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Understanding the dynamics of a batch distillation column with a middle vessel
Computers
Pergamon PII: SOO98-1354(98)00036-2
them. Engng Vol. 22, Suppl., pp. S37-S44, 1998 0 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0098-1354/98 $19.00 + 0.00
Understanding the Dynamics of a Batch Distillation Column with a Middle Vessel Massimiliano Barolo’, Gian Berto Guarise, Sergio A. Rienzi and Antonio Trotta Istituto di Impianti Chimici, Universita di Padova, via Marzolo, 9 - I-35 13 1 Padova PD (Italy)
Abstract - The dynamic behavior of a batch distillation column with a middle vessel is studied A detailed mathematical model of a pilot-plant column is developed and validated against experimental data on a highly nonideal system. The simulated operation includes the column startup phase, during which the empty trays are sequentially filled with liquid from the top down. Then, the model is used to investigate the effect of different operating and design parameters on the column operability and productivity. In particular, it is shown that restrictions exist in the choice of the column operating variables. These restrictions are related to both the total material balance and the component balance. Interactions between the operating parameters may result in unexpected responses of the plant. All the results make clear that the dynamic behavior of a complex batch column is not so easily understandable as the one of conventional batch rectifiers and batch strippers. 0 1998 Elsevier Science
Ltd. All rights reserved.
Keywords: Batch distillation, Middle vessel, Distillation dynamics, Operation
INTRODUCTION Batch distillation is frequently employed as a means of separating small amounts of high added value products in fine chemicals and pharmaceutical industries. Typically, a batch rectitier is employed for these separations. In this column, the feed is charged to the still, while products and slop cuts are withdrawn sequentially from the top, according to their relative volatilities; the heavier fraction is eventually recovered from the r&oiler at the end of the batch. Although optimal operation of this column with variable reflux ratio policies can be employed (Diwekar, 1995; Macchietto and Mujtaba, 19%) classical operation at constant reflux ratio is still used in the industry very frequently (Grassi et al., 1990, Muhrer and Luyben, 1992). This is due to the fact that the engineering effort for the development and implementation of a constantreflux-ratio operating policy is low, and less instrumentation is needed. In addition, this strategy, and the consequent column behavior, is easily understood by the plant operators. In fact, after the startup period the temperature on each tray of the column is always increasing. An alternative configuration for a batch column is the one of a batch stripper (also called inverted batch distillation column). In this case, the feed is charged to the reflux drum, while main and off cuts are withdrawn from the bottom of the column. Although this column is not the true inverse of a batch rectifier (Sorensen and Skogestad, 19%), from a practical standpoint the dynamic behavior of a batch stripper can be regarded as ??
Author to whom ail co~espondence should be addressed. E-mail: max@polochi . cheg. unipd. it s37
the mirror image of the dynamic behavior of a batch rectifier. The only dilference is that in a batch stripper the products are taken out with the less volatile component first, then the second less volatile, etc., so that the temperature on a certain tray is always decreasing during the operation. A third configuration for a batch column has gained a lot of attention in the last few years. This configuration may be viewed as the coupling of a regular batch cohmm and of an inverted batch column. In this column the feed is charged to a vessel that is placed approximately in the middle of the column A liquid stream is then continuously recycled from a feed tray and the middle vessel, while products and impurities are taken off from both column ends. Thus, similarly to continuous distillation, this column is equipped with a rectifying section and a stripping section. Following Hasebe et al. (1996), we will call this column a “complex” batch column in the following. As a matter of fact, the concept of “someway” combining a batch rectifier and a batch stripper has been long known (Robinson and Gilliland, 1950). However, the llrst clear representation of a complex batch column (at least as currently meant) is due to Bortolini and Guarise (1970). This kind of column has gained renewed attention after a recent work by Hasebe er al. (1992). The performance optimization of a complex column has been considered by a number of authors (Mujtaba and Macchietto, 1992, 1994; Davidyan er al., 1994; Meski and Morari, 1995; Bar010 er al, 19%a), while the issue of feedback composition
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control has been investigated by Farschman and Diwekar (1996). The first comprehensive experimental results on a pilot-plant middle vessel batch column have been provided by Bar010 et al. (19%b). A “multivessel” column was introduced by Hasebe ef al. (1995), and further studied by Skogestad ef al. (1997) and by Hasebe ef al. (1997). However, this column contiguration, which can be viewed as a stacking of several columns on top of each other, will not be considered in this work. Although optimization studies have proved very useful to point out the potential of complex batch cohnnns, one should be aware that they do not tell the entire story. In fact, these studies provide a picture of the column only at the end of the opemtion, but give no information on the column dynamics, i.e. on the feasibility of the separation, and on its sensitivity to changes in the operating variables. We would like to point out that, apart from the case of operation at total reflux and total reboil (Bar010 et aL, 1996b), operating practice on our pilot plant revealed that the dynamics of a complex batch column is not so clearly and immediately understandable as the dynamics of conventional batch rectifiers and batch strippers, even when a binary mixture is to be separated. As a matter of fact, a clear idea of which parameter affects the column behavior, and how it does it, is missing at the moment. It should also be noted that the degrees of freedom of a complex batch column are more than those of conventional columns, and therefore the choice of the operating variables is not straightforward. Also, due to the presence of recycling streams, interactions between the dynamics of the rectifying and stripping sections are present, in such a way that the opemtion itself is more complicated, and unexpected responses of the plant may be encountered. This is a major problem when this unconventional operation is to be implemented industrially, owing to practitioners’ reluctance to operations differing significantly from the usual “reflux-and-go” policies. There is therefore a need to study the dynamic behavior of middle vessel batch columns in more detail at the present time. Up to now, all works on complex batch columns have employed simplified models in order to carry out the optimization and control studies. Usual assumptions are: constant molar overflows, constant molar holdups on the trays, ideal (or near-ideal) vapor-liquid equilibrium, no subcooling of any liquid stream. Even more restrictive approximations have been invoked sometimes, such as no stage holdup and minimum reflux conditions. In this paper we will relax many of the approximations which are usually considered in the modeling and simulation of complex batch columns. A detailed model of a pilot-plant complex column will be developed and validated against experimental data on a highly nonideal system. Then, the model will be used to study the dynamic behavior of the column, with the aim of offering a clearer understanding of how different operating parameters may affect the column operability and productivity.
