Introduction to API Process Simulation, Example 2
Fed-batch Reaction with Safety Constraint
Objective
The purpose of this example is to simulate and optimize the operation of a fedbatch reactor. The process being studied involves an exothermic reaction with a safety
constraint. There is also a constraint on the maximum volume of material that can be
contained within the reactor. The objective to determine a feed profile that will
minimize the time required to achieve the desired product amount, while ensuring that
the volume of material in the reactor does not exceed the specified limit, and also
ensuring that the reactor can be shut down safely in the event of a cooling failure.
feed1
header
bulk
jacket
Process Description
Exothermic Reaction: substrate + reagent → product
Operating Conditions: Isothermal, fed-batch
Objective: Minimize the time needed to produce a given amount of product
Manipulated Variable: Feed rate of reagent
Variables and Parameters: c X ,bulk , concentration of species X; Vbulk , volume of material
in reactor; Vmax , maximum volume; qin , feed rate; c X ,header , concentration of X in header
tank; k , kinetic rate constant; Tbulk , reactor temperature (normal operation); MTSR ,
Maximum temperature of synthetic reaction (temperature attained after cooling failure);,
Tmax , maximum temperature; H r , heat of reaction;  , density; c p ,bulk , heat capacity.
Comments: In case of cooling failure the best strategy is to stop the feed. Yet due to the
presence of unreacted components in the reactor, the reaction goes on, which will cause
an increase in the reactor temperature. The maximum attainable temperature under
cooling failure at any time t is given by the following expression:
Introduction to API Process Simulation, Example 2
MTSR (t )  Tbulk  min( c substrate,bulk (t ), c reagent,bulk (t )) (H r ) c p
The term min( c substrate,bulk (t ), creagent,bulk (t )) represents the maximum extent of reaction that
can occur after a cooling failure. Without any constraints, optimal operation would
simply consist of adding all the available reagent at the initial time (i.e. batch
operation). However, because of the safety constraint, the feeding of reagent has to
account for the possible cooling failure. Additionally, the feed rate must be set to zero
once the maximum volume has been attained.
Optimal Feed Profile
In general the optimal feed profile will consist of several segments as shown in the
figure below (the number and order of segments of different types depends on the
specific initial conditions and constraints).
Maximum Flow: The feed is at its upper limit so that the concentration of reagent can
build up in the reactor. The end point of this type of segment is determined by the time
at which the safety or volume constraint is reached.
Controlled Flow: The flow is set at an intermediate value to replenish the reagent that is
being consumed by the reaction.
No Flow: The feed is turned off due to one of the following reasons: (i) header tank is
empty; (ii) reactor is full;.
3
1
qinMax
q
Max
in
2
qincon
qin
qinMin
4
time
Process Parameters
The process parameters, operating bounds and initial conditions for Example 2 are
given in the table below.
k (rate constant)
Tbulk (operating temperature)
Theader (feed temperature)
0.0482
70
L/mol hr
C
70
C
Introduction to API Process Simulation, Example 2
H r (heat of reaction)
c p ,bulk (heat capacity)
-60
4.2
kJ/mol
kJ/kg K
c reagent,header (conc of reagent in header)
2.33
mol/L
qinmin (minimum feed rate)
0
L/hr
qinmax (maximum feed rate)
10
L/hr
Tmax (maximum temp)
80
C
Vmax (maximum volume)
nC,des (desired product amount)
c0,substrate,bulk (initial conc of substrate)
100
L
60
2
mol
mol/L
c0,reagent,bulk (initial conc of reagent)
0.49
mol/L
V0 ,bulk (initial volume in reactor)
70
L
V0,header (init volume in header tank)
30
L
Mass of solvent in reactor
Mass of solvent in feed tank
UA (constant h.t. coefficient)
sUA (specific h.t. coefficient)
Coolant flow rate
60
25.75
100
0.5
0.1
kg
kg
W/K
W/LK
kg/s
DynoChem Model Summary
The process can be simulated using the DynoChem library template for a fed-batch
reactor with accumulation effects. This template for this example has been provided in
the file TemplateFedBatch.xls. The following information is specified under the
Components tab, Process tab and Scenarios tab.
Components. The components defined for this example include the solvent (MW=18),
coolant (MW=18), reagent (MW=18), substrate (MW=18), and product (MW=36).
Process Definition (Statements). The process statements define the bulk liquid and
header tank phases, heat transfer through a jacket, and the transfer of feed material from
the header tank into the bulk liquid. A reaction with the appropriate reactants and
products is defined for the bulk liquid phase. The rate constant should match the value
from the table above. The MTSR value is calculated from the bulk liquid temperature,
and concentrations of substrate and reagent.
Scenarios (Initial Values and Parameters). The table above contains the process
parameters and initial values for process variables. These can be entered into the
scenario tab after conversion to the appropriate units (Note: The DynoChem model is
set up to use number of moles rather than concentrations to specify the amount of
reactants). Finally, the data sheet for the fed-batch scenario specifies the imposed feed
profile and temperature profile for the reactor.
Jacket Parameters. The DynoChem model in the spreadsheet incorporates heat transfer
through a jacket. For isothermal operation, the temperature in the jacket must be
adjusted to compensate for the heat of reaction. DynoChem will perform the required
Introduction to API Process Simulation, Example 2
calculations if the desired value for the bulk liquid temperature is imposed in the
datasheet. The overall heat transfer coefficient is calculated from the relationship
UAtot=UA+sUA*V, where V is the volume of material in the reactor, and sUA is the
specific heat transfer coefficient. The UA and sUA values from the table above should
be entered into the scenario tab.
Feed and Temperature Profiles for Fed Batch Reactor
80
70
see legend
60
50
Qin L/hr
40
Temperature C
30
20
10
0
0
200
400
600
800
1000
1200
1400
Time, min
Optimization of feed profile
The rate of addition of B is constrained by the need to maintain the MTSR below the
specified Tmax value. This will ensure the safe shut down of the reactor in the event of a
cooling failure. The simulator plots the MTSR variable defined in the process
description. The feed profile in the datasheet can be adjusted manually to ensure that the
MTSR value remains below Tmax at all times. The feed must be set to zero once the
volume of material in the reactor reaches the maximum value. The simulation can be
used iteratively to determine the feed profile which minimizes the time at which the
amount of product reaches the desired value while satisfying all constraints.
Introduction to API Process Simulation, Example 2
Results
Simulation results include plots of the volume of material in the reactor and the MTSR
as a function of time. In the initial period the reactor flow is kept at the maximum value
until the MTSR constraint becomes active, after which the flow is controlled to keep the
MTSR at the maximum value until the volume reaches the maximum value. At this
point the feed is turned off and the reaction proceeds until the desired amount of product
is obtained.
Controlled flow
Volume (l)
110
100
90
Volume (l)
80
70
60
0
200
400
600
800
1000
1200
1400
Time (min)
Maximum flow
No flow
Safety constraint active
Volume constraint active
Temperature (C)
MTSR
80.5
80
79.5
79
78.5
78
77.5
77
76.5
MTSR
0
200
400
600
800
Time (min)
Safety and volume constraints inactive
1000
1200
1400
Introduction to API Process Simulation, Example 2
Additional simulation runs can be made to determine the impact of the volume
constraint on the reaction time.
Volume constraint no longer active
120
110
Vol (l)
100
Run1
90
Run2
80
70
60
0
200
400
600
800
1000
1200
1400
Time (min)
70
Product (mol)
60
50
40
Run1
30
Run2
20
10
0
0
200
400
600
800
Time (min)
1000
1200
1400