Dynamics and Regulatory Control of Biodiesel Purity from a Reactive Distillation Process

Transcription

1 Dynamics an Regulatory Control of Bioiesel Purity from a Reactive Distillation Process Saiat Olanipekun GIWA 1, Abel Aekanmi ADEYI 2, Abulwahab GIWA 3 1 Chemical Engineering Department, Faculty of Engineering an Engineering Technology, Abubakar Tafawa Balewa University, Tafawa Balewa Way, , Bauchi, Bauchi State, Nigeria 2,3 Chemical an Petroleum Engineering Department, College of Engineering, Afe Babalola University, M. 8.5, Afe Babalola Way, , Ao- Ekiti, Ekiti State, Nigeria s: 1 sogiwa@atbu.eu.ng; 2 abelaeyi@abua.eu.ng; 3 agiwa@abua.eu.ng Abstract The open loop an isturbance rejection (regulatory) close loop ynamic simulation of a reactive istillation process use for the prouction of bioiesel, etails of which are given in the work of Giwa et al. (2015a), have been carrie out in this work. The first-orer-plus-eatime transfer function moel of the system use was evelope with the ai of System Ientification Toolbox of MATLAB. The input an output variables of the process were the reboiler uty of the column an the mole fraction of bioiesel obtaine from the bottom section of the column, respectively while the isturbance variable was the reflux ratio. Both the open loop an the close loop simulations of the system were achieve from the Simulink moel of the system evelope an run via written m-file coes. The results obtaine from the open loop ynamic simulation of the process reveale that the isturbance variable ha effects on the output (bioiesel mole fraction obtaine from the bottom section) of the process because the steps applie to it mae the output not to be at the esire set point. Furthermore, the application of P, PI an PID controllers tune with Cohen-Coon an Ziegler-Nichols techniques showe that the process coul be mae to behave in a esire manner. However, the response given by the simulation of the system with P-only controller was foun not to settle at the esire set-point value, while the simulations with PI an PID were able to bring the output to the esire reference value. Moreover, the performance of PID controller tune with Cohen-Coon technique was foun to be the best among the ones consiere for this case of regulatory control of the process because its IAE an ISE were obtaine to be the lowest. This fining was observe to be in contrary to that of Giwa et al. (2015b) who obtaine that the best controller for bioiesel prouction using reactive istillation process was PID controller tune with Ziegler-Nichols. However, it was iscovere that their own work consiere set-point tracking only but not isturbance rejection. This has, therefore, shown that a particular controller type may not be able to hanle both set-point tracking an isturbance rejection in a best way in all cases. eywors: Bioiesel, reactive istillation, System Ientification Toolbox, MATLAB, isturbance rejection control. INTRODUCTION Bioiesel is an alternative fuel that is currently receiving attention owing to the limite availability of conventional petroleum iesel an, also, ue to environmental concerns. This material can be use to replace petroleum iesel without any moification because of their similar properties (Simasatitkul et al., 2011; Giwa et al., 2014; Giwa et al., 2015a). Furthermore, it has a number of avantages as it can be erive from a renewable omestic resource. In aition, it reuces emission of carbon ioxie apart from being nontoxic an bioegraable (Wang et al., 2004; Jaya an Ethirajulu, 2011; Giwa et al., 2014; Giwa et al., 2015a). Bioiesel can be obtaine in high purity by carrying out an esterification reaction of a fatty aci an an alcohol via a reactive istillation process (Giwa et al., 2014). The use of reactive istillation process is preferre for the prouction of bioiesel in orer to overcome the problems associate with the use of conventional batch reactor, which inclue low conversion, heavy capital investments an high energy costs (usmiyati an Sugiharto, 2010; Giwa et al., 2014; Giwa et al., 2015a; Giwa et al., 2015b). Generally, reactive istillation is efine as a process that combines both separation an chemical reaction in a single unit (Giwa an Giwa, 2012). It is foun to be more avantageous than a conventional process having reaction an separation sections separately (Al- Arfaj an Luyben, 2002a; Giwa an aracan, 2012b; Giwa, 2013a; Giwa an aracan, 2012; Giwa an aracan, 2012e; Giwa an aracan, 2012f; Giwa an aracan, 2012g; Giwa, 2012; Giwa an Giwa, 2013a; Giwa, 2013a; Giwa et al., 2013; Giwa an Giwa, 2013b; Giwa, 2014). It has been use in a small number of inustrial applications for many years, but the last ecae has shown an increase in both its research an applications (Al-Arfaj an Luyben, 2002b; Giwa et al., 2015a). In reactive istillation, the temperature levels for both reaction an vapour-liqui equilibrium must overlap (Al-Arfaj an Luyben, 2002a; Giwa et al., 2015a). By carrying out chemical reaction an separation in one process, the operating an investment costs can be minimize. Some aitional benefits offere by reactive istillation technology inclue: (i) increase yiel, because of overcoming chemical an thermoynamic equilibrium limitations, (ii) improve selectivity via suppression of sie reactions (Giwa an aracan, 2012c), (iii) reuce energy consumption, ue to effective utilization of reaction heat, in the case of exothermic reactions, (iv) avoiance of hot spots by simultaneous liqui evaporation, (v) ability to separate close boiling components (Prakash et al., 2011; Giwa et al., 2015a) an (vi) ability to avoi azeotropes (Giwa an aracan, 2012a). Due to these avantages an with growing process unerstaning, the chemical process inustry has evelope an increasing number of processes base on reactive istillation (Bock et al., 1997; Giwa et al., 2015a). However, this process is not extensively use in inustry because it is perceive that unerstaning its ynamics will be problematic an that its operation an control are more ifficult than those of the conventional systems

