Modelling and simulation of semi-batch polymerisation reactor for improved reactants dosing control Nadja Hvala a,⇑ , Dolores Kukanja b a Joz ˇef Stefan Institute, Department of Systems & Control, Jamova cesta 39, SI-1000 Ljubljana, Slovenia b Mitol d.d., Partizanska cesta 78, SI-6210 Sez ˇana, Slovenia article info Article history: Available online 21 December 2012 Keywords: Emulsion polymerisation Semi-batch industrial reactor Calorimetry model gPROMS Control abstract This paper presents a temperature model of an industrial, semi-batch, emulsion-polymer- isation reactor, which together with the already designed chemical reactions model is able to predict the temperature in the reactor as a result of varying operating conditions. The model was derived from the energy balance equations and validated on real-plant data. The model was used to analyse the influence of reactants dosing during the batch on the reactor temperature. The analysis shows that during the batch dosing of the two reactants, initiator and monomer, needs to be mutually balanced and adjusted to the current process situation, otherwise, the temperature in the reactor may become oscillatory and unstable towards the end of the batch because of the limited heat removal capacity of the con- denser. To keep the reactor temperature in a narrow region also the control strategy was proposed that adjusts the monomer flow and initiator addition, using reactor temperature as a controlled variable. Simulation results show that the proposed reactants dosing control significantly reduces the variations in the reactor temperature and at the same time results in more uniform final batch results. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction Emulsion polymerisation is an important industrial process for the production of synthetic polymers, e.g., paints, adhe- sives, coatings and binders. Batch and semi-batch reactors are the most common reactors used in polymer engineering. The production requirements typically addressed in polymerisation reactors are the following: – to achieve tight temperature control during the reaction, – to achieve high conversion of reacting chemicals, – to reduce the total batch time. The most often addressed control problem in polymerisation reactors is the control of a reactor’s temperature, which is required because of the heat released in the exothermic reaction. Production requirements are to keep the temperature in a narrow region around the desired set-point (e.g. ±1 K). Tight temperature control enables to reach the desired molecular weight and distribution of final polymer particles and helps to prevent the synthesis of an off-spec polymer at elevated temperatures. The temperature of the polymerisation reactors is normally controlled by manipulating the temperature of the coolant, which is circulated through the cooling jacket, and various advanced control methods are used in these cases, e.g. 1569-190X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.simpat.2012.10.003 ⇑ Corresponding author. Tel.: +386 14773606. E-mail addresses: [email protected](N. Hvala), [email protected](D. Kukanja). Simulation Modelling Practice and Theory 33 (2013) 102–114 Contents lists available at SciVerse ScienceDirect Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
Transcript
Simulation Modelling Practice and Theory 33 (2013) 102–114
Contents lists available at SciVerse ScienceDirect
Modelling and simulation of semi-batch polymerisation reactorfor improved reactants dosing control
Nadja Hvala a,⇑, Dolores Kukanja b
a Jozef Stefan Institute, Department of Systems & Control, Jamova cesta 39, SI-1000 Ljubljana, Sloveniab Mitol d.d., Partizanska cesta 78, SI-6210 Sezana, Slovenia
1569-190X/$ - see front matter � 2012 Elsevier B.Vhttp://dx.doi.org/10.1016/j.simpat.2012.10.003
⇑ Corresponding author. Tel.: +386 14773606.E-mail addresses: [email protected] (N. Hvala), d
This paper presents a temperature model of an industrial, semi-batch, emulsion-polymer-isation reactor, which together with the already designed chemical reactions model is ableto predict the temperature in the reactor as a result of varying operating conditions. Themodel was derived from the energy balance equations and validated on real-plant data.The model was used to analyse the influence of reactants dosing during the batch on thereactor temperature. The analysis shows that during the batch dosing of the two reactants,initiator and monomer, needs to be mutually balanced and adjusted to the current processsituation, otherwise, the temperature in the reactor may become oscillatory and unstabletowards the end of the batch because of the limited heat removal capacity of the con-denser. To keep the reactor temperature in a narrow region also the control strategy wasproposed that adjusts the monomer flow and initiator addition, using reactor temperatureas a controlled variable. Simulation results show that the proposed reactants dosing controlsignificantly reduces the variations in the reactor temperature and at the same time resultsin more uniform final batch results.
� 2012 Elsevier B.V. All rights reserved.
1. Introduction
Emulsion polymerisation is an important industrial process for the production of synthetic polymers, e.g., paints, adhe-sives, coatings and binders. Batch and semi-batch reactors are the most common reactors used in polymer engineering.
