2006-2012 Aian Reearch Publihing Network (ARPN. All right reerved. DECOUPLING CONROL OF A REACIVE DISILLAION PROCESS USING YREUS-LUYBEN ECHNIQUE Abdulwahab Giwa and Süleyman Karacan Department of Chemical Engineering, Faculty of Engineering, Ankara Univerity, Ankara, urkey E-Mail: agiwa@ankara.edu.tr ABSRAC hi work ha been carried out to demontrate the application of yreu-luyben PI and PID method in the decoupling temperature control of a reactive ditillation proce uing the production of ethyl acetate and water (byproduct from the eterification reaction between acetic acid and ethanol a the cae tudy. For comparion purpoe, Ziegler-Nichol PI control method wa alo imulated. he proce model, from which the decoupling matrix wa etimated, wa developed with the aid of Sytem Identification oolbox of MALAB uing the experimental data generated from the reactive packed ditillation column et up. he developed decoupling control wa imulated for etpoint tracking uing MALAB/Simulink. he top egment temperature, the reaction egment temperature and the bottom egment temperature were elected a the controlled variable while the reflux ratio, the feed ratio and the reboiler duty were repectively choen a the manipulated variable. he good repone with low ocillation obtained from the imulation of the decoupling control of the proce uing yreu-luyben PI and PID control method have hown that the control of the reactive ditillation proce ha been achieved uccefully with each of thee method and that the developed control ytem uing thee method can thu be applied to the real proce. In addition, due to it lowet value of IAE and ISE, yreu-luyben PID method ha been found to be the bet one among the method that were tudied. Keyword: reactive ditillation, decoupling control, MALAB/Simulink, tyreu-luyben technique, ethyl acetate. INRODUCION Reactive ditillation i a proce that combine both eparation and chemical reaction in a ingle unit. It combine the benefit of equilibrium reaction with ditillation to enhance converion provided that the product of interet ha the larget or the lowet boiling point (Giwa and Karacan, 2012c. It ha a lot of advantage epecially for thoe reaction occurring at temperature and preure uitable for the ditillation of the reulting component (Giwa and Karacan, 2012b which include hift of chemical equilibrium and increae of reaction converion by imultaneou reaction and eparation of product, uppreion of ide reaction and utilization of heat of reaction for ma tranfer operation. It ha been ued in a mall number of indutrial application for many year, but the lat decade ha hown an increae in both reearch and application (Al-Arfaj and Luyben, 2002. By carrying out chemical reaction and eparation in one proce tep, the operating and invetment cot can be minimized. However, reactive ditillation i not extenively ued in indutry ince it i perceived that it operation will alway be more difficult and will poe higher requirement on the quality of the deign and control ytem than the conventional flow heet. hi behaviour can be mainly attributed to the complex interaction between the underlying phenomena taking place in the reactive column. he control of reactive ditillation ha received ome attention only recently. Bock et al. (1997 developed a control tructure for a reactive column with a recovery column by analyzing the reaction column teady tate and dynamic enitivity of poible diturbance and manipulated variable. Sneeby et al. (1999 ued an ethyl tert-butyl ether reactive ditillation column a a cae tudy to how how a two-point control configuration, which recognized the importance of both compoition and converion, can be developed and implemented for a reactive ditillation proce. Kumar and Daoutidi (1999 tudied the dynamic behaviour and control of an ethylene glycol reactive ditillation column by deriving a detailed tray-by-tray model that explicitly included the vapor-phae balance. Monroy-Loperena et al. (2000 alo tudied the control problem of an ethylene glycol reactive ditillation column with the control objective of regulating the ethylene glycol compoition in the product by manipulating the reboiler boil-up ratio. hey propoed a new idea for robut tabilization baed on an analyi of the underlying input/output bifurcation diagram and on modelling error compenation technique. Al-Arfaj and Luyben (2000 explored the cloed-loop control of a reactive ditillation column with two product and dicovered that ingle-end temperature control could