accuracy and error measurement

[omby]

How do I work out the overall accuracy of the following measurement, or at least make a reasonable estimate of % error?

I am measuring a gas flow using an orifice plate/dp cell to give a signal to a DCS, and compensating for pressure and temp using a seperate pressure transmitter and resistance thermometer also to the DCS. (Compensation done in softwate)
The problem I see is that each of the above elements of the loop have their own possible +/- % accuracies that compound to affect the final reading. Just to throw a spanner into the calcs, the gas itself is not of constant density.

For the sake of an upcoming audit I would like to be able to
state that the expected error of the calculated gas flow is "xx.x%" and then be able to explain why. How do I do this?

 

[zdas04]

If you look at the assumptions that went into the development of Square-edged Orifice Measurement, you'll be really concerned about your varying density. The equation development starts with Euler's simplification of Navier-Stokes and his first assumption is constant density. The only way to successfully infer a volume flow rate from a pressure, temperature, and dP is to have constant density fluids.

I would add several "x's" to the left of the decimal in your xx.x% question. Just tell the auditors that you have a random number generator driving your cash register.

One of the appendices of ASME 14.3 has the procedures for developing total uncertainty from the instrument dead bands. It is too complex to go into here.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[Assumptions]

The max possible error for each device is addded together as an absolute value. Thus your orifice, flow transmitter and recording device are all added together. This will give you the max possible error when conditions are as per the orifice calculations. Depending on the P & T calculations that are done in the DCS one has to know how they are done. Are they recalculating the differential or just doing a P & T correction.(This usually is not a big deal for small excursions for most compressible fluids)

To obtain the probable error square each value, add them together and take the square root and you will have the most probable error. This assumes that all components have been calibrated correctly.

Now to establih the error when conditions change, one goes back to the origional calculations and does an error calculation.(This includes changes for P, T and density, unless your instrumentation included this calculation). This can be done by taking derivatives and relating everything back to your DP. Another way would be to do a sensitivity analysis. Take some limit values and see what your flow would be and what your measured flow wa smeasured to be.

Throw the data out there. If they want a more accurate reading then install a correction for density.

It is not a simple calculation. If I was in a rush I would do the boundary conditions and recommend that a detailed calculation be done if greater assurance is desired.

 

[omby]

Thanks zdas04/Assumptions.

Yes, the varying density is somewhat of a headache, but the equiptment installed is part of an air/gas ratio system for a burner (with analysis on the waste gas to trim the ratio), and has worked with success for many years. I think maybe the system is being asked to provide data beyond its original design scope.

As for Assumptions query in the first paragraph of the post, the signal to the DCS from the tx is a raw differential with root extraction carried out in software.

Thanks again.

 

[IRstuff]

The general rule for propagation of error analysis is a weighted RSS of the individual error terms. The weighting factors are the partial derivatives as a function of the individual factor.

Since that tends to be complicated to derive in the best case and nearly impossible to derive in the worst-case, just plain RSS is usually acceptable.

TTFN

 

[jsummerfield]

Yeah, what everyone else said; add the errors, etc.

The orifice plate dp relationship to volumetric flow has the largest error even with constant composition. Visit a few standards on the topic. ASME MFC 1M is a flow measurement glossary; chapter 2 addresses uncertainties. Uncertainties are also addressed in ASME PTC 19.1. ASME MFC-3M is a standard on fluid flow in pipes using orifice, nozzle and venturi devices. This includes lots of practical information. API MPMS 14.3.1 also addresses error pertaining to flow through orifice meters.

"Uncertainty Of Flow Rate
The overall uncertainty is the quadrature sum (square root of the sum of the squares) of the uncertainties associated with the pertinent variables:
For practical considerations, the pertinent variables are assumed to be independent to provide a simpler uncertainty calculation. rn fact, no significant change in the uncertainty estimate will occur if the user applies the simplified uncertainty equations presented below.
The total uncertainty of the flow rate through an orifice meter may be calculated by one of two methods:
a. Empirical coefficient of discharge using flange-tapped orifice meters.
b. In-situ calibration using orifice meters."

ADDENDUM 1 — ERROR ANALYSIS EXAMPLE
- steps through the analysis of the error due to plate deflection for the mass flow rate through a simply supported orifice plate (316 stainless steel) ... ... …

More good stuff in ISA, etc.


John

 

[omby]

Thanks everyone, thats given me plenty of ideas to base some calculations on.

omby

 

[Assumptions]

Just to add a bit.

Richard W. Miller's book "Flow Measurement Engineering Handbook" discusses this in chapter four, titled Accuracy.

One way that I thought about this, is in addition to the normal errors as covered in the above methods, is to do a calculation for the additional error from the composition change. Which is perhaps what you might be searching for.

If you have a program for calculating orifice sizes, then you could put in different densities at various flow rates and see what the dp is for your given bore. This could then be compared to the value that you are recording for that dp. If this was done for three to five densities above and below your design value then it could be presented in an understandable graph for quick viewing. Otherwise hand calculations would be required.

 

[omby]

Yes, I was thinking along the same lines. Once I had calculated an overall error for the physical system, I could apply it to flows adjusted for the minimum, expected, and maximum possible densities of the gas.