Dynamics and control of totally refluxed reactive distillation columns

Journal of Process Control 22 (2012) 1182–1197Contents lists available at SciVerse ScienceDirectJournal of ProcessControlj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /j p r o c o ntDynamics and control of totally refluxed reactive distillation columnsWei Liu a ,Kejin Huang a ,∗,Liang Zhang a ,Haisheng Chen a ,San-Jang Wang ba College of Information Science and Technology,Beijing University of Chemical Technology,Beijing 100029,People’s Republic of China bDepartment of Chemical and Material Engineering,Ta Hwa Institute of Technology,Chiunglin,Hsinchu 307,Taiwana r t i c l ei n f oArticle history:Received 3August 2011Received in revised form 3May 2012Accepted 10May 2012Available online 15 June 2012Keywords:Reactive distillation column Totally refluxed operation Process dynamics Inventory control Process operationa b s t r a c tAccording to the mechanism of the reaction operation involved,reactive distillation columns are often designed to work in a totally refluxed operation mode.The totally refluxed operation mode makes the reflux drum interact solely with the reaction operation involved and retards considerably the dynamics of the latter.The resultant great difference in process dynamics between the reaction operation and the separation operation involved leads frequently to under-damped responses with the degree of under-dampness closely dependent on the inventory control of the reflux drum.With the tight inventory control of the reflux drum,the degree of under-dampness can be suppressed and this presents a favorable effect to process dynamics and controllability of the totally refluxed reactive distillation columns.Two hypothet-ical ideal reactive distillation columns with and without a side reaction,respectively,and a high-purity ethylene glycol reactive distillation column are employed to examine the unique dynamics and control-lability of the totally refluxed reactive distillation columns.The results obtained are in good accordance with the above interpretation.The current work reveals the general behaviors of the totally refluxed reactive distillation columns and can be particularly useful in control system synthesis and design.© 2012 Elsevier Ltd. All rights reserved.1.IntroductionAccording to the mechanism of the reaction operation involved,reactive distillation columns are often designed to work in a totally refluxed operation mode.For example,in case of carrying out a reaction,A +B ↔C,in a reactive distillation column,the desired product C should be withdrawn from the bottom of the process because it is the heaviest component.At the top of the reactive dis-tillation column,the reactants,A and B,are usually accumulated and they should be recycled back to the reactive section through a totally refluxed operation mode in reflux drum.Since there is no rectifying section in the reactive distillation column,the reflux drum is directly connected to the reactive section and this leads to an intimate interaction between them.Such interaction affects considerably the reaction operation involved and can eventually present a strong impact to the dynamics and controllability of the totally refluxed reactive distillation columns.These should repre-sent the unique behaviors of the totally refluxed reactive distillation columns and are worthwhile to be studied carefully.Recent years have seen increasingly more studies conducted on the dynamics and operation of reactive distillation columns [1–6].For the totally refluxed reactive distillation columns,there have also appeared a number of papers dealing with their operation∗Corresponding author.Tel.:+861064434801;fax:+861064437805.E-mail address:huangkj@ (K.Huang).issues.Luyben once compared the operation of two ternary ideal reactive distillation columns with and without chemically inert components,respectively [7].He found that the presence of a chemically inert component could alter the process from a totally refluxed operation mode into a partially refluxed operation mode.In particular,a direct measurement of stage composition is required for the effective process control.Recently,Kaymak et al.fur-ther explored the inferential temperature control of the ternary ideal reactive distillation columns with and without chemically inert components [8,9].They insisted that the direct measure-ment of stage composition might not be necessary provided that the control structure and control tray locations were properly chosen.Ethylene glycol reactive distillation column represents a typical example for the totally refluxed reactive distillation col-umn and has received considerable attention in the aspects of process dynamics and controllability.Although Kumar and Daou-tidis claimed that nonlinear controller was superior to linear PI controller in its