The production requirements typically addressed in polymerisation reactors are the following:
– to achieve tight temperature control during the reaction,– to achieve high conversion of reacting chemicals,– to reduce the total batch time.
The most often addressed control problem in polymerisation reactors is the control of a reactor’s temperature, which isrequired because of the heat released in the exothermic reaction. Production requirements are to keep the temperature in anarrow region around the desired set-point (e.g. ±1 K). Tight temperature control enables to reach the desired molecularweight and distribution of final polymer particles and helps to prevent the synthesis of an off-spec polymer at elevatedtemperatures.
The temperature of the polymerisation reactors is normally controlled by manipulating the temperature of the coolant,which is circulated through the cooling jacket, and various advanced control methods are used in these cases, e.g.
A heat-transfer area (cm2)Closs reactor heat-losses parameter (J s�1 K�1)Cp,mon specific heat capacity of monomer (J g�1 K�1)Cp,pol specific heat capacity of polymer (J g�1 K�1)Cp,water specific heat capacity of water (J g�1 K�1)Cp,PVOH specific heat capacity of PVOH (J g�1 K�1)G0 total mass of PVOH (g)DHjacket the heat from the heating jacket (J s�1)DHr heat of polymerisation (J mol�1)KR reaction heat capacity (J K�1)mw mass of water in the reactor jacket (g)Mconv mass of monomer converted into polymer (mol)Mm mass of monomer in the reactor (mol)MWm monomer molecular weight (g mol�1)qm monomer feed flow rate (mol s�1)Qcond heat removed by the reflux through the condenser (J s�1)Qcond,max maximum heat removal capacity of the condenser (J s�1)Qloss heat losses of the reactor (J s�1)Qmon energy of the feeding monomer (J s�1)Qpol heat produced in the polymerisation reaction (J s�1)rpol polymerisation reaction rate (mol s�1)T temperature in the reactor (K)Text outside temperature (K)Tjacket temperature in the reactor jacket (K)Tmon temperature of the feeding monomer (K)U heat transfer coefficient (W cm�2 K�1)Vw volume of water (l aq)qw water density (g l aq�1)
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feedforward control using an inverse reactor model [7], exact linearisation [3], nonlinear adaptive control based on differ-ential geometric concepts [5] and model predictive control [13]. However, much less often the cases are addressed, wherethe reaction heat is removed only by evaporative cooling. In such a case, the control of the temperature is only possiblethrough the reactants dosing control.
In this study we present the design and validation of the reactor temperature model, which was derived from the energybalance equations. Together with the chemical reactions model [1,9], the model is used to optimise the process through reac-tants dosing control. The control approach is similar to the one presented in the recent paper by Arora et al. [2], but differs inthat in this case the feed rates of both reacting chemicals, the monomer and initiator, are used to control the reactor tem-perature. The approach has also been presented in [8], but is in this paper improved with the analysis and choice of controllerparameters that enable both tight temperature control and short batch processing time.
This paper is organised as follows. In the next section we present the semi-batch polymerisation process under study. Thereactor temperature model derived from energy balance equations is presented in Section 3 and its simulation results in Sec-tion 4. Section 5 presents simulation analysis of initiator and monomer dosing and the designed reactants dosing controlscheme. The obtained control results are shown in Section 6. The paper ends with the conclusions, where the main findingsand directions for future work are described.
2. Process description
The process considered in the study is a semi-batch emulsion polymerisation reactor in Mitol d.d. company, Slovenia(Fig. 1). The components involved in the reaction are water, monomer (vinyl acetate), initiator (potassium persulfate –KPS) and stabiliser (polyvinyl alcohol – PVOH). The reaction is initiated by the thermal decomposition of the initiator inthe water phase, where free radicals are formed; these radicals then react with the monomer to form longer chains (oligo-mers). At a certain critical length oligomers precipitate and form particles, which are the target final product.
In the industrial operation, the process starts by adding initial amounts of monomer and initiator to the reactor as well asthe whole amount of polyvinyl alcohol and water. The reactor is then heated up to 338–343 K (see also Fig. 2) by pumpinghot water into the heating jacket. The exothermic reaction and the heat of the remaining water filling the heating jacket con-tinue to increase the reactor temperature. When temperature reaches a certain value, the monomer begins to be pumpedinto the reactor with a continuous flow to preserve the reaction. During the reaction, heat is removed by evaporative coolingin the condenser. A temperature decrease in this phase indicates a slow-down of the reaction, so a certain amount of initiator
T
T
TT
T
TTInitiatorMonomerWater Stabiliser
nitaeHretawgnitaeH g water
Cooling water Cooling waterCondenser
Fig. 1. Scheme of an industrial polymerisation reactor.
