Summary module 6 - Predicting Food Quality (31306)

Module 6:

 Reactor knowledge and reactor kinetics is combined to describe the dynamics in
food processes.

 A pineapple is a closed system and can be considered a complete batch
reactor.
 When it comes to an industrial oven, there is a continuous in- and outflow of breads.

 The general balance is: Accumulation = In – Out + Production. This general balance
can be applied to all kinds of reactors:
o Stirred tank.
o Fermenter.
o Mixing unit.
o Pasteurization unit.
 This general balance can be rewritten in more mathematical
terms (see formula on the right).
o V: reactor volume (m3).
o c: concentration (mol/m3).
o t: time (s).
o : volume flux (m3/s).
o r: reaction rate (mol/(m3*s)).

- Batch reactor: a closed system without any flow in or out.
 in = out = 0.
 All components are put inside the reactor at the beginning, where they are
left to react, under stirring.
 The concentration changes over time in the whole reactor. The
volume does not change over time.
o The general balance must be adapted (see formula on the
right).
 The shape of the concentration vs. time graph strongly depends on the order of the
reaction.

- Continuously Stirred Tank Reactor (CSTR): there is a continuous
flow in and out of the system. Ideally mixed.
 The concentration does not change over time  accumulation = 0.
o The in- and outflow are equal in = out.
 The concentration at the outlet is thus constant in time.
 Again, the general balance must be adapted (see formula on
the right).

- Plug flow reactor: there is again a continuous flow in and
out  accumulation = 0. Moving batch.
 It is similar to a CSTR, but it is a very long reactor.
 in = out  accumulation = 0.
 Not ideally mixed  only ideally mixed at the level of a
plug.

,  Ideally, heat exchangers are plug flow reactors  the same heat treatment to all
products allow for microbial inactivation and constant product quality.
 The concentration is constant in time, per position in the reactor only.

 As has already been discussed in previous sections, there are
different rate equations for different reaction orders (see
formulas on the right).
 Remember that the general formula for a batch reactor is:
dV c out
=r .
dt
o Based on the different rate equations, for a zero-order
reaction, the reaction rate (r) equals the reaction rate
constant (k). The concentration decreases linearly over time.
o For a first-order reaction, the reaction rate (r) equals k∗c . There is a
logarithmic dependency in time.
 The reaction order has a great influence on the outcome and should always be
checked carefully.

 Remember that the general formula for a CSTR is:
0=ϕ ¿∗c ¿ −ϕ out∗c out + r∗V .
o For a zero-order and first-order reaction, the formulas
on the right are obtained.

 Mean residence time: τ =V /ϕ .
o V : volume.
o ϕ : flow.

 Generally, reactor performance is determined by 3 factors:
1. Mean residence time.
2. Residence time distribution: E(t).
3. Kinetics.
 Reactor performance is a function of space (volume), time, yield and residence time
(distribution)!

Mean residence time:
- Mean residence time: the time a molecule spends in a reactor.
 For a batch reactor, the means residence time (τ ) equals the reaction time, since there
is no in- or out flow.
 For a CSTR and plug flow reactor, the following formula for average residence time
applies: τ =V /ϕ .

Residence time distribution: E(t):
 For a batch and plug flow reactor, there is no residence time distribution  all fluid
elements get the same treatment.
 For a CSTR, there is a wide residence time distribution. This can be problematic for
inactivation kinetics and product quality.
 Assume a CSTR. A pulse of a component is put and added in the first reactor.
o The concentration will immediately be very high at
t=0.