CSTBR productivity

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.

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. 

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 ...

Figure 13.9 also contains plots of the productivity of the CSTBR as a function of the dilution rate for operation with and without recycle of cells. The recycled cells enable one to operate at dilution rates considerably above those characteristic of the close-to-washout conditions that would prevail in the absence of recycle. The higher density of cells leads to very substantial increases in reactor productivity. The recycle mode of operation is particularly important in the use of microorganisms for the treatment of wastewaters (see Section 13.3.1). 

An additional benefit of employing multiple CSTBRs in series is the possibility of using a quasi- cross-flow mode of operation in which the feed to the second (and/or subsequent) reactor in the cascade consists of a second fresh feed stream in addition to the effluent from the previous reactor. Use of a second fresh feed stream is optional, but this mode of operation is advantageous when this stream contains an inducer to elicit production of a targeted protein in order to circumvent problems of genetic instability. 

At this point in our discussion of well-stirred continuous-flow bioreactors it is helpful to consider a straightforward extension of our analysis to encompass the possibility of using more than a single feed stream. Illustration 13.5 considers a situation in which a supplementary feed stream is suppUed to the second CSTBR. This illustration lets us address situations in which it is desirable to include additional components (e.g., inducers) in the growth medium to enhance the selectivity of the cascade for the production of desired product species. Induction enhances the production of secondary metabolites becanse of the presence of particular chemical species in the growth medium. 

Of the phenolic compounds that are fed to the second CSTBR in the cascade, 99% (mass basis) is converted to benign products in this bioreactor. 

In the second CSTBR the specific rate at which the degradation proceeds is 0.085 g phenolics/(g cells h). This parameter is functionally similar to a -value but refers to the rate of degradation of a solute rather than a rate of formation of a desired product. The degradation reaction has no impact on cellular growth processes. 

Studies of the production of an organic acid using Aspergillus niger in continuous cultivation with recirculation of the biomass indicate that under the conditions employed = 0.835 h and = 0.10 g/L. The yield coefficient T /s i . 01 g dry biomass/g substrate and p/s is 0.48 g/g. Use a spreadsheet to prepare plots of the concentrations of biomass, substrate, and product leaving the CSTBR, as well as the productivity of the process. 

Smart Dent is smdying the effects of cell recycle on steady state productivity for culture of a yeast strain in a CSTBR with a working volume of 20 L. The growth medium contains 30 g/L of the limiting substrate and the sterile fresh feed stream is supplied at a rate of 25 L/h. Determine the concentrations of yeast (x) and substrate (s) in the effluent from the process depicted in Figure P13.15. 

The subscripts on the usual process parameters indicate the positions in the process to which these parameters refer. The kinetics of yeast growth can be described by a Monod rate expression with = 0.625 h and Kg = 2 g/L. Cell death and cell maintenance effects are negligible, as is formation of products other than yeast cells. The yield coefficient x/s is 0.44. The effluent from the bioreactor flows directly to a membrane filtration apparams. The membrane is completely permeable to the substrate, so the concentrations of the substrate in the CSTBR, the effluent from the bioreactor, and the permeate from the membrane and in the recycle stream are all identical. The membrane rejects a substantial proportion of the yeast cells so that the ratio of the concentration of yeast in the recycle stream is a factor of 4 larger than that in the effluent from the CSTBR. Volumetric expansion and contraction effects may be considered negligible. 

For purposes of the analysis, you may assume that cell death and cell maintenance metabolism effects are negligible, as is formation of any products other than biomass. The concentration of substrate in the feed is 25 g/L and the yield coefficient x/s is 0.52 g cells (dry weight)/g substrate. The kinetics of cell growth are characterized by a rate law of the Monod form with = 0.6 h" and Kg = 0.5 g/L. The dilution rate for the CSTBR is 0.95 h" and the concentration factor / is 2.5. 

The kinetic model was incorporated to the CSTBR model. The following mass balance was used to evaluate the product composition from a set of kinetic constants for each temperature ... 

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