operation [10],Al-Arfaj and Luyben showed that the process could be effectively controlled by a simple PI con-trol scheme plus a feed-forward compensator [11].Huang et al.addressed internal heat integration to a high-purity ethylene gly-col reactive distillation column [12,13].They found that seeking further internal heat integration between the reaction operation and the separation operation involved helped to improve the process dynamics and lessened the difficulties in process opera-tion.Furthermore,the tight inventory control of the reflux drum could function to suppress the inherent process nonlinearity and0959-1524/$–see front matter © 2012 Elsevier Ltd. All rights reserved./10.1016/j.jprocont.2012.05.007W.Liu et al./Journal of Process Control22 (2012) 1182–11971183NomenclatureA hypothetical componentA vp vapor pressure constant(Pa)B hypothetical componentBot bottom productflow rate(mol s−1)B vp vapor pressure constant(Pa K)C hypothetical componentCC composition controllerD hypothetical componentDEG diethylene glycolE activation energy of reaction(J mol−1)EG ethylene glycolEO ethylene oxideF feedflow rate(mol s−1)FCflow controllerH stage holdup(mol)H R heat of reaction(J mol−1)H V latent heat of vaporization(J mol−1)k controller gaink con controller gain of reflux drum level(s−1)L liquidflow rate(mol s−1)LC level controllernc total number of componentsNT total number of stagesPC pressure controllerR ideal gas law constant(J mol−1K−1)r reaction rate(mol mol−1s−1or mol m−3s−1)T temperature(K)T i reset time(s)V vaporflow rate(mol s−1)W waterx liquid compositionz feed compositionGreek symbols˛pre-exponential factorstoichiometric coefficient of a reactionSubscriptsb backward reactionf forward reactioni component indexj stage indexm main reactions side reactionnon-minimum phase behavior,favoring therefore process oper-ation significantly.Although this conclusion was acquired from the high-purity ethylene glycol reactive distillation column,it invoked us to anticipate that the interesting phenomenon might be closely related to the particular structure of the totally refluxed reactive distillation columns.This consideration stimulated us to acquire the insights of the phenomenon.To the best of our knowl-edge,until now no pertinent work has been conducted on the relationship between process configuration and process dynam-ics and controllability for the totally refluxed reactive distillation columns.The primary objective of the current work is to investigate the dynamics and control of the totally refluxed reactive dis-tillation columns.Two hypothetical ideal reactive distillation columns with and without a side reaction,respectively,and a high-purity ethylene glycol reactive distillation column are cho-sen as representative examples.Both open-loop process dynamics and closed-loop operation are examined with special atten-tion focused on the effect of inventory control of reflux drum. The unique behaviors of the totally refluxed reactive distillation columns are analyzed and the acquired insights are then summa-rized.2.Unique process dynamics and its implications on the control of the totally refluxed reactive distillation columns Unlike the conventional reactive distillation columns with distillate and bottom withdrawal,the totally refluxed reactive distillation columns contain a reactive section with a direct con-nection to the reflux drum(because there is no rectifying section). In an extreme point of view,it is even reasonable to treat them as an equivalent reactor with heat exchange in the condenser. Because of the large liquid holdup in the reflux drum,once the light and/or heavy reactants enter the reflux drum,they will gen-erally need a long time to be driven back to the reactive section and this retards considerably the dynamics of the reaction operation involved.In the totally refluxed reactive distillation columns,the sep-aration operation involved is solely carried out in the stripping section.Since the heat duty of reboiler(or the reboilflow rate) serves as the manipulated variable to control the purity of bottom product,it should be taken as the main variable to represent the dynamics of the separation operation involved.Because the bottom reboiler has much faster dynamics than the liquid hydraulics in the reflux drum and in the reactive section compounded further with the reaction kinetics,sharp difference exists in process dynam-ics between the reaction operation and the separation operation involved.This causes generally under-dampness in the open-loop dynamic responses of the bottom product.The greater the differ-ence is,the severer the degree of the under-dampness becomes. Moreover,the sharp difference in process dynamics between the reaction operation and the separation operation involved can also induce a certain degree of degradation in system