keep both product at or above pecified purity value, even for large diturbance, if reactive-zone holdup wa ufficiently large. Vora and Daoutidi (2001 tudied the dynamic and control of an ethyl acetate reactive ditillation ytem and deigned model-baed linear and nonlinear tate feedback controller, along with conventional SISO PI controller. hey demontrated the uperior performance of the nonlinear controller over both the linear controller and the conventional PI controller. Khaledi and Young (2005 invetigated the nonlinearity of an ethyl tert-butyl ether reactive ditillation column and developed a 2 x 2 uncontrained model predictive control cheme for product purity and reactant converion control by uing the proce dynamic approximated by a firt-order plu dead time model to etimate the proce model for the model predictive controller. hey found that the controller 1263
2006-2012 Aian Reearch Publihing Network (ARPN. All right reerved. wa very efficient for diturbance rejection and et-point tracking. Giwa and Karacan (2012e ued the decoupling technique to accomplih the model predictive control of a reactive packed ditillation column that wa ued for the production of ethyl acetate. In their work, they ued neural network and tranfer function model a the controller model and dicovered that the performance of the neural network model predictive controller wa better than that of the tranfer function model predictive controller. herefore, thi work ha been carried out to implement the control of a reactive ditillation proce with the aid of Proportional-Integral-Derivative Controller uing yreu-luyben a the tuning technique. he production of ethyl acetate from the eterification reaction between acetic and ethanol wa ued a the cae tudy proce. 2. PROCEDURES (a Proce decription he proce involved in thi work wa an eterification reaction occurring imultaneouly with ditillation operation that wa carried out in the reactive packed ditillation column (RPDC et up a hown pictorially in Figure-1 (alo decribed in the work of Giwa and Karacan (2012a, 2012b, 2012c, 2012d and 2012e. he column, excluding the condener and the reboiler, had a height of 1.5 m and a diameter of 0.05 m. It conited of a cylindrical condener with a diameter and a height of 5 and 22.5 cm, repectively. he main column ection of the plant wa divided into three ubection of 0.5 m each. he upper, middle and lower ection were the rectifying, the reaction and the tripping ection repectively. he rectifying and the tripping ection were packed with rachig ring while the reaction ection wa filled with Amberlyt 15 olid catalyt that had a urface area of 5300 m 2 /kg, a total pore volume of 0.4 cc/g and a denity of 610 kg/m 3. he reboiler wa pherical in hape with a volume of 3 Litre. he column wa fed with acetic acid at the top (between the rectifying and the reaction ection while ethanol wa fed at the bottom (between the reaction and the tripping ection with the aid of peritaltic pump which were operated with the aid of a computer via MALAB/Simulink program. All the ignal input (reflux ratio (R, feed ratio (F and reboiler duty (Q to the column and the meaured output (top egment temperature ( top, reaction egment temperature ( rxn and bottom egment temperature ( bot from the column were ent and recorded repectively on-line with the aid of MALAB/Simulink computer program and electronic input-output (I/O module that were connected to the equipment and the computer ytem. he eterification reaction occurring in the column wa an equilibrium type that i given a: K eq 3 2 5 3 2 5 + CH COOH + C H OH CH COOC H H O (1 2 Figure-1. Reactive packed ditillation column. (b Proce identification he data generated by operating the reactive ditillation column decribed above and hown in Figure-1 below were ued for the development of the tranfer function model of the proce uing Proce Identification echnique. he form of the tranfer function developed for thi proce are given a hown in Equation (2 - (4. he proce model parameter were etimated with the aid of Sytem Identification oolbox of MALAB. 1264
