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ACFM to SCFM conversion problem

ACFM to SCFM conversion problem

ACFM to SCFM conversion problem

(OP)
I am having trouble determining the proper equation to convert from actual air flow (acfm) to standard (scfm).  The way that most sources say to make this conversion is a manipulation of the ideal gas law that looks like:
 scfm=acfm*(Pact/Pstd)*(Tstd/Tact)
It makes sense to me, but on the literature for a certain flow meter we use, this conversion has the pressure and temperature ratios under a square root sign:
 scfm=acfm*sqrt((Pact/Pstd)*(Tstd/Tact))
The rep from this company told me that it is derived from the Ideal Gas Law AND Bernoulli's Equation, and that Bernoulli is required since the air is in motion.  I don't understand where Bernoulli would factor into this, since air is compressible.  Any help anyone could offer would be appreciated.  

RE: ACFM to SCFM conversion problem

The first equation, I use.

SCFM = ACFM*(T2a/T1a)*(P1a/P2a)

T1 = actual, deg R
T2 = standard, deg R
P1 = actual (psia)
P2 = standard (psia)
 

RE: ACFM to SCFM conversion problem

The first equation is what is regularly used.  The flow meter equation comes into play because that is flow within a pipe.

RE: ACFM to SCFM conversion problem

pcvallin,
The rep was blowing smoke up your pant legs and you were enjoying it.  Bernoulli has nothing to do with this conversion, but not because air is compressible.  The Bernoulli equation is used to determine lift of AIRPLANES, which fly in AIR for goodness sake.  The Bernoulli Equation is irrelevant for the same reason the Coulomb's Law is irrelevant--neither has anything to do with what you are trying to do.

The square root of the quantity pressure over temp is a very common term in many inferential measurement devices (like square edged orifice measurement which infers a flow rate from a dP at a pressure and temperature), but that term is multiplied times a meter-specific constant that embodies orifice size, pipe size, unit conversions, and various fluid-specific coefficients.  

In the conversion of actual flow rate of a specific fluid at a given pressure and temperature to volume flow rate at at "standard" temperature and pressure there is no square root.  I put "standard" in quotes because STP is anything but standard, it is a contractual/regulatory set of values that must be selected for each operation.

The only problem I see with your basic equation is that if your actual pressure is much over 44 psig (305 kPag) then you have to include compressibility (it goes with the temp term, i.e., T(a) should be [T(a)Z(a)]).  Below about 3 bar(g) it doesn't make enough of a difference to matter except in custody transfer.

Psafety,
Your designators are about as confusing as any that I've ever seen and I've been doing this a long time.  There really isn't any reason to make this particular problem any more complex than it started with.  In fact, if I've puzzled it out properly, then your equation is wrong.  The correct equation is (the time is immaterial, you would use the same equation for SCFM or MCF/day):

SCF = ACF [(Pact*Tstd*Zstd)/(Pstd*Tact*Zact)]

The way I'm interpreting your subscripts it looks like you have reversed the actual and standard (I just looked for the 8th time and your equation looks correct this time, but dang it was a challenge--I guess I was confused by temp being first and everything haveing an "a", now  I'm assuming that the "a" in your equation means "absolute" not "actual").

David

RE: ACFM to SCFM conversion problem

The combined Boyle's and Charles's Law from high school chemistry (or was it Physical Science in the 7th grade) is the most simple explanation:

P1V1/T1 = P2V2/T2

It rearranges to:

V2 = V1(P1/P2)(T2/T1)

Remember to use absolute temperatures (oK or oR) and pressures (psia).
 

Good luck,
Latexman

RE: ACFM to SCFM conversion problem

I learned that equation as the "Ideal Gas Law" which has helped me keep it in perspective for real gases since the 60's.  For a real gas you need a compressibility term.

David

RE: ACFM to SCFM conversion problem

One and the same.  I've also seen it called the "Combined Gas Law".  A rose by any other name . . .  

Good luck,
Latexman

RE: ACFM to SCFM conversion problem

Yeah, but my point was that the word "Ideal" reminds me to use compressibility.

David

RE: ACFM to SCFM conversion problem

pcvallin:

I have come across this before with respect to turbine meters.  The ideal gas treatment is correct for displacement meters.  However, turbine meters are inferential meters and the square root expression is correct.  I used to have a Rockwell turbine meter handbook that gave a pretty good explanation of this.  Essentially, what you are doing is making a correction on a flow rate rather than on displacement volume.