properties,e.g., in the aspects of process nonlinearity and non-minimum phase behavior.This inevitably gives rise to additional difficulties in pro-cess operation.In terms of the above analysis,one can now understand that the sharp difference in process dynamics between the reaction oper-ation and the separation operation involved is the main reason for the occurrence of the under-damped behaviors in the totally refluxed ideal reactive distillation columns.To suppress the degree of the under-dampness,one must therefore rely on the acceleration of reaction kinetics and liquid hydraulics in the reactive section and in the reflux drum.Although operating pressure can be increased to accelerate reaction kinetics,it is generally determined by the match of operating conditions between the reaction operation and the separation operation involved.For the liquid hydraulics in the reactive section and in the reflux drum,it is decided by process capacity and is usually operationally infeasible to be enhanced through the reduction of their sizes.The only way left is to acceler-ate the dynamics of the reflux drum through tight control of liquid level.Remember,however,that this differs totally from the conven-tional design practice,i.e.,the inventory of the reflux drum should be loosely controlled in order to avoid strong interaction between different control loops.In the remainder of this paper,we will employ three totally refluxed reactive distillation columns,including two hypotheti-cal ideal reactive distillation columns with and without a side reaction,respectively,and a high-purity ethylene glycol reac-tive distillation column,to examine their unique dynamics and the effect of inventory control of reflux drum on process opera-tion.1184W.Liu et al./Journal of Process Control22 (2012) 1182–1197Table1Physicochemical properties and operating conditions of Example I.Parameter Value Column pressure(bar)8.0Number of stages Rectifying section0 Reactive section9 Stripping section5Liquid hodlup(mol)Condenser20,000.0 Column tray1000.0 Reboiler20,000.0Reaction activation energy(J mol−1)Forward125,520 Backward125,520Specific reaction rate at366K(mol s−1mol−1)Forward0.008 Backward0.0004Feedflow rate(mol s−1)A12.63 B12.82Feed location A10 B2Feed thermal condition A 1.0B 1.0Relative volatility(A:B:C)4:2:1 Heat of reaction(J mol−1)0Latent heat of vaporization(J mol−1)29,053.7 Bottom product specification(C,mol%)98Vapor pressure constants A(A vp/B vp)12.3463/3862 B(A vp/B vp)11.6531/3862 C(A vp/B vp)10.9600/38623.Example I:A totally refluxed ideal reactive distillation system involving one reaction with two light reactants and one heavy product3.1.Process descriptionThis hypothetical ideal reactive distillation system is taken from Sun et al.[14].As is shown in Fig.1,this reactive distillation column consists of a reactive section above the stripping section with9and 5stages,respectively.The reactive distillation column is operated in a totally refluxed operation mode,and two pure reactant feeds,F A and F B,are fed to stages10and2(numbered from the top condenserCFig.1.Scheme of a totally refluxed ideal reactive distillation column with one reac-tion(Example I).down to the bottom reboiler,and similarly hereinafter),respec-tively,with the latter in slight excess.Detailed physicochemical properties and operating conditions are listed in Table1,and other relevant information can be found in the corresponding reference.In the reactive section of this totally refluxed ideal reactive distil-lation column,reactants A and B undergo a reversible liquid-phase reaction to form the desired product C.The detailed reaction mech-anism isA+B↔C(1) The volatilities are such that the product C is the heavy key,A is the light key,and B is the intermediate key.The net reaction rate for component i on reactive stage j is given byr i,j= i H j(K f,j x A,j x B,j−K b,j x C,j)(2) where K f,j and K b,j are the forward and backward specific reaction rate constants,respectively,described by the Arrhenius law asK f,j=˛f exp−E fRT j(3.1) K b,j=˛b exp−E bj(3.2)Equimolar overflow is assumed in the nonreactive section.As the reaction reduces the molecular number,i.e.,nci=1i=−1(4) the mass balance equations in the reactive section becomeV j=V j+1−r j H RV(5) L j=L j−1+nci=1r i,j+r j H RH V(6)Ideal vapor and liquid phase behaviors are assumed in the vapor–liquid equilibrium calculation.The steady-state profiles of temperature,vapor and liquidflow rates,liquid composition,and net reaction rates are calculated and shown in Fig.2.W.Liu et al./Journal of Process Control 22 (2012) 1182–11971185370390410430450abcd161310741T (K )Stage nu mber0204060161310741L & V F l o w r a t e (m o l ·s –1)Stage nu mberLV0.00.2 0.4 0.6 0.8 1.0 161310741x (m o l e f r a c t i o n )Stage numberABC12345161310741R e a c t i o n R a t e (m o l ·s –1)Stage nu mberFig.2.Steady-state profiles of Example I.