Chemical Engineering Science 60 (2005) 4661 – 4677
www.elsevier.com/locate/ces
Effects of feed tray locations to the design of reactive distillation and its
implication to control
Yu-Cheng Cheng, Cheng-Ching Yu
∗Department of Chemical Engineering, National Taiwan University, Taipei 106-17, Taiwan Received5 September 2004; receivedin revisedform 3 February 2005; accepted14 March 2005
Available online 13 May 2005
Abstract
The effects of feed locations to the design of reactive distillation are explored. In this work, ideal reactive distillation systems are usedto illustrate the advantage of feedtrays optimization in design andcontrol. Process parameters such as relative volatilities between reactants, relative volatilities between products, column pressure, activation energies, andpre-exponential factors are variedto seek possible generalization. For all systems studied, the percentage of energy saving ranges from 6% to 47%, and this is obtained by simply rearranging the feed locations. Finally, the idea of optimal feed trays is extended to the operation/control of reactive distillation systems. First, steady-state analysis is carriedout to findthe optimal feedtrays as measurable loadvariable varies. Then, a control structure is proposedto rearrange the feeds as the disturbance comes into the system. The results indicate that, again, substantial energy can be saved by feed rearrangement via the coordinated control structure.
䉷2005 Elsevier Ltd. All rights reserved.
Keywords: Reactive distillation; Feed tray; Control structure design
1. Introduction
The reactive distillation combines both chemical reaction andmulticomponent separation into a single unit. It offers significant economic advantages in some systems, particu-larly when reactions are reversible or when the presence of azeotropes makes conventional separation systems complex andexpensive. The applications of reactive distillation in the chemical andpetroleum industries have increasedrapidly in the past decade (Taylor andKrishna, 2000; Doherty and Malone, 2001). A number of papers andpatents have ex-ploredthe RD systems. The literature up to 1992 was reviewedbyDoherty andBuzad(1992). Most of the papers were discussed by steady-state design and optimization problems. Only a few papers studied the dynamic of reactive distillation or the interaction between design and control. Re-cent books byDoherty andMalone (2001)andSundmacher andKienle (2003) present detailed discussions of the ∗Corresponding author. Tel.: +886 2 3365 1759; fax: +886 2 2362 3040.
E-mail address:ccyu@ntu.edu.tw(C.-C. Yu).
0009-2509/$ - see front matter䉷2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.03.033
technology andits current status. The literatures state that the most common applications of reactive distillation are etherification andesterification reactions. Most of these papers focus on real chemical systems, andeach system has its own set of complexities in vapor–liquidequilib-rium nonideality (azeotropes), reaction kinetics, physical properties, etc. The discrete nature of chemical species andspecific complexities in the VLE seems to cloudthe picture in understanding reactive distillation systems. On the other hand, the ideal reactive distillation of Luyben (2000) and Al-Arfaj andLuyben (2000) seems to offer a continuous spectrum in studying the process behavior by stripping away all the non-ideal VLE and specific re-action rates. Only a limitednumber of papers study the ideal reactive distillation systems. Al-Arfaj andLuyben (2000)studied the control of an ideal two-product reactive distillation system. Simple ideal physical properties and kinetics are assumedso that the control issue can be ex-ploredwithout being cloudedby complexities of a specific chemical system. Sundmacher and Qi (2003) also com-pare the conceptual design of reactive distillation process
configurations for ideal binary mixtures, and comparisons are made to the conventional process. A recent paper by Kaymak andLuyben (2004)also makes quantitative com-parisons of simple reactive distillation for different chemical equilibrium constants andrelative volatilities (Kaymak et al., 2004).
The reactive distillation differs from the conventional dis-tillation in that a tubular type of reactor, the reactive flash cascades to be specific (Doherty andMalone, 2001), is cas-caded with separation units. From this perspective, the com-position profile inside the reactive zone becomes important for an effective operation of the reactive flash cascades. Moreover, typical distillation columns follow certain tem-perature profile. That is, the temtem-perature increases as one steps down the column. The composition as well as the
tem-perature effects shouldplay some role for the performance
of a reactive distillation column. The reactant feed location is an obvious design degree of freedom to locate optimal composition andtemperatures profiles inside the column. It then becomes obvious that the feedtray location shouldbe included as a design variable. Therefore, the objective of this work is to explore the effects of feedtray location to the performance of reactive distillation systems.
In this work two types of chemical systems are studied. One is systems with larger activation energies (temperature sensitive reaction) andthe other is systems with smaller activation energies. For each type, the effects of relative volatilities between reactants andbetween products are also studied. The results clearly indicate that it is necessary to rearrange the feedtray locations to obtain optimal design (i.e., minimum energy consumption). Qualitative explana-tions to the shifting in the feedlocaexplana-tions are also given. Furthermore, the optimal feedlocations also vary as the capacity of the column is changed. This mimics the sce-narios of the catalyst deactivation and/or production rate increases. Therefore, the optimizedfeedtray location can be extended to the operation aspect of reactive distillation systems. Control structures are devised to maintain optimal composition andtemperature profiles as operating condition changes.
2. Process studies
Consider an ideal reactive distillation (Fig.1) with a re-versible liquid-phase reaction in the reactive section.
A+ B ⇔ C + D.
The forwardandbackwardspecific rates following the Arrhenius law on trayj are given by
kFj= aFe−EF/RTj, (1)
kBj= aBe−EB/RTj, (2)
whereaF andaBare the pre-exponential factors,EF andEB are the activation energies, andTjis the absolute temperature
Fig. 1. The reactive distillation with NR rectifying trays, Nr×n reac-tive trays, andNS stripping trays under conventional feed arrangement (NF,B= Nr×n,topandNF,A= Nr×n,bot).
on tray j. The reaction rate on tray j can be expressedin terms of mole fractions (xj,i) andthe liquidholdups (Mj).
Rj,i=iMj(kFjxj,Axj,B− kBjxj,Cxj,D), (3) whereRj,iis the reaction rate of componenti on the jth tray (kmol/s), i is the stoichiometric coefficient which takes a negative value for the reactants, andMjis the kinetic holdup on trayj (kmol) andtakes a constant value throughout the simulation (This is typically true for catalyst weight based kinetics.)
The assumptions made in this work include:
(1) The forwardreaction rate is specifiedas 0.008 kmol/s at 366 K, andkBis set to 0.004 kmol/s at the same temper-ature. Kinetic andphysical property data for the system are given inTable 1(Al-Arfaj andLuyben, 2000).
(2) The kinetics holdup (Mj) of 1000 moles is assumed (Al-Arfaj andLuyben, 2000).
(3) Ideal vapor–liquid equilibrium is assumed, in which constant relative volatilities are used. The tray tempera-ture is computedfrom Antoine vapor pressure equation (Table 1). Note that as the result of constant relative volatility, the Antoine coefficients,BV P’s , are the same for all four components.
