Control of batch and semibatch reactors

1

Control of batch and semibatch reactors

Margarida Vicente

Chemical Engineer Department, Instituto Superior Técnico, Lisbon, Portugal

Abstract

The present work consisted in the implementation of an efficient controller, in a discontinuous reactor

operating in semibatch mode, where an exothermic reaction system with two reactions is carried out. These

reactions are 𝐼 + 𝑅 → 𝐴 + 2𝐷 and 𝐴 + 𝑅 → 𝐼𝑀𝑃𝑆 where the first one is the main reaction while the second is a

parasite reaction. It is desired to maximize the specific gross profit associated to the formation of compound A

(main product) as well as to minimize the formation of compound IMPS (impurities).

A general PID controller was implemented and three situations were studied, regarding which

manipulated variables to use. The first used the reactant feed flow, the second the cooling flow and the third

used a combination of both as manipulated variables. It was observed that the first case allowed a good controller

when a PD controller was implemented while, in the second case, none of controllers studied provided good

responses because the system was limited by the heat transfer. However, when the third case was studied it was

noted that the PD controller also provided a good temperature control. The minimization criterion used to tune

the controllers was ISE although IAE is also suitable for the present case.

It is noteworthy that, although the goal of temperature control is achieved, the specific gross profit

decreases, in relation to the operation of a batch reactor, due to the increase of reaction time. It was also

concluded that the development of a successful control strategy requires a clear control objective in terms of

operation and economic parameters. Furthermore, the PD controller induces a marked oscillatory response of

manipulated variables and further improvements in the control strategy would be advisable.

Keywords: discontinuous reactor, exothermic reaction, control, PID controller

1. Introduction

There is a renewed interest in the use of

discontinuous processes [1] due to the changing

market conditions and the flexibility they offer [2],

[3], [4]. Discontinuous processes allow a quick

adaptation to the turbulent market as well as to the

appearance of new technologies [2], [3], [4] and are

suitable for multiproduct plants [1], [2], [5].

Discontinuous reactors are used in processes

such as polymerization [2], [4], [6], [7], [8]

fermentation [7], [9] as well as in the wastewater

treatment plants [10], [11] and, concerning

products, are used to produce fine chemicals,

pharmaceuticals and specialized chemicals [4], [6],

[12], [13], [14].

Some advantages of using discontinuous

reactors are related to their usefulness when there

are reactions involving dangerous material [4], [15],

[16]. They are also quite useful to study the kinetic

of a reaction as well as to model thermal effects [6],

[7], [14], [17].

Discontinuous reactors are also frequently

employed in cases where highly exothermic

reactions are involved [16], [18], [19]. In these

cases, there is a significant potential for thermal

runaway if there is an insufficient heat removal [19].

This may lead to a sudden temperature increase in

a short period of time [20] making the control of

reactor difficult.

This, in turn, can generate a domino effect

because a thermal runaway can trigger an accident

which can lead to an explosion sequence, whenever

there are, for example, failures on security devices

[18], [21]. One way to prevent a thermal runaway

can be by using an inhibitor agent or by quenching

the reaction [16], [22], [23], [24].

Discontinuous reactors can operate in two

modes: batch and semibatch. Frequently, the first

one is used when there are slow reactions while the

second is used when there are fast reactions [2],

[12], in particular with significant thermal effects.

Semibatch mode allows a better control, in the


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presence of exothermic reactions, when compared

to batch mode due to the fact that there is another

flow which is possible to control: the feed flow [6],

[14], [19], [21] that can be used to control the

reaction progress. Another advantage of using

semibatch mode is the minimization of reactants

accumulation [6].

The control of discontinuous reactors can be

done in two ways: through the control of

temperature over the entire range of operation or

only after the heating step has been done [5], [6],

[25], [26]. In the second case, it is desired to heat

the reactor as quickly as possible, in order to reduce

the time cycle, but with care so that a thermal

runaway is prevented [26], [27]. It is expected that

the control is robust, easy to maintain as well as

easy to implement [28].

However, the control of discontinuous reactors

is still a challenge [5], [6], [15], [26]. Control of these

reactors can be done with the use of classical

controllers such as PID controller and on-off

controller [2], [6], [29]. Other strategies can be

implemented including, for example, the Dual

Mode control, using, for instance, both the on-off

controller and the PID controller [25], [26], [30] to

allow a better control over the entire range of

operation.

