Monod kinetics with death rate

Monod kinetics with death rate (cf. Sect. 5.3.4.1) ... 

Model 1 (Monod kinetics with constant specific death rate)... 

The growth of biomass in the reactor is assumed to follow Monod kinetics with a first-order death rate. A mass balance on the biomass in the reactor yields the following differential equation (assuming that no biomass enters the reactor in the feed) ... 

Figure 6.36. Plot of the dimensionless concentration of cell mass x and substrate s for a continuous culture as a function of the dimensionless mean residence time I as in Fig. 6.1b with Xq > 0 Calculated comparison between a CSTR with maximum mixing (ST m) or one with total segregation (ST J and a continuous plug flow reactor (PF), assuming Monod kinetics with a death rate (Tsai et al., 1969).

The cell density X at any point within this layer can grow according to Monod kinetics. In addition, a first-order rate constant for cell death, d, is usually introduced net cell growth, which equals zero at steady state, is equal to the difference (/x, — d). (In other than shallow biofilms, /x is not independent of location as implied here, but varies with location in the biofilm.)... 

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 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. 

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