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is added in the reactor every time the temperature falls below a certain value. When all the monomer is added to the reactor,a larger amount of initiator is added in order to terminate the reaction. The temperature is then allowed to reach 363 K, andthe reaction is considered to be finished when the temperature starts to decrease again.
The final quality of the production process is evaluated by the product quality parameters, i.e. the conversion, the solidscontent and the viscosity. In the production process, these measurements are available only at the end of the batch and aftermixing the batches from several reactors.
3. Reactor temperature model
For the analysis of the influence of reactants dosing on the reactor temperature, and for the design of reactants dosingcontrol strategy, the reactor temperature model was designed from the energy balance equations. The temperature modeltakes into account the reaction heat capacity, and the energy produced and consumed during the reaction [6,14,15].
The reaction heat capacity KR is calculated from the heat capacities of the reactor ingredients, i.e., the monomer present inthe reactor Mm, the monomer converted into the polymer Mconv, polyvinyl alcohol G0 and water. These process variables aresimulated by a complex chemical reactions model describing the reacting variables during the reaction [9]. Hence, KR isdetermined as
where Cp denote the specific heat capacities of the reactor ingredients, MWm is monomer molecular weight, Vw is the watervolume and qw is the water density.
Energy is consumed or released as a result of the following:
(i) The heating of the reactor through the heating jacket DHjacket
DHjacket ¼ UAðTjacket � TÞ ð2Þ
where T is the temperature in the reactor, Tjacket is the temperature in the reactor jacket, U is the heat-transfer coefficient andA is the heat-transfer area. The temperature in the jacket is kept constant (around 363 K) during the heating phase, whileafterwards it is modelled as follows:
dTjacket
dt¼ � UA
mwCp;waterðTjacket � TÞ ð3Þ
where mw is the mass of water in the reactor jacket.(ii) The heating of the incoming monomer Qmon
Fig. 2. Reactor temperature as measured on the plant and simulated by the model (top diagram), together with the corresponding real plant monomer andinitiator flows (middle diagram). The bottom diagram shows the contribution of different terms in energy balance equation (Eq. (8)) as obtained insimulation (note: cooling and heat losses are plotted with opposite sign).
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The heating of the incoming monomer depends on the monomer’s feed flow rate qm, its specific heat capacity Cp,mon andits temperature Tmon
Q mon ¼ qmMWmCp;monTmon ð4Þ
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(iii) The heat produced in the exothermic reaction Qpol
It is proportional to the polymerisation reaction rate rpol, which is modelled by the chemical reactions model [9], and theheat of polymerisation DHr
Qpol ¼ �DHrrpol ð5Þ
(iv) The cooling of the reactor by the reflux through the condenser Qcond
It is modelled experimentally. As no information on the condenser flow is available, the model was simplified. Qcond isequal to Qpol, but limited by the experimentally determined maximum capacity of the cooling system Qcond,max
Q cond ¼Q pol; if Q pol < Q cond;max
Q cond;max; if Q pol > Q cond;max
(ð6Þ
(v) The heat losses to the surroundings Qloss
Qloss ¼ ClossðT � TextÞ ð7Þ
where Closs is an adjustable parameter and Text is the outside temperature.By taking into account all the contributing elements, the temperature in the reactor can be modelled from the reactor
The left-hand side of the equation accounts for the changes in the internal energy of the reactor, which are due to thechange of the reactor’s temperature (first term) and the change of its heat capacity (second term). The right-hand side in-cludes all the terms contributing to energy production or consumption. To get the proper shape of the temperature profilethroughout the whole batch, all the terms in the above equation need to be considered. However, the importance of eachterm varies depending on the stage of the process (see also Fig. 2, bottom diagram). During the initial part of the batchthe most important are the heating of the reactor through the jacket, the exotermic reaction heat and the heat removedby the condenser. During the main part of the batch, the heating through the heating jacket is no more present, and alsothe contribution of heat losses is small. At the last stage, when the reaction is finished, only the heat losses affect the reactortemperature.
The values of model parameters in Eq. (8) are given in Table 1. They were taken from the literature [10] or estimated sothat a satisfactory agreement of the model with the real-plant temperature data is obtained.
