How to calculate flame length for flare stack calculation without using figure-7/8 of API? Any Empirical formula with Reference and Basis available?
Dear Bhavin Sheth,
Flare stack height
The height is generally based on the radiant-heat intensity generated by the flame
According to The Hajek and Ludwig equation
D =(τE Q/4ᴨK)0.5
Where
D=minimum distance from the midpoint of the flame to the object being considered, ft;
E=fraction of heat radiated;
K=allowable radiation level, BTU/hr-ft2
Q=heat release (lower heating value), BTU/hr; and;
τ=fraction of heat intensity transmitted, defined by following equation Equation
τ = 0.79(100/r)1/16 (100/R)1/16
Where
r=relative humidity, fraction;
R=distance from flare center, ft;
And
τ=fraction of heat transmitted, in range of 0.7 to 0.9.
Velocity Determination. The sonic velocity of a gas can be calculated with
Vs =(1720kTZ/S)1/2
Gas velocity can be determined from
V =(60 Qg T Z)/di2 PCL
and the critical flow pressure at the end of the relief system can be calculated with
PCL = (2.02)Qg/di2 X {(TS/k(k+1)}1/2
Where
di=pipe inside diameter, in.
k=ratio of specific heats, CP/CV;
PCL=critical pressure at flare tip, always ≥ 14.7, psia;
Qg=gas-flow rate, MMscf/D;
S=specific gravity, ratio;
T=temperature,
°R;V=gas velocity, ft/s;
VS=sonic velocity, ft/s
;and Z=gas compressibility at standard conditions,
where air = 1, psi −1 .
API FLAME LENGTH: 0.00604*(heat release)^0.4776
SONIC FLAME LENGTH: 0.004503 * (heat release)^0.459882
EFFECTIVE FLAME LENGTH: (1- Tip MACH Number) *API Flame Length + (Tip MACH Number * Sonic Flame Length)
Milton Beychok fitted the data points from API STD 521 in his book "fundamentals of stack gas dispersion". The result for flame height is shown on the Book cover
hfv = 0.0042*Q^0.478
Q is heat released (lower heating value) in BTU/hr hfv is flame height in feet
Since he assumed a 45 degrees angle, the flame length is:
Flame length = 0.0059*Q^0.478
Reagrds,
Prem Baboo
As a rule of thumb, flame effective length is calculated based on following experimental equation:
L=A* Q^B
Where Q is duty of burner and A , B are constant. A and B are experimental values.
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