Start-up of Homogeneous Azeotropic Distillation Columns with

Ind. Eng. Chem. Res. 2004, 43, 553-565

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Start-up of Homogeneous Azeotropic Distillation Columns with Multiple Steady States Nicola´ s J. Scenna,*,†,‡ Sonia J. Benz,† Javier A. Francesconi,† and Ne´ stor H. Rodrı´guez† Grupo de Investigacio´ n en Informa´ tica Aplicada a la Ingenierıá Quı´mica (GIAIQ) (Facultad Regional Rosario, Universidad Tecnolo´ gica Nacional), E. Zeballos 1341, 2000 Rosario, Repu´ blica Argentina, and Instituto de Desarrollo y Disen˜ o (INGAR-CONICET), Avellaneda 3657-3000 Santa Fe, Repu´ blica Argentina

The impact of different start-up procedures on the behavior of two azeotropic distillation columns with multiple steady states is analyzed. Several dynamic simulation results for the two study cases are presented. Through an examination of the profile evolutions corresponding to given open-loop start-up policies (manual start-up strategies), it can be seen how the column arrives at different steady states as a function of the start-up policy. This shows that it is possible to identify a set of critical values for supervision of the start-up. Also, guidelines of general validity are given with the aim of finding the appropriate start-up policy for obtaining a desired solution. A mechanistic (qualitative) approach is presented for the interpretation of the system behavior. Some connections among the system responses and the phenomenon of multiplicity are presented. Also, a quantitative, semiempirical relationship is introduced to corroborate the qualitative explanation of the system responses. Finally, closed-loop start-up policies using a simple PI controller are analyzed, showing that the desired steady state can always be achieved in these cases. 1. Introduction 1.1. Multiplicity and Operability in Distillation. The presence of multiple solutions at steady state in ideal, azeotropic, and/or reactive distillation columns has been extensively discussed in several works.1-9 Most of these works intended to explain the hysteresis curve behavior or the influence of different variables to reach a better understanding of critical features for proper design, simulation, and control. During the past decade, various experimental works have reported the verification of the phenomenon of multiplicity in distillation. Jacobsen and Skogestad10 analyzed the operability and instability of a binary distillation column during continuous operation, stating that hysteresis can be experienced in actual operation. Moreover, Kienle et al.11 and Koggersbøl et al.12 verified the existence of multiple steady states experimentally in the separation of a binary mixture of methanol and 1-propanol in a pilot-plant distillation column and in a semi-industrialscale distillation column. Regarding azeotropic distillation operations, Gu¨ttinger and Morari13 found two stable steady states for the ternary homogeneous methanol-methyl butyratetoluene (MMT) system on an industrial pilot column. In addition, Dorn et al.14 verified the existence of a third unstable steady state and studied the transient behavior of this azeotropic column. Moreover, Lee et al.15 found periodic oscillations while processing a ternary homogeneous azeotropic (MMT) mixture in a column, as well as a limit cycle (sustained oscillations) while analyzing the dynamic behavior of the open-loop column. * To whom correspondence should be addressed. Fax: 54342-4553439. E-mail: [email protected]. † GIAIQ. ‡ INGAR-CONICET.

Bossen et al.9 found four steady states for the dehydration of ethanol with benzene by dynamic simulation. Later, Gani and Jorgensen5 also reported multiple steady states for this system and pointed out that the movement of the internal composition front could be the cause of the possible connection between multiplicity and operability. They realized that the system reached a different steady state as fronts corresponding to temperature and composition profiles moved up or down depending on small positive or negative pulse disturbances in the reboiler heat duty. We will show that this factor will also be critical during start-up operation. On the other hand, Mu¨ller and Marquardt16 intended to verify, in a dynamic experiment, both the existence of multiple steady states in heterogeneous azeotropic distillation (ethanol dehydration with cyclohexane as the entrainer) and the hysteresis behavior due to multiple steady states. Wang et al.17 theoretically and experimentally studied the multiplicity of the heterogeneous azeotropic system isopropyl alcohol-cyclohexane-water (IPA-CyH-H2O). Using residue curves, the authors estimated the hysteresis curve and the different profile types according to the different column stationary regimes. The desired operating zone for the IPA-CyH-H2O system involves three regimes that can be characterized by three different temperature fronts along the column. The first temperature rise represents the separation between the ternary and binary azeotropes, and the second temperature front is due to the cyclohexane stripping from the binary azeotrope. This front appears when there is an excess of entrainment in the column. Otherwise, it vanishes when the reflux flow rate is too high and there is not enough vapor flux to strip the cyclohexane out of the binary azeotrope. Finally, the upper temperature front can disappear if there is not enough entrainment to trap and remove water. Thus, if the reflux flow rate

10.1021/ie030155q CCC: $27.50 © 2004 American Chemical Society Published on Web 12/17/2003

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is low and the reboiled vapor flow rate is too high, the entrainment is stripped from the column. Indeed, the authors emphasized that the start-up strategy is very important for this system. They proposed a start-up policy using a conservatively high reflux and heat duty to achieve the desired operating conditions. They did not analyze the proposed strategy experimentally or by simulation. They also did not discuss alternative startup policies to achieve the desired steady state. These results showed that azeotropic distillation column multiplicity is, in fact, a phenomenon of practical relevance that might lead to operational problems during continuous and discontinuous operation, depending on the way the column is started up. Although several interesting experimental works have reported the achievement of different steady states in azeotropic columns, the way the start-up operations were carried out and the difficulties that were found were not explained. Thus, once the importance of multiplicities for column operation is discussed, we will focus here on the question of how the start-up operation should be managed. It will be seen that the temperature (or composition) fronts are also very important in explaining the column behavior during start-up in azeotropic systems. In fact, when a manual (open-loop) start-up strategy is used, different regimes dominate the transient evolutions according to the different applied policies, driving the system to a particular steady state. In contrast, it will be shown that a closed-loop start-up strategy greatly facilitates the achievement of the desired steady state. Undoubtedly, the start-up procedure represents the most complex transient operation because of the simultaneous changes in many relevant process variables. As these dynamic paths are always nonproductive periods, the start-up policy must avoid achieving an undesirable steady state. Indeed, conceptually, the connection between multiplicities and transient dynamics during start-up in columns processing homogeneous azeotropic mixtures requires an explanation. Such an interpretation will assist in the understanding the nature of the phenomenon of multiplicity, which has been explained using different approaches by several authors.4,13 1.2. Scope of this Work. Scenna et al.18,19 presented some preliminary dynamic simulation results of startup operations for columns with multiple steady states. The ability of the system to reach different possible steady states was studied by applying different startup procedures using the dynamic simulator READYS (Ruiz et al.20) and a commercial simulator (HYSYS). Bisowarno and Tade´21 explored the importance of input multiplicities during the start-up of a reactive distillation column. Monroy-Loperena and Alvarez-Ramirez22 recognized how complex the start-up of an ethylene glycol reactive distillation column that operates in the multiplicity region could become. Furthermore, the effects of manipulating different start-up variables and applying various start-up strategies on achieving the desired steady state in this reactive column were studied by Scenna and Benz.23 Also, they reported useful guidelines for supervising the reactive column start-up operation considering the initial charge, the heating rate manipulation, the fixed set point for the level condenser, or/and the feed manipulation approach. A start-up policy space was mathematically defined by Benz and Scenna,24 assuming ramp and/or stepwise perturbations using open-loop start-up strategies. They

