them. Engng Vol. 19, Suppl., pp. S525S530.1995 Copyright @ 1995 Elsevier Science Ltd 009%1354(95)00069-O Printed in Great Britain. AI1 rights reserved 009%1354/95 $9.50 + 0.00
M. Rovaglio, T. Faravelli, P. Gaffuri, C. Di Palo, A. Dorigo Dipartimento di Chimica Industriale ed Ingegneria Chimica ‘%. Natta” Politecnico di Milano, Ita& ABSTRACT Controllability, observability and flexibility are relevant operational indexes for the identification of a complete and effective control structure for a chemical plant. In this work, we present and discuss the application of such a structural analysis to an azeotropic heterogeneous system, which is a very sensitive plant. No new theoretical aspects have been introduced, but the main feature of this paper is the extension of linear procedures to a strongly non-ideal systems. All the results have been carried out on the basis of a rigorous dynamic model, which allows to identify and verify the operational points of different control schemes. Two operating designs have also been compared, showing that an “upper tie line ’ (UTL) design, close to the heterogeneous boundary, is generally more flexible than a “lower tie line” (LTL) design close to the ternary azeotrope. Moreover, the results here reported show how a suitable feedforward control structure allows to increase the operability of the analyzed design configurations with a general improvement of the corresponding operational flexibility. INTRODUCTION The azeotropic heterogeneous distil&ion system is an interesting topic for a large number of research groups and still very debated in literature. One of the reasons of such attention is due.to the presence of multiple steady-state solutions or, generally speaking multiple operating regimes corresponding to the same column geometry and to the same input data. Several attempts to explain the nature of these mathematical results have been reported in literature in the last decade, see for example Magnussen et al. (1979), Kovach and Seider (1987). Venkataraman and Lucia (1988), Rovaglio and Doherty (1990), Cairns and Furzer (1990), Ganiand Jorgensen(1994), Bekiarisetal. (1994). However, even though it is difftcult to highlight a simple and common interpretation and a final word has not been said yet, all the papers underline at least that such systems are affected by a strong parametric sensitivity with respect to small variations on the corresponding operating conditions. In particular in some cases, as a result of such changes, the system looses the correct heterogeneous interface condition with a corresponding sharp decrease of the separation efficiency. For this reason, the main issue that this paper would address is the design of a suitable control structure but, at the same time, great attention will be devoted to the choice of the optimal process specifications. The former objective can be achieved by detailed studies (State Controllability, Output Controllability and Observability) related to the interactions among selected sets of state, manipulated and output variables. On this subject, the theory developed by Lin (1977) or Morari and Stephanopoulos (1980) in terms of linear programming is extended to the highly non linear system considered in this work. Moreover, the choice of the best design configuration together with the optimal operating conditions to be adopted is accomplished on the basis of new definitions of stationaty flexibility and dynamic operability indexes which are derived as extensions of Operability and Flexibility studies presented earlier by Swaney and Grossman (1985 a,b) and Morari (1983). In all the examples repotted in this work, the theoretical developments and their extensions, are applied through the use of a general non linear model. Details related to the structure, assumption and algorithms adopted for the model solution have been reported in previous publications, see for example Rovaglio and Doherty ( 1990), Gani and Jorgensen ( 1994). THEAZETROPICHETEROGENEOUSDISTILLATIONSYSTEM The separation process analyzed here is that of the well known purification of the ethanol-water system using benzene as an entrainer. A schematic representation of the plant is shown in Fig. 1. The main column is fed by a binary mixture of ethanol-water with a composition close to its azeotrope and by a stream, coming from the second column, rich in benzene. The entrainer allows the formation of a ternary minimum azetrope that, at the liquid state, is unstable and splits in two liquid phases: one rich in benzene (light phase) and one rich in water (heavy phase). The light phase is totally recycled back to the first column while the heavy phase is partially recycled back to the first column. The remaining heavy phase constitutes the feed for the second homogeneous column. Pure ethanol (up to 0.9998) is the main product obtained from the