As seen from the table, two model parameters (Qcond,max and UA) had to be adjusted for each batch to get a good agree-ment with process data. The heat-transfer parameter UA was adjusted for each batch to obtain a good fit during the temper-ature rise. This is because the heat-transfer coefficient U decreases significantly from batch to batch due to increased foulingof the reactor walls between cleaning periods, as well as during a batch, because of the increasing batch viscosity. These phe-nomena are also reported in the literature [5,7]. In our case, UA is most influential during the heating up of the reactor andless important during the reaction as the cooling of the reactor is not performed by the cooling jacket. Hence, UA was onlyadjusted from batch to batch, but considered as a constant during the batch. As described in [15], UA is equal (1/s)KR, where sis estimated from the temperature profile at low temperatures, where the reaction is not yet present.
Also, the experimentally determined maximum capacity of the cooling system Qcond,max was adjusted for each batch in therange of ±10% of the average value. With too low values of Qcond,max the average temperature during the batch slowly in-creases, and with too high values it decreases. The adjustment of Qcond,max was necessary due to the simplified model ofthe cooling system. Although more comprehensive evaporative cooling models can be found in the literature [2,4], the sim-plified model presented in this paper proved sufficient for a good estimate of the reactor temperature and also exhibits goodcorrelation between the modelled unremoved heat and the increased temperature at the outlet of the condenser (the tem-
Table 1The values of temperature model parameters.
Parameter Value Reference
Closs 0.2 J s�1 K�1 EstimatedCp,mon 1.17 J g�1 K�1 Polymer Data HandbookCp,pol 1.77 J g�1 K�1 Polymer Data HandbookCp,water 4.18 J g�1 K�1 –Cp,PVOH 1.65 J g�1 K�1 Polymer Data HandbookDHr �87.5 kJ mol�1 Polymer Data HandbookMWm 86.09 g mol�1 Polymer Data HandbookMWPVOH 205000 g mol�1 Polymer Data HandbookQcond,max [85–105] J s�1 EstimatedText, Tmon 283 K EstimatedUA (1/s)KR, s = [4000–6250] s�1 Estimatedqw 1000 g l�1 –
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perature increase indicates inability of the condenser to remove all the surplus heat). The adjustment of the maximumcapacity model parameter can be easily performed both in on-line as well as off-line simulations.
4. Process simulation
The presented model was simulated together with the chemical reactions model [9] using the gPROMS modelling tool[11]. The complete set of differential and algebraic equations representing the chemical reactions and energy balance equa-tions was programmed in gPROMs from scratch and solved by the numerical DAE solvers provided by the gPROMS. Scalingwas applied to solve numerical problems related to different scales of simulated variables. The package provides the connec-tion to Excel that was used to import data from the recorded real-plant SCADA system. It also provides connection to Matlabfor easier implementation of advanced control methods, but was not used in our case. The process was simulated continu-ously, while the designed controllers were discrete, resembling the real control applications in the SCADA system. The gPR-OMS environment appeared more appropriate for continuous implementation and the inclusion of discrete controllersprolonged simulations.
Simulations were based on real-plant data, where the inputs to the model were the real plant’s initial reactants dosing,and during the batch the monomer and initiator flows. Fig. 2 shows results for one batch. Middle diagram shows the realplant monomer flow and initiator additions during the batch, and the top diagram shows the resulting temperature profileas obtained in the plant and simulated with the presented model. From the figure we can see that with the presented modelwe are able to get good estimates for the reactor temperature. In this particular batch only the first temperature peak is notmodelled very accurately. Note also that in the production process the temperature variations during the batch are quitelarge.
In Fig. 2 initial temperature rise (during the 1st hour) is because of the heating of the reactor through the temperaturejacket. At approximately 338 K the initiator’s thermal decomposition starts and afterwards the temperature is controlledonly by monomer and initiator additions. Monomer is filled in the reactor continuously to retain enough monomer, whichis responsible for the reaction rate. Due to the large monomer mass, the influence of monomer flow on the reactor tem-perature is rather slow. On the other hand, initiator is added occasionally, when the reaction rate is slowing down be-cause of a lack of radicals to form new growing chains. In the reactor’s operation this can be noticed by a decrease ofreactor temperature. The additions of initiator are small, but have an almost immediate effect on the increase of the reac-tor temperature, as by the formation of new initiator radicals a large amount of monomer is reacted, and hence energyreleased.
