5.3 Biochemical Reactor Design
Bioreactor design involves the careful control of process parameters, such as temperature, which can optimise cell growth to increase the industrial process’ yield when producing products like bioethanol, for fuel. This lesson outlines the stages and scale-up considerations in designing a bioreactor.
Mass Balances
The design of biochemical reactors begins with the general mass balance equation shown in Equation 1. This can then be applied to a cell, giving the equation shown in Equation 2. The left hand term describes the rate of cell accumulation, where the flow rate terms describe the rate of cells entering and leaving the control volume. The final term describes the rate of generation of live cells.
\(\text{Accumulation \: = \: Input \: - \: Output \: + \: Reaction}\)
\(\frac{d(VC_c)}{dt} = Q_{in}C_{in} - Q_{out}C_{out} + Vr_g\)
This mass balance can be applied to the three types of fermenter discussed in Lesson 5.2 Industrial Biochemical Engineering.
For batch processes there is no inlet or outlet flow rate, and the volume can be assumed to be constant, so the growth rate is calculated using the equation shown in Equation 3.
\(\frac{dC_c}{dt} = r_g = \mu C_c\)
A fed batch process does not have an in or out-flow, so the rate of cell accumulation is equal to the generation rate of live cells, leading to the equation shown in Equation 4.
\(\frac{d(VC_c)}{dt} = Vr_g = V\mu C_c\)
Assuming that a continuous bioreactor reaches steady state, there will be no accumulation. There is also an assumption that the vessel is well-mixed, so the bulk concentration \(C_c\) is equal to the outlet concentration \(C_{out}\). Therefore, the equation shown in Equation 5 can be obtained.
\(V\mu C_c = QC_{out} \rightarrow \mu = \frac{Q}{V} = D\)
The dilution rate, \(D\) (s-1), shown in Equation 5 is particularly useful as it is the reciprocal of the necessary residence timeAverage time of a molecule spent within the reaction vessel. for the fermentation vessel.