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Ind. Eng. Chem. Res. 1998, 37, 506-515
Stabilization of an Unstable Distillation Column Cornelius Dorn, Thomas E. Gu 1 ttinger, Gary J. Wells, and Manfred Morari* Automatic Control Laboratory, ETH-Z, Swiss Federal Institute of Technology, CH-8092 Zu¨ rich, Switzerland
Achim Kienle, Eberhard Klein, and Ernst-Dieter Gilles Institut fu¨ r Systemdynamik und Regelungstechnik, Universita¨ t Stuttgart, Pfaffenwaldring 9, D-70550 Stuttgart, Germany
Bekiaris et al. (Ind. Eng. Chem. Res. 1993, 32 (9), 2023) explained the existence of multiple steady states in homogeneous azeotropic distillation on the basis of the analysis of columns with infinite reflux and infinite length (infinite number of trays). They showed that the predictions of multiple steady states for such infinite columns have relevant implications for columns of finite length operated at finite reflux. The first experimental verification of the existence of such multiple steady states was published by Gu¨ttinger et al. (Ind. Eng. Chem. Res. 1997, 36 (3), 794). Using an industrial pilot column without an automatic control system, they confirmed the existence of two stable steady states for the ternary homogeneous system methanol-methyl butyrate-toluene. That is, two different column profiles occurred for the same operating parameters, feed flow rate, and feed composition. In this paper, experiments for the same ternary system are described which show the existence of a third unstable steady state. The unstable steady state is stabilized with PI control. Furthermore, the transition from an unstable to a stable operating point is demonstrated when the control action is removed. 1. Introduction Azeotropic distillation is one of the most widely used and important separation processes in the chemical and the specialty chemical industries. Laroche et al. (1992b) have shown that azeotropic distillation columns can exhibit unusual features not observed in nonazeotropic distillation, the understanding of which is critical for proper column design, control, and simulation. Multiple steady states have been discovered among the surprising features of azeotropic distillation columns. By multiple steady states in a column we mean the general notion of multiplicities; i.e., that a system with as many parameters specified as there are degrees of freedom exhibits different solutions at steady state. For a given design, column pressure, feed flow rate, composition, and temperature, we define (1) output multiplicities, if there exist different product compositions and therefore different column profiles at steady state for the same set of operating parameters, and (2) input multiplicities, if the same product compositions are obtained for different values of the operating parameters. In this paper, the term “multiple steady states” (MSS) refers to output multiplicities only. An overview of research related to steady-state multiplicity in distillation is given in Kienle et al. (1995) and Gu¨ttinger et al. (1997). Here, multiplicities of type II, which are caused by the vapor-liquid equilibrium (VLE), will be investigated. The ∞/∞ analysis was used by Bekiaris et al. (1993) as a powerful tool for predicting type II multiplicities from minimal data. (We are grateful to an anonymous reviewer for pointing out that prior to the work by Bekiaris et al. (1993) Petlyuk and Avetyan (1971)
suggested the possible occurrence of multiple steady states via ∞/∞ analysis.) By looking at the limiting case of infinite column length (infinite number of trays) and infinite reflux flow, only a little information is needed (pure-component and azeotropic boiling points and compositions, curvature of residue curve boundaries) to determine the feed region that leads to multiple steady states. MSS can be examined using a bifurcation study that tracks all possible composition profiles along a “continuation path”. A bifurcation diagram can be constructed using one product flow rate as the bifurcation parameter. Simulations (Bekiaris et al., 1993) and experiments (Gu¨ttinger et al., 1997) show that the ∞/∞ multiplicity predictions carry over to the case of finite column length and finite reflux flows. 2. Problem Statement In Gu¨ttinger et al. (1997), the existence of output multiplicities of type II was verified by varying the distillate flow rate to track two stable steady-state branches (Figure 1). For constant inputs, they found that these branches are overlapping for a certain region of distillate flow rates, thus exhibiting multiple steady states. The aim of the current experiment was to (a) verify the existence of the third branch for the same mixture and (b) demonstrate that the steady states on this branch are unstable. To succeed in both tasks, a controller must be designed that stabilizes the unstable operating points. 3. Predictions and Simulations
* Author to whom correspondence should be addressed. Phone: +41 1 632 2271. Fax: +41 1 632 1211. E-mail:
[email protected].