(a)Temperature,(b)vapor and liquid flow rates,(c)liquid composition and (d)net reaction rates.3.2.Evaluation of open-loop process dynamicsIn Fig.3,the open-loop transient responses of the totallyrefluxed ideal reactive distillation column with different k con (i.e.,k con =0.2,1.0,and 2.5s −1)are depicted,when it is subjected to a ±5%step change in the reboil flow rate,respectively.Sharp differ-ences can be found between the positive and negative responses,irrespective of the detailed parameters assigned to the inventory controller of the reflux drum.In the case of the positive change in the reboil flow rate,the totally refluxed ideal reactive distil-lation column exhibits under-damped responses with the degree of under-dampness inversely proportional to the controller gain of the reflux drum.In the case of the negative change in the reboil flow rate,the totally refluxed ideal reactive distillation column still displays under-damped responses with the degree of under-dampness inversely proportional to the controller gain of the reflux drum and this can clearly be observed before the time instant of 4h.After that time instant,transition between the inherent multiple steady states occurs and this moves the totally refluxed ideal reactive distillation column to an unexpected steady state.This is why a high degree of asymmetry has been noticed between the positive and negative responses in this sit-uation.The open-loop transient responses of the totally refluxed ideal reactive distillation column with different k con are shown in Fig.4,when it is confronted with a ±2%step change in the feed flow rate of reactant B,respectively.No under-damped responses are observed and the variation in the controller gain of the reflux drum shows almost no impact on the system responses.Regard-less of the positive and negative changes in the feed flow rate of reactant B,the composition of the bottom product settles down to two values lower than the initial steady state,imply-ing the possible transition between the inherent multiple steady states.0.97 80.980.9820.98 40.98 60.98 8ab12108642x C (m o l e f r a c t i o n )Time (h)kcon = 0.2kcon = 1.0kcon = 2.50.930.950.970.99403224168x C (m o l e f r a c t i o n )Time (h)kcon = 0.2kcon = 1.0kcon = 2.5Fig.3.Open-loop transient responses of the totally refluxed ideal reactive distilla-tion column with different k con in the face of a ±5%step change in the reboil flow rate,respectively (Example I).(a)Positive responses and (b)negative responses.1186W.Liu et al./Journal of Process Control 22 (2012) 1182–1197Table 2Controller parameters for Example I.ParameterControl loopReflux drum levelBase levelStoichiometric balanceBottom Ck0.2/1.0/2.50.211.130.9T i (min)–––0.423.3.Evaluation of closed-loop control performanceClosed-loop control of the totally refluxed ideal reactive distil-lation column is conducted to evaluate the impact of the inventory control of the reflux drum.A control scheme that uses two direct composition control loops is selected in the current study and Fig.5provides the detailed control structure [7].The pressure is assumed to be perfectly controlled at the nominal steady-state by the heat removal of condenser.The level of the reflux drum is controlled by reflux flow rate,and a P-only controller is used.The level of rebolier is controlled by the bottom product flow rate,and a P-only controller is chosen.The composition of the bottom product is controlled by the heat duty of reboiler,and a PI controller is adopted.According to the steady-state com-position profile in Fig.2,the composition of stage 3is selected to be controlled by the feed flow rate of reactant B because it changes rapidly there.This composition loop serves to regulate the stoichiometric balance between the two reactants,and a P-only controller is adopted.The feed flow rate of reactant A is the production rate handle and flow controlled.The composition con-trollers are tuned with Ziegler–Nichols tuning method and all the controller parameters are listed in Table 2.A first-order lag with a time constant of 5-min is inserted in all composition control loops.0.95 50.96 50.97 50.9850 8 16 24 3240x C (m o l e f r a c t i o n )Time (h)kcon = 0.2kcon = 1.0kcon = 2.50.90.930.960.99816 243240x C (m o l e f r a c t i o n )Time (h)kcon = 0.2kcon = 1.0kcon = 2.5abFig.4.Open-loop transient responses of the totally refluxed ideal reactive distilla-tion column with different k con in the face of a ±2%step change in the feed flow rate of reactant B,respectively (Example I).