April 03, 2008

Flow Measurement - Errors & Corrections

Using flowmeters, but totally frustrated when they give inaccurate readings???

Considering flow meters, completing all mass balance & then finding the meter reading is wrong????

Calibrating, Checking Re-installing & still finding incorrect readings?????

Oh! GOD......What to do? Why....??
Read on for better understanding of flow measurement.

Let us start from basics of flow metering from orifice type devices which are the simplest one & most commonly used. Let me start this with an example so that its more clear........without covering too much theory.

So let us say that upstream conditions in case of an orifice are P1, T1 which are also the design conditions. Let us consider fixed mass flow rate m. So the density of this gas will be

rho1 = P1 x M / ( R x T1 ), where M is the mol wt of gas.

Let us assume that design condition for downstream pressure is P2.

Now the orifice equation is

m = Cv Y A (2 rho1 x (P1-P2))^0.5
Find it Here.

Now during the design based on above condition Cv & A are fixed, P1 & T1 varies so that rho1 also varies. so now let us simplify this equation for our use as below.

m = K x (DP x P1 x M / ( R x T1))^0.5

Ultimately, it will reduce to

m = k x ( DP x P1 / T1)^0.5.......................Eqn(1)

Now to understand the actual phenomenon, let us understand that how DP varies with the variation in P & T Or say collectively it is density (rho).

Remember there are two different things one is actual DP experienced by orifice due to changes in density. Orifice never measures volume or mass flow it measures only DP. Second thing is the indication of this DP in terms of volumetric flow or mass flow which is obatined by its full range DP (Volume flow) & then multiplying it by an assumed constant density figure (Mass flow) by your instrument people. This is the actual point of error.

So let us first understand what will be the new DP when mass flow m is fixed as per our assumption. There are two cases only....

  1. Density increases (due to variation in P&T)

  2. Density decreases (due to variation in P&T)

In case-1, when density increases, the volume flow will go down (mass flow remaining same) & hence velocity across orifice will go down. Therefore it will read lesser DP (more velocity means more DP). So indication will read less flow, but when you apply correct density your mass flow will remain same. Similarly, vice versa happens with the case-2. So there is a correction formula for reading actual figures as below.

Corrected actual flow = Indicated flow x ((Pa/Pd) x (Td/Ta) x (Ma/Md))^0.5

This is a general formula for any gas flow including variation in mol wt. Subscript 'a' indicates actual values during measurement & 'd' indicates design values for which orifice is designed.

This part is often missed by production, process engineers & instrument people. Once you apply this correction, you can have more accurate readings.

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Edwin Nguyen said...

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caleb mott said...

I Would like some confirmation on the formula you used. Honeywell used the same formula; however the Ma & md were flipped( I Think)

Corrected actual flow = Indicated flow x ((Pa/Pd) x (Td/Ta) x (Md/Ma))^0.5

Honeywell's definition of the MW

Md reference MW(Configured)

Ma= MW

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