Page 345 - Dust Explosions in the Process Industries

3 74 Dust Explosions in the Process Industries

4.2.6.4
Theories of Minimum and Maximum Explosible Dust Concentrations

The first attempt to predict the minimum and maximum explosible concentrations for
dust clouds theoretically was probably made by Jaeckel (1924), who considered the
one-dimensional heat transfer from a plane flame front to the adjacent unburned layer
of dust cloud.
The minimum explosibleconcentration,accordingto Jaeckel, is the minimum amount
of dust, per unit volume of dust cloud, that by complete combustion liberates enough
energy to heat the next unit volume of dust cloud to the ignition temperature.This means
that the assumption of the existence of such a temperatureis as basic in Jaeckel’stheory
as the classical flame propagation theory of Mallard-le Chatelier (1883).
According to Jaeckel, the maximum explosible concentration arises from the fact that
the air contains a limited amount of oxygen, which is totally consumedby the complete
combustion of a given amount of dust, the stoichiometric concentration C,. A further
increase in the dust concentration therefore merely has the effect that more energy is
required for heating the next volume to the ignition temperature, since the excess dust
acts only as a coolant or heat sink.
Jaeckel (1924)formulatedthe condition for self-sustainedflame propagation through
the dust cloud of concentration C < C, at constant volume as

CQ2 L+(q -T0)(Cc, +d,c,) (4.68)
where
c, is the specific heat at a constant volume of the gas;
dgis the density of the gas;
Q is the heat of combustion of the dust;
cd is the specific heat of the dust particles;
Tois the initial temperature of the dust cloud;
Tiis the ignition temperature of the dust cloud;
L is the heat losses by radiation and conduction.

By equating the two sides and rearranging, one obtains the expression for the mini-
mum explosible concentration C,:

(4.69)

For dust concentrationsabove the stoichiometricconcentrationthe heat production is con-
stant and equal to Q x C,, whereas the heat consumption increases with the dust con-
centration. In this case, the condition for self-sustained flame propagation is
CsQ2L+(T -T,)(Ccd+dgc,) (4.70)

By rearranging, Jaeckel’s theoretical upper explosible limit becomes equal to

(4.71)