tested several perturbation series by varying systematically scheduled actions over manipulated start-up variables in a column separating an ideal binary mixture, a system theoretically and experimentally studied by other authors.10-12 Benz and Scenna24 showed that the evolution of the internal flow rates during start-up becomes critical for the achievement of the desired steady state. Indeed, they detected different regions in the start-up variable space taking into account the methanol-propanol column regimes. However, a comprehensive explanation of the relationships among the manipulated variables and the different multiple regimes was not presented. Moreover, the behavior of the start-up of more complex systems such as azeotropic columns was not analyzed. Finally, closed-loop startup strategies were not considered either. Following this line of reasoning, a comprehensive mechanistic explanation based on the temperature/ composition front displacement is proposed here to obtain useful relationships and guidelines for starting up homogeneous azeotropic distillation systems with multiplicity. Moreover, such a qualitative interpretation will be useful in explaining the nature of the phenomenon of multiplicity by understanding the attraction characteristics that each possible steady state displays over the transient evolution resulting from each startup policy. Also, an original quantitative (semiempirical) relationship among the start-up manipulated variables is presented for estimation of the system response. The results obtained with this quantitative approach will validate our qualitative or mechanistic explanation. Thus, we will show that it is possible to represent the start-up policies space (open-loop start-up strategies) over a plane surface defined by the two operating variables used to manage the start-up operation. Such a diagram displays the column dynamic behavior (bifurcations during the transient evolution) due to the applied open-loop start-up strategies, instead of indicating static relationships between the operating variables as in common bifurcation diagrams. Moreover, using simple relationships, it is possible to estimate a suitable manual start-up strategy to drive the column to the desired steady state. Finally, it will be shown that simple closed-loop start-up strategies using conventional PI controllers for holding a certain top plate temperature are suitable to drive the column to the desired steady state. Two well-known study cases4,13 will be analyzed here: (a) a homogeneous azeotropic column separating a methanol-methyl butyrate-toluene (MMT) mixture and (b) a column separating a benzene-heptaneacetone (BHA) mixture. The paper is organized as follows: In the next section, an overview of the startup operation is presented, and the general strategy to be used for the generation of different manual start-up policies is briefly described. In section 3, the particular open-loop strategies applied to start up the BHA and the MMT columns are presented, and their results analyzed. Section 4 presents a mechanistic (qualitative) interpretation of the system responses and briefly introduces a semiempirical relationship that quantitatively explains the system behavior. Finally, in section 5, closed-loop start-up strategies and their corresponding advantages are analyzed. 2. Start-up Policy Space In terms of the dynamics and control of the distillation column, a two-product distillation column with a given

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Figure 1. Azeotropic column configuration.

feed has five degrees of freedom, as the pressure (vapor holdup) and reboiler and condenser levels can vary dynamically. There are various different possibilities for a level control, and therefore, many control configurations, such as LD, QRD, and LQR. Therefore, if the pressure is controlled with the condenser duty while the bottom (B) and reflux (L) flow rates are used to control the liquid levels of the reboiler and the condenser, respectively, the distillate (D) and the reboiler duty (QR) are left as independent inputs. Precisely, the QRD control configuration is used for operating both azeotropic columns studied in this work. Figure 1 shows the scheme of the azeotropic column configuration. Here, the same control configuration proposed by Bekiaris et al.4 and Gu¨ttinger and Morari13 is adopted so that our resulting hysteresis cycles can be compared to theirs. For a deep analysis of the selection of adequate control strategies, the reader can analyze different works (Hurowitz et al.25). Column start-up requires a different coordination between reflux and boil-up from that required for continuous operation. As previously stated by Benz and Scenna,24 a representative open-loop start-up policy can be defined by introducing a scheduled sequence of perturbation functions over the operating variables. Thus, when considering the QRD control configuration, a particular start-up policy (open-loop strategy) is defined here by manipulating the reboiler heating rate through different ramp times (TQ), the distillate switching time (τD), and/or the distillate valve opening ramp time (TD). The feeding system is also important to define the start-up column configuration. Because the large number of possible start-up policies prohibits an exhaustive treatment, two particular start-up procedures commonly used in the industry are examined in this paper. Thus, the flow and the batch start-up column strategies are briefly described below. They are applied to test different start-up policies for both study cases (section 3). Consequently, given a start-up configuration, different open-loop start-up policies will be tested via dynamic

simulation to analyze their effects (section 3). The boilup rate (V) is operatively determined by the manipulation of the heat input rate (QR). In the same way, the distillate and feed flow rates (D and F, respectively) are set by the manipulation (opening/closing) of the corresponding valves, using ramp and/or step perturbations over these operating variables. The system behavior is also analyzed using a closed-loop start-up strategy (section 5). The target is not to find the best policy to start up the column in terms of time and cost, but to explore the common start-up procedures and conditions yielding different steady states. 2.1. Flow Start-Up Strategies (F ). A start-up strategy included in this family is characterized by a continuous feed flow through the whole start-up operation; it is generated as follows: (i) The column is initially empty (dry), and a single liquid feed stream is introduced. No distillate, reflux rate, or vapor boil-up perturbations are introduced until the liquid feed fills the plates below the condenser (or the feed tray) and a certain liquid holdup is achieved. (ii) After a certain reboiler level is established, the reboiler heating rate is introduced according to a given strategy. Thus, a well-established liquid-vapor flow rate profile (L/V) arises along the whole column, with a low initial energy delivery. During this start-up step, because the distillate flow valve is kept closed, the column is operated at total reflux (D ) 0). (iii) Then, different heating rates can be manually tested by setting different heating ramp times (TQ) to reach the steady-state condition (QRS). For the closedloop strategy, QR could be a manipulated variable. (iv) The distillate valve is manually opened using either different ramp times (TD) or a step function (TD ) 0) to reach the specified distillate flow rate (D), so the distillate flow is initiated. In addition, different switching times (τD) can be tested to learn about the effects of delaying the activation of the distillate stream. Again, when considering a closed-loop start-up strategy, D could be a manipulated variable for the control device. Using scheduled TQ, TD, and τD values, or similar parameters values associated with the feed stream, we generate different open-loop start-up policies to be tested, which are gathered in a family denoted by the symbol F (flow start-up procedures). This, in turn, allows us to analyze the dynamic system response (openloop). In section 5, closed-loop start-up strategies will also be analyzed. 2.2. Batch Start-Up Procedure (B). Another conventional procedure (most often used) in the industry consists of operating the column in batch mode from the initial start-up condition. It is described as follows: (i) The column, initially empty (dry), is fed until the liquid feed fills the plates below the condenser (or the feed tray) and a certain liquid holdup is achieved in each of them. The reboiler liquid level is specified at a very high value to ensure that the bottom flow rate (B) will be zero. (ii) The feed stream is cut off. Then, a fraction of the steady-state value of the reboiler duty (QS) is introduced to generate an internal vapor stream. The condenser level is set at a given value while tied to the reflux rate (L). The distillate valve is closed, and the column is operated at total reflux and total boil-up mode, so that no product stream is wasted.