(a)Positive responses and (b)negative responses.The composition transmitter spans are set to be 0.1and all thecontrol valves are designed to be half open at the nominal steady state.The servo responses of the totally refluxed ideal reactive distil-lation column are illustrated in Fig.6,when the controller of the bottom product purity is subjected to a ±0.3mol%step change in its set-point,respectively.It is noted that strong effect has been generated by the variation in the controller gain of the reflux drum for both the positive and negative changes in the set-point of the bottom control loop.With increasingly tight inventory control of the reflux drum,the totally refluxed ideal reactive distillation col-umn displays a consistent improvement in dynamic responses in the case of positive change in the set-point of the bottom control loop.In the case of the negative change in the set-point of the bot-tom control loop,sustainable oscillations occur when the controller gain of the reflux drum has been set at 0.2and 1.0s −1respectively.After it has been increased to 2.5s −1,the sustainable oscillation is vanished.Fig.7presents the regulatory responses of the totally refluxed ideal reactive distillation column,when a ±2%step change is introduced to the production rate,respectively,in terms of a corre-sponding variation in the feed flow rate of reactant A.Quite similar to the circumstances of the step changes in product purity for the bottom control loop,the totally refluxed ideal reactive distillation column exhibits improved responses with the increasingly tight inventory control of the reflux drum.More specifically,whereas the low controller gain (i.e.,k con =0.2s −1)of the reflux drum resultsCFig.5.Control scheme of Example I.W.Liu et al./Journal of Process Control 22 (2012) 1182–119711870.97 90.9810.98 30.98 5024681012x C (m o l e f r a c t i o n )Time (h)kcon = 0.2kcon = 1.0kcon = 2.50.960.970.980.9902468 1012x C (m o l e f r a c t i o n )Time (h)kcon = 0.2kcon = 1.0kcon = 2.53334353637024681012V [16](m o l ·s –1)Time (h)kcon = 0.2kcon = 1.0kcon= 2.53032.53537.54002468 1012V [16](m o l ·s –1)Time (h)kcon = 0.2kcon = 1.0kcon = 2.534353637024681012R e f l u x (m o l ·s –1)Time (h)kcon = 0.2kcon = 1.0kcon = 2.532333435363702468 1012R e f l u x (m o l ·s –1)Time (h)kcon = 0.2kcon = 1.0kcon = 2.5abFig.6.Servo responses of the totally refluxed ideal reactive distillation column with different k con in the face of a ±0.3mol%step change in the set-point of the bottom composition control loop,respectively (Example I).(a)Positive responses and (b)negative responses.in sustainable and yet magnified oscillations,the high ones (i.e.,k con =1.0or 2.5s −1)achieve a stable operation.4.Example II:A totally refluxed ideal reactive distillation column with one main and one side reactions4.1.Process descriptionThis hypothetical ideal reactive distillation system is developed from Example I with the inclusion of an additional reversible side reactionB +C ↔D(7)As shown in Fig.8,the process configuration is exactly similar to that of Example I (c.f.,Fig.1).The main and side reaction rates for component i on reactive stage j are given byr m i,j = m i H j (K f m ,j x A ,j x B ,j −K b m ,j x C ,j )(8.1)r s i,j = s i H j (K f s ,j x B ,j x C ,j −K b s ,j x D ,j )(8.2)In terms of relative volatilities,these four components can be arranged in the following order:A >B >C >D(9)which means the component D is also withdrawn with component C from the bottom of the totally refluxed ideal reactive distilla-tion column.Detailed physicochemical properties and operating conditions are tabulated in Table 3.The steady-state profiles of tem-perature,vapor and liquid flow rates,liquid composition,and net reaction rates are calculated and shown in Fig.9.4.2.Evaluation of open-loop process dynamicsIn Fig.10,the open-loop transient responses of the totally refluxed ideal reactive distillation column with different k con (i.e.,k con =0.2, 1.0,and 2.5s −1)are depicted,when there is a ±5%step change in the reboil flow rate,respectively.1188W.Liu et al./Journal of Process Control 22 (2012) 1182–11970.97 80.980.98 202468 1012x C (m o l e f r a c t i o n )Time (h)kcon = 0.2kcon = 1.0kcon= 2.50.97 80.980.98202468 1012x C (m o l e f r a c t i o n )Time (h)kcon = 0.2kcon = 1.0kcon = 2.53434.53535.53602468 1012V [16](m o l ·s –1)Time (h)kcon = 0.2kcon = 1.0kcon= 2.53333.53434.53502468 1012V [16](m o l ·s –1)Time (h)kcon = 0.2kcon = 1.0kcon = 2.53434.53535.502468 1012R e f l u x (m o l ·s –1)Time (h)kcon = 0.2kcon = 1.0kcon = 2.533343502468 1012R e f l u x (m o l ·s –1)Time (h)kcon = 0.2kcon = 1.0kcon = 2.5ab Fig.7.Regulatory responses of the totally refluxed ideal reactive distillation column with different k con in the face of a ±2%step change in the production rate,respectively (Example I).