Multiphase Bioreactor Design

Calculation of Reactor Volume

Let Q be the volumetric flow rate of the liquid through the system, S 1 the inlet substrate
concentration and S 2 the substrate concentration at the reactor outlet. A simple mass
balance to the substrate, from the inlet to the outlet of the reactor, results in:

(36a)

In the case where the substrate concentration varies continuously along the reactor, it is
advisable to write a differential balance:

(36b)

Af is the surface area of the biofilm (the external mass transfer area), which will be here
supposed to be smooth, that is, without filaments or protuberances. The case of spherical
support (or carrier) particles will be considered below, although the biofilm can be
modelled as a flat geometry.

Ideal continuous stirred tank reactor

Let rp be the radius of the bare carrier particles (i.e., without biofilm) and Lf the thickness
of the microbial layer. The surface area of the biofilm can then be related to the reactor
volume (VR) through:

(37)

where ε is the porosity of the reactor (liquid volume over reactor volume, the latter
containing liquid and particles with biofilm). Therefore, the reactor volume will be given
by:

(38)

In an ideal stirred tank reactor, the substrate concentration in the liquid will be the same
in every point and equal to the outlet concentration. Therefore, the observed reaction rate
rA (per unit surface area of biofilm) will be given by equations (16) to (18) in the case of
intrinsic first order reaction, with S=S 2 , and by Equations (24) and (25) in the case of
intrinsic zero order reaction, also with S=S 2.
If the biofilm is thin, (Lf+rp) can be replaced by rp.

Ideal plug flow reactor

In this case, the following simplified expressions can be used (Harremoes, 1978;
Harremöes and Henze, 1995), assuming pseudo-homogeneity in the reactor (i.e., uniform
substrate concentration along the cross section area of the reactor):

i) First order reaction:

Biofilm reactors 311