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PILOT PLANT DESCRIPTION
AND MODELING
The pilot-plant complex batch column considered in this work has been described in detail elsewhere (Bar010 et al., 1996b). For the sake of conciseness, the main plant characteristics only will be recalled here. The plant consists of a 30-sieve-tray distillation column (0.3 m diameter, 9.9 m total height), with a vertical &oiler (maximum steam-heated thermosiphon capacity: -90 L), and a horizontal water-cooled shelland-tube condenser. The retlux drum is open to the atmosphere, and its maximum capacity is -40 L. The middle vessel has a maximum capacity of -500 L. The mixture employed consists essentially of water and ethanol. Traces of a lighter component similar to methanol were detected by chromatographic analysis of the commercial hydroalcoholic mixture. In order to keep the ethanol vapor pressure low, the reflux was cooled well below its boiling temperature; thus, it entered the column as a subcooled liquid. Also, in order to avoid cavitation of the withdrawal pump (Bar010 et al., 1996a), the liquid witMrawn Born the feed tray was subcooled, too. It is well recognized that modeling of batch distillation is a hard task. In fact, due to the integrating nature of the process, parametric and structural inadequacy of the model may cause the error in predicted compositions to increase in magnitude throughout the duration of a simulated batch run (Bosley and Edgar, 1995). This is a possible reason for the limited mnnber of papers dealing with a comparison between experimental and simulated results in batch distillation columns. Bosley (1994) has given an excellent review on this matter. As a matter of fact, to date no paper dealing with the rigorous modeling of a middle-vessel batch distillation column separating a highly non-ideal mixture has been published. The modeling approach we have taken is based on first principles. Classical dynamic mass and component balances are written for each accumulation point in the column. Fast energy dynamics is assumed, although we are aware that in certain circumstances this assumption may lead to erroneous composition evaluation (Ranzi et al., 1988). All the vessels are supposed to be well mixed; in the pilot plant, a recircuhition pump provides mixing of the liquid in the middle vessel. The liquidphase activity coefftcients (for the ternary system) are calculated through the NRTL model, while the vapor phase is considered ideal. The internal liquid flow rates are calculated through the nonlinear version of the Francis weir formula. A linear pressure profile in the column is considered, since no significant improvement in the composition predictions was observed with a detailed (i.e. time consuming) calculation of the pressum drop profile. The steam flow rate to the &oiler is assumed to be constant (a pressurecompensated flow controller keeps the steam rate to its setpoint in the plant). All of the other external streams can be either fixed to a constant value or manipulated according to the relevant control loop. However, note that all of the external flows are specified on a volumetric basis, as is done in practice. The sequential
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time (min) Figure 1. Prccedure for the adjustment of the Murphree tray etliciency. Dotted line: experimental temperature profile; full lines: model predictions with different values of the Mqhree eficiency filling of the reflux drum, and of the trays from the top
tray down to the bottom one (startup phase), is modeled, too. The integration of the system differential equations is performed through a Runge-Kutta-Fehlberg algorithm. The model adjustable parameters are the heat losses, the nominal tray holdups and the Murphree hay efficiency. An estimate of total heat losses due to thermal exchange with the ambient was first performed, and this value was then slightly adjusted in order to take the expected error in the steam flowmeter signal into account (similarly to the procedure outlined by Subawalla et al., 19%). The nominal tray holdups were determined by turning off the steam and the reflux flows during nominal operation, and by measuring the subsequent holdup change of the reflux drum and of the reboiler (Wittgens and Skogestad, 1995). Following the procedure usually employed in the industry (Grassi et al., 1990), the Murphree tray efficiency EM was then adjusted until the model provided good reproduction of the experimental temperature profile on a selected tray in the column. Figure 1 illustrates this fitting procedure. The bottom flow rate was repeatedly stepped in the plant and in the model in order to excite the system; the bottom level was controlled by the feed rate during the excitation procedure, while the reflux drum level was controlled by manipulating the tetlux rate (total reflux). Thus, the middle vessel holdup kept decreasing during the batch. As a confirmation of the reliability of the result, it should be noted that the fitted value of the tray efficiency ( E,,., = 0.6) is close to the one calculated through the A.1.Ch.E. method for the same column (Baratti et al, 1995). It should be observed that all the simulated profiles were found to anticipate the experimental ones of about 8 min. This is because of the lag time due to heating of the column shell and internals in the pilot plant (the plant is usually started up “cold”). Since this capacitance effect is not modeled, the time axis has
been shifted of 8 min in order to provide a fair comparison between experimental and simulated results. The predicted controller output (i.e. manipulated variable) profiles and the composition in the vessels are compared to the experimental values in Figure 2. It can be seen that the model simulations are very satisfactory.
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Figure 2. Comparison between experimental (symbols and dotted lines) and calculated (fidl lines) profiles of (a) manipulated flow rates and (b) compositions in the vessels
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Figure 3. Control scheme adopted in the complex column Thus, the model provides a good representation of the
dynamic response of the plant. For this reason, the results derived from this model will be used here to illustrate the main dynamic characteristics of the complex batch column. SEPARATION
OBJECTIVE AND OPERATING PROCEDURE
The separation task considered in this work will be quite simple, so that attention will be focused on the main dynamic characteristics of the column rather than on a specific production objective. For a given feed mixture of composition z,., = 0.002/0.246/0.752 (mole fraction of methanol/ethanol/water, respectively), two cuts at different ethanol purities are required. The . . . lighter cut speclficatton IS x,,~,~ 2 xstoH,Sp,= 0.84, while the heavier specification is cut xsloHM ;?:x,,,,,, = 0.6. The lighter cut is removed from the top of the column (and possibly accumulated in the reflux drum), while the heavier one is accumulated in the middle vessel. No additional constraiut is considered on the amount to be recovered of each cut. Note that we are not claiming that using a complex column is necessarily more profitable than using a conventional one for this separation task.
Following the startup phase, the same described by Bar010 er al. (1996b), a reasonable operating procedure is as follows: The distillate withdrawal starts as soon as the ethanol composition in the reflux drum satisfies the lighter cut purity specification; the distillate withdrawal (at a constant volumetric rate) may be intermittently stopped and re-started according to the purities of the accumulated product and of the reflux drum, respectively; In order to avoid ethanol losses from the bottom, the water removal from the bottom is started as soon as the ethanol mole fraction in the rehoiler is lower than 0.01; the water removal (at a constant volumetric rate) may be intermittently stopped and re-started according to the purities of the middle vessel and of the &oiler, respectively; The distillation is stopped when both products are within specifications. The control loops are closed as indicated in Figure 3. The distillate rate DWI during the distillate removal period is one degree of freedom saturated by the operator, for a given vapor boilup rate V’, this corresponds to assigning the reflux ratio (which may vary if the top composition changes significantly). The other degrees of freedom which need to be specified are the feed tray withdrawal rate Fz’ and the “net feed
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me” ( Fzt = F$ - Fz’ ). For a given withdrawal rate (which is chosen according to plant construction considerations; Barolo et al., 1996a). ass@@ Fst amounts to defining the value of the reboil ratio during the water removal period. The reflux drum and the reboiler mass holdups are kept close to their &points by manipulatingthe reflux rate &, and the bottoms rate E,,, respectively. A proportional-onlycontrol law is employed in this case.
UNDERSTANDING TEE DYNAMIC BEHAVIOR OFTEECOMPLEXCOLUMN A single complex batch column can be run either at total reflux and total reboil (Bar010et al., 1996%Barolo and Botteon, 1997), or in a semi-continuous way (Hasebe et al., 1992; Mujtaba and Macchietto. 1994). The former operating procedure is very simple, since it can be accomplished by using two level controllers; no product changeovers are necessary. However, in practice this procedure is favorable only for columns having enough stages with respect to the separation objective; also, the top and bottom capacities should be large enough to allow the accumulationof a product or an impurity. The latter procedure is mote complicated In fact, when products or impuritiesare withdrawnfrom the top and from the bottom of the column, and the reflux drum and reboiler holdups are controlled by the relevant level controllers, for each value of Fs’ two degrees of freedom for column operation (i.e. optimization) are left. According to the control scheme of Figure 3, these two degrees of freedom are identified in the distillate rate and in the net feed rate. However, these two variables are not independent.To show that, we can consider the total material balance of the column:
Nrx c
I=, dt
dM, dM, +-+-+dr
dt
d”b+D+B,O dt
1 (1)
where M,, M,, M, , and My are the hay, reflux drum, bottom and middle vessel molar holdups, respectively, N, is the total number of trays, and D and B are the distillateand bottoms molar rates. Thus, since dM,ldt=-FNt and dMildtrO, if good top and bottom level control is desired, the bottom mtemustbesuchthat B=F”‘t-D. Since B>O, the following restriction on the net feed rate results: F”’ 2 D
.
(2)
Equation (2) applies on a molar basis, When the molar rates are not constant along the column sections, it is not immediite to apply equation (2) on a volumetric or a mass basis. Figure 4a compares three runs with the same values of the feed tray withdrawal rate ( Fzt = 270 L/h) and net feed rate (Fzt = 70 L/h), but with three different values of the distillate rates. It is clear that for Dd = 180 L/h. the bottom level cannot be controlled satisfactorily. Figure 4b clarifies that the oscillations in
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the bottom holdup always follow the distillate removal periods.
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Figure 4. ((I) E3ottomholdup profile for three different values of the distillate rate, (b) detail of the bottom holdup profile at a distillate rate of 180 Uh
is related to the fulfillment of the total material balance of the column, and is somewhat similar to the restriction found by Mujtaba and Macchietto (1994). These authors also showed that the optimal (i.e. minimum) batch distillation time is strongly dependent on the mtio F’” /V’ for Fin 5 V’, but it is weakly dependent on such a mtio for F’” > V’. They conclude that F’” is a very important parameter which has to be optimized. On the other hand, Barolo ef al. (19%a; 1996b) showed both by simulation and experimentallythat increasingthe feed/withdrawalrates indeed decreases the batch distillation time. We have investigatedin more detail these findings. The feed tray withdrawal rate G’ was set to the constant value of 270 LA, and different combinationsof D,, and Fzt were considered,all of which fulfilling constraint (2) in order to prevent draining of the colwnn bottom. Figure 5 shows that, for a given distillate rate, increasing the net feed rate does reduce the batch distillation time. However, there is no further advantage in increasing FE; above a certain value; also, this limiting value (-90 L/h in the case of Figure 5) is basically independent of the distillate rate (that is: it hoids for both optimal and non-optimal operations). The limiting total distillation time is related only to the fractionating capacity of the column (i.e., to the number of stages of the strippingsection, for the example considered in this work). When the net feed rate is “low”, the water fractionated by the strippingsection is not removed from the column at a sufficiently high rate, and this occurrence slows Constraint (2)
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Figure 5. Effect of the net feed rate on the total distillation time for different values of the distillate rate
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down the ethanol enrichment of the middle vessel. Conversely, if F,“: is too high, the column has not enough trays to condense off the water at a high rate. This fact can be further understood by noting that, for certain combinations of F,“: and D,,,, , the distillation time grows up very markedly, to a point that in certain cases the distillation itself is not feasible. It should not be forgotten that this happens even though the total material balance constraint is satisfied ( F”” ;1 D ). To understand this, one should recognize that the driving force for the separation of water from the middle vessel is the difference between the ethanol concentration on the feed tray (x~~~,,~) and on the feed vessel ( xEKIHM). Figure 6u shows that when a distillate rate of 40 L/h is chosen, a positive (i.e. xEIoH.,6> x,~,) driving force throughout the batch exists, so that the separation can take place and it stops at about 130 min. However, for D,, = 60 Lib, from a certain time on the driving force reverses (Figure 6c) and the middle vessel is drained before the separation can be achieved. Physically, this is due to the fact that the higher the distillate rate, the more quickly the ethanol depletion in the middle vessel occurs. So, either the water can be removed from the bottom quickly enough (i.e. FE/ is sufficiently large), or all the ethanol will be removed from the top of the column, with the result that the middle vessel is emptied. Note that in this respect the distillate rate may have a critical value (for each value of the net feed rate). At this critical distillate rate, the distillation time may increase due to a sign&ant reduction of driving force during the distillation (Figure 66).
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Figure 7. Effect of the distillate rate on the total distillation time for differentvalues of the feed tray
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Figure 6. Ethanol composition profiles on the feed tray and on the feed vessel for a distillate rate of (a) 40 L/h, (6) 48 Lib and (c) 60 L/h. Withdrawal rate from the feed tray (all cases): 270 Lh
Another dynamic aspect which is not immediately intuitive is represented in Figure 7. Here, the effect of the distillate rate on the total distillation time is plotted for a given net feed rate ( Fst = 90 L/h) at different withdrawal rates from the feed tray. It should be noted that there might be a physical constraint to the maximum achievable withdrawal rate; this is due to plant construction considerations (Bar010et al., 1996a). Figure 7 clarifies that when the withdrawal rate F$’ is small, working at high distillate rates results in a marked decrease of the total distillation time. This decrease is not observed when large withdrawal rates are employed.
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Figure 8. Profile of the residence time in the middle vessel as a function of time for different values of the feed tray withdrawal rate. Net feed rate (all cases): 90 LAl
This behavior can be attributed to the role of the “residence time” z of the liquid in the middle vessel. The residence time is defined as: M 7(f)
= *
F vol
.
When it is not possible to withdraw liquid from the feed tray at a “high” rate (Fs’ “low”), the initial value of 7 is large (for a given amount of feed charged to the middle vessel), in such a way that the residence time in the vessel limits the “quickness” of the distillation. In this case, the higher the distillate rate chosen, the more quickly the middle vessel holdup decreases; therefore 7 decreases quickly during the operation (Figure S), and a decrease of the total distillation time is observed (Figure 7). However, if (for the same initial charge) Fs’ is large, 7 is small from the beginning of the operation, i.e. the renewal rate of the middle vessel is not a limiting factor for the distillation. In this case, if one works at high distillate rates, a marked decrease in 7 is not observed during the operation (Figure 8); rather, the total distillation time may slightly increase be-cause the cohunn is quickly depleted of ethanol, and the driving force for the distillation decreases, as previously explained. These considerations can be also used to analyze how the size. of a feed charge may affect the duration of the batch. Note that when the distillate rate exceeds the value of -55 wh, no reduction, or increase, in the distillation time is observed. Working with D,, c 55 wh results in an increase of the amount of product eventually collected in the middle vessel at the expense of the amount of the accumulated lighter cut (which will be usually purer than needed). For higher distillate rates, the total amount collected for each product is basically independent of Owl (and both products are exactly on specification). CONCLUSIONS A detailed dynamic model of a pilot-plant batch column with a middle vessel has been developed and verified
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against experimental data. The model has then been used to study the dynamic behavior of such a column. For a given operating sequence, the column operating parameters (i.e., the degrees of freedom) have been chosen to be the distillate rate and the net feed rate. It has been shown that for the total material balance to be fultilled (that is, in order not to drain the bottom of the c&mm), the net feed rate should never be lower than the distillate rate. However, additional restrictions in the choice of the operating parameter values exist. These restrictions are related to the component balance. An incorrect choice of the operating parameters will result in a reduction of the driving force available for the separation, to the point that the middle vessel may drain prior to achieving the desired separatioa The total distillation time is a&&d by the distillate rate. When the initial residence time of the liquid in the middle vessel is large (i.e., the feed charge is large, or the withdrawal rate from the feed tray is low, or both), increasing the distillate rate results in a decrease of the distillation time. The reverse is true (even though less markedly) when the initial residence time in the middle vessel is low, i.e. when the residence time is not a limiting factor for the separation. All the results make clear that the dynamic behavior of a complex batch column is not as easily understandable as the one of conventional batch rectifiers and batch strippers. Interactions between the operating parameters may result in unexpected plant responses. This is a very important issue to be aware of when implementing a production strategy on an industrial plant_ because plant operators are often reluctant to operations which differ significantly from well-established techniques. ACKNOWLEDGEMENTS We would like to thank Ing. Stefania Mariano for her help in running some of the simulations presented in this work. Financial support granted by CNR (Progetto Strategic0 Tecnologie Chimiche Innovative) and by MURST (ex-40%) is gratefully acknowledged. LIST OF SYMBOLS B = molar bottoms rate = volumetric bottoms rate Owl molar distillate rate D = volumetric distillate rate IZE’= Murphree tray efficiency wef F = molar net feed rate to the column pn WI = volumetric feed rate to the column Ml F wl = volumetric net feed rate to the column FW’ wl = volumetric withdrawal rate from the column = molar bottom holdup MB = molar reflux drum holdup MD MF = molar middle vessel holdup Mi = molar tray holdup M v0l.F = volumetric holdup of the middle vessel N, = total number of trays &I = volumetric reflux rate t =time V’ = molar vapor boilup rate X EIOH.,6 = ethanol mole fraction in the feed tray B
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Complex Batch Distillation Cohunn, J. Chem. Eng Jap., 29, 1000-1006. Hasebe, S., T. Kurooka and I. Hashimoto (1995). XEIOH,M = ethanol mole fraction in the middle vessel Comparison of the Separation Performances of a xEIOH.spl= ethanol purity specification for the lighter cut (mole fraction) Multi-Effect Batch Distillation System and a Continuous Distillation System, IFAC Symposium XElOH,,2 = ethanol purity specification for the heavier cut (mole fraction) DYCORD+‘9S (J. B. Rawlings, Ed.), Elsinore z,.~ = feed composition (mole fraction) (Denmark), June 7-9, pp.249-254. Hasebe, S., M. Noda and I. Hashimoto (1997). Optimal z = residence time in the middle vessel Operation Policy for Multi-Effect Batch Distillation System, Computers them. Engng, 2 1, S 122 1-S 1226 REFERENCES Macchietto, S. and I. M. Mujtaba (1996). Design of Operation Policies for Batch Distillation. In: Batch Baratti, R., A. Bertucco, A. Da Rold and M. Morbidelli Processing Systems Engineering: Current Status (1995). Composition Estimator for Binary and Future Directions (G. V. Reklaitis et al., Eds), Distillation Columns. Application to a Pilot Plant. Springer, Berlin (Germany). Chem. Eng. Sci., 50, 1541-1550. Barolo, M. and F. Botteon (1997). Simple Method of Meski, G. A. and M. Morari (1995). Design and Operation of a Batch Distillation Column with a Obtaining Pure Products by Batch Distillation, Vessel, Computers them. Engng, 19, S597Middle AIChE JI, 43, 2601-2604. S602. Barolo, M., G. B. Guarise, N. Ribon, S. A. Rienzi, A. Trotta and S. Macchietto (1996a). Some Issues in Muhrer, C. A. and W. L. Luyben (1992). Batch Distillation. In Practical Distillation Control (W. L. the Design and Operation of a Batch Distillation Luyben, Ed.), Van Nostrand Reinhold (New York). Column with a Middle Vessel, Computers them. -I(’Mujtaba, I. M. and”!% Macchietto~1992).$‘Optimal Engng, 20, S37-S42. Operation of Reactive Batch Distillatio&@resented Barolo, M., G. B. Guarise, S. A. Rienzi, A. Trotta and at the AIChE Antma/ Meeting. I,L, S. Macchietto (1996b). Running Batch Distillation Mujtaba, I. M. and?% Macchietto (1994): Optimal in a Column with a Middle Vessel, Ind Eng. Chem. Operation of Multicomponent Batch Distillation - A Res., 35, 4612-4618. Comparative Study Using Conven ‘onal and Bortolini, P. and G. B. Guarise (1970). A New Practice Unconventional Columns, IFAC p % onference of Batch Distillation (in Italian), Quad. Ing. Chim. ADCHEM’94, Kyoto (Japan), May 25-27, p@415Ital., 6(9), 150-159. _i 420. Bosley, J. R. (1994). An Experimental Investigation on M. Rovaglio, T. Faravelli and G. Biardi Ranzi, E., Modeling, Control, and Optimization Techniques (1988). Role of Energy Balances in Dynamic for Batch Distillation, Ph.D. Thesis, University of Simulation of Multicomponent Distillation Texas at Austin. Columns, Computers them. Engng, 12,783-786. Bosley, J. R. and T. F. Edgar (1995). An Efftcient Robinson, C. S. and E. R. Gilliland (1950). Elements of Dynamic Model for Batch Distillation, J. Proc. Fractional Distillation; McGraw-Hill Book Co. Cot&.., 4, 195-204. (New York). Davidyan, A. G., V. N. Kiva, G. A. Meski and M. Skogestad, S., B. Wittgens, E. Sorensen and R. Litto Morari (1994). Batch Distillation in a Column With (1997). Multivessel Batch Distillation, AIChE JI, 43, a Middle Vessel, Chem. Eng. Ski., 49, 3033-3051. 97 l-978. Diwekar, U. M. (1995). Batch Distillation. Simulation, Sorensen, E. and S. Skogestad (1996). Comparison of Design and Control. Taylor & Francis, London Regular and Inverted Batch Distillation. Chem. Eng. (U.K.). Sci. 51,4949-4962. Farschman, C. A. and U. Diwekar (1996). Dual Subawalla, H., V, P. Paruchuri, A. Gupta, H. G. Pandit Composition Control in a Novel Batch Distillation and R. R. Rhinehatt (I 996). Comparison of ModelColumn, presented at the AIChE Annual Meeting. Based and Conventional Control: A Summary of Grassi, V. G., C. A. Muhrer and W. Silowka (1990). Experimental Results, Ind Eng. Chem. Res., 35, Process Improvements in Batch Distillation through 3547-3559. Dynamic Simulation, presented at the AIChE Wittgens, B. and S. Skogestad (1995). Evaluation of Annual Meeting. Dynamic Models of Distillation Columns with Hasebe, S., B. B. Abdul Aziz, I. Hashimoto and T. Emphasis on the Initial Response, IFAC Symposium Watanabe (1992). Gptimal Design and Operation of DYCORD+‘95 (J. B. Rawlings, Ed.), Elsinore Complex Batch Distillation Column, IFAC (Denmark), June 7-9, pp.26 l-267. Workshop on Interactions Between Process Design and Process Control (J. Perkins, Ed.), London (UK), September 7-8, Pergamon Press (Oxford). Hasebe, S., T. Kurooka, B. B. Abdul Aziz, I. Hashimoto and T. Watanabe (1996). Simultaneous Separation of Light and Heavy Impurities by a product
Pergamon PII: SOO98-1354(98)00036-2
them. Engng Vol. 22, Suppl., pp. S37-S44, 1998 0 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0098-1354/98 $19.00 + 0.00
Understanding the Dynamics of a Batch Distillation Column with a Middle Vessel Massimiliano Barolo’, Gian Berto Guarise, Sergio A. Rienzi and Antonio Trotta Istituto di Impianti Chimici, Universita di Padova, via Marzolo, 9 - I-35 13 1 Padova PD (Italy)
Abstract - The dynamic behavior of a batch distillation column with a middle vessel is studied A detailed mathematical model of a pilot-plant column is developed and validated against experimental data on a highly nonideal system. The simulated operation includes the column startup phase, during which the empty trays are sequentially filled with liquid from the top down. Then, the model is used to investigate the effect of different operating and design parameters on the column operability and productivity. In particular, it is shown that restrictions exist in the choice of the column operating variables. These restrictions are related to both the total material balance and the component balance. Interactions between the operating parameters may result in unexpected responses of the plant. All the results make clear that the dynamic behavior of a complex batch column is not so easily understandable as the one of conventional batch rectifiers and batch strippers. 0 1998 Elsevier Science
Ltd. All rights reserved.