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Table 1. Column Data case study I reference flow rate composition

temperature pressure feed tray

Bekiaris et

case study II

al.4

Gu¨ttinger and Morari13

Feed 180 kmol/min (mole fraction) 0.4440 benzene (Bz) 0.5000 acetone (Ac) 0.0560 n-heptane (H) 334.8 K 1 atm nf ) 4

number of trays reboiler condenser top-tray pressure

nt ) 42 n)0 n ) 43 1 atm

Murph eff holdup

1 3.00 m3

type holdup

partial 236 m3

type holdup

total 311 m3

120 kg/min (mass fraction) 0.6566 methanol (M) 0.2806 toluene (Tol) 0.0628 methyl butyrate (MB) 337.3 K 1 atm nf ) 21

Column

nt ) 40 n)0 n ) 41 1 atm

Trays 1 0.1126 m3 Reboiler partial 6.90 m3 Condenser total 6.72 m3

Thermodynamic Model extended NRTL product purity (mol %) reflux ratio (L/D) boilup ratio (V/B)

UNIQUAC

inferior solution

superior solution

inferior solution

superior solution

97.11 Ac (D) 10.73 10.25

98.99 Ac (D) 10.29 10.85

25.88 Tol (B) 2.198 26.17

99.55 Tol (B) 2.059 39.92

(iii) After internal vapor and liquid profiles have been developed, the following manual actions are performed: (a) The column is newly fed. The nominal feed flow rate can be reestablished by using either different feeding ramp times (TF) or a step function (TF ) 0) at different feed activation times (τF), generating different policies. (b) The steady condition (QRS) is reached by manually applying different heating ramp times (TQ). For the closed-loop start-up strategies, QR could be a manipulated variable. (c) The distillate valve is opened manually at different switching times (τD). Then, the distillate flow rate (D) is manipulated by applying different distillate ramp times (TD) or a step function (TD ) 0). If closed-loop start-up strategies are used, the distillate flow rate (D) could be the manipulated variable. Therefore, as the material balance is closed, the reflux and bottom flow rates will vary according to the setpoint values at the condenser and reboiler level controllers. Thus, TQ, TF, TD, τD, τQ, and τF are the start-up operating variables in the start-up policy space (open loop). Therefore, by scheduling these variables, we generate different start-up policies to be tested, gathered in the B family (batch start-up set). Mostly, the main difference between the F and B policies is the way in which the feed is manipulated. Whereas, for the F policies, the feed flow rate is permanently maintained along the whole start-up operation, for the B policies, the feed stream is interrupted during a period of time for carrying out separately another start-up phase, such as heating, in which an initial profile is achieved. 2.3. Computing the Start-up Time. To detect the time required to attain a steady state (start-up time), we introduce a numerical criterion that satisfies the

global mass balance in such a way that the dynamic mass variation is lower than 10-4. Also, the quantitative indicator for determining the optimal switching time proposed by Yasuoka et al.26 is adopted here to compute the start-up time. Then, the characteristic function MT, defined as the difference between the tray temperature within the column during start-up and during steadystate operation, is used to determine the start-up parameters. As there are two different steady states, these criteria can be satisfied for any of the steady states according to the column evolution. However, the resulting start-up time values depend on the admitted error value. The dynamic model (including mass and energy balances, volumetric holdups, level control for reboiler and condenser, etc.) incorporated in the process simulator HYSYS 1.2 (Hyprotech Ltd., 1998) is used for the simulation of start-up operations. Here, the rigorous column hydraulic evolution during the start-up operation is not simulated because the extra required computational time is considered unnecessary given our target. However, the holdups and liquid and vapor internal flows are supervised during the transient evolution to check feasible values. Moreover, to simplify our simulations, unitary tray efficiencies are used. As a result, the start-up times will be lower than the real values, because the overall holdup of the column is substantially reduced using a reduced number of trays. Nevertheless, all of the qualitative results and achieved conclusions are independent of this fact. 3. Open-Loop Start-up Strategies. Study Cases 3.1. Study Case I (BHA System) 3.1.1. BHA Process Description. This example is taken from Bekiaris et al.4 and refers to the separation of a


Figure 2. Hysteresis diagram in xAcD -L-D three-dimensional space.

heptane-acetone azeotropic mixture (7% H-93% Ac) by azeotropic distillation using benzene as the entrainer. The column has 42 trays, which are numbered from the bottom (reboiler, tray 0) to the total condenser (tray 43), and the feed stream enters on tray 4. We assume ideal trays and negligible pressure drops. The azeotropic column pressure is 1 atm. The NRTL (nonrandom twoliquid) model is used for activity coefficient calculations in the liquid phase. An ideal vapor phase is assumed. For binary parameters, see Bekiaris et al.4 The complete data on the azeotropic column are reported in Table 1. In this work, the presence of a single phase along the column is assumed. Multiple solutions reported by other authors (Laroche et al.,27 Bekiaris et al.,4 and Benz and Scenna7) are reproduced here when the reflux flow (L) is varied between 100 and 3000 kmol/min. A high-purity acetone curve (superior solution) and a low-purity acetone curve (inferior solution) are obtained. As different variables can be used as bifurcation parameters, multiple solutions are also checked by using the HYSYS process simulator when the distillate flow rate goes from 90 to 91.4 kmol/min. The entrainer molar flow (E) is fixed at 80 kmol/min as the operating condition. Thus, we find a multiple solution space that is delimited by surfaces associated with both bifurcation parameters, L and D. The hysteresis diagram represented in three-dimensional space for the BHA column is shown in Figure 2. 3.1.2. Open-Loop Start-up Results. An operating condition (here, D ) 90.9 kmol/min) in the multiplicity region was selected, and several start-up policies were tested according to the strategies generically described in section 2. The start-up policies tested in this case are outlined in the next paragraphs. For B start-up policies, the initial heating target adopted here corresponds to 0.8 QS. Then, for all cases, the column is allowed to stabilize up to 2.5 h. Thus, liquid and vapor internal flows evolve to a wellestablished vapor-liquid flow rate profile. Then, the nominal feed is newly introduced at tray 4. Subsequently, the column is continuously fed, and the steady heat duty QS is achieved using different heating ramp times (TQ). Figure 3a and b represents the start-up strategies for F and B groups, respectively. The evolutions of the operating variables during the start-up, TQ and τD, are shown in each case. The FI family gathers the policies that consider a heating rate defined by a TQ value of 10 min and various

