Performance Equations of Biofilm Reactors

Complicated models for film bioreactors may be simplified when pseudohomogeneity can be assumed (see Sect. 4.2)—that is, when the S-concentration profile is flat throughout the cross section of the trickling filter. 

There is a concentration gradient present in the fluid flowing over the length of the reactor at a rate F [m /h]. This requires dealing with the mass conservation for S using differential volume elements, as in Fig. 3.38 and Equ. 3.95 (with no recycling). 

The important value for X is not the total mass of X rather it is the active mass of X in the external surface of the film. The volume of the active biomass, Fx, may be calculated as the product of several factors the differential thickness, dz the cross-sectional area, A the specific surface area of the falling body, as [m /m ] and the film thickness, d 

Using Monod kinetics, the mass conservation becomes 

With constant film thickness and constant K, the integration with bounds z = 0 at So and z = z at s gives Equ. 6.116  

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