In the following sections, methods are presented which predict column behavior and provide a basis for
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Figure 1. Steady-state measurements (Gu¨ttinger et al., 1997) and ∞/∞ theoretical predictions of the toluene mass fraction in the bottoms.
Figure 3. Illustration of a boiling temperature diagram of a 001 class mixture (methanol (L)-methyl butyrate (I)-toluene (H)) with the product paths of a ∞/∞ analysis.
Figure 4. Illustration of a bifurcation diagram obtained from ∞/∞ predictions.
Figure 2. Residue curve diagram (in mass fractions) of the mixture methanol (L)-methyl butyrate (I)-toluene (H) and boiling point temperatures at 1 bar.
the design of experiments. First, the feasibility of stabilizing control using tray temperatures is examined. Residue curves and ∞/∞ predictions are used to develop a qualitative picture of temperature profile shapes and positions. These predictions are confirmed by rigorous numerical simulations and are used to develop a stabilizing control scheme. Second, the issue of instability is examined by dynamic simulations. The divergence of the system from unstable steady states is observed after switching off the stabilizing controller. 3.1. Mixture. For the experiments, a ternary mixture was found which met the various constraints introduced by the plant setup, safety considerations, cost concerns, and operational requirements. The mixture (methanol-methyl butyrate-toluene), feed composition, and thermodynamic properties chosen by Gu¨ttinger et al. (1997) are used here. The feed composition (mass fractions: 0.66 methanol, 0.06 methyl butyrate, 0.28 toluene) was optimized to obtain a large product flow rate multiplicity range (parameter interval where MSS exist). The residue curve diagram for this mixture is
Figure 5. Mass balance lines of selected steady states (nos. 1-6) for columns with an infinite number of trays operating at infinite reflux.
given in Figure 2. The mixture is in the class 001 according to the classification by Matsuyama and Nishimura (1977). 3.2. ∞/∞ Predictions of Temperature Profiles. Column temperature control is common practice. Using flow as the manipulated variable, the temperature on a given location is controlled often as a substitute for
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Figure 6. Illustrations of ∞/∞ temperature profiles corresponding to the steady state nos. 1-6 in Figure 5.
product composition. In the case of columns with multiple steady states, the applicability of this technique needs to be further investigated. In this section, the ∞/∞ analysis will be used to generate qualitative pictures of the temperature profiles for all steady states. The argumentation presented here can be applied to any column operating on a 001 class mixture like methanolmethyl butyrate-toluene. In section 3.3 it will be discussed how temperature profile control can be used to stabilize the column and to track different unstable steady states. For the ∞/∞ case, the product compositions of a distillation column can be predicted along the bifurcation path (as the distillate flow rate D is varied from zero to the feed flow rate F) to obtain the product paths. These ∞/∞ product paths are illustrated in Figure 3. Each product path is composed of three sections of operating points (steady states) of a different type (I, II, or III). For type I, the distillate is located at the
unstable node (Az), for type II, the bottoms is at H, and for type III, the column profile includes at least one saddle point (L or I). The corresponding types are also shown in the bifurcation diagram (Figure 4), where the first branch (starting at D ) 0) contains only profiles of type I, the next branch contains only type III profiles, and the last branch (ending at D ) F) contains type III and II profiles. In the following, these branches will be called low, intermediate, and high branch, respectively. In the case of infinite reflux flow, the composition profile of a packed column follows a residue curve (Laroche et al., 1992a). The temperature is monotonically increasing along residue curves (Doherty and Perkins, 1978). Columns with an infinite number of stages must contain at least one pinch point (singular point) in the column profile. These facts can be used to generate a qualitative picture of temperature profiles in ∞/∞ columns. We define the following:
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A temperature plateau is the part of the temperature profile at a pinch point. A temperature front is a part of the temperature profile where a sharp change in temperature occurs along a finite length. Therefore, ∞/∞ temperature profiles contain at least one plateau. The plateaus are connected by temperature fronts. In order to describe the ∞/∞ temperature profiles of a 001 class mixture, we denote (Figure 5) the following: Plateau a is the plateau at the L-H azeotrope (TAz). Plateau l is the plateau at the light component (TL). Plateau i is the plateau at the intermediate component (TI). Plateau h is the plateau at the heavy component (TH). Front 1 is the front containing temperatures between TAz and TL. Front 2 is the front containing temperatures between TL and TI. Front 3 is the front containing temperatures between TI and TH. Taking the composition profiles obtained from the ∞/∞ analysis, the corresponding temperature profiles can be constructed using the boiling temperature diagram (Figure 3). Figure 6 shows the temperature profiles for selected steady states depicted in Figure 5. For an operating point of type I (e.g., steady state no. 1 in Figures 5 and 6.1), the distillate is located at the azeotrope (pinch point) and, hence, there is a plateau with TAz at the top of the column. The part of the residue curve between D and B results in a temperature front at the bottom of the column. For an operating point of type III (e.g., steady state no. 3 in Figures 5 and 6.3), there is a front at the top and a plateau at TL. Then, the temperature rises to TI (Front 2), and another plateau is obtained for the saddle pinch point I. In the same way, the third front at the bottoms of the column is obtained. Similarly, the shapes of the other profile types are obtained. 3.3. Predictions of Temperature Profile Movement. Moving along the continuation path defined in the previous section and starting at D ) 0, first all type I profiles are obtained (Figure 4). All of them have the shape depicted in Figure 6.1, with temperature fronts of varying size at the bottom. The type II profiles are obtained at the end of the bifurcation path ending at D ) F. They have the shape of Figure 6.6. The remaining profiles on the intermediate and the high branch of the continuation path are of type III. The product paths and composition profiles of all type III operating points coincide with the residue curve boundary running from Az over L and I to H (Figure 3). Since the temperature is monotonically increasing along any residue curve (Doherty and Perkins, 1978), the temperature will monotonically increase along the mentioned residue curve boundary:
TAz < TL < T1 < TI < T2 < TH
(1)
Looking at the temperature profile of steady state no. 2 in Figure 6.2, it is obvious that only temperatures between TAz and T2 occur along the temperature profile. Similarly, only temperatures between T1 and TH occur along the temperature profile of steady state no. 5. Therefore, only temperatures between T1 and T2 occur somewhere along the temperature profile for all steady states with type III profiles.
Figure 7. Simulation setup for the pilot column.
Thus, if all operating points of type III need to be controlled using a fixed reference temperature, this temperature has to be chosen between T1 and T2. After fixing T1 < Tref < T2, it remains to show that there will be a unique measurement location for each of the operating points of type III. Then it would be possible to control all type III steady states by an appropriate selection of the measurement location (using Tref as the reference temperature). In the following, the column is divided into an “upper part” above the reference temperature and a “lower part” below it. Imagine that we move along the type III section of the product paths shown in Figure 3. The distillate starts at the azeotrope, moves over to the light component corner and ends at point 1. Since D is located on the residue curve boundary, the distillate temperature TD will monotonically increase along this section of the path, starting at TD ) TAz and ending at TD ) T1. Thus, the difference between the constant reference temperature Tref (Tref > T1) and the distillate temperature, i.e., |Tref - TD|, will monotonically decrease along this section of the path. Similarly, the bottoms temperature increases from TB ) T2 to TB ) TH and, hence, the difference |TB - Tref| is monotonically increasing along this section. Therefore, measuring the “sizes” of the lower and upper parts of the column on a temperature scale, the upper part would become smaller and the lower part would get larger as D and B move along the product paths. In other words, the reference temperature dividing the column into the parts is “moving” toward the top of the column (from a relative point of view). Thus, the temperature front containing Tref is moving upward. Note that this illustration can only be formulated in the ∞/∞ case. The spatial location of the reference temperature is difficult to interpret since each plateau and the whole column is of infinite length. However, as we go to a finite but sufficiently large number of stages while keeping the reflux flow infinite, the location of the reference temperature will be defined. This location will move up even in the finite column, since (a) the temperature properties of the profiles are still the same (at infinite reflux, the profiles follow residue curves and subcooling of streams can be neglected) and (b) the product paths change only by a little as long as the number of trays is large enough (they will not approach the pinch points any more).
