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Heterogeneous bioreactors usually
are
by design,
and results from the introduction of the carriers on which
is implemented the
immobilization
of the microbes performing the bio-reaction. This form of
by-design heterogeneity, however, is distinctly different from the
heterogeneity that characterizes scale up issues. The
heterogeneity due to scale up is mostly characterized by variations
in the reaction mixture environment, and is addressed
through fluid dynamic analysis of the bioreactor at time of
development. The heterogeneous character obtaining from the
introduction of carriers, however, effectively creates a Random
Newtonian Many Body Problem out of each such bioreactor. In effect,
the computational
design of heterogeneous bioreactors transforms into the
computational analysis of a variant of Random Media Analysis, which,
of course, can always be reduced to a Newtonian Single Body Problem.
The single body problem of
each bioreactor, however, will also depend on the specifics of the
microbes immobilization. In effect, the characterization of the
carrier for analysis will vary with each carrier, as was the case in
the
multi-packed bed reactor. All the same, the underpinning issues
of such analysis, however, are effectively elicited through the
consideration of the biofilm beads obtained with the microbe
immobilization by
entrapment. The method of creating the beads and the characteristics
have been clearly and completely
documented from experimental studies. The characteristics as
such provide the features for consideration.
The salient
characteristics of the beads while in use were the following: The
bead grew larger in size, hence diameter where the sugar
concentrations were high such as at the entry of the reactor.
Obviously substrate also could permeate into the bead, implying a
level of permeability to substrates and minerals. Dissolved gases as
oxygen also permeate the walls to support microbial respiration
necessary for sustenance of metabolic functions. The issues of the
single body problem effectively is the computational evaluation of
the impact of the above characteristics within the context of a
particle flow dynamics.
The context of the single body
problem of a heterogeneous bioreactor is best depicted as a single
bead or particle of microbe immobilization in suspended flow within
the reaction mixture in a bioreactor. This situation obtains in
several bioreactors such as Entrained or Transport Bed Bioreactor,
Moving Bed Bioreactor, Fluidized Bed
Bioreactor, Continuous Flow Tank Bioreactor, and in the extreme case Packed Bed
Bioreactor. Each of these case can effectively be reduced to the
Single Body problem hence the applicability of the considerations.
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Now for a given single body
within a bioreactor, as the body moves about in the reactor, it is
characterized by a specific velocity of travel, transport of
substrates and minerals into the particle; the microbes takes these
into their cells and oxidizes or reduces the nutrients producing as
a products the end-results of the metabolic reactions; and the
microbes during these reactions grow and possibly subdivide into new
cells; and consequentially, the volume of the beads increases. This
change will continue until there is no longer enough substrate to
support such growth of the microbes and the particle volume will
then cease to grow. However, with this increase, three possibilities
come into play: The overall net composite density of the bead
increases, The overall net composite bead density remains the same,
The overall net composite bead density decreases. The results of
these development are varied, each of which causes specific changes
or no changes in the fluid dynamics of the reactor and hence the
performance of the reactor.
First, for the
development of net increase in density, the particle being heavier
suffers lower relative velocity and travels along the flow direction
somewhat slower and therefore for a non batch reactor, experiences
longer residence time in the reactor for the case of Entrained and
Transport Bed Bioreactors. However, for the case of Moving Bed
Bioreactor such development will shorten the residence time the
particle spends in the reactor. For a Continuous Flow Tank
Bioreactor the result will depend on whether the outlet is at the
top or bottom of the bioreactor: The residence time will increase
for outlet at the top and vice versa. Yet, in these cases the
overall volume of the reaction mixture including the submerged
particle will increase.
Next, for the development of
zero net change in density, the particle being neither heavier nor
lighter maintains the same velocity along the flow direction and as
such will be subject to the same residence time for both the upward
traveling beds of Entrained or Transport Bed Bioreactor and the
Moving Bed Bioreactor as well as for a Continuous Flow Tank Bioreactor. In this
case the overall volume of the reaction mixture including the
submerged particle will increase.
Finally, for the development
of net decrease in density, the particle being much lighter suffers
relative higher velocity and travels along the flow direction
somewhat faster and therefore for a non batch reactor, experiences
shorter residence time in the reactor for the case of Entrained and
Transport Bed Bioreactors and the opposite effect for the case of
Moving Bed Bioreactor as the development will shorten the residence
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the particle spends in
the reactor. For a Continuous Flow Tank Bioreactor again the result
will depend on whether the outlet is at the top or bottom of the
bioreactor: The residence time will decrease for outlet at the top
and vice versa. All the same, in these cases the overall volume of
the reaction mixture including the submerged particle will increase.
Of course, this inferred particle
behavior is not absolute and will different in a bioreactor that
suffers heterogeneity, in which different portion of the reaction fluid
tends to have variations in concentrations of substrates and
minerals, temperature and other factors. Naturally, these
variations in the reaction fluid environment will cause dynamic
changes in the particle. Then the particle enters a region of the
reactor where there is large substrate concentrations, the particles
will grow as the microbes grow, however, when the particle enters a
portion that is starved of substrates then the particles size may
decrease as some of the microbes possibly die. The entire dynamic of
the reactor may them be continual non-steady state through the
reaction time for the reaction mixture.
One of the advantages of
the transformation of the Random Newtonian Many Body Problem into a
Single Body Problem is because of the clarity of issues that needs
to be incorporated into the analysis that may not be so easily
accomplished otherwise. Besides the ability to satisfy the boundary
conditions in such many body problem is known to be readily
accomplished indirectly through the single body problem than with
the solution of the many body problem. Satisfying the boundary
conditions in these problems is by no means simple although such
have been accomplished using an approach called the Method of
Reflections, in which the non-zero deviation at the boundaries are
repeatedly reflected and zeroed - first on the particle and then on
the reactor wall and then on the particle and so forth - until the
non-zero deviation is zeroed out on one of the boundaries. |
