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The
analyses of
fermentation reactors design have shown various aspects of the
physics of the reactors that need to be accounted for in the general
case of all such reactors regarding the
performing of
material balances and in particular for the heterogeneous
reactors the criteria for deciding on the
method of
immobilization that should be adopted, and as a result of which
the biofilm
bioreactor has been proffered as a design that satisfies most of
the design constraints. As per the general design philosophy, the
reactor equipment
design evaluation by computational design should be performed in
two parts, of which the first part addresses the computational
analysis of the design: Develops a mathematical model of the
fermentation reaction dynamics and conducts simulation of the
performance to ascertain that the production volume output and other
calculations are within tolerable or pre-set bounds of variation.
Although the choice of a
reactor type effects implicit incorporation into a computational
design model the consideration of real-time or dynamic
immobilization of the microbes during the reaction progress, the
design model must yet explicitly reckon with the issue of real-time
cell factor variation as well as the consequential issue of possible
net reaction volume variation.
Design Model Concept Analysis
The real-time cell factor
variation as has been determined from analysis results from the
growth of microbes and the dynamic assumption of sessile state by
the new cells. Mathematical description and
performance assessment of the fermentation reaction essentially
entails use of the reaction description equation of the
cell growth
kinetics, which is a composite of the catabolic reaction rate
equation and the
Monod equation
for which the constants have been appropriately adjusted for the
prevailing reaction conditions. As per the physics, the variation of cell fraction is directly
related to cell growth, hence cell fraction change-velocity is
related to the cell-growth kinetics:
dΦ/dt = ((-dX/dt)/gw).Ce
where Φ is the cell fraction
and has the range of { 0 ≤ Φ ≤ 1}, X
is the microbes concentration in the reaction mixture - fluid and
solids together, the germ-weight, gw, is the weight of a
single microbe, and Ce is the
Cylinder of
exclusion of a single microbe, and t is the time progress of the
reaction. Now dividing the cell-fraction change-velocity by the
cell-growth rate of the Monod equation yields:
dΦ/dX = Cegw
the basic differential
increase relationship between the cell fraction to cell-growth yield
ratio. Strictly,
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the above ratio
is a general relationship. A very rigorous computational
design model would have to incorporate the geometric layout of the microbes as to
be able to determine the actual form of the inter-microbes
interstices as to evaluate the impact of the changes on the mass
transport diffusivity in the reaction model. Absent of that,
however, the value of the diffusivity, for each time slice of the
reaction progress, has to be calculated by the
well-documented method, after each integration from X(t)
to X(t + Δt).The increase of the cell
fraction necessarily causes a change of the overall volume of the
reaction mixture.
Experimental observation has that with reaction
progress and cell growth, entrapment beads immobilizing microbes
tend to grow larger in diameter. Such increase in bead diameter is
attended with fluid displacement and hence resulting in possibly
larger reaction volume. The same dynamic is expected for the biofilm
reactor, at least because there is expected to be a density
different between the microbes that form from the depletion of the
reaction fluid and the reaction fluid consumed.
The details of the
incorporation of this dynamic into a computational design model is
reactor design-specific. However, suffice to note that such changes
will affect the fluid dynamic of the reaction mixture, both by
changing the operational momentum balance equation boundary
conditions as well as possibly the flow pattern itself.
In general, however, this
change in the volume of the reaction mixture change is captured
through a careful development of the material balance equation of
the reaction based on the initial design volume and then allowing
for a change of the volume as well. The details are better reflected
in specific developments. Nonetheless, there is therefore the need
to capture the fluid dynamics characteristics of the reactor and
fully document the impact of the fluid dynamics on the performance
of the reactor and to then develop through parametric analysis and
operational revisions, the optimal method of production management.
The need for incorporation of
the fluid dynamics characteristics of this change in reaction volume
stems from the prospective changes that occur as a result of such volume changes: In
general the dynamics of a reactor changes with changes in size. In
the old, when computational knowledge was developing as was
computational power, the issue of scale was handled by methods of
dimensional analysis and similitude. However, over the years it has
been determined that this
method does not really lead to final
designs that are consistent with the observed performances of
the smaller scale designs, and in some cases had resulted in huge
expenses as projects had to be scrapped. The reason |
for these failures was
that fluid dynamical features of most systems do not scale up well,
if at all, while straight mechanical designs did. As systems sizes
change the fluid dynamics also changes.
The importance of reckoning
with these criteria in the computational analyses of bioreactors is
buttressed by the impacts they have on the dynamics of the reactors,
and therefore in using the the results of the computational analyses
for the assessment of the reactor design. In effect, these
constraints are very significant in the computational analyses of
fermentation reactors in particular and bioreactors in general.
Development Computation Designs
The computational design of a
reactor can also be an intrinsically critical component of any
reactor development effort. For one thing, such development stage
computational design model, serves in providing effective guide to
the experimental development efforts. Although, the computational
design model may not be developed before concept validation, the
design model should and ought be developed soon after.
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