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Dynamics and Control of Heterogeneous Azeotropic Distillation Columns
Copyright © IFAC 12th Triennial World Congress, Sydney, Australia, 1993
DYNAMICS AND CONTROL OF HETEROGENEOUS AZEOTROPIC DISTILLATION COLUMNS R.G. Corrb* and S.B. J0rgensen**,t *Department of Chemical Engineering, Federal University afSaa Car/os, 13565-905 Saa Carlas SP, Brazil uDepartmenJ of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngl7y, Denmark
Abstract: The control properties of one type of heterogeneous azeotropic distillation are investigated. The case considered is that of a minimum boiling ternary heterogeneous azeotropic and three binary azeotropes of which one is heterogeneous. The plant is described and investigated with the main purpose of controlling the two product purities; i.e., the bottom products from th e azeotropic and the dehydrating column, respectively. A number of actuator configurations are investigated for control of the top conditions and bottom composition in the azeotropic column, respectively. A special distance measure d B1N is introduced for the top condition with the purpose of ensuring one liquid phase in the column, yet ensuring phase split in the decanter. Model Predictive Control (MPC) is used based on a linear dynamic model of the azeotropic column in order to deal with the output constraint problem in dBIN. Linear simulations show the potential of an MPC controller design to eliminate the presence of two liquid phases in the azeotropic column during disturbance rejection and set-point tracking. Key Words: Distillation columns; dynamic response ; dual control; PI control; predictive control ; multivariable control systems; simulation; chemical industry
1
Introduction
of multiple steady states if the azeotropic column is overdesigned (Gani et al., 1992). Therefor th e first goal in this work is attempted satisfied while ensuring homogeneity; i.e., no liquid phase split in the column. This approach may be generalized to ensuring the occurrence of heterogeneity at a specific location in the azeotropic column . Thus the purpose of this paper is to investigate different control structures and design methods for the azeotropic column for ensuring the above two modified goals. The ability of multi-loop versus multivariable predictive control to perform set-point tracking and disturbance rejection is investigated for the most promosing control configuration.
Heterogeneous Azeotropic Distillation or Azeotropic Distillation is one way to separate binary azeotropic or difficult-toseparate-components by adding a third component, the entrainer. This entrainer alters the relative volatility between the key components and induces an immiscible region such that it is possible to obtain the constituents of the azeotrope in pure form . Most recent work in this area has focused on thermodynamic models (Cairns and Furzer, 1990a,b and Widagdo et al., 1992b), steady-state simulation (Widagdo et al., 1989a, and Rovaglio and Doherty, 1990), column sequencing (Pham and Doherty, 1990 and Stichlmair and Herguijuela, 1992) , and dynamic simulation (Widagdo, et al., 1992c, Bossen et al., 1993, and Gani et al., 1992) . Few papers relate to control of azeotropic distillation with little insight and only few general results (Wong et al., 1991, Rovaglio et al., 1991 and 1992, and Correa et al., 1991). The purpose of this work has been to develop an understanding of the type of azeotropic distillation represented by the traditional ternary ethanol-water-benzene (EWB), in order to evaluate control problems and to enable control design . The ternary system isopropanol-water-cyclohexene (IWC), which belongs to the class of the EW B-system, is used in most of the simulations reported in this paper. A goal structu re for control of a heterogeneous azeotropic plant is to ensure:
2
Process Presentation
The se paration takes place in a plant consisting of two distillation columns and a decanter, as shown in figure I. A concentrated feed stream which has its composition close to the binary azeotrope is fed to the first (azeotropic) column. A stream which must condense into two liquid phases is taken overhead and sent to the decanter. The heavy phase from the decanter is fed to some intermediate tray of the second (dehydrating) column. A fraction of the condensed overhead stream from this column is recycled to the original feed stream. The light phase from the decanter is recycled to the top tray of the first column together with the reflux stream. A small make-up stream of entrain er is necessary to replace small losses in both product streams. A CM-simulation model is used to investigate the steadystate characteristics of minimum boiling ternary azeotropic distllations. The main focus is upon the azeotropic column which operates with a ternary mixture , whereas the dehydrating column operates with a nearly binary mixture and thus resembles binary distillation. This latter small diameter column is overdesigned with 10 trays, whereas the azeotropic column has 8 (IWC) or 14 (EWB) trays. An operation point design procedure is established to spe-
1. Liquid-liquid phase split in the decanter
2. Purity of the two primary product streams 3. Limit on entrain er content in product streams. The first goal is one of operability, whereas the two latter are quality related . The main focus of this paper lies upon the first two goals. The third goal may be directly addressed using available degrees of freedom and the results of this paper. Satisfying the first goal can give rise to the occurrence
t Author to whom correspondence should be addressed. 11
Figure l: Schematic representation of a heterogeneolls distillation sequence.
