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1 Available online at ScienceDirect Proceia Engineering 1 (215 ) th DAAAM International Symposium on Intelligent Manufacturing an Automation, DAAAM 214 Enhancement of a Semi-Batch Chemical Reactor Efficiency through its Dimensions Optimization Lubomír Macků*, Davi Novosa Tomas Bata University in Zlin, Faculty of Applie Informatics, nám. T.G.Masaryka 5555, 76 5 Zlín, Czech Republic Abstract Efficiency of manufacturing processes is very important in toay's competitive worl with har economic rules. In chemical engineering area the efficiency epens on the prouction heart, which is often a chemical reactor. In this paper authors escribe process of optimal semi-batch exothermic reactor imensions fining. The task is to fin reactor imensions which lea to process efficiency improving, i.e. to processing the greater chemicals amount in the same or shorter time. The optimizing process uses an objective function which inclues also the reactor mathematical moel. The objective function is moifie here to fin better results an necessary limitations an penalizations are use to improve the imensions searching. An evolutionary approach represente by the Self-Organizing Migrating Algorithm (SOMA) was use to minimize the efine function. A suitability of the reactor with newly foun imensions was then verifie by the process control simulations. 215 The Authors. Publishe by Elsevier by Elsevier Lt. This Lt. is an open access article uner the CC BY-NC-ND license ( Peer-review uner responsibility of DAAAM International ienna. Peer-review uner responsibility of DAAAM International ienna Keywors: Temperature control; Online ientification; Semi-batch reactor; Exothermic process; SOMA 1. Introuction Even if the problem of the chemical reactors efficiency is quite important an is connecte with the reactor imensions, there are not many stuies publishe about the reactor imensions optimization these ays. Usually, the process is place to existing vessel an then the authors try to control the process with ifferent control techniques. But, the process is often not suitable for the given reactor geometry. Here, the authors are trying ifferent way to suite the reactor geometry to the exact process to achieve the best control results. * Corresponing author. Tel.: ; fax: aress: macku@fai.utb.cz The Authors. Publishe by Elsevier Lt. This is an open access article uner the CC BY-NC-ND license ( Peer-review uner responsibility of DAAAM International ienna oi:1.116/j.proeng

2 Lubomír Macků an Davi Novosa / Proceia Engineering 1 ( 215 ) Some publishe papers which escribe an effect of a reactor size on the process control are mentione further. The performance of three bubble column reactors with the same volume but varie geometry (height to iameter ratios.93; 2.4; 3.98) was investigate in [1]. It was emonstrate, that larger height-to-iameter ratio coul enhance CO 2 capture efficiency. Paper [2] tries to observe more efficient membrane reactor setups in orer to improve prouction yiel. Optimization has been carrie out by a ifferential evolution consiering 4 ecision variables incluing imensions of membrane reactor. The authors conclue that the obtaine variables improve the performance of the continuous catalyst regeneration reformer process. Park et al. [3] evelope a 2D mathematical moel of a pilot-scale fixe-be reactor for a Fe-base Fischer-Tropsch synthesis. The evelope moel clearly showe the effects of the tube iameter on the temperature profiles, in terms of the raial heat transfer area. arga et al. [4] trie to fin optimal feeing profile of fe-batch chemical reactor. The optimal feeing profile was generate with sequential quaratic programming, classical evolutionary strategy an the avance version of evolutionary strategy base on covariance matrix aaptation. Any publications ealing with a semi-batch reactor imensions optimization to compare it with here presente results were not foun unfortunately. Our paper is organize as follows: In section 2, the semi-batch reactor, its structure, mathematical moel an the process control are escribe; section 3 presents simulation results an section 4 conclues the current work an suggests new areas for investigation. 2. Methos section 2.1. Current situation In past ifferent control techniques have been applie on fe-batch reactor presente in this paper [5,6,7]. The goal was to optimize the reactor temperature using two manipulate variables (the reactor feeing an the cooling water temperature) to achieve the shortest possible one batch cycle time. Nomenclature A [s -1 ] Pre-exponential factor a FK ( [-] Mass concentration of the chromium sluge c FK R [J.kg -1.K -1 ] Chromium sluge specific heat capacity c [J.kg -1.K -1 ] Reactor content specific heat capacity c [J.kg -1.K -1 ] v Coolant specific heat capacity E [J.mol -1 ] Activation energy [J.kg -1 ] Reaction heat H r K [J.m -2.K -1.s -1 ] Conuction coefficient k [s -1 ] The reaction rate constant m ( [kg] Weight of the reaction components in the system m [kg.s -1 ] FK Mass flow of the entering chromium sluge m [kg.s -1 ] Coolant mass flow v m [kg] vr Coolant mass weight in the reactor ouble wall R [ J.mol -1.K -1 ] Gas constant S [m 2 ] Heat transfer surface T ( [K] Temperature of reaction components in the reactor T [K] FK Chromium sluge temperature T v ( [K] Temperature of coolant in the reactor ouble wall T [K] vp Input coolant temperature