Still due to the dynamic nature of these

reactors, another strategy may consist on the use of

Gain Scheduling [2], [6], [9], [28], [31] where the

controller gain is adjusted in different periods [6],

[25]. A frequently used strategy was the use of

cascades in order to have a quicker response [6],

[25].

Another advanced strategies involves the use

of an adaptive controller [26], [32], [31] a predictive

controller [1], [5], [28], [31], [33], [34] and by using

the generic model control [26], [30], [35].

Last but not the least, there is also the

possibility of using fuzzy logic [28], [29], [31] as well

as the iterative learning control [1], [27], [36].

The main goal of this work was to analyse

several control strategies, using simple control

strategies, in order to obtain a good reactor’s

temperature control, in a discontinuous reactor,

where two exothermic reactions occur, but, at the

same time, having in consideration if the gross

profit could be increased by controlling the reactor

temperature.

2. System

The reaction system studied and the reactor’s

characteristics as well as the cooling jacket were

described in [37], for a discontinuous reactor in the

batch mode.

2.1. Case Study

The discontinuous reactor, represented in

Figure 1, was used to carry out a reaction system

involving two exothermic reactions:

𝐼 + 𝑅 → 𝐴 + 2𝐷

𝐴 + 𝑅 → 𝐼𝑀𝑃𝑆

Where I and R are the reactants, A is the main

product, D is a secondary product and IMPS are the

impurities.

Figure 1 – Discontinuous reactor operating in semibatch mode. When the reactor is operating in batch mode, there is no inflow of reactant R, as the reactor is full with both of reactants with a volume equal to the total volume.

The reactions are exothermic, but as can be

seen in Table 1, the secondary reaction, which has a

higher activation energy, is more sensitive to the

increase in temperature. Moreover, the reactions

are in series with respect to A and k1 and k2 are

obtained from the Arrhenius law.

Table 1 – Data of reactions [37]. 𝑰 + 𝑹

𝒌𝟏→ 𝑨 + 𝟐𝑫 𝑨 + 𝑹

𝒌𝟐→ 𝑰𝑴𝑷𝑺

Ea (J/ mol) 8,31E+04 1,43E+05

A0 (l/mol min) 7,20E+10 4,27E+18

∆Hreaction (J/mol) -1,00E+05 -1,00E+05

Next are introduced the characteristics of

reactor as well as the cooling jacket.


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Table 2 - Characteristics of reactor and the cooling jacket [37].

Di, reactor (m)

Di, jacket

(m) Dout, jacket

(m) U

(J/min m2 K) A

(m2)*

1 1,01 1,02 9300 4,04 *Note that it was assumed the reactor was cylindrical, so this value is different

from the used in [34].

In order to calculate the gross profit, as it

will be mentioned next, it is necessary to know the

specific costs associated with all the compounds,

Table 3. Table 3 - Cost of compounds.

Cost (£/mol)

Reactant I 1

Reactant R 1

Product A 5

Product D 0,5

Product IMPS 1

Two approaches related to the cooling jacket

were studied: in the first one, it was assumed that

the cooling jacket is always at a constant

temperature (298K) while, in the second one, the

changes in the temperature of jacket are computed

by the corresponding energy balance made.

2.2. Mass and Energy Balances

Next are introduced the mass and energy

balances for the first case described, that is, the

cooling jacket temperature is always constant.

𝑑𝐶𝐼

𝑑𝑡= −𝐶𝐼 (𝑘1𝐶𝑅 +

𝑄𝑅

𝑉) (2.1)

𝑑𝐶𝑅

𝑑𝑡=

𝑄𝑅

𝑉(𝐶𝑅𝑒 − 𝐶𝑅) − 𝐶𝑅 (𝑘1𝐶𝐼 + 𝑘2𝐶𝐴) (2.2)

𝑑𝐶𝐴

𝑑𝑡= 𝐶𝑅 (𝑘1𝐶𝐼 − 𝑘2𝐶𝐴) −

𝑄𝑅𝐶𝐴

𝑉 (2.3)

𝑑𝐶𝐷

𝑑𝑡= 2𝑘1𝐶𝐼𝐶𝑅 −

𝑄𝑅𝐶𝐷

𝑉 (2.4)