In Fig. 2 we can see that each initiator addition (at approx. 2.5 h, 4.5 h, 5.5 h and 7.5 h) results in an increase of reactortemperature. The temperature increase depends on the new radicals formed (i.e. initiator addition) and the monomer massin the reactor. In the presented batch the increase of reactor temperature at initiator additions is quite large. To prevent evenhigher temperature peaks, the monomer flow in the real plant was lowered towards the end of the batch. Discontinuity ofthe monomer flow as appeared in simulations and seen in Fig. 2 is because of 5-min sampling of real-plant input data forgPROMS simulation, averaging of real-plant data in 5-min interval, and estimation and quantisation of monomer flow signals(monomer flow is not measured but determined from the weight change of the monomer dosing vessel) in the existing SCA-DA system. In simulations the initiator addition was simulated as a 5-min initiator flow, although in the real plant the ini-tiator is added at once; with 5 min addition a time-delay was approximated, which exists in the real-plant before the addedinitiator is well mixed in the reactor.
5. Reactants dosing control
The designed model was used in a search for the most appropriate initiator and monomer dosing to optimise the processoperation. During the batch the dosing of reactants is important to keep the desired reaction rate; but because of the exo-thermic reaction, it also affects the temperature in the reactor. For the product quality reasons, the temperature during thebatch should be kept within tight limits (e.g. ±1 K) around the desired constant set-point. In our case the desired temperatureduring the reaction is 354 K.
As explained in Section 4, the monomer is dosed continuously during the batch, while the initiator is added when thetemperature decreases, with the latter indicating that the reaction is slowing down. While discrete dosing of initiator causessudden increases of reaction rate and thus unavoidable temperature oscillations because of a limited heat removal capacity,the oscillations may become too large if the dosing of reactants is not properly adjusted.
To analyse the influence of reactants dosing on the reactor temperature two cases were considered in simulations. In thefirst case the reactor was simulated at a constant monomer flow of 1.7 mol/s but at different initiator flows of 0.0002 mol/s,0.0006 mol/s and 0.0008 mol/s in three different simulations, respectively (Fig. 3). Initiator was added for 5 min every timethe temperature was below the set-point (354 K). From the figure it is clear that with larger initiator additions the reactionrate is higher and hence more energy is released. The cooling system is not able to remove all the released heat, so the tem-perature peaks are higher and, consequently, more time is needed before the temperature is decreased to a value (354 K)when the next initiator addition is started. During this time, the amount of unreacted monomer accumulates in the reactorbecause of the monomer addition, so at the next initiator addition the reaction rate (which is also proportional to the mono-
0 1 2 3 4 5 6 7 8 9350
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Fig. 3. Temperature and monomer mass in the reactor for different initiator additions (0.0002 mol/s, 0.0006 mol/s, 0.0008 mol/s as indicated in the legend)and a constant monomer flow of 1.7 mol/s in all cases. Initiator is added every time the temperature is below the set-point (354 K).
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mer mass) is even higher and results in an even higher temperature peak. From the figure it is clear that large initiator addi-tions may result in unstable temperature oscillations toward the end of the batch. On the contrary, by keeping the initiator
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Fig. 4. Temperature and monomer mass in the reactor for different monomer flows (1.6 mol/s, 1.8 mol/s, 1.9 mol/s as indicated in the legend) and initiatoradditions of 0.0002 mol/s when the temperature is below the set-point (354 K).
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flow low, the oscillations are well controlled. However, the initiator flow should not be too low, as in this case the reactionrate may become limited by the shortage of initiator and the desired temperature set-point could not be reached (see Fig. 3,an initiator addition of 0.0002 mol/s).
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The second case shows the temperature profiles for different monomer flows of 1.6 mol/s, 1.8 mol/s and 1.9 mol/s (Fig. 4),while initiator additions at temperatures below the set-point were always small and equal 0.0002 mol/s. In this case the in-crease of temperature oscillations may appear because of a too large monomer flow. Similarly as in the previous case, with atoo large monomer flow the amount of unreacted monomer is larger, leading to a higher reaction rate and high temperaturepeaks despite of small initiator additions. On the contrary, with a too low monomer flow, the reaction rate may become lim-ited by the shortage of the monomer and the temperature set-point could not be reached (see Fig. 4 and the monomer flow of1.6 mol/s). In the figure it is also clear that with a high monomer flow the first temperature peak results in a significant over-shoot of the desired temperature set-point. In addition, the final temperature rise after the end of the monomer addition isalso much higher, being the result of a lower conversion during the batch, so larger amounts of monomer do not react untilthe final initiator addition. Note however that with higher monomer flow the batch time is significantly shorter resulting alsoin a higher production rate.
From the simulations it can be concluded that dosing of both reactants during the batch need to be mutually balanced andproperly adjusted to the current process state. In the case of too large monomer or initiator flows, the magnitude of temper-ature oscillations may increase towards the end of the batch. On the contrary, with too low monomer flow or initiator flowsthe reaction rate may become limited because of the shortage of reacting chemicals. Hence, while temperature should becontrolled within tight limits, small temperature oscillations during the batch are desired, indicating that the process isnot limited by the amount of the reacting chemicals.