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column. Pure water is obtained from the bottom of the second column. It should be noted that a benzene makeup is always needed to compensate the entrainer losses, even very small, from the column bottoms. The design configurations for the system described above are analyzed below in terms of the vapor composition leaving the top of the first column which corresponds to a different overall composition of the decanter. Two alternative plant designs, based on the position of the vapor composition within Water 1 the two-liquid phase (see fig. 2), can be Fig. I: Two-column sequence for ethanol-water separation named as follows: l lower tie-line (LTL)design; l upper tie line (UTL) design. ETHANOL The design specifications as well as the main operating conditions are given in Table 1. Finally, the LTL design is analyzed in two alternative operating regimes, related to different entrainer makeup rates, whose composition profiles are shown in Fig. 3a and b. ofthe
STRU~~URALCONTROLLABILITY ANDOBSERVABILITY WATER 0 0.2 0.4 0.6 0.6 1 As already observed by Morari and Stephanopoulos (1980), it should be Fig. 2: Composition pro3les for the LTL and UTL designs very helpful to define a quantitative controllability matrix at the design level. in UTL 1. 1 28 Stages Number 28 Despite different attempts toward this 23.78 Refhx Ratio 16.644 direction, no general criteria have been 2.2E-04 Entminer Make-up 1SE-04 addressed. Nevertheless, a qualitative .I0002 Feed(Kmol/min) .09736 363.39 Rekder Thermal Duty (I’.‘) 407.81 analysis (cause/effect) contains most of 363.43 409.64 condenser lhlmal Duty (WI the information that can contribute to 23 FeedStage 26 develop an effective control scheme. 21 Stages Number Referring to the general definition of 9 2.75 R&x Ratio 1.26 controllability and the analysis 5 Feed Stage 5 I presented by Sevaston and Logman (1985), in this paper we introduce a Tab. 3: UTL and LTLprocess specllfications structural controllability matrix in order to represent the possibility for a specified manipulated variable to control a state variable. Table 2 shows the state, output and manipulated variables adopted to investigate the system given in fig. 1. These variables allow to perfectly identify performances and general behavior of the azeo column. In particular, the two levels describe completely the decanter fluid dynamics, while the top pressure can be related to the global pressure profile (being practically constant the pressure drops on the trays). Finally the average temperature between stages 4 to 8 allows to [email protected]
the shape of the temperature profile in the bottom of the column. Moreover, the manipulated variables refer to the degrees of freedom (i.e. valves), generally present in a distillation column. Therefore, the controllability analysis has been performed by disturbing each manipulated variable and observing the effect on the different state variables. Fig. 4 shows the behavior of the state variables for ramp disturbances on the manipulated ones. Of course, the qualitative trends are influenced by the amplitude of the imposed disturbance, related to dimension of the corresponding flexibility region (see next paragraph). For example, even very small variations (0.4%) in the reboiler duty brings the column toward infeasible states. In order to take into account these aspects and to introduce a semi-quantitative analysis a “response parameter” (W) can be adopted to define the effect, in terms of deviation from the intial conditions, of the response variables with respect to the corresponding scaled
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Fig. 3: Composition pro$ies for two alternative operating regimes
variation of the input variable: w=
Nominal Value - Final Value -Nominal Value - Final Value 1yrt vlnablc Nominal Value Nominal Value ) [email protected]
The resulting structural matrix assumes the presence of a direct interaction between the state variable and the manipulated variable if the response parameter is greater than a lower limit (Wc.& that has been assumed 0.015.
DMWl~t&llevel(H& Hwy phase l&lx valve(aa) Daxnter irhafbz lewl (I&) Lightphase refluxvalve(aL) Avaags tcmpaatlne 44 (‘L) Rhik m duty(Q) Benzenemake-up(Fe&)
Tab. 2: Variables adopted&r controllability and observability studies.
The only effective output variable for the azeotropic heterogeneous column is the bottom purity. Then, the previous analysis has been also applied to the bottom ethanol mole fraction to observe the effect of the different manipulated variables on the product specifications. The resulting structural vector is: aT X,,=[ 0 1100
Q, i Feed, J
The general result of such analysis is the possibility of individuating different control structures for the Fig. 4: State variables transient. same goal. As a matter of fact, the qualitative approach does not directly identify the best pairing between state variables and manipulated variables. This choice can only be addressed by comparing the behavior of the system when the corresponding feedback controllers are introduced. Fig. 5 shows the performances of different PI controllers when a -15% ramp disturbance in the feed flowrate is imposed. The top pressure is not reported, being only marginally influenced by external disturbances. The control of the top pressure is mainly due to safety purposes rather than to operating conditions. Table 4 shows the best pairing for a complete feedback control scheme. This result is fully in agreement with the general control scheme assumed for distillation columns and particularly for the azeo column (Bozenhardt, 1988). Nevertheless the structural approach is a useful instrument that allows to confirm and validate the control design on the basis of the intrinsic phenomenological behavior of the system.