Figure 3. Ramp and stepwise functions applied to manipulated variables for defining start-up policies: (a) F strategy group, (b) B strategy group.

distillate switching times τD (shown in Figure 4a). Figure 4b illustrates the distillate acetone composition evolution. Thus, the presence of two different final solutions becomes evident. In Figure 4b, the system evolves toward the superior solution when τD is lower than 213 min. Otherwise, the inferior solution is obtained. According to our simulations, for every TQ value (tested up to 240 min), a similar behavior is verified (repeated). Evidently, a critical policy for a τD value must exist between 213 and 214 min. An analysis of the dynamic behavior of benzene profiles (temperature profiles are qualitatively equivalent) during start-up policies can help to explain these results. For FI policies (see Figure 4a), the benzene profile evolutions going to the superior and the inferior solutions are shown in parts a and b of Figure 5, respectively. The presence of entrainment along the tower is strongly correlated with the operating reflux flow rate. If the reflux stream is considered as a driving force, this force will tend to drag the heaviest compounds (including the benzene) toward the column bottom, inhibiting acetone separation along the rectification section. Considering the control scheme used and the start-up strategies plotted in Figure 4a, the column operates at total reflux until the moment at which the distillate valve is opened. Then, the reflux flow rate decreases to compensate for the distillate being drawn, because reflux stream is tied to the control condenser level. Thus, the lower the τD value, the lower the reflux stream capacity to carry the heaviest compounds toward the bottom. Consequently, a lower τD value will enable the benzene to stay longer and mainly be distributed along the rectification section. This corresponds to the

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Figure 4. Temporal evolution of variables for FI start-up policies for different τD values: (a) QR vs t for TQ ) 10 min and D vs t and (b) xAcD vs t.

result shown in Figure 5a, where the benzene profile evolves to reach the superior solution, which is obtained at τD values lower than 213 min. The benzene front is slowly driven to the column top, thus favoring azeotrope rupture and yielding a solution of higher purity. Consequently, it is concluded that τD ) 213 min becomes a critical start-up condition for reaching the superior solution. The opposite fact is confirmed for τD values higher than 214 min reaching the inferior solution (Figure 4b); the benzene is dragged down to the stripping section, and the benzene front evolves dynamically to the steady state corresponding to the inferior solution branch (Figure 5b). The presence of enough entrainer is critical to promote the necessary azeotropic rupture and good acetone separation. Thus, the distribution of the benzene along the BHA column will determine the possibility of azeotrope rupture and, consequently, the achievement of a high-purity top product. The results presented in Figure 4b show that a separatrix exists dividing the start-up policy plane (τD vs TQ), given that two very similar policies, constructed by applying a very slight perturbation to τD, produce drastically different results. The period that the system delays in reaching the steady state (start-up time) is computed to find the critical start-up parameter values when applying different start-up policies. The start-up time is plotted versus τD in Figure 6. The start-up time is almost constant, except for policies in the neighborhood of the critical policy. In this zone, the period to reach the steady state is much longer. Then, if the start-up conditions are far from the critical set, the start-up time

Figure 5. Evolution of benzene profiles for F I start-up policies, TQ ) 10 min: (a) τD ) 213 min (superior solution) and (b) τD ) 214 min (inferior solution).

Figure 6. Start-up time vs τD for FI start-up policies, BHA case.

is quite a bit lower. Moreover, to reach the superior solution, it is always necessary to spend more time. In summary, the critical start-up policies (open-loop strategy) stand for a frontier line that divides the startup space into two regions (Figure 7). Each of these regions yields different solutions. A policy given by a point located in the superior region (subplane) takes the system toward the inferior solution. On the other hand, the start-up policy given by a point located in the inferior subplane allows the superior solution to be reached. It is interesting to note that, for critical policies, infinite time is spent to reach a “steady”-state solution.


Figure 7. FI start-up policy space: τD vs TQ, BHA case.

However, this will be an unstable solution. Therefore, the compositions of the unstable solution branch could be calculated by using critical start-up policies, but the computation time is very long, and the actual steady state can be achieved only at infinite time. It is important to note that the regions in the graph are specific for both the column design and the configuration used. Any changes to the plates or the condenser and reboiler volumes will influence (shift) the position of the frontier line. Recall, for example, that we assume ideal trays here. Nevertheless, a general conclusion is evident. Feasible policies located at the upper left corner will always take the system to the inferior solution, whereas policies located on the opposite site will drive the system to the desired solution. A second group of flow start-up policies, FII, was tested by simultaneously applying different ramp functions to manipulate F, D, and QR after the filling operation had been completed. Once again, the presence of a frontier was established, dividing the start-up space (TD vs TF) into two zones, each one corresponding to a different steady-state solution (Figure 8b). The behavior of the BHA system under the B policy set represented in Figure 3b was also analyzed. The start-up time was computed for the BI set, defined by a given TQ and different τD values. We achieved results similar to those shown in Figure 6. The BHA system evolves to the superior or inferior solution depending on how early or late the distillate valve is opened. Again, the start-up time required to reach the superior solution is noted to be longer than that for the inferior solution. Likewise, “infinite” time is needed to “achieve” the unstable solution. Once more, two operating regions are determined over the start-up plane (τD vs TQ), similar to the start-up plane shown in Figure 7 for the FI policy set. For BI policies, the frontier is almost horizontal because critical τD values only fluctuate over a few minutes around 200 min for a wide range of heating ramp times (from 0 to 1200 min). This means that, because most of the duty has already been delivered, now the influence of this variable is negligible. To test the impact of the feed flow rate, we tried policies in which the feed stream was manipulated as an operating variable. In this case, after the filling stage had been completed and the feed stream had been cut off, the heating phase was finished (TQ ) 30 min). The system evolved for 2.5 h (total time ) 4 h). Then, the reboiler level set point was set at 50%. The feed flow

Figure 8. FII start-up policy space, TD vs TF: (a) MMT case and (b) BHA case.

Figure 9. Hysteresis diagram for MMT azeotropic column.

rate was reestablished using different feeding ramp times (TF), and the distillate flow rate was activated by opening the distillate valve at different τD values. Using this policy set (BII), we again found a bifurcation. Two operating zones were also determined in the start-up space (τD vs TF), which is divided by a frontier line (graphics here not shown because they are similar to those shown in Figure 8b). 3.2. Study Case II (MMT System). 3.2.1. Process Description. Gu¨ttinger and Morari13 analyzed this system experimentally to verify the existence of multiple solutions. However, they did not explain the strategy used to start up the column. Table 1 indicates the column characteristics. As in the previous example, HYSYS was used for dynamic simulations. Figure 9 shows the hysteresis diagram for this system. The operating condition D ) 100 kg/min, included in the multiplicity region, was adopted.