(4) Vapor holdup and pressure drop are neglected.
As shown in theFig. 1, the column is divided into three sections. The first one is the reactive section containingNr×n trays. The rectifying section (which is above the reactive
Y.-C. Cheng, C.-C. Yu / Chemical Engineering Science 60 (2005) 4661 – 4677 4663 Table 1
Physical properties for the high activation energies case
Activation energy (cal/mol) Forward(EF) 30 000
Backward(EB) 40 000
Specific reaction rate at 366 K (kmol/s/kmol) Forward(kF) 0.008
Backward(kB) 0.004
Heat of reaction (cal/mol) −10 000
Heat of vaporization (cal/mol) 6944
Relative volatilities (C/A/B/D) 8/4/2/1
C A B D
Vapor pressure constantsa AV P 13.04 12.34 11.45 10.96
BV P 3862 3862 3862 3862
alnPS
i = AV P ,i− BV P ,i/T where T in Kelvin and PiS is the vapor pressure of pure componenti in bar.
section) has NR trays andthe stripping section (which is below the reactive zone) hasNS trays. Thus, we are consid-ering a reactive distillation column in which reaction only occurs in the reactive section, which implies a solid-catalysis catalyzedreaction.
The relative volatilities of the components are in the fol-lowing order:
C>A>B>D.
The products C andD are the lightest andheaviest com-ponents, respectively, with the reactants A andB as mid-dle boilers. The thermodynamic behavior indicates that we should remove the product C from the distillate and obtain heavy product D from the bottoms.Fig. 1 also shows that the fresh feedstream FOA containing reactant A is fedto the bottom of the reactive zone, andthe heavier reactant B is fedto the top of the reactive zone. Quite volatile as com-paredto B andD, the light reactant A goes up the column andleaves small traces in the stripping section. Likewise, the heavy reactant B goes down the column, after being fed on the top tray of the reactive zone, andlittle component B can be foundin the rectifying section. Thus, the primary separation in the stripping section is between B andD and in the rectifying section is between C andA.
2.1. Modeling
In Fig. 1, the component balances for the column are expressedas
rectifying andstripping trays:
d(xj,iMj)
dt = Lj+1xj+1,i+ Vj−1yj−1,i− Ljxj,i
− Vjyj,i. (4)
reactive trays: d(xj,iMj)
dt = Lj+1xj+1,i+ Vj−1yj−1,i− Ljxj,i
− Vjyj,i+ Rj,i. (5)
feedtrays: d(xj,iMj)
dt = Lj+1xj+1,i+ Vj−1yj−1,i− Ljxj,i− Vjyj,i
+ Rj,i+ Fjzj,i. (6)
Herexj,iandyj,i denote liquidandvapor mole fraction of component i on tray j, with Lj and Vj stands for liquid andvapor flow rates for thejth tray. Liquidhydraulic time constant () is includedby using a linearizedform of the Francis weir formulation, and is set to 6 s in this work. Since equimolal overflow is assumed, the vapor and liquid flow rates are constant throughout the stripping andrecti-fying sections, except for the reactive zone as a result of an exothermic reaction (Al-Arfaj andLuyben, 2000). The heat of reaction vaporizes some liquidon each tray in this section. Therefore the vapor flow rate increases up through the reactive zone, while the liquid flow rate decreases down through the reactive zone:
Vj= Vj−1−H
vRj,i, (7)
Lj= Lj+1+H
vRj,i, (8)
whereis the heat of reaction (−10 000 cal/mol) andHv is the latent heat of vaporization (6944 cal/mol).
The vapor–liquidequilibrium is assumedto be ideal and the bubble point temperature calculation is usedto findthe tray temperature (seeTable 1for the vapor pressure data of pure component).
P = xj,APA(TS j)+ xj,BPB(TS j)+ xj,CPC(TS j)
+ xj,DPD(TS j), (9)
where total pressure P andvapor pressures PS are in bar. The column pressure is fixedat 5.1 bar.
Table 2
Effects of feed locations to design for systems with different relative volatilities and rate constants (temperature sensitive kinetics;EF= 30 000 and
EB= 40 000 cal/mol)
Base case AB= 2 AB= 1.5 AB= 3.0 AC= 4.0 BD= 4.0 OptimalP (9 bar) Lowk Highk C/A/B/D 8/4/2/1 8/4/2/1 6/3/2/1 12/6/2/1 16/4/2/1 16/8/4/1 8/4/2/1 8/4/2/1 8/4/2/1 kF,366(s−1) 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.0048 0.016 kB,366(s−1) 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.0024 0.008 NS/Nr×n/NR 8/11/9 8/11/9 9/11/9 8/11/8 5/11/5 6/11/6 8/11/9 8/11/9 6/11/6 Nr×n,bot/Nr×n,top 9/19 9/19 10/20 9/19 6/16 7/17 9/19 9/19 7/17 NF,A/NF,B 9/19 11/15 11/13 10/17 12/14 8/10 14/17 9/17 10/13 XD,C/XB,D 0.95/0.95 0.95/0.95 0.95/0.95 0.95/0.95 0.95/0.95 0.95/0.95 0.95/0.95 0.95/0.95 0.95/0.95 FOA,FOB,D, B (kmol/s) 0.0126 0.0126 0.0126 0.0126 0.0126 0.0126 0.0126 0.0126 0.0126 R (kmol/s) 0.0366 0.0332 0.0409 0.0274 0.0198 0.0284 0.0263 0.0445 0.0277 VS (kmol/s) 0.0320 0.0285 0.0362 0.0227 0.0152 0.0237 0.0217 0.0399 0.0230
Percent energy savinga(%) 0 −10.9 −15.2 −6.9 −46.8 −15.6 −27.1 −5.5 −21.9
aComparedto the conventional feedarrangement (i.e.,N
rxn,bot= NF,AandNrxn,top= NF,B).
2.2. Steady-state design
Typical design variables of a reactive distillation column include: (1) the column pressureP , (2) the number of reac-tive traysNr×n, (3) the numbers of trays in the stripping and rectifying sections (NS andNR, respectively), and(4) the locations of the feedtrays (NF,AandNF,B, respectively).
In this work, the column pressureP is fixedat a constant value, andthe number of reactive trays (Nr×n) is selected to ensure the desired conversion with the conventional feed arrangement (heavy reactant to the top of the reactive zone, andthe light reactant to the bottom of the reactive zone). The number of trays in the stripping andrectifying sections is set to twice of the minimum number of trays according to the Fenske’s Equation (Douglas, 1988), which is N = 2Nmin= 2 ln x D,LK xD,HK xB,HK xB,LK ln LK HK , (10) where the subscripts LK and HK standfor the light key and heavy key, respectively. For the rectifying tray number (NR), we use the liquidcomposition right above the reactive tray for xB, andfor NS, we use the vapor phase composition right below the reactive zone asxD. This leaves us with the feedtray locations as the design variables. Because all tray numbers are determined, effects of feed tray locations can be comparedby simply looking at the energy consumption (i.e., vapor rate).
