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Steady-state transitions in the reactive distillation of MTBE
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Computers Chem. Engng Vol. 22, No. 7—8, pp. 879—892, 1998 ( 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain S0021-9290(97)00273-1 0098—1354/98 $19.00#0.00
Steady-state transitions in the reactive distillation of MTBE M.G. Sneesby,* M.O. Tade´ and T.N. Smith School of Chemical Engineering, Curtin University of Technology, Perth, Western Australia (Received 2 April 1997; revised 29 October 1997) Abstract The reactive distillation process for MTBE synthesis can produce multiple steady states which reduce column operability and controllability, particularly during start-up. A rigorous dynamic simulation of a MTBE reactive distillation column has been developed for a column which was suspected to exhibit multiplicity. Three distinct steady states were found at the nominal design point. Certain perturbations in the feed composition or the manipulated variables were found to cause transitions between parallel steady states and these were plotted using the dynamic capabilities of the column model. Steady-state transitions were only found when neither product flow rate was used as a column input (i.e. when an energy balance control configuration was used). Appropriate closed-loop control was also found to essentially prevent steady-state transitions. No practical mechanism of controlling a transition from an undesirable steady state to a desirable steady state was found: the controlled perturbations of a manipulated variable, the initiation of closed-loop control and the direct manipulation of the column material balance were all found to be either ineffective or impractical. A catastrophic shift can be contrived by manipulating an input variable but destabilisation of the column operation is a potential consequence of the rapid change in internal flows which occurs during the transition. ( 1998 Elsevier Science Ltd. All rights reserved Keywords: steady-state transitions; reactive distillation of MTBE 1. Introduction Reactive distillation is an important technology which has been developed substantially since it was first patented for MTBE synthesis (Smith, 1980). Prior to 1980, reactive distillation had been used for esterification (particularly for methyl and ethyl acetate) but was under utilisation in other areas. It was commercialised for MTBE synthesis in 1982 (Smith and Huddleston, 1982) and MTBE production is now its most important area of application. It offers several significant advantages compared with the conventional process where the reaction and distillation stages are completed sequentially rather than concurrently: (a) reduced capital costs resulting from the combination of two unit operations into a single item of equipment; (b) increased reactant conversion via the continuous recycling of reactants to the reaction zone and removal of products from the reaction zone which improves the reaction stoichiometry; and (c) increased energy efficiency through direct utilis-
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author.
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ation of the heat of reaction for separation. Of the many new MTBE plants that are currently in either the planning or construction phases, most will use processes based around reactive distillation (Hydrocarbon Processing, 1996). Research on reactive distillation, especially for MTBE synthesis, has also been prevalent in the last decade. Active areas have included simulation, design methods, reactive azeotropy and, more recently, the phenomenon of multiplicity of steady states. Since 1993, various researchers have proposed explanations for the existence of multiple steady states in the reactive distillation of MTBE (e.g. Jacobs and Krishna, 1993; Hauan et al., 1995; Gu¨ttinger et al., 1997a), demonstrated the existence of multiple steady states experimentally (e.g. Sundmacher and Hoffman, 1994) and discussed the implications this phenomenon has for the design and control of reactive distillation columns (e.g. Sneesby et al., 1997a). The importance of using the correct frames of reference and simulation basis have also been discussed (e.g. Sneesby et al., 1997b). There are parallels between observations of multiple steady states in reactive distillation and the behaviour of some azeotropic distillation columns. Related research at both an experimental
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(Gu¨ttinger et al., 1997b) and theoretical level (Bekiaris and Morari, 1993, 1996) has provided additional insights into this phenomenon. This paper utilises previously developed simulation models (Sneesby et al., 1997c,d) to further investigate multiple steady states in reactive distillation. In particular, the transitions between parallel steady states are examined. Here, we define parallel steady states to be the different steady-state solutions to a unique set of operating conditions (process inputs). The synthesis of ETBE has been considered in previous contributions but no evidence of multiple steady states was found for the column studied, and a MTBE reactive distillation column has been used as the basis for the current study. Steady-state simulations can be used to adequately identify multiple steady states but dynamic simulations are required to reveal the transition path. If no readily accessible path exists, the presence of multiple steady states has less significance compared with the case where minor perturbations in feed conditions or process disturbances produce a transition to a less desirable steady state. Transition paths have been plotted previously (Schrans et al., 1997; Mohl et al., 1997) but these results rely on physically unrealisable molar flow control of a product stream. Physically realisable transitions are shown in this paper. Multiplicity has obvious implications for the operability and controllability of a column and these issues are briefly addressed. Both open-loop operation and closed-loop control are considered to clarify the potential for steady-state transitions in an operating environment. The problem of “programming” a transition from an undesirable steady state to a desirable steady state by manipulating the column operating conditions is also discussed. This issue has practical relevance in maximising the profitability of a column which is susceptible to steady-state transitions. 