2006-2012 Aian Reearch Publihing Network (ARPN. All right reerved. top rxn bot ( ( ( (- (- (- d1,1 d1,2 d1,3 k p e k e k e 1,1 p1,2 p1,3 R( + F( + τ + 1 τ + 1 τ + 1 1,1 1,2 (- (- (- d2,1 d2,2 d2,3 k p e k e k e 2,1 p2,2 p2,3 R( + F( + τ + 1 τ + 1 τ + 1 2,1 2,2 (- (- (- d3,1 d3,2 d3,3 k p e k e k e 3,1 p3,2 p3,3 R( + F( + τ + 1 τ + 1 τ + 1 3,1 3,2 1,3 2,3 3,3 Q( Q( Q( (c uning of controller he controller deigned for the reactive ditillation proce were tuned uing yreu-luyben (2 (3 (4 technique by conidering it PI and PID. In addition, for comparion purpoe, the PI verion of Ziegler-Nichol technique wa alo deigned and imulated. Given the tranfer function of the controller a (Equation (5, 1 ( G c K c 1 + + τ D (5 τ I the relationhip ued for the calculation of the tuning parameter of the technique for the PI and PID verion are a hown in able-1 below. Parameter K c able-1. Relationhip for the calculation of the tuning parameter. yreu-luyben PI uning.31kcu yreu-luyben PID uning.45k Ziegler-Nichol PI uning 0.45K 0 0 cu cu τ I τ D 0 Source: Seborg et al. (2004. 2.2Pu 2.2Pu P u 6.3 P u 1.2 0 (d Deign of decoupler In thi tudy, the interaction decoupler applied to the control of the reactive ditillation proce were calculated in form of a matrix (decoupling matrix with reference to Equation (2, (3 and (4 and uing the mathematical relationhip hown in Equation (6 below. k p k 1,1 p k 1,2 p 1,3 K k p k 2,1 p k I 2,2 p2,3 (6 k p k 3,1 p k 3,2 p3,3 he decoupler, after being applied to the proce, were expected to be able to eliminate the effect of the interaction among the variable involved in the control of the 3 x 3 MIMO reactive ditillation ytem. A uch, the control of the MIMO ytem wa expected to be accomplihed eaily like thoe of three different SISO ytem. 1 (e Control configuration and imulation he reactive ditillation proce being controlled in thi work wa a Multi-Input Multi-Output (MIMO type that had three controlled variable (top egment, reaction egment and bottom egment temperature and three manipulated variable (reflux ratio, feed ratio and reboiler duty. In order to facilitate eay control, the MIMO proce wa decoupled and thu controlled like three different SISO procee by the application of the decoupler that were etimated from the MIMO tranfer function model of the ytem. After the decoupling, the reflux ratio, the feed ratio and the reboiler duty were ued a the manipulated variable of the top egment, the reaction egment and the bottom egment temperature repectively for the control tudie. he control tudie were achieved uing code written with MALAB-mfile in combination with the control algorithm (Figure-2 developed in Simulink environment of MALAB (Mathwork, 2011. 1265
2006-2012 Aian Reearch Publihing Network (ARPN. All right reerved. Figure-2. Simulink algorithm of decoupling control of reactive ditillation proce. 3. RESULS AND DISCUSSIONS (a Experimental tudie Figure 3, 4 and 5 how the repone of the egment temperature obtained after the application of the input (R- reflux ratio, F - feed ratio and Q - reboiler duty that were alo hown a ubfigure in the main figure. A can be een from the figure, a tep value from 3 to 5 wa applied to the reflux ratio while a PRBS ignal between 0.5 and 2 wa applied to the feed ratio. Alo applied to the reboiler duty wa a PRBS ignal between 0.595 and 0.63 kj/. bot ( o C Q (kj/ 93 92 91 5 4 3 2 1 0.62 0.6 t ( R F Figure-3. Experimental dynamic repone and proce input of top egment temperature. Figure-3 how the repone of the top egment temperature (one of the proce output to the proce input. A can be oberved from the figure, the application of the input reulted in a change in the top egment temperature profile of the proce. hat wa an indication that thi output variable wa able to repond to the input variable and that the input variable could be ued a the manipulated variable of the aid output (controlled variable. In Figure-4, the experimental repone of the reaction egment temperature i hown. A wa oberved in the cae of the top egment temperature profile, the application of the input to the proce alo reulted in a change in the profile of the reaction egment temperature. 1266
2006-2012 Aian Reearch Publihing Network (ARPN. All right reerved. rxn ( o C Q (kj/ 76.5 R F 76 5 4 3 2 1 0.62 0.6 t ( Figure-4. Experimental dynamic repone and proce input of reaction egment temperature. Another profile obtained from the experimental work wa that of the bottom egment temperature hown in Figure-5. From the figure, a change wa noticed in the bottom egment temperature profile due to the application of the input to the proce. hi change in the profile can be een clearly from the figure by noticing the upward rie in the temperature profile of the bottom egment temperature from it teady-tate. bot ( o C Q (kj/ 93 92 91 5 4 3 2 1 0.62 0.6 t ( R F Figure-5. Experimental dynamic repone and proce input