Gas flow through an Orifice

[YEngineer]

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…)

 

[BigInch]

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

 

[YEngineer]

A presentation about chokes found here:

https://www.aiche.org/sites/default/files/cep/20131068_r.pdf

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
.............(inches).......MCF/D/PSIA
4/64..........0.0625.........0.08
6/64..........0.0938.........0.188
7/64..........0.1094.........0.261
8/64..........0.125...........0.347
9/64..........0.1406..........0.444
10/64.........0.1563.........0.553
12/64.........0.1865.........0.802
16/64.........0.25............1.47
24/64..........0.375..........3.4
32/64..........0.5.............6.26

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.

 

[BigInch]

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.

 

[BigInch]

Here's a spreadsheet using the Pacific Gas & Electric method

 

[YEngineer]

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

 

[BigInch]

I'll try again,

 

[BigInch]

No "&" allowed in the filename.
It should work now.

 

[YEngineer]

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