2. Dynamic simulation There are essentially two main modelling techniques in use for distillation simulation: the equilibrium stage model, and the rate-based mass transfer model. The equilibrium stage model uses the MESH (material balances, vapour—liquid equilibrium, sum of component fractions and heat balance) equations and can readily be extended to reactive distillation with the inclusion of appropriate equations to model the relevant chemical reactions. Chemical equilibrium can be assumed or kinetic expressions can be incorporated into the model. This modelling method has previously been successfully applied to produce a rigorous equilibrium model of a reactive distillation column for ETBE synthesis (Sneesby et al., 1997c), and then extended to the dynamic case (Sneesby et al., 1997d). This model was found to produce accurate estimates of operating conditions and product composi-
tions when compared with published experimental results (Smith, 1980). The model was also used to validate the assumption of chemical equilibrium for MTBE (and ETBE) which simplifies the overall model and increases the speed of dynamic simulations. Similarly, the dimerisation side reaction, which produces di-isobutylene from isobutylene, was assumed to be negligible but it can be shown that this does not affect the existence of multiplicity or significantly affect the results (Sneesby et al., 1997a). Consequently, these is considerable confidence that the simulation results presented here reflect actual processes and that steady-state transitions are possible at an experimental or industrial scale. The MTBE reaction system includes hydrocarbons (isobutylene and other, non-reactive, C components), 4 an alcohol (methanol) and an ether (MTBE), and is, therefore, highly non-ideal. It is necessary to use component activities in all calculations rather than concentrations. The UNIFAC model was used to provide the required activity coefficient data. Published vapour pressure data was used in the VLE calculations and the Soave—Redlich—Kwong method was used to estimate other required properties. The MTBE reaction model of Zhang and Datta (1995) was used to provide the necessary chemical equilibrium data. The full simulation model was implemented within the SpeedUpTM simulation environment (Aspen Tech, 1993). It is important to recognise that the reactive distillation system which is used to synthesise MTBE is actually a hybrid column consisting of one reactive section and two non-reactive sections. The reaction only occurs on the surface of the catalyst (Amberlyst 15TM or a similar protonated ion-exchange resin) and can, therefore, be easily constrained within a column environment. The interaction between the reactive and non-reactive sections allows favourable reaction conditions to be maintained in the column despite the equilibrium limitations of the synthesis reaction. A 17-stage column, shown in Fig. 1, was used as the basis of the simulation results presented here. A similar column has previously been simulated by Schrans et al. (1996). This column is possibly smaller than would be found in a commercial process but Bekiaris and Morari (1996) have suggested that an increase in the number of stages only makes multiplicity more likely. A reflux ratio of approximately 5.0 is used to produce industrially significant isobutylene conversion and MTBE product purity. In industrial situations, a lower reflux ratio might be more practical to minimise the utility demand. Lower reflux ratios decrease the column internal vapour—liquid traffic and, thereby, reduce the likelihood of multiplicity (Jacobsen and Skogestad, 1991) but there is no evidence to suggest that multiplicity is not possible in many commercial reactive distillation columns. The feed conditions and key operating conditions (inputs) are given in Table 1. The dynamic behaviour of the column is based on stage-to-stage
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Fig. 1. MTBE reactive distillation column configuration. Table 1. Operating conditions for MTBE reactive distillation column Feed conditions Temperature Total feed rate Composition (mol%)
Excess MeOH
Column specification 70°C 2.75 kmol/h 28.2%MeOH, 25.6% iBut, 46.2%nC 4 10.0 mol%
hold-up times of approximately 20—4 s and approximately 4—5 min in the reboiler sump and reflux accumulator. 3. Multiplicity As indicated above, the output conditions (i.e. the temperature profile, product flow rates and compositions, etc.) for this MTBE column are ambiguous for the set of inputs given in Table 1. Each set of output conditions shown in Table 2 corresponds to a separate and distinct steady state and each set is an acceptable solution. These solutions will, henceforth, be denoted as high, medium and low conversion steady states. The high conversion steady state is the desirable state and the “normal” operating condition. The low conversion steady-state is associated with much higher temperatures, particularly in the stripping section, and high concentrations of methanol throughout the column. The medium conversion steady-state operating conditions are all between the high conversion and low conversion solutions.