of bottom egment temperature. Due to the fact that change were noticed in the dynamic repone of the egment temperature owing to the change in the elected input of the proce, it wa concluded that the egment temperature were function of the elected proce input. hee verification of the different egment temperature to be function of the elected input were very important before uing the input a the manipulated variable of thi proce control. (b Proce identification tudie Uing the dynamic repone of the egment temperature hown in Figure 3-5 above, the tranfer function model of the proce were developed between the proce input and output with the aid of Sytem Identification oolbox of MALAB. he tranfer function model had three input variable (reflux ratio, feed ratio and reboiler duty and three output variable (top egment temperature, reaction egment temperature and bottom egment temperature. he developed tranfer function model are a given in Equation (7-(9. top rxn ( ( (-9.20E -04-79.32e R 5.50 + 1 (-4.89E-01 31.95e R 8.47 + 1 ( ( (-4.96E -01-1.37e + F( + 5.18 + 1 (-9.04E-03 427.90e + F 5.27 + 1 ( - 89.11e (-1.78E -03 5.17 + 1 (-9.02E-03-18434.90e + 5.29 + 1 Q( Q( (7 (8 1267
2006-2012 Aian Reearch Publihing Network (ARPN. All right reerved. bot ( (-8.59E-06-739.47e R 35.64 + 1 ( (-4.99E-01 6.79e + F 1.01 + 1 ( (-5.00E-01-231.19e + 0.79 + 1 Q( (9 A can be oberved from the model parameter, while ome tatic gain of the proce (K p were poitive, other were negative. hat i, there were ign change among the tatic gain of thi reactive ditillation proce. hi phenomenon of tatic-gain ign change ha been found in the literature to be one of the peculiar characteritic of reactive ditillation proce. he ign change were occurring a a reult of the complex behavior of the proce. Oberving the time contant (τ of the proce, the tranfer function of the relationhip between the reflux ratio and the bottom egment temperature wa found to poe the highet value. hi i indicating that if the ame input unit i applied to the proce, thi part of the proce i mot likely to have the highet effect on the time required for the proce to get to the teady tate. According to the value of the delay time ( d of the proce, the maximum delay poeed by thi proce being 0.5 min implied that the output variable of the reactive ditillation proce tudied in thi work were reponding fat to the change in the elected input variable of the proce. Since the method ued in thi work for the etimation of the tuning parameter of the controller required model, and ince the control ytem wa decoupled, there wa the need to have a many controller a there were controlled variable. hu, having three controlled variable and three manipulated variable reulted in having three different controller. In order to tune thee controller, three different tuning model were required. It wa mentioned before that, after the decoupling, the MIMO proce of thi work would be controlled like three different SISO procee. herefore, the model ued for the etimation of the tuning parameter of the yreu-luyben PI, yreu-luyben PID and Ziegler-Nichol PI method were etimated a SISO type and they are a hown in Equation (10, (11 and (12, repectively for the top egment temperature, the reaction egment temperature and the bottom egment temperature controller. top rxn bot ( ( ( (-0.34 23.64e 165.14 + 1 (-0.13 47.80e 18.94 + 1 (-0.21 173.01e 579.53 + 1 R( F( Q( (10 (11 (12 (c uning parameter Uing the controller model given in Equation (10, (11 and (12, and with reference to the controller equation given in Equation (5, and alo applying the equation contained in able-1, the value obtained from the calculation of the tuning parameter of the controller are a hown in able-2 below. he table preent the tuning parameter of the yreu-luyben PI, yreu- Luyben PID and Ziegler-Nichol PI controller. able-2. Etimated tuning parameter of the controller. Controller yreu-luyben PI yreu-luyben PID Ziegler-Nichol PI K c τ I τ D K c τ I τ D K c τ I τ D PIDC1 10.02 2.99 0.00 14.55 2.99 0.22 19.39 0.68 0.00 PIDC2 1.52 1.12 0.00 2.20 1.12 0.08 2.94 0.25 0.00 PIDC3 7.70 1.86 0.00 11.18 1.86 0.13 14.91 0.42 0.00 A can be oberved from able-2, among the tuning parameter (controller gain, integral time and derivative time of the controller, the one with the highet value, for the three controller (PIDC1, PIDC2 and PIDC3 and for the three method (yreu-luyben PI, yreu-luyben PID and Ziegler-Nichol PI, wa found to be the controller gain, which wa the proportional apect of the controller. (d Decoupler In thi tudy, the decoupling matrix wa etimated uing the mathematical relationhip given in Equation (6. he etimated and applied decoupling matrix of thi control work i a given in Equation (13 below. K I - 0.0005-0.2788-0.0065 0.0000 0.0010-0.0000-0.0013 0.0300 0.0007 (13 (e Control tudie Before going into the control apect of thi proce, it teady value were invetigated and found to be 69.89, 70.81 and 87.97 o C, repectively for the top egment temperature, reaction egment temperature and bottom egment temperature. However, it wa dicovered 1268