2.3. Base case
Equations describing the material balances were pro-grammedin FORTRAN code, andall simulations were carriedout on Pentium PC. It shouldbe emphasizedthat the convergence of the reactive distillation is far more difficult than conventional distillation is. Typically, a steady-state simulation is carriedout in a two-step procedure. First, the Wang–Henke methodis usedto converge the flowsheet
(MESH equations) to a certain degree (actually to the point at which the objective function fluctuates). Then, the tem-perature andcomposition profiles are fedto a dynamic pro-gram that is integrateduntil temperatures andcompositions converge.
Saturatedliquidfeeds were assumed, andtwo feedflow rates are 0.0126 kmol/s each with pure A (NF,A) or B (NF,B), which were introduced to the bottom (Nr×n,bot) or the top (Nr×n,top) of the reactive section (seeFig. 1 or base case in Table 2). Note that this is the typical feed arrangement for reactive distillation, which is termed as the conventional feedarrangement hereafter. In this work, the conversion is specifiedto be 95%, andthis corresponds to purities of 95% C in the distillation and 95% D in the bottoms.
Fig. 2 (thickest line) shows the composition profiles of all four components at the nominal design. Reactant A has the highest concentration (xA) on the feedtray (NF,A= 9). The profile shows that xA decreases toward the upper re-active zone as a result of the reaction andalso decreases towardthe bottoms of the column as a result of separa-tion. Similar behavior is observedfor the heavy reactant B (Fig.2). Both the light product C and heavy product D meet the specification towardthe ends of the column.
Luyben andAl-Arfaj (2000) show the steady-state tem-perature profile at which a non-monotonic temtem-perature pro-file is observedandat which the local temperature mini-mum on the lower feedtray is causedby the presence of a significant amount of the light reactant A. This behavior is not uncommon for reactive distillation columns but is rarely seen in the conventional distillation.
2.4. Feedlocations versus reactants distribution
It shouldbe emphasizedthat the reactive section of a reactive distillation column can be viewed as a cascade-type two-phase reactor with the reactor temperature determined
Y.-C. Cheng, C.-C. Yu / Chemical Engineering Science 60 (2005) 4661 – 4677 4665
Fig. 2. Composition profiles by changing the feedlocation of: (A) the heavy reactant B (NF,B) and(B) the light reactant A (NF,A).
by the bubble-point temperature of the tray liquidphase composition. It is clear that the composition andtemperature profiles will certainly affect the performance of the reactive zone, andthe feedtray locations appear to be one of the most effective variables for these profiles redistribution. In this section, we are interestedin how the composition profile will be affectedby changing the feedtray location, andthe individual feed tray is changed one at a time.
First we fix theNF,A at the bottom of the reactive zone andchange the feedlocation of the B component from top to bottom. At constant volatilities systems, the feedlocation
of B (NF,B) is variedfrom 19 down to 14 andthen to 11 (NF,B= 19, 14, or 11).Fig. 2A shows the composition pro-files in the column asNF,Bchanges. As the feedlocation of component B moves down the column, the mole fraction of heavy reactant B (xB) increases towardthe lower section of reactive zone, as can be seen inFig. 2A. That means we have a wider and less variation in the distribution of component B throughout the reactive zone as the feedtray is lowered. Consequently, the mole fraction of the light reactant A (xA) becomes smaller in the lower reactive zone while the profiles of two products (xC andxD) remain qualitatively similar as
Fig. 3. Reactant composition, fraction of the total conversion, andtemperature profiles in the reactive zone by changing the feedlocation of the heavy reactant B: (A)NF,B= 19, (B) NF,B= 14, and(C) NF,B= 11.
shown inFig. 2A. This rearrangement of the reactant compo-sition certainly alters the “fraction of total conversion” (i.e., reaction rate in each tray divided by the overall reaction rate) as well as the temperature profile in the reactive zone.Fig. 3
shows the profiles of the fraction of total conversion, of the reactants, andof the temperature in the reactive section as NF,B varies. When we moveNF,Bdown, both the reactant B andconversion increase in the lower reactive section. This implies that the lower reactive trays are better utilized, but at the cost of smaller conversion in the upper reactive trays (i.e., upper reactive trays are underutilized;Fig. 3A–C). It seems a balancedusage of the reactive trays is necessary to achieve optimality andthis means an optimal feedlocation exists for component B. The energy consumption (vapor rate VS to be exact) is a goodmeasure the column performance. In this case, the vapor rate changes from 0.0320 to 0.0315 andthen to 0.0397 (kmol/s) asNF,Bchanges from 19 down to 14 then to 11. The results clearly indicate that the energy penalty can be significant if one places the feedat an inap-propriate location, andthe conventional design seems to be a pretty goodchoice.
The same analysis can be carriedover to the feedloca-tion of the light component A. Now we fix theNF,B at the top reactive zone (i.e.,NF,B= Nr×n,top) by varying NF,A. The feedlocation (NF,A) is variedfrom 9, to 11, andthen to 12. Again,Fig. 2B shows that the mole fraction of A in-creases towardthe top of the reactive section (xAinFig. 2B) while the mole fraction of the heavy reactant B decreases (xB inFig. 2B). However, the heavy reactant B increases towardthe bottom of the reactive zone, as can be seen in
Fig. 4. Feedtray locations andcorresponding energy consumption (com-paredto the base case) throughout the optimization step.
Fig. 2B. This reactant redistribution leads to a significantly different energy consumption, and in the case of variable NF,A, the vapor rate changes from 0.0320 to 0.0292 and then to 0.0386 kmol/s asNF,A moves from 9 up to 11, and then to 12.
The on-going analysis clearly indicates that the feed tray locations are important design/operation parameter. Improvedprocess design can be achievedby simply ad -justing the feedlocations. One question then arises: how much energy can be savedif we adjust the feedlocations simultaneously?
Y.-C. Cheng, C.-C. Yu / Chemical Engineering Science 60 (2005) 4661 – 4677 4667
Fig. 5. Profiles of temperature, composition, fraction of total conversion, andreaction rate constant in the reactive zone for the base case with: (A) conventional feedarrangement (NF,A= 9 and NF,B= 19), and(B) optimal feedarrangement (NF,A= 11 and NF,B= 15) with 11% energy saving.
2.5. Optimal feedlocations
Finding the optimal feedlocations can be formulatedas an optimization problem in which the vapor rate is minimized by varying the feedtray locations.
