Process Safety Management, Combustion Engineering & Hazard Analysis
Le Chatelier Flammable Gas Mixture LEL & NFPA 69 Formula
Calculate Mixed Combustible-Gas Concentration in Air (vol%), Le Chatelier Mixture Lower Explosive Limit LEL_mix (vol%), Stream %LEL Fraction, and NFPA 69 25% LEL Interlock Status.
Never take an arithmetic average of gas LELs—Le Chatelier’s harmonic rule governs ignition!
When a vent header or battery-room exhaust carries multiple flammable gases in air—such as Methane (LEL = 5.0 vol%), Propane (LEL = 2.1 vol%), and Hydrogen (LEL = 4.0 vol%)—taking a simple weighted average of LELs dangerously overpredicts the mixture explosion threshold! Under Le Chatelier’s Flammable Mixing Law, Mixture LEL (in vol% of total air+fuel stream) is the harmonic fuel-weighted sum LEL_mix = (y_1 + y_2 + y_3) / (y_1 / LEL_1 + y_2 / LEL_2 + y_3 / LEL_3), and the stream’s Composite %LEL simplifies directly to %LEL = (y_1 / LEL_1 + y_2 / LEL_2 + y_3 / LEL_3) * 100! Under NFPA 69 Standard on Explosion Prevention Systems, unmonitored exhaust ducts must stay strictly below 25% LEL!
Verify on a Petrochemical Vent Stream in Air—Methane_VolPct = 0.60% (LEL = 5.0%, B2), Propane_VolPct = 0.30% (LEL = 2.1%, B3), Hydrogen_VolPct = 0.30% (LEL = 4.0%, B4), and NFPA69_Trip_Threshold = 25.0% LEL (B5): Total Fuel Concentration is 1.20 vol% (E2), Le Chatelier Mixture LEL equals 1.20 / (0.60/5.0 + 0.30/2.1 + 0.30/4.0) = 3.55 vol% (E3), Composite %LEL hits 33.79% LEL (E4), and Interlock Status triggers "TRIP: >=25% LEL" (E5)!
| Le Chatelier Vent Safety KPI (0.60% CH4, 0.30% C3H8, 0.30% H2 in Air) | Formula | Verified Output |
|---|---|---|
| Total Combustible Gas (vol%) | y_CH4 + y_C3H8 + y_H2 | 1.20% (0.505% Diluted) |
| Le Chatelier Mixture LEL (vol%) | y_tot / (y_CH4/5.0 + y_C3H8/2.1 + y_H2/4.0) | 3.55% (3.74% Diluted) |
| Stream Composite %LEL (%) | (y_CH4/5.0 + y_C3H8/2.1 + y_H2/4.0) * 100 | 33.79% LEL (13.50% Diluted) |
| NFPA 69 25% LEL Interlock Gate | IF(Pct_LEL >= Limit, "TRIP: >=25% LEL", "SAFE: <25% LEL") | TRIP: >=25% LEL |
Le Chatelier Harmonic Mixture LEL Formula
Validate non-negative component vol% with Total_Fuel > 0 and Total_Fuel < 100, and NFPA_Limit in (5, 50]!
=LET(y_c1, B2, y_c3, B3, y_h2, B4, lm_p, B5, y_tt, y_c1 + y_c3 + y_h2, IF(OR(y_c1 < 0, y_c3 < 0, y_h2 < 0, y_tt <= 0, y_tt >= 100, lm_p <= 5, lm_p > 50), "Invalid Gas Mixture Input", ROUND(y_tt / (y_c1 / 5 + y_c3 / 2.1 + y_h2 / 4), 2)))Sweep-Air Dilution Interlock Clearance Check (0.30% CH4, 0.105% C3H8, 0.10% H2)
Increase dilution sweep air to cut concentrations to B2 = 0.30%, B3 = 0.105%, and B4 = 0.10%: Mixture LEL E3 shifts to 3.74 vol%, Composite %LEL E4 drops to 13.50% LEL, and Interlock Gate E5 clears to "SAFE: <25% LEL"!
=IF(ISTEXT(E3), E3, IF(E4 >= B5, "TRIP: >=25% LEL", "SAFE: <25% LEL"))Try the example
Use the original values or change them to test your understanding.