of the ultrasonic flow meter based on the measured velocity for the first chordal path and estimated chordal velocities for all other chordal paths of the plurality of chordal paths, the estimated chordal velocities estimated based on the measured velocity for the first chordal path and calculated velocities for all other chordal paths of the plurality of chordal paths, the calculated velocities calculated based on the measured velocity for the first chordal path and the reference chordal velocity ratios for all other chordal paths of the plurality of chordal paths.

16. The system of claim 15 , wherein the condition monitor is configured to:

compute the first estimated mean flow velocity of the ultrasonic flow meter with each chordal path of the plurality of chordal paths successively being the first chordal path; and

compute, for each chordal path of the plurality of chordal paths, a difference between the second estimated mean flow velocity and a measured mean flow velocity.

17. The system of claim 16 , wherein the condition monitor is configured to generate, for each chordal path of the plurality of chordal paths, a display of the difference.

18. The system of claim 16 , wherein the condition monitor is configured to determine whether the differences are indicative of a change in site conditions.

19. The system of claim 15 , wherein the condition monitor is configured to:

for each chordal path of the plurality of chordal paths:

compute, for the chordal path, a predicted chordal velocity based on the reference chordal velocity ratio for the chordal path and measured flow velocities for all other chordal paths of the plurality of chordal paths;

compute a second estimated mean flow velocity for the ultrasonic meter, the second estimated mean flow velocity based on the predicted chordal velocity for the chordal path and the measured flow velocities for all other chordal paths of the plurality of chordal paths; and

compute, for each other chordal path of the plurality of chordal paths, a predicted chordal velocity ratio based on the measured flow velocity for the other chordal path and the first estimated mean flow velocity.

20. The system of claim 19 , wherein the condition monitor is configured to, for each other chordal path of the plurality of chordal paths:

compute a difference between the predicted velocity ratio and the reference chordal velocity ratio for the other chordal path; and

identify a largest of the differences across the other chordal paths of the plurality of chordal paths.

21. The system of claim 20 , wherein the condition monitor is configured to generate, for each chordal path, a display of the largest difference across the other chordal paths of the plurality of chordal paths.

22. The system of claim 19 , wherein the condition monitor is configured to compute, for each chordal path of the plurality of chordal paths, a degree of measurement error attributable to the chordal path based on the predicted chordal velocity for the chordal path and the measured flow velocity for all other of the chordal paths.

23. A method for monitoring operation of an ultrasonic flow metering system, comprising:

in an ultrasonic flow meter comprising a spool piece defining a central passage for fluid flow; and a plurality of pairs of ultrasonic transducers disposed in the spool piece, each of the pairs of ultrasonic transducers disposed to form a chordal path across the central passage; wherein the ultrasonic flow meter comprises a plurality of chordal paths:

determining a reference chordal velocity ratio for each of a plurality of chordal paths of an ultrasonic flow meter; and

determining, for a first chordal path of the plurality of chordal paths, a first estimated mean flow velocity of the ultrasonic flow meter based on the measured velocity for the first chordal path and estimated chordal velocities for all other chordal paths of the plurality of chordal paths, the estimated chordal velocities estimated based on the measured velocity for the first chordal path and calculated velocities for all other chordal paths of the plurality of chordal paths, the calculated velocities calculated based on the measured velocity for the first chordal path and the reference chordal velocity ratios for all other chordal paths of the plurality of chordal paths.

24. The method of claim 23 , further comprising:

determining the first estimated mean flow velocity of the ultrasonic flow meter with each chordal path of the plurality of chordal paths successively being the first chordal path; and

determining, for each chordal path of the plurality of chordal paths, a difference between the second estimated mean flow velocity and a measured mean flow velocity.

25. The method of claim 24 , further comprising determining whether the differences are indicative of a change in site conditions based on relative trends in velocity change of the chordal paths.

26. The method of claim 23 , further comprising:

for each chordal path of the plurality of chordal paths:

determining, for the chordal path, a predicted chordal velocity based on the reference chordal velocity ratio for the chordal path and measured flow velocities for all other chordal paths of the plurality of chordal paths;

determining a second estimated mean flow velocity for the ultrasonic meter, the second estimated mean flow velocity based on the predicted chordal velocity for the chordal path and the measured flow velocities for all other chordal paths of the plurality of chordal paths; and

determining, for each other chordal path of the plurality of chordal paths, a predicted chordal velocity ratio based on the measured flow velocity for the other chordal path and the first estimated mean flow velocity.

27. The method of claim 26 , further comprising, for each other chordal path of the plurality of chordal paths:

determining a difference between the predicted velocity ratio and the reference chordal velocity ratio for the other chordal path; and

identifying a largest of the differences across the other chordal paths of the plurality of chordal paths.

28. The method of claim 26 , further comprising determining, for each chordal path of the plurality of chordal paths, a degree of measurement error attributable to the chordal path based on the predicted chordal velocity for the chordal path and the measured flow velocity for all of the other chordal paths.