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same behavior as in the BHA case. Again, the presence of entrainment along the tower is strongly correlated with the imbalance between the different “forces” affecting the system dynamics. Analyzing the flow start-up strategy, all of the policies, including those in the FI family, drove the system to the inferior solution. In contrast, by applying the FII family, we found a frontier, as indicated in Figure 8a. 4. Qualitative Interpretation of the Open-Loop Start-Up Strategy

Figure 10. Evolution of temperature profiles for BII start-up policies, MMT case: (a) from 1 to 8.3 h and (b) (b) from 8.3 h to start-up time.

Different start-up policies considering the general guidelines described in section 2 were used. The same policies as used for case I are analyzed here. 3.2.2. Open-Loop Start-up Results. First, batch policies were simulated. In this particular experiment, the column was fed while the reboiler was being filled to reach the specified level (90%) (to avoid drying the boiler). The column was filled in 0.75 h. This phase required 1 h. Then, the feed was cut off, and a ramp for delivering 0.8QS was introduced in 0.5 h. The system evolved for 2.5 h (total time ) 4 h). Then, the reboiler level set point was set at 50%, and the feed was newly incorporated. The distillate switching time (τD) was the other start-up operating variable. Finally, the remaining heat duty was incorporated using different heating ramp times TQ (policy BI defined above for study case I). In all tests, the inferior solution was achieved. To test the impact of the feed flow rate, we tried policies in which the feed stream was manipulated as an operating variable. In fact, the BII strategy described in section 3.2 introduced the feeding ramp time (TF) and the distillate switching time τD as operating variables. Now, for low TF values, the lower solution was achieved, in contrast to the opposite strategy, for which the upper solution was obtained. Again, different forces were acting on the entrainment composition front, facilitating or inhibiting the entrainment front traveling to the upper trays, above the feed. Thus, the feed incorporation strategy was also a key factor here. Figure 10 shows the evolution of the temperature profile for a policy in which a bifurcation occurs. The analysis of the temperature profiles dynamics (methyl butyrate profile is qualitatively equivalent) shows us the

Analyzing the results presented here for the openloop (manual) start-up strategies, we find a great similarity in approach with the conclusions obtained for the previously studied ideal binary column (Benz and Scenna24). It is possible to define start-up strategies systematically and to determine the set of policies yielding each steady state. Thus, there exists a frontier dividing the start-up space. As the start-up policy approaches this frontier, the time required to reach the steady state becomes longer. In the limit of the critical start-up policy, the start-up time approaches infinity. These critical policies drive the system to the unstable branch in the steady-state hysteresis diagram. In azeotropic columns, the presence of entrainment plays an important role in separation; thus, the dynamics of the entrainment front at the top trays during the start-up period, which, in turn, is a function of the startup policy employed, is a key factor in achieving the desired solution. Along the evolution of the start-up period, the entrainment composition front (or the equivalent temperature front) should travel from bottom to upper trays. The evolution of the front is influenced by the imbalance among the opposite and transient forces caused by the reflux, feed, and vapor flow rates. Thus, the achievement of a steady state depends on the net effect between the two opposite forces, one pushing the front to the bottom and the other pushing it to the top. This imbalance allows the front to expand or not along the column. Moreover, if these opposite dynamical effects are similar in magnitude, the system evolves to an unstable steady-state solution (critical frontier policies). Consequently, we postulate the present mechanistic explanation as a qualitative interpretation of the system behavior during start-up operation. When the reflux flow rate is increased, the entrainment front is pushed toward the bottom. On the other hand, when the boilup rate is increased, the opposite effect is produced. Moreover, because the feeding policy can contribute to the downward driving force (similarly to the reflux rate), feed-tray allocations and feed thermal conditions (vaporized or liquefied feeds) are important factors that can condition the start-up evolution. This mechanistic explanation allows us to improve our understanding of this phenomenon under different conditions and tointerpret the consequences directly. In fact, many different factors can influence the evolution of the driving forces whose net result affects the achieved steady state. For example, under the batch strategy, the column works at total reflux until the moment at which the distillate valve is opened. The liquid accumulation in the condenser affects the change in reflux rate at the beginning of the start-up, so level set points and controller constants can influence the achieved steady state (assuming that all other parameters in our defined open-loop procedure remain un-


changed; see Benz and Scenna24). That means that the high reflux “pushes” the entrainment front toward the column bottom. Nevertheless, the distillate valve aperture will decrease the reflux stream, diminishing the pushing effect of the reflux stream. As a result, the front ascension to the upper trays is favored. The net balance between these opposite effects can explain the existence of two distinct zones separated by a frontier. Critical policies correspond to operating values for which the opposite effects are neutralized; therefore, the system evolves slowly toward one of the two solutions, but never achieves them. Finally, different start-up configurations can be considered, such as the initial feed composition (pure components or different mixtures) used to fill the column. To verify the importance of the feed thermal condition and its effects, we tested the start-up operation with various F and B policies using nominal and undercooled feed. The results showed that, in most tests in which the superior solution was achieved with the nominal feed condition, the lower solution was obtained with an undercooled feed. To summarize, a mechanistic explanation for manual start-up operation of the studied azeotropic columns has been proposed. In our study cases, we observed very different behaviors. In fact, whereas the BHA system gives well-divided zones that yield different steady states over the start-up plane, suchfrontiers are not observed for some strategies in the operating variable space when using the same policies in the MMT case. Therefore, even if an equilibrium between the different forces can qualitatively explain the existence of critical policies (or space division), some kind of quantitative relationship explaining the equilibrium effect among the competing forces must be postulated to explain the system behavior. Such a relationship will make our qualitative explanation more solid. To achieve such a relationship, a simple expression is used to represent the postulated equilibrium among the previously identified competing forces. The instantaneous resulting net force, r(t), acting on the movement of the entrainment front is as follows

r(t) ) KVV(t) + KDD(t) - KFF(t)

(1)

where KF, KD, and KV represent the relative instantaneous force factors due to the boil-up, distillate, and feed streams, respectively. Integrating these forces during the start-up (according to the given policy) from the initial time (activation time, τ) to a generic time t, we obtain the resulting net force R(t) for each time t (where we assume the force factors as mean values)

R(t) ) KV

∫τt V(t) dt + KD∫τt D(t) dt - KF∫τt F(t) dt V

D

F

(2)

In Appendix I, it is shown that this equation can be solved for the start-up strategies tested here, and a general expression linking the start-up operating variables for each policy can be built. Moreover, equations fitting each particular case can be derived. In fact, eq A7a in Appendix I represents the relationship between TD and TF when these variables are manipulated during the open-loop start-up policy (FII) previously described. Comparing our simulated results with this equation, we can conclude that the slope is correct, but the simulated values are shifted (Figure 8a and b). Thus, a constant

must be added to eq A7a, giving eq A7b, to reproduce the simulated values properly. For the MMT case, the constant value is CTD ) -42 min, and for the BHA case, CTD ) 153.5 min. Thus, using eq A7b, very good agreement with the simulated results can be achieved (see Figure 8a or b).