equilibrium with a vapor phase which when condensed lies inside the two-liquid phase region. Thus a suitably selected dBlN can ensure the phase split in the decanter, even in the presence of some static feed composition and flowrate disturbances. Another major advantage of the d B1N measurement, is that it can help ensuring a single liquid phase on the top tray and thus nontrivial static multiplicity of solutions seems to be avoided for the investigated systems. Thus this measurement is most usefull for satisfying the first modified control goal. The static properties within the two operating regions form a basis for building an understanding of two possible azeotropic column actuators, which are considered in this section. The by-pass split flow rate ratio effectively manipulates the flow rate of water which is recycled to the azeotropic column. For a low by-pass split ratio, nearly all overhead vapor passes through the decanter and the highest possible amount of water, at the act ual liq lIid-liq uid eq uili bri um conditions, flows to the dehydrating column. Thus the lowest possible amount of water flows to the azeotropic column. The entrainer feed flow rate FE actuator mainly affects the relative volatility of alcohol to water in operating region I, whereas its dominating action in operating region II only is the mass action effect of entrainer. The behavior of V A in the stripping section of the azeotropic col umn is analogous to the well known behavior for simple binary distillation.
cify the decanter by-pass split flow ratio RA in order to obtain the best liquid split in the decanter; i.e., obtain the larger amount of entrainer in the entrainer-rich phase and the larger amount of water in the water-rich phase. This procedure attempts to locate the condensed overhead vapor composition as close as possible to the heterogeneous ternary azeotrope inside the two liquid phase region. The investigation is based upon mapping the static operating region whereby two distintic regions are identified. If only the costs of energy and entrainer are minimized the statically optimal operating point will lie in operating region I, as presented in figure 2 for the lWC-column. The steady-state properties are investigated based upon a new top composition measurement d B1N which measures the minimum distance between the top tray liquid composition and the binodal curve, together with bottom purity for the azeotropic tower. Two azeotropic column bottom actuators are investigated: the vapor flow rate, VA and the entrainer flow rate, FE. The top actuator is the decanter by-pass split flow rate ratio, RA. 100
3
Control Configuration
Since the main focus in this work is upon the azeotropic column, the dehydrating column, which is nearly binary, will be operated with a fixed refl ux ratio of 9 and with a bottom loop XBD2 - VD. To satisfy the two control goals mentioned in the introduction for the azeotropic column, two loops are required. In the first mentioned loop the composition measure dBl N will be used whereas x BA I will be used in the other loop. The control configurations investigated here are: RAVA, RAL BA , RA(VA/LBA), RAFE , FEL BA , and LDHVA . Prokopakis and Seider (1983b) and Rovaglio and Doherty (1990) suggested the use of the split ratio RA as a manipulated variable. The split ratio has an interesting feature since it regulates part of the energy and material balances by regulating the amount of water recycled from the decanter. The boilup V A regulates the operating lines in the azeotropic column. The LBA and LDll actuators have been suggested to
Figure 2: Relation between VA and FE at fixed product specifications for the ternary isopropanol-water-cyclohexane with 8 trays in the azeotropic column and RA 0.56.
=
The proposed new top composItIOn measure d B1N seems to have very promising dynamic properties. One most desirable property is the possibility to specify a dB! N which statically ensures a single liquid phase on the top tray in
12
maintain the column material balance at the bottom and top of the azeotropic column. The FE actuator, albeit a small stream, was investigated by Rovaglio et al. (1992), who used the entrainer make-up stream in a feed forward scheme to reset an entrainer flow rate controller through the knowledge of the incoming disturbances in the feed. The boil-up ratio V A / LBA causes some configurations to have better disturbance rejection properties by incorporating the action of the level loops. From a steady-state point of view, operation of the azeotropic column with the RA V A configuration does not give any difficulty. The operation of the azeotropic column at point 2 in the RA FE configuration however would be more difficult than operation in region I, since FE has only a very small impact on the outputs at operation point 2.
