Fermentation Technologies
Designing Batch Heterogeneous Fermentation Reactors

A Batch Fermentation Reactor by design rationale can be either homogeneous or heterogeneous. The design rationale, however, consists of several considerations one of which is the prospective cell growth dynamics of the microbes during the reaction, and of particular critical consideration is the case where the form of cell-growth goes beyond individual cell enlargement in size but possibly cell division as well. Although the generic bioreactors design rationale has a Mash Feeder integrated with the bioreactor in order to minimize such cell-growth resulting from controlled preparation of the Mash, engineering analysis preferred condition is the complete absence of cell-growth during the reaction. Of course, this requirement almost makes the use of homogeneous reactors virtually unsuitable because of the inherent heterogeneity of the broth during operations that is likely to result in local and heterogeneous cell-growth. For the purposes of contrasting then  an analysis of heterogeneous bioreactor become imperative when making any decision of design of bioreactors.

As is well known heterogeneous bioreactor provide both advantages and disadvantages, all of which derive mostly from the immobilization of the microbes.  For a batch heterogeneous bioreactor some of the inherent form of microbes immobilization some of the obvious advantages are the use of pathogenic microbes without the risk of pathogenic attacks, and the design of more complex reactors that can overcome certain reaction limiting conditions. correspondingly obvious disadvantages related to issue of microbes immobilization has to do with the changing of the dimensions of the interstices between the microbes as the reaction progresses. the flow of the broth within the reactor also must not allow non-uniform exposure of the microbes to the broth. Clearly these obvious factors  introduces difficulties into the design of the heterogeneous bioreactors.

This analysis based on the  concept design of batch  fermentation reactor is an attempt at critical examination of the design of heterogeneous bioreactors in general, in the context of the obvious advantages and disadvantages that have so far been delineated in suggestion for consideration in such designs.

Batch Reactor Design Rationale
A crucial design rationale, with respect to the design of any bioreactor is the selection of microbe supporting the target fermentation reaction,  however, the selection is often by the reality that a particular fermentation reaction is supported by more than one microbe. In the case, however, the selection is further constrained by the requirement that the immobilization process must prevent  microbial growth by cell division or the microbe must support spontaneous self-immobilization, given the in-use inaccessibility of the reactor.

Now, as is well known, of the two types of microbes: Yeast and Bacterium; that support fermentation only for bacterium that form biofilms

 has self-organization or self-colonization been observed to occur in quiescent fluids; hence allowing to subsume stagnant broth for the fermentation, then invariably, admittedly, using biofilms-forming microbes for batch fermentation reactors is the preferred choice in the use of bacterium in heterogeneous bioreactors design

Effectively, the microbe selection for the heterogeneous reactor therefore defines a Biofilm bioreactor as the default, based on the recognition that analysis of microbes immobilization suggests the use of immobilized biofilm microbe as offering the best option for the design of heterogeneous reactors for which cell division growth is not explicitly inhibited by the immobilization process.

Mass Balance Analysis
The determination of the production volumes and substances properties is determined to ensure compliance with the Conservation of Mass. Though explicit calculations are not proffered here, the validation of the methods presented in another analysis is evaluated. The batch reactor mass balance equation of critical consideration for cellular maintenance has been given as

         dX/dS = (K_m/k)/(K + S)                          (1)

and is to be integrated from S = So to (1- ξ)So,  where ξ is the final conversion of substrate required to support operations viability, to get the final concentration of the microbes; and then obtain the values of the other reactants - at the end of the reaction - using the applicable biochemical pathway-based  techniques of materials evaluation, given that the feed state must also be consistent with the constituents of typical ethanol fermentation reactor stream used in the material balance calculations.

This equation though originally developed for use with homogeneous reactors, careful examination shows it to be applicable to biofilm reactors as well, given that new microbes produced should instinctively organize themselves into the sessile colony environment from which they were produced. Needless to state that this expectation will hold without regard to the form of initial formation of the colony and hence the manner of immobilization, except for provision for the spontaneous immobilization that is anticipated, as has been shown in the ReviewBook, Ethanol Fermentation batch Reactor - Design Basics.

Now given that the batch reactor must remain inaccessible throughout the course of the reaction, the cell fraction of the carrier must be carefully evaluated prior to immobilization and introduction into the reactor, in order to allow room for microbes self-colonization during the reaction. Such evaluation can again be made by following the method of calculating the growth cell-count using the Monod equation. For the evaluation suppose the following values about a single immobilized microbe length l:

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Angle of vertical orientation  = ω
Horizontal resolution   w        = lCos(ω)
Vertical resolution       h        = lSin(ω)
Cylinder of exclusion   C_ε       = π(lCos(ω))³ tan(ω)/4

So then, for a total carrier surface area of size A then the immobilization coverage, A_c relation is

       A_c = (N_o + N_c)C_ε/lSin(ω)

where No is the microbe cell-count of initial immobilization and Nc is the new cell count for in-use spontaneous immobilization. Alternatively the cell fraction at start of reaction can be used as follows

  Initial cell fraction                  =  (N_oC_ε/AlSin(ω))
  Initial cumulative interstices   =  1 - (N_oC_ε/AlSin(ω))

Equipment Design
The equipment design of the reactor task, actually, is the determination of  the structural configuration of the equipment, and which for all intents and purpose, is a manifestation of concept design subsumed in the material balances calculations. Transitively then the feed volume and mass are the same as evaluated with the material balances.

In this context, the equipment design becomes the development of features for handling different aspects of the operational consideration of the fermentation reaction. These choices become part of the proprietary aspects of the design rationale. In any case, a very simple sizing of the equipment obtains from use of the rule of thumb  leading to the volume calculation

• the height of the reactor <= 12-feet,
• the interior diameter of the reactor  <= 6-feet,:
• Volume of reactor (Vrxtor) = π(D/2)²H

By inference, based on the issues so far elicited, makes the biofilm type as preferred for designing heterogeneous bioreactors. The design of heterogeneous bioreactors therefore  assumes at the core the use of possibly pathogenic bacteria, and for fermentation bioreactor then an ethanologenic bacteria.

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