Start-up Operation of Reactive Columns with Multiple Steady States

Ind. Eng. Chem. Res. 2003, 42, 873-882

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Start-up Operation of Reactive Columns with Multiple Steady States: The Ethylene Glycol Case Nicola´ s J. Scenna*,†,‡ and Sonia J. Benz‡ Instituto de Desarrollo y Disen˜ o (INGAR-CONICET), Avellaneda 3657-3000 Santa Fe, Repu´ blica Argentina, and 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

The reactive distillation process for the synthesis of ethylene glycol (EG) can produce multiple steady states, reducing column operability, particularly during start-up. Thus, the operability of this reactive distillation column with multiple steady-state output during start-up is analyzed by dynamic simulation. It can be shown that different steady states can be reached by applying different start-up configurations and/or policies. The transient responses of the reactive distillation column yielding different steady states during start-up operation are shown. The aims are to provide an idea about how a start-up policy/configuration can define the steady state to be achieved and to show the relationships among the critical operating variables in this procedure. Also, some considerations about convenient start-up strategies are outlined. 1. Introduction In reactive distillation, as both reaction and distillation take place simultaneously in a single unit, the reactants and products are continuously separated from the liquid reaction phase to the nonreactive vapor phase. This technique allows for enhanced conversions in equilibrium-limited reversible reactions and higher product selectivities in the case of multiple competing reactions, and it provides an efficient means of handling the energy balance in the case of reactions with high reaction heats. Thus, reactive distillation offers numerous advantages over conventional configurations of reactors followed by separators. Several works1-7 have reported the existence of multiple steady states. Both input and output multiplicities have been described for MTBE (methyl tertbutyl ether), ETBE (ethyl tert-butyl ether), and ethylene glycol (EG) reactive distillation columns.8 The open literature indicates that the complex behavior arising from the coupled reaction and distillation leads to challenging problems in design, operation, and control. Yet, the causes and implications of multiplicity for operation and control have recently been discussed.9-14 Indeed, analysis of operating procedures such as startup and shutdown strategies, which are transient and discontinuous by nature, becomes more critical when applied to reactive distillation presenting a multiplicity of steady states. Scenna et al.15,16 studied the dynamic behavior of reactive distillation columns under the application of different start-up procedures. Bisowarno and Tade´17 investigated the importance of input multiplicity in ETBE reactive distillation during start-up by means of dynamic simulation. Mohl et al.18 analyzed steady-state multiplicities experimentally in reactive distillation columns for MTBE and TAME (tert-amyl methyl ether) production. Start-up to achieve a desired steady state

was said to be a very difficult task. The authors mentioned described some start-up procedures for the experiment, but they did not present an in-depth analysis of them. Nevertheless, they pointed out that heating rates and feed compositions are critical variables during the start-up operation. On the other hand, Monroy-Loperena and AlvarezRamirez8 studied the bifurcation diagram with respect to the reboiler boilup ratio (RBR) for an ethylene glycol (EG) reactive column. They pointed out the importance of defining a good strategy for start-up and suggested a policy based on the shape of the bifurcation diagram, assuming that, in this way, the conditions for the process trajectory to avoid the attraction of undesired steady states in the region of output multiplicities could be created. However, they did not test their proposed start-up strategy by simulation. The aim of this paper is to test start-up procedures by means of dynamic simulation and to show their implication in obtaining the desired steady state. Thus, different start-up policies are proposed to assess and understand the causes that might be responsible for yielding different stable steady states as a consequence of the start-up strategy. In addition, the start-up policies are based not only on the shape of the bifurcation diagram (heating rate) but also on the initial operating conditions and the evolution of liquid residence times (hold-ups). However, our objective is not to find the best strategy for start-up of the column in terms of time and cost, but to explore typical start-up procedures yielding different steady states with the aim of investigating the nature of the output multiplicity from this point of view. Consequently, qualitative guidelines to use as a convenient tool for selecting appropriate start-up operations are obtained. The ethylene glycol distillation reactive column case is studied in this work. 2. Process Description

* To whom the correspondence should be addressed. Fax: 54-342-4553439. E-mail: [email protected]. † Instituto de Desarrollo y Disenõ (INGAR-CONICET). ‡ Universidad Tecnolo´gica Nacional.