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A fiuther coaGrmatioa caa arise from the observability analysis to individuate the best inferential control scheme for the bottom purity. A new structural vector is ideatied to relate the output variable to the state variables. A servo problem, i.e. a set point disturbauce, is introduced for each PI controller aad the transient of the output variableis recorded. Fig. 6 shows the behavior of the bottom ethanol mole fraction for the various ramp disturbaaces. The result confirms that 8n average temperature caa be directly assumed for this control purpose. The above analysis, both in texms of coatrollabilty and observability, refers to the UTL design conditions. The Same results have also been obtaiaed for the LTL design. This is aa implicit confirmation that controllability aad observability are iatriasic properties of the system aad are not aEected by the operatjug conditions. FLEXIBILWY ANDOmmkm Aim of this section is to define a procedure which allows to choose among alternative designs or, at the same time, among alternative regimes. The Flexibilih, can be defined as the system capaciw to exhibit, without any control action, steady-state conditions which [email protected]
the design specification even with input variables modtped with respect to the nominal values. Fig. 5. Controllerspe#onnance. It will be named ODerabilitv the system capaci?Y to reject disturbances imposed on the main uncertain variables while adopting a feasible control structure. Both these definitions can be used to determine representative index values. Therefore, such simple data are vety useful predicting the system behavior when the process is subject to several operating Tab. 4: Best pairtngfor feedback control. coastraiats. As a matter of fact, an azeotropic heterogeneous distillation system to be operated correctly requires both the presence of a liquid-liquid phase splitting inside the decaater aad a total benzene inventory enough to enable the water separation (as ternary azeotrope). The control scheme adopted to perform the operability analysis is schematically reported in Fig. 1. This Steady-state,T, (setpoint) configuration is based on the feedback control structure derived from the previous controllability analysis and completed with the use of a feedforward control strategy PTOP (@POW to improve the control performances ia terms of control objectives. The feedforward action is accomplished by 0 saca *mm 15m maa smn two loops. The first one allows to keep constant the TUC mw Fig. 6: Outputvariable. ratio between water and benzene inventory inside the column which turas out to be a critical parameter for the separation efftcieacy. The corresponding manipulated variable is the entraiaer make-up rate. The second feedforward controller allows to define the setpoiat of the temperature control loop needed to [email protected]
a specified ethanol composition on tray a. 4. Ia practice, the introduction of aa ideal feedforward control, as here proposed, means to perform aa operability study related to a dynamic system evolution which does not involve any off-specification problems. In such a way, aa operating condition will be considered “operable” not on the basis of the ethanol purity (which is always satisfied by a constraia equation) but rather on the basis of the value assumed by the manipulated variables to reach the objective functions. In other words, aa operating condition caa be considered “inoperable” if, aad only if, one of the manipulated variable exceeds the corresponding physical limits. Therefore, we assume that, ia the range of process conditions here examiaed, the use of a real feedforward controller (with time delay, uacertaiaty aad so on) does not moditjr the conclusions here
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The flexibility aualysis cau be performed through steady-state simulations when imposing variations on the reboiler duties, on the condenser duty in the first column and finally on the feed composition and flowrate. The uncertain parameters and the corresponding maximum deviations (with respect to the nominal value) are reported in Tab. 5. A new definition of a flexibility index can be given as follows:
where exRj Aexpj = maximum expected deviation for the uncertain parameter j; maximum deviation (feasible in both Amaxj’ positive and negative directions) for the uncertain parameter j; Tab. 5: Expected akviafions. N = number of uncertain parameters (5 in the example here examined). This value represents an average scaled measure of the maximum acceptable deviations imposed on all the possible input variables. Using this definition for the LTL and UTL design configuration the flexibility index becomes: FLTL = 0.45 hJTL = 1. The value obtained for the UTL conditions reflects the system capacity to admit steady-state conditions corresponding to the maximum variation on the uncertain parameters satis$ing at the same time, all the process specifications. The conclusions drawn from this index can be generally confirmed by a more detailed, but also more time consuming, operability study. The operability analysis is