3 362 Lubomír Macků an Davi Novosa / Proceia Engineering 1 ( 215 ) Here authors escribe other achievements obtaine by further optimization. The aim was to optimize the reactor imensions, i.e. the raius an the height. Default imensions of the original reactor were: raius:.78 m, height: 1.11 m, volume: 2.12 m 3, surface: 7.35 m 2. The initial values use by simulations follow: flow of the cooling water 4.67 kg.s -1, temperature of the cooling water K, temperature of the filter cake K, temperature insie the reactor K The mathematical moel The fe-batch reactor process optimization is performe on a ata obtaine from a real chromium sluge regeneration process. This process is escribe in previous work [7]. The leather inustry is a proucer of pollutants in the form of chrome-tanne soli waste. This waste is a potential threat to human health, because it contains trivalent chromium (Cr III), which can uner various conitions oxiize to its hexavalent form (Cr I). One of the numerous possible solutions of this problem is the chrome-tanne waste enzymatic echromation [9]. The whole process is suppose to run in the reactor locate in Kortan company in Hráek na Nisou [1]. Because of that fact the mathematical moel was esigne for this reactor, which imensions an geometry are shown in the Fig. 1. To simulate tanning salts from the chromium sluge regeneration process a mathematical moel is use. The reactor has four input signals m FK (, m (, T FK (, T P ( an one output signal T ( (see the Table 1.). The chemical reactor scheme is shown in Fig. 2. The fe-batch reactor mathematical moel is efine by four ifferential equations - Eq. (1-4). m FK m( (1) t m FK k m( afk( m( afk( (2) t m FKcFKTFK H rk m( afk( K S T ( T ( m( cr T( (3) t m c T P K S T ( T ( m c T ( m c T( (4) R The first equation expresses the total mass balance of chemicals in the reactor. The symbol m FK [kg.s -1 ] expresses the mass flow of entering chromium sluge, m( the accumulation of the in-reactor content. t The secon equation expresses the chromium sluge mass balance. The input is m FK [kg.s -1 ] again, the accumulation is m( afk t an the express k m[ t] afk [ t] means the chromium sluge extinction by the chemical t reaction. Symbol k[s -1 ] means reaction rate constant expresse by an Arrhenius equation (5). k Ae E RT[t] (5) The Arrhenius equation parameters are important for the process control, especially for the process safety as is escribe in [11]. All reactor variables an parameters are escribe in nomenclature part on the previous page.

4 Lubomír Macků an Davi Novosa / Proceia Engineering 1 ( 215 ) Fig. 1. Exothermic chemical semi-batch reactor. Fig. 2. Chemical reactor scheme. The thir equation escribes enthalpy balance. The reactor input heat is expresse by m FKcFKTFK, the heat rising from the chemical reaction is H rk m[ t] afk[ t], the reactor wall heat transmission is K S ( T[ t] T [ t])] an the accumulate heat insie the reactor is escribe by m( cr T(. The last equation escribes a coolant balance. t The coolant input heat is expresse by, m c TP the heat entering the coolant from the reactor by the reactor wall is K S ( T[ t] T [ t]), the heat going out with the coolant is m c T [t] an the heat accumulate in the ouble wall