TD ) TF + CTD Similar equations can be derived to relate other variables (policies). In general, an empirical constant must be added to achieve a very good approximation of the system behavior. Thus, we can conclude that we have achieved a semiempirical expression to explain the open-loop start-up responses and also to support the qualitative explanation suggested above. In this way, a conceptual explanation of the nature of the mechanisms favoring the achievement of both steady states is derived. Finally, it is interesting to emphasize that this line of reasoning is strongly related to similar ones presented in the literature. In fact, many works have analyzed equilibrium between competing forces in separation or other physicochemical processes. For example, it has been shown that nonlinear wave models27,28 can capture the essential dynamic behavior of the distillation process. The wave is defined as a spatial structure moving at a constant propagation velocity, with a constant shape, along a spatial coordinate (here the number of stages). From theoretical considerations, the propagation velocity of the front can be calculated along the column.27-29 Also, the movement and settlement of the wave are interpreted as an equilibrium between two opposite forces, the nonequilibrium effects at the end of the absorber and the operating flow rates (L/V). According to this interpretation, during start-up, the profile fronts begin at the column end and travel to the column center, to the desired position. As regards the start-up, each policy can be seen as a perturbation set to guide the front or wave to the desired steady-state position. As more than one steady state occurs, there are different positions where the wave, or front, can settle after the start-up “perturbations” are introduced. Kienle et al.11 used the nonideal wave model to explain and to estimate the nature of the hysteresis curve in a binary column with multiplicity (methanol-propanol column). All of the concepts mentioned in that work (composition front or wave movement due to an imbalance between different forces) are very similar to those addressed in our approach. A balanced wave (zero velocity) is a concept similar to our equilibrium of forces. In this work, we explain the bifurcation between different policies in a dynamic open-loop start-up space, rather than a bifurcation diagram between steady-state variables. However, our relationships are derived using a semiempirical approach. A relationship between the two points of view will be explored in future works to obtain a better explanation of the nature of the phenomenon of multiplicity, from the start-up-operation (dynamic) point of view. 5. Closed-Loop Start-up Strategy In this section, we analyze the start-up performance using a closed-loop control strategy. The automatic control of the start-up of a column is a very challenging problem. The control objective is the reduction of waste products, start-up time, and utility consumption. To

562


consult different approaches to this problem, see, for example, Barolo et al.30 and Ganguly and Saraf.31 Han and Park32 used a control scheme based on temperature profile positions as the controlled variables. It is important to emphasize that our target is only to compare the open-loop vs the closed-loop start-up strategies as we have defined above, rather than to develop an optimal control configuration for the start-up, or an optimal control policy for this operation. These will be the objectives of future works. Indeed, we are not interested in the design of the optimal configuration for the steady-state control of the process. It is supposed that, after the desired steady state is achieved (detected using the supervision function introduced by Yasuoka et al.26 that is explained in section 2.3), the control configuration is switched to the steady-state one. Considering the column performance using a temperature controller, given different perturbations, it is better to control the average of the different tray temperatures (defining a given temperature front) rather than a single value [see, for example, the interesting work of Chien et al.33 for an analysis of different alternatives for the control of an isopropyl alcohol (IPA)-cycloexane-water heterogeneous azeotropic distillation column]. For simplicity, the control configuration to be used for both study cases (no advanced control configurations are used here) is the following: A PI controller for a given top-tray temperature (representative of the temperature, or the equivalent entrainment, front) using the distillate flow rate (D) as a manipulated variable. The manipulation of the reboiler heat duty will also be analyzed as an alternative control strategy. In the MMT column, the representative temperature of the top temperature front or plateau is the tray-33 temperature. For the BHA case, the representative temperature is that of tray 28. Now, we first analyze the MMT column using a PI controller to control the tray-33 temperature by manipulating the distillate flow rate during the start-up operation. Thus, for the same open-loop policies as studied before (open-loop start-up strategies),we now use the same heating rate policy, but we activate the temperature controller instead of manipulating the distillate flow rate. Different start-up policies will be analyzed in this section. The general target is to test the cases in which only the undesired steady state has been achieved using the manual start-up strategy. As mentioned above, to compare the two alternatives, instead of manipulating the distillate flow rate as was done in the open-loop strategy, here we activate the control loop. The controllers for each column are tuned using the ATV (auto-tuning variation) technique (see the HYSYS manual). A small limit cycle disturbance is set up between the manipulated variables and the controlled variables at their steady-state values. This response can be used to obtain the ultimate gain Ku and the ultimate period Pu. The following equations are then used to calculate the tuning parameters of the PI controller

Kc ) Ku/3.2 TI ) 2.2Pu where Kc and TI represent the proportional gain and integral time, respectively.

Figure 11. Evolution of tray-33 temperature and distillate flow rate for closed-loop start-up policies, MMT case: (a) FI start-up policy and (b) BI start-up policy

Figure 11 shows the evolutions of the tray-33 temperature and the distillate flow rate during the startup for a batch policy (MMT column). This time, the superior solution is always attained when different points in the start-up space for which the inferior solution was achieved with the open-loop strategy are tested. It is clear that, to obtain the desired temperature, the controller drives the distillate flow rate to the maximum value during a period of time for a given heating rate policy, thus favoring a rising temperature front. Consequently, this result is coincident with our qualitative interpretation. Obviously, for a given heating rate, a policy that maximizes the distillate flow rate while keeping the operating conditions at feasible operating points will favor the upper solution. Another interesting point is the time taken to reach steady state, namely, 21 h, which is similar to the time required for the open-loop strategy. We found similar results in other simulated cases as well. Therefore, the advantage is now to obtain always the desired solution. To minimize the time required to achieve the desired steady state, more sophisticated control policies must be designed. For the BHA case, we obtained similar results. In fact, different policies in the batch family that, in the openloop operating mode, produced the undesired steady state now yield the desired solution. However, the time spent to achieve the steady state was again similar to the one required for the open-loop strategy. Considering now the F family, for the MMT case, we obtained similar results. For policies in which the