RE: ACFM to SCFM conversion problem

You know, I think you are mistaken, the "Ideal Gas Las" is PV = nRT.  I don't see why we're talking about compressibility.  I don't think the OP gave any indication that complexity was needed.  Nope, he didn't.

Good luck,
Latexman

RE: ACFM to SCFM conversion problem

vzeos,
You couldn't be more wrong.  Every commercial flow meter is inferential.  A turbine meter infers a volume from the speed of the rotor (which includes some optimistic assumptions about the displacement per pulse).  A Vortex meter infers a volume from inferring a number of Von Karmen streets from pressure variations.  An Ultrasonic meter infer es a volume from a shift in sound frequency.  Coriolis meters infer a volume from the movement of a pipe.  It goes on and on.  Counting molecules in the field is beyond us.

Several of the commercial meters will give you an ACF value and the coversion to SCF is the equation above.  All sorts of fancy arithmetic is required to create the ACF number, but to go on to the SCF is a pretty simple ratio.  But the bottom line is that any time you have an ACF value from any source, you can convert it an SCF (at whatever standard you want to use) with that equation.  No square roots required.

Latexman,
I brought up compressibility because the error in the conversion from ACF to SCF gets pretty significant very quickly above 3 barg.  The OP is talking about air which is really close to an ideal gas so it isn't terribly important to him, but others will read this thread and might be looking at something like Natural Gas that is distinctly non-ideal.

Boyle's Law, Charles' Law, and the Ideal Gas Law were all developed for a single chunk of gas at a measured set of conditions. If you take the Ideal Gas Law for one temperature and pressure and divide it by the Ideal Gas Law for another temperature and/or pressure (with the same number of gas molecules) then you get the equation that you put above.  Is it still the Ideal Gas Law?  I don't know or care.  I call that equation a useful version of the Ideal Gas Law.

David

RE: ACFM to SCFM conversion problem

"I call that equation a useful version of the Ideal Gas Law."

I don't.

Good luck,
Latexman

RE: ACFM to SCFM conversion problem


Quote (zdas04):

You couldn't be more wrong.

I'm very impressed!!

RE: ACFM to SCFM conversion problem

If I could add... Bernoulli is valid for any fluid, be it gas or liquid.  Both gas and liquids are compressible, although liquids much less than gas.  The use of Bernoulli implies a differential measurement between two points is being taken.

Compressibility factors for gases and (its inverse, the bulk modulus for liquids) become increasingly significant as either pressure OR temperature deviate farther away from the specific fluid's reduced pressure and temperature, as you can see in the following chart,

The ideal gas equation of state is modified to account for nonideal behavior by the introduction of the compressibility factor z as follows,
P1 * V1 / z1 / T1 = P2 * V2 / z2 / T2

where z1 and z2 are values at Pn and Tn, respectively.

https://www.e-education.psu.edu/png520/m8_p2.html

**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/

RE: ACFM to SCFM conversion problem

BigInch,
I don't know why I can't help being a pedantic jerk in this thread, but apparently I can't help myself.  Bernoullis equation applies to any [b]Newtonian[/b} fluid (i.e., stress varies lineraly with strain).  Fluids such as paint and toothpaste do not behave like the equation predicts.

David

RE: ACFM to SCFM conversion problem

The Bernoulli equation parameter for headloss (should you desire to include flow effects) between the two points is simply Hl.  Bernoulli did not define how to calculate that.  The Bernoulli equation does not therefore care in itself how you chose to model Hl.  If the effects of friction factor for flow for compressible gas, a nearly incompressible liquid, or a Bingham plastic, or any other variant of a nonlinear shear stress vs shear rate function is to be modeled using some different equation for Hl, how that is to be done is left up entirely to you.  Otherwise you can simply substitute some variant of the Darcy equation, Panhandle, Churchill or any other more common equation used to calculate the friction factor and arrive at something to substitute in place of Bernoulli's general Hl parameter.

Wasn't that a stroke of genius on the part of Mssr. Bernoulli?

**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/

RE: ACFM to SCFM conversion problem

(OP)
Thanks everyone, I believe this discussion answers my question; for the relatively low pressures we'll be dealing with, it seems that the ideal gas ratios should suffice.

RE: ACFM to SCFM conversion problem

pcvallin:

What kind of meter were you talking about?  

RE: ACFM to SCFM conversion problem

(OP)
The meter in question is a variable-area flow meter.