5 364 Lubomír Macků an Davi Novosa / Proceia Engineering 1 ( 215 ) coolant expresses mr c T (. This moel cannot be solve by analytical means. It is necessary to use numerical t methos the Matlab an Mathematica software were use for this task SOMA (Self-Organizing Migrating Algorithm) An objective function was efine for the reactor imensions optimization. As was sai before, the mathematical moel has to be solve by numerical means. Because of it, also the objective function has to be solve numerically. To fin the objective function minimum a SOMA algorithm was use. SOMA is a stochastic optimization algorithm that is base on the social behavior of cooperating iniviuals. It can be also classifie as an evolutionary algorithm, espite the fact that no new generations of iniviuals are create uring the search. Only the positions of the iniviuals in the search space are change uring a generation (also calle a migration loop ). Iniviuals are generate ranomly accoring to what is calle specimen of the iniviual principle [12]. SOMA algorithm was chosen for its ability to converge towars the global minimum. This algorithm trie to fin three optimal variables: raius of the reactor, height of the reactor an feeing of chromium sluge. There is no requirement of the constant volume in contrast to the mentione work [1]. The only limits are minimum an maximum raius <.1 m, 6 m>, height <.1 m, 6 m> an feeing <.1 kg.s -1, 3 kg.s -1 >. The main input variables of SOMA were set as follows: Step - inicates the size of a migration step, was chosen.3, PRT - perturbation parameter moifies the movement vector of an iniviual to the leaer (.1), NP - number of iniviuals in population was equale 5, Migrations - number of migration cycles was 1, AccepteError - the maximum allowe ifference between the best an the worst iniviual in the population (.1) Objective function Objective function helps to fin the reactor with require properties. This function was forme graually. Basic formula (Eq. 6) is use to fin minimum of the ifference w T[t], where w is the esire an T[t] is the current inreactor temperature. The formula in (Eq. 6) will be referre as OF 1. f t OF w T t (6) The esire in-reactor temperature value was 37 K. Processing of the chromium sluge is faster at higher temperature, i.e. close to the esire value. For safety reasons the temperature shoul not excee 37 K. Using this objective function SOMA algorithm foun new imensions of the reactor: raius = m; height = 1.44 m. The reactor with these new imensions values was then use to simulate the control of whole process. The simulation was finishe when the in-reactor temperature roppe to the efault temperature K. The time to process one batch took 2485 s (Fig. 3). The amount of the processe chromium sluge obtaine from the first simulation was 219 kg (Fig. 3. Filling up the reactor). It is actually the ifference between the weight of the initial filing an the weight of the final batch, i.e =219 kg. The reactor performance was calculate from the two above mentione values - the batch time an the processe chromium sluge weight amount. Its value was.81 kg.s -1. The value was further ivie by coefficient 3.15 to be compare with the original reactor whose volume is 3.15 times smaller. The final performance of newly esigne reactor was then.258 kg.s -1. The new reactor imensions cause a small performance improvement, as the original reactor performance was.237 kg.s -1.

6 Lubomír Macků an Davi Novosa / Proceia Engineering 1 ( 215 ) Fig. 3. The mixture temperature an weight insie the reactor, OF 1. The further results obtaine by the reactor control simulation are showe in Fig. 4. an Fig. 5. In the Fig. 4. can be seen the coolant temperature evelopment an the actuating signal (the reactor feeing) changes cause by the controller. The coolant temperature has the similar course as the in-reactor temperature an is not so important in this case. The actuating signal changes are important from the practical point too many fast changes can significantly shorten the actuator working life. The concentration of the chromium sluge (Fig. 5.) is also important, chromium sluge accumulation is connecte with the heat evelopment elay, i.e. the temperature oes not follow the concentration immeiately as the chromium sluge is ose because of the reaction kinetics. 29 Coolant temperature 285 T[K] t[s] 3 4 x 1 4 Fig. 4. Temperature of the cooling meium an the feeing mixture amount, OF 1. To get even better results, the objective function was extene with the concentration term t a FK t, see (Eq. 7): f OF t w T t t a FK t (7) The newly ae term shoul allow faster ecrease of concentration of chromium sluge which leas to faster completion of the process. This extene objective function is further referre as OF 2.The results obtaine by simulation show that the hypothesis was right, but the impact was negligible. The reactor performance increase