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Figure 8. Steady-state bifurcation diagram showing the distillate compositions of the simulations (Aspen Plus) and the ∞/∞ theoretical predictions.
To summarize, the ∞/∞ predictions can be used to generate a qualitative picture of the temperature profiles and their behavior as the continuation path is tracked. They were used to show the suitability of temperature control for 001 class mixtures. The temperatures T1 and T2 can be determined at a very preliminary stage of the control system design and bound the interval of feasible reference temperatures (in the ∞/∞ case). However, it is not possible to quantify the column length (number of stages) and reflux flow sufficient for the predictions to carry over. Therefore, simulations were done to show that control via temperature is applicable to the current pilot column described in section 4. 3.4. Steady-State Simulations. The predicted steady-state solution branches were verified using the RADFRAC distillation model and the commercial steadystate simulator Aspen Plus (Aspen, 1995). The simulation setup is shown in Figure 7. The simulation parameters were chosen to approximate as closely as possible the real operating conditions described in section 4. A Murphree efficiency of 0.5 was assumed. The coefficients for the thermodynamic models (Antoine and Wilson) are taken from Gu¨ttinger et al. (1997). In Figures 8 and 9, bifurcation diagrams are shown that compare steady-state simulation results obtained from Aspen with ∞/∞ predictions. The ∞/∞-predicted operating points requiring high separation power (e.g., close to the limit point at D ) 2.6 kg/h) could not be obtained with the Aspen model because of the finite reflux and the finite number of trays assumed in that model. The column temperature profiles generated by Aspen for the steady states in Figure 10a are given in Figure
Figure 9. Steady-state bifurcation diagram showing the bottoms compositions of the simulations (Aspen Plus) and the ∞/∞ theoretical predictions.
10b. For steady state nos. 1-9, at least one temperature front exists in the column. Note that due to the finite reflux and column length, the simulations for steady state nos. 1-5 exhibit Front 2 in the rectifying section rather than at the top of the column as predicted by the ∞/∞ analysis. The differences between the simulated and the predicted temperature profiles have various reasons. First, the boiling temperature difference between the azeotrope and pure methanol is very small. Thus, Front 1 is hard to see. Then, the part of Front 3 with temperatures between the boiling temperatures of methyl butyrate and toluene is flat compared to the other part of that front. Finally, the profiles are disturbed by the (subcooled) feed causing a front not matched by the predictions in sections 3.2 and 3.3. 3.5. Control Strategy. The aim of the experiments was to show the existence of multiple steady states including the intermediate (unstable) steady-state solution branch. Hence, a suitable control strategy for stabilizing the unstable steady states was required. Using the ∞/∞ predictions, it was shown that temperature fronts move monotonically upward through the column as the intermediate branch is tracked. Thus, control of the temperature front position can be used for stabilization on this branch. Rigorous simulations confirm these results obtained from the ∞/∞ analysis and are presented in Figure 10. These simulations predict the existence of a steep temperature front in the stripping section of the column for all intermediatebranch (unstable) solutions. Furthermore, a front moves through the rectifying section of the column as the high branch is tracked. Note that, in open-loop configura-
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Figure 10. Bifurcation diagram showing (a) the toluene composition in the bottoms and (b) the temperature profiles for selected steady states simulated with Aspen Plus.
