Industrial Biotransformations

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5 Basics of Bioreaction Engineering
Input
Reaction
Change in Concentration
Output
Fig. 5.9 Influence on the mass-balance in a volume element.
error. The main part of the simulation model is the coupled system of differential equations
of the first order, which are the mass balances of all reactants and products. The
change in the concentration of one compound in time and in a volume element (= “accumulation”)
is the sum of convection, reaction and diffusion.
accumulation= convection + reaction + diffusion (32)
The convection term describes the change in the concentration of one compound in
the reactor as the difference between the influx into the reactor and the efflux. The reaction
term describes, by using the kinetic model, the change in the concentration of one
compound as a result of the reaction. The reaction velocity v is the sum of the individual
reaction velocities describing the consumption of a substrate or formation of a product.
Diffusion is only given in the case where no ideal mixing is stated. Depending on the
reactor type chosen, the mass balance can be simplified, stating ideal mixing.
5.3.1.1 Mass Balance in Stirred Tank Reactor
The mass balance of each compound is defined by the reaction rate only, as no fluid
enters or leaves the reactor. At a defined time the concentrations are the same in every
volume element (diffusion = 0). There is no influx or efflux of substrate or products for a
single volume element in time (convection= 0).
The mass balance is simplified to:
d‰SŠ
dt
ˆ v (32)
The time t that is necessary to reach a desired conversion X can be determined by integrating
the reciprocal rate equation from zero to the desired conversion X.
dt ˆ d‰SŠ
v ˆ ‰SŠ 0 dX
v
) t ˆ‰SŠ 0
R x
0
1
v
dX (33)
5.3.1.2 Mass Balance in a Plug-flow Reactor
The change in reaction rate within a unit volume passing the reactor length is equivalent
to a change corresponding to the residence time within the reactor. Diffusion is neglected