Cnh

mixing point

The tower contains a single medium with fixed characteristics

Se excess biomass

Figure 16.1 Schematic diagram of a packed tower with recirculation of clarified effluent.

Grady and LimJ assumed that the flow of fluid through a packed tower behaved in a plug-flow manner, with no vertical intermixing. We now know that intermixing occurs due to the flow of droplets from protrusions from the biofilm,^ so the assumption of perfect plug-flow is not correct. The implications of this will be discussed later. Under the assumption of perfect plug-flow a steady-state mass balance on substrate can be written over an infinitesimal volume element of the packed tower as shown in Figure 16.1. Application of the usual limiting process and use of the overall effectiveness factor as presented in Section 15.2.2 to account for simultaneous transport and reaction leads to:

dSs„ / qn'SSi, \/ asA, dx + Us + Ss„Af(1 +a)'/VB"'"

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