inferior solutions were achieved using the open-loop strategies, we now obtain the superior solution using the closed-loop start-up policies. Figure 11 shows the evolutions of the tray-33 temperature and the distillate flow rate for a representative policy of this set. This behavior was repeated for all of the studied policies. In all cases where the inferior solution was achieved using the open-loop strategy, now, the upper solution is obtained for the closed-loop policies. In a similar form, we arrive at the same conclusion concerning the BHA case. It is clear that this closed-loop start-up strategy is interesting because it permits the achievement of the desired steady state in all the strategies analyzed here. Therefore, it must be considered to be a good alternative for the start-up of these columns. Finally, it is important to mention that, if we use the heating rate as a manipulated variable (using different τD values), poor results are achieved. As previously mentioned, in both study cases, the top-tray temperature is slightly sensitive to the heating rate, so the heat duty is highly increased for a long time, drying the boiler and tending to flood the condenser. Of course, for a final conclusion, a specific study of this manipulated variable using different distillate flow rate manipulation strategies should be performed. 6. Conclusions This work shows how a given start-up policy can upgrade or degrade the overall process. It is clear that, at least by simulation, it is possible to identify the strategies that are useful in achieving a desired steady state. The transient responses of the azeotropic distillation column using open-loop start-up strategies are used to follow the effects of different policies and to determine the critical values for the start-up operating variables. A mechanistic interpretation to explain why each steady state can be achieved (according to the start-up policy used) is presented. Thereby, qualitative guidelines to supervise this operation are derived. Moreover, a general semiempirical equation that confirms our qualitative or mechanistic interpretation of the nature of the phenomenon of multiplicity from the start-up point of view is presented. Finally, a closed-loop start-up strategy is analyzed for both study cases. A tray temperature (placed at the upper temperature front or plateau) is controlled by using the distillate flow rate as the manipulated variable. For all of the tests in which the open-loop strategies yielded the lower solution, it was verified that the desired solution was achieved for the closed-loop startup strategy. In addition, in the simulations where the upper solution was attained with the open-loop strategies, the same behavior was observed with the closedloop start-up strategy. The postulated mechanistic interpretation is also useful in explaining why the use of a closed-loop start-up strategy using an adequate control loop is a good practice when multiplicity exists. Acknowledgment This work was supported by Universidad Tecnolo´gica Nacional (UTN), Consejo Nacional de Investigacioń Cientı´fica y Tećnica (CONICET), and Agencia Nacional de Promocioń Cientı´fica y Tecnolo´gica -SEPCYT. The research assistance received from Mr. Carlos G. Hess,

advanced chemical engineering student, in running the case studies is gratefully acknowledged. Nomenclature C ) constant value D ) distillate flow rate (kmol/min) F ) feed flow rate (kmol/min) K ) force factor Kc ) proportional gain TI ) integral time L ) reflux flow rate (kmol/min) LC ) level controller MT ) Yasuoka coefficient Q ) heat duty (kJ/min) t ) time (h) T ) ramp time (min) V ) boil-up flow rate (kmol/min) x ) molar fraction Greek Letters B ) batch start-up strategy family F ) flow start-up strategy family τ ) switching or activation time Subscripts R ) reboiler F ) feed D ) distillate Q ) heat duty V ) boilup I ) specific policy family Superscript S ) steady state

Appendix As seen in the paper, we can write the resulting net force R(t) as

∫τt V(t) dt + KD∫τt D(t) dt - KF∫τt F(t) dt

R(t) ) KV

V

D

F

(A1)

Solving the above expression, after replacing the ramp evolution as a function of time and after some algebraic manipulation, we obtain

[( ) ( )

KFF (TF + 2τF) 2 KDD K VV (TD + 2τD) (TV + 2τV) (A2) 2 2

R(t) ) t(KDD + KVV - KFF) +

( )

]

Therefore, to achieve equilibrium at each time t, the following expressions must be satisfied

KDD + KVV - KFF ) 0

[( )

( )

(A3)

KFF KDD (TF + 2τF) (TD + 2τD) 2 2 KVV (TV + 2τV) ) 0 (A4) 2

( )

]

Solving this system, we obtain the general equation

(KFF)(TF + 2τF) - (KDD)(TD + 2τD) (KFF - KDD)(TV + 2τV) ) 0 (A5)

564


A simple test to verify the impact of the above three force factors consists of perturbing the operating variables Q, F, and D at their lower steady-state values and measuring the relative changes in the variables’ values that are required to “push” the front to the position corresponding to the upper solution. The relative variations among them can be considered as an approximation of the relative force factors (K) to be used in the above equations. Following this procedure for the MMT column, we found that a step perturbation of 5% in the feed flow rate produces the above-described effect. Also, the same order of perturbation is necessary for D to achieve the same effect. Finally, QR must be doubled to obtain the same order effect. Therefore, KQ and KV are almost negligible compared with the other two quantities in this operating column configuration. Again, for the BHA system, the same conclusions are obtained (KQ and KV are negligible compared with the other force factors). This also explains why temperature control using QR as the manipulated variable is an unwise choice. Thus, considering KV ≈ 0 and using eq A3, we have

KFF )1 KDD Taking this expression into account, from eq A5, we finally obtain

(TF + 2τF) - (TD + 2τD) ) 0

(A6)

Using the above equation, we can characterize the different policies tested by adopting appropriate values for the activation times (τ) and ramp times (T). For instance, for the FII strategy, τD ) 0 and τF ) 0, so we can obtain the following relation

TD ) TF

(A7a)

Comparing the results obtained from this equation with the simulated values, we can conclude that the same slope (1) is achieved, but the simulated values are shifted (Figure 8). To reproduce these simulated values, a constant must be added to eq A7a giving eq A7b

TD ) TF + CTD

(A7b)

Of course, it is possible to relate each variable as a function of the others, adopting appropriate values in eq A6. Each derived expression agrees with the simulated results, provided that a constant is included to fit the data. The value of this constant is calculated using one or two simulated data points (these results are not shown here). Even though these semiempirical relationships provide a very good approximation, they are clearly very limited, because time delays, holdups, number of stages, feed position, and number of feed points are not considered. All of these factors are included implicitly in the K force factors, and they can explain the shift and the necessity of incorporating a constant C. Another topic to consider is that the quantities D and F used in these equations refer to the desired steady state. However, there is no causal relationship or information in eq A5 that predicts the existence of multiplicity. This fact is external information that must be assumed. For example, for the BHA system, the existence of multiple solutions is valid only for a very

