Gas Volume to Reach LEL, Stoichiometric, and UELFor propane and other heavier-than-air gases stored as liquid

What this calculates

This sheet calculates the volume of liquid propane (inside a storage tank) that would be required to reach the LEL, stoichiometric and UEL mixtures in a compartment.

It could also be used to calculate other gases that are stored as liquid (under pressure) in a tank and are heavier than air when at ambient pressure. In this case the values of cells C7 through C12 would need to be adjusted to be appropriate to the other gas.

This spreadsheet does not do any conversions to metric, as the gas industry in the US generally uses British units.

How to use it

Enter the area of the compartment in which the leak is suspected into cell C3. If multiple rooms are open to each other, the area for all of them should be included.

Enter the height of the leak in cell C4. The calculation assumes that because propane is heavier than air it will only fill the volume below the level of the leak.

The LEL, stoichiometric mixture and UEL of propane are entered in cells C7 through C9 (2.1%, 6.26% and 9.5%). The vapor density and liquid density for propane are provided in cells C11 and C12 (0.097 lb/ft3 and 36.2 lb/ft3). These should be left as is, unless you need to look at other gasses or have different local data for propane.

Variables

A
Area of compartment [ft²]
H
Height above or below leak [ft]
V
Compartment volume below leak [m³]
V_g
Volume of gaseous fuel at the target mixture [ft³]
V_L
Equivalent volume of liquid fuel [gal]
m_g
Weight of gaseous fuel [lb]
ρ_v
Vapor density of gas [kg/m³]
ρ_L
Liquid density of gas [kg/m³]
LEL, stoich, UEL
Lower / stoichiometric / upper flammability limit [% by volume]

Equations

$$ V = A \cdot H $$Compartment volume below leak
$$ V_{g} = \text{mixture}\,\% \times V $$Gaseous fuel volume to reach a target mixture
$$ m_{g} = V_{g} \cdot \rho_{v} $$Weight of gaseous fuel
$$ V_{L} = \dfrac{ m_{g} }{ \rho_{L} } $$Equivalent volume of liquid fuel

Discussion

This is a simplified equation intended to determine a rough idea of the mixture that will be formed in a space given different amounts of liquid fuel in a storage tank.

Worked example

Example

A 20’ x 10’ basement contains a pipe running from an above-grade propane storage tank. The pipe is knocked loose, causing a leak at 5’ above the floor. How much liquid (from the tank) is required to reach the LEL, stoichiometric ration and UEL in that space?

Calculate the area of the basement as 20x10 = 200 square feet, enter this into cell C3. Enter the leak height of 5 into cell C4. Leave all the other “green cells” at the default properties of propane.

The liquid volumes should be:

LEL = 0.4 gallons

Stoichiometric = 1.3 gallons

UEL = 1.9 gallons

References

  1. Propane and other gas properties — www.engineeringtoolbox.com and the SFPE Handbook of Fire Protection Engineering.
  2. Liquid-to-gallon conversion uses 7.48052 gallons per cubic foot.