based on process dynamic simulations including the control scheme mentioned above. Such analysis must be preceded by a careful study of the possible effects on the uncertain input variables. For the process in object the uncertainty on the input variables can be limited to the feed flowrate and to the feed water content. The study here developed allows to defme the operability region in a “feed flowrate - feed water content” plane where all the specifications are satisfied (heterogeneity, benzene inventory greater then 0, ethanol purity) but with a boundary on the manipulated variable of f10 % around the nominal values. An increase of both the uncertain parameters selected moves the system towards a worse region of the operating conditions. Therefore, defining in a Feed-XH20 plane the region A of the maximum expected deviation, the operability study can be performed along the semi-diagonal d (see Fig.7) representing the path of the worst operating conditions. Finally, through the use of a general simulation model it will be easy to define, for both the design configurations, the maximum rectangle that can be expanded around the nominal parameters represented by point N. Defining Lop a characteristic length of the feasible region and Lmax the corresponding one for the maximum rectangle (see fig. 7), the operability index can be evaluated as 0 = Lo,,&,,,,. Using the results schematically reported in Fig. 7 it is possible to derive the following values: OLTL = 0.833 Ou+TL = 1. As mentioned above, this result confirms the predicting capacity of a flexibility analysis. In the situations here examined the manipulated variable that allow to distinguish between the alternative design configurations is the reboiler duty for the main cohunn. As a matter of fact, at the boundary of the maximum region (feed flowrate +3O%, xH20 +20%), the purity controller requires for the LTL design a thermal duty exceeding the bound limits to [email protected]
the bottom specifications. For the UTL design the reboiler duty evolution lies perfectly inside the corresponding boundaries. The bound limits adopted are defined symtnetric with respect to the nominal value and equal to f 10 % of such value. This corresponds, for example, to assume a possible maximum variation of the steam reboiler pressure equal to 2 bars. It must be underlined that even outside the feasible region, the UTL contiguration still has a ethanol purity which [email protected]
the process specifications. This result confirms from one side the efficiency of a feedforward control strategy which allows to clearly improve the process operability but from the other side highlights the importance of choosing a correct set of boundaries for the manipulated variables. For a second regime of the LTL configuration with a lower feed make-up (see the composition profiles in Fig. 3b) the flexibility index decrease to: F= 0.18. This result can be explained on the basis of a minor total benzene~inventory which involves a reduced capacity to admit steady-state conditions corresponding to large variations of the uncertain parameters. However, from the operability point of view, the optimal control configuration allows to satisfy all the objective functions with a set of correct values for the corresponding manipulated variables: the operability can be considered unchangeable with respect to the adopted regime.
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. :: ....
Fig. 7: Operabilityregionfor LTL and UTL configrattotw. This allows to underline that the flexibility analysis can predict only partially the real system behavior. In particular, two operating conditions cham&&ed by a different flexibility index can be judged equivalent from the operability point of view when an optimal control structure has been adopted. CONCLUSIONS
Heterogeneous azeotropic columns are very sensitive systems which often show erratic behaviors or auomalous answers. The use of well known theoretical approaches such as the controllability and observability matrixes, extended to these strongly non linear problems, have been conveniently applied in the analysis and design of control schemes, especially in determining the correct pairing between state or output variables and the manipulated ones. Moreover, both a steady-state flexibility and a dynamic operabiity study can show that an upper tie-line design (characterized by a large amount of entrainer inventory) enlarges the operative condition limits, when it is preferred to a lower tie-line design. Finally the introduction of a f&forward control strategy improves the system operability for the analyzed regimes, even in presence of different value for the flexibility index. ACKNOWLEDGMENTS The authors acknowledge the very
useful suggestions of Prof. Ratlqul Gani.
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Formulation and Theory”, AIChE J., 31, 1985. Swaney R: E., and I. E. Grossman, ‘An index for operational jlexibili~ in chemical process design, II: Computational Algorithms ‘I,AIChE J., 31, 1985. Venkataraman S., and A. Lucia, “Solving Distillation Problems by Newton-Like Methods “, Comp.Chem. Engng.,l2, 55, 1988.