Experimental Verification of Multiple Steady States in Heterogeneous

Nov 1, 1997 - An experimental study of ethanol dehydration with cyclohexane as the entrainer has been carried out in order to verify the existence of ...
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Ind. Eng. Chem. Res. 1997, 36, 5410-5418

Experimental Verification of Multiple Steady States in Heterogeneous Azeotropic Distillation Dirk Mu 1 ller and Wolfgang Marquardt* Lehrstuhl fu¨ r Prozesstechnik, RWTH Aachen, D-52056 Aachen, Germany

An experimental study of ethanol dehydration with cyclohexane as the entrainer has been carried out in order to verify the existence of multiple steady states in heterogeneous azeotropic distillation. As a basis, the bifurcation diagram for the ethanol product purity is determined from thermodynamic considerations using the distillate flow rate as the bifurcation parameter. The predicted multiple steady states are then verified by rigorous simulation and by experiments on a laboratory tray column with a decanter. The hysteresis behavior due to multiple steady states is also verified in a dynamic experiment. 1. Introduction Heterogeneous azeotropic distillation is an economically interesting process to separate azeotropic or close boiling mixtures at a low-energy consumption and on a low-temperature level. However, in industrial applications the economic potential of heterogeneous azeotropic distillation is sometimes not considered due to potentially severe control problems. In this contribution the complex stationary and dynamic process behavior is analyzed with regard to the existence of multiple steady states. The objective of these investigations is the development of a deeper process understanding as a basis for an integrated design also considering operability. Several simulation studies have been published analyzing the behavior of heterogeneous azeotropic distillation. In particular, ethanol dehydration processes using benzene as the entrainer have been studied extensively. Magnussen et al. (1979) first reported simulation results for this process showing the existence of different composition profiles and product compositions for the same column specifications, i.e., output multiplicities, in this paper denoted by the general term multiple steady states. Subsequent contributions present further simulation results showing the existence of multiple steady states for different heterogeneous mixtures (e.g., Prokopakis and Seider, 1983; Kovach and Seider, 1987a; Cairns and Furzer, 1990b; Bossen et al., 1993). Recently, the sources of multiple steady states in distillation processes have been analyzed. Three different sources are known (Kienle et al., 1995): first, the nonlinear input transformation between mass or volumetric and molar flow rates (Jacobsen and Skogestad, 1991), second, interactions between flows and compositions (Jacobsen and Skogestad, 1991), and third, the thermodynamic behavior (Petlyuk and Avet’yan, 1971; Kienle and Marquardt, 1991; Bekiaris et al., 1993). For homogeneous distillation processes experimental verifications have been presented for the first type of multiple steady states (Kienle et al., 1995; Koggersbøl et al., 1996) as well as for the third type (Gu¨ttinger et al., 1997). Furthermore, Bekiaris et al. (1996) have shown that multiple steady states due to the thermodynamic behavior of the mixture can also arise over a wide range of operating parameters in heterogeneous * Author to whom correspondence should be addressed. Phone: +49 241 80 4668. Fax: +49 241 8888 326. E-mail: [email protected]. S0888-5885(97)00283-2 CCC: $14.00

Figure 1. Azeotropic column with a decanter for ethanol dehydration using cyclohexane as the entrainer. For illustration molar flow rates and molar compositions of a typical laboratory test run are presented.

azeotropic distillation. They presented the corresponding thermodynamic considerations for columns with a decanter and formulated a multiplicity condition which is necessary and sufficient for thermodynamically induced multiplicities. However, to our knowledge no experimental data reported in the literature confirm the existence of multiple steady states in heterogeneous azeotropic columns as predicted theoretically. The few data available from heterogeneous azeotropic distillation experiments (Kovach and Seider, 1987b; Wang et al., 1997) belong to steady states with different operating parameters. Thus, these data cannot answer the question if multiple steady states exist in reality. This work presents the first experimental verification of multiple steady states in heterogeneous azeotropic distillation. Ethanol dehydration is considered as a sample problem, which has been chosen due to its technical importance. Several sequences with two, three, or four distillation columns have been proposed for this process (e.g., Ryan and Doherty, 1989), and several entrainers have been discussed (e.g., Furzer, 1994). As a first step, this paper focuses on the behavior of the azeotropic column with a decanter, as shown in Figure 1. Cyclohexane is chosen as a favorable entrainer. Typically, the feed to the azeotropic column does contain not only ethanol and water but also a small fraction of the entrainer cyclohexane (e.g., 0.07 mol/mol) coming from a recycle. The azeotropic column produces pure ethanol as the bottoms product. The overhead vapor is condensed and split into two liquid phases. The organic, entrainer-rich phase is totally recycled as reflux, whereas the aqueous phase is partially taken off © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5411