4
reported above. Once the mod els are id entified with an acceptable uncertainty, the next step is to select the design parameters for th e constrained M PC . For disturbance in FA, the sampling time is t::..t = 1 min, in order to catch all the fast dynamics observed in the plant, specially the RH P-zero observed between V A and XBAI, although it is removed in the multi variable case . The model horizon is set eq ual to T 1870, which was sufficient to obtain less than 1% static error in the step response model of the individual transfer functions. These two parameters are together responsible for the slow simulation observed in the implementation of the constrained MPC, due to the large order of the step response models obtained. The control horizon was set equal to m = 1, while the prediction horizon was set equal to p = 20. These two values tend to stabilize the system, but they increase the compu tation time . The weighting matrices are W 1 = I and W 2 =0 . Figures 3a through d present the closed-loop (PI+MPC) and open-loop (AO) behavior of both outputs and actuators for a step disturbance of +10% in FA. Observe in figure 3a (PI) that a diagonal PI-controller is not able to dynamically avoid the presence of a second liquid phase in the top tray of the azeotrpic column. However , the constrained MPC keeps the top liquid composition outside the two-liquid phase region, and thus dBIN is always positive (figure 3a). The idea of including the closed-loop step responses of the diagonal PIcontroller together with the closed-loop step responses of the constrained M PC is to show th e constraint-handling capability of th e constrain ed M PC structure rath er than to co mpare both the PI and the M PC structures in terms of performance. Similar simulations were p erformed with the alcohol composition disturbances in th e feed, XAl, the entrainer feed flow rate, FE, and the set point for XBAl: T XBA I (Correa, 1992) and equivalent observations were obtained with respect to the advantage of the MPC structure over the multi-loop PI structure.
=
Process Dynamics
In the single variable case, the presence of inverse response is observed in XBAI in all operating regions for changes in V A , while overshoot is observed in dBI N, but no inverse res ponse . For changes in RA, only overshoot is observed in both dB! N and XBAI for all operating regions . However , changes in FE produce no overshoot or inverse response in both outputs (Correa and J{1Srgensen, 1992a,b) . The split ratio provides much faster action than does the entrainer feed flow rate actuator on the azeotropic column variables. This property is clearly connected to th e low entrainer feed flow rate, compared with the effect of RA in the azeotropic column . Thus the higher the purity requirements the slower the dynamics of the entrainer feed flow rate actuator, specially when operating at conditions dictated by dominating energy prices ; i.e., operating point 2. A very simple dynamic model is identified for each input-output pair and further used in the next section for control design and closed-loop simulations.
5
Model Predictive Control 6
The RA V A configuration presents the bes t set-point tracking and disturbance rejection characteristics among the control configurations RA FE , RA L BA , RA(VA / L BA ) , FEL BA , and LDH V A analysed with the frequency dependent RGA and CLOG (Correa, 1992) . Operating point 2 represents the best operating point in terms of energy efficiency in region I. The decentralized multi-loop control scheme implemented could not dynamically eliminate the presence of two liquid phases in the rectification section of the azeotropic column for step disturbances in FA and XAI (Correa et al., 1991) . This limitation is due to the diagonal PI-control structure implemented rather than an inability of dB I N measurement in providing the necessary information of closeness to heterogeneity on the top tray. The main benefits of using M PC instead of more traditional techniques is that the M PC incorporates explicity input and output constraints in its design. A M PC structure is implemented with the RA V A configuration for the IWC-column for compatison with a decentralized multi-loop control scheme. Since only linear simulations of constrained M PC are performed, the azeotropic column (plant) and the measured disturbances are modelled with a full linear model (FL) obtained from a state-space realization at an operating point in region 2. For the model of the plant, the simplified transfer functions id entified for the RA V A configuration at operating point 2 of the IWC-column, are used. This procedure incorporates a plant/mod el mismatch, which is normally the case . Models of the measured disturbances were identified at the same operating point in region 2, as
Conclusions
The d BIN measurement seems to have very prOlnISlIIg dynamic properties , by statically ens uring one single liquid phase on the top tray in equilibrium with a vapor phase which when condensed lies insid e the immiscible reg ion. Comparison of disturbance rejection and th e set-point tracking characteristics of a constrained Model Predictive Control design and a multi-loop PI-control design indicates that multi variable controller design is most adequate to dynamically ensure homogeneity on trays and heterogeneity in th e decanter. The above control structure with the composition meas ure d BIN can also be a most useful structure in case wh ere operational conditions di ctate heteroge neity on trays , by limiting the total number of trays with two liquid phases to a minimum. Thus the two primary control goals of heterogeneo us azeotropic distillation may be fulfill ed by using an RA VA configurat ion and a M PC control strategy.
Bibliography Bossen, B. S., Jl'lrgensen, S. B., and Gani, R. (1993). Simulation, Design and Analysis of Azeotropic Distillation Operations , lnd. Eng. Chem. Res .. To appear. Cairns, B. P. and Furzer, I. A. (1990a). Multicompon ent Three- Phase Azeotropic Distillation . 2. Phase-Stability and Phase-S plitting Algorithms. lnd. Eng. Chem.
13
-
••
u u
PI /~---_ I I
,
...........
