Modeling an Unconfined Liquid Spill on a Sloped Surface

When determining the consequences of a vapor cloud or fire from a liquid spill, the area of the liquid pool is a key variable.  If the pool is contained by walls or berms, dispersion or flame parameters can be evaluated directly from the pool area using correlations that are well known to consequence analysts.  For a spill onto an unconfined paved area or sloping deck, there is no simple formula for the pool area.  For an unconfined pool, area must be calculated from flow modeling.  The progressive movement and size of a liquid spill onto a sloped surface can be accurately modeled using the Darcy formula for fluid flow, or other formula using an empirical friction factor.  The Darcy equation is very well known, but many engineers are acquainted only with the application of frictional flow formula within round piping.  The formulas for piping can be applied to a more-or-less flat spill surface by including a correction for the ratio of flow area to wetted area of the frictional surface.  For uncomplicated flow surfaces, spreadsheet calculation is sufficient.  In addition to modeling the shape of a pool as it spreads, the question should be answered: “At what point is the spill thickness too low to produce a toxic or fire hazard?”  This question can be answered by running typical consequence analysis models and comparing the results for different thicknesses to published probit criteria for harm from absorbed toxic chemicals or radiant heat.

Outline:

• Overview
• Release Model trajectory, droplet size
• Darcy Formula general, sloping surface, dynamic case, limitations
• Minimum Pool Thickness surface factors, hazard criteria
• Example 1 evaporation from truck unloading driveway
• Example 2 flammable spill on checker-plate deck
• References