tions, the steady state nos. 6-9 in Figure 10 are unstable, whereas the others are stable. To obtain the steady states on the high and the intermediate branches, the temperature front was fixed at different positions in the column by adjusting the distillate flow rate with simple PI control. Note that the front is easily fixed by specifying a given temperature on a certain tray. To move the front from one position to another, the location of the control input was switched from one tray to another as shown in Figure 14. The temperature setpoint was fixed at 361 K (i.e., on Front 2) for this procedure. 3.6. Dynamic Simulations. The second major task of this study was to examine dynamic stability. To study this stability and transient behavior in the region of multiple steady states, dynamic simulations were performed with Diva (Kro¨ner et al., 1990). Note that the steady-state predictions from Diva are in good agreement with the Aspen model. The same thermodynamic models and parameters were used for the calculation of VLE in both simulations. The dynamic simulations are illustrated in Figure 11. The transient propagation of the temperature profiles is given for two different disturbances (described below) imposed on the same plant at an open loop-unstable steady state. The arrows in Figure 11 indicate the directions of profile propagation. Further, the corresponding transient plots of the product compositions in the bottoms and the distillate for both simulations are shown in Figures 12 and 13, respectively. In the present case, the unstable steady state lies on a separatrix between the domains of attraction of the
Figure 11. Simulated (Diva) transient processes from the intermediate unstable steady state toward (a) the high and (b) the low stable steady-state branch (∆t ) 2 h between different profiles). Note that there is an overshoot of the temperature profiles during the transient in part a.
two stable steady states. Therefore, small disturbances differing only in sign were applied to generate Figure 11. The nominal value of the distillate flow rate in Figure 11 is 3.937 L/h. The other specifications are as shown in Figure 7. For Figure 11a, the distillate flow rate was increased by 0.5% over a period of 0.5 h and afterward set back to its nominal value in order to push the temperature profile in the direction of the upper steady state. Likewise, the distillate flow rate was decreased by 0.5% over a period of 0.5 h for Figure 11b. Note that an increased distillate flow rate corresponds to a reduced reflux flow rate at constant boilup. Since the external flow rates were small compared to the internal flow rates, holdup changes inside the column were slow. The transient responses in Figures 12 and 13 are strongly asymmetric, indicating that the system is highly nonlinear. 4. Pilot-Plant Description Experiments were carried out in a pilot-plant distillation column located at the Institut fu¨r Systemdynamik und Regelungstechnik in Stuttgart, Germany. The simplified flow sheet of the column configuration used for the experiments is shown in Figure 14. The column is made of glass and is equipped with 40 bubble cap trays. It has a diameter of 100 mm and a height of about 7 m. The column is equipped with a total condenser and a partial reboiler that is heated electrically. The column was operated at atmospheric pressure. The temperature and flow rate of the feed
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Figure 14. Simplified flow sheet of the column configuration used for the experiments.
Figure 12. Distillate compositions corresponding to the simulated transient processes in parts a and b of Figure 11.
Figure 15. Measured temperatures of (a) selected trays and (b) distillate flow rate before and after a setpoint change. Figure 13. Bottoms compositions corresponding to the simulated transient processes in parts a and b of Figure 11.
entering on tray 21 were controlled automatically. The temperature is measured on each tray of the column. Liquid flow rates are measured with reciprocating piston flowmeters. An industrial distributed control system (PLS 80 from IC Eckhardt) was used for column operation and the recording of about 100 analog and 200 binary signals.
About 30 basic control loops for level, flow, or heating control were implemented on the PLS 80 system. A detailed description of the pilot plant is given in Lang (1991). 5. Experimental Results 5.1. Application of the Control Strategy. For the high and intermediate steady-state branches, simple PI
Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 513 Table 1. Distillate Flow Rates and Positions of the Temperature Front in the Column for the Steady States Measured no. of SS 1 temp. control on tray no. D [kg/h] D [L/h]
10 3.21 4.00
2 13 3.12 3.91
3 15 3.09 3.87
4 17 3.08 3.87
5 19 3.03 3.81
Figure 16. Bifurcation diagram showing (a) the measured toluene composition in the bottoms and (b) the measured temperature profiles at steady state.