I
I
~u
, I
I
"
I
... :, I " PI u '... '
(a)
.. PC
(b)
lIm .. mln
11 ..... mln
(c)
(d)
Figure :3: Dis turb a nce rejec tio n ch a ract eristics of th e PI- controller (PI-SL) a nd th e cons tra i ned M PC (M P C- F L+S L) for th e azeot ro pi c colll!nn und er a ste p disturbancf' in FA of + 10% (a)d n I N, (b) RA, (c) x /I A I , a l\d (d) VA .
Pham , 11 . N. a nd Do he rty, M. F. (1990). D es ign an d Sy n t.hesis o f ll e tero~e n eo lls A" eotro pi c Dist.ill at io n .- Ill. ( :011111111 Se q lI e ll ce~ . (.'ht'lll im l [~' 1Iyi1l1 ·e1· i1l9 Scie1l ce , 45, 110 . 7 , 18 45- 1854.
Res., 29 , 1364- 1382 . Cairn s, B . P . a nd Furze r , I. A. (1990b). Multicompon e n t Three-Phase Azeotrop ic Distill at io n . 3. Modern Th e rm ody nami c M od e ls a nd M ul tipl e Soluti o n s. Incl. Ellq. Ch em . Res., 29 , 1.18 :~- 1.19.5.
Pr o ko paki s , (; . .I . and Seid c r , W. D . (1 ~1 8J). DYlI ,uni c S imulatioll o f Azeotropi c Distill at ion Towe rs. A IC h E J ou r,wl, 29, no. 6 , 1017- 1029.
Co rre a, R. G. , (1992). Co ntrol D es i91! of lIcttT09 fneo ll s Azeotmpic Dislillali(m Plants. Ph. D. t.h es is, De l't.. o f C h e mi cal E n g in ee rin g, Technical U nive rsity o f De nm ar k , Lyngby, D e nm a rk. 2.5 0 pp.
Stichlmair , J . (;. and lI e rgllijll e la, Juan-R. (1992). Dist illation Pr ocesses fo r th e Se p a rati o n of Te fllary Zeotro pi c and Azeotropic Mixtllr es. In : ICh e mE: SY lllp os illm Seri es 11 0. 128, pp . A :J09-A J28. Distillati o n and A bsorpt.ion ' 92 , Birminghalll , 7-9 Se pt e mb e r, Ul\.
Corr e a, R. G ., Anderse n, P. H. , Anders e n , H. W. , a nd Jprge nse n , S. H. (1991). Co nt rol of He t.e rop;e neo u s Azeo tro pi c Distillation Co lumn s. Prese nted at Am e rica n Co ntro l Co nfe re n ce - ACC '9 1, 26-2 8 .lun e, Bos t.o n , USA.
Widagdo , S ., Seid e r , W. D ., a nd Scllil;; tian , D. 11 . (19 89 ). Bifllrcilti o ll All itlysi s in lIet e roge ll eo ll s Azeot.ropi c Dist.illa1.iulI . A f( :hE .!ou nwl, 35 , 110 .9, 14 57- 14 61.
Co rre a, R . G. a nd J0rge nse n , S. (1992a). U nd e rstandi ng the Dynamic C h a racte ris ti cs of He t e roge neo u s Azeotropic Di s tillati o n Co lumns for Effect.ive Operat.ion and ( :o ntro l. In: Eu ro p ea n Sy mposium o n Comput.er Appli cati o ns in Process Engin ee rin p;. ESCA PE-I , 24 - 28 M ay , pp. 9-22 .
Widitgdo , S. , Seid e r , W. \)., and Se bastian , D. H. (1992a). Phase EqlliIibria for He t e roge llolls Azeotropcs with Two Partially-Miscible Binary Pairs. Submitt ed 10
Fluid 1'/1(1.'1' Equilib,·i(l.
Corre a, R . G. and .lprge nse n , S. (1992b). S t.ati c and Dy n a mi c Behavior o f He t. e roge neo us Az eo tropic Di st illati o n Co lumn s. Pf(·'se nt ed at Distillation a nd Absorption '92, Birmi ng h a m , 7-9 Septe mb e r , U 1\ .
Widagdo, S., Seider , W . D., and Se bastian , D. H. (1992b). Dy,wrllic A,w[ysis of IIdcmqc 1I1'olls AZf'oiTopic Vi s lilla/ io 1l. In k fllal Re port , De partlll e nt o f ( : he mi cal E ngilI ee ring , U llive rsity of Pe nllsy lv
Gani , R. , H a nse n , A. , and J0rge nse n S. (1992). Analysis o f th e Behaviour of Azeo tropi c Distillation Ope rat. io ns : Mult.ipl e Steady S t. a t es and Th e ir Effect o n Operabilit.y and Cont.rol. Prese nt ed at. A IC hE Annnal ~v1 ect ing , Miami Beac h , Florida , Nov. 1-6 , P a p e r n o. 14 1e.
WOlI g , D . S. H., .Ian~ , S. S ., and C han~ , ( :. F. (1991) . S illlIdat.i o n o f Dy nami c and Phase l'att e fll C h a ng es fo r a ll Azco1.ropic Dist.ill at. ioll ( :0 11111111 . (.'ompu/,' ,·s (lwl Ch t' mint! 1~' 1I!J i lt e (.,.i1l!l, 15 . no. 5, :U5 -:UFi.
Rovagli o , M. a nd Doh e rty, M. F. (1990). Dy n a mi cs o f Het. e roge n eous Az eot ropi c Distill a ti o n Co l um n s. A I C'hE J ou rnal, 36, n o. I , 39-52. Rov ag li o, M .. Faravelli , T., and Do he rty , M. F. ( 1991) . Ope r a bility and Control of Azeotropi c He t e roge n eo us Di stillation Sequences . In : Proceedin gs o f the 4t.h Inte rn at. io n a l Sy mp osium o n Process Syste m s F: np;in cc ring , pp. 11.17 . 1- 11.17 . I Fi. PS E'9 1, Fi-9 August , Mont e b e ll o, Qu e b ec, Canada. Rov ag li o , M., Faravelli, T., Biardi , C ., C;affllri , 1'., and Soccol , S. (1992). Prec ise Co mp os iti o n Co ntr ol o f He t.e roge neo us Azeo tro pi c Dis t ill at io n T owe rs . I n : E ll rup ea n Sy mp os ium o n Computer Appli ca tions in Pr ocess E ng in ee rin g, pp. S3~1 5-S 40 2. ESCA P E- I , 24-28 May , pp . SI81-SI88 . ESCAPE- I , 24-2 8 May , I';lsin o re, \) c nIII ar k.
14
DYNAMICS AND CONTROL OF HETEROGENEOUS AZEOTROPIC DISTILLATION COLUMNS R.G. Corrb* and S.B. J0rgensen**,t *Department of Chemical Engineering, Federal University afSaa Car/os, 13565-905 Saa Carlas SP, Brazil uDepartmenJ of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngl7y, Denmark
Abstract: The control properties of one type of heterogeneous azeotropic distillation are investigated. The case considered is that of a minimum boiling ternary heterogeneous azeotropic and three binary azeotropes of which one is heterogeneous. The plant is described and investigated with the main purpose of controlling the two product purities; i.e., the bottom products from th e azeotropic and the dehydrating column, respectively. A number of actuator configurations are investigated for control of the top conditions and bottom composition in the azeotropic column, respectively. A special distance measure d B1N is introduced for the top condition with the purpose of ensuring one liquid phase in the column, yet ensuring phase split in the decanter. Model Predictive Control (MPC) is used based on a linear dynamic model of the azeotropic column in order to deal with the output constraint problem in dBIN. Linear simulations show the potential of an MPC controller design to eliminate the presence of two liquid phases in the azeotropic column during disturbance rejection and set-point tracking. Key Words: Distillation columns; dynamic response ; dual control; PI control; predictive control ; multivariable control systems; simulation; chemical industry
1
Introduction
of multiple steady states if the azeotropic column is overdesigned (Gani et al., 1992). Therefor th e first goal in this work is attempted satisfied while ensuring homogeneity; i.e., no liquid phase split in the column. This approach may be generalized to ensuring the occurrence of heterogeneity at a specific location in the azeotropic column . Thus the purpose of this paper is to investigate different control structures and design methods for the azeotropic column for ensuring the above two modified goals. The ability of multi-loop versus multivariable predictive control to perform set-point tracking and disturbance rejection is investigated for the most promosing control configuration.
Heterogeneous Azeotropic Distillation or Azeotropic Distillation is one way to separate binary azeotropic or difficult-toseparate-components by adding a third component, the entrainer. This entrainer alters the relative volatility between the key components and induces an immiscible region such that it is possible to obtain the constituents of the azeotrope in pure form . Most recent work in this area has focused on thermodynamic models (Cairns and Furzer, 1990a,b and Widagdo et al., 1992b), steady-state simulation (Widagdo et al., 1989a, and Rovaglio and Doherty, 1990), column sequencing (Pham and Doherty, 1990 and Stichlmair and Herguijuela, 1992) , and dynamic simulation (Widagdo, et al., 1992c, Bossen et al., 1993, and Gani et al., 1992) . Few papers relate to control of azeotropic distillation with little insight and only few general results (Wong et al., 1991, Rovaglio et al., 1991 and 1992, and Correa et al., 1991). The purpose of this work has been to develop an understanding of the type of azeotropic distillation represented by the traditional ternary ethanol-water-benzene (EWB), in order to evaluate control problems and to enable control design . The ternary system isopropanol-water-cyclohexene (IWC), which belongs to the class of the EW B-system, is used in most of the simulations reported in this paper. A goal structu re for control of a heterogeneous azeotropic plant is to ensure:
2
Process Presentation
The se paration takes place in a plant consisting of two distillation columns and a decanter, as shown in figure I. A concentrated feed stream which has its composition close to the binary azeotrope is fed to the first (azeotropic) column. A stream which must condense into two liquid phases is taken overhead and sent to the decanter. The heavy phase from the decanter is fed to some intermediate tray of the second (dehydrating) column. A fraction of the condensed overhead stream from this column is recycled to the original feed stream. The light phase from the decanter is recycled to the top tray of the first column together with the reflux stream. A small make-up stream of entrain er is necessary to replace small losses in both product streams. A CM-simulation model is used to investigate the steadystate characteristics of minimum boiling ternary azeotropic distllations. The main focus is upon the azeotropic column which operates with a ternary mixture , whereas the dehydrating column operates with a nearly binary mixture and thus resembles binary distillation. This latter small diameter column is overdesigned with 10 trays, whereas the azeotropic column has 8 (IWC) or 14 (EWB) trays. An operation point design procedure is established to spe-
1. Liquid-liquid phase split in the decanter
2. Purity of the two primary product streams 3. Limit on entrain er content in product streams. The first goal is one of operability, whereas the two latter are quality related . The main focus of this paper lies upon the first two goals. The third goal may be directly addressed using available degrees of freedom and the results of this paper. Satisfying the first goal can give rise to the occurrence
t Author to whom correspondence should be addressed. 11
Figure l: Schematic representation of a heterogeneolls distillation sequence.
equilibrium with a vapor phase which when condensed lies inside the two-liquid phase region. Thus a suitably selected dBlN can ensure the phase split in the decanter, even in the presence of some static feed composition and flowrate disturbances. Another major advantage of the d B1N measurement, is that it can help ensuring a single liquid phase on the top tray and thus nontrivial static multiplicity of solutions seems to be avoided for the investigated systems. Thus this measurement is most usefull for satisfying the first modified control goal. The static properties within the two operating regions form a basis for building an understanding of two possible azeotropic column actuators, which are considered in this section. The by-pass split flow rate ratio effectively manipulates the flow rate of water which is recycled to the azeotropic column. For a low by-pass split ratio, nearly all overhead vapor passes through the decanter and the highest possible amount of water, at the act ual liq lIid-liq uid eq uili bri um conditions, flows to the dehydrating column. Thus the lowest possible amount of water flows to the azeotropic column. The entrainer feed flow rate FE actuator mainly affects the relative volatility of alcohol to water in operating region I, whereas its dominating action in operating region II only is the mass action effect of entrainer. The behavior of V A in the stripping section of the azeotropic col umn is analogous to the well known behavior for simple binary distillation.
cify the decanter by-pass split flow ratio RA in order to obtain the best liquid split in the decanter; i.e., obtain the larger amount of entrainer in the entrainer-rich phase and the larger amount of water in the water-rich phase. This procedure attempts to locate the condensed overhead vapor composition as close as possible to the heterogeneous ternary azeotrope inside the two liquid phase region. The investigation is based upon mapping the static operating region whereby two distintic regions are identified. If only the costs of energy and entrainer are minimized the statically optimal operating point will lie in operating region I, as presented in figure 2 for the lWC-column. The steady-state properties are investigated based upon a new top composition measurement d B1N which measures the minimum distance between the top tray liquid composition and the binodal curve, together with bottom purity for the azeotropic tower. Two azeotropic column bottom actuators are investigated: the vapor flow rate, VA and the entrainer flow rate, FE. The top actuator is the decanter by-pass split flow rate ratio, RA. 100
3
Control Configuration
Since the main focus in this work is upon the azeotropic column, the dehydrating column, which is nearly binary, will be operated with a fixed refl ux ratio of 9 and with a bottom loop XBD2 - VD. To satisfy the two control goals mentioned in the introduction for the azeotropic column, two loops are required. In the first mentioned loop the composition measure dBl N will be used whereas x BA I will be used in the other loop. The control configurations investigated here are: RAVA, RAL BA , RA(VA/LBA), RAFE , FEL BA , and LDHVA . Prokopakis and Seider (1983b) and Rovaglio and Doherty (1990) suggested the use of the split ratio RA as a manipulated variable. The split ratio has an interesting feature since it regulates part of the energy and material balances by regulating the amount of water recycled from the decanter. The boilup V A regulates the operating lines in the azeotropic column. The LBA and LDll actuators have been suggested to
Figure 2: Relation between VA and FE at fixed product specifications for the ternary isopropanol-water-cyclohexane with 8 trays in the azeotropic column and RA 0.56.
=
The proposed new top composItIOn measure d B1N seems to have very promising dynamic properties. One most desirable property is the possibility to specify a dB! N which statically ensures a single liquid phase on the top tray in
12
maintain the column material balance at the bottom and top of the azeotropic column. The FE actuator, albeit a small stream, was investigated by Rovaglio et al. (1992), who used the entrainer make-up stream in a feed forward scheme to reset an entrainer flow rate controller through the knowledge of the incoming disturbances in the feed. The boil-up ratio V A / LBA causes some configurations to have better disturbance rejection properties by incorporating the action of the level loops. From a steady-state point of view, operation of the azeotropic column with the RA V A configuration does not give any difficulty. The operation of the azeotropic column at point 2 in the RA FE configuration however would be more difficult than operation in region I, since FE has only a very small impact on the outputs at operation point 2.
4
reported above. Once the mod els are id entified with an acceptable uncertainty, the next step is to select the design parameters for th e constrained M PC . For disturbance in FA, the sampling time is t::..t = 1 min, in order to catch all the fast dynamics observed in the plant, specially the RH P-zero observed between V A and XBAI, although it is removed in the multi variable case . The model horizon is set eq ual to T 1870, which was sufficient to obtain less than 1% static error in the step response model of the individual transfer functions. These two parameters are together responsible for the slow simulation observed in the implementation of the constrained MPC, due to the large order of the step response models obtained. The control horizon was set equal to m = 1, while the prediction horizon was set equal to p = 20. These two values tend to stabilize the system, but they increase the compu tation time . The weighting matrices are W 1 = I and W 2 =0 . Figures 3a through d present the closed-loop (PI+MPC) and open-loop (AO) behavior of both outputs and actuators for a step disturbance of +10% in FA. Observe in figure 3a (PI) that a diagonal PI-controller is not able to dynamically avoid the presence of a second liquid phase in the top tray of the azeotrpic column. However , the constrained MPC keeps the top liquid composition outside the two-liquid phase region, and thus dBIN is always positive (figure 3a). The idea of including the closed-loop step responses of the diagonal PIcontroller together with the closed-loop step responses of the constrained M PC is to show th e constraint-handling capability of th e constrain ed M PC structure rath er than to co mpare both the PI and the M PC structures in terms of performance. Similar simulations were p erformed with the alcohol composition disturbances in th e feed, XAl, the entrainer feed flow rate, FE, and the set point for XBAl: T XBA I (Correa, 1992) and equivalent observations were obtained with respect to the advantage of the MPC structure over the multi-loop PI structure.
=
Process Dynamics
In the single variable case, the presence of inverse response is observed in XBAI in all operating regions for changes in V A , while overshoot is observed in dBI N, but no inverse res ponse . For changes in RA, only overshoot is observed in both dB! N and XBAI for all operating regions . However , changes in FE produce no overshoot or inverse response in both outputs (Correa and J{1Srgensen, 1992a,b) . The split ratio provides much faster action than does the entrainer feed flow rate actuator on the azeotropic column variables. This property is clearly connected to th e low entrainer feed flow rate, compared with the effect of RA in the azeotropic column . Thus the higher the purity requirements the slower the dynamics of the entrainer feed flow rate actuator, specially when operating at conditions dictated by dominating energy prices ; i.e., operating point 2. A very simple dynamic model is identified for each input-output pair and further used in the next section for control design and closed-loop simulations.
5
Model Predictive Control 6
The RA V A configuration presents the bes t set-point tracking and disturbance rejection characteristics among the control configurations RA FE , RA L BA , RA(VA / L BA ) , FEL BA , and LDH V A analysed with the frequency dependent RGA and CLOG (Correa, 1992) . Operating point 2 represents the best operating point in terms of energy efficiency in region I. The decentralized multi-loop control scheme implemented could not dynamically eliminate the presence of two liquid phases in the rectification section of the azeotropic column for step disturbances in FA and XAI (Correa et al., 1991) . This limitation is due to the diagonal PI-control structure implemented rather than an inability of dB I N measurement in providing the necessary information of closeness to heterogeneity on the top tray. The main benefits of using M PC instead of more traditional techniques is that the M PC incorporates explicity input and output constraints in its design. A M PC structure is implemented with the RA V A configuration for the IWC-column for compatison with a decentralized multi-loop control scheme. Since only linear simulations of constrained M PC are performed, the azeotropic column (plant) and the measured disturbances are modelled with a full linear model (FL) obtained from a state-space realization at an operating point in region 2. For the model of the plant, the simplified transfer functions id entified for the RA V A configuration at operating point 2 of the IWC-column, are used. This procedure incorporates a plant/mod el mismatch, which is normally the case . Models of the measured disturbances were identified at the same operating point in region 2, as
Conclusions
The d BIN measurement seems to have very prOlnISlIIg dynamic properties , by statically ens uring one single liquid phase on the top tray in equilibrium with a vapor phase which when condensed lies insid e the immiscible reg ion. Comparison of disturbance rejection and th e set-point tracking characteristics of a constrained Model Predictive Control design and a multi-loop PI-control design indicates that multi variable controller design is most adequate to dynamically ensure homogeneity on trays and heterogeneity in th e decanter. The above control structure with the composition meas ure d BIN can also be a most useful structure in case wh ere operational conditions di ctate heteroge neity on trays , by limiting the total number of trays with two liquid phases to a minimum. Thus the two primary control goals of heterogeneo us azeotropic distillation may be fulfill ed by using an RA VA configurat ion and a M PC control strategy.
