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Gas flow through an Orifice

Gas flow through an Orifice

Gas flow through an Orifice

I am building an spreadsheet which would calculate the time needed to depressure a gas pipeline. The spreadsheet will calculate the depressurizing time for two scenarios.
Scenario 1 - the ppl is depressurized using a pipe with high opening valve. (flow calculations are done using Fisher universal Gas/Vapor formula).
Scenario 2 - the ppl is depressurized using a tailpipe and an orifice. In this case flow through the orifice is calculated using the formula:

Q = 16,330 (1 + β^4) (d2) (H (29.32 + 0.3H))^0.5 • Ftf • Cg (Eq 3-12 GPSA).

When I checked the calculated results against those calculated from a flare simualtion software (Flaretot), the results for the case 2 where VERY different. I checked and rechecked the calculation but the results were still very different. Then I used an very simple formula which the testers use on the field, which calculates the flow rates based on downstream flow pressure (Pf) and a the choke coefficient (C);

Flow rate formula is: Q = C * ( Pf + 101.3)

Choke sizes and coefficients in SI for different choke sizes are as follow:
# Inches mm Coefficients (m3/d/kPa)
4/64 0.0625 1.59 0.3460
6/64 0.0938 2.38 0.7620
8/64 0.1250 3.18 1.4312
10/64 0.1563 3.97 2.2660
12/64 0.1875 4.76 3.2865
14/64 0.2188 5.56 4.5361
16/64 0.2500 6.35 5.8736
20/64 0.3125 7.94 9.0312
24/64 0.3750 9.53 12.8515
28/64 0.4375 11.11 18.4183
32/64 0.5000 12.70 23.1221
36/64 0.5625 14.29 28.5498
40/64 0.6250 15.88 34.9715
48/64 0.7500 19.05 51.0870
56/64 0.8750 22.23 70.2701
64/64 1.0000 25.40 92.3574
1 1/8 1.1250 28.58 118.2894
1 1/4 1.2500 31.75 149.3343
1 3/8 1.3750 34.93 183.4877
1 1/2 1.5000 38.10 227.5804

Surprisingly the rates (and times) calculated by this formula matched very closely those calculated by the software.
I have no other information on this formula and Google was no joy, so my question is:
Can somebody point on some literature which deals with this formula (how is derived, any possible limitations and wher it can be used…)

RE: Gas flow through an Orifice

It looks pretty much an orifice flow equation with some numbers thrown in to limit the max pressure drop and adjust some units.

RE: Gas flow through an Orifice


A presentation about chokes found here: https://www.aiche.org/sites/default/files/cep/2013... These factors are called as positive choke factors. Based on that presentation it seems that these factors have been derived based on SG = 1; gas temp t = 60F and for critical flow.
Some of these factors in imperial units are:
...............Bore Diam.....Choke Coefficient

What baffles me is the fact that this formula cannot be found in literature and the very different results that produces when compared with GPSA 3.12 formula.

RE: Gas flow through an Orifice

I wouldn't worry too much about that. Choke valves have vastly different coefficients than do typical valves. In the vast majority of cases, these will be gate, ball or plug valves. A blowdown valve will usually be fully open and limited, if by anything, sonic velocity of the gas. Not the case for choke valves.

RE: Gas flow through an Orifice

Thanks for your input BigInch. The link to the spreadsheet however, seems to be broken. can you please reup.
Thanks again

RE: Gas flow through an Orifice

Thanks BigInch. I tested it and gave me very close results - 8% differennce with what I had calculated. But much more simple.
Thanks again BigInch

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