𝑑𝐶𝐼𝑀𝑃𝑆

𝑑𝑡= 𝑘2𝐶𝐴𝐶𝑅 −

𝑄𝑅𝐶𝐼𝑀𝑃𝑆

𝑉 (2.5)

𝑑𝑇

𝑑𝑡=

𝑄𝑅

𝑉(𝑇𝑖𝑛,𝑅 − 𝑇) −

𝐶𝑅

𝐶𝑝

(𝑘1𝐶𝐼∆𝐻𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 1

+ 𝑘2𝐶𝐴∆𝐻𝑟𝑒𝑎𝑐tion 2)

−𝑈𝐴

𝑉𝐶𝑝

(𝑇 − 𝑇𝑖𝑛,𝑗𝑎𝑐𝑘𝑒𝑡)

(2.6)

When the jacket temperature changes are

computed, it is necessary to also introduce the

energy balance of cooling jacket. This way, instead

of Equation (2.6), Equation (2.7) and Equation (2.8)

are used, as it can be seen next.

𝑑𝑇

𝑑𝑡=

𝑄𝑅

𝑉(𝑇𝑖𝑛,𝑅 − 𝑇) −

𝐶𝑅

𝐶𝑝

(𝑘1𝐶𝐼∆𝐻𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 1

+ 𝑘2𝐶𝐴∆𝐻𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 2)

−𝑈𝐴

𝑉𝐶𝑝

(𝑇 − 𝑇𝑜𝑢𝑡,𝑗𝑎𝑐𝑘𝑒𝑡)

(2.7)

𝑑𝑇𝑜𝑢𝑡,𝑗𝑎𝑐𝑘𝑒𝑡

𝑑𝑡=

Q

𝑉𝑗𝑎𝑐𝑘𝑒𝑡

(𝑇𝑖𝑛,𝑗𝑎𝑐𝑘𝑒𝑡 − 𝑇𝑜𝑢𝑡,𝑗𝑎𝑐𝑘𝑒𝑡)

+𝑈𝐴

𝑉𝑗𝑎𝑐𝑘𝑒𝑡𝐶𝑝

(𝑇 − 𝑇𝑜𝑢𝑡,𝑗𝑎𝑐𝑘𝑒𝑡)

(2.8)

Where

𝑉𝑗𝑎𝑐𝑘𝑒𝑡 = 𝜋 ×(𝐷𝑜𝑢𝑡,𝑗𝑎𝑐𝑘𝑒𝑡

2 − 𝐷𝑖,𝑗𝑎𝑐𝑘𝑒𝑡2 )

4× 𝐿 (2.9)

On the other hand, when semibatch mode

is used, the volume of reactional mixture as well as

the heat transfer area are time dependent. It is then

necessary to take these factors into account, as it

can been seen in Equation (2.10) and (2.11),

respectively.

𝑉 = 𝑉𝑖 + ∫ 𝑄𝑒 𝑑𝑡 (2.10)

𝐴 = 𝜋 × 𝐷𝑖,jacket × 𝐿 (2.11)

Where

𝐿 =4 × 𝑉

𝜋 × 𝐷𝑖,𝑟𝑒𝑎𝑐𝑡𝑜𝑟2 (2.12)

2.3. Calculations

The study of current work included the need to

calculate the specific gross profit, as introduced

next:

𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐺𝑟𝑜𝑠𝑠 𝑃𝑟𝑜𝑓𝑖𝑡 =𝐺𝑟𝑜𝑠𝑠 𝑃𝑟𝑜𝑓𝑖𝑡

𝑡𝑟 + 𝑡𝑝

(2.13)

Where the gross profit is calculated by using:

∑(𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑖 ± 𝐶𝑖) × 𝑉 × 𝑐𝑜𝑠𝑡𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑖

𝑖

(2.14)

And the signal (+) corresponds to the

compounds formed and the signal (-) to the

remaining compounds. However, in semibatch

mode, the calculations need to take into account

the dilution effect and the introduction of reactant

R. So, concerning the reactants, instead of Equation

(2.14), Equation (2.15) is used.