Minimize NF,B,NF,A VS
subject to: XD,C= XB,D= 0.95. (11)
Because the total tray number (NT) is finite, one can findthe optima by exhausting allNT2possibilities. It is reasonable to restrict the search space to the reactive zone so that the possi-ble choices are further reduced toNr×n2 . In this work, a brute force approach is taken by fixingNF,A first while varying
NF,Buntil a minimumVS is found. Next,NF,Ais changed, andthe procedure repeats itself until a global minimum is located.Fig. 4shows the variation of the vapor rate through-out the process. The results indicate that one should move the feedlocation of the heavy reactant B down toNF,B=15 (from 19) andmove the feedtray of the light reactant A up toNF,A= 11 (from 9). This corresponds to a 10.9% energy saving, comparedto the conventional feedarrangement (see
Table 2). Furthermore, simulation results from this andmany other examples reveal that the feedlocation of the heavy reactant should not be placed lower then the feedtray of the light reactant. This reduces the search space further down to(Nr×n+ 1)Nr×n/2.
In addition to the percentage of energy saving, compar-isons are also made in terms of profiles of temperature, of composition, of reaction rate on each tray, andreaction rate constants.Fig. 5 shows that the case of optimal feed arrangement (Fig. 5B) has a much sharper temperature profile in the reactive zone than the case of conventional
feedlocations (Fig. 5A). It is also observedthat the tray temperature almost reaches 390 K in the former case, while the latter barely reaches 380 K. Furthermore, the profiles of tray conversion andrate constant also take qualitatively similar shape as that of the temperature. The composition profiles in Fig. 5 explain how it happens. First, as the re-sult of movingNF,Bdownward andNF,Aupward, we have non-monotonic reactant distributions for the optimal case as opposedto the monotonic reactant distribution for the con-ventional one. This is advantageous for the forward reac-tion. Next, one obtains an almost monotonic product distri-bution for the optimal case, especially for the heavy product D, andxD (tray composition of product D) almost reaches 60% at the bottom of the reactive section, which has pro-foundeffect on the temperature profile. On the other hand, the mole fraction of D gives a non-monotonic profile for the conventional case, andxD takes a downturn toward the bottom of the reactive tray as the result of dilution from the excess light reactant A which is introduced on the bottom of the reactive zone. The results presentedin Fig. 5reveal the complicatedinteraction between temperature andcom-position in the reactive zone, andit is almost certain that a better profile can always be achievedby varying the feed locations.
In summary, for the system with relative volatilities of C/A/B/D= 8/4/2/1, one shouldmove the feedloca-tions of the heavy reactant downwardandlight reactant up-ward. In terms of the search space for the optimal feed trays, we have the following heuristics:
Heuristic H1. Never place the heavy reactant feedbelow the feedtray of the light reactant (similarly, do not place the light reactant feedabove the feedtray of the heavy rea-ctant).
3. Effects of relative volatilities
Up to now, only one specific example is explored, it will be interesting to see whether the results can be extended to different cases (e.g., different relative volatilities) and how the process change will impact the location of optimal feed trays andthe percent of energy saving. Note that for every case studied, the column is re-designed using the procedure in Section 3. This means the columns may have differentNR,
NS, andNr×nandthe location of the feedtrays are descried in terms of their relative position in the reactive zone.
3.1. Changing relative volatilities of reactants
In this section, we will explore the effects of relative volatilities of reactants to the feedtray locations. By rela-tive volatilities of reactants, we mean that the separation be-tween the two reactants (A andB) becomes easier or more difficult while keeping the relative values of the products constant. Two cases are studied: one is a more difficult sep-aration (i.e., A/B = 3/2) andthe other one is an easier one (i.e., A/B = 6/2), comparedto the base case (i.e., A/B= 4/2).
In the first case, the relative volatilities areC=6,A=3, B = 2, and D = 1, respectively. With the conventional
feedarrangement, we have 33% more energy consumption (0.0428 kmol/s), comparedto that of the base case. This shows that, similar to the conventional distillation, difficult separation, even between reactants A andB, requires more energy. Moreover, the composition of A is higher toward the lower reactive zone as comparedto the base case (cf. Figs. 5A and6A) and this leads to a decrease in product D composition which subsequently requires a larger vapor rate to meet the specification. Following the optimization proce-dure, the result shows the optimum feed trays areNF,A=11 and NF,B = 13 (Fig. 6B) which corresponds to a 15.2% energy saving (from 0.0428 to 0.0363 kmol/s) over the con-ventional feedarrangement (Table 2). It shouldbe empha-sizedhere that the percent of energy saving is computedwith respect to the conventional feedarrangement in each case. One immediately observes that the two feeds move closer to each other (only two trays apart), anda non-monotonic re-actant composition distribution can be seen (Fig.6B). Sim-ilar to the base case (e.g.,Fig. 5B), we also have an almost monotonic composition distribution in D. This results in a higher temperature in the lower section of the reactive trays andleads to a higher reaction rate andconsequently higher conversion, as shown inFig. 6B.
The other case is just the opposite where we have easy sep-aration between two reactants. In this example, the relative volatilities areC= 12,A= 6,B= 2, andD= 1, respec-tively. Unlike in the previous example, the energy consump-tion (0.0227 kmol/s) is only 84.4% (0.0227/00320*100%) of the base case. This again reconfirms that well known fact of the conventional distillation—easy separation requires
less energy—is also applicable to reactive distillation. It is also observedthat the composition of D is higher toward the lower reactive zone as comparedto the other two cases (cf. Figs. 5A,6A), andthis implies a smaller vapor rate to meet the specification. The optimization result shows that the optimum feedtrays are NF,A = 10 and NF,B = 17, andthis corresponds to a 6.9% energy saving (from 0.0244 to 0.0227 kmol/s) over the conventional feedarrangement.
Table 2 reveals that the two feeds move away from each other, anda little improvedreactant composition distribution can be observed. In fact, the optimal feed trays are located quite close to the conventional feedtrays (e.g., one andtwo trays away). An almost monotonic composition distribution in D is also observedandthis leads to a little higher tem-perature in the lower section of the reactive trays but not by much. This explains why the improvement is not as signifi-cant as in the previous case.
3.2. Changing relative volatilities of products
Now let us consider the cases in which the relative volatil-ities of two products are different from the base case value of 2. Two cases are explored: one is that the light prod-uct (C) is easy to separate from the light reactant A (i.e., C/A= 4), andthe other is that the relative volatility be-tween the heavy reactant B andthe heavy product D (i.e., B/D= 4) is larger than the base case value of 2.