Two exothermic competing series reactions occur inside the reactive column. Ethylene glycol (EG) is the major product of these reactions. EG is produced by the

10.1021/ie020099d CCC: $25.00 © 2003 American Chemical Society Published on Web 01/16/2003

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Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003

Table 1. Reaction Data and Column Specifications column

number of trays

trays 1-10 reboiler condenser thermodynamic model reactions

Murphee efficiency holdup type holdup type holdup Wilson

reaction of ethylene oxide (EO) with water

(1)

In a second reaction, the product (EG) reacts with the ethylene oxide (EO) to produce diethylene glycol (DEG), a byproduct

C2H4O + C2H6O2 w C4H10O3

reboiler condenser m3 m3 m3

r1 ) 3.15 × 109 exp[-9.457/T(K)]xEOxH2O [mol/(cm3 s)] r2 ) 6.3 × 109 exp[-9.457/T(K)]xEOxEG [mol/(cm3 s)]

Figure 1. Reactive distillation column configuration.

C2H4O + H2O w C2H6O2

10 n)0 n ) 11 1 0.1855 partial 5.0 total 4.0

(2)

Table 1 shows the reaction data and some column characteristics. The reactive column configuration is presented in Figure 1. The 10-tray column comprises two sections: the reaction section above tray 4 and the distillation section below tray 5. The tray hold-up is evenly distributed along the column, except for the condenser and reboiler hold-ups, which are larger. A water feed stream is fed onto the top tray, and 27.56 kmol/h total ethylene oxide (EO) feed is distributed through six EO feed streams entering different trays along the reaction zone.19 As the column operates at total reflux and atmospheric pressure, the only product stream is drawn from the bottom of the column. Ciric and Miao3 showed that a column similar to the one described above presented multiple solutions using a series of homotopic continuation studies with the holdup volume as the bifurcation parameter. Later, Monroy-

Loperena and Alvarez-Ramirez8 applied a bifurcation analysis and detected two stable steady-state branches using the RBR as bifurcation parameter. Previous works assumed the ideal liquid-phase behavior. In this work, the column is more rigorously modeled using the Wilson model to estimate the component activities (in the liquid phase) due to the nonideality of the reaction mixture. Numerical experiments are processed with the HYSYS20 simulator. The column control configuration for start-up simulation is shown in Figure 1. The column pressure is perfectly controlled, while the bottom (B) and reflux (L) flow rates are used to control the liquid levels of the reboiler and condenser, respectively. As the primary control objective to regulate the operation of a reactive distillation (total reflux) is to check the product purity, the reboiler heat input is used as the main manipulated variable. In addition, different level set points in the condenser are used to produce different trajectories of the liquid/vapor flow rate ratio during start-up. Also, according to the way the column is initially charged and the way the nominal feeding process is manipulated, different initial structural configurations for the startup operation are explored (described in section 3.2). 2.1. Bifurcation Diagram. Figure 2a shows the composition profiles for the EG mole fraction in the bottom stream versus the reboiler heating rate (bifurcation parameter), when the liquid-phase behavior is modeled according to ideal and Wilson paradigms. Also, the impact of the tray hold-up volume on the multiplicity diagram is studied. Thus, three bifurcation diagrams are built assuming tray hold-up values of 0.1855, 0.5, and 1 m3. Two different steady states corresponding to the specified operating input heat duty of 7777 kW are found by simulating a given start-up policy when the reactive distillation column is initially filled with water or EO. Starting from these different solutions, each steady state is dynamically perturbed by decreasing the reboiler heat input. Therefore, the existence of two different stable steady-state branches is verified using the reboiler heating rate in the range from 8000 to 100 kW. The computational results obtained with the Wilson and ideal liquid models for the superior branches are similar, as can be observed in Figure 2a for each fixed tray hold-up. On the other hand, comparing the inferior branches obtained with the ideal and nonideal packages, it is noted that there is a shift for low values of heating rates (or RBR values); meanwhile, the curves are almost coincident for high values. Nevertheless, there are significant differences in the shapes of the obtained bifurcation diagrams for 0.1855-, 0.5-, and 1-m3 tray hold-up values.

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Figure 2. Bifurcation diagrams for 0.1855-, 0.5-, and 1-m3 tray hold-up values, using ideal and Wilson packages. Composition profiles for the EG mole fraction in bottom stream versus (a) the reboiler heat duty and (b) the RBR value.