(𝑉 × (𝐶𝑅𝑒 − 𝐶𝑅) − 𝑉𝑖 × 𝐶𝑅𝑒) × 𝑐𝑜𝑠𝑡𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑅

+ (𝐶𝐼𝐼 × 𝑉𝑖 − 𝐶𝐼 × 𝑉)× 𝑐𝑜𝑠𝑡𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝐼

(2.15)


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3. Results and Discussion

The software used was Microsoft Excel and the

integration method consisted in using the Euler

method (in the absence of controller) as well as the

Runge-Kutta of 2nd order (in the presence of

controller), with an adequate step, in order to have

a maximum relative error of 2,5%.

3.1. Reactor operating conditions

The reactor is going to work at a stoichiometric

proportion of 1:1, at a temperature of 355K, with a

final volume equal to 1m3.

It is assumed that, at start-up, there are no

products and that, in batch mode, the

concentration of reactants is 1M. For the gross

profit calculations it was assumed that the reactants

that do not completely react, are completely

recycled to the next batch.

3.2. Absence of controller

At this point, the controller was not yet

implemented and the open loop behaviour was

analysed. This was also aimed at checking if there

was any risk for the operation of plant as well as to

make some decisions such as what mode of

reactor´s operation to use.

3.2.1. Thermal Runaway

Before implementing the controller, it was

necessary to analyse if the current system could

lead to a runaway situation. It was observed, by the

Figure 2, that the current system was safe to the

operators in case of a cooling failure since adiabatic

temperature raise was limited.

Figure 2 - Response of reactor in the absence of cooling flow.

3.2.2. Choice of reactor’s operation mode

One particularity of present system is that it is

desirable to maximize the formation of product A.

However, observing the reactions, it can be

observed that A, in turn, reacts with R to produce

IMPS. Then, besides the advantages of semibatch

mode concerning the goal of reactor´s temperature

control, the semibatch offers another advantage:

the inflow of R allows the control of production of

IMPS, in every instant, when compared to batch

mode.

However, as in semibatch mode the reactant R

is being introduced, the reaction mixture is

continuously being diluted. Consequently, it is

necessary to double the initial concentrations used

in batch mode, since it is assumed that initial

volume of reactor is half of desired volume.

Moreover, it is assumed that the initial reactor´s

temperature is equal to the inflow temperature of

reactant R.

After the reactor operation mode was chosen,

a study concerning the gross profit was made. It is

expectable to have a bigger specific gross profit

when semibatch reactor is used, due to presence of

less R.

The results are presented in the Table 4-5, and

Table 6-7 are related to the reaction time required,

respectively.

Table 4 - Maximum specific gross profit when CII=CRe=1M. The reactor is operated in batch mode.

Table 5 - Maximum specific gross profit, for different inflow of reactant R, when CII=CRe=2M. The reactor is operated in semibatch mode.


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Table 6 – Reaction time corresponding to the results obtained in Table 4.

Table 7 – Reaction time corresponding to the results obtained in Table 5.

Despite the considerations made on the

possible advantages of semibatch mode, it can be

seen by Table 3 and Table 4 that batch reactor

provides better results for gross profit. This

difference is related to the increase of reaction´s

time, due to extra time that is required to fulfil the

final reactor´s volume. So, if the goal was to

maximize the specific gross profit, the batch mode

should be chosen.

3.2.3. Impact of IMPS cost in the specific

gross profit

Since the reaction is exothermic, it is

possible to confirm that the increase of reactor

temperature allows the production of more product

A, although, in turn, this could also lead to an

increase on the production of IMPS. With the base

values that were used there is no significant penalty

for production of impurity and working at high

temperature would be possible. Thus, a sensitivity

analysis concerning the IMPS cost was made, in

order to check which would be the best

temperature to work depending on this parameter.

Since both the batch and semibatch mode

showed the same conclusions, the results will be

only presented in the batch mode. Moreover, batch

mode has always provided better results concerning

the goal to maximize the specific gross profit.

Table 8 - Impact of IMPS cost in the maximum specific gross profit, in batch mode.

Table 9 – Reaction time corresponding to the Table 8.

It can be observed that increase of IMPS

cost leads to the choice of lower working

temperatures. This was expectable since increase of

temperature will produce more IMPS that will, in

turn, decrease specific gross profit.

However, the best values obtained for the

different costs exhibit differences due to two

reasons: the increase of IMPS cost and the increase

of reaction time.

3.2.4. Impact of inflow reactant R in the specific gross profit

Semibatch mode can never reach the values of

batch mode in terms of gross profit, mainly due to

the fact that the reaction time increases.