7 366 Lubomír Macků an Davi Novosa / Proceia Engineering 1 ( 215 ) only to the value.288 kg.s -1. The performance was again calculate from the total process time (22212 s) an the amount of processe chromium sluge (311 kg). The total time an the processe amount can be observe in graphs (Fig. 6.). Dimensions of the reactor here were: The reactor raius = 2.73 m; height =.44 m..5 Concentration of the chromium sluge.4 afk[-] t[s] 3 4 x1 4 Fig. 5. Concentration of the mixture insie the reactor, OF 1. The last change in objective function efinition was one by multiplying the concentration term by 2 (Eq. 8). This last objective function is further referre as OF 3. f OF t w T t t t 2 a (8) FK Fig. 6. Temperature of the cooling meium an the feeing mixture amount, OF 2. The above mentione change shoul increase the impact of the concentration term in the objective function an thus help to fin better solution. The results place in Fig. 7. valiate the hypothesis again. Here the performance improve significantly, the new value was.395 kg.s -1. The total process time was in this case s an the amount of processe chromium sluge 2788 kg. The new imensions: The reactor raius = 3.41 m; height =.25 m. The time an the processe amount are showe in Fig. 7.

8 Lubomír Macků an Davi Novosa / Proceia Engineering 1 ( 215 ) Fig. 7. Temperature of the cooling meium an the feeing mixture amount, OF 3. In the last simulation step the task was to restrict the reactor volume near to specific value to prevent the reactor of being too small or large. To o so the interval in objective function was limite by penalization. The penalization is use in case of exceeing the minimum or the maximum volume. The minimum volume was set as 1 m 3, the maximum as 1 m 3. If the algorithm goes out of these values, the objective function is penalize by the 5. This value was foun experimentally. The performance.7 kg.s -1 obtaine here has the best value from all simulations roun an increase the value almost 3 times, if compare to the original reactor (.237 kg.s -1 ). The other values were: process time 911 s, amount of processe chromium sluge 248 kg, raius = 4.42 m; height =.13 m. The time an the processe amount can be foun in Fig Results section Fig. 8. Temperature of the cooling meium an the feeing mixture amount, penalization. As was alreay sai, the task was to fin such reactor, whose imensions fit our process better than the original one. Practically, it means that we woul be able to process a larger quantity of material in a shorter time than it was possible with the original reactor. To o so, we were looking for such reactor iameter, height an input chemical osing which fulfil best these requirements. We proceee in the following manner at first, the new reactor imensions were foun by the static optimization an some other corresponing ata as the total in-reactor mass an the initial reactor filling were counte. Seconly, the newly foune reactor obtaine by the static optimization was use for the process control simulation an was controlle by the Ziegler-Nichols controller to fin the total process