2006-2012 Aian Reearch Publihing Network (ARPN. All right reerved. from the literature that very high compoition of ethyl acetate (deired product could be obtained when the top egment temperature wa 70.75 o C. A uch, thi work wa purpoely aimed at raiing the top egment temperature to 70.75 o C from 69.89 o C. In addition to that, in order to tet the performance of the controller in the control of other egment temperature, 0.5 and 2.5 o C tep unit were applied to the teady tate value of the reaction egment temperature and the bottom egment temperature repectively. he control ytem wa imulated for 40 minute and the reult obtained from the imulation are a hown in Figure 6-8. top ( o C 71 70.8 70.6 70.4 70.2 70 yreu-luyben PI yreu-luyben PID Ziegler-Nichol PI Set point R 3 2.8 2.6 2.4 t (min yreu-luyben PI yreu-luyben PID Ziegler-Nichol PI t (min Figure-6. Dynamic repone of top egment temperature and reflux ratio to a et-point change from 69.89 to 70.75 o C. From Figure-6, the repone of the top egment temperature obtained uing the three tuning method (yreu-luyben PI, yreu-luyben PID and Ziegler- Nichol PI revealed that while the top egment temperature repone of the yreu-luyben PI and PID method were able to get to the deired teady-tate value within 10 minute, that of the Ziegler-Nichol PI method wa only able to get there at approximately the 15 th minute. hi wa howing that yreu-luyben wa fater than Ziegler-Nichol in taking the temperature to the deired teady-tate for the proce tudie in thi work. Alo, it wa noticed that the repone of the Ziegler- Nichol PI method wa more ocillatory than thoe of the yreu-luyben PI and PID method. Apart from that, the overhoot of the Ziegler-Nichol PI method wa dicovered to be very large compared to the other two method ued. hee behavior of the Ziegler-Nichol PI method were found to correpond to what are available in the literature becaue it ha been dicovered that among the characteritic of a PI controller wa the production of ocillatory repone and large overhoot for et-point change. According to Bequette (2003, the fact that the cloed-loop behavior of Ziegler-Nichol technique tend to be ocillatory and enitive to uncertainty i the reaon why it i not widely ued today. Among the three method tudied, for the repone of the top egment temperature, the method with the lowet overhoot wa found to be the yreu-luyben PID method. At the deired teady-tate, each value of the input (reflux ratio for each of the three method wa found to be approximately 3. 1269
2006-2012 Aian Reearch Publihing Network (ARPN. All right reerved. rxn ( o C 72 71.5 71 yreu-luyben PI yreu-luyben PID Ziegler-Nichol PI Set point 70.5 t (min F 6 4 2 yreu-luyben PI yreu-luyben PID Ziegler-Nichol PI 0 t (min Figure-7. Dynamic repone of reaction egment temperature and feed ratio to a 0.5 o C unit et-point change. Conidering the repone of the reaction egment temperature hown in Figure-7, it wa dicovered that yreu-luyben PID method wa the fatet to take the reaction egment temperature of the proce to the deired teady-tate value within about 18 minute; that of the yreu-luyben PI wa able to take the repone of the reaction egment temperature to the deired teady-tate after about 20 minute while that of the Ziegler-Nichol PI method wa only able to take the reaction egment temperature to the deired teady-tate value after 29 minute. At the teady tate of each of the method, the value of the manipulated variable (feed ratio were found to be approximately 1.84 for both yreu-luyben PI and PID method, while that of the Ziegler-Nichol PI wa approximately 1.83. 92 bot ( o C Q (kj/ 91 90 yreu-luyben PI yreu-luyben PID 89 Ziegler-Nichol PI Set point 88 t (min 0.8 0.6 yreu-luyben PI 0.4 yreu-luyben PID 0.2 Ziegler-Nichol PI 0 t (min Figure-8. Dynamic repone of bottom egment temperature and reboiler duty to a 2.5 o C unit et-point change. Alo imulated uing the three tuning method conidered in thi work wa the control ytem involving the repone of the bottom egment temperature. he reult of thi imulation are hown in Figure-8. A can be 1270
