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Dispersion 7/151

concentration

c__

Ground level

-

Depressure wave
Figure 7.6 Vapor cloud from pipeline rupture

to find an ignition source or to harm living creatures. This A second simplifying parameter is the effect of molecular
should be reflected in the risk assessment. weight on dispersion. Molecular weight is inversely propor-
To fully characterize the maximum dispersion potential, tional to the rate of dispersion. A higher molecular weight tends
numerous scenarios run on complex models would be required. to produce a denser cloud that has a slower dispersion rate.
Even with much analysis, such models can only provide bound- A denser cloud is less impacted by buoyancy effects and air
ing estimates, given the numerous variables and possible turbulence (caused by temperature differences, wind, etc.) than
permutations of variables. So again, we turn to a few easily a lighter cloud. Using this fact yields another risk variable:
obtained parameters that may allow us to determine a relative product molecular weight.
risk ranking of some scenarios. An exact numerical solution is In the absence of more exact data, it is therefore proposed
not always needed orjustified. that the increased amount of risk due to a vapor cloud can be
Dispersion studies have revealed a few simplifying truths assessed based on two key variables: leak rate and product
that can be used in this risk assessment. In general, the rate molecular weight. Meteorological conditions, terrain, chemical
of vapor generation rather than the total volume of released properties, and the host of other important variables may be
vapor is a more important determinant of the cloud size. intentionally omitted for many applications. The omission may
A cloud reaches an equilibrium state for a given set of be justifiable for two reasons: First, the additional factors are
atmospheric conditions. At this equilibrium, the amount of highly variable in themselves and consequently difficult to
vapor added from the source theoretically exactly equals the model or measure. Second, they add much complexity an4
amount of vapor that leaves the cloud boundary (the cloud arguably, little additional accuracy for purposes of relative risk
boundary can be defined as any vapor concentration level). evaluation.
So when the surface area of the cloud reaches a size whereby Therefore, measures of relative leak rate and molecular
the rate of vapor escaping the cloud equals the rate entering the weight can be used to characterize the relative dispersion of a
cloud, the surface area will not grow any larger (see Figure released gas.
7.6). The vapor escape rate at the cloud boundary is governed
by atmospheric conditions. The cloud will therefore remain Liquid spill dispersion
this size until the atmospheric conditions or the source rate
change. This fact thus yields one quantifiable risk variable: Physical extent ofspill
leak rate.
So, given a constant weather condition, the cloud size is most The physical extent of the liquid spill threat depends on the
sensitive to the leak rate. The cloud will reach an equilibrium extent of the spill dispersion, which in turn depends on the size
where the rate of material added to the cloud balances the rate ofthe spill, the type ofproduct spilled, and the characteristics of
of material leaving the cloud, thereby holding the cloud size the spill site. The size of the spill is a function of the rate of
constant. The sensitivity is not linear, however. A IO-fold release and the duration. Slow leaks gone undetected for long
increase in leak rate is seen as only a 3-fold increase in cloud periods can sometimes be more damaging than massive leaks
size, in some models. that are quickly detected and addressed.