2 In orer to aress those issues concerning the ynamics an control of the process, ifferent investigations have been carrie out on it by some researchers. For instance, Sneesby et al. (1997) carrie out the ynamic simulation an control of reactive istillation process use for ethyl tert-butyl ether synthesis. They presente recommenations for the control of the reactive column of this type such as the nee for early aressing of the control issues in the esign process. Bock et al. (1997) evelope a structure for the control of a reactive column with recovery by analysing the steay state an ynamic sensitivity of the column with respect to possible isturbances an manipulate variables. Sneesby et al. (1999) worke on an ethyl tert-butyl ether reactive istillation column as a case stuy to emonstrate how a two-point control configuration recognizing the importance of both composition an conversion coul be evelope an implemente for a reactive istillation process. umar an Daoutiis (1999) investigate the ynamic behaviour an control of a reactive istillation column use for the prouction of ethylene glycol. They erive a etaile tray-by-tray moel that explicitly inclue the vapour-phase balances. Also evelope in their work was a nonlinear controller that yiele goo performance with stability in the high-purity region. The superior performance of the evelope controller over linear PI controllers was emonstrate in the work through simulations. Monroy-Loperena et al. (2000) stuie the control problem of an ethylene glycol reactive istillation column in orer to regulate the ethylene glycol composition in the prouct by manipulating the reboiler boil-up ratio. A new iea for robust stabilization base on an analysis of the unerlying input/output bifurcation iagram an on moelling error compensation techniques was propose in the work. Al-Arfaj an Luyben (2000) stuie the close loop control of a reactive istillation column with two proucts an iscovere that single en temperature control coul be use to keep both proucts at or above specifie purity values, even in the presence of large isturbances, because the reaction zone holup was sufficiently large. Vora an Daoutiis (2001) stuie the ynamics an control of an ethyl acetate reactive istillation process an esigne moel-base linear an nonlinear state feeback controllers along with classical single-input single-output (SISO) proportional-integral (PI) controllers. The superior performance of the nonlinear controller over both the linear an the classical PI controllers was emonstrate in the work. Grüner et al. (2003) carrie out the simulation of an inustrial reactive istillation column unto which asymptotically exact input/output-linearization was applie an iscovere that, in comparison with a well-tune linear controller, it showe a superior performance with respect to set-point changes an isturbances, even in the presence of unknown input elays. halei an Young (2005) stuie the nonlinearity of a reactive istillation column proucing ethyl tert-butyl ether an evelope a 2 x 2 unconstraine moel preictive control scheme for prouct purity an reactant conversion control using the process ynamics approximate by a first-orer-plus-ea-time moel as an estimate of the process moel of the controller. They foun from the stuy carrie out that the controller was very efficient for isturbance rejection an set-point tracking. Völker et al. (2007) esigne a multivariable controller for a meium-scale semi-batch reactive istillation column an emonstrate that the controller performe well for large set-point changes an in the face of isturbances. Furthermore, Giwa an aracan (2012a) use two black-box moels (AutoRegressive with exogenous Inputs (ARX) an AutoRegressive Moving Average with exogenous Inputs (ARMAX) moels) they evelope using experimental ata to stuy the ynamics of a reactive istillation column use for ethyl acetate prouction, an iscovere that the performance of ARMAX moel was better because of its higher calculate fit value. They also foun that ARX moel was faster in getting to steay state upon the application of a step input to the two moels. However, the moels evelope in their work were not utilize to stuy the control of the process. Giwa an aracan (2012c) evelope ynamic moels for a reactive packe istillation starting from first principles an solve them (the evelope moels) with the ai of MATLAB. The comparisons mae between the experimental an the theoretical results obtaine reveale that there were goo agreements between them because the calculate percentage resiuals were small. Also, the moels they evelope were not use for the control of the column in the work. Giwa an aracan (2012) stuie the application of ecouplers in the esign of moel preictive controllers for a reactive istillation process use for the prouction of ethyl acetate. In the work, top segment temperature, reaction segment temperature an bottom segment temperature were taken as the controlle variables while reflux ratio, fee ratio an reboiler uty were the manipulate variables of the control system. The results obtaine from the work showe that the performance of neural network ecoupling moel preictive controller (NNDMPC) was better than that of transfer function ecoupling moel preictive controller (TFDMPC) as the integral square error values calculate for the top segment an the reaction segment temperatures from the control simulation carrie out with NNDMPC were foun to be less than those of the TFDMPC. Moreover, Giwa an aracan (2012e) applie ecoupling proportional-integral-erivative control to a reactive istillation column for set-point tracking an isturbance rejection using tuning parameters calculate with Ziegler-Nichols an Cohen-Coon techniques, an the results obtaine from the simulations of the work showe that ecoupling PID control with Cohen-Coon tuning technique was better than that of Ziegler- Nichols, for the process consiere in the work. Giwa et al. (2015b) stuie the ynamics an set-point tracking control of a reactive istillation process use for bioiesel prouction by taking the bioiesel purity obtaine from the bottom section of the column as the controlle variable, the reboiler uty as the manipulate variable an consiering Cohen-Coon an Ziegler-Nichols tuning techniques. From the comparisons mae among the controllers consiere by them, they were able to iscover that the best one for the system was PID controller tune with Ziegler-Nichols metho because its integral absolute error (IAE) an integral square error (ISE) were foun to be the lowest. It can be seen from the literature review carrie out that the ynamics an control of a reactive istillation process for bioiesel prouction has been carrie out, but the control there was a servo (set-point tracking) type. It is important that the behaviour of the system to the presence of a isturbance be known so as to know how it shoul be hanle in that case because, even, when trying to make a system to follow a particular set point, any isturbance can set into it anytime. Therefore, this work was carrie out to stuy 372