Figure 3. Feasible product compositions for ∞/∞ columns with a decanter. Figure 2. Residue curve diagram (mole fractions) of ethanol/ water/cyclohexane at a pressure of 101.3 kPa. Binodal curves are shown for boiling point conditions (VLLE) and for a constant temperature of 298.15 K (LLE-298.15 K). b: azeotropic points. O: critical points.

as distillate. For illustration purposes, Figure 1 shows molar compositions and flow rates from a typical test run on a laboratory column. 2. Predictions for ∞/∞ Columns Thermodynamics. The multiple steady states discussed in this paper are due to the thermodynamic behavior of the system ethanol/water/cyclohexane. Mixture thermodynamics can be represented by a residue curve diagram, as shown in Figure 2. To calculate the residue curves, a high-quality extended NRTL model fitted to experimental vapor-liquid-liquid equilibrium (VLLE) data (Connemann et al., 1990) has been used, as experimental VLLE data are only poorly represented by common GE models such as NRTL or UNIQUAC. The correlation parameters are given in the appendix. In addition, Figure 2 shows two binodal curves. The inner binodal curve is calculated at boiling point conditions to describe the liquid phase split on column trays. The outer binodal curve is calculated at a constant temperature of 298.15 K to describe the liquid phase split in the decanter. Note that for an accurate liquidliquid equilibrium (LLE) description at 298.15 K a second set of NRTL parameters (see appendix) has been fitted to experimental data from Moriyoshi et al. (1991). The composition triangle further shows the corresponding critical points as well as the three binary azeotropes and the ternary heteroazeotrope. The system ethanol/water/cyclohexane is characterized by three distillation regions. This thermodynamic behavior implies that the bottoms product of a distillation column approaches either pure ethanol, pure water, or pure cyclohexane. In all regions the top composition tends toward the heterogeneous azeotropic point. If the top composition is inside the heterogeneous region, then a liquid phase split occurs in the decanter and the composition of the distillate, taken from the aqueous phase, corresponds to a point on the outer binodal curve. ∞/∞ Analysis. To analyze the existence of multiple steady states in azeotropic columns with a decanter, ∞/∞ analysis is applied as introduced by Petlyuk and Avet’yan (1971) for homogeneous columns and reformulated by Bekiaris et al. (1996) for heterogeneous columns. A theoretical column with an infinite number of trays and

Figure 4. ∞/∞ Predictions for the distillate compositions.

with an infinite reflux is considered. The molar feed composition is fixed to 0.823/0.107/0.070 (ethanol/water/ cyclohexane). For ∞/∞ columns the composition profiles can be approximated by residue curves and must further satisfy two constraints. First, the product compositions must satisfy the component mass balances. Second, the composition profiles must contain at least one pinch point; i.e., they must contain at least one pure component or azeotrope as the number of stages is assumed to be infinite. From these constraints it can be concluded that all possible compositions of the distillate and the bottoms product belong to the paths shown in Figure 3. These product composition paths can easily be obtained by tracking all mass balances by varying the molar flow rate ratio of the distillate and the feed (D/F) from 0 to 1. In Figures 4 and 5 the distillate and the bottoms compositions are plotted versus the molar flow

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Figure 5. ∞/∞ Predictions for the bottoms compositions.