The resulting multiplicity diagrams are transformed into the plots presented in Figure 2b, where the RBR is used as the bifurcation parameter.8 It is observed that, as the hold-up value increases, each pair of solutions bifurcates at higher RBR values (for 0.1 and 1 m3, the solutions bifurcate around RBR values of 0.2 and 0.8, respectively). Thus, the lower the total holdup volume used, the more extended the multiplicity region. It is noted that, for a 0.5-m3 tray hold-up value, the bifurcation curve is similar to the results presented by Monroy-Loperena and Alvarez-Ramirez,8 who assumed ideal liquid behavior and used unevenly distributed tray hold-up values with approximately 0.5 m3 as the average hold-up in the reactive trays. 3. Start-up Operation Production engineers describe practical experiences concerning the start-up of column operation. The concern ranges from the start-up strategy and a checklist for control equipment to practical hints and experience in troubleshooting.22-24 Conventional column start-up characteristics were extensively studied earlier by Ruiz25 and Ruiz and

Gani26 through simulation studies. They established that the start-up operation involves complex transient responses in hydraulic and thermodynamic variables that result in highly nonlinear behavior of the output variables of the column, i.e., product compositions. According to the results of their studies, Ruiz et al.27 broke down the start-up period into three characteristic stages during which the column undergoes different transient behavior: (1) the discontinuous stage, which lasts a short period and is characterized by drastic changes in the hydraulic variables; (2) the semicontinuous stage, which extends over a much longer period and is characterized by small changes in the hydraulic variables and large changes in the thermodynamic variables; and (3) the continuous stage, which is similar to a distillation column operating around a condition close to the desired steady state. In our case, although the discontinuous phase is not rigorously simulated (the pressure gradients are not considered), the internal fluxes are continuously monitored to verify that they are inside the feasible zone of operation. Therefore, the start-up phase is a critical operation, often neglected in plant design. Indeed, this stage becomes more critical when applied to reactive distillation because the question of how to initiate and maintain the activity of the reaction at the same time that separation is being carried out and controlled does not always have a trivial answer.8,15-18 Assuming a given column structure, different startup policies can be generated from a basic sequence of instructions by changing the manipulated variables. This problem can be stated for both automatic and manual start-up operations. Therefore, design and configuration variables (fixed before the start-up policy is stated) define the start-up configuration. Thus, different start-up configurations can be proposed by changing structural variables such as the feed stream allocation or the number of feed streams entering/leaving the column at different times during the start-up operation. On the other hand, start-up policies are defined by a sequence of scheduled actions applied to manipulate variables at different times, mainly involving the opening and/or closing valves. Thus, the dynamic model requires knowledge about the variables that must be switched from one value to another, the magnitudes of the perturbations, and the timing of these actions. 3.1. Scope. Consequently, considering the proposed target, information about the behavior of the reactive distillation column during start-up is first gathered, to further explore the characteristics of the start-up space. Thus, the attainment of desired or undesired products under the application of different start-up policies/ configurations is analyzed. The impact of using different initial charges in the column is also evaluated. Start-up simulations are performed with the column initially filled with different components: water, EO, or a saturated mixture of reagents. Then, given a start-up configuration, different start-up policy families are tested via numerical experimentation by dynamical process simulation. The transient responses of the system are analyzed throughout the start-up space, and the corresponding results are compiled to identify the causes or conditions that might be responsible for yielding different steady states. 3.2. Start-up Policies Description. As presented by Benz and Scenna,28 a start-up policy φi can be defined through the introduction of a scheduled sequence of

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perturbation functions over the operating variables. Possible perturbation functions can be originated either by a discontinuous stepwise strategy or, in the limiting case when the number of steps tends to infinity, by a continuous ramp function. Thus, for a start-up policy φi, a ramp perturbation function is defined by the ramp time (Tij) required to change variable j from its initial value to its steady-state value. Otherwise, a stepwise policy is defined by the number of steps (Mij) and the period (∆tij) each step has to be applied for manipulated variable j to reach its steady-state value. A particular policy Ni(t) must be defined considering the control configuration of the column during the startup operation. Thus, according to the control configuration of the reactive column described in section 2, the two operating variables to be manipulated are the reboiler heat duty (Qri) and the feed rate (Fi), which are denoted as j ) 1 and j ) 2, respectively. Different ramp times (Ti1) to deliver the steady-state heat duty (QSr ) and a one-step function (Mi2 ) 1) to allow the feed streams to enter the column are applied. In addition, the instant τi2 at which this variable is perturbed along the start-up period must be known. As heat is introduced immediately after the column is filled, τi1 ) 0. Also, different initial-level set points (LC0)i in the condenser are used as a parameter to produce different trajectories of the internal liquid/vapor flow rate ratio during start-up. Generic policies are expressed through the following families

φi(t) ) {Qi(t,Ti); Fi(t,∆t,τ)}

(3)