3 the ynamics an perform regulatory (isturbance rejection) control of a reactive istillation process use for the prouction of bioiesel from an esterification reaction. METHODOLOGY Transfer Function Moelling of the Process The process moel use in this work was formulate by aing the transfer function relation between the output variable (reflux ratio) an the isturbance variable evelope using the ata generate from the prototype plant setup with the ai of Aspen HYSYS an reporte in etail in the work of Giwa et al. (2015a). The process moel formulation was one with the ai of the System Ientification Toolbox containe in MATLAB (MathWorks, 2015). The type of the transfer function moel of the isturbance relation was also chosen to be the same as that of the main process transfer function, that is, first-orer-plus-ea-time, an this mae the moel of the process to be as shown in Equation (1). x bio s -Tps pe Q s s 1 p -T s e s 1 Rs Simulink Moelling an Open Loop Simulation of the Process After obtaining the transfer function of the process, as given in Equation (1), it was thereafter moelle in Simulink, also containe in MATLAB, by combining the ifferent appropriate blocks require, an the evelope Simulink moel for the open loop case of the system is as shown in Figure 1. Furthermore, the open loop ynamics of the process was stuie by applying step changes to the isturbance variable of the evelope moel, while keeping the main input variable of the process at its steay state value, an running it using the coes written in m-file of MATLAB. (1) Figure 1. Open loop moel of the process Simulink Moelling an Close Loop Simulation of the Process After eveloping the moel of the process an stuying its open loop behaviours, its close loop simulations were also carrie out using the close loop moels, shown in Figures 2 4, evelope with the ai of Simulink for P-only, PI an PID controllers, respectively. The evelope close loop moels of the process were simulate for regulatory (isturbance rejection) with the controllers (P-only, PI an PID) tune with both Cohen-Coon an Ziegler-Nichols techniques by applying a unit step change to the steay state value of the isturbance variable. The controlle, manipulate an isturbance variables of the close loop moels were bioiesel bottom mole fraction, reboiler uty an reflux ratio, respectively

4 The calculations of the values for the tuning parameters of the controllers, using Cohen-Coon an Ziegler-Nichols tuning techniques, were carrie out by taking the transfer function of the controllers to be as shown in Equation (2) an applying the expressions given in Table 1. G c s c 1 1 Ds (2) I s Figure 2. Close loop moel of the process with P-only controllers tune with Cohen-Coon an Ziegler-Nichols techniques Figure 3. Close loop moel of the process with PI controllers tune with Cohen-Coon an Ziegler-Nichols techniques 374

5 Figure 4. Close-loop moel of the process with PID controllers tune with Cohen-Coon an Ziegler-Nichols techniques Table 1: Cohen-Coon an Ziegler-Nichols tuning parameter expressions Type of Control Cohen-Coon Tuning Technique Ziegler-Nichols Tuning Technique 1 Proportional (P) T 1 u c c p T 3 2 Proportional-Integral (PI) c T 0. 9 T 12 1 p c u 2.2 I T 30 3T 9 20T P u I 1.2 c 4 T T p c u 1.7 Proportional-Integral-Derivative (PID) Source: Stephanopoulos, 1984 I D T T 32 6T 138T T Pu I 2 D Pu 8 RESULT AND DISCUSSION The resulting moel obtaine for the process after the incorporation of the isturbance transfer function moel term was as given in Equation (3), 375

6 x bio s s s e 0.283e Qs Rs (3) s s 1 From Equation (3), it was observe that all the parameters (static gain, time constant an ea time) of the isturbance transfer moel were, in magnitue, less than those of the main process transfer function moel of the process. The lower time constant of the isturbance moel was foun to be an inication of the fact that the isturbance woul respon faster than the main process if the same unit step change is applie to the two of them. Shown in Figures 5 7 are the open-loop responses of the process to 1, 2, an 3 step unit(s) change in the reflux ratio, which was the isturbance variable of the process. As can be seen from the figure, the process was able to respon to the changes in the reflux ratio, but not as esire. Normally, it was expecte of the output of the system to remain at zero, which was its set point in this case, even, in the presence of any isturbance. However, the observations mae from the results (Figures 5 7) inicate that the simulation of the moel with the applie step input changes were correct, as can be notice from the magnitues of the output variable (bioiesel mole fraction) of the three simulations carrie out. As such, it was clear from the euctions mae from the figures that the process ha to be controlle so as to keep its output at its esire set point (in this case of regulatory control, zero). Base on this, the results obtaine from the control of the process carrie out with a unit step change in the isturbance variable using proportional (P), proportional-integral (PI) an proportional-integral-erivative (PID) controllers were as given in Figure In each of the figures, the close-loop ynamic responses of the process to a unit step change in the isturbance variable obtaine using the three controller types tune with Cohen-Coon an Ziegler-Nichols techniques are shown. Figure 5. Open loop response of the process to 1 unit step change in the reflux ratio of the process 376

7 Figure 6. Open loop response of the process to 2 units step change in the reflux ratio of the process Figure 7. Open loop response of the process to 3 units step change in the reflux ratio of the process From Figure 8, it was clear that the performance of P-only controller was not goo for the process because it was not able to make the system settle at the esire set point at the en of the simulation time of 450 min chosen. Looking at the results, there seeme to be offsets associate with the responses of the P-only controllers tune with Cohen-Coon an Ziegler-Nichols techniques, but the response of the Cohen-Coon tuning technique was foun to be closer to the esire set-point of the system than that of the Ziegler- Nichols. From the responses given in Figure 8, it was very obvious that the performance of Cohen-Coon was better than that of Ziegler-Nichols for this case of the P-only controller in hanling this process of bioiesel prouction for the regulatory control

8 Figure 8. Close loop responses of P-only controlle process Shown in Figure 9 are the close loop ynamic responses of the system obtaine when Cohen-Coon an Ziegler-Nichols tune PI controllers were use to control it. From the figure, it was seen that the performances of the two controllers (PI controller tune with Cohen-Coon an Ziegler-Nichols techniques) were better than those of the P-only controllers consiere before. Moreover, it was also notice that even though the overshoot of the PI controller tune with Ziegler-Nichols metho was higher than that of the one tune with Cohen-Coon technique, its number of oscillations was foun to be lesser an ecay faster. All in all, the responses of both of them were foun to get stabilize at the esire set point within the simulation time of 450 min consiere. Figure 9. Close loop responses of PI controlle process Although the performances of the Cohen-Coon an Ziegler-Nichols tune PI controllers were foun to be better than those of the P- only controllers an satisfactory, it was still eeme necessary to get the responses of the system when controlle with Cohen-Coon an Ziegler-Nichols tune PID controllers, an given in Figure 10 are the responses obtaine

9 Figure 10. Close loop responses of PID controlle process From the figure (Figure 10), it was seen that the response with the higher overshoot was the one obtaine from the simulation carrie out using PID controller tune with Ziegler-Nichols technique, just as it was obtaine in the case of the PI controller investigate earlier, but its magnitue was foun to be less than that given by the PI controller tune with the same technique (Ziegler-Nichols). Also notice from the results given in Figure 10 was that less oscillations were foun to occur with the use of PID controllers. In orer to get a clearer picture on the performances of the controllers consiere, their performance criteria values were calculate, an given in Table 2 are the results obtaine from the estimation of the integral absolute error (IAE) an the integral square error (ISE) of the controllers (P, PI an PID) tune with Cohen-Coon an Ziegler-Nichols techniques. Table 2. Performance criteria values of the controllers Controller Cohen-Coon Tuning Technique Ziegler-Nichols Tuning Technique IAE ISE IAE ISE P PI PID From the results given in Table 2, for this case of isturbance rejection (regulatory) control stuy of the reactive istillation process, the performances of the controllers tune with Cohen-Coon technique were iscovere to be better than those of the ones tune with Ziegler-Nichols technique because most of their corresponing IAEs an ISEs were foun to be lower. CONCLUSION The results obtaine from the open loop ynamic simulation of the reactive istillation process use for bioiesel prouction have shown that the isturbance variable ha effects on the output of the process because the steps applie to it mae the output not to be at the esire set point. Furthermore, the application of P, PI an PID controllers tune with Cohen-Coon an Ziegler-Nichols techniques reveale that the process coul be mae to behave as esire. However, the response given by the simulation of the system with P- only controller was foun not to settle at the esire set-point value, while the simulations with PI an PID were able to bring the output to the esire reference value within the time consiere. Moreover, the performance of the PID controller tune with Cohen- Coon technique was foun to be the best among the ones stuie for this case of the regulatory control of bioiesel prouction using reactive istillation because its IAE an ISE were foun to be the lowest. This fining was, actually, foun to be in contrary to that of Giwa et al. (2015b) who obtaine that the best controller for the bioiesel prouction system was PID controller tune with Ziegler