RE: ACFM to SCFM conversion problem

pcvallin:
This is interesting,  the square root equation you posted is very similar to the turbine meter minimum capacity equation for elevated pressure Pg:

Qmin @ Pg = Q min @ 0.25 psig * √((Pg + Pa)/ Pb)) √(0.60/G) √S
where Pg = gauge press., Pa = atmos. press., Pb= base press., G = Gas Specific Gravity, S = Compressibility Ratio.)

Is it possible that the square root equation your vendor gave you is the means of calculating minimum flow capacity of variable-area flow meters and not a means of converting acfm to scfm?
 

RE: ACFM to SCFM conversion problem

That makes more sense.

David

RE: ACFM to SCFM conversion problem

sorry for the diversion, but we called PV=nRT the "pervert" equation in OP's class.

RE: ACFM to SCFM conversion problem

That's just a typical equation used for calculating gas flowrate across any flow resisting, element given the differential pressure.  Its Q at any pressure, just that the flowrate the meter is reading is at a pressure of 0.25 psig, therefore they are just ratioing that to Pg.

In other words, both are basically the same equation.  Although vezos has printed the equation corrected for standard pressure, there being the a pressure of 0.25 psig, ie. Pb = 14.69 psia + 0.25 psig and also shows the correction for a typical natural gas specific gravity of 0.6 / G, G being that of air = 1.00.  Air flow is assumed in the OP's equation.


 

**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/

RE: ACFM to SCFM conversion problem

When its corrected to a base pressure, Pb = meter reading pressure, or some other base pressure you care to define in a sales contract, effectively you have converted to STANDARD cf.

If you want to divide by time, go ahead and you get cubic feet, or multiply by time and get a flowrate.

**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/

RE: ACFM to SCFM conversion problem

dcasto,

Two curiousities.

What's "OP's class"?  The only thing I can think of is Unit Operations.

Why "pervert"?  Emil Clapeyron is credited to be the first person to write PV=nRT in 1834 from Boyle's, Charles', Guy-Lussac's, and Avogadro's Laws.  Is there something about Emil we might like to know about?

Good luck,
Latexman

RE: ACFM to SCFM conversion problem

I would think that if you have a reasonable idea of the RMM and the ACFM of the gas, the conversion to SCFM via the consideration of mass would be somewhat straightforward, as the Z-factors for various temperatures and RMMs are charted in GPSA.

Regards,

SNORGY.

RE: ACFM to SCFM conversion problem

Yes it is, just the point here is this application is a low pressure meter where z factors are = 1.

**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/

RE: ACFM to SCFM conversion problem

Here is what Lake Monitors uses to correct their scfm meter reading actual conditions to scfm at their meter calibration conditions where the meter reads directly in scfm:
http://www.lakemonitors.com/pneumatic_flow.htm

Ted

RE: ACFM to SCFM conversion problem

Yeah, I think it was unit ops where we used the pv rt equation, notice the letter oreintation

RE: ACFM to SCFM conversion problem

Good one!

Good luck,
Latexman

RE: ACFM to SCFM conversion problem

"That's just a typical equation used for calculating gas flowrate across any flow resisting, element given the differential pressure......"

The minimum capacity equation for elevated pressure does not calculate the flowrate across any flow resisting element.  It calculates the minimum flowrate that the meter can be expected to give an accuracy greater than 1%.  Since the meter infers the gas flowrate from the gas stream velocity it is necessary to adjust the minimum allowable flowrate when metering at pressures greater than 0.25 psig because the gas stream velocity deminishes as the metering pressure increases and we need to maintain at least a minimum velocity.  The metering pressure of 0.25 psig is an industry standard for catalog capacities.


I should point out that the turbine meter maximum capacity equation for elevated pressure Pg does not contain any square roots nor specific gravity.  This equation is similar to the pressure factor adjustment for displacement meters:

Qmax @ Pg = Q max @ 0.25 psig * ((Pg + Pa)/ Pb) * S
where Pg = gauge press., Pa = atmos. press., Pb= base press., S = Compressibility Ratio.)
 

RE: ACFM to SCFM conversion problem

The rep. confused the ACFM/SCFM conversion with an equation that is used to convert an observed variable area flowmeter reading at nonstandard conditions into an ACFM reading.


SCF = ACF [(Pact*Tstd*Zstd)/(Pstd*Tact*Zact)]

Actual volumetric flow =
(Observed Flowmeter Reading)*SQRT{ [(Pact*Tstd*Zstd)/(Pstd*Tact*Zact)]}

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