In the first case, we have:C= 16,A= 4,B= 2, and D = 1. With the conventional feedarrangement, the en-ergy consumption (0.0285 kmol/s) is 10.9% less than the base case because of the large relative volatility between C andA. Following the optimization procedure, the optimum feedtrays becomeNF,A= 12 and NF,B= 14 (Fig.7B). As comparedto the conventional feedarrangement, this corre-sponds to a 46.8% energy saving (from 0.0285 to 0.0152 kmol/s)! This is a very significant energy saving by very simple means (feedrearrangement). Two observations can be made immediately. First, the two feeds are quite close to each other andthe feedlocations move to the upper section of the reactive zone. Second, the fraction of total conversion is distributed relatively uniform throughout the reactive zone (at least comparedto other cases) as shown inFig. 7B. This implies none of the reactive trays are under utilized, and they are achievedwith the interplay between the composition and temperature distributions (e.g., showing temperature upturn whenever necessary). Again, an almost monotonic compo-sition distribution in D can also be seen, and significantly smaller amount of the product C is also observed in the up-per reactive zone, which allows for higher reactant concen-tration. All these factors result in much smaller vapor rate as comparedto the conventional feedarrangement.
The other example is just the opposite in which we have an easy separation between the heavy reactant and the heavy product. In this case, the relative volatilities are C = 16, A = 8, B = 4, and D = 1, respectively. For
Y.-C. Cheng, C.-C. Yu / Chemical Engineering Science 60 (2005) 4661 – 4677 4669
Fig. 6. Profiles of temperature, composition, fraction of the total conversion, andreaction rate constant in the reactive zone for the system C/A/B/D= 6/3/2/1 with: (A) conventional feedarrangement (NF,A= 10 and NF,B= 20), and(B) optimal feedarrangement (NF,A= 11 and
NF,B= 13) with 15% energy saving.
Fig. 7. Profiles of temperature, composition, fraction of total conversion, andreaction rate constant in the reactive zone for the system C/A/B/D= 16/4/2/1 with: (A) conventional feedarrangement (NF,A= 6 and NF,B= 16), and(B) optimal feedarrangement (NF,A= 12 and
NF,B= 14) with 46.8% energy saving.
the conventional feedarrangement, the energy consumption (0.0281 kmol/s) is only 87.8% of the base case. All these four cases confirm that the well-known fact of the conventional distillation—easy separation requires less energy—can also be appliedto reactive distillation. It is also observedthat the concentration of D is smaller towardthe lower reactive zone as comparedto the other two cases (cf.Figs. 5A and
8A), andthis allows a higher reactant concentration in the
same section. The optimization result shows that the opti-mum feedtrays areNF,A= 8 and NF,B= 10 (Fig.8B), and this corresponds to a 15.6% energy saving (from 0.0281 to 0.0237 kmol/s) over the conventional feedarrangement (Table 2). It is also observedthat these two feeds are quite
close to each other andthey are locatedin the lower section
of the reactive zone, as can be seen inFig. 8B. In addition to an almost monotonic composition distribution in D, a
Fig. 8. Profiles of temperature, composition, fraction of total conversion, andreaction rate constant in the reactive zone for the system C/A/B/D= 16/8/4/1 with: (A) conventional feedarrangement (NF,A= 7 and NF,B= 17), and(B) optimal feedarrangement (NF,A= 8 and
NF,B= 10) with 15.6% energy saving.
high concentration of B throughout the reactive zone is also observedinFig. 8B, andthis improves the effectiveness of the reactive trays. This is allowedbecause B can be sepa-ratedeasily from the heavy product D. However, unlike in the previous case, the decreasing trend of the temperature towardthe upper reactive zone leads to a monotonically decreasing fraction of total conversion in the same direction (Fig.8B). The underutilized reactive trays in the upper re-active zone explain why the margin of improvement is not quite as significant as in the previous case.
3.3. Summary
On-going analyses clearly indicate that the feed locations are important design parameters, and significant energy sav-ing (rangsav-ing from 7% to 47%) will result if we place the feedtrays optimally (Table 2). As for the specific feedloca-tions, the following heuristics are useful.
Heuristic H2. Place the light andheavy reactant’s feedlo-cation close to each other when the relative volatility be-tween the reactants is small (e.g.,Fig. 6B). Similarly, move the feedtray locations away from each other when the rel-ative volatility between the reactants is large.
Heuristic H3. When the relative volatility between the light
reactant andthe light product is large, move the
feedloca-tions upward (i.e., to the upper reactive zone; e.g.,Fig. 7B). Similarly, when the relative volatility between the heavy
reactant andthe heavy product is large, move the feed
locations downward (i.e., to the lower reactive zone; e.g.,
Fig. 8B).
These were observednot only for systems with base case kinetics (Table 2), but also for processes with temperature less sensitive kinetics (Table 3). Also note that the terms “small” and“large” usedare in a relative sense.
4. Effects of reaction kinetics
In this section, the effects of reaction kinetics to the opti-mal feedtray locations to the corresponding energy saving are explored. Two scenarios are studied. One is the acti-vation energies for both forwardandbackwardreactions are reduced by an order of magnitude and this implies a less temperature-sensitive reaction rate. The other is the case where the pre-exponential factor is varied. We are interestedin how these changes will impact the optimal feedlocations andthe corresponding percentage of energy saving.
4.1. Reducing activation energies
Consider the case in which the forwardandbackward activation energies are reduced to 3000 cal/mol, an order of magnitude smaller. In both cases, we fix the rate con-stants to 0.008 and0.004 at 366 K for the forwardand backwardreactions (Table 1). This has two impacts to the reactive distillation. First, the reactions are not quite as temperature sensitive as in the previous case. Second, the heat of reaction is zero, as opposedto the previous case where 10 000 cal heat is releasedfor every mole reactant converted.
Y.-C. Cheng, C.-C. Yu / Chemical Engineering Science 60 (2005) 4661 – 4677 4671 Table 3
Effects of feed locations to design for systems with different relative volatilities (temperature insensitive kinetics;EF = 3000 and EB= 3000 cal/mol) Base case AB= 2 AB= 1.5 AB = 3.0 CA= 4.0 DB= 4.0 C/A/B/D 8/4/2/1 8/4/2/1 6/3/2/1 12/6/2/1 16/4/2/1 16/8/4/1 kF,375(s−1) 0.0215 0.0215 0.0215 0.0215 0.0215 0.008 kB,375(s−1) 0.0150 0.0150 0.0150 0.0150 0.0150 0.004 NS/Nr×n/NR 7/11/8 7/11/8 8/11/8 8/11/8 5/11/6 6/11/6 Nr×n,bot/Nr×n,top 8/18 8/18 9/19 9/19 6/16 9/19 NF,A/NF,B 8/18 11/15 13/15 10/17 14/15 9/12 XD,C/XB,D 0.95/0.95 0.95/0.95 0.95/0.95 0.95/0.95 0.95/0.95 0.95/0.95 FOA,FOB,D, B (kmol/s) 0.0126 0.0126 0.0126 0.0126 0.0126 0.0126 R (kmol/s) 0.0267 0.0225 0.0264 0.0185 0.0105 0.0185 VS (kmol/s) 0.0393 0.0351 0.0390 0.0311 0.0231 0.0311
Percent energy savinga(%) 0 −10.7 −19.1 −5.4 −33.6 −14.7
aComparedto the conventional feedarrangement (i.e.,N
rxn,bot= NF,AandNrxn,top= NF,B).