Nevertheless, concerning the goal of controlling the

reactor’s temperature, semibatch mode is better.

Yet, it was still necessary to check how much impact

the inflow of reactant R would have on the specific

gross profit.

In order to evaluate the impact of inflow

reactant R at different temperatures, two cases

were studied: in the first one it is assumed that

initial temperature of reactor is equal to

temperature of reactant R that is supplied, while in

the second one it is assumed that these

temperatures are different. The results are shown

in Figure 3 and Figure 4.

Figure 3 - Impact of inflow reactant R, when it is assumed the temperature of reactant R introduced is equal to initial temperature of reactor, in the specific gross profit.


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Figure 4 - Impact of inflow reactant R, for different temperatures of reactant R introduced when the initial temperature of reactor is 355K, in the specific gross profit.

It can be noted that the increase of inflow of

reactant R corresponds to an increase of specific

gross profit. However, after a certain value, the

inflow of reactant R has no significant impact on the

maximum specific gross profit. Therefore, the value

of 200 l/min was chosen as the starting point.

3.3. Control of reactor

Given that there was no control of temperature

until now, it was conducted a study of reactor

response while operating with a PID controller.

Three situations concerning the use of manipulated

variables were studied: the use of feed flow of

reactant R, the use of cooling flow and the use of

both of them. This way, the results will be organized

according to the situation studied.

The best controller performances was related

with the use of PD controller. Therefore, the results

will be introduced only for this controller. In order

to have into account the delay introduced by the

sensors, a 5s delay was used.

Moreover, it was assumed that the maximum

flow rate delivered by the pump was 250 l/min and

that 𝑡𝑝 is equal to 30min.

3.3.1. Reactant R Flow as the manipulated

variable

The chosen value of initial reactant inflow has

an impact on the response in the reactor’s

temperature because as more reactant is

introduced, more heat is generated through the

reactions which, in turn, leads to a faster increase of

reactor’s temperature. In the following results, only

the worst case tested is shown, that is, the initial

feed flow of reactant R is equal to 200 l/min.

Figure 5 - Response of reactor’s temperature of PD controller, when QR=200 l/min (t=0), where Kc= 12299,21 l/min K and τD=1,62 min with ISE=0,013 K2 min.

Figure 6 - Response of manipulated variable, in the presence of PD controller, when QR=200 l/min (t=0), where Kc= 12299,21 l/min K and τD=1,62 min with ISE=0,013 K2 min.

It can be observed that the deviations of set

point are low, but there are many oscillations

around it due to changes in the manipulated

variable. It should be noted that there is an initial

cooling of reactor because the reactor is being

cooled by the cooling system before a significant

amount of heat is generated by the reaction.

3.3.2. Cooling flow as the manipulated

variable

In the following results, the cooling flow is used

as the manipulated variable. Consequently,

Equation (2.7) as well as Equation (2.8) are used

instead of Equation (2.6). Once again, only the

response for the worst case of QR, in other words,

200 l/min is represented.


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Figure 7 - Response of reactor’s temperature in the presence of PD controller, when QR=200 l/min (t=0), where Kc=-287161,99 l/min K and τD=7,06 min with ISE=103,38 K2 min.

Figure 8 - Response of manipulated variable, in the presence of PD controller, when QR=200 l/min (t=0), where Kc=-287161,99 l/min K and τD=7,06 min with ISE=103,38 K2 min.

It can be observed that the system is limited by

the heat transfer. Hence, the controller cannot

control the temperature well and the actuator is

saturated all the time, either in the fully open or the

fully closed position.

3.3.3. Reactant R flow and Cooling flow as

the manipulated variables

Since both flows are used as manipulated

variables in this case, the same equations as in the

previous situation were used.

Once again, the worst case is presented,

although it is different from the previous one,

because the effect that the increase of initial inflow

reactant R has in the control of reactor’s

temperature was already seen, leading to more

difficulties. Thus, instead of using 200 l/min, the

initial flow rate was fixed at 100 l/min.

Figure 9 - Response of reactor’s temperature, in the presence of PD controller, with QR=100 l/min (t=0).

Figure 10 - Response of manipulated variable (inflow of reactant), in presence of PD controller, when QR=100 l/min (t=0), where Kc= 16886,35 l/min K and τD=1,81 min with ISE=0,0095 K2 min.