control was used to fix the temperature on a given tray. Figure 15a shows the dynamic measurements of the temperatures around tray no. 25 during a setpoint change from steady state no. 7 to no. 8. The path of the control variable D is given in Figure 15b. For steady states on the low branch there is no sharp temperature front along the column. As these steady states are open loop stable, that branch was tracked without stabilizing control by adjusting the distillate flow rate to different values. Similar to Gu¨ttinger et al. (1997), the heating rate was adjusted to keep the measured reflux approximately constant under steady-state conditions. The condenser level was controlled using the reflux flow rate. The level of the reboiler was controlled with the bottoms flow rate. Since the bottoms flow rates on the intermediate unstable steady-state branch are very small, continuous control was not possible. Instead, a two-point controller with hysteresis was used. Steady-state deviations of the reboiler level were always smaller than (2%. 5.2. Steady-State Measurements. The steadystate distillate flow rates D of the 12 measured steady states are given in Table 1. As the temperature front was shifted along the column from top to bottom, the
6 22 3.07 3.85
7 26 3.17 3.96
8 30 3.21 4.01
9 34 3.24 4.05
10
11
12
D was adjusted 3.21 4.00
3.15 3.93
3.07 3.83
Figure 17. Measured and simulated (Aspen Plus) steady-state distillate compositions.
corresponding steady-state distillate flow rates decreased (SS nos. 1-5). After the temperature front passed the feed tray, D increased (SS nos. 5-9). For steady state nos. 10-12, D was manually adjusted to decreasing values because no temperature front was available for control. Obviously for some distillate flow rates within the observed interval, three different steady-state temperature profiles exist. The distillate flow rate was measured with a reciprocating piston flowmeter. Measurement errors are smaller than (0.5% of the actual flow rate, whereas the multiplicity region is on the order of 6%. Furthermore, the flow rates presented in Table 1 are averaged over a period of several hours of steadystate operation. The measured temperature profiles at steady state are shown in Figure 16. The differences between measured and predicted temperature profiles can be explained with the same arguments used in section 3.4 to explain the differences between simulated and predicted temperature profiles. GC analysis of the bottoms (Figure 17) and distillate products (Figure 18) at the different steady states showed markedly different compositions. Because the product compositions on the different solution branches differ by up to 40%, measurement errors can be excluded as a reason for the multiplicities.
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Figure 18. Measured and simulated (Aspen Plus) steady-state bottoms compositions.
Thus, it can be claimed that three different steadystate column profiles exist for any given D in the interval from 3.03 to 3.24 kg/h. 5.3. Dynamic Measurements. For the dynamic measurements, the plant was restarted with the controller set to stabilize the column at the open-loop unstable steady state no. 7. After the controller was switched off, volumetric flow rates were fixed at the steady-state values. For the next 20 h, only bottoms samples were drawn in order to reduce the disturbances to a minimum. After the bottoms composition analysis clearly indicated that the plant was diverging from the unstable steady state, distillate samples were taken at regular intervals. In Figure 19, bottoms compositions are plotted together with the steady-state measurements. These figures clearly indicate that the process reached a stable steady state on the high branch. Product flow rates were measured by volume. Therefore, measurements were converted to mass flow rates by Aspen given the measured compositions and temperatures. Because the volumetric flow rates were held constant throughout the dynamic process but product compositions changed, the calculated mass flow rates as shown in Figure 19 were not constant. Due to slight variations in the calibrations of the flowmeters, steady state no. 7 was not reproduced exactly, but with a flow rate what was 1.5% smaller. The dynamic responses of the bottoms and distillate compositions are shown in Figures 20 and 21. Also shown is a comparison between the measured compositions and the dynamic simulation in Diva. Measurements and simulations are in good agreement. Note that the disturbance assumed in the dynamic simulations (see section 3.6) was chosen to meet the measured
Figure 19. Measured steady-state bottoms compositions together with the measured bottoms compositions during the transient process.
