## Model of a Well Mixed Rotating Drum Bioreactor

The system modeled is a rotating-drum bioreactor, as shown in Fig. 23.1. It is divided into three subsystems, the substrate bed, the headspace, and the bioreactor wall. Each is assumed to be well mixed. In other words, each system is represented by a single value for each state variable. Note that this means that the drum wall has a single temperature, uniform across the whole drum, from inside to outside and from the section of the wall in contact with the substrate bed to the section of the wall in contact with the headspace.

23.2.1 Synopsis of the Mathematical Model and its Solution

Figure 23.2 summarizes the model, which is a modified version of that of Stuart and Mitchell (2003). Water and energy balances are done over the substrate bed and headspace gases and an energy balance is written over the bioreactor wall. Many assumptions are made about the system, the most important ones being:

• Although the solid is consumed during the process, this affects only the density of the bed and not the volume that it occupies, which remains constant at the original value;

• The total amount of dry gas in the headspace is constant;

• The gas flow rates at the air inlet and air outlet are the same (that is, the exchange of O2 for CO2 does not cause any difference between the mass of dry gas entering and leaving).

dry air _ vapor

theat ! SURROUNDINGS (s)

theat ! SURROUNDINGS (s) part represented by Fig. 23.2

S=total mass of bioreactor wall

G = total mass of dry air in the headspace H = humidity of the headspace dry air vapor

S=total mass of bioreactor wall

G = total mass of dry air in the headspace H = humidity of the headspace Fig. 23.1. (a) The rotating-drum system as modeled in the case study. The letters in parentheses represent the subscripts that are used in the model equations to denote the various subsystems within the model equations. (b) The meaning of the symbols related to the masses and water contents of the various subsystems

Fig. 23.1. (a) The rotating-drum system as modeled in the case study. The letters in parentheses represent the subscripts that are used in the model equations to denote the various subsystems within the model equations. (b) The meaning of the symbols related to the masses and water contents of the various subsystems