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P&T compensation for flow measurement

Hai I wish to compensate for the kg/hr flow indication sent by a dp (orifice) meter. I want to use the below formula F_comp = F_act * (((T_ref * P_act)/(T_act*P_ref))^0.5) F_ comp = compensated flow in kg/hr F_act = actual flow in kg/hr form transmitter T_ref = T_ref in degC + 273.15 P_ref = P_ref in kgf/cm2g + 1.033 T_act & P_act are operating pressure
What is the correct reference temp and pressure to use? 2 sets of information I have are the design data in meter datasheet calibration sheet of the transmitter where a 0 to 2500mmH2O at 20degC water was used calibrating from 0 to 100% of transmitter range. Instrument engineers do have the correction but the underlying principle is not clear. I wanted to know the principle and correct quantities that must be used. 

zdas04 (Mechanical) 
23 Apr 12 7:20 
You have several concepts confused here. kg/hr is the units of mass flow rate. Mass flow rate is not compensated or adjusted for temperature and pressure. It is an absolute unit. Trouble is it is really difficult to measure directly.
Now, if you were talking about volume flow rate then it is appropriate to state it in either actual flowing conditions or based on a reference condition. The reference condition is usually called "standard temperature and pressure". The problem is that "standard" is whatever two people agree it is. There are dozens of "standards" written into contracts, regulations, and conventions. None of them is anything like universal. I've seen 1 bar (14.5 psia) and 0C (32F). I've seen 101.56 kPa (14.73 psia) and either 0C or 15C (59F), etc. There are many standards. I regularly see one set of numbers used for a gas sales contract and another used to report volumes to the government.
In your equations above, the first one is a mess. It should be:
F_comp=F_act*(P_act*T_ref*Z_ref)/(P_ref*T_act*Z_act)
(I added compressibility and deleted the square root), but the units would be something like m^3/hr or Nm^3/hr, or Sm^3/hr (where the "N" is "normal" and the "S" is "Standard".
Finally the 1.033 kgf/cm^2(g) is supposed to be local atmospheric pressure, which has the value you referenced in very (rare) specific cases.
If you are going to use the horrible term "kgf" then you have to be prepared to convert it to "kg" using a metric version "g_{c}" which I'm not going to get into here.
David 

When you do the compensation for pressure and temperature for compressible gas you should ensure that the system is not compensated for the actual pressure and temperature. In fact, most numbers from the flowmeters have been compensated for the actual operating temperatures and pressures and that's why the unit for the flow rate is standard cubic feet (meters) per second. The compensation is done either in the DCS (distribution control system) or in the instrument itself. When you purchased the instrument, you supplied the process conditions to the vendor. The vendor will use that condition to convert the real condition flow to the standard condition. 

Sorry I skipped explaining current set up. It is basic that for a orifice meter the vol flow rate (and not mass flow rate) is proportional to square root of DP/rho. Since Transmitters have the capability to perform the square root extraction, a signal of 4 to 20 is sent proportional to the measured differential head (ie., DP/rho). Instead of interpreting the signal as vol flow rate in DCS, it is directly scaled for the mass flow rate.Afterall for constant density mass flow rate is proportional to vol rate. But when rho varies the DP put by the fluid also changes. Hence it needs compensation though DCS is scaled for a mass flow rate. Had the signal been from a coriolis this would not be neccessaray. Therefore the reference density becomes important for compensation. I wanted help on that part to which of the values to be used as reference. 

zdas04 (Mechanical) 
25 Apr 12 9:46 
Your "clarification" made things much less clear. If your statement that "F_ comp = compensated flow in kg/hr" is accurate then no compensation is required, it is already in absolute units. You are confusing inputs to the calculation with outputs from the calculation.
Your statement that if the meter were a Coriolis meter the compensation wouldn't be necessary is ludicrous. Coriolis meters infer a velocity from the vibration frequency of a bent pipe and an assumed density. You have to then convert the frequency to a velocity somewhere. At that point you have velocity, assumed density, and flow area and can get a mass flow rate "directly". Oh yeah, velocity times flow area is volume flow rate, so you are not really skipping a step.
You really need to get your head around what is happening in the process. Step 1: measure something that can be used to infer a velocity. Step 2: convert the velocity to a volume flow rate. Step 3: convert the volume flow rate to a mass flow rate. Step 4: convert the mass flow rate to a volume flow rate at standard conditions. Your equation was trying to combine step 3 and step 4. That is a common (and reasonable) thing to do, but when you don't have it clear in your head that it is two steps you muddle it. Mass flow rate is volume flow rate times density.
Whether a particular mathematical operation happens in a transmitter or an RTU or a DCS really doesn't matter as long as the right math is done. Volume flow rate at actual conditions gets converted to volume flow rate at reference conditions. Mass flow rate does not require a compensation.
If your question really is "what temperature and pressure should I use for "standard"?", then the answer is "check your contract or regulatory requirements". There actually are dozens of possible values.
David 

Whn people talk about pressure & temperature compensation, they are usually talking about compressible fluid flow. For you case, the formula ZDAS04 posted is exactly the formula you need. Of course, you most time can assume compressible factor Z equal to 1 for your compensation if the system operating pressure is not too high.
Now let's find the reference point. The design conditins of the flow meter is your reference point regardless the design condition for standard condition or for a specific T & P. 

zdas04 (Mechanical) 
25 Apr 12 12:48 
For a CBM stream with 95% methane and 5% CO2 that I have in my open MathCad file, I get a ratio of Z(flowing)/Z(actual) at 30 psig of 1.0 (assuming Pstd=14.73 psia and Tstd=60F). At 100 psig it is 0.989. At 500 psig it is 0.946. At 1000 psig it is 0.898.
It depends on what you are going to do with the data. For custody transfer I'm not going to give away 1.1% of my revenue (at 100 psig) because I'm too lazy to do a simple calculation. For a plant balance I probably still have a problem with an error of 10.2% (at 1000 psig) out of the box.
Any pressure above about 3 bar(g) should have compressibility. When I was doing gas measurement (custody transfer more than anything else), we jumped through every hoop we could find to minimize uncertainty. Skipping this simple calculation (without acid gas or Nitrogen in the stream, the GPSA simplified calculation is excellent and it doesn't require iteration) does not seem reasonable to me.
David 