4.1.1. Base case for the low activation energy example With the conventional feedarrangement, the profiles of temperature, composition, andfraction of total conversion are qualitatively similar to that of the high activation exam-ple (Fig.5A), except for the profile of the reaction rate where the low activation energy example exhibits a much lower rate for the backwardreaction. However, the energy consumption is higher in the present example as comparedto one with a higher activation energy (0.0393 versus 0.0320 kmol/s). The reason for that is that the heat is no longer released from the reactions, andthe effect of direct heat integration disappears. Following the optimization procedure, the opti-mal feedtrays becomesNF,A= 11 and NF,B= 15, andthis results in a 10.7% energy saving, when comparedto the conventional feedarrangement (Table 3). Similar to the ex-ample of high activation energy, these two trays are located 4 trays apart. But, unlike the previous case, the relative position moves up a little. This is within one’s expectation because, here, we have a less temperature-sensitive reaction, andthe effects of the temperature profile is not as important as in the previous example. This indicates that composition profile is much more important in this example. The fraction of total conversion on reactive trays clearly indicates a non-monotonic profile throughout the reactive zone, comparedto the high activation energy case (Fig.5B). The temperature insensitivity is also illustratedin the profile of the rate con-stants where the ratio of the maximum over the minimum rate constants is 1.3 in this case, while the high activation energy example gives a value of 22! In terms of energy saving via feedtray optimization, both cases show quite similar results (10.7% versus 10.9% as shown inTables 2
and3).
4.1.2. Changing relative volatilities of reactants
Similar to the previous example, first we explore the case of the difficult separation between the two reactants. The relative volatilities areC= 6,A= 3,B = 2, andD= 1, respectively. Following the optimization procedure, the optimal feedtrays are NF,A = 13 and NF,B = 15, anda
19.1% energy saving (from 0.0482 to 0.0390 kmol/s) can be achievedby the feedre-arrangement (Table 3). It is clear that the heuristic H2 applies here, andthe percentage of energy savedis quite similar to the high activation energy counterpart (Table 2).
Next, the case of difficult separation between reactants is examined. The relative volatilities areC=12,A=6,B=2, andD=1, respectively. The feedtray location optimization gives: NF,A= 10 and NF,B = 17. In this case, only 5.4% energy can be saved(from 0.0328 to 0.0310 kmol/s) because the conventional feedarrangement is a pretty gooddesign to begin with (Table 3). Again, the heuristic H2 applies here, andthe percentage of energy savedis also similar to the high activation energy counterpart (Table 2).
4.1.3. Changing relative volatilities of products
Following the high activation energy example, here, we study the case of an easy separation between the light re-actant andthe light product. The relative volatilities in this case areC= 16,A= 4,B= 2, andD= 1, respectively. Recall that this scenario results in the largest energy saving for the high activation energy case (Fig.7B). Following the optimization procedure, the optimal feed trays areNF,A=14 andNF,B= 15, anda 33.6% energy saving (from 0.0348 to 0.0231 kmol/s) can be achievedby the feedre-arrangement (Table 3). Again, the heuristic H2 applies here, andthe per-centage of energy savedis quite significant but not quite as large as that of the high activation energy counterpart (33.6% versus 46.8%).
Finally, the case of easy separation between the heavy re-actant and the heavy product is explored. The relative volatil-ities are C = 16, A= 8, B = 4, and D = 1, respec-tively. The feedtray location optimization gives:NF,A= 9 and NF,B = 12. In this case, 14.7% energy can be saved (from 0.0365 to 0.0311 kmol/s) (Table 3). Again, the heuris-tic H2 applies here, andthe percentage of energy saved is also similar to the high activation energy counterpart (Table 2).
4.1.4. Summary
For the low activation energy kinetics, the reaction rate constants are relatively insensitive to temperature. Thus, the composition profile plays a more important role than the temperature profile. Again, the feedtray locations play an important role in design. Generally, the average percentage of energy saving is a little less than the high activation energy counterpart (cf.Tables 2and3). Again, this example clearly illustrates that heuristics H2 andH3 offer goodguidelines to place the feeds.
4.2. Effects of pre-exponential factor
In this work, we change the pre-exponential factor of the rate expressions while fixing the activation energies to 30 000 and40 000 cal/mol (the high activation energy case). The rate constants are reducedandincreasedat 366 K by ad-justing the pre-exponential factors. These can be viewedas two different systems or the scenarios of changing catalyst activity. Again, the optimal feedtray location andpercent of energy saving are of interest here.
4.2.1. Lower reaction rate constant
In this work, we consider a lower reaction rate constant with the following relative volatilities C/A/B/D = 8/4/2/1. The specific reaction rates at 366 K are changedto 60% of the nominal values,kF = 0.0048 and kB= 0.0024. Because the reaction rates are almost 60% smaller, under the conventional feedarrangement, the vapor rate increases by a factor of 30% to meet product specifications as com-paredto the nominal case (Table 2). Here the product D takes a slightly lower value than the base case (Fig.5A), andmore energy is requiredto separate the product from the reactants. Following the optimization procedure, the optimal feedlocations are:NF,A= 9 and NF,B= 17. This results in only a 5.5% energy saving (Table 2).Fig. 9shows the profiles of temperature, composition, conversion, and rate constants in the reactive zone. Because of smaller rate constants, the reactants do not decrease as fast as the case of high rate constants (e.g., Fig. 5A). In fact, a favorable reactant compositions profile is observed, and this is essen-tial for goodperformance. In other words, the conventional feedarrangement is already a goodchoice, andthe opti-mizedfeedtrays provide a little improvement in the reactant distribution.
4.2.2. High reaction rate constant
In this case, the reaction rate constants are doubled at 366 K (i.e.,kF= 0.016 and kB= 0.008). Because of higher reaction rates, the numbers of trays in the stripping and rectifying sections decrease, and in addition, the vapor rate is also reduced by a factor of 8%. With the conventional feed arrangement, the reactant compositions decrease dras-tically towardthe opposite ends of the reactive zone as shown in Fig. 9A. These are not favorable profiles from
the reaction standpoint. It is expected that optimizing the feedtraylocation can reduce operating cost. Following the procedure, the optimal feed trays are: NF,A= 10 and
NF,B= 13 (Fig.9B). This results in a 21.9% saving in the vapor rate which is quite significant as comparedto that of the base case (Table 2). It is also observedthat the fractional conversion is distributed relatively uniform throughout the reactive section, comparedto the conventional feedarran-gement.