Figure 20. Measured and simulated (Diva) composition of the distillate during the transient process from an unstable to a stable steady state on the high branch.
behavior of the plant after stabilizing control was switched off. The real disturbance which caused the
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Acknowledgment We gratefully acknowledge ALOWAG AG, Reinach BL, Switzerland for lending us excellent mixing equipment. Further, we thank G. Kolios and Prof. G. Eigenberger from ICVT Stuttgart for providing the gas chromatograph. The help of A. Spieker with the Diva real-time environment is gratefully acknowledged. We also thank our students L. Berninger, F. Bitsch, P. Holl, and E. Mayer and our colleague A. Rehm for their support during the very time-consuming experiments. Finally, the experiments would not have been possible without the never-ending support provided by Adelheid and Karl-Henning Seemann. Literature Cited
Figure 21. Measured and simulated (Diva) composition of the bottoms during the transient process from an unstable to a stable steady state on the high branch.
plant to diverge from the unstable steady state could have been of an entirely different nature. 6. Conclusions Multiple steady states were observed for the homogeneous azeotropic mixture methanol-methyl butyratetoluene in a pilot-plant distillation column. To examine both stable and unstable steady states, a control strategy is applied that utilizes the propagation of a temperature front along the column. Arguments are given which indicate that this strategy is also applicable to other mixtures of the same type. Since the departure from the unstable steady state was very slow in the current experiment, stabilization of the unstable steady states was possible with simple PI control. Open-loop instability was confirmed experimentally and in simulations. In addition, the transient response of the plant from an unstable to a stable steady state was observed. The steady-state experiments are shown to be in good qualitative agreement with the theoretical predictions obtained for the limiting case of an infinitely long column operated at infinite reflux. Furthermore, the steady-state and dynamic experiments are in good agreement with predictions obtained from numerical simulations.
Aspen. Aspen Plus Release 9 Reference Manual: Physical Property Methods and Models; Aspen Technology Inc.: Ten Canal Park, Cambridge, MA, 1995. Bekiaris, N.; Meski, G. A.; Radu, C. M.; Morari, M. Multiple Steady States in Homogeneous Azeotropic Distillation. Ind. Eng. Chem. Res. 1993, 32 (9), 2023. Doherty, M. F.; Perkins, J. D. On the Dynamics of Distillation Processes I: The Simple Distillation of Multicomponent NonReacting Homogeneous Liquid Mixtures. Chem. Eng. Sci. 1978, 33, 281. Gu¨ttinger, T.; Dorn, C.; Morari, M. Experimental Study of Multiple Steady States in Homogeneous Azeotropic Distillation. Ind. Eng. Chem. Res. 1997, 36 (3), 794. Kienle, A.; Groebel, M.; Gilles, E. D. Multiple Steady States in Binary DistillationsTheoretical and Experimental Results. Chem. Eng. Sci. 1995, 50 (17), 2691. Kro¨ner, A.; Holl, P.; Marquardt, W.; Gilles, E. Divasan open architecture for dynamic simulation. Comput. Chem. Eng. 1990, 14, 1289. Lang, L. Prozessfu¨hrung gekoppelter Mehrstoffkolonnen am Beispiel einer Destillationsanlage mit Seitenabzug. Ph.D. Dissertation, University of Stuttgart, Stuttgart, Germany, 1991. Laroche, L.; Bekiaris, N.; Andersen, H. W.; Morari, M. Homogeneous Azeotropic Distillation: Separability and Flowsheet Synthesis. Ind. Eng. Chem. Res. 1992a, 31 (9), 2190. Laroche, L.; Bekiaris, N.; Andersen, H. W.; Morari, M. The Curious Behavior of Homogeneous Azeotropic Distillations Implications for Entrainer Selection. AIChE J. 1992b, 38 (9), 1309. Matsuyama, H.; Nishimura, H. Topological and Thermodynamic Classification of Ternary Vapor-Liquid Equilibria. J. Chem. Eng. Jpn. 1977, 10 (3), 181. Petlyuk, F. B.; Avetyan, V. S. Investigation of Three Component Distillation at Infinite Reflux (in Russian). Theor. Found. Chem. Eng. 1971, 5 (4), 499.
Received for review May 13, 1997 Revised manuscript received October 29, 1997 Accepted October 30, 1997X IE9703447
X Abstract published in Advance ACS Abstracts, December 15, 1997.