Figure 11 - Response of manipulated variable (cooling flow), in the presence of PD controller, when QR=100 l/min (t=0), where Kc= -1990,52 l/min K and τD=5,06 min with ISE=0,0095 K2 min.

It can be observed that, in this situation,

the limitation of heat transfer is not critical due to

the slower introduction of reactant R. It is also clear

the impact that reactant R has on the reactor´s

temperature.

However, once again the manipulated

variables have very aggressive responses, so the

controller should be improved.


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4. Conclusion

The inflow of reactant R provides one way

to control the temperature of reactor, when

compared to the batch mode. This way, semibatch

mode provides a useful way to better control the

reactor’s temperature, when it is in the presence of

two exothermic reactions.

However, it was observed that if the

economic goal was to maximize the specific gross

profit, semibatch mode does not provide as good

results as batch mode. Even so, a sensitivity analysis

was made in order to know what would be the best

temperature to work depending on the cost of

producing more impurity. It was observed that the

increase of IMPS cost lead to the choice of lower

values concerning the reactor’s temperature due to

reaction time increase and the cost itself.

The control of present reactor was only

switched on when the reactor was already at the

desired temperature, thus the heating phase time

was disregarded. Two manipulated variables were

studied: the feed flow of reactant R and the cooling

flow. It was observed that the PD controller

provided a good response on the first situation

while in the second was limited by the heat transfer

limitation.

One particularity of controller is related to

criterion used to tune controller´s parameters.

Despite the fact that results reported are based on

ISE criterion, IAE criterion is also adequate.

Although only the responses for one value

of initial QR were represented, the worst case

tested, other values were studied. It was concluded

that, as long as reactant R feed flow is slow, a better

control is achieved. However, this also increases

significantly the value of 𝑡𝑟. This way, specific gross

profit has a substantial decrease when compared to

the results obtained in the absence of controller.

To sum up, in order to minimize the

oscillations of manipulated variables, it is desirable

to test other controllers and, for the present

reactional mixture, semibatch mode does not

compensate if the main objective is to maximize the

specific gross profit, under the assumptions used.

Another important conclusion is that,

when optimizing control strategies for this type of

processes, a detailed objective has to be put

forward, based on real information from the

process, both in terms of kinetics but also in terms

of separation and purification steps.

5. Nomenclature

𝐴 – Heat transfer area in m2.

A0 – pre-exponential factor of Arrhenius law in l/mol min. 𝐶𝐴 – Concentration of product A in mol/l.

𝐶𝐷 – Concentration of product D in mol/l.

𝐶𝐼 – Concentration of reactant I in mol/l.

𝐶𝐼𝐼 – Initial concentration of reactant I in mol/l.

𝐶𝐼𝑀𝑃𝑆 – Concentration of impurities IMPS in mol/l.

𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑖 – Initial concentration of compound i in mol/l.

𝑐𝑜𝑠𝑡𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝐼 – cost of reactant I in £/mol.

𝑐𝑜𝑠𝑡𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑅 - cost of reactant R in £/mol.

𝐶𝑝 – Calorific capacity in J/m3 K.

𝐶𝑅 – Concentration of reactant R in mol/l.

𝐶𝑅𝑒 – Concentration of inflow reactant R in mol/l.

𝐷𝑖,jacket – Inner diameter of cooling jacket in m.

𝐷𝑖,reactor – Inner diameter of reactor in m.

𝐷𝑜𝑢𝑡,jacket – Outer diameter of cooling jacket in m.

Ea – Activation energy in J/mol.

𝐺𝑟𝑜𝑠𝑠 𝑃𝑟𝑜𝑓𝑖𝑡 – gross profit in £/min.

𝑘1 – Coefficient of main reaction in l/mol min.

𝑘2 – Coefficient of secondary reaction in l/mol min.

𝐿 – Height of reactional mixture in m.

Q – Flow of cooling jacket in l/min.

𝑄𝑅 – Flow of reactant R in l/min.

𝑇 – Temperature of reactor in K.

𝑇𝑖𝑛,𝑅 – Temperature inlet of reactant R in K.

𝑇𝑜𝑢𝑡,𝑗𝑎𝑐𝑘𝑒𝑡 – Temperature of exit of cooling jacket in K.

𝑡𝑝 – time to charge, discharge and cleaning in min.

𝑡𝑟 – time of reaction in min.

