Material balance fermenter

Although dynamic responses of microbial systems are poorly understood, models with some basic features and some empirical features have been found to correlate with actual data fairly well. Real fermentations take days to run, but many variables can be tried in a few minutes using computer simulation. Optimization of fermentation with models and reaf-time dynamic control is in its early infancy however, bases for such work are advancing steadily. The foundations for all such studies are accurate material Balances. 

At steady-state condition for chemostat operation, change of concentration is independent of time. Material balance for the fermentation vessel is ... 

In designing a bioreactor, material balance is used for all the streams associated with the fermentation vessel. The biomass at inlet, outlet and the generated biomass must be balanced while the fermentation proceeds. The cell balance without any cell accumulation is shown in the following equation ... 

Before energy balance is calculated, we need to make mass balance. Figure 9.1 shows the material balance for ethanol and glycerol fermentation. Put simply, mass into the system is equal to mass out of die system. The mass of carbon dioxide is calculated by adding mass of dry cell, mass of glycerol, mass of edianol and mass of water at product stream and then subtracting die sum from die feed stream. As a result, die mass of carbon dioxide is defined. The heat of the reaction is calculated by the following equation ... 

Material balance is earned out at the inlet and outlet of the fermenter, which is summarised in Table 9.2. Also, the density and mass fraction of the inlet and outlet of the fermenter are shown in Table 9.3. 

TABLE 9.2. Summary of material balance for inlet and outlet of the fermenter... 

A material balance for biomass over the first fermenter, as discussed in section 5.11.3, leads to the equation ... 

Fermentation systems obey the same fundamental mass and energy balance relationships as do chemical reaction systems, but special difficulties arise in biological reactor modelling, owing to uncertainties in the kinetic rate expression and the reaction stoichiometry. In what follows, material balance equations are derived for the total mass, the mass of substrate and the cell mass for the case of the stirred tank bioreactor system (Dunn et ah, 2003). 

The generalised material balances for a well-stirred tank fermentation can be represented as ... 

At start-up, before any ethanol is generated by fermentation, the initial mass of yeasf (wafer plus yeast dry solids) in the bed is niy. Any ethanol accumulation in the bed is in excess of niy so fhaf af equilibrium the total mass in the bed (yeast plus ethanol) is niy -t m. A material balance for the bed mass is then... 

After inoculation, assuming no lag phase, the resultant growth can be analysed by considering the unsteady-state material balances for the substrate and biomass. The general form of this balance for a fermenter is ... 

If a CSTF is considered (Fig. 5.56), which has a volume V, volumetric feed flow rate F, with influent substrate and biomass concentrations S0 and X0 respectively, then suppose that the substrate and biomass concentrations in the fermenter are 5 and X. A material balance can be established over the fermenter in the same manner as for the batch fermenter. This is ... 

The operation of the system outlined in Fig. S.61 is analysed by taking material balances over the fermenter vessel. It is assumed that in this idealised case, there is no biochemical reaction or growth occurring in the separator, so that the substrate concentration S in the entering stream is the same as that in the clarified liquid effluent stream, in the recycle stream and in the exit biomass rich stream. The material balance then becomes ... 

A material balance over both fermenters gives the biomass concentration in the second vessel as ... 

For a series of fermenters as shown in Fig. 5.64, the material balance for biomass... 

The resultant equations are non-linear and in this general case numerical solution techniques must be used. However, there exists a special case where an analytical solution may be obtained. If the increase in biomass concentration during flow through the reactor is small then an average value for the biomass concentration, independent of the distance Z along the fermenter, may be used. The material balance for the substrate over the reactor element may then be written ... 

The material balance for the biomass in the fed-batch fermentation gives ... 

It has been shown (equation 3.127) that the material balance for substrate across a continuous stirred-tank fermenter gives ... 

If during the beginning of the experiment the fermentation is at a quasi-steady state, that is the growth rate is such that the biomass concentration X may be considered to be constant during the experiment, then a material balance for the oxygen gives ... 

If all cells are recycled back into the fermenter, the cell concentration will increase continuously with time and a steady state will never be reached. Therefore, to operate a CSTF with recycling in a steady-state mode, we need to have a bleeding stream, as shown in Figure 6.19. The material balance for cells in the fermenter with a cell recycling unit is... 

Let s examine the stability of recombinant cells in the continuous stirred-tank fermenter. The material balance for the plasmid-carrying cells around a CSTF yields... 

Figure 11-18 shows the notations used in modeling and analysis of the fermentation process. The material balance on the microorganism in a CSTR at constant volume, assuming perfect mixing (i.e., concentrations of the cell and substrate inside and at the exit are the same) is expressed by ... 

A waste with characteristics as listed in Table IV has been assumed. The assumed composition is similar to that for a municipal primary treatment waste sludge for which data on methane fermentation was available for comparison. The concentrations are expressed in milhelectron equivalents since the materials balances and calculations were made on this basis. One milhelectron equivalent per liter is equivalent to 8 mg/liter of chemical oxygen demand (COD), a more commonly used measure of waste strength. 

By using the dynamic technique [20], the kifl value for the oxygen transfer during a fermentation process can be estimated. This technique is based on the oxygen material balance in an aerated batch bioreactor while microorganisms are actively growing as... 

Table III contains a material balance showing the composition of the corn used for the calculations and the products produced. In addition to fuel alcohol, a high-protein cattle feed called distillers dark grain (DDG) is also produced in the fermentation process. As will be seen later, inclusion of DDG in the cattle ration provides more weight gain than if the cattle had been fed the original corn which was used to produce the fuel alcohol and DDG. Carbon dioxide is a second byproduct produced in the fermentation, but for purposes of this analysis, it has been assumed to be vented to the atmosphere.

Figure 28 shows typical results from the simulation of the system of material balance equations which are parameterized with the results from the CFD simulations as described before. In this figure, a snapshot of distributions of dissolved oxygen concentrations and the production rate of butanediol after eight hours of simulated batch fermentation are shown. Figure 29 illustrates a comparison of measured [76] and simulated ratios of the two products acetoin... 

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