General Model for a Single Vessel

Consider an idealized fermentation proeess in whieh growing eells are eonsuming substrate and produeing more eells as represented by the following seheme. 

Cell balance aeeumulation = (d/dt)(VCc) Input terms bulk flow = U C,(j generation = r V Output terms bulk flow = UgC,  

874 Modeling of Chemioal Kinetios and Reaotor Design Substituting these terms in the material balanee equation gives 

Additionally, the ehange in reaetor (liquid) volume ean be aeeounted for by 

Assuming that the reaetor is well mixed and that the flowrate is eonstant (i.e., U = u, = u), reaiTanging Equations 11-41 and 11-42 gives 

Consider an idealized fermentation process in which growing cells are consuming substrate and producing more cells as represented by the following scheme. 

Cs = substrate concentration, kg/m3 rsx = rate of substrate consumption, kg/m3 h rx = rate of cell growth, kg/m3 h 

Input terms bulk flow = UiCxi generation = rxV Output terms bulk flow = u0Cx 

Additionally, the change in reactor (liquid) volume can be accounted for by 

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