rate ratio D/F, which is used as the bifurcation parameter. Three regions are shown. For D/F below 0.22 (region I) one steady state is predicted, which is characterized by liquid phase splitting in the decanter. For D/F between 0.22 and 0.48 (region II) three steady states are shown. Two of them show phase splitting in the decanter; the third one is characterized by a homogeneous state in the decanter. Finally, for D/F larger than 0.48 (region III) one homogeneous steadystate is predicted. In the following the different steady state branches are as usual denoted as low-purity branch, unstable branch, and high-purity branch. Note that this denotation refers to the ethanol purity in the bottoms product. Note further that for simplification residue curves have been considered instead of distillation lines, which should generally be used if tray columns are analyzed. However, this simplification does not yield significant errors for the system ethanol/water/cyclohexane as the relevant section of the boundary residue curve used in the ∞/∞ analysis is nearly a straight line and therefore coincides with the corresponding boundary distillation line. Thus, the ∞/∞ criterion predicts multiple steady states over a wide range of the distillate flow rate and product composition. Hence, the considered industrially relevant sample problem is well suited for a reproducible experimental verification of multiple steady states. 3. Rigorous Modeling and Simulation Modeling Heterogeneous Azeotropic Distillation. In order to extend the bifurcation analysis to real columns with a finite number of trays and a finite reflux, a rigorous model of heterogeneous azeotropic distillation is required. In this work the azeotropic column is described by a three-phase distillation model based on

Figure 6. Comparison of ∞/∞ predictions (s) with simulation results for the laboratory column (+, stable; *, unstable steady states). Bifurcation diagrams for the distillate compositions.

the concept of equilibrium stages. The model equation system comprises mass and energy balance equations, equilibrium conditions, mole fraction summations, the volume constraint, and relations for the vapor and liquid flows from the stage. As the equation system shows a variable structure depending on the number of coexisting phases, the model must further include a method to determine the phase number and to adapt the model to the phase number. For this purpose a method for quick phase determination based on necessary equilibrium conditions is applied (Mu¨ller and Marquardt, 1997). Basic assumptions of the equilibrium stage model are that each phase is ideally mixed and that the phases are in thermodynamic equilibrium. In reality, however, three-phase distillation stages contain vapor-liquidliquid dispersions, where a number of kinetically controlled processes occur, i.e., mass transfer, particle breakage, coalescence, nucleation, and dissolution, which are not considered in the equilibrium stage model. From published investigations on three-phase distillation (Kovach and Seider, 1987b; Davies et al., 1987; Herron et al., 1988; Cairns and Furzer, 1990a) contradictory conclusions concerning three-phase tray or column efficiencies have been drawn as pointed out by Widagdo and Seider (1996). Therefore, the equilibrium stage model has been validated for the considered ethanol dehydration process in a previous study (Mu¨ller et al., 1997). The model prediction has shown a generally good agreement with experimental data if the overall column efficiency is adjusted accordingly. An overall column efficiency of about 70% has been established in all cases regardless of phase splitting on individual trays.

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Figure 7. Comparison of ∞/∞ predictions (s) with simulation results for the laboratory column (+, stable; *, unstable steady states). Bifurcation diagrams for the bottoms compositions.

Simulation of Multiple Steady States. The validated model is used to calculate the bifurcation diagram for the laboratory column with a decanter as presented in the next section. Six theoretical stages are used to describe the eight-tray laboratory column, corresponding to an overall column efficiency of 0.75. In the simulations the molar feed composition is set to 0.823/ 0.107/0.070 (ethanol/water/cyclohexane) and the molar feed rate is fixed to 1.049 × 10-3 mol s-1. In addition, the column top pressure (101.3 kPa), the decanter pressure (101.3 kPa), the decanter temperature (298.15 K), and the reboiler heat input (285 W) are specified. The distillate flow rate is varied as in the ∞/∞ analysis. Figures 6 and 7 illustrate that the simulation results show basically a good agreement with the ∞/∞ predictions, confirming the conjecture of multiple steady states for the laboratory column. Conversely, the good agreement implies that the multiple steady states predicted by the equilibrium stage model are due to the characteristics of the thermodynamic behavior and not due to other sources. The deviations shown in Figures 6 and 7 illustrate the limitations of real columns which contain a finite number of trays and which are operated at finite reflux. For example, real columns cannot produce pure ethanol as predicted for ∞/∞ columns. The maximum molar ethanol purity found in simulations for the short laboratory column is 0.985. Column composition profiles of three different steady states are shown in Figure 8. All three column profiles have been calculated for the same set of operating parameters given above. Furthermore, in all cases the molar ratio D/F is set to the same value (0.40). The three composition profiles I, II, and III correspond to operating points on the high-purity branch, the unstable