The above control problem of properly feeding the two reactants to control the reactor temperature could be generallyclassified as a multivariable control with two inputs and one output, and is in similar applications in chemical engineeringtypically solved by a ratio control. Ratio control methods are used to maintain the flow rate of one stream in the process at aspecified proportion relative to that of another. One of the reactor feed streams is chosen as a control variable in a feed-backcontrol of a given output, while the other feed stream is determined by the desired ratio of the two process variables.Although the concept proved successful in chemical industry, it has not been extensively used in polymer reactor control,where flow controllers are designed typically for each of the reactor feed streams [12]. In our case the ratio between thetwo feeding streams, the monomer and initiator, could not be determined in advance for precise temperature control. A de-sired ratio to maintain would be the ratio between the unreacted monomer and initiator in the reactor, but both variablescould not be measured on-line. Therefore, the control algorithm for reactants dosing was designed as a combined monomerand initiator dosing-control that adjusts the reactants dosing in two control loops, both using the reactor temperature as acontrolled variable (Fig. 5).
The initiator addition is required only when the reaction rate is slowing down, which is indicated by a low temperature inthe reactor. Therefore, initiator controller was designed as a discrete one-sided proportional control with cut-off if the tem-perature is above the set-point. With cut-off nonlinearity, the control signal is non-zero only when the reactor temperature isbelow the set-point. The control action of such a controller is similar to an on–off controller, but improved with the controlsignal that is proportional to control error to speed up the reaction if the temperature is very low. The flow of the addedinitiator uI is determined as
uIðkÞ ¼Kp;IeIðkÞ; if T < Tsp;init
0; if T P Tsp;init
�ð9Þ
where eI(k) is the control error, i.e. the difference between the initiator dosing temperature set-point Tsp,init and the measuredtemperature in the reactor T, and Kp,I is the gain of the controller. The control signal was discretised and determined as amultiplication of a predefined initiator flow uI,0. The initiator dosing control starts after the first temperature peak. The algo-rithm sampling time is 5 min, and the initiator is added for 5 min. After the addition, the next control action is delayed for10 min to account for the process delay. When all the monomer is added to the reactor, a larger amount of initiator is added,like in the real plant.
The aim of the monomer dosing control is to adjust the monomer flow to stabilise reactor temperature around the desiredvalue. For monomer dosing a discrete linear PI controller was designed
uMðkÞ ¼ uM;0 þ Kp;M eMðkÞ þTs
Ti
Xk
j¼1
eMðjÞ !
ð10Þ
where uM(k) is the monomer flow, uM,0 is a predefined monomer flow, eM(k) is the control error, i.e. the difference betweenthe monomer-dosing temperature set-point Tsp,mon and the measured temperature in the reactor T, parameter Kp,M is the pro-
Initiator dosing
Monomer dosing
Initiator flow
Monomerflow
Processmodel
TemperatureT
Tsp,ini
+-
Tsp,mon
+eI
eMuM
uI-
Fig. 5. Initiator and monomer dosing-control scheme.
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portional gain of the controller, Ti is the integral time constant and Ts is the sampling time. The monomer dosing controlstarts after the first temperature peak or when the reactor temperature first reaches the monomer dosing temperatureset-point. The algorithm sampling time is 1 min.
The monomer controller is responsible for the stabilisation of the reactor temperature, so the PI structure with the inte-gral term was chosen to achieve small steady state errors. Simulations have shown, however, that very tight temperaturecontrol obtained when choosing the same temperature set-point for both initiator and monomer controller [8] may resultin very reduced monomer flow and consequently, prolonged batch time, which is not desired. In fact, the monomer flowshould be adjusted to the size of temperature oscillations around the temperature set-point; the control algorithm shoulddecrease the monomer flow if the magnitude of temperature oscillations is above the specified limits; on the contrary, ifthe oscillations are small it should increase the monomer flow and thus prevent the reaction rate to become limited bythe shortage of monomer.
To implement such a non-linear control law by a simple linear controller as (10), we chose different temperature set-points for the initiator and monomer dosing controller. The monomer-dosing temperature set-point Tsp,mon is always higheror equal to the initiator-dosing temperature set-point Tsp,ini. Lower Tsp,ini forces the process to reach lower temperatures be-fore the initiator addition; during this time the monomer controller has a positive error, which increases the monomer flowand thus prevents the process reaction rate to become limited by the shortage of monomer. With such a control, the mag-nitude of temperature oscillations could be adjusted by the choice of the difference between the Tsp,mon and Tsp,ini as shown inthe next section.
