Chemical Engineering November 2013 - 45

The impact of vessel size and geometry
on heat-transfer capacity can
be calculated. But how will the heattransfer
coefficient change with increasing
scale? The overall heat-transfer
coefficient will be a function of the
sum of the resistance to heat transfer
for the cooling water, the vessel wall,
and the process liquid in the tank. The
coolant-side resistance does not vary as
a function of scaleup since the physical
dimension of the jacket, the coolant
flowrates, and the coolant's physical
properties are independent of scale.
No matter how big the tank size gets,
multiple parallel circuits would be required
to maintain the coolant-return
temperature, because the log-mean
temperature difference (LMTD) is not
a function of scale. The vessel wall
provides resistance to heat transfer
and the wall thickness typically grows
significantly with vessel size. However,
steel is a relatively good conductor of
heat, so a thicker wall on a steel fermentation
reactor would not have a
significant negative impact on overall
heat transfer. And, in any case, the impact
of thicker metal on heat transfer
can be accurately calculated.
The thermal resistance of the process
side can vary greatly as a function
of vessel size. For instance, larger
vessels will have different processside
thermal resistance compared to
smaller vessels. At larger scales, the
vessel wall tends to be a greater distance
from any agitator blade - thus
the turbulence and flowrate across internal
heat-transfer surfaces are both
expected to decrease for larger vessels.
External heat exchangers have the
advantage of allowing controlled conditions
to be maintained on both sides
of the heat-transfer surface, and thus
can eliminate the uncertainty of heattransfer
coefficients at huge scale.
If huge fermenters employ one or
more external heat exchangers, there
is no longer a need to provide a jacket,
baffle or coil. This reduces some of the
business risk associated with scaleup,
because the heat-transfer coefficients
are known and not dependent on vessel
agitation. Some of the risks associated
with external heat exchange include
the following: Can the microbe tolerate
the time spent outside of the vessel, the
temperature excursion, and the much
colder wall temperature? Resolving
these questions will be one of the primary
goals of pilot-plant testing.
The external heat exchanger will
require a pump to extract a stream of
fermentation broth from the fermenter.
The stream will be exposed to shear in
the pump, as well as relatively cold surfaces
inside the heat exchanger, and the
resultant temperature change of the
slipstream liquid. An investigation of
the impact of all of these factors needs
to be carried out at the pilot scale.
Using roughly estimated parameters
for a hypothetical case that are
within the authors' industrial experience,
a highly aerobic fermenter could
consume 100 mmol O2/L/h. If the fermenter
is operating at 50% dissolved
oxygen (DO) saturation and has no
back pressure, the DO could be 0.25
mmol O2/L. That means that the DO of
the stream would go to zero within 10
s. If the cooling stream is designed for
5 ft/s velocity then the DO would go to
zero in the first 50 ft. Productivity at
the large scale will depend in part on
how well the microbes can tolerate that
dissolved oxygen excursion.
A hypothetical case
In order to understand the implications
of the scaleup principles, the following
hypothetical case is considered:
* Fermenter with 1,000,000-gal working
volume
* Fermentation broth with physical
properties similar to water
* Batch temperature of 30°C (86°F)
* 100-mmol O2/L/h uptake rate
with metabolic heat load of 500
Btu/mol O2
* Chilled water at 2°C (36°F), rising
by 6°C (11°F) to 8°C (47°F)
* Power input of 10 hp agitation per
1,000 gal
Heat load = Qagitation + Qmetabolic =
[(10,000 hp)(2,544 Btu/hp×h)] + [(0.1
mole O2/L/h)(1,000,000 gal)(3.785 L/
gal)(500 Btu/mol O2)]
= 25×106 + 190×106 = 215×106 Btu/h
Where:
Q = Heat flow, Btu/h
This heat load could be provided by
three 6,000-ton (24 million Btu/h)
chillers. The fact that the heat load is
too big for a single chiller shows that
this process is beyond the range of
economy of scale from a chiller point
of view. Using multiple chillers is not a
problem; they would be necessary for
any 1,000,000-gal process, no matter
how many fermenters are involved.
Also, the use of multiple units provides
a more fault-tolerant process.
Wcoolant = (215×106 Btu/h)(7.48 gal/
ft3)/(0.8 Btu/lb×°F)(11°F)(66 lb/ft3)(60
m/h)
= 46,000 gal/min
Where:
W = Volume flow, gal/min
This may seem like a very high flowrate,
but a single pump could provide
even much more. And, multiple pumps
should be used to provide for redundancy
and better temperature distribution
inside the tank. The biggest
commercial plate-and-frame type heat
exchanger tops out at about 18,000
gal/min for this application. Therefore,
three heat exchangers would be
required. Larger exchangers could be
built, but the special tools and dies,
engineering and labor needed would
cause them to far exceed the cost per
Btu/h of multiple commercial units.
Assume that each chiller supplies
chilled water to one pump, and each
pump delivers chilled water to one heat
exchanger that cools the fermenter
broth. Each fermenter has three cooling
circuits, and each consists of one of
the above-mentioned exchangers and
a fermentation broth cooling-circuit
pump running at 16,000 gal/min. They
are connected by 36-in. pipe.
Since the pumps are not at a size
greater than their economy of scale,
the overall heat-transfer system can
grow without adding pumps. Therefore,
the overall system does not yet
exceed overall economy of scale range.
Demonstration scale. Scaleup efforts
are about managing business
risk. In order to evaluate the risk involved,
it is important to determine
what elements of the design involve
performance uncertainty. An intermediate-scale
demonstration plant might
be required to prove that scaleup considerations
are well understood.
Thanks to the use of external heat
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Chemical Engineering November 2013

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