(a)Positive responses and (b)negative responses.Under-dampness is presented in both the positive and negative responses with its degree inversely proportional to the controller gain of the reflux drum.Similar to Example I,there exists a high degree of asymmetry (i.e.,process nonlinearity)between the pos-itive and negative responses.In particular,a much larger variation is caused in the negative response in case k con is equal to 0.2s −1than in case k con is equal to 1.0and 2.5s −1.It is apparently related to the slow dynamics of the reflux drum.Although not shown here,the difference in steady states can finally vanish after a long time period.Non-minimum phase behavior (i.e.,initial inverse response)is observed,which is evidently attributed to the existence of a side reaction.It is noted here that the severity of process nonlinearity and non-minimum phase behavior is also inversely proportional to the controller gain of the reflux drum.Fig.11gives the open-loop transient responses of the totally refluxed ideal reactive distillation column with different k con ,when it is in the face of a ±2%step change in the feed flow rate of reactant A,respectively.Extremely similar to Example I,the impact from the variation of the controller gain of the reflux drum is hardly observed in this situation.4.3.Evaluation of closed-loop control performanceFig.12illustrates the detailed control scheme for the totally refluxed ideal reactive distillation column with a main and a side reactions.In the light of the steady-state composition profile given in Fig.9,stage 11is chosen and controlled with the feed flow rate of reactant A to regulate the stoichiometric balance between theTable 4Controller parameters for Example II.ParameterControl loopReflux drum levelBase levelStoichiometric balanceBottom Ck0.2/1.0/2.50.2 4.58 2.7T i (min)–––16.67W.Liu et al./Journal of Process Control 22 (2012) 1182–11971189Table 3Physicochemical properties and operating conditions of Example II.ParameterValueColumn pressure (bar)8.0Number of stagesRectifying section 0Reactive section 9Stripping section 5Liquid hodlup (mol)Condenser 20,000.0Column tray 1000.0Reboiler 20,000.0Main reaction activation energy (J mol −1)Forward 125,520Backward 125,520Side reaction activation energy (J mol −1)Forward 125,520Backward 125,520Specific main reaction rate at 366K (mol s −1mol −1)Forward 0.008Backward 0.0004Specific side reaction rate at 366K (mol s −1mol −1)Forward 0.005Backward 0.0002Feed flow rate (mol s −1)A 12.63B 12.82Feed locationA 10B 2Feed thermal conditionA 1.0B1.0Relative volatility (A:B:C:D)8:4:2:1Heat of reaction (J mol −1)Latent heat of vaporization (J mol −1)29,053.7Bottom product specification (C,mol%)98Vapor pressure constantsA (A vp /B vp )12.3463/3862B (A vp /B vp )11.6531/3862C (A vp /B vp )10.9600/3862D (A vp /B vp )10.2669/3862reactants,A and B.A P-only controller is again used here.The feed flow rate of reactant B is the production rate handle and flow con-trolled.The controller parameters are tabulated in Table 4.The servo responses of the totally refluxed ideal reactive distil-lation column are illustrated in Fig.13,when there is a ±0.3mol%step change in the set-point of bottom control loop,respectively.In case k con is set to be 0.2s −1,while the totally refluxedidealFig.8.Scheme of a totally refluxed ideal reactive distillation column with one main and one side reactions (Example II).reactive distillation column settles down with a large deviation in the face of the positive change in the set-point of bottom con-trol loop,a magnified oscillation occurs in the face of the negative change in the set-point of bottom control loop.In case k con is set to be 1.0and 2.5s −1,fairly smooth operation can be achieved for both the positive and negative changes in the set-point of bottom control loop.The responses with k con as 2.5s −1outperform those with k con as 1.0s −1.Fig.14presents the regulatory responses of the totally refluxed ideal reactive distillation column in the face of a ±2%step change in the feed flow rate of reactant B,respectively.When k con is set to be 0.2s −1,rather oscillating responses are obtained for both the posi-tive and negative changes in the feed flow rate of reactant B.With relatively tight inventory control of the reflux drum (i.e.,1.0and 2.5s −1),sharp improvement in control performance is achieved,giving much smaller overshoots and shorter settling times.A coun-terintuitive phenomenon is observed here,i.e.,the heat duty of reboiler changes inversely proportional to the production rate.It is considered to be caused by the existence of input multiplicities in the totally refluxed ideal reactive distillation column.The transi-tion between the inherent multiple steady states distorts actually the relationship between the production rate and the heat duty of reboiler.5.Example III:A high-purity ethylene glycol reactive distillation column5.1.Process descriptionEthylene glycol (C 2H 6O 2)is produced by hydration of ethylene oxide (C 2H 4O),i.e.,the main reaction:C 2H 4O(EO)+H 2O →C 2H 6O 2(EG), H R =–80.0×103J mol −1(10.1)r m =3.15×1015exp−9547Tx EO x W (10.2)。