6. Control results
From the description of monomer and initiator dosing in Section 5 it is clear that the process has different and conflictinggoals. While temperature oscillations during the batch should be kept small, this contradicts the requirement on short batch
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9.8
Prop. gain Kp,I [mol/(s K)]
Batch duration [h]
Set-point difference [K]
Fig. 6. The influence of the proportional gain of the initiator controller Kp,l and temperature set-point difference on the range of temperature variations andbatch duration time.
0 1 2 3 4 5 6 7 8 9 10320
325
330
335
340
345
350
355
360
365
370
Time [h]
Tem
pera
ture
[K]
T measuredT controlled
1
1.5
2
Mon
omer
flow
[mol
/s]
Monomer
0 1 2 3 4 5 6 7 8 9 100
0.5
1
1.5
2x 10
-3
Initiator flow [m
ol/s]
Time [h]
Initiator
Fig. 7. Reactor temperature as measured on the plant and simulated together with the designed initiator and monomer dosing control algorithm, and thecorresponding control signals of monomer and initiator flows.
112 N. Hvala, D. Kukanja / Simulation Modelling Practice and Theory 33 (2013) 102–114
time. To properly tune the controller parameters and thus achieve the balance between the conflicting goals, an analysis wasperformed evaluating both the range of temperature variations during the batch and the batch duration time as a function ofcontroller parameters, i.e. the proportional gain of the initiator controller Kp,I and the temperature set-point difference. Theresults are presented in Fig. 6. It can be seen that by choosing small temperature set-point difference and large proportionalgain of the initiator controller, the temperature variations are very small, but in this case, the batch duration is very pro-longed. On the contrary, with large temperature set-point difference and small proportional gain of the initiator controllerthe batch duration time is minimised, but the range of temperature variations is large. To obtain the balance between theconflicting goals the temperature set-point difference was selected as 0.3 K and the proportional gain of the initiator control-ler was selected as Kp,I = 3 mol/(s K). The other parameters of the controllers were chosen as follows: uI,0 = 0.0002 mol/s,uM,0 = 1.65 mol/s, Tsp,ini = 353 K, Tsp,mon = 352.7 K, Kp,M = 0.08 mol/(s K), Ts = 60 s, Ti = 500 s.
Simulation results of the designed reactants dosing control are shown in Fig. 7 for one batch. The simulated batch in Fig. 7is the same as in Fig. 2, but in this case the monomer and initiator flows during the batch were determined by the proposedcontrol algorithm. To evaluate the control performance, also the real plant temperature profile from Fig. 2 is shown for com-parison. From the figure it is clear that with the applied control, the temperature during the batch is kept in a narrower re-gion, compared to the real plant-temperature. A tighter temperature control is achieved by the initiator dosing that preventsvery high temperature peaks by using small initiator additions; at the same time, by using more frequent additions it doesnot allow the temperature to drop off and so preserves the high reaction rate. The monomer dosing control adjusts, i.e. re-duces the monomer flow to prevent the accumulation of unreacted monomer in the reactor, which may cause oscillatory andunstable temperature behaviour towards the end of the batch; at the same time, it keeps the monomer flow high enough topreserve stable temperature oscillations indicating that the process reaction rate is not limited by the shortage of monomer.
Temperature control also affects the final product quality parameters, i.e. conversion, solids content and viscosity. In pro-duction process, these parameters are only measured at the end of the batch and after the mixing of several batches, but for a
Fig. 8. Standard deviations of conversion, solids content and viscosity as measured in the process, predicted by the model based on real plant data, andwhen applying the proposed reactants dosing control.
N. Hvala, D. Kukanja / Simulation Modelling Practice and Theory 33 (2013) 102–114 113
small set of industrial batches (five batches) they were determined immediately after the end of the batch for the purpose ofmodel validation. Fig. 8 presents the standard deviations of these parameters as measured on the plant, simulated with theoverall process model [9] and simulated together with the designed control.
From the figure it can be seen that the standard deviations of these output parameters as predicted by the model are inthe range of the process measurements, while the standard deviations of the control results are significantly smaller. Thisindicates that a tighter temperature control also contributes to more uniform final output results. With the designed controlthe range of temperature variations was reduced from 9 to 2 K, while the average batch duration was approximately thesame (9.4 h).