10 Nichols. However, their own work consiere set-point tracking only. This has, therefore, shown that a particular controller type may not be able to hanle both set-point tracking an isturbance rejection best in all cases. NOMENCLATURE D I p G c (s) G p (s) IAE ISE c p u NNDMPC P PI PID P u Q R SISO T T p TFDMPC x bio Derivative time of the controller (min) Time constant of the isturbance process moel (min) Integral time of the controller (min) Time constant of the main process moel (min) Controller transfer function Process transfer function Integral Absolute Error Integral Square Error Proportional gain of the controller Static gain of the isturbance process moel Static gain of the main process moel Ultimate gain Neural Network Decoupling Moel Preictive Controller Proportional Proportional-Integral Proportional-Integral-Derivative Ultimate perio (min/cycle) Reboiler uty (kj/s) Reflux ratio Single-input single-output Dea time of the isturbance process moel (min) Dea time of the main process moel (min) Transfer Function Decoupling Moel Preictive Controller Bottom bioiesel mole fraction REFERENCES: 1) Al-Arfaj M.A. an Luyben W.L. (2002a). Design an Control of an Olefin Metathesis Reactive Distillation Column. Chemical Engineering Science. 57, ) Al-Arfaj M.A. an Luyben W.L. (2002b). Comparative Control Stuy of Ieal an Methyl Acetate Reactive Distillation. Chemical Engineering Science. 57, ) Al-Arfaj, M.A. an Luyben, W.L. (2000). Comparison of Alternative Control Structures for an Ieal Two-Prouct Reactive Distillation Column. Inustrial an Engineering Chemistry Research, 39, ) Bock, H., Wozny, G. an Gutsche, B. (1997). Design an Control of a Reaction Distillation Column Incluing the Recovery System. Chemical Engineering an Processing, 36, ) Giwa, A. (2012). Steay-State Moeling of n-butyl Acetate Transesterification Process Using Aspen PLUS: Conventional versus Integrate. ARPN Journal of Engineering an Applie Sciences, 7(12), ) Giwa, A. (2013a). Sensitivity Analysis of ETBE Prouction Process Using Aspen PLUS. International Journal of Avance Scientific an Technical Research. 3(1), ) Giwa, A. (2014). Solving the Dynamic Moels of Reactive Packe Distillation Process Using Difference Formula Approaches. ARPN Journal of Engineering an Applie Sciences, 9(2), ) Giwa, A. an Giwa, S.O. (2012). Optimization of Transesterification Reaction Integrate Distillation Column Using Design Expert an Excel Solver. International Journal of Avance Scientific an Technical Research. 2(6): ) Giwa, A. an Giwa, S.O. (2013a). Isopropyl Myristate Prouction Process Optimization Using Response Surface Methoology an MATLAB. Journal of Engineering Research & Technology, 2(1), ) Giwa, A. an Giwa, S.O. (2013b). Estimating the Optimum Operating Parameters of Olefin Metathesis Reactive Distillation Process. ARPN Journal of Engineering an Applie Sciences, 8(8), ) Giwa, A. an aracan, S. (2012a). Moeling an Simulation of a Reactive Packe Distillation Column Using Delaye Neural Networks, Chaotic Moeling an Simulation, 2(1),

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