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.
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.