Obviously, infinite feasible combinations exist to define such start-up policies. Moreover, different control configurations can be considered according to how the column is fed during the start-up period and/or how the internal streams are induced to circulate in the column. Regarding the strategy of manipulating feed streams, two different start-up families are considered for the present analysis. In both cases, the column is first conveniently charged until the reboiler level reaches its set point (in these cases, 50%). As the filling phase is completed, the charging stream is cut up and removed. For flow start-up policies gathered in family F, the column is continuously fed with the nominal feed streams during the whole start-up operation, covering the heating and self-starting phases. Thus, a product stream is continuously drawn to satisfy the mass balance. To prevent the bottom stream from being wasted during start-up, it is accumulated in a deposit. For batch start-up policies gathered in family B, the column feeding process is interrupted while the startup heating phase is initiated and completed. During this phase, no bottom product is drawn from the column either. Once the reboiler duty QSr has been reached, the nominal feeding process is simply reestablished. In short, regardless of the feeding method, it is assumed that the control structure is capable of allowing ramp-function manipulation of the reboiler heat duty (Qri) and step-function manipulation of the feed streams (Fi) during start-up procedures. The general start-up strategy applied to start the reactive column is described in the following subsections. Filling Stage. The column is initially empty (dry). As the initial charge stream enters the column, the liquid fills the plates below the initial feed tray, achiev-

ing a certain liquid hold-up in the trays. The bottom flow rate (B) is zero until the reboiler liquid level achieves the set point value (specified at a very high value during the filling stage). No perturbations in the distillate (D), reflux rate (L), or vapor boil-up (V) are introduced during this phase. Start-up Heating Stage for Family F. After the specified reboiler level is set, heat flow is introduced, and the nominal feed streams are allowed to enter continuously along the reaction section since zero time. The boil-up rate is the only start-up manipulated variable during the flow (F ) strategy. Testing different heating rates, start-up policies belonging to the F family can be generated. Thus, the column is heated as the reboiler steady condition is established and maintained. The produced boil-up stream (V) travels up to the condenser, where the vapor condenses and is accumulated as liquid. As the column is operated at total reflux (D ) 0) and the condenser level is controlled by opening/ closing the reflux stream valve, an internal liquid reflux stream descending to the reboiler is generated. As a result, a transient vapor-liquid flow rate profile develops along the whole column. Eventually, after the hydraulic period is completed, both the flow and composition transient responses of the product streams evolve to the desired steady state. Start-up Heating Stage for Family B. On the other hand, no feed stream enters the column while the heat duty is introduced in the reboiler generating internal vapor and liquid streams inside the column. Consequently, for any batch policy of family B, as the column operates in total boil-up mode and total reflux mode during the heating stage, no product stream is wasted during this start-up phase. Then, after the heat ramp reaches the steady-state value, the feeding process is newly established with the whole nominal set of feed streams entering along the reaction zone. According to set points at the condenser and reboiler levels, the bottom product flow rate varies as the material balance is closed. Thus, the boil-up rate and the activation time of the feeding phase are the main manipulated variables during the batch start-up operation. Testing different heating rates and feed activation times allows for the generation of start-up policies belonging to the B family. It is important to remark here that different alternatives (configurations) for the F and B families can be explored by considering the tray allocation through which the column is charged. In fact, the charging feed stream can enter the column below the reactive trays or onto these trays. Also, a distributed stream set or only one stream can be used during the filling phase. Finally, the column can be initially filled with a pure component such as water or EO or, alternatively, with a mixture of the reagents of different compositions. All of these options are analyzed in the next section. To compute the start-up time, a numerical criterion based on the quantitative indicator for determining the optimal switching time proposed by Yasuoka et al.29 is introduced. Then, the characteristic function MT, defined as the difference between the tray temperature within the column during start-up and the tray temperature during steady-state operation, is used here. However, the resulting start-up time values depend on the allowed error value (here, 10-4). Note that there are two different steady states; these criteria can be satisfied for each of them according to the column evolution.


Figure 3. Evolution of EG mole fraction for the flow start-up policy (LC ) 50%, Ti ) 240 min) when the column is initially charged with EO, water, and a 1:1 mixture.