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-
••
u u
PI /~---_ I I
,
...........
I
I
~u
, I
I
"
I
... :, I " PI u '... '
(a)
.. PC
(b)
lIm .. mln
11 ..... mln
(c)
(d)
Figure :3: Dis turb a nce rejec tio n ch a ract eristics of th e PI- controller (PI-SL) a nd th e cons tra i ned M PC (M P C- F L+S L) for th e azeot ro pi c colll!nn und er a ste p disturbancf' in FA of + 10% (a)d n I N, (b) RA, (c) x /I A I , a l\d (d) VA .
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Widagdo , S ., Seid e r , W. D ., a nd Scllil;; tian , D. 11 . (19 89 ). Bifllrcilti o ll All itlysi s in lIet e roge ll eo ll s Azeot.ropi c Dist.illa1.iulI . A f( :hE .!ou nwl, 35 , 110 .9, 14 57- 14 61.
Co rre a, R . G. a nd J0rge nse n , S. (1992a). U nd e rstandi ng the Dynamic C h a racte ris ti cs of He t e roge neo u s Azeotropic Di s tillati o n Co lumns for Effect.ive Operat.ion and ( :o ntro l. In: Eu ro p ea n Sy mposium o n Comput.er Appli cati o ns in Process Engin ee rin p;. ESCA PE-I , 24 - 28 M ay , pp. 9-22 .
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Fluid 1'/1(1.'1' Equilib,·i(l.
Corre a, R . G. and .lprge nse n , S. (1992b). S t.ati c and Dy n a mi c Behavior o f He t. e roge neo us Az eo tropic Di st illati o n Co lumn s. Pf(·'se nt ed at Distillation a nd Absorption '92, Birmi ng h a m , 7-9 Septe mb e r , U 1\ .
Widagdo, S., Seider , W . D., and Se bastian , D. H. (1992b). Dy,wrllic A,w[ysis of IIdcmqc 1I1'olls AZf'oiTopic Vi s lilla/ io 1l. In k fllal Re port , De partlll e nt o f ( : he mi cal E ngilI ee ring , U llive rsity of Pe nllsy lv
Gani , R. , H a nse n , A. , and J0rge nse n S. (1992). Analysis o f th e Behaviour of Azeo tropi c Distillation Ope rat. io ns : Mult.ipl e Steady S t. a t es and Th e ir Effect o n Operabilit.y and Cont.rol. Prese nt ed at. A IC hE Annnal ~v1 ect ing , Miami Beac h , Florida , Nov. 1-6 , P a p e r n o. 14 1e.
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Rovagli o , M. a nd Doh e rty, M. F. (1990). Dy n a mi cs o f Het. e roge n eous Az eot ropi c Distill a ti o n Co l um n s. A I C'hE J ou rnal, 36, n o. I , 39-52. Rov ag li o, M .. Faravelli , T., and Do he rty , M. F. ( 1991) . Ope r a bility and Control of Azeotropi c He t e roge n eo us Di stillation Sequences . In : Proceedin gs o f the 4t.h Inte rn at. io n a l Sy mp osium o n Process Syste m s F: np;in cc ring , pp. 11.17 . 1- 11.17 . I Fi. PS E'9 1, Fi-9 August , Mont e b e ll o, Qu e b ec, Canada. Rov ag li o , M., Faravelli, T., Biardi , C ., C;affllri , 1'., and Soccol , S. (1992). Prec ise Co mp os iti o n Co ntr ol o f He t.e roge neo us Azeo tro pi c Dis t ill at io n T owe rs . I n : E ll rup ea n Sy mp os ium o n Computer Appli ca tions in Pr ocess E ng in ee rin g, pp. S3~1 5-S 40 2. ESCA P E- I , 24-28 May , pp . SI81-SI88 . ESCAPE- I , 24-2 8 May , I';lsin o re, \) c nIII ar k.
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