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Flow meter-Fiscal metering of petroleum liquids- http://courses.cmr.no - Need Help in understanding and solving this

What is the random uncertainty of the average of the meter proving runs for the 43 m3/h flow rate proving? Use the information in the tables below together with the equation to calculate this uncertainty. 

Answer:  

Hint: The repeatability range is the highest meter factor in the proving sequence minus the lowest.

darwin k

• 10 Apr 2017 12:35 PM
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2 Replies

• Marc Buttler

  

  • 10 Apr 2017 7:28 PM

  Hi Darwin K.
  
  A more thorough explanation of these calculations can be found in API MPMS Chapter 4.8 and in Chapter 13.
  
  For the specific problem you have listed:
  n = 5 because there are five proving runs at 43 m3/h
  t (5-1) = t (4) = 2.78 from the table
  w = (max MF - min MF) = 0.9998 - 0.99922 = 0.00058 (0.058%)
  D(5) = 2.326 from the second table
  SQRT (n) = SQRT(5) = 2.236
  so the random uncertainty of the average of the five meter factors (which is 0.99956) is: a(MF) = 0.00031 or 0.031% using the equation given in the problem statement.
  
  Note that this result is slightly above the standard API target uncertainty of 0.027% that would be your answer if the range of meter factors w(5) had been 0.0005 or 0.05%. Most people are familiar with 0.05% in 5 runs, but may not know that this is the range of MF values that will give you the target uncertainty of 0.027% in 5 runs.
  
  It is very interesting to also note that, with more runs, your uncertainty will always get smaller because D(n) gets larger and SQRT(n) in the denominator, while t(n-1) gets smaller in the numerator.
  For example, if you had the same w of 0.00058 after taking 10 runs, then the random uncertainty would only be 0.00013 or 0.013% (well below the 0.027% target - less than half, in fact).
  This decreasing uncertainty in the average with an increasing number of runs is the same reason that the 0.0012 (0.12%) tolerance allowed for the range of MF with 10 runs is so much larger than the 0.0005 (0.05%) tolerance that is allowed with 5 runs. Both of these tolerances are designed to assure that you have 0.027% uncertainty of the average MF or better at the end of the day.
  
  Hopes this helps explain it a little better. If you want more detail, API MPMS Chapters 4.8 and 13 explain all this clearly.

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• darwin k

  

  • 11 Apr 2017 2:11 AM

  In reply to Marc Buttler:

  Thanks a lot, you made it very simple for me.

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