5.1 Gas velocity
In both horizontal and vertical dilute phase transport it is desirable
to operate at the lowest possible velocity in order to minimise frictional
pressure loss, reduce attrition and running costs.
For a particular pipe size and solids flowrate, the saltation velocity
is always higher than the choking velocity. Therefore, in a transport system
comprising both vertical and horizontal lines, the gas velocity must be selected
to avoid saltation. In this way choking will also be avoided.
These systems would ideally operate at a gas velocity slightly to the right
of point D in Figure 4. In practice, however, USALT is not known
with great confidence and so conservative design leads to operate well
to the right of point D with the consequent increase in frictional losses.
Another factor encouraging caution in selecting the design velocity is the fact
that the region near to point D is unstable; slight perturbations in the system
may bring about saltation.
If the system consists only of a lift line then the choking velocity
becomes the important criterion. Here again, since UCH cannot
be predicted with confidence, conservative design is necessary.
In systems using centrifugal blower, characterised by reduced capacity
at increased pressure, choking can almost be self-induced. For example,
if a small perturbation in the system gives rise to an increase in solids
feed rate, the pressure gradient in the vertical line will increase (Fig. 3).
This results in a higher back pressure at the blower giving rise to reduced
volume flow of gas. Less gas means higher pressure gradient and the system
soon reaches the condition of choking. The system fills with solids
and can only be restarted by draining off the solids.
Bearing in mind the uncertainty in the correlations for predicting choking
and saltation velocities, safety margins of 50% and greater are recommended
when selecting the operating gas velocity.
5.2: Pipeline pressure drop
Eq. 15 applies in general to the flow of any gas-particle mixture in a pipe.
In order to make the equation specific to dilute phase transport,
we must find expressions for terms 3 (gas-to-wall friction)
and 4 (solids-to-wall friction).
In dilute transport the gas-to-wall friction is often assumed independent
of the presence of the solids and so the friction factor for the gas
may be used (the Fanning friction factor - see worked example on dilute
pneumatic transport).
Several approaches to estimating solids-to-wall friction are presented
in the literature. Here we will use the modified Konno and Saito (1969) correlation
for estimating the pressure loss due to solid-to-pipe friction
in vertical transport and the Hinkle (1953) correlation for estimating
this pressure loss in horizontal transport. Thus for vertical transport:
CD is the drag coefficient between the particle and gas.
Note: Hinkle's analysis assumes that particles lose momentum by collision
with the pipe walls. The pressure loss due to solids-wall friction is
the gas pressure loss as a result of re-accelerating the solids.
Thus the drag force on a single particle is given by:
Expressing this in terms of a friction factor, fp we obtain
Equations 17 and 19.
Equation (15) relates to pressure losses along lengths of straight pipe.
Pressure losses are also associated with bends in pipelines and estimations
of the value of these losses will be covered in the next section.
5.3: Bends
Bends complicate the design of pneumatic dilute phase transport systems,
and when designing a transport system it is best to use as few bends as possible.
Bends increase the pressure drop in a line, and also are the points
of most serious erosion and particle attrition (Fig. 6).
Fig. 6: Example of wear on a dilute-phase pneumatic conveying pipe
Solids normally in suspension in straight, horizontal, or vertical pipes
tend to salt out at bends due to the centrifugal force encountered
while travelling around the bend. Because of this operation, the particles
slow down and are then re-entrained and re-accelerated after they pass
through the bend, resulting in the higher pressure drops associated with bends.
There is a greater tendency for particles to salt out in a horizontal pipe
which is preceded by a downflowing vertical to horizontal bend than
in any other configuration. If this type of bend is present in a system,
it is possible for solids to remain on the bottom of the pipe for very long distances
following the bend before they redisperse. Therefore, it is recommended that
downflowing vertical to horizontal bends be avoided if at all possible
in dilute phase pneumatic transport systems.
As noted above, bends increase the pressure drop in a transport system.
In addition to the pressure drop due to the bend itself, because the bend
slows down the solids there is also a pressure drop due to subsequent particle
re-acceleration by the gas. The length of straight pipe needed before the solids
re-attain their steady state velocity can be considerable.
Fig. 7: Examples of long-radius bends used in pneumatic conveying lines
to reduce wear and pressure losses.
Fig. 8: Blinded Tee bend
In the past, designers of dilute phase pneumatic transport systems intuitively
thought that gradually sloped, long radius elbows (Figure 7) would reduce the erosion
and increase bend service life relative to 90 degree elbows. Zenz (1964), however,
recommended that blinded tees (Fig. 8) be used in place of elbows
in pneumatic transport systems. The theory behind the use of the blinded tee
is that a cushion of stagnant particles collects in the blinded or unused branch
of the tee, and the conveyed particles then impinge upon the stagnant particles
in the tee rather than on the metal surface, as in a long radius or short radius elbow.
Bodner (1982) determined the service life and pressure drop of various bend configurations.
He found that the service life of the blinded tee configuration was far better
than any other configuration tested and that it gave a service life 15 times greater
than that of radius bends or elbows. This was due to the cushioning accumulation
of particles in the blinded branch of the tee which he observed in glass bend models.
Bodner also reported that pressure drops and solid attrition rates for the blinded tee
were approximately the same as those observed for radius bends.
In spite of a considerable amount of research into bend pressure drop,
at present there is no reliable method of predicting accurate bend pressure drops
other than by experiment for the actual conditions expected. In industrial practice
bend pressure drop is often approximated by assuming that it is equivalent
to approximately 7.5 m of vertical section pressure drop. In the absence of any reliable
correlation to predict bend pressure drop, this crude method is probably as reliable
and as conservative as any.
5.4: Equipment
Dilute phase transport is carried in systems in which the solids are fed into the air stream.
Solids are fed from a hopper at a controlled rate through a rotary air lock into the air stream.
The system may be positive pressure, negative pressure or employ a combination of both.
Positive pressure systems are usually limited to a maximum pressure of 1 bar gauge,
and negative pressure systems to a vacuum of about 0.4 bar by the types of blowers
and exhausters used.