Figure 8. Three different steady states for the same column specifications. Simulated molar composition profiles for the laboratory column (equilibrium stage model, six ideal stages).

branch, and the low-purity branch, respectively. The following characteristics are obvious from Figure 8. Profiles I and II are characterized by a top composition within the heterogeneous region, whereas profile III is entirely within the homogeneous region. Both heterogeneous profiles approach pure ethanol as the bottoms product, but the paths are different. Profile I approaches the product ethanol from the ethanol/cyclohexane edge corresponding to an ∞/∞ column profile with a pinch at the binary azeotrope of ethanol/cyclohexane. In contrast, profile II approaches the product ethanol from the ethanol/water edge corresponding to an ∞/∞ column profile with a pinch at the binary azeotrope of ethanol/water. Volumetric Specification of the Distillate Flow. So far, it has been assumed that the distillate flow rate used as the bifurcation parameter is given on a molar basis. However, in the experiments presented in the next section the distillate flow rate is manipulated by adjusting the power of a pump. Thus, in fact the distillate flow rate is specified on a volumetric basis. Figure 9 illustrates the effect of the transformation from molar to volumetric flow rates on the predicted multiplicity region. Obviously, the range of the multiplicity region becomes smaller due to the transformation

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Figure 9. Bifurcation diagrams showing the transformation of molar to volumetric specification of the distillate flow rate. Simulation results (equilibrium stage model, six ideal stages).

to volumetric specifications. Nevertheless, the predicted region of multiple steady states is sufficiently large for a reliable experimental verification. The reason for this reduction is that the molar density of the distillate changes along the product composition path. More specifically, on the high-purity branch the operating points are characterized by a high distillate density due to the high water content of the distillate taken from the aqueous phase of the decanter. In contrast, on the low-purity branch the molar density of the distillate taken from a homogeneous decanter is significantly lower due to a lower water and higher cyclohexane content. The density differences cause in our case the reduction of the multiplicity region when the bifurcation diagram is transformed from molar to volumetric specifications. Note that, in general, the transformation from molar to mass or volumetric specifications may even cause the disappearance of multiple steady states predicted for molar specifications or, conversely, the occurrence of additional multiple steady states (Gu¨ttinger and Morari, 1997). 4. Experimental Verification Experimental Setup. The experiments are performed at Bayer AG, Leverkusen, on a laboratory plant shown in Figure 10 consisting of the main components condenser (a), column (b), reboiler (c), and decanter (f). The condenser is operated as a total condenser. The glass column contains bubble cap trays with a diameter of 50 mm. The rectifying section includes three trays; the stripping section includes five trays. The reboiler is equipped with two electrical heating elements. The liquid leaving the condenser is cooled to 293.15 K (e) and fed into the decanter to separate the two liquid phases. The organic phase is totally recycled into the column. The aqueous phase is split: A stream with a specified flow rate is taken off as the distillate; the remaining stream is recycled. The reflux is heated to 323.15 K (g) before it is supplied to the column.

Figure 10. Laboratory column with a decanter: (a) condenser, (b) bubble cap tray column, (c) reboiler with electrical heating elements, (d) feed preheater, (e) cooler, (f) decanter, (g) reflux heater.

To avoid internal reflux caused by heat losses, an adiabatic jacket is placed around the column which consists of two insulation layers with integrated heating elements. The heating elements are adjusted to prevent wall heat flux. For this purpose, temperatures measured within the insulation are controlled to be equal to the temperatures measured within the column. The experimental analysis is performed by measuring the top pressure, the pressure drop, and the internal and external flow rates as well as tray temperatures and compositions. The internal flow rates are measured indirectly via the heat released in the condenser, which is determined from the measured flow rate and temperature increase of the cooling water. The internal flow rate is then calculated from the heat of condensation and the measured composition of the condensate. Preliminary experiments to test this indirect technique have shown that internal flow rates can be measured with an accuracy of 2-3%. To determine tray compositions, vapor samples are taken from each tray with a syringe and dissolved in N-methyl-2-pyrrolidone (NMP) in order to avoid measurement errors due to partial condensation and subsequent splitting of the condensate. These samples are then analyzed by gas chromatography. The accuracy of the measured vapor mole fractions is (0.005. For details on the experimental techniques we refer to Mu¨ller et al. (1997). Steady-State Experiments. (a) Experimental Procedure. To verify experimentally the predicted

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Figure 11. Experimental measurements of the distillate composition in comparison with simulation results. s: equilibrium stage model, six ideal stages. +: experiment.