𝑈 – Global coefficient of heat transfer in J/min m2 K.

𝑉 – Volume of reactional mixture in dm3.

𝑉𝑖 – Initial volume of reactor in dm3.

𝑉𝑗𝑎𝑐𝑘𝑒𝑡 – Volume of cooling jacket in dm3.

∆𝐻𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 1 – Enthalpy of main reaction in J/mol.

∆𝐻𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 2 – Enthalpy of secondary reaction in J/mol.


9

6. References

[1] D. Bonvin, B. Srinivasan and D. Hunkeler, “Control and

Optimization of Batch Processes,” IEEE Control. Syst. Mag.,

pp. 34-45, 2006.

[2] D. Bonvin, “Optimal operation of batch reactors - a

personal view,” J. Proc. Cont., vol. 85, no. 5-6, pp. 313-325,

2002.

[3] C. Filippi, J. L. Greffe, J. Bordet, J. Villermaux, J. L. Barnay,

P. Bonte and C. Georgakis, “Tendency Modelling of

Semibatch Reactors for Optimization and Control,” Chem.

Eng. Sci., vol. 41, no. 4, pp. 913-920, 1986.

[4] A. Arpornwichanop, P. Kittisupakorn and I. M. Mujtaba,

“On-line dynamic optimization and control strategy for

improving the performance of batch reactors,” Chem. Eng.

Process., vol. 44, pp. 101-114, 2005.

[5] A. Arpornwichanop, P. Kittisupakorn and M. A. Hussain,

“Model-Based Control Strategies for a Chemical Batch

Reactor with Exothermic Reactions,” Korean J. Chem. Eng.,

vol. 19(2), pp. 221-226, 2002.

[6] R. Caetano, M. A. Lemos, F. Lemos and F. Freire, “Modeling

and control of an exothermal reaction,” Chem. Eng. J., vol.

238, pp. 93-99, 2014.

[7] W. L. Luyben, Chemical Reactor Design and Control, John

Wiley & Sons, 2007.

[8] N. Hvala and D. Kukanja, “Modelling and simulation of

semi-batch polymerisation reactor for improved reactants

dosing control,” Simul Model Pract Th, vol. 33, pp. 102-

114, 2013.

[9] W. L. Luyben, “Fed-Batch Reactor Temperature Control

Using Lag Compensation and Gain Scheduling,” Ind. Eng.

Chem. Res., vol. 43, pp. 4243-4252, 2004.

[10] D. Aguado, J. Ribes, T. Montoya, J. Ferrer and A. Seco, “A

methodology for sequencing batch reactor identification

with artificial neural networks: A case study,” Comput.

Chem. Eng., vol. 33, pp. 465-472, 2009.

[11] M. N. Kashani and S. Shahhosseini, “A methodology for

modeling batch reactors using generalized dynamic

netural networks,” Chem. Eng. J. , vol. 15, pp. 195-202,

2010.

[12] P. Terwiesch, M. Agarwal and D. W. Rippin, “Batch unit

optimization with imperfect modelling: a survey,” J. Proc.

Cont., vol. 4, no. 4, pp. 238-258, 1994.

[13] J. Zhang and Z. Xiong, “A batch-to-batch iterative optimal

control strategy based on recurrent neural network

models,” J. Process. Contr., vol. 159, pp. 195-202, 2005.

[14] M. D. Grau, J. M. Nougués and L. Puigjaner, “Batch and

semibatch reactor performance for an exothermic

reaction,” Chem. Eng. Process., vol. 39, pp. 141-148, 2000.

[15] N. Aziz and I. M. Mujtaba, “Optimal operation policies in

batch reactors,” Chem. Eng. J., vol. 85, pp. 313-325, 2002.

[16] R. Saada, D. Patel and B. Saha, “Causes and consequences

of thermal runaway incidents - Will they ever be

avoided?,” Process Saf. Environ., vol. 97, pp. 109-115,

2015.

[17] F. Lemos, J. M. Lopes and F. R. Ribeiro, Reactores

Químicos, 3rd Edition, IST Press, 2014.

[18] L. Ni, A. Mebarki, J. Jiang, M. Zhang, V. Pensee and Z. Dou,

“Themal risk in batch reactors: Theoretical framework for

runaway and accident,” J. Loss Prevent. Prco., vol. 43, pp.