4. Results and Discussion We adopt a 7777-kW input heat duty value as the steady-state operating condition. Different start-up strategies driving toward this operating condition are simulated to test the effects of different configurations and/or policies (different mixtures in the initial charge, different heating rates, different feed policies, and/or different condenser levels). During the simulations, both the liquid and vapor flow rates are checked to ensure that they are included in a feasible operation zone. The empty column can be initially charged with different components, e.g., water, EO, or a water/EO mixture. Moreover, the column separation section (charge stream enters tray 4) or the whole column can be filled (charge stream enters tray 10). The start-up operation is timed to begin just after the filling process has ended. For family F, the nominal operating feed structure is activated at the same time as the final reboiler duty is being introduced, specifying the desired nominal value as well as the heating ramp time (Ti) to reach it. Thus, for a given heating ramp time (Ti ) 240 min) and condenser level value (LCi ) 50%), the impact of different initial charges can be tested. Figure 3 shows the evolution of the EG mole fraction as the system is initially filled with (i) EO, (ii) water, and (iii) a mixture of reactants with a 1:1 ratio. It can be observed that two different EG compositions in the bottom stream are achieved depending on the initial charge. This graph clearly displays how the column initially filled with water or with the mixture reaches the superior steady state after 50 h, whereas the system charged with EO arrives at the inferior solution within 15 h. Evidently, the column producing EG has a very long settling time for composition variables. To judge the importance of the start-up policy parameters in obtaining the desired solution for the column charged with EO (initial configuration), various heating rate values and different level condenser set points were tested following different flow start-up policies. A plot of the start-up time (period the system delays in reaching the steady state) versus the applied heating ramp time is presented in Figure 4 (LCi ) 50%). When fast heating rates are applied (Ti , 591 min), the inferior solution is always found. In contrast, when very

Figure 4. Start-up time versus heating ramp time (Ti) for flow policies with LC ) 50% when the column is initially charged with EO.

slow heating rates are applied (Ti . 592 min), only the superior solution is reached. Indeed, a heating ramp time within the range 591 min e Ti e 592 min determines whether the column behavior will achieve one steady state or the other. Therefore, a critical zone is detected within the 591-592-min range, where a jump is produced and the two solutions bifurcate. Thus, these policies become frontiers between two zones, one defining the set of start-up policies that bring about the desired solution and the other pertaining to the undesired solution. In other words, one zone is attracted by the superior solution, and the other subspace of policies is attracted by the inferior solution. Regarding the startup time, it is interesting to observe that the system delays either about 50 h or less than 15 h. Thus, there is an important gap between the start-up times corresponding to the desired and undesired solutions. It is clear from Figure 4 that the start-up time does not depend strongly on the applied heating policy but rather depends on the solution quality. In fact, system trajectories converging to the same solution are very similar. On the other hand, depending on the heating rate and the allowable condenser liquid hold-up or residence time (depending on fixed level set points), the availability of water is affected during the first few hours. In fact, the trajectories of the water mole fractions on trays 10 and 5 for two bordering policies are presented in Figure 5 (LCi ) 50%). It is interesting to observe that, when the superior solution (Ti . 592 min) is reached, the water mole fraction begins to increase in a sustained way from tray 10 to tray 5 through the reaction zone as the heating phase is completed. Consequently, the presence of higher water mole fractions along the reaction zone explains how the EG formation rate is supported through the first reaction. Moreover, the side reaction is limited to very low rates, because of dilution effects. Therefore, in this case, when the whole column is initially charged with EO, the provision of water (the other reagent) is critical. To analyze the impact of the liquid residence time in the condenser, two start-up policies with Ti ) 550 min but with different specified condenser level set points (LCi) are compared. It can be expected that the dynamics of the initial liquid flow rate at the top of the column could modify both the compositions of the mixtures on the traysin the reaction zone and, consequently, the

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Figure 5. Evolution of water mole fraction in trays 5 and 10 into the reaction zone for flow policies (Ti ) 591 min, Ti ) 592 min) with LC ) 50% when the column is initially charged with EO.

Figure 6. Evolution of EG mole fraction for flow start-up policies with two different condenser levels (LC ) 50%, LC ) 80%), when the column is initially charged with EO.

reaction progress. Figure 6 shows the evolution of the EG molar composition for Ti ) 550 min with 50 and 80% LCi values. It can be observed that, when the liquid hold-up in the condenser is 80%, the system becomes capable of producing EG, reaching the superior solution. In fact, a larger condenser accumulation (80% level set point) allows an increasing mole fraction of water to be present in the reflux stream during the first few hours, thereby giving support to the desired reaction and the superior solution. Consequently, it is clear that the initial charge, the heating rate, and the condenser level set point are very important start-up parameters in determining which solution will be achieved. Then, if pure EO is used as the initial charge, it becomes necessary to provide reactive trays with water (the other reagent) to produce the reaction. Also, the delay and the instantaneous reflux flow rate (and composition) will depend on the level set point in the condenser, as the reflux stream is activated after this variable is satisfied. According to Hauan et al.13 and Monroy-Loperena and Alvarez-Ramirez,8 multiplicity mechanisms can be qualitatively explained by considering that intermediate

products are recycled via separation stages, leading to an increase in both the reaction rate and the heat production due to exothermic reactions. Monroy-Loperena and Alvarez-Ramirez8 showed that higher values of internal recycling rates or back-mixing (the average number of times a pack of reagents is incorporated into the separation/reaction path) imply higher probabilities of finding multiple solutions, according to the way the separation and reaction mechanisms reconcile their internal competition. They provided a statical analysis, emphasizing that the heating rate and initial charge composition are very important in defining the initial conditions and the subsequent system evolution. Here, the same variables are analyzed from a dynamical point of view. Lower ramp times (higher heating rates) promote higher rates of vaporization of the reactive mixture at the beginning of the operation. Although the vaporization process is more difficult for water, some water is recycled to the column reaction zone. Moreover, the EO is not extracted from the reboiler at the beginning of the heating operation because the bottom stream is tied to the boiler level set point. Consequently, the system is unable to continue increasing the water concentration in the reactive trays to the necessary levels during the development of the heating phase. In contrast, when lower heating rates are applied, the instantaneous total vaporization is relatively smaller. Thus, as the level set point is achieved, the bottom liquid stream drawn from the column at the beginning carries mainly EO, because of the misbalance caused by the initial EO charge. As the effect of the nominal feed composition grows in importance, the water concentration in the vapor stream increases, and consequently, water will also go up to the reactive trays. On the other hand, the condenser behaves as an accumulator during this transient operation. Thus, the resulting concentration of water in the liquid inside depends on the system history (integration) since the beginning of the heating phase. Then, the initial water concentration in the reflux stream will depend on the dynamical integration of the instantaneous concentration in the condensate. This seems to be explain how the inferior solution could turn into the superior one as the specified condenser level set point is changed from 50 to 80% (see Figure 6). The system is able to accumulate a larger quantity of water along the reaction section, as is described above. The impact of using different feeding points during the filling phase is also analyzed. Two identical startup F policies are simulated for a column initially charged with a 1:1 water/EO mixture and LCi fixed at 5%, considering the two following cases: (i) the initial charge stream enters the column just below the reaction zone (tray 4, as in the previous cases) and (ii) the initial charge stream enters the top of the column (tray 10), above the reaction zone. Figure 7 presents a plot of the start-up time versus the heating ramp time for these cases. The start-up space is again divided into two zones, one for the upper solution and the other for the lower solution. However, the critical heating rate appears shifted as a consequence of the different configurations used. In Figure 7a, the filling process occurs just below the column reactive zone, and consequently, no product can be produced by the reaction until the internal circulation begins. The undesired solution is reached for Ti < 710


Figure 8. Start-up time vs water concentration in the water/EO mixture used initially to charge the column; Ti ) 30 min. Figure 7. Start-up time versus heating ramp time (Ti) for flow policies with LC ) 5% when the column is initially charged with a 1:1 mixture. (a) The filling stream enters tray 4 (just below the reaction section). (b) The filling stream enters tray 10 (just above the reaction section).

min; otherwise, the superior solution is obtained (for Ti > 720 min). Again, an important gap between the two corresponding start-up times is also verified. Figure 7b shows the results obtained for case ii. As the 1:1 water/OE mixture is distributed along the reactive trays, the reaction begins during the filling phase. The exothermicity of the reaction causes the temperature profile to increase dynamically along the reaction zone; in turn, higher temperatures promote higher water concentrations (dynamical trajectories not shown here). This fact sustains the production of mainly EG and makes the composition profiles evolve to the superior solution. Obviously, the filling period is longer than in case i. Indeed, because of the effect of the reaction during the column charge, the bifurcation point appears shifted to a Ti value in the interval from 210 to 220 min. That is, the operating zone (start-up subspace) corresponding to the desired solution is increased (Figure 7b). In addition, it is interesting to note that the start-up times for the desired solution in Figure 7b are almost twice the start-up times recorded in Figure 7a, being about 80 and 50 h, respectively. As the reactive trays are charged with the reactive 1:1 water/EO mixture (Figure 7b), initial product composition profiles are developed along the whole column as a result of the early reaction effect. Therefore, the separation mechanism is activated immediately after the heating phase begins. Although the critical heating rate is shifted to lower values, the period required to obtain the product of the desired composition is elongated because of the internal conditions established at the beginning of the process. Finally, considering both filling procedures, it is verified that the upper solution is always found when the condenser level is set at 50%. However, the upper solution is not obtained for LCi ) 5%. This result can be explained by the effect of condenser accumulation, as mentioned above. Finally, the impact of different water contents in the charging mixture is analyzed by testing the following start-up F policy: After the column is charged (on tray 10) with the mixture of interest, the nominal feed

streams are activated, and heat (Ti )30 min) is applied while the condenser level is set at 50%. The resulting start-up times as a function of the water mole fraction in the charge mixture are shown in Figure 8. If the initial charge contains less than 22% water, the system evolves to the inferior solution, but for mixtures of 23% water and higher, the column reaches the superior solution. However, the start-up time appears to be strongly dependent on the percentage of water in the initial charge. For the inferior solution, the start-up time tends first to increase slowly from 12 to 50 h and then decreases very quickly. For the superior solution, the start-up time is about 100 h for mixtures containing up to 50% water. Otherwise, for mixtures with higher water contents, the start-up time rises continuously. If pure water is used, the system requires more than 250 h to reach the steady state. Therefore, the high-conversion solution becomes easier to attain when the water concentration is higher in the initial charge (Figure 8). Moreover, if the column is charged with pure water, the upper solution is always obtained, although the start-up time is significantly longer. In addition, a better product quality is achieved along the transient trajectory, because the EG concentration is higher than the concentration specification (see Figure 3). Now, we analyze the batch start-up family by testing two B family start-up procedures considering the following conditions: Charging a 1:1 water/EO mixture in tray 10 using LCi ) 5% or LCi ) 50%. A plot of start-up time versus heating ramp time is presented in Figure 9. The inferior solution is obtained when LCi ) 5%, whereas the superior one is reached when LCi ) 50%. Again, because of the minor accumulation of reagents in the condenser (LC ) 5%), the batch policy drives toward the undesired solution for all heating rates. Because the feed is interrupted during the heating phase, lower amounts of reactants enter into the reactive trays. On the other hand, when the level set point in the condenser is set at 50%, the upper solution is obtained for all tested heating ramp times. The importance of the numerical method used is another topic that deserves discussion. Benz and Scenna27 studied the impact of the integration strategy and the integration step size on the detection of the dynamical frontier (the borderline indicated in Figures 4 and 5) in the start-up space for a conventional binary column

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Figure 9. Start-up time versus heating ramp time (Ti) when LC ) 5% and LC ) 50% for batch policies.

that presents multiplicity. They verified that the integration step (or method) used during the numerical calculation does not affect the column response when the start-up parameters are far enough from the critical conditions (the frontier between two operating zones), but the opposite effect is found near the critical borderline. We will show here that the integration step is also important. To evaluate the effect of the integration step length, two different integration steps are tested using Euler. Thus, the evolution of the temperature profiles for maximum integration steps at 10-1 and 10-3 s is presented in Figure 10. Four instantaneous states (“snapshots”) are sequenced to show temperature profile

trajectories for both cases. It can clearly be noted that both profiles separate themselves and evolve progressively to both the inferior solution and the superior one. Indeed, a zone with oscillations in convergence is found for heating ramp times in the 200-300-min interval, when 1 s is set as the maximum integration step. On the other hand, it can be observed in Figure 11 that a saw-toothed jump from one solution to the other is detected. If shorter steps are applied (reducing the maximum integration step to 10-1 s), three of the five points (inferior solution) migrate to the superior one. Using a maximum step of 10-3 (Euler), the last remaining two points migrate to the superior solution (the final result is presented in Figure 7b). Indeed, these two points also converge to the upper solution when the Runge-Kutta algorithm (4th-order) is used (maximum integration step, 10-3). Thus, the simulation runs converge to the inferior or superior solution, as the maximum integration step is 1 or 10-3 sec, respectively. Also, it is verified that the integration step used during the numerical calculations does not affect the response of the system when the start-up parameters are far enough from the critical conditions. Effectively, for heating ramp values outside the “borderline zone”, the trajectories and the final solution achieved are independent of the maximum integration step used. 5. Conclusions It is concluded that dynamic simulation is a valuable tool for assessing and understanding reactive column start-up characteristics. It is shown how a given startup policy can upgrade or degrade the overall process.

Figure 10. Comparison of the temporal evolution of temperature profiles for flow start-up policies with LC ) 5%. The column is initially charged with a 1:1 mixture from tray 10. Two different integration step lengths are used.


Figure 11. Start-up time vs heating ramp time for flow policy charged from tray 10 with a 1:1 mixture when an integration step length of 1 s is used.

