FLARES - NOISE LEVEL

L = NOISE INTENSITY PARAMETER, WHICH DEPENDS ON PRESSURE RATIO ACROSS THE SAFETY VALVE RELEASING INTO THE STACK HEADER ( RELATION WITH PRESSURE GIVEN BELOW )

M = MASS FLOW RATE THROUGH SAFETY VALVE RELEASING TO FLARE STACK, slugs/Sec. [ 1 slug/Sec. = 32 lb/Sec. ]

C = SPEED OF SOUND IN THE WASTE GAS, ft/Sec.

= 223 * [ K * T / M_w ]^0.5 WHERE

K = C_p / C_v OF THE GAS

T = GAS TEMPERATURE, ^O R AND

M_w = MOLECULAR WEIGHT OF THE GAS, lb/lb mol.

IF P_r = PRESSURE RATIO ACROSS THE SAFETY VALVE

= UPSTREAM PRESSURE / DOWNSTREAM PRESSURE OF SAFETY VALVE

THEN THE RELATION BETWEEN PRESSURE RATIO AND NOISE INTENSITY PARAMETER, L IS AS FOLLOWS :

FOR P_r < 2.9

L = 13.3 + 88.1 * Log₁₀ P_r

FOR P_r > 2.9

L = 51.9 + 5.06 * Log₁₀ P_r

HERE L IS NOISE INTENSITY PARAMETER THAT IS USED TO CALCULATE THE NOISE INTENSITY FROM STACK & P_r IS PRESSURE RATIO AS DEFINED ABOVE.

SO USING THE ABOVE EQUATIONS, ONE CAN FIND OUT NOISE LEVEL AT 100 ft FROM THE STACK. THE FOLLOWING EQUATION CAN BE USED TO ESTIMATE NOISE LEVEL FOR DISTANCES THAT DIFFER FROM THE 100 ft - REFERENCE BOUNDARY :

L_p = L₁₀₀ - 20 * Log₁₀ ( r /100 )

WHERE

L_p = NOISE LEVEL AT DISTANCE r, dB

r = DISTANCE FROM THE SOUND SOURCE, ft

L₁₀₀ = NOISE INTENSITY AT 100 ft FROM STACK,dB

EXAMPLE : FOR A FLARE STACK, IF THE MAXIMUM GAS FLOW RATE IS 200,000 lb/Hr., THE PRESSURE RATIO IS 3.0 AND THE GAS TEMPERATURE IS 150⁰F, WHAT IS THE NOISE LEVEL 400ft FROM FLARE STACK. ASSUME A GAS MOLECULAR WEIGHT OF 54 AND THE K (C_p/C_v) OF 1.1.

SOLUTION : SINCE P_r> 2.9, L = 51.9 + 5.06 * Log₁₀P_r

SO L = 51.9 + 5.06 * Log₁₀(3.0) = 54.3

FOR T = 150⁰F = 610⁰R, C = 223*[ (K*T) / M_w]^0.5

C = 223 * [ 1.1 *610 / 54 ]^0.5 = 786 ft / Sec.

GAS FLOW RATE = 200,000 lb/Hr.=55.6 lb/Sec.

= 1.74 slugs/Sec.

SO, L₁₀₀ = 54.3 + 10 * Log₁₀[ 0.5 * 1.74 * 786² ]= 111.6 dB

SO, NOISE LEVEL AT A DISTANCE OF 400 ft IS :

L₄₀₀ = 111.6 - 20 * Log₁₀ [ 400 / 100 ]

= 99.6 dB.