75-82, 2016.

[19] S. Copelli, M. Derudi and R. Rota, “Topological Criteria to

Safely Optimize Hazardous Chemical Processes Involving

Consecutive Reactions,” Ind. Eng. Chem. Res., vol. 49, pp.

4583-4593, 2010.

[20] A. Kummer and T. Varga, “Feeding trajectory optimization

in fed-batch reactor with highly exothermic reactions,”

Comput. Chem. Eng., vol. 98, pp. 1-11, 2017.

[21] L. Ni, A. Mebarki, J. Jiang, M. Zhang and Z. Dou, “Semi-

batch reactors: Thermal runaway risk",” J. Loss Prevent.

Proc., vol. 43, pp. 559-566, 2016.

[22] A. Milewska and E. Molga, “Safety aspects in modelling

and operating of batch and semibatch stirred tank

chemical reactors,” Chem. Eng. Res. Des., vol. 88, pp. 304-

319, 2010.

[23] E. J. Molga, M. Lewak and K. R. Westerterp, “Runaway

prevention in liquid-phase homogeneous semibatch

reactors,” Chem. Eng. Sci., vol. 62, pp. 5074-5077, 2007.

[24] F. Caccavale, M. Iamarino, F. Pierri and V. Tufano, Control

and Monitoring of Chemical Batch Reactors, Springer,

2011.

[25] D. E. Seborg, T. F. Edgar, D. A. Mellichamp and F. J. Doyle

III, Process Dynamics and Control, 3rd Edition, John Wiley

& Sons, 2011.

[26] B. J. Cott and S. Macchietto, “Temperature Control of

Exothermic Batch Reactors Using Generic Model Control,”

Ind. Eng. Chem. Res., vol. 28, pp. 1177-1184, 1989.


10

[27] W. Cho, T. F. Edgar and J. Lee, “Iterative learning dual-

mode control of exothermic batch reactors,” Control Eng.

Pract., vol. 16, pp. 1244-1249, 2008.

[28] M. Friedrich and R. Perne, “Design and Control of Batch

Reactors - an industrial viewpoint,” Comput. Chem. Eng.,

vol. 19, pp. 357-368, 1995.

[29] A. Traoré, S. Grieu, S. Puig, L. Corominas, F. Thiery, M. Polit

and J. Colprim, “Fuzzy control of dissolved oxygen in a

sequencing batch reactor pilot plant,” Chem. Eng., vol.

111, pp. 13-19, 2005.

[30] N. Aziz, M. A. Hussain and I. Mutjaba, “Performance of

different types of controllers in tracking optimal

temperature profiles in batch reactors,” Comput. Chem.

Eng., vol. 24, pp. 1069-1075, 2000.

[31] L. Mears, S. M. Stocks, G. Sin and K. V. Gernaey, “A review

of control strategies for manipulating the feed rate in fed-

batch fermentation processes,” J. Biotechnology, vol. 245,

pp. 34-46, 2017.

[32] D. Tyner, M. Soroush and M. C. Grady, “Adaptive

Temperature Control of Multiproduct Jacketed Reactors,”

Ind. Eng. Chem. Res., vol. 38, pp. 4337-4344, 1999.

[33] S. Aumi, B. Corbett, T. Clarke-Pringle and P. Mhaskar,

“Data-Driven Model Predictive Quality Control of Batch

Processes,” AIChE J., vol. 59, no. 8, pp. 2852-2861, 2013.

[34] E. Pahija, F. Manenti, I. M. Mutjaba and F. Rossi,

“Assessment of control techniques for the dynamic

optimization of (semi-)batch reactors,” Comput. Chem.

Eng., vol. 66, pp. 269-275, 2014.

[35] I. M. Mutjaba, N. Aziz and M. A. Hussain, “Neural Network

Based Modelling and Control in Batch Reactors,” Chem.

Eng. Res. Des., vol. 84(A8), pp. 635-644, 2006.

[36] R. Chi, B. Huang, Z. Hou and S. Jin, “Data-Driven high-order

terminal iterative learning control with a faster

convergence speed,” Int. J. Robust Nonlin, vol. 28, pp. 103-

119, 2018.

[37] A. J. O'Reilly, “Batch Reactor Optimization, Profitability vs

Waste Minimization,” Trans IChemE, vol. 80A, pp. 587-596,

2002.

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