9 368 Lubomír Macků an Davi Novosa / Proceia Engineering 1 ( 215 ) time. From the processing time an the processe amount the reactor performance was counte. All results presente here were obtaine after the successful control applie on the reactor optimize by the static optimization. The control is necessary here to keep the in-reactor temperature at the highest levels, because the process chemical reaction runs faster with higher temperature, an also to keep the process safe. The values obtaine by the simulations can be seen in Table 1. The first three columns contain values calculate by SOMA algorithm for the reactor imensions static optimization. Fourth column contains the objective function value. The fifth column shows reactor performance. The performance means how much of chromium sluge can reactor process per secon. The performance is in relationship with the reactor volume. Practically, the performance means that if the new reactor has ouble volume, an obtaine value of processe chromium sluge is multiplie by a coefficient.5 to compare it with the original volume reactor. Even if the simulations were one just as a first try, the calculations showe that the newly foun reactor imensions can improve our process efficiency. As can be seen from the results of simulations in the Table 1, all new reactors were with better performance. From the performance point of view the original reactor shows the performance.237 kg.s -1, the new average value obtaine by simulations was.766 kg.s -1 i.e. approximately 3 times higher. Table 1. alues foun by SOMA algorithm. Raius [m] Height [m] Feeing [kg.s -1 ] Objective Function [-] Performance [kg.s -1 ] olume [m 3 ] Conclusion The task was to fin such reactor imensions which leas to better process efficiency. It practically means to process greater amount of inputs in the same or shorter time then it was with the original reactor. The optimizing process use an objective function which inclue also the reactor mathematical moel. The objective function was moifie graually to fin better results an necessary limitations an penalizations were use to improve the imensions searching. An evolutionary approach represente by the Self-Organizing Migrating Algorithm (SOMA) was use to minimize the efine function. A suitability of the reactor with newly foun imensions was then verifie by the process control simulations. The efficiency of a suggeste reactor was compare with the original reactor previously use for the same process. It was foun that the reactor geometry characterize by height an iameter plays an important role in the process efficiency. Base on the satisfactory control results an better reactor performance, we can say that the new reactor imensions are more suitable for our exothermic process. In future, the impact of height-to-with ratio will be investigate to fin even more suitable variations for this process. The winning reactors escribe in this paper have the ratio reciprocal first is low an wie, secon high an slim. References [1] B. Zhao, Y. Su, Y. Peng, Effect of reactor geometry on aqueous ammonia-base carbon ioxie capture in bubble column reactors, International Journal of Greenhouse Gas Control, Issue 17, 213, pp [2] D. Iranshahi, M. Jafari, R. Rafiei, M. Karimi, S. Amiri, Rahimpour, R.M., Optimal esign of a raial-flow membrane reactor as a novel configuration for continuous catalytic regenerative naphtha reforming process consiering a etaile kinetic moel, International Journal of Hyrogen Energy, Issue 38, 213, pp [3] N. Park, J.-R. Kim, Y. Yoo, J. Lee, M.-J. Park, Moeling of a pilot-scale fixe-be reactor for iron-base Fischer Tropsch synthesis: Twoimensional approach for optimal tube iameter, Fuel, Issue 122, 214, pp [4] T. arga, F. Szeifert, J. Abonyi, Evolutionary Strategy for Feeing Trajectory Optimization of Fe-batch Reactors, Acta Polytechnica Hungarica, ISSN , ol. 4, No. 4, 27, pp

10 Lubomír Macků an Davi Novosa / Proceia Engineering 1 ( 215 ) [5] D. Novosa, L. Macků, Eitor B. Katalinic Ziegler-Nichols controller with online ientification versus PID controller comparison, Annals of DAAAM for 21 & Proceeings of the 21st International DAAAM Symposium, pp , ISBN , ISSN [6] D. Novosa, L. Macků, Pole placement controller with compensator aapte to semi-batch reactor process, In Recent Researches in Automatic Control. Montreux : WSEAS Press, 211, ISBN [7] F. Gazoš, Robust Control Design for a Semi-Batch Reactor, International Review of Automatic Control. vol. 5, no. 6, 212, pp ISSN [8] L. Macků, Control esign for the preparation of regenerate for tanning, PhD. Thesis, UTB in Zlin, 23. [9] D. Janáčová, K. Kolomazník, P. Mokrejš,. ašek, Optimization of enzymatic hyrolysis of leather waste, Proceeings of the 6th WSEAS International Conference on Applie Informatics an Communications, 26, Elouna, Greece, pp [1] K. Kolomazník, M. Aámek, M. Uhlířová, Potential Danger of Chromium Tanne Wastes, In Proceeings of the 5th IASME/WSEAS International Conference on Heat Transfer, Thermal Engineering an Environment, IASME/WSEAS, 27, pp [11] L. Macků, Ientification of Arrhenius equation parameters for control purposes, 13th WSEAS International Conference on Automatic Control, Moelling & Simulation (ACMOS '11), WSEAS Press, 211, pp [12] I. Zelinka, G. Onwubolu, B.. Babu, New Optimization Techniques in Engineering, Springer-erlag, chap.7 SOMA - Self Organizing Migrating Algorithm, 24, ISBN X.