Figure 12. Experimental measurements of the bottoms composition in comparison with simulation results. s: equilibrium stage model, six ideal stages. +: experiment.

multiple steady states, composition profiles are measured for stable operating points both on the high-purity branch and on the low-purity branch. The operating parameters feed flow rate, reboiler heat input, column top pressure, decanter pressure, and decanter temperature are kept constant (Table 1) by fixing the power of the feed pump and of the electrical reboiler heating elements, by ventilating the column and decanter to the atmosphere, and by thermostating the decanter. Furthermore, the feed composition is kept constant and analyzed in each experiment. The remaining degree of freedom is satisfied by specification of the distillate flow rate which is used as the bifurcation parameter; i.e., the distillate flow rate is varied from experiment to experiment by adjusting the power of the distillate pump. Note that for the feed composition, chosen according to technically relevant conditions in ethanol dehydration, it is not possible to operate the laboratory plant on the unstable branch. The reason is that the unstable operating points are characterized by a top composition close to the critical point, as indicated in Figure 8. Batch settling experiments carried out for decanter design show that, in this case, the required decanter residence time is significantly higher compared to a top composition at normal operation, i.e., closer to the heterogeneous azeotrope. Thus, the liquid-liquid separation in the laboratory decanter designed for a top composition near the heteroazeotropic point becomes impossible. Hence, unstable steady states are not possible for the design parameters and operating conditions chosen. Consequently, the theoretical predictions cannot be verified in this case as kinetic phenomena in the decanter which have been neglected in the theoretical predictions become crucial.

The distillate flow rate taken as the bifurcation parameter is varied to track the stable branches of steady states. The experiments are started in region I, where only one steady state exists. Then the distillate flow rate is increased from experiment to experiment, step by step, in order to follow the high-purity branch. Conversely, the low-purity branch is measured starting from an operating point in region III by step by step reduction of the distillate flow rate. (b) Experimental Results. The bifurcation diagrams in Figures 11 and 12 present experimental results in comparison with simulation results. Excellent agreement of predicted and measured compositions is obtained for both stable branches, for the high-purity branch, and for the low-purity branch. Figure 13 shows the corresponding mass balance lines of these experiments in the composition triangle. The figure illustrates how the mass balance line turns around the feed point, when the distillate flow rate is varied. Let us consider the experimental data of different steady states for the same specifications more closely. The specified operating conditions and the measured composition profiles are listed in Tables 1 and 2. Steady state 1 is measured on the high-purity branch. Figure 14 shows the corresponding experimental composition profile in comparison with simulation results in the composition triangle as well as along the column height. The compositions of the feed, the bottoms, and both liquid phases in the decanter are denoted by F, B, D1, and D2, respectively, and the mass balances of the column and the decanter are represented by broken lines. Figure 14 shows good agreement between simulated and experimental results for the entire distillation process including the decanter. The overall column efficiency is 70%. It is further shown that the top tray

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Figure 13. Experimental product compositions and mass balance lines for different distillate flow rates. Operating conditions according to Table 1. Table 1. Heterogeneous Azeotropic Distillation Experiments: Specified Operating Parametersa feed rate (mL/h) feed temperature (K) molar feed composition top pressure (kPa) reflux temperature (K) reboiler heat input (W) decanter temperature (K)

217 333.15 0.823/0.107/0.070 101.3 323.15 285 293.15

a The molar feed composition is given in the order ethanol/water/ cyclohexane.

of the azeotropic column is heterogeneous whereas the lower trays are homogeneous. In the decanter a phase split occurs. The mass balance line of the decanter coincides with a tie-line of the corresponding isothermal binodal curve, which in this work is approximated by the binodal curve calculated for 298.15 K (see the appendix). Steady state 2 is measured on the low-purity branch. Again, good agreement between simulated and experimental results is obtained for the entire distillation process, as shown in Figure 15. In this case, the column profile is entirely within the homogeneous region. Even in the decanter no phase split is observed. Obviously, no effective separation is obtained at steady state 2 and, as a consequence, the product purity is low. Note that steady states 1 and 2 are obtained for exactly the same set of operating conditions. This verifies the existence of multiple steady states in real heterogeneous columns. Further, the experiments con-

