We will see in section 4 that the total pressure drop across a length
of transport line has in general six components:
1. pressure drop due to gas acceleration
2. pressure drop due to particle acceleration
3. pressure drop due to gas-to-pipe friction
4. pressure drop related to solid-to-pipe friction
5. pressure drop due to the static head of the solids
6. pressure drop due to the static head of the gas
Fig. 3. Phase diagram for dilute phase vertical transport, showing
the general relationship between pressure gradient 
p /
L and gas velocity for a vertical transport line.
Curve AB represents the frictional pressure loss due to gas only
in a vertical transport line.
Curve CDE is for a solids flux of G1.
Curve FG is for a higher feed rate G2.
At point C the gas velocity is high, the concentration is low, and frictional
resistance between gas and pipe wall predominates. As the gas velocity is decreased
the frictional resistance decreases, but since the concentration of the suspension
increases the static head required to support these solids increases.
If the gas velocity is decreased below point D then the increase in static head
outweighs the decrease in frictional resistance and
p / L rises again.
In the region DE the decreasing velocity causes a rapid increase
in solids concentration and a point is reached when the gas can no longer entrain
all the solids. At this point a flowing, a slugging fluidized bed is formed
in the transport line. The phenomenon is known as "choking"
and is usually attended by large pressure fluctuations.
The choking velocity, UCH is defined as the lowest velocity at which
this dilute phase transport line can be operated at the solids feed rate G1.
At the higher solids feed rate, G2, the choking velocity is higher.
The choking velocity marks the boundary between dilute phase and dense phase
vertical pneumatic transport. Note that choking can be reached by decreasing
the gas velocity at a constant solids flow rate, or by increasing
the solids flow rate at a constant gas velocity.
It is not possible to theoretically predict the conditions for choking to occur.
However, many correlations for predicting choking velocities are available
in the literature. Knowlton (1986) recommends the correlation of Punwani (1976),
which takes account of the considerable effect of gas density.
This correlation is presented below:
(Eq. 1 and Eq. 2)
where
CH is the voidage in the pipe at the choking velocity UCH
p is the particle density
f is the gas density
G is the mass flux of solids (= Mp / A)
UT is the free fall or terminal velocity, of a single particle in the gas
(Note that the constant is dimensional and that S.I. units must be used).
Equation 1 represents the solids velocity at choking and includes
the assumption that the slip velocity USLIP is equal to UT
(see section 4 below
for definition of slip velocity). Equations 1 and 2 must be solved simultaneously
by trial and error to give CH and UCH.