7. Conclusions
In this paper we presented the design of a temperature model of an emulsion polymerisation reactor, which together withthe already acquired chemical reactions model was used to analyse the influence of reactants dosing on process perfor-mance, and finally led to the design of an improved reactants dosing control. Simulations have shown that initiator andmonomer dosing during the batch, if not properly adjusted, can led to the oscillatory and unstable temperature behaviourtowards the end of the batch. For this purpose the initiator and monomer dosing-control algorithms were designed usingreactor temperature as a controlled variable. While both control algorithms use temperature as a control variable, the dif-ference in temperature set-points of the two control algorithms prevents the process reaction rate to become limited bya shortage of the reacting chemicals, but at the same time preserves limited and stable temperature oscillations.
The simulation results indicate that the proposed control scheme efficiently controls the reactor temperature so as tokeep it close to the desired value, and also significantly reduces the batch-to-batch variations in the final output results.While the obtained control results are very satisfactory, some further improvements could be possible by implementing alsomore advanced model-based control schemes like model predictive control. Potential improvements are expected with re-spect to shorter batch time and more stable control signal.
Acknowledgment
The support of the European Commission in the context of the 6th Framework Programme (PRISM, Contract No. MRTN-CT-2004-512233) is greatly acknowledged.
References
[1] F. Aller, D. Kukanja, V. Jovan, M. Georgiadis, Modelling the semi-batch vinyl acetate emulsion polymerization in a real-life industrial reactor,Mathematical and Computer Modelling of Dynamical Systems 15 (2009) 139–161.
[2] S. Arora, R. Gesthuisen, S. Engell, Model based operation of emulsion polymerization reactors with evaporative cooling: application to vinyl acetatehomopolymerization, Computers & Chemical Engineering 31 (2007) 552–564.
[3] M.-A. Beyer, W. Grote, G. Reinig, Adaptive exact linearization control of batch polymerization reactors using a Sigma-Point Kalman Filter, Journal ofProcess Control 18 (2008) 663–675.
[4] J. Brandrup, E.H. Immergut, E.A. Grulke, A. Abe, D.R. Bloch, Polymer Handbook, John Wiley & Sons, 2005.[5] T. Clarke-Pringle, J.F. MacGregor, Nonlinear adaptive temperature control of multi-product, semi-batch polymerization reactors, Computers and
Chemical Engineering 21 (1997) 1395–1409.[6] F.B. Freire, R. Giudici, Temperature oscillation calorimetry by means of a Kalman-like observer: the joint estimation of Qr and UA in a stirred tank
polymerization reactor, in: J.B.P. Soares (Ed.), Polymer Reaction Engineering V, Macromolecular Symposia, Wiley, Quebec, Canada, 2004.[7] K. Graichen, V. Hagenmeyer, M. Zeitz, Feedforward control with online parameter estimation applied to the Chylla–Haase reactor benchmark, Journal
of Process Control 16 (2006) 733–745.[8] N. Hvala, D. Kukanja, Modelling and simulation of semi-batch polymerization reactor for improved reactants dosing control, in: Proceedings of the 7th
EUROSIM Congress on Modelling and Simulation, Prague, Czech Republic, September 6–10, 2010, vol. 2, Full papers (CD), 2010.[9] N. Hvala, F. Aller, T. Miteva, D. Kukanja, Modelling, simulation and control of an industrial, semi-batch, emulsion-polymerization reactor, Computers
and Chemical Engineering 35 (2011) 2066–2080.
114 N. Hvala, D. Kukanja / Simulation Modelling Practice and Theory 33 (2013) 102–114
[10] J.E. Mark, Polymer Data Handbook, second ed., Oxford University Press, New York, 2009.[11] PSE Ltd. gPROMS 3.0.4 Introductory User Guide, London, UK, 2004.[12] J.R. Richards, J.P. Congalidis, Measurement and control of polymerization reactors, Computers & Chemical Engineering 30 (2006) 1447–1463.[13] H. Seki, M. Ogawa, S. Ooyama, K. Akamatsu, M. Ohshima, W. Yang, Industrial application of a nonlinear model predictive control to polymerization
reactors, Control Engineering Practice 9 (2001) 819–828.[14] O. Ubrich, B. Srinivasan, P. Lerena, D. Bonvin, F. Stoessel, The use of calorimetry for on-line optimisation of isothermal semi-batch reactors, Chemical
Engineering Science 56 (2001) 5147–5156.[15] J. Zeaiter, V.G. Gomes, J.A. Romagnoli, G.W. Barton, Inferential conversion monitoring and control in emulsion polymerisation through calorimetric
measurements, Chemical Engineering Journal 89 (2002) 37–45.