Keywords: Batch distillation, Middle vessel, Distillation dynamics, Operation
INTRODUCTION Batch distillation is frequently employed as a means of separating small amounts of high added value products in fine chemicals and pharmaceutical industries. Typically, a batch rectitier is employed for these separations. In this column, the feed is charged to the still, while products and slop cuts are withdrawn sequentially from the top, according to their relative volatilities; the heavier fraction is eventually recovered from the r&oiler at the end of the batch. Although optimal operation of this column with variable reflux ratio policies can be employed (Diwekar, 1995; Macchietto and Mujtaba, 19%) classical operation at constant reflux ratio is still used in the industry very frequently (Grassi et al., 1990, Muhrer and Luyben, 1992). This is due to the fact that the engineering effort for the development and implementation of a constantreflux-ratio operating policy is low, and less instrumentation is needed. In addition, this strategy, and the consequent column behavior, is easily understood by the plant operators. In fact, after the startup period the temperature on each tray of the column is always increasing. An alternative configuration for a batch column is the one of a batch stripper (also called inverted batch distillation column). In this case, the feed is charged to the reflux drum, while main and off cuts are withdrawn from the bottom of the column. Although this column is not the true inverse of a batch rectifier (Sorensen and Skogestad, 19%), from a practical standpoint the dynamic behavior of a batch stripper can be regarded as ??
Author to whom ail co~espondence should be addressed. E-mail: max@polochi . cheg. unipd. it s37
the mirror image of the dynamic behavior of a batch rectifier. The only dilference is that in a batch stripper the products are taken out with the less volatile component first, then the second less volatile, etc., so that the temperature on a certain tray is always decreasing during the operation. A third configuration for a batch column has gained a lot of attention in the last few years. This configuration may be viewed as the coupling of a regular batch cohmm and of an inverted batch column. In this column the feed is charged to a vessel that is placed approximately in the middle of the column A liquid stream is then continuously recycled from a feed tray and the middle vessel, while products and impurities are taken off from both column ends. Thus, similarly to continuous distillation, this column is equipped with a rectifying section and a stripping section. Following Hasebe et al. (1996), we will call this column a “complex” batch column in the following. As a matter of fact, the concept of “someway” combining a batch rectifier and a batch stripper has been long known (Robinson and Gilliland, 1950). However, the llrst clear representation of a complex batch column (at least as currently meant) is due to Bortolini and Guarise (1970). This kind of column has gained renewed attention after a recent work by Hasebe er al. (1992). The performance optimization of a complex column has been considered by a number of authors (Mujtaba and Macchietto, 1992, 1994; Davidyan er al., 1994; Meski and Morari, 1995; Bar010 er al, 19%a), while the issue of feedback composition
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control has been investigated by Farschman and Diwekar (1996). The first comprehensive experimental results on a pilot-plant middle vessel batch column have been provided by Bar010 et al. (19%b). A “multivessel” column was introduced by Hasebe ef al. (1995), and further studied by Skogestad ef al. (1997) and by Hasebe ef al. (1997). However, this column contiguration, which can be viewed as a stacking of several columns on top of each other, will not be considered in this work. Although optimization studies have proved very useful to point out the potential of complex batch cohnnns, one should be aware that they do not tell the entire story. In fact, these studies provide a picture of the column only at the end of the opemtion, but give no information on the column dynamics, i.e. on the feasibility of the separation, and on its sensitivity to changes in the operating variables. We would like to point out that, apart from the case of operation at total reflux and total reboil (Bar010 et aL, 1996b), operating practice on our pilot plant revealed that the dynamics of a complex batch column is not so clearly and immediately understandable as the dynamics of conventional batch rectifiers and batch strippers, even when a binary mixture is to be separated. As a matter of fact, a clear idea of which parameter affects the column behavior, and how it does it, is missing at the moment. It should also be noted that the degrees of freedom of a complex batch column are more than those of conventional columns, and therefore the choice of the operating variables is not straightforward. Also, due to the presence of recycling streams, interactions between the dynamics of the rectifying and stripping sections are present, in such a way that the opemtion itself is more complicated, and unexpected responses of the plant may be encountered. This is a major problem when this unconventional operation is to be implemented industrially, owing to practitioners’ reluctance to operations differing significantly from the usual “reflux-and-go” policies. There is therefore a need to study the dynamic behavior of middle vessel batch columns in more detail at the present time. Up to now, all works on complex batch columns have employed simplified models in order to carry out the optimization and control studies. Usual assumptions are: constant molar overflows, constant molar holdups on the trays, ideal (or near-ideal) vapor-liquid equilibrium, no subcooling of any liquid stream. Even more restrictive approximations have been invoked sometimes, such as no stage holdup and minimum reflux conditions. In this paper we will relax many of the approximations which are usually considered in the modeling and simulation of complex batch columns. A detailed model of a pilot-plant complex column will be developed and validated against experimental data on a highly nonideal system. Then, the model will be used to study the dynamic behavior of the column, with the aim of offering a clearer understanding of how different operating parameters may affect the column operability and productivity.
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PILOT PLANT DESCRIPTION
AND MODELING
The pilot-plant complex batch column considered in this work has been described in detail elsewhere (Bar010 et al., 1996b). For the sake of conciseness, the main plant characteristics only will be recalled here. The plant consists of a 30-sieve-tray distillation column (0.3 m diameter, 9.9 m total height), with a vertical &oiler (maximum steam-heated thermosiphon capacity: -90 L), and a horizontal water-cooled shelland-tube condenser. The retlux drum is open to the atmosphere, and its maximum capacity is -40 L. The middle vessel has a maximum capacity of -500 L. The mixture employed consists essentially of water and ethanol. Traces of a lighter component similar to methanol were detected by chromatographic analysis of the commercial hydroalcoholic mixture. In order to keep the ethanol vapor pressure low, the reflux was cooled well below its boiling temperature; thus, it entered the column as a subcooled liquid. Also, in order to avoid cavitation of the withdrawal pump (Bar010 et al., 1996a), the liquid witMrawn Born the feed tray was subcooled, too. It is well recognized that modeling of batch distillation is a hard task. In fact, due to the integrating nature of the process, parametric and structural inadequacy of the model may cause the error in predicted compositions to increase in magnitude throughout the duration of a simulated batch run (Bosley and Edgar, 1995). This is a possible reason for the limited mnnber of papers dealing with a comparison between experimental and simulated results in batch distillation columns. Bosley (1994) has given an excellent review on this matter. As a matter of fact, to date no paper dealing with the rigorous modeling of a middle-vessel batch distillation column separating a highly non-ideal mixture has been published. The modeling approach we have taken is based on first principles. Classical dynamic mass and component balances are written for each accumulation point in the column. Fast energy dynamics is assumed, although we are aware that in certain circumstances this assumption may lead to erroneous composition evaluation (Ranzi et al., 1988). All the vessels are supposed to be well mixed; in the pilot plant, a recircuhition pump provides mixing of the liquid in the middle vessel. The liquidphase activity coefftcients (for the ternary system) are calculated through the NRTL model, while the vapor phase is considered ideal. The internal liquid flow rates are calculated through the nonlinear version of the Francis weir formula. A linear pressure profile in the column is considered, since no significant improvement in the composition predictions was observed with a detailed (i.e. time consuming) calculation of the pressum drop profile. The steam flow rate to the &oiler is assumed to be constant (a pressurecompensated flow controller keeps the steam rate to its setpoint in the plant). All of the other external streams can be either fixed to a constant value or manipulated according to the relevant control loop. However, note that all of the external flows are specified on a volumetric basis, as is done in practice. The sequential
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time (min) Figure 1. Prccedure for the adjustment of the Murphree tray etliciency. Dotted line: experimental temperature profile; full lines: model predictions with different values of the Mqhree eficiency filling of the reflux drum, and of the trays from the top
tray down to the bottom one (startup phase), is modeled, too. The integration of the system differential equations is performed through a Runge-Kutta-Fehlberg algorithm. The model adjustable parameters are the heat losses, the nominal tray holdups and the Murphree hay efficiency. An estimate of total heat losses due to thermal exchange with the ambient was first performed, and this value was then slightly adjusted in order to take the expected error in the steam flowmeter signal into account (similarly to the procedure outlined by Subawalla et al., 19%). The nominal tray holdups were determined by turning off the steam and the reflux flows during nominal operation, and by measuring the subsequent holdup change of the reflux drum and of the reboiler (Wittgens and Skogestad, 1995). Following the procedure usually employed in the industry (Grassi et al., 1990), the Murphree tray efficiency EM was then adjusted until the model provided good reproduction of the experimental temperature profile on a selected tray in the column. Figure 1 illustrates this fitting procedure. The bottom flow rate was repeatedly stepped in the plant and in the model in order to excite the system; the bottom level was controlled by the feed rate during the excitation procedure, while the reflux drum level was controlled by manipulating the tetlux rate (total reflux). Thus, the middle vessel holdup kept decreasing during the batch. As a confirmation of the reliability of the result, it should be noted that the fitted value of the tray efficiency ( E,,., = 0.6) is close to the one calculated through the A.1.Ch.E. method for the same column (Baratti et al, 1995). It should be observed that all the simulated profiles were found to anticipate the experimental ones of about 8 min. This is because of the lag time due to heating of the column shell and internals in the pilot plant (the plant is usually started up “cold”). Since this capacitance effect is not modeled, the time axis has
been shifted of 8 min in order to provide a fair comparison between experimental and simulated results. The predicted controller output (i.e. manipulated variable) profiles and the composition in the vessels are compared to the experimental values in Figure 2. It can be seen that the model simulations are very satisfactory.
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Figure 3. Control scheme adopted in the complex column Thus, the model provides a good representation of the
dynamic response of the plant. For this reason, the results derived from this model will be used here to illustrate the main dynamic characteristics of the complex batch column. SEPARATION
OBJECTIVE AND OPERATING PROCEDURE
The separation task considered in this work will be quite simple, so that attention will be focused on the main dynamic characteristics of the column rather than on a specific production objective. For a given feed mixture of composition z,., = 0.002/0.246/0.752 (mole fraction of methanol/ethanol/water, respectively), two cuts at different ethanol purities are required. The . . . lighter cut speclficatton IS x,,~,~ 2 xstoH,Sp,= 0.84, while the heavier specification is cut xsloHM ;?:x,,,,,, = 0.6. The lighter cut is removed from the top of the column (and possibly accumulated in the reflux drum), while the heavier one is accumulated in the middle vessel. No additional constraiut is considered on the amount to be recovered of each cut. Note that we are not claiming that using a complex column is necessarily more profitable than using a conventional one for this separation task.
Following the startup phase, the same described by Bar010 er al. (1996b), a reasonable operating procedure is as follows: The distillate withdrawal starts as soon as the ethanol composition in the reflux drum satisfies the lighter cut purity specification; the distillate withdrawal (at a constant volumetric rate) may be intermittently stopped and re-started according to the purities of the accumulated product and of the reflux drum, respectively; In order to avoid ethanol losses from the bottom, the water removal from the bottom is started as soon as the ethanol mole fraction in the rehoiler is lower than 0.01; the water removal (at a constant volumetric rate) may be intermittently stopped and re-started according to the purities of the middle vessel and of the &oiler, respectively; The distillation is stopped when both products are within specifications. The control loops are closed as indicated in Figure 3. The distillate rate DWI during the distillate removal period is one degree of freedom saturated by the operator, for a given vapor boilup rate V’, this corresponds to assigning the reflux ratio (which may vary if the top composition changes significantly). The other degrees of freedom which need to be specified are the feed tray withdrawal rate Fz’ and the “net feed
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me” ( Fzt = F$ - Fz’ ). For a given withdrawal rate (which is chosen according to plant construction considerations; Barolo et al., 1996a). ass@@ Fst amounts to defining the value of the reboil ratio during the water removal period. The reflux drum and the reboiler mass holdups are kept close to their &points by manipulatingthe reflux rate &, and the bottoms rate E,,, respectively. A proportional-onlycontrol law is employed in this case.
UNDERSTANDING TEE DYNAMIC BEHAVIOR OFTEECOMPLEXCOLUMN A single complex batch column can be run either at total reflux and total reboil (Bar010et al., 1996%Barolo and Botteon, 1997), or in a semi-continuous way (Hasebe et al., 1992; Mujtaba and Macchietto. 1994). The former operating procedure is very simple, since it can be accomplished by using two level controllers; no product changeovers are necessary. However, in practice this procedure is favorable only for columns having enough stages with respect to the separation objective; also, the top and bottom capacities should be large enough to allow the accumulationof a product or an impurity. The latter procedure is mote complicated In fact, when products or impuritiesare withdrawnfrom the top and from the bottom of the column, and the reflux drum and reboiler holdups are controlled by the relevant level controllers, for each value of Fs’ two degrees of freedom for column operation (i.e. optimization) are left. According to the control scheme of Figure 3, these two degrees of freedom are identified in the distillate rate and in the net feed rate. However, these two variables are not independent.To show that, we can consider the total material balance of the column:
Nrx c
I=, dt
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dt
d”b+D+B,O dt
1 (1)
where M,, M,, M, , and My are the hay, reflux drum, bottom and middle vessel molar holdups, respectively, N, is the total number of trays, and D and B are the distillateand bottoms molar rates. Thus, since dM,ldt=-FNt and dMildtrO, if good top and bottom level control is desired, the bottom mtemustbesuchthat B=F”‘t-D. Since B>O, the following restriction on the net feed rate results: F”’ 2 D
.
(2)
Equation (2) applies on a molar basis, When the molar rates are not constant along the column sections, it is not immediite to apply equation (2) on a volumetric or a mass basis. Figure 4a compares three runs with the same values of the feed tray withdrawal rate ( Fzt = 270 L/h) and net feed rate (Fzt = 70 L/h), but with three different values of the distillate rates. It is clear that for Dd = 180 L/h. the bottom level cannot be controlled satisfactorily. Figure 4b clarifies that the oscillations in
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the bottom holdup always follow the distillate removal periods.
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Figure 4. ((I) E3ottomholdup profile for three different values of the distillate rate, (b) detail of the bottom holdup profile at a distillate rate of 180 Uh
is related to the fulfillment of the total material balance of the column, and is somewhat similar to the restriction found by Mujtaba and Macchietto (1994). These authors also showed that the optimal (i.e. minimum) batch distillation time is strongly dependent on the mtio F’” /V’ for Fin 5 V’, but it is weakly dependent on such a mtio for F’” > V’. They conclude that F’” is a very important parameter which has to be optimized. On the other hand, Barolo ef al. (19%a; 1996b) showed both by simulation and experimentallythat increasingthe feed/withdrawalrates indeed decreases the batch distillation time. We have investigatedin more detail these findings. The feed tray withdrawal rate G’ was set to the constant value of 270 LA, and different combinationsof D,, and Fzt were considered,all of which fulfilling constraint (2) in order to prevent draining of the colwnn bottom. Figure 5 shows that, for a given distillate rate, increasing the net feed rate does reduce the batch distillation time. However, there is no further advantage in increasing FE; above a certain value; also, this limiting value (-90 L/h in the case of Figure 5) is basically independent of the distillate rate (that is: it hoids for both optimal and non-optimal operations). The limiting total distillation time is related only to the fractionating capacity of the column (i.e., to the number of stages of the strippingsection, for the example considered in this work). When the net feed rate is “low”, the water fractionated by the strippingsection is not removed from the column at a sufficiently high rate, and this occurrence slows Constraint (2)
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Figure 5. Effect of the net feed rate on the total distillation time for different values of the distillate rate
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down the ethanol enrichment of the middle vessel. Conversely, if F,“: is too high, the column has not enough trays to condense off the water at a high rate. This fact can be further understood by noting that, for certain combinations of F,“: and D,,,, , the distillation time grows up very markedly, to a point that in certain cases the distillation itself is not feasible. It should not be forgotten that this happens even though the total material balance constraint is satisfied ( F”” ;1 D ). To understand this, one should recognize that the driving force for the separation of water from the middle vessel is the difference between the ethanol concentration on the feed tray (x~~~,,~) and on the feed vessel ( xEKIHM). Figure 6u shows that when a distillate rate of 40 L/h is chosen, a positive (i.e. xEIoH.,6> x,~,) driving force throughout the batch exists, so that the separation can take place and it stops at about 130 min. However, for D,, = 60 Lib, from a certain time on the driving force reverses (Figure 6c) and the middle vessel is drained before the separation can be achieved. Physically, this is due to the fact that the higher the distillate rate, the more quickly the ethanol depletion in the middle vessel occurs. So, either the water can be removed from the bottom quickly enough (i.e. FE/ is sufficiently large), or all the ethanol will be removed from the top of the column, with the result that the middle vessel is emptied. Note that in this respect the distillate rate may have a critical value (for each value of the net feed rate). At this critical distillate rate, the distillation time may increase due to a sign&ant reduction of driving force during the distillation (Figure 66).
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Figure 7. Effect of the distillate rate on the total distillation time for differentvalues of the feed tray
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Figure 6. Ethanol composition profiles on the feed tray and on the feed vessel for a distillate rate of (a) 40 L/h, (6) 48 Lib and (c) 60 L/h. Withdrawal rate from the feed tray (all cases): 270 Lh
Another dynamic aspect which is not immediately intuitive is represented in Figure 7. Here, the effect of the distillate rate on the total distillation time is plotted for a given net feed rate ( Fst = 90 L/h) at different withdrawal rates from the feed tray. It should be noted that there might be a physical constraint to the maximum achievable withdrawal rate; this is due to plant construction considerations (Bar010et al., 1996a). Figure 7 clarifies that when the withdrawal rate F$’ is small, working at high distillate rates results in a marked decrease of the total distillation time. This decrease is not observed when large withdrawal rates are employed.
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Figure 8. Profile of the residence time in the middle vessel as a function of time for different values of the feed tray withdrawal rate. Net feed rate (all cases): 90 LAl
This behavior can be attributed to the role of the “residence time” z of the liquid in the middle vessel. The residence time is defined as: M 7(f)
= *
F vol
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When it is not possible to withdraw liquid from the feed tray at a “high” rate (Fs’ “low”), the initial value of 7 is large (for a given amount of feed charged to the middle vessel), in such a way that the residence time in the vessel limits the “quickness” of the distillation. In this case, the higher the distillate rate chosen, the more quickly the middle vessel holdup decreases; therefore 7 decreases quickly during the operation (Figure S), and a decrease of the total distillation time is observed (Figure 7). However, if (for the same initial charge) Fs’ is large, 7 is small from the beginning of the operation, i.e. the renewal rate of the middle vessel is not a limiting factor for the distillation. In this case, if one works at high distillate rates, a marked decrease in 7 is not observed during the operation (Figure 8); rather, the total distillation time may slightly increase be-cause the cohunn is quickly depleted of ethanol, and the driving force for the distillation decreases, as previously explained. These considerations can be also used to analyze how the size. of a feed charge may affect the duration of the batch. Note that when the distillate rate exceeds the value of -55 wh, no reduction, or increase, in the distillation time is observed. Working with D,, c 55 wh results in an increase of the amount of product eventually collected in the middle vessel at the expense of the amount of the accumulated lighter cut (which will be usually purer than needed). For higher distillate rates, the total amount collected for each product is basically independent of Owl (and both products are exactly on specification). CONCLUSIONS A detailed dynamic model of a pilot-plant batch column with a middle vessel has been developed and verified
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against experimental data. The model has then been used to study the dynamic behavior of such a column. For a given operating sequence, the column operating parameters (i.e., the degrees of freedom) have been chosen to be the distillate rate and the net feed rate. It has been shown that for the total material balance to be fultilled (that is, in order not to drain the bottom of the c&mm), the net feed rate should never be lower than the distillate rate. However, additional restrictions in the choice of the operating parameter values exist. These restrictions are related to the component balance. An incorrect choice of the operating parameters will result in a reduction of the driving force available for the separation, to the point that the middle vessel may drain prior to achieving the desired separatioa The total distillation time is a&&d by the distillate rate. When the initial residence time of the liquid in the middle vessel is large (i.e., the feed charge is large, or the withdrawal rate from the feed tray is low, or both), increasing the distillate rate results in a decrease of the distillation time. The reverse is true (even though less markedly) when the initial residence time in the middle vessel is low, i.e. when the residence time is not a limiting factor for the separation. All the results make clear that the dynamic behavior of a complex batch column is not as easily understandable as the one of conventional batch rectifiers and batch strippers. Interactions between the operating parameters may result in unexpected plant responses. This is a very important issue to be aware of when implementing a production strategy on an industrial plant_ because plant operators are often reluctant to operations which differ significantly from well-established techniques. ACKNOWLEDGEMENTS We would like to thank Ing. Stefania Mariano for her help in running some of the simulations presented in this work. Financial support granted by CNR (Progetto Strategic0 Tecnologie Chimiche Innovative) and by MURST (ex-40%) is gratefully acknowledged. LIST OF SYMBOLS B = molar bottoms rate = volumetric bottoms rate Owl molar distillate rate D = volumetric distillate rate IZE’= Murphree tray efficiency wef F = molar net feed rate to the column pn WI = volumetric feed rate to the column Ml F wl = volumetric net feed rate to the column FW’ wl = volumetric withdrawal rate from the column = molar bottom holdup MB = molar reflux drum holdup MD MF = molar middle vessel holdup Mi = molar tray holdup M v0l.F = volumetric holdup of the middle vessel N, = total number of trays &I = volumetric reflux rate t =time V’ = molar vapor boilup rate X EIOH.,6 = ethanol mole fraction in the feed tray B
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European
xEtOH,D = ethanol mole
Symposium
on Computer
fraction in the distillate
Aided Process
Englneerlng-_h
Complex Batch Distillation Cohunn, J. Chem. Eng Jap., 29, 1000-1006. Hasebe, S., T. Kurooka and I. Hashimoto (1995). XEIOH,M = ethanol mole fraction in the middle vessel Comparison of the Separation Performances of a xEIOH.spl= ethanol purity specification for the lighter cut (mole fraction) Multi-Effect Batch Distillation System and a Continuous Distillation System, IFAC Symposium XElOH,,2 = ethanol purity specification for the heavier cut (mole fraction) DYCORD+‘9S (J. B. Rawlings, Ed.), Elsinore z,.~ = feed composition (mole fraction) (Denmark), June 7-9, pp.249-254. Hasebe, S., M. Noda and I. Hashimoto (1997). Optimal z = residence time in the middle vessel Operation Policy for Multi-Effect Batch Distillation System, Computers them. Engng, 2 1, S 122 1-S 1226 REFERENCES Macchietto, S. and I. M. Mujtaba (1996). Design of Operation Policies for Batch Distillation. In: Batch Baratti, R., A. Bertucco, A. Da Rold and M. Morbidelli Processing Systems Engineering: Current Status (1995). Composition Estimator for Binary and Future Directions (G. V. Reklaitis et al., Eds), Distillation Columns. Application to a Pilot Plant. Springer, Berlin (Germany). Chem. Eng. Sci., 50, 1541-1550. Barolo, M. and F. Botteon (1997). Simple Method of Meski, G. A. and M. Morari (1995). Design and Operation of a Batch Distillation Column with a Obtaining Pure Products by Batch Distillation, Vessel, Computers them. Engng, 19, S597Middle AIChE JI, 43, 2601-2604. S602. Barolo, M., G. B. Guarise, N. Ribon, S. A. Rienzi, A. Trotta and S. Macchietto (1996a). Some Issues in Muhrer, C. A. and W. L. Luyben (1992). Batch Distillation. In Practical Distillation Control (W. L. the Design and Operation of a Batch Distillation Luyben, Ed.), Van Nostrand Reinhold (New York). Column with a Middle Vessel, Computers them. -I(’Mujtaba, I. M. and”!% Macchietto~1992).$‘Optimal Engng, 20, S37-S42. Operation of Reactive Batch Distillatio&@resented Barolo, M., G. B. Guarise, S. A. Rienzi, A. Trotta and at the AIChE Antma/ Meeting. I,L, S. Macchietto (1996b). Running Batch Distillation Mujtaba, I. M. and?% Macchietto (1994): Optimal in a Column with a Middle Vessel, Ind Eng. Chem. Operation of Multicomponent Batch Distillation - A Res., 35, 4612-4618. Comparative Study Using Conven ‘onal and Bortolini, P. and G. B. Guarise (1970). A New Practice Unconventional Columns, IFAC p % onference of Batch Distillation (in Italian), Quad. Ing. Chim. ADCHEM’94, Kyoto (Japan), May 25-27, p@415Ital., 6(9), 150-159. _i 420. Bosley, J. R. (1994). An Experimental Investigation on M. Rovaglio, T. Faravelli and G. Biardi Ranzi, E., Modeling, Control, and Optimization Techniques (1988). Role of Energy Balances in Dynamic for Batch Distillation, Ph.D. Thesis, University of Simulation of Multicomponent Distillation Texas at Austin. Columns, Computers them. Engng, 12,783-786. Bosley, J. R. and T. F. Edgar (1995). An Efftcient Robinson, C. S. and E. R. Gilliland (1950). Elements of Dynamic Model for Batch Distillation, J. Proc. Fractional Distillation; McGraw-Hill Book Co. Cot&.., 4, 195-204. (New York). Davidyan, A. G., V. N. Kiva, G. A. Meski and M. Skogestad, S., B. Wittgens, E. Sorensen and R. Litto Morari (1994). Batch Distillation in a Column With (1997). Multivessel Batch Distillation, AIChE JI, 43, a Middle Vessel, Chem. Eng. Ski., 49, 3033-3051. 97 l-978. Diwekar, U. M. (1995). Batch Distillation. Simulation, Sorensen, E. and S. Skogestad (1996). Comparison of Design and Control. Taylor & Francis, London Regular and Inverted Batch Distillation. Chem. Eng. (U.K.). Sci. 51,4949-4962. Farschman, C. A. and U. Diwekar (1996). Dual Subawalla, H., V, P. Paruchuri, A. Gupta, H. G. Pandit Composition Control in a Novel Batch Distillation and R. R. Rhinehatt (I 996). Comparison of ModelColumn, presented at the AIChE Annual Meeting. Based and Conventional Control: A Summary of Grassi, V. G., C. A. Muhrer and W. Silowka (1990). Experimental Results, Ind Eng. Chem. Res., 35, Process Improvements in Batch Distillation through 3547-3559. Dynamic Simulation, presented at the AIChE Wittgens, B. and S. Skogestad (1995). Evaluation of Annual Meeting. Dynamic Models of Distillation Columns with Hasebe, S., B. B. Abdul Aziz, I. Hashimoto and T. Emphasis on the Initial Response, IFAC Symposium Watanabe (1992). Gptimal Design and Operation of DYCORD+‘95 (J. B. Rawlings, Ed.), Elsinore Complex Batch Distillation Column, IFAC (Denmark), June 7-9, pp.26 l-267. Workshop on Interactions Between Process Design and Process Control (J. Perkins, Ed.), London (UK), September 7-8, Pergamon Press (Oxford). Hasebe, S., T. Kurooka, B. B. Abdul Aziz, I. Hashimoto and T. Watanabe (1996). Simultaneous Separation of Light and Heavy Impurities by a product