It is clear that, at least by simulation, it is possible to define which strategies are useful to achieve the desired steady state. On the other hand, the transient responses of the reactive distillation column are used to follow the effects of manipulating different start-up variables and applying various start-up strategies. In fact, depending on the initial column charge, the heating rate manipulation, the set point fixed for the level condenser, or/and the feed manipulation, the undesired steady state can be obtained. Thus, dynamic simulation is an interesting tool for obtaining qualitative guidelines to supervise this operation. As a general guideline, it is convenient for the EG reactive distillation column to set a relatively high condenser liquid level during the start-up operation, giving preference to the use of very low heating rates. Also, an excess of water at the very beginning is recommended. Finally, regarding the start-up performance, it is convenient to introduce the feed below the reactive trays (shorter start-up time). It is important to remark that hold-ups are also important in explaining multiplicities in this system.3 As explained in section 2.1, the operating zone that corresponds to the upper solution is expanded when higher hold-ups are used. In other words, the upper solution is easier to attain. In contrast, with smaller liquid holdups (residence times), the operating zone corresponding to the desired steady state is decreased. Indeed, for very small holdups, Ciric and Miao3 found nine steady states. Obviously, a deeper analysis of the impact of the residence time must be done. However, as a general guideline, when small residence times are adopted, special start-up strategies should be used, for example, charging the column with water. Other interesting parameters useful in judging the benefits given by each strategy are the EG production rate and the DEG waste rate during the start-up period. As the start-up time is longer for an F -type policy, the energy consumed is also greater. On the other hand, the EG production rate is faster, and less out-ofspecification product is lost. Also, the DEG production rate decreases more quickly, although DEG is produced while the bottom valve is closed in a batch policy.

Finally, the evolutions of the EG and DEG production rates differ depending on the initial column charge (water or a 1:1 water/EO mixture). Longer start-up times are expected for an initial charge of water. However, the product quality is better along the transient response, and the EG flow (out-of-specification) loss is smaller. Moreover, the DEG production is almost zero during start-up. Finally, the desired solution is always obtained. Monroy-Loperena and Alvarez-Ramirez8 remarked on the importance of having a good strategy for the column start-up, and they suggested a general policy based on the shape of the bifurcation diagram, to create the conditions such that the process trajectory avoids the attraction of undesired steady states in the region of output multiplicities. Exploiting the shape and properties of the bifurcation diagram, they proposed to reach the upper branch (superior solution) by starting the column (normal feed) among operating conditions corresponding to a zone having only one steady state. Then, this operating state should be perturbed by increasing the RBR slowly up to the design value. Here, judging from our results, we agree with their proposed strategy, and we can ensure that a high ramp time (low heating rate) can be used to achieve the desired solution. In addition, other start-up alternatives are also convenient to be considered as is demonstrated here. Finally, from the point of view of the simulation theory, it is important to stress that, near the critical zone, it is very difficult to achieve the “exact” trajectory because the trajectory is strongly affected by the integration step and the integration method. Indeed, different behaviors can be achieved using different physicochemical packages in this zone. Acknowledgment The authors gratefully acknowledge the financial support given by the Universidad Tecnolo´gica NacionalFacultad Regional Rosario (UTN-FRRo), Asociacioń Gremial de Docentes de la Universidad Tecnolo´gica Nacional (FAGDUT), and Consejo Nacional de Investigaciones Cientı´ficas y Tećnicas (CONICET), which made this work possible. They also thank two advanced chemical engineering students and GIAIQ fellows, Mr. Javier A. Francesconi and Mr. Ne´stor H. Rodriguez, who did simulations and graphics of the example presented in this work. Nomenclature D ) distillate flow rate (kg mol/h) F ) feed flow rate (kg mol/h) L ) reflux flow rate (kg mol/h) LC ) level controller M ) number of steps MT ) Yasuoka coefficient Q ) heat duty (kW) t ) time (h) T ) ramp time (min) V ) boilup flow rate (kg mol/h) Greek Letters τ ) time at which action k is applied ∆tij ) period for which each step has to be applied for manipulated variable j to reach its steady-state value with start-up sequence i φ ) start-up policy function B ) batch start-up strategy family

882


F ) flow start-up strategy family Subscripts c ) critical value i ) policy number j ) manipulated variable number k ) perturbing action number n ) tray number r ) reboiler Superscripts S ) steady state 0 ) initial value

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Received for review February 4, 2002 Revised manuscript received November 26, 2002 Accepted November 26, 2002 IE020099D

Start-up Operation of Reactive Columns with Multiple Steady States

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