Chemical Engineering November 2014 - 59

Solids Processing
Funnel flow
Solids in
Gas out
Solids in
Moving
Stagnant
Gas in
Gas out
Mass flow
Gas in
FIGURE 3. Two types of flow typically
arise in bulk-solids vessels. In general,
mass flow (right) is preferred over funnel
flow (left)
Solids out
FIGURE 1. In countercurrent designs,
injected gas passes upward through a
moving bed of solids
In order for a direct-contact heat
exchanger to operate effectively, the
following are required:
Adequate heat transfer. Sufficient
thermal mass (that is, the
product of the gas flowrate and its
heat capacity) must be provided to
allow the solids to be cooled to the
desired temperature.
Uniform solids flow. The solidsvelocity
profile must be uniform,
otherwise, the exposure of the solids
to the cooling gas will be inconsistent,
and heat transfer will
be insufficient. In extreme cases,
solids will only flow in a central
channel above the cooler outlet,
resulting in significantly less
residence time and insufficient
heat transfer.
Proper outlet size. The outlet of the
cooler must be large enough to prevent
obstructions to flow from developing
and allow discharge of the tempered
product at the desired rate.
Reliable gas flow. For countercurrent
designs, the distributor that
injects the gas must provide a constant
gas velocity throughout the
cross-section of the vessel. The gas
velocity must be low enough to prevent
fluidization, otherwise, channeling
will cause the gas to bypass
a portion of the solids and create
other flow instabilities.
With cross-flow designs, the gas
velocity must be low enough to prevent
pinning, which occurs when
Solids out
FIGURE 2. In cross-flow designs, the
injected gas passes perpendicular to the
solids flow in the vessel
the friction between the solids and
the permeable wall through which
the gas exits becomes too great and
prevents solids flow along the wall.
Excessive gas velocity may also push
the solids away from the permeable
wall through which the air enters
the cooler. As a result, the air will
begin to escape upward along the
wall rather than through the bed.
Sufficient cooler volume. The
required heat duty depends on the
heat-transfer coefficient between
the gas and solids, the total surface
area and the temperature driving
force. The available heat-transfer
area in a direct-contact bulk solids
heat exchanger is the product of the
powder's specific surface area (that
is, its surface area per unit volume)
and the volume of the bed of material
in the cooler.
Heat transfer
The temperatures of the gas and solids
streams entering or leaving the
cooler are generally known. In most
cases, the temperatures of the solids
entering and leaving the cooler
are specified, as is the temperature
of the cooling gas. A steady-state
energy balance of the gas and solids
can be written as according to
Equation (1):
GCpg
(T gout
T gin ) = SCps
(T sin
T sout
)
(1)
(Table 1 provides the nomenclature
for all terms used here.) The energy
balance, as written, assumes that
only sensible heat is transferred -
thus, that there is no condensation
or evaporation. Otherwise, a term
that describes the latent heat would
have to be included in the energy
balance. In addition, Equation (1)
assumes that heat losses from the
cooler are negligible.
The minimum gas injection required
to obtain the target temperature
of the solids product, Gmin, can
be determined by performing the
energy balance over an infinitely
tall cooler, using Equation (2):
Gmin
=
SCps(T sin
Cpg (T sin
T sout
T gin
)
)
The design gas feedrate must exceed
the Gmin. Alternatively, an approach
temperature (the difference
between the inlet gas and outlet solids
temperatures) can be specified.
[]
m˙ f pickup
Solids flow
Two primary flow patterns can
occur in a bin or silo: mass flow and
funnel flow (Figure 3).
Funnel flow. When funnel flow occurs,
an active flow channel forms
above the outlet, with stagnant material
(this solids buildup is called a
rathole) remaining at the periphery.
Funnel flow can cause erratic flow,
reduces the solids residence time,
and induces high loads (depending
on vessel size) on the structure and
downstream equipment due to collapsing
ratholes and eccentric flow
channels. In the case of countercurrent
designs, gas is likely to flow
preferentially in the central flow
channel because of its lower perme[]
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f feeder leakage
Fw dg Vrad
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p
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m˙ f pickup
= m˙ f blowerinlet
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ChemiCal engineering www.Chemengonline.Com noVemBer 2014 59
= m˙ f blower inlet
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m˙ f bleed
(2)
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Chemical Engineering November 2014

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