narrow interval of distillate flow rates (90.0-91.4 kmol/ h). If we use, for example, D ) 80 kmol/h, eq A5 still predicts two zones, each one pertaining to policies yielding different steady states. In this case, the inferior and superior subplanes above and below the line calculated by eq A5 are artificial. Literature Cited (1) Cairns, B. P.; Furzer, I. A. Multicomponent Three-Phase Azeotropic Distillation. 3. Modern Thermodynamic Models and Multiple Solutions. Ind. Eng. Chem. Res. 1990, 29, 1383. (2) Kienle, A.; Marquardt, W. Bifurcation Analysis and SteadyState Multiplicity of Multicomponent, Non-equilibrium Distillation Processes. Chem. Eng. Sci. 1991, 46, 1757. (3) Jacobsen, E. W.; Skogestad, S. Multiple Steady States in Ideal Two-Product Distillation. AIChE J. 1991, 37, 499. (4) Bekiaris, N.; Meski, G. A.; Radu, C. M.; Morari, M. Steady States in Homogeneus Azeotropic Distillation. Ind. Eng. Chem. Res. 1993, 32, 2023. (5) Gani, R.; Jørgensen, S. B. Multiplicity in Numerical Solution of Nonlinear Models: Separation Processes. Comput. Chem. Eng. 1994, 18, S55. (6) Hauan, S.; Hertzberg, T.; Lien, K. M. Why Methyl tert-Butyl Ether Production by Reactive Distillation May Yield Multiple Solutions. Ind. Eng. Chem. Res. 1995, 34, 987. (7) Benz, S. J.; Scenna, N. J. The Influence of Different Models in Obtaining Multiple Solutions in Distillation Columns. Can. J. Chem. Eng. 1997, 75, 1145. (8) Mohl, K.-D.; Kienle, A.; Gilles, E.-D.; Rapmund, P.; Sundmacher, K.; Hoffmann, U. Steady-State Multiplicities in Reactive Distillation Columns for the Production of Fuel Ethers MTBE and TAME: Theoretical Analysis and Experimental Verification. Chem. Eng. Sci. 1999, 54, 1029. (9) Bossen, B. S.; Jørgensen, S. B.; Gani, R. Simulation, Design, and Analysis of Azetropic Distillation Operations. Ind. Eng. Chem. Res. 1993, 32, 620. (10) Jacobsen, E. W.; Skogestad, S. Multiple Steady States and Instability in Distillation. Implications for Operation and Control. Ind. Eng. Chem. Res. 1995, 34, 4395. (11) Kienle, A.; Groebel, M.; Gilles, E. D. Multiple Steady States in Binary DistillationsTheoretical and Experimental Results. Chem. Eng. Sci. 1995, 50, 2691. (12) Koggersbøl, A.; Andersen, T. R.; Bagterp, J.; Jørgensen, S. B. An Output Multiplicity in Binary Distillation: Experimental Verification. Comput. Chem. Eng. 1996, 20, S835. (13) Gu¨ttinger, T. E.; Morari, M. Predicting Multiple States in Distillation: Singularity Analysis and Reactive Systems. Comput. Chem. Eng. 1997, 21 Supp., S995. (14) Dorn, C.; Gu¨ttinger, T. E.; Wells, G. J.; Morari, M. Stabilization of an Unstable Distillation Column. Ind. Eng. Chem. Res. 1998, 37, 506. (15) Lee, M.; Dorn, C.; Mesky, G. A.; Morari, M. Limit Cycles in Homogeneous Azeotropic Distillation. Ind. Eng. Chem. Res. 1999, 38, 2021. (16) Mu¨ller, D.; Marquardt, W. Experimental Verification of Multiple Steady States in Heterogeneous Azeotropic Distillation. Ind. Eng. Chem. Res. 1997, 36, 5410. (17) Wang, C. J.; Wong D. S. H.; Chien, I.-L.; Shih, R. F.; Liu, W. T.; Tsai, C. S. Critical Reflux, Parametric Sensitivity, and Hysteresis in Azeotropic Distillation of Isopropyl Alcohol + Water + Cyclohexane. Ind. Eng. Chem. Res. 1998, 37, 2835. (18) Scenna, N. J.; Ruiz, C. A.; Benz, S. J. Dynamic Simulation of Start-up Procedures of Reactive Distillation Columns. Comput. Chem. Eng. 1998, 22, S719. (19) Scenna, N. J.; Munõz, M. A.; Benz, S. J. Dynamic Simulation for the Start-up Operation of Distillation Columns with Multiple Steady States. Lat. Am. Appl. Res. 1998, 28, 257. (20) Ruiz, C.; Basualdo, M.; Scenna, N. Reactive Distillation Dynamic Simulation. Trans. Inst. Chem. Eng. A 1995, 73, 363. (21) Bisowarno, B.; Tade´, M. Dynamic Simulation of Startup in Ethyl tert-Butyl Ether Reactive Distillation with Input Multiplicity. Ind. Eng. Chem. Res. 2000, 39, 1950. (22) Monroy-Loperena, R.; Anarez-Ramı´rez, J. On the SteadyState Multiplicities for an Ethylene Glycol Reactive Distillation Column. Ind. Eng. Chem. Res. 1999, 38, 451.

Ind. Eng. Chem. Res., Vol. 43, No. 2, 2004 565 (23) Scenna, N. J.; Benz, S. J. Start-up Operation of Reactive Columns with Multiple Steady States: The Ethylene Glycol Case. Ind. Eng. Chem. Res. 2003, 42, 873. (24) Benz, S. J.; Scenna, N. J. An Extensive Analysis on the Start-Up of Distillation Columns with Multiple Steady States. Can. J. Chem. Eng. 2002, 80, 865. (25) Hurowitz, S.; Anderson, J.; Duvall, M.; Duvall, M.; Riggs J. B. Distillation Control Configuration Selection. J. Process Control 2003, 13, 357. (26) Yasuoka, H.; Nakanishi, E.; Kunigita, E. Design of an Online Startup System for a Distillation Column Based on a Simple Algorithm. Int. Chem. Eng. 1987, 27, 466. (27) Laroche, L.; Bekiaris, N. H.; Andersen, W.; Morari, M. The Curious Behavior of Homogeneous Azeotropic Distillation. Implications for Entrainer Selection. AIChE J. 1992, 38 (9) 1309. (28) Hwang, Y.-L. Nonlinear Wave Theory for Dynamics of Binary Distillation Columns. AIChE J. 1991, 37, 7 (5) 705. (29) Marquard, W. Traveling waves in chemical processes. Int. Chem. Eng. 1990, 30 (4), 585.

(30) Barolo, M.; Guaries, G. B.; Rienzi, S.; Trotta, A. On-line Startup of a Distillation Column Using Generic Model Control. Comput. Chem. Eng. 1993, 17(S), 349. (31) Ganguly, S.; Saraf, D. N. Startup of Distillation Column Using Nonlinear Analytical Model Predictive Control. Ind. Eng. Chem. Res. 1993, 32, 1667 (32) Han, M.; Park, S. Startup of Distillation Columns Using Profile Position Control Based on a Nonlinear Wave Model. Ind. Eng. Chem. Res. 1999, 38, 1565 (33) Chien, I.-L.; Wang, C. J.; Wong, D. S. H. Dynamics and Control of a Heterogeneous Azeotropic Distillation Column: Conventional Control Approach. Ind. Eng. Chem. Res. 1999, 38, 468.

Received for review February 19, 2003 Revised manuscript received October 27, 2003 Accepted October 27, 2003 IE030155Q

Start-up of Homogeneous Azeotropic Distillation Columns with

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