4.2.3. Summary
We gain some insight by studying these three systems with low (60%), nominal (100%), andhigh (200%) rate con-stants. First, as expected, the energy consumption goes up as the rate constant becomes smaller (Table 2), andthis is true for either the conventional feedarrangement or the op-timizedfeedlocations. Second, the percentage of the en-ergy savedby optimizing the feedlocations increases up as the rate constant becomes larger. The reason for that is that the shapes of reactant profiles are not favorable for reaction when the rate constants are large under the conventional feed arrangement. Third, the optimal feed trays move closer to each other when the rate constants go up. This results in the following heuristic:
Heuristic H4. Place the feedtrays away from each other when the rate constants become smaller. Similarly, move the feedtray locations closer to each other when the rate constants become larger (e.g.,Fig. 9B).
This heuristic is useful in design as well as for operation when the reaction rate constants vary.
5. Operation and control
On-going analyses clearly show that improveddesign can be achievedby treating the feedtray location as an optimiza-tion variable andresults indicate that significant energy sav-ing can be obtainedby simply rearrangsav-ing the feeds. How-ever, these analyses are limitedto the design aspects with different thermodynamics parameters (i.e., relative volatili-ties) as well as kinetics parameters (i.e., activation energy andpre-exponential factor). In this section, we are more in-terestedin how this finding will affect the operation andthe control of reactive distillation.
Despite clear economic incentives of reactive distillation, only a few papers studying the dynamics and control of reactive distillation have been published.Al-Arfaj andLuy-ben (2000)give a review on the closed-loop control of re-active distillation. Several control structures for an ideal two-product reactive distillation system and real chemical systems (Al-Arfaj andLuyben, 2002, 2004; Huang et al., 2004) have been proposed. One important principle in the control of reactive distillation is that we need to control one
Y.-C. Cheng, C.-C. Yu / Chemical Engineering Science 60 (2005) 4661 – 4677 4673
Fig. 9. Profiles of temperature, composition, fraction of total conversion, andreaction rate constant in the reactive zone for the system C/A/B/D= 8/4/2/1 when rate constants increasedto 200% with: (A) conventional feedarrangement (NF,A= 7 and NF,B= 17), and(B) optimal feedarrangement (NF,A= 10 and NF,B= 13) with 22% energy saving.
intermediate composition (or tray temperature) in order to maintain stoichiometric balance (Al-Arfaj andLuyben, 2000).
5.1. Optimal feed location under production rate variation
In general, production rate variation is one of the most important load disturbance in plantwide control and opera-tion (Luyben et al., 1999), andmore importantly, it can be measured. In this work, we are interested in whether signif-icant energy saving can be obtainedby adjusting the feed tray locations as the production rate changes. If apprecia-ble amount of operating cost can be reduced, the feed tray location is not only dominant design variable but useful ma-nipulatedvariable for control.
Let us take the base case (Table 2) as an example, the op-timal feedtrays are:NF,A= 11 and NF,B= 15 as shown inFig. 5B. The control objective is to maintain the product compositions (C andD) at 95%. Both positive andnegative production rate variations are explored. First, consider the case with+40% feedflow rate increase. The optimization is performedto findthe optimal feedlocations by minimizing the vapor rate. One obtainsNF,A= 10 and NF,B= 16 and this corresponds to a 28% of energy saving! This is not to-tally unexpected, because an increasing the production can be viewed, in a sense, as a short of reaction capability. The closest scenario to this situation is a decrease in the rate con-stant. Therefore, we shouldmove the feedtrays away from each other as suggestedby heuristic H4. But the percentage of energy saving is larger than our expectation, because we do not explore the non-optimal cases in Section 4 (what if
the feedlocations are placedincorrectly). The findings here clearly show that the optimal feedtrays can change as the feedrate varies. Next, the optimization is carriedout for a
−40% change in the feedflow rate. The optimal feedtrays
becomeNF,A=12 and NF,B=15 anda 9% saving in the va-por rate is observed. As pointed out earlier, this has the same effect as that from reaction rate increases, andone should moves the feedtrays closer to each other. The results clearly indicate that one shouldchange the feedtray locations as the production rate changes, because 9 or 28% energy can be savedby simply moving the feedtrays. The next question then becomes how can we implement such a control strat-egy? The coordinated control ofDoukas andLuyben (1976)
offers some light in this direction (Chang et al., 1998).
5.2. Control structure
Before getting into the feedrearrangement control struc-ture, let us first construct the fundamental control configura-tion for the reactive distillaconfigura-tion with two feeds. Recall that, unlike the control of conventional distillation, one needs to control an internal composition (or temperature) to main-tain stoichiometric amounts of the two fresh feeds (Al-Arfaj andLuyben, 2000). For the purpose of illustration, in this work, we choose to control composition of the reactant A on tray 13 where a large change in the composition A is ob-served(Fig. 5B). Thus, we have three compositions to be controlled, top composition of C, bottoms composition of D andcomposition A on tray 13. For the manipulatedvari-ables, the ratio scheme (Chiang et al., 2002) is used, and these three ratios are: reflux ratio, boilup ratio, andfeed
Fig. 10. Control structure of reactive distillation with fixedfeedlocations.
ratio. The steady-state sensitivity analysis gives the follow-ing steady-state gain matrix between the controlledandma-nipulatedvariables: xA xD,C xB,D = 20.61 7.53 −8.94 0.2 0.18 −0.1 0.32 −0.13 0.26 FOA/FOB R/D VS/B .
The relative gain array (RGA,) can be computedfrom the gain matrix. FOA/FOB R/D VS/B = 0.85 −0.78 0.93 −0.20 1.83 −0.63 0.35 −0.05 0.7 xA xD,C xB,D .
The result of the RGA indicates that one should pair the internal composition with the feedratio, pair the top com-position with reflux ratio, andpair the bottoms composi-tion with boilup ratio (xA− FOA/FOB,xD,C− R/D, and
xB,D− VS/B). After the variable pairing, the basic control loops are in place.Fig. 10shows the control configuration for the reactive distillation without feed rearrangement.
(1) The fresh feedFOBis the throughput manipulator which is flow control.
(2) FOAis ratioedtoFOB, andthe ratio is set by the tray 13 composition (xA).
(3) The top composition of C is maintainedby changing the reflux ratio.
Fig. 11. Control structure of reactive distillation with coordinated feed locations as the production rate changes.
(4) The bottoms composition of D is controlledby changing the boilup ratio.
(5) The base level is controlledby manipulating bottoms flow rate.
(6) The reflux drum level is maintained by adjusting the distillate flow rate.
This structure consists of 3 composition loops and2 level loops. In this paper, decentralized control structure with PI controllers is employedfor the composition loops, andper-fect level control is assumedfor the level loops. In the identi-fication phase, the relay feedback method (Yu, 1999) is used to obtain the ultimate gain andultimate periodandthe con-trollers are tunedusing the Tyreus–Luyben turning method (Tyreus andLuyben, 1992). Note that five minutes of ana-lyzer deadtime was assumedfor the composition measure-ment.
Because both fresh feedflows are measured, one can co-ordinate the feed location as the production rate changes. Let us take the upper feedflow as an example to illustrate the feedrearrangement. Nominally, the feedtray for the heavy reactant is tray 15, andas the flow rate (FOB) increases by a factor of 40%, the feedlocation shouldbe switchedto tray 16. Thus, the idea is to use the feed tray location as a manip-ulatedvariable as the feedflow changes (Doukas andLuy-ben, 1976). Insteadof making discontinuous switch, a linear combination of valve opening between trays 15 and16 is in placedandthis provides a gradual transition as the feed flow rate increases. Let us use the fresh feedof B,FOB, to
Y.-C. Cheng, C.-C. Yu / Chemical Engineering Science 60 (2005) 4661 – 4677 4675
Fig. 12. Closed-loop responses for a+40% production rate increase with fixedfeedlocations (dashed) andcoordinatedfeedtrays (solid).
Fig. 13. Closed-loop responses for a 40% production rate decrease with fixed feed locations (dashed) and coordinated feed trays (solid).
illustrate the coordination between the valve openings into tray 15 and16. At nominal flow rate (FOB/ ¯FOB= 0 in the box in the upper corner ofFig. 11), only valve to tray 15 is open, while the valve to tray 16 is shut. As the feedflow rate increases (i.e.,FOB/ ¯FOB> 0), the valve to tray 16 is open gradually, while closing the valve to tray 15. When the
feedflow rate reaches 40% increase (FOB/ ¯FOB=0.4), only the valve to tray 16 remains open, andthe valve to tray 15 is totally closed. This provides a mechanism to coordinate the openings of these two valves. The same idea can be ex-tendedto the feedflow of A, switching between trays 10, 11, and12 as shown in the lower box inFig. 11. This can be
implementedin distributedcontrol system (DCS) with little difficulty.
5.3. Closed-loop performance
Next, the closed-loop performance of both control struc-tures (with andwithout feedrearrangement) is evaluated (Figs. 10 and11). First, consider the case of a 40% pro-duction rate increase. The control structure with coordinated control (Fig.11) gives fast dynamics in the product com-position, as can be seen in Fig. 12where top andbottoms composition return to set point in less than 10 h (solidline in
Fig. 12). On the other hand, the conventional control struc-ture (Fig.10) shows a little slower dynamic responses and the product compositions do not return to the set points af-ter 10 h. More importantly, the coordinated control structure results in a 21% energy, comparedto the conventional con-trol structure, which can be seen from the smaller vapor rate inFig. 12. Note that a 21% energy saving is smaller than a 28% from steady-state analysis, and the reason is that we fix the tray 13 composition of A to the nominal value. Nonethe-less, the amount of energy savedis still quite significant.
Fig. 13shows the responses for−40% step changes in the production rate. Again, faster dynamics for top and bottoms products are observed for the coordinated control structure (Fig.11). Moreover, a 7.5% energy saving can be achieved with this improveddynamics.
The results presentedin this section clearly show that the concept of optimal feedtray location can be carriedover to process operation andcontrol. With a simple modification in the control structure (Fig.11), improvedclosedloop per-formance can be achievedwith substantial energy saving.
6. Conclusion
In this paper, the effects of feedlocations to the d e-sign of reactive distillation are explored, and ideal reactive distillation systems are used to illustrate the advantage of feedtrays optimization. Reactive distillation columns with various process parameters were explored. They include: relative volatilities between reactants, relative volatilities between products, column pressure, activation energies, and pre-exponential factors. The results from all system studied indicates a 6% to 47% energy saving, which can be achieved by simply rearrange the feedlocations. Because the tem-perature andcomposition profiles play a vital role for the effective utilization of the reactive section, the optimal feed locations are essential to obtain improvedperformance. Qualitatively, heuristics are also given to place the feeds at the vicinity of optimal locations. Quantitatively, a sys-tematic procedure is proposedto findthe right feedtrays. Finally, the idea of optimal feedtrays can be carriedover to the control of reactive distillation system. First, steady-state analysis is performedto findthe optimal feedtrays as the measurable loadvariable changes. Then, a coordinated
control structure is proposedto rearrange the feeds as the disturbance comes into the system. The results indicate that, again, substantial energy can be savedduring process operation by feedrearrangement while showing improved closed-loop dynamics.
Notation
aB pexponential factor for the reverse re-action (kmol/s/kmol)
aF pre-exponential factor for the forwardre-action (kmol/s/kmol)
A light reactant
B heavy reactant
B bottoms flow rate (kmol/s)
C light product
CO normalizedcontroller output (between 0 and1)
COj fraction of valve opening to trayj (imply-ing fraction of total feedflow to trayj)
D heavy product
D distillate flow rate (kmol/s)
EB activation energy of the reverse reaction (cal/mol)
EF activation energy of the forwardreaction (cal/mol)
Fj feedflow rate on trayj (kmol/s)
FOA fresh feedflow rate of reactant A (kmol/s)
FOB fresh feedflow rate of reactant B (kmol/s)
kBj specific reaction rate of the reverse reac-tion in trayj (kmol/s/kmol)
kFj specific reaction rate of the forwardreac-tion in trayj (kmol/s/kmol)
Lj liquidflow rate from trayj (kmol/s)
Mj liquidholdup on trayj (kmol)
NF,A number of fresh feedA tray
NF,B number of fresh feedB tray
Nr×n number of reactive trays
NR number of rectifying trays
NS number of stripping trays
P total pressure (bar)
PS
i vapor pressure of componenti (bar)
R reflux flow rate (kmol/s)
R perfect gas law constant (cal/mol/K)
Rj,i reaction rate of component i on tray j (kmol/s)
Tj temperature in trayj (K)
Vj vapor flow rate from trayj (kmol/s)
Vj vapor flowrate in the stripping section (kmol/s)
xj,i composition of componenti in liquidon trayj (mole fraction)
yj,i composition of componenti in vapor on trayj (mole fraction)
zj,i composition of component i in feedon trayj (mole fraction)
Y.-C. Cheng, C.-C. Yu / Chemical Engineering Science 60 (2005) 4661 – 4677 4677
Greek letters
relative volatility
liquidhydraulic time constant (s)
Hv heat of vaporization (cal/mol)
heat of reaction (cal/mol of C
pro-duced)
relative gain array
i stoichiometric coefficient of the ith
component Superscript
− nominal steady-state value
Acknowledgements
This work was supportedby the National Science Council of Taiwan under Grant NSC 93-2214-E002-013 and YCC was supportedin part by the Ministry of Economic Affairs under Grant 92-EC-17-A-09-S1-019.
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