Optimal operating strategies for semi-batch reactor used for chromium sludge regeneration process

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1 Latest Trens in Circuits, Automatic Control an Signal Processing Optimal operating strategies for semi-batch reactor use for chromium sluge regeneration process NOOSAD DAID, MACKŮ LUBOMÍR Tomas Bata University in Zlin Faculty of Applie Informatics nám. T.G.Masaryka 5555, Zlín CZECH REPUBLIC Abstract: - This paper eals with controlling of a semi-batch nonlinear reactor use for chromium sluge regeneration process. The aim is to process the largest amount of chromium filter cake (chromium sluge) in the shortest possible time. The reactor has to be coole because of strongly exothermic process. For safety reasons the temperature shoul not excee 100 C. In this stuy the reactor is controlle by two manipulating inputs: filter cake feeing flow rate an cooling water temperature. The spee of the whole process epens on the filter cake feeing flow rate in case of a large amount filter cake aition a sharp temperature rise follows. The controller must be able to fin optimal strategy between the filter cake osing an the cooling temperature to reach the shortest possible process time. In orer to eal with process nonlinearities here an online ientification must be use. Results obtaine using the propose control metho are then compare with our previous research, especially with control metho using only one manipulating input - filter cake feeing flow rate. Key-Wors: temperature control; online ientification; semi-batch reactor; PID; pole placement 1 Introuction 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 [1]. One part of the chromium waste recycling process can take place in batch or semi-batch reactors. This process releases consierable amount of heat which can enanger the reactor safety. Thus temperature control is necessary. The temperature profile uring the recycling operation usually follows three stages [2]: (i) heating of the reaction mixture up to the esire reaction temperature, (ii) maintenance of the system at this temperature an (iii) cooling stage in orer to minimize the formation of by-proucts. Any controller use to control the reactor must be able to take into account these ifferent stages. In the literature some papers have been publishe which iscuss the control of a batch or semi-batch reactor. For example Beyer et al. applie a global linearization control strategy with online state an parameter estimation for a polymerization reactor [3]. However, the authors conclue that the implementation of the propose metho is still ifficult ue to the missing support of require mathematical functions. The other approach was use in the stuy [4], where the authors applie a ual-moe (DM) control improve by iterative learning technique. Simulations showe that the propose metho can enhance the conventional DM control with moest efforts. For rapi an suitable reference-trajectory tracking a self-aaptive preictive functional control algorithm by Škrjanc [5] was recommene. This approach was successful in a reactor with switching between col an hot water in the inlet. Neural network was applie to similar system [6] to accommoate the online ientification of a nonlinear system. The authors foun this strategy effective for ientification an control time-varying-elaye nonlinear ynamic systems. Neural networks are often presente as a goo metho to reach useful results in batch processes. An appropriate selection of the manipulate variable is necessary to selecting the proper control strategy. In a recent article ealing with prouction of ethyl acrylate in CSTR, five ifferent pairs of manipulate variables were compare [7]. The final recommene control ISBN:

2 Latest Trens in Circuits, Automatic Control an Signal Processing strategy containe two manipulate variables feeing flow rates of both reactants. This newly propose metho showe better results than the previously use strategy with only one manipulate variable. Similarly, in our article we will focus on the use of two manipulate variables instea of one. This paper presents results of experiments obtaine by real process simulations. These simulations involve the control of the semi-batch process using PID controller tune using pole placement metho (PIDPP). This metho using only one manipulate variable was teste in our previous works [8] an is now extene to control two manipulate variables simultaneously. The whole process is suppose to run in the reactor locate in Kortan company in Hráek na Nisou [9]. 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 mɺ (t), ɺ (t), T (t), T P (t) an one output signal T (t) [10]. The chemical reactor scheme is shown in Fig. 2. m Figure 2. Chemical reactor scheme Implementation of the metho an all simulations are one in MATLAB/Simulink software. The mathematical moel of the fe-batch reactor is efine by ifferential Eq. (1-4). mɺ = m(t) (1) t mɺ = k m a + [ m( t) a ] (2) t Figure 1. Exothermic chemical semi-batch reactor The paper is organize as follows. In section II, the semi-batch reactor an structure of the controller are escribe; section III presents simulation results an section I conclues the current work an suggests new areas for investigation. 2 Methos section 2.1 The semi-batch reactor moel mɺ c = K S mɺ c T + H k m( t) a t = [ T T ] + [ m( t) c T ] T = mɺ c T + m c P + K S r [ T T ] R T = R (3) (4) The first equation expresses the total mass balance of the chemical solution in the reactor. The symbol mɺ [kg.s -1 ] expresses the mass flow of entering chromium sluge, m(t) the accumulation of the t in-reactor content. The secon equation expresses the chromium sluge mass balance. The input is mɺ [kg.s -1 ] again, the accumulation is m a an the express t k m[ t] a [ t] means the chromium sluge extinction by the chemical reaction. Symbol k[s -1 ] means ISBN:

3 Latest Trens in Circuits, Automatic Control an Signal Processing reaction rate constant expresse by an Arrhenius equation (5). E RT [t] k = Ae (5) Knowlege of the Arrhenius equation parameters leas to the correct mathematical moel, which islinke with safe an successful control [11]. ariables an parameters of the reactor are given in Table 1. Table 1 - ariables an parameters of the reactor moel (1) mɺ [kg.s -1 ] Mass flow of the entering chromium sluge m (t) [kg.s -1 ] Accumulation of the in-reactor content accumulate heat insie the reactor is escribe by m cr T. The last equation escribes a t coolant balance. The coolant input heat is expresse by, mɺ c T the heat entering to the coolant from P the reactor by the reactor wall is, K S ( T[ t] T [ t]) the heat going out with the coolant is mɺ c T [t] an the heat accumulate in the ouble wall coolant expresses mr c T (t). Detaile escription of t this moel is given in [12]. This moel moel cannot be solve analytically. It is necessary to use numerical methos, which was one using MATLAB software. (2) (3) a (t) [-] Mass concentration of the chromium sluge m (t) [kg] Weight of the reaction components in the system k [s -1 ] c The reaction rate constant [J.kg -1.K -1 ] Chromium sluge specific heat capacity c [J.kg -1.K -1 ] R Reactor content specific heat capacity T [K] Chromium sluge temperature H r [J.kg -1 ] Reaction heat K [J.m -2.K -1.s -1 ] Conuction coefficient S [m 2 ] Heat transfer surface T (t) [K] Temperature of reaction components in the reactor T v (t) [K] Temperature of coolant in the reactor ouble wall mɺ [kg.s -1 ] v Coolant mass flow 2.2 Structure of the Pole Placement controller A controller base on the assignment of poles in a close feeback control loop is esigne to stabilize the close loop while the characteristic polynomial shoul have previously etermine poles [13]. This controller esign comes from the general close loop block iagram shown in Fig. 3, where: ( Y ( B( G P = = (6) U ( A( z 1 ) is the iscrete transfer function of the controlle plant with polynomials 2 A ( = 1+ a z + a z B ( = b1 z + b2 z (7) ( U ( Q( G R = = (8) E( P( z 1 ) (4) (5) c [J.kg -1.K -1 ] v T [K] vp Coolant specific heat capacity Input coolant temperature m [kg] Coolant mass weight in the reactor ouble wall vr A [s -1 ] E [J.mol -1 ] R [ J.mol -1.K -1 ] Pre-exponential factor Activation energy Gas constant a [t] means mass fraction of chromium sluge in the chemical reactor, m[t] weight of reaction components in the reactor. The thir equation escribes enthalpy balance. The reactor input heat is expresse by mɺ ct, the heat rising from the chemical reaction is H rk m[ t] a[ t], the reactor wall heat transmission is K S ( T[ t] T [ t])] an the is the transfer function of a controller with polynomials P( = (1 (1+ γ 1 2 Q ( = q0+ q1z + q2z (9) From Eq. (8) it is possible to etermine the controller equation in the form Q( U ( = E( (10) P( an by inserting polynomials (9) into equation (10), the relation to calculate the controller output becomes ISBN:

4 Latest Trens in Circuits, Automatic Control an Signal Processing u k = q0 ek + q1ek 1+ q2ek 2+ ( 1+ γ ) uk 1+ γuk 2 Further, the following relation can be obtaine for the control transfer function of the close loop shown in Fig. 3. Figure 3. Block iagram of control loop for a PIDPP controller Y ( B( Q( G W ( = = (11) W ( A( P( + B( Q( where the characteristic polynomial is to be foun in the enominator of (11). By choosing the characteristic polynomial D n i ( = 1+ i z, 4 i= 1 n (12) in the polynomial equation A ( P( + B( Q( = D( (13) the esire pole placement for the transfer function is fixe (11). This is achieve by selecting the correct parameters for controller polynomials (10) which are the solution to polynomial equation (13). Detaile escription of this controller is given in [13]. The positions of the poles vary accoring to the position of the operating point ue to the system nonlinearity. It has a strong influence on the stability of the system. Therefore it is necessary to use the estimate values generate from the online system ientification. The poles an zeros location of our system are further iscusse in [14]. Figure 4. In-reactor temperature, coolant temperature an reactor filling up profiles On the other han, temperature must not excee this value for safety reasons. It can be seen that the setpoint is change from 370 K to 323,15 K in time s. At this point all filter cake is processe an feeing is stoppe. The entire process is complete at the time when the temperature falls to 323,15 K which was the initial temperature insie the reactor. 3 Results Section The goal of the propose metho in this paper is to process the largest amount of filter cake in the shortest possible time. In contrast to the previously use approach, this new control esign is newly extene by the controller to control the temperature of cooling water. Temperature of the coolant was set constant in the previous metho, now it is controlle in the range from 283 to 323 K. Processing of the filter cake is faster at higher temperature; therefore the setpoint is set to 370 K (Fig. 4). Figure 5. Manipulate variables Fig. 5 shows the suen change of manipulate variables especially at the beginning of the process. These changes are seen in the following graph (Fig. 6). Initially, appropriate heating of the reaction mixture is necessary ue to the start of a chemical reaction. After that the reaction mixture must be coole because of highly exothermic nature of this type reaction. Comparison of temperature profiles current an previously use metho is shown in Fig. 7. It can be seen that aing a secon controller, the uration of processing the same amount of filter ISBN:

5 Latest Trens in Circuits, Automatic Control an Signal Processing cake is significantly reuce. The total processing time of one batch is s in case of one controller an s in case of two controllers. The ifference is s. There are still some other methos, which coul possibly improve this process. In the future work, some other approaches will be applie to the batch process to fin out other possible ways. This work has been supporte by the Tomas Bata University uner grant IGA/FAI/2012/058. These supports are gratefully acknowlege. Figure 6. Manipulate variables etaile view 4 Conclusion The semi-batch reactor control is a complex an ifficult problem. Problems arise especially from its nonlinearity connecte with a wie control range. Controllers must be able to eal with ifferent stages (heating up, steay state). In this stuy, the PIDPP controllers for the temperature control of cooling water an for the feeing flow rate of a filter cake in a semi-batch reactor was emonstrate by simulation means. The implemente control strategy was also compare with another strategy applie on the same process in the previous works. Base on presente results it can be conclue that propose metho using two manipulate variables significantly reuces the time require to process one batch which can be seen in Figure 7. Figure 7. Comparison of temperature profiles of two ifferent methos References: [1] Kolomazník, K., Aámek, M., Uhlířová, M., 2007, Potential Danger of Chromium Tanne Wastes, In Proceeings of the 5th IASME/WSEAS International Conference on Heat Transfer, Thermal Engineering an Environment, IASME/WSEAS, [2] Bouhenchir, H.; Cabassu, M.; Le Lann, M.., Preictive functional control for the temperature control of a chemical batch reactor, Computers an Chemical Engineering, Issue 30, 2006, pp [3] Beyer, M.A.; Grote, W.; Reinig, G., Aaptive exact linearization control of batch polymerization reactors using a Sigma-Point Kalman, Journal of Process Control, Issue 18, 2008, pp [4] Cho, W.; Egar, T.F.; Lee, J., Iterative learning ual-moe control of exothermic batch reactors, Control Engineering Practice, ol.16, 2008, pp [5] Škrjanc, I., Self-aaptive supervisory preictive functional control of a hybri semi-batch reactor with constraints, Chemical Engineering Journal, ol.136, Issues 2-3, 2007, pp [6] Wu, X.; Zhang, J.; Zhu, Q., A generalize proceure in esigning recurrent neural network ientification an control of timevarying-elaye nonlinear ynamic systems. Neurocomputing, Issue 73, 2010, pp [7] Chien, I-L., Chen K., Kuo Ch-L., Overall control strategy of a couple reactor/columns process for the prouction of ethyl acrylate, Journal of Process Control, ol.18, 2008, pp [8] Novosa, Davi; Macků, Lubomír, Pole placement controller with compensator aapte to semi-batch reactor process. In Recent Researches in Automatic Control. Montreux : WSEAS Press, 2011, ISBN [9] Janáčová, D., Kolomazník, K., Mokrejš, P., ašek,., 2006, Optimization of enzymatic hyrolysis of leather waste, Proceeings of the ISBN:

6 Latest Trens in Circuits, Automatic Control an Signal Processing 6th WSEAS International Conference on Applie Informatics an Communications, Elouna, Greece, [10] Gazoš, F., Macků, L., 2009, Control-Oriente Simulation Analysis of a Semi-Batch Reactor International Review of Automatic Control, vol.2, no. 5, ISSN , [11] Macků, L., 2011, Ientification of Arrhenius equation parameters for control purposes, 13th WSEAS International Conference on Automatic Control, Moelling & Simulation (ACMOS '11), WSEAS Press, [12] Macků, L., 2003, Control esign for the preparation of regenerate for tanning. PhD. Thesis, UTB in Zlin. [13] Bobál,., Böhm, J., Fessl, J., Macháček, J., 2005, Digital Self-tuning Controllers, Springer, ISBN [14] Gazoš, F.; Macků, L. Analysis of a semi-batch reactor for control purposes. 22n European Conference on Moelling an Simulation, Proceeings. European Council Moelling & Simulation, 2008, pp ISBN: