CSTBR

When used in laboratory-scale operations CSTRs are frequently referred to as chemostats. Chemostats are often employed in scientific studies intended to elucidate the metabolic processes associated with particular microorganisms because they are better equipped to monitor transient situations involving a transition from one set of operating conditions to another, for example, when there is a shift in the composition of the stream being fed to a unit operating at steady state. By comparison with large-scale CSTBRs, small-scale chemostats are characterized by shorter response times and are more readily instrumented to facilitate acquisition of data that are useful in optimization of the performance of these reactors. 

The productivity (T) of a CSTBR is defined as the amount of product formed per unit time per unit volume of reactor. Another way to characterize the productivity is to employ the product of the dilution rate (D) and the effluent concentration of the fermentation product of primary interest. Thus, if the biomass itself is the desired product,... 

Figure 13.7 Effects of dilution rate on the productivity of a CSTBR and on the effluent concentration of biomass at steady state. The maximum productivity is observed at a dilution rate of 2.43 h. Parameter values Kg = 2.78, = 3.16 h , Xq = 50, and...

To indicate the need for caution in selecting the dilution rate at which to operate, we have prepared plots of the productivity T and the effluent concentration of biomass versus the dilution rate D (see Fignre 13.10) using equations (13.2.39) and (13.2.33) as the basis for spreadsheet calcnlations. Readers shonld note that the dilution rate that maximizes the productivity of the CSTBR approaches small values of Kg. Consequently,... 

For a chemostat or a single CSTBR, the maximum rate of production ( T) of biomass is equal to the product of the dilution rate and the effluent concentration of biomass corresponding to complete conversion of substrate to biomass ... 

Even in the best-case situation, for the batch reactor in which tg approaches zero (a highly unlikely scenario ) the productivity of the CSTBR will exceed that of a batch reactor whenever the ratio (Xjjj x/Xq) exceeds e, the base of natural logarithms (2.718). Despite this fact, the disadvantages of employing a CSTBR noted in the introduction to this section can outweigh its productivity advantage. 

Figure 13.8 Schematic flow sheet for a process coupling use of a CSTBR and a generic unit operation for separation and concentration of a suspension of cells for recycle to enhance reactor productivity. The concentration factor /=X2/Xj.

Operation of a Single CSTBR in Conjunction with Cell Separation and Recycle... 

Biochemical transformations that are mediated by microorganisms are characterized by autocatalytic behavior. The fact that the rates of these reactions increase as the concentration of the organism increases provides opportunities for engineers to consider a variety of modes of operation to enhance the performance (and productivity) of a CSTBR facility. One fruitful approach is to do a partial separation and concentration of the cells contained in the efQnent from the CSTBR (see Figure 13.8) and recycle the resnlting process stream back to a point where it is mixed with the contents of the CSTBR. 

In addition to the variables we have used previously in our analysis of the behavior of a CSTBR, we employ the recycle ratio (R) to represent the ratio of the volumetric flow rate of the suspension of cells leaving the separation device to the volumetric flow rate of the net product stream. The symbol / represents the ratio of the concentration of biomass in the recycle stream to that in the gross product stream so /=X2/jCi. This concentration factor characterizes the degree to which the separation operation increases the amount of biomass present in the recycle stream beyond... 

The volumetric flow rates at various points in the process flow sheet are indicated in Figure 13.8. The relative flow rates of the recycle and net product streams are linked by the definition of the recycle ratio R. If one presumes that any differences in the densities of the fresh feed and net product streams are inconsequential, an overall material balance indicates that the volumetric flow rates of these streams are then essentially identical. In similar fashion one can conclude that total mass balances around the CBSTR and around the separator dictate that the volumetric flow rates of the recycle stream and the effluent from the CSTBR proper are RV and (1 + Ryv, respectively. 

A material balance for the microorganism around the CSTBR in Figure 13.8 indicates that for a sterile feed (Xq = 0) the rates of various terms obey the relation... 

Here we have also recognized that if the contents of the bioreactor are perfectly mixed, JCj = j cstbr- Algebraic manipulation of equation (13.2.58) combined with use of the definition of the dilution rate yields... 

Because the concentration factor vp must exceed unity to render operation in a recycle mode viable, the quantity 1 (1 - /) must be negative and the dilution rate D must exceed mef Consequently, the use of separation and recycle of a portion of the cells permits one to operate with a steady-state dilution rate that exceeds the net biomass specific growth rate in the CSTBR. 

Inspection of equation (13.2.65) indicates that the effect of the recycle is to reduce the amount of biomass in the effluent from the CSTBR by the factor 1 -I- R(1 - p) relative to the total amount of biomass that would be obtained from a single CSTBR operating at steady state. Consequently, the biomass in the recycle stream can serve to increase the amount of biomass in the CSTBR well above that obtained in the absence of recycle. 

The corresponding concentration of the substrate in the effluent from the CSTBR can be determined by recognizing that (1) at steady state, equation (13.2.59) is again applicable, and (2) in the absence of cell death and cell maintenance effects, the biochemical reaction obeys a biomass-specific rate law of the Monod form ... 

Combination of equations (13.2.65) and (13.2.67) followed by further algebraic manipulation gives the following relation for the steady-state concentration of cells in the effluent from the CSTBR ... 

Figure 13.9 Effects of dilution rate on the total quantity of biomass produced and on the rate of production of biomass during steady-state operation in the presence and absence of partial separation and recycle of biomass to the entrance of a single CSTBR. Parameter values used in generating plots Kg = 2.78 g/L p = 3.16 h" 7x/s = 9.7 ...

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