2006-2012 Aian Reearch Publihing Network (ARPN. All right reerved. een from the figure, imilar to what wa obtained in the cae of the top egment temperature; the repone of the yreu-luyben PI and PID method were found to have le ocillation and overhoot than that of the Ziegler- Nichol PI. However, the rie time of the bottom egment temperature repone of Ziegler-Nichol PI method wa found to be the lowet among the three method, followed by that of the yreu-luyben PID while that of the yreu-luyben PI had the highet rie time. he firt method to take the bottom egment temperature to the deired teady-tate wa yreu-luyben PID method at about the 13th minute. he repone obtained from the yreu-luyben PI wa able to get to the teady tate after about 20 minute while that of the Ziegler-Nichol PI method got there at approximately the 27 th minute. At the teady tate of each of the control method, the value of the manipulated variable (in thi cae, the reboiler duty for each of the method wa found to be 0.69 kj/. Furthermore, in order to quantitatively determine the bet one among the control method that were tudied in thi work, their performance criteria were calculated. he performance criteria ued in thi work were Integral Abolute Error (IAE and Integral Squared Error (ISE. he calculation of the performance criteria were carried out imultaneouly with the control imulation in Simulink Environment of MALAB and the reult obtained from the calculation are a hown in able-3 below. he concept of the criteria i that the lower the value of thee performance criteria (IAE and ISE for a particular control method or technique, the better the control method or technique becaue low value of the criteria generally imply that the controller i able to take the controlled variable to the deired teady-tate (alo known a the et point within the hortet poible time. able-3. Performance criteria for the control method. uning method Integral abolute error (IAE Integral quared error (ISE top rxn bot top rxn bot yreu-luyben PI 0.57 2.67 10.22 0.22 0.60 12.21 yreu-luyben PID 0.35 1.77 7.44 0.10 0.35 8.38 Ziegler-Nichol PI 0.84 8.06 11.74 0.19 4.79 14.08 From the able-3 hown above, among all the three method invetigated, the one with the lowet IAE and ISE for all the three egment temperature conidered wa found to be yreu-luyben PID control method. hee obervation from the performance criteria of the egment temperature (hown in able-3 have been een to be in agreement with what wa oberved from their graphical repone (Figure 6-8. 4. CONCLUSIONS he good repone with low ocillation obtained from the imulation of the decoupling et-point tracking temperature control of the reactive ditillation proce ued for the production of ethyl acetate uing yreu-luyben PI and PID control method have hown that the control of the reactive ditillation proce ha been achieved uccefully with each of thee method. herefore, the developed control ytem uing thee method can be applied to the real proce. In addition, yreu-luyben PID method wa found to have the lowet value of IAE and ISE and thu dicovered to be the bet one among the control method that were invetigated in thi work. ACKNOWLEDGEMENS Abdulwahab Giwa wihe to acknowledge the upport received from the Scientific and echnological Reearch Council of urkey ( ürkiye Bilimel ve eknolojik Araştırma Kurumu - ÜBİAK for hi Ph.D. Programme. In addition, thi reearch wa upported by the Scientific Reearch Project Office of Ankara Univerity ( A.Ü. BAP under Project No. 09B4343007. NOMENCLAURES τ ime contant of the proce (min τ D Derivative time contant of the controller (min τ I Integral time contant of the controller (min F Feed ratio (ml -1 of acetic acid feed rate / ml -1 of ethanol feed rate IAE Integral Abolute Error ISE Integral Squared Error K c Proportional gain of the controller K cu Ultimate gain K p Static gain of the proce MIMO Multi-Input Multi-Output PI Proportional-Integral PID Proportional-Integral-Derivative PRBS Peudo-Random Binary Sequence P u Ultimate period Q Reboiler duty (kj/ R Reflux ratio RPDC Reactive Packed Ditillation Column SISO Single-Input Single-Output t ime (min or bot Bottom egment temperature ( o C rxn Reaction egment temperature ( o C top op egment temperature ( o C 1271
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