Conversions of Volumetric Flow Rate to Mass Flow Rate 1

[MattC1234]

Hi Guys

I am trying to put together a spreadsheet, whereby a volumetric flow rate can be input, along with the properties of the fluid (IE Molecular Weight, Compressibilty and Specific Heat Ratio) and the process conditions (IE Temperature and Pressure), then this can be converted into mass flow rate of the fluid.

I am trying to do this for Nm3/hr, Sm/hr and mmSCFD and guess what the required mass flow is in kg/hr.

Obviously i have read up on conversions and the conditions for the measurement of the Nm3/hr and Sm3/hr been important. I would say that the Nm3/hr was at 0degC and the standard at 15degC.

The various conversions i have looked at on my travels are giving me a much higher value for the mass flow rate than for the volumetric one. However i am trying to calculate the Cv of a valve (whereby this is calculated in either Nm3/hr or in Kg/hr).

I know that Cv = Q / (2.12E3 x p1 x Y ) * (SQRT (( M x T1 x Z)/ X)

Y is the expansion factor of the gas and is calculated by:
1 - ( X / 3Fy x XT ) (XT is constant set by manufacturer in this case 0.8) (Fy is the specific heat ratio factor which is the specific heat ratio of the gas / 1.4)

M is molecular weight
T1 is inlet temp in Deg K
X is ratio of pressure differential to inlet pressure (delta p / p1 )

Q = Nm3/hr

There is also a seperate equation for calculating Cv if the flow rate is in kg/hr:

Cv = ( W / ( 94.8 x p1 x Y )) * SQRT((T1 x Z)/ (X x M))

The calculated Cv should be the same if i convert the mass flow into vol flow or vice versa... however it isn't working that way.. Thus i need some help.

The example i am working is, is 10000 Sm3/hr, Z=0.96, M=18, and Specific heat Ratio of 1.33.

p1=30bara , p2=15bara and T1 = 523K.

W=kg/hr

I would appreciate any input, especially one where the answer is given! Lol

Cheers Folks

Matt

 

[zdas04]

As they say in Vegas, you are making your point the hard way. To convert a volume flow rate to a mass flow rate you multiply the volume flow rate by the density of the gas. For "standard" or "normal" flow rates, you calculate that density as though the gas were actually at your standard or normal conditions. That is all there is to the conversion. You don't need expansion factors or any of that stuff. That was already included in the arithmetic used to calculate the volume flow rate you are starting with.

To get the volume flow rate from one base to another, you convert to mass flow rate and then divide by the new implied density (i.e., sm^3/hr=nm^3/hr * rho@nm^3/rho@sm^3. Very easy with none of the empirical crap like expansion factors or Cv's.

By the way, none of the "standard" or "normal" pressures or temperatures are actually standard or normal. Every contract, every jurisdiction, every manager has every right to require volumes to be reported at whatever pressure and temperature makes them happy. 15C is often used for a temperature, but 15.6C is just as common. 101.3 kPa is often used as a base pressure, but 100.8 kPa also shows up. In the spreadsheet you are working on you should accept a volume, a volume unit (MMSCF/d, m^3/hr, or whatever), Specific Gravity, an input pressure, an input temperature, an output temperature, and then calculate the mass flow rate and the converted volume flow rate. Any assumptions of "standard" or "normal" will lead you down an stupid path.

David

 

[dcasto]

by the way, the 8.4 mmscfd (16600 lb/hr density of .0477 lb/cf at 14.696 and 60F ) going from 420 to 205 psig mmscfd requires a Cv of 29.2 with a Cf of .8. Thats a good 2" full port valve. Use this as a sanity check on your spread sheet.