Rectification stages Reaction stages Stripping stages Total stages Feed stage Overhead pressure Reflux rate Reboiler duty
3 8 6 17 11 1100 kPa 1.20 m3/h 50.6 kW
A simple single-feed, dual-product distillation column has five degrees of freedom: the distillate product draw rate, the bottoms product draw rate, the reflux rate, the reboiler duty and the condenser duty. Three degrees of freedom must be used to control the column inventory (i.e. the reboiler sump level, reflux accumulator level and the pressure). The remaining two degrees of freedom can be specified independently and determine the operation of the column. In this case, the reflux rate and the reboiler duty have been specified. This mode of operation is described as the LV control structure where the following nomenclature is employed: f distillate product draw rate D; f bottoms product draw rate B; f reflux rate ¸ (indicating equivalence to the internal liquid rate); f reboiler duty » (indicating equivalence to the internal vapour rate); f condenser duty Q (normally reserved for pressure # control).
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Table 2. Multiple steady-states for MTBE reactive distillation column
Isobutylene conversion (mol%) Bottoms ether purity (wt%) Distillate methanol purity (wt%) Bottoms rate (m3/h) Temperatures (°C): Condenser Bottom rectification section Middle reactive section Bottom reactive section Top stripping section Middle stripping section Reboiler
High-conversion steady state
Medium-conversion steady state
Low-conversion steady state
97.0 99.9 5.3 0.118 81.0 83.4 84.6 92.3 108.5 144.5 152.2
90.9 96.8 4.9 0.108 80.8 83.5 88.3 109.6 124.8 131.7 143.8
67.1 80.6 2.5 0.093 80.7 83.3 95.2 111.7 126.1 131.4 133.1
If the reflux rate and the bottoms rate were specified independently, the control structure would be designated LB. With either of the product draw rates (D or B) specified, the material balance of the column is effectively set and the control structure is described as a material-balance configuration. Otherwise, the control configuration is described as an energy-balance configuration. The definitions of control strcutures apply equally to both open- and closed-loop operation. In each case, the designation indicates the manipulated variables or column inputs. The control structure is a crucial consideration in ascertaining multiplicity. In this column, the LV structure produces mutliple steady states but the LB structure results in an unique set of output conditions for all possible inputs, unless a molar basis is used, in which case multiple steady states can again be found. This difference highlights a second crucial consideration in ascertaining multiplicity: the unit basis. A molar basis has traditionally been used for distillation simulations as it simplifies the calculations required. However, it is not physically possible to control a molar flow rate so that the results of simulations based on the assumption of constant molar flow do not correspond to physically realisable conditions. This distinction has been described previously (Sneesby et al., 1997b) and multiplicity that occurs only when considering constant molar flows has been referred to as pseudo-multiplicity to indicate its lack of practical significance. The difference between a molar basis and a mass or volume basis arises as the product compositions change across the spectrum of operating conditions. The simulation results presented here use physically realisable units only (e.g. power or heat duty, and volumetric flows) except for feed streams where the composition is constant so that all bases are equivalent. Thus, all of the steady-state transitions shown are physically realisable. 4. Open-loop transitions A series of dynamic simulations were performed with the column operating in open-loop mode using
the LV control structure. Three different initial conditions were considered: (a) the high-conversion steady state; (b) the low-conversion steady state; and (c) the medium-conversion steady state. In each case, the column bottom temperature was used to determine how the column responded to various perturbations. 4.1. Transitions from the high-conversion steady state Initially, the effect of pertrubations in the feed composition was investigated. Starting with stable operation at the high-conversion steady state, various increases and decreases in the methanol feed rate of 10% and 15% over 30, 60 and 120 min were considered. The column returned to the initial operating point without significant perturbation from the original condition in most cases. Numerical errors associated with rapid changes in state variables produced incomplete solutions in the other cases, possibly indicating an instability caused by a depletion of liquid in one part of the column. There was no evidence of a transition to another steady state for any of the perturbations considered. Figure 2 plots the column responses for a 10% increase in the methanol feed rate over 120 min and a 10% decrease over 60 min. Interestingly, a 10% decrease in the methanol feed rate for 60 min had almost no effect on the column, while a 10% increase for 120 min substantially changed the bottoms temperature for a considerable period. Disturbances in the reboiler duty were also considered. In these simulations, the feed rate, feed composition and reflux rate were all fixed, while the reboiler duty was varied by $5% over 30 and 120 min (four different cases). In three of the four cases, the column returned to the initial operating point quickly and smoothly, while a 5% increase over 120 min caused the column flows and temperature to oscillate divergently. The response to a 30 min increase and decrease is shown in Fig. 3. As would be expected, a much greater deviation from the initial conditions is observed for longer perturbations in the reboiler duty. The results presented above suggest that the highconversion steady state is locally stable. Neither per-
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Fig. 2. 10% methanol feed rate increase/decrease from the high-conversion steady-state.
Fig. 3. 5% Reboiler duty increase/decrease from the high-conversion steady-state.
turbations in the feed nor in a primary manipulated variable (i.e. reboiler duty) produced a steady-state transition. This result is important as it implies that column operation should be stable once the highconversion steady state has been attained. This reduces the implications of steady-state multiplicity for the operation of this MTBE column. However, it does not eliminate the possibility of a start-up sequence ending with the column in an undesirable steady state nor does it eliminate the possibility of an unstable highconversion steady state in other columns.
4.2. Transitions from the low-conversion steady state A similar series of tests was simulated starting from the low-conversion steady state. The methanol feed rate was increased and decreased by 10% over 120 min. In both cases, the column settled to the original operating point. However, if the methanol feed rate was temporarily increased or decreased by 15% over the same period, the column jumped to the high-conversion solution! The response to a 15% increase is shown in Fig. 4. Steady-state transitions were not detected for perturbations in the reboiler
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Fig. 4. 10% and 15% methanol feed rate increase from the low-conversion steady-state.
Fig. 5. 1% reboiler duty increase (30 min) from the medium-conversion steady state.
duty although relatively small increases (e.g. #3% over 30 min) caused the reboiler sump to run dry and destabilise the column. Similarly, relatively small decreases in the reboiler duty increased the internal column liquid rate significantly and induce flooding. 4.3. Transitions from the medium-conversion steady state Starting from the medium-conversion steady state, several unusual results were found. Firstly, every perturbation which was considered produced a steadystate transition. This is emphasised in Fig. 5 which
indicates that a steady-state transition occurs after a short, temporary increase of only 1% in the reboiler duty. Second, the column could shift to either the high- or low-conversion steady state. Figure 6 indicates the effect of a 10% and a 15% increase in the methanol feed rate and shows that the column stabilised to the low-conversion steady-state in the first case (10% perturbation) and the high-conversion steady state in the second case (15% perturbation). Third, some transitions were very smooth and had been fully manifested within 120 min, while some transitions took more than 15 h. An example of this is
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Fig. 6. 10% and 15% methanol feed rate increase from the medium-conversion steady state.
Fig. 7. 5% methanol feed rate decrease/increase from the medium-conversion steady state.
given by Fig. 7 which indicates the response to a perturbation of $5% in the methanol feed rate. The response to a 5% decrease was rapid, while a 5% increase initiated a transient response which lasted for several hours. Fourth, slight changes in the initial operating point sometimes resulted in completely different column responses. Figure 8 compares the response to a 10% increase in the methanol feed rate from two slightly different initial conditions. In Fig. 8, the solid line corresponds to the same base case as used for all the
previous simulations (reboiler duty of 50.6 kW), while the dashed line shows the response for a reboiler duty of 50.0 kW with all other variables equal. Note that the initial bottoms temperature shifts from 144°C to 141°C due to the difference in the column energy balance. The column shifted from the medium-conversion steady state to the high-conversion steady state when the reboiler duty was 50.0 kW, whereas it shifted to the low-conversion steady state when the initial operating point equated to the original base case (50.6 kW).
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Fig. 8. 10% methanol feed rate increase from two similar medium-conversion steady states.
5. Closed-loop transitions Steady-state transitions are clearly possible for a range of realistic disturbances when open-loop operation is considered. Are transitions still possible if closed-loop control is used? Output multiplicity implies that there is more than one set of output variables which satisfy a single set of inputs. If each set of outputs are separate and distinct, perfect control of any output variable will confine the column to a single steady state for any known set of inputs. However, if the parallel output sets have common elements, control of one of those common elements might not be sufficient to prevent a transition to a parallel steady state. Thus, the choice of controlled variable(s) within the control scheme is critical. The usual criteria for selecting a controlled variable are the set-point sensitivity and the correlation with the principal operating objective. In this case, the most important product is the bottoms and the primary objective is the MTBE purity. Therefore, potential controlled variables include the MTBE purity (measured directly via an on-line process analyser), the reboiler temperature (used to infer the MTBE purity) and temperatures from the stripping section (also used to infer the bottoms product composition but, perhaps, providing increased set-point sensitivity). The manipulated variables (i.e. the control structure) should be chosen to ensure good dynamic responsiveness. The reboiler duty, Q , or the bottoms 3 product draw rate, B, are preferred choices for the primary manipulated variable in order to minimise the process lags since the controlled variable is likely to be located close to the reboiler. This implies that either the LV or the LB control structure will be used. This is consistent with previous studies of an ETBE
reactive distillation column which identified the LV and LB control structures as the best choices in that instance via rigorous dynamic simulations of various linear control systems (Sneesby et al., 1997d). The inherent similarities between the ETBE column and the current MTBE column generate further confidence in this result. It is not feasible to consider all combinations of controlled and manipulated variables but the importance of making appropriate choices when steady-state transitions must be avoided can be demonstrated by considering four combinations of variables for this MTBE column. Figure 9 shows the relationships between the reboiler temperature, ¹ , and the temper" ature on stage 12 (i.e. top of the stripping section), ¹ , and the reboiler duty, Q . Figure 10 examines the 12 3 relationships between ¹ and ¹ and the bottoms " 12 draw rate, B. The relationships between the MTBE purity and Q and B are very similar to the ¹ !Q 3 " 3 and ¹ !B relations shown in Figs 9 and 10, respec" tively. The upper part of Fig. 9 indicates the variation in ¹ with the reboiler duty. The important aspect of this " plot is that most values of ¹ correspond to two " separate values of Q . In contrast, the lower part of 3 Fig. 9 shows that each value of ¹ corresponds to 12 one (and only one) value of Q . Thus, the perfect 3 control of ¹ will confine the column to a single 12 operating point (i.e. a single steady state) but control of ¹ will not. Figure 10 shows that either ¹ or " " ¹ could be used in conjunction with B without 12 risking an unwanted steady-state transition. In fact, open-loop operation is sufficient with the LB control structure as only one steady state exists for all values of B. However, this analysis conceals that a linear controller for the reboiler sump level would be unsta-
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Fig. 9. Relationships between reboiler duty and column temperatures.
Fig. 10. Relationships between reboiler duty and column temperatures.
ble as the sign of the gain is indeterminate between A and A@ (or B and B@). This can be inferred from Figs 9 and 10 together which shows that some values of B correspond to multiple values of Q . 3 Therefore, the only acceptable combination of controlled and manipulated variables for a linear controller is ¹ !Q . Such a controller will prevent 12 3
unwanted steady-state transitions and simplify the associated inventory control system. However, a linear controller will be unstable for 124.5(¹ (125.5°C as the process gain is negative 12 in this interval and positive elsewhere. The controller may also be inefficient for ¹ '125.5°C (i.e. the low 12 conversion steady state) because of tuning as the
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Fig. 11. Steady-state transition by material balance manipulation.
process gain is approximately 50 times lower than for ¹ (124.5°C (i.e. the high-conversion steady state 12 and normal operating region). So far, only linear controllers and one-point control systems have been considered. With respect to multiplicity, there is essentially no difference between a linear controller and a more complex, multivariable controller. In either case, steady-state transitions are only possible where the controlled variables are common to multiple steady states. Two-point control makes steady-state transitions less likely as two elements (i.e. the values of both controlled variables) of each output set must be common. In practice, reasonably tight control (but not necessarily perfect control) of almost any temperature within the column should be sufficient to prevent a steady-state transition. This ensues from the differences between the temperature profile of the different steady states, particularly in the stripping section where the controlled variable is most likely to be (see Table 2). Note that although tight control of any temperature is adequate, this might only be realisable for some temperatures. For example, the process gain, ¹ !Q , " 3 is both positive and negative in the normal operating region (i.e. the high-conversion steady state) so that a linear controller would not be globally stable. This result provides further encouragement that once the high-conversion steady state is reached, the column operation should be stable, especially if closed-loop control is used. However, the possibility of a start-up sequence ending at an undesirable steady state still remains as start-up is almost always conducted in open loop. If this situation arises, a means of