Figure 14. Validated operation point on the high-purity branch (steady state 1). *: experiment, 7/24/96. s: equilibrium stage model (column efficiency: 70%). Operating conditions according to Table 1.

firm the theoretical predictions obtained by ∞/∞ analysis and simulation. Dynamic Experiment. One of the unusual phenomena induced by multiple steady states in distillation columns is the hysteresis behavior in operation and sudden excursions if a manipulated variable is switched for some time. To show experimentally the hysteresis due to multiple steady states, a dynamic experiment recording three tray temperatures is performed, as illustrated in Figure 16. The experiment is started from steady state A within the multiplicity region on the high-purity branch. At time 14 h the distillate flow rate is changed from 70 to 150 mL/h for a period of 6 h. For the high distillate flow rate only one steady state on the low-purity branch exists. As a consequence, a cata-

Table 2. Measured Molar Composition Profiles of Different Steady States for the Same Specifications (See Table 1; Distillate Flow Rate, 78 mL/h)a steady state 1 (high-purity branch) stage 1 (V) stage 2 (V) stage 3 (V) stage 4 (V) stage 5 (V) stage 6 (V) stage 7 (V) stage 8 (V) reboiler (V) decanter (L1) decanter (L2) reboiler (L) a

steady state 2 (low-purity branch)

ethanol

water

cyclohexane

ethanol

water

cyclohexane

0.362 0.389 0.406 0.430 0.441 0.487 0.536 0.667 0.822 0.107 0.631 0.958

0.111 0.078 0.065 0.045 0.038 0.011 0.016 0.019 0.039 0.004 0.250 0.013

0.527 0.533 0.529 0.525 0.521 0.502 0.448 0.314 0.139 0.889 0.119 0.029

0.712 0.835 0.864 0.884 0.888 0.891 0.889 0.883 0.888 0.644

0.094 0.105 0.108 0.107 0.110 0.109 0.111 0.117 0.112 0.086 no phase split 0.109

0.193 0.059 0.028 0.009 0.001 0.000 0.000 0.000 0.000 0.270

0.891

V: vapor measurement. L: liquid measurement (experiments: 7/24/96 and 9/11/96).

0.000

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5417

Figure 15. Validated operation point on the low-purity branch (steady state 2). *: experiment, 9/11/96. s: equilibrium stage model (column efficiency: 70%). Operating conditions according to Table 1.

Figure 16. Measured hysteresis due to multiple steady states. The transients are induced by temporary disturbances in the distillate flow rate from D0 to D+ or D- (gray regions). T1, T4, and T8 denote the temperatures on trays 1, 4, and 8, respectively.

strophic jump toward the low-purity branch is observed. Even though the distillate flow rate is changed back to the original value at time 20 h, the column does not tend toward the original steady state A but reaches a different steady state B on the low-purity branch. This hysteresis is also observed in the opposite direction. Continuing the experiment above, the distillate flow rate is disturbed during the time interval 4461 h to a value of 40 mL/h, for which only a steady state on the high-purity branch is possible. Consequently, a transient toward the high-purity branch is observed to be unaffected by the end of the disturbance at time 61 h. The final steady state is the same as the initial steady state A.

caused by the thermodynamic behavior of the system ethanol/water/cyclohexane. The focus of this work has been on the azeotropic column with a decanter of an ethanol dehydration process. In technical applications the azeotropic column and the decanter are integrated in a column sequence, which in many cases is highly integrated due to entrainer recycles. The analysis of interaction phenomena within these sequences is the next step in our current research directed toward the implications of multiple steady states on operation and control of heterogeneous azeotropic distillation.

Conclusions

Financial support of Bayer AG, Leverkusen, is appreciated. We are further grateful to Bayer AG for the opportunity to carry out these experiments in their laboratory. In particular, we thank T. Hauschild, G. Ronge, and H. Steude for many fruitful discussions and important suggestions. We also thank H. W. Kramer and G. Schnabel for their technical advice. Finally, we thank W. Klein, A. Du¨x, B. Rotter, and P. Dahlmeyer for their substantial contributions in carrying out the experiments.

In this work the existence of multiple steady states in heterogeneous azeotropic distillation has been verified experimentally for the first time. The different composition profiles, measured for the same column specifications, and the hysteresis, measured in a dynamic experiment, confirm the existence of multiple steady states as predicted in simulations. The experimental data are very close to simulation results obtained for the laboratory column using the equilibrium stage model with an overall column efficicency of 70%. In addition, the results are in good agreement with predictions from thermodynamic considerations for columns with an infinite number of trays and infinite reflux. This agreement implies that the existence of the validated multiple steady states is

Acknowledgment

Appendix In the following the thermodynamic models and parameters are presented, which are used in this study to calculate the VLLE and LLE of the system ethanol/ water/cyclohexane. LLE in the decanter is described

5418 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 Table 3. NRTL Model Parameters for the System Ethanol (1)/Water (2)/Cyclohexane (3) Fitted to LLE Data at 298.15 Ka ethanol/water g12 - g22 g21 - g11 R12 a

ethanol/cyclohexane g13 - g33 g31 - g11 R13

-10618.9 5987.95 0.35

3234.23 4567.51 0.47

g23 - g33 g32 - g22 R23

14213.9 2023.23 0.21

gij are given in J mol-1.

Table 4. Extended NRTL Model Parameters for the System Ethanol (1)/Water (2)/Cyclohexane (3) Fitted to p(x,T) Data at 333.1 K (Keil et al., 1994)a ethanol/water g12 - g22 g21 - g11 R12

241.824 4634.91 0.34750

ethanol/cyclohexane

water/cyclohexane

g13 - g33 g31 - g11 R13

g23 - g33 g32 - g22 R23

3663.26 5966.76 0.46261

36767.0 14036.3 0.21159

ethanol/water/cyclohexane ∆g123 ∆g213 a

water/cyclohexane

5789.98 -9645.53

∆g132 ∆g312

2573.26 -6122.53

∆g231 ∆g321

17804.3 151.907

gij and ∆gijk are given in J mol-1.

using the original NRTL equation:

GE ) RT

xi

∑jτjiGjixj ∑i ∑kxkGki

(1)

gij - gjj RT

(2)

τij )

Gij ) exp(-Rijτij)

(3)

where GE denotes the excess Gibbs energy, T the temperature, R the ideal gas constant, and x the molar liquid composition. The NRTL parameters, gij - gjj and Rij, fitted to LLE data at 298.15 K from Moriyoshi et al. (1991) are listed in Table 3. Note that the parameter fit has been restricted to the range of compositions considered in this work in order to obtain high accuracy. VLLE in the column is described using an extended NRTL model (Connemann et al., 1990; Keil et al., 1994) with modified interaction parameters

τ′ij )

∑

gij - gjj + kxk∆gijk RT

(4)

The NRTL parameters gij - gjj and Rij as well as the additional parameters ∆gijk improving the flexibility of the GE function are taken from Keil et al. (1994) and summarized in Table 4. These parameters are fitted to p(x,T) data at 333.1 K. Literature Cited Bekiaris, N.; Meski, G. A.; Radu, C. M.; Morari, M. Multiple Steady States in Homogeneous Azeotropic Distillation. Ind. Eng. Chem. Res. 1993, 32, 2023. Bekiaris, N.; Meski, G. A.; Morari, M. Multiple Steady States in Heterogeneous Azeotropic Distillation. Ind. Eng. Chem. Res. 1996, 35, 207. Bossen, B. S.; Jørgensen, S. B.; Gani, R. Simulation, Design, and Analysis of Azeotropic Distillation Operations. Ind. Eng. Chem. Res. 1993, 32, 620. Cairns, B. P.; Furzer, I. A. Multicomponent Three-Phase Azeotropic Distillation. 1. Extensive Experimental Data and Simulation Results. Ind. Eng. Chem. Res. 1990a, 29, 1349. Cairns, B. P.; Furzer, I. A. Multicomponent Three-Phase Azeotropic Distillation. 3. Modern Thermodynamic Models and Multiple Solutions. Ind. Eng. Chem. Res. 1990b, 29, 1383.

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Received for review April 11, 1997 Revised manuscript received August 28, 1997 Accepted August 29, 1997X IE970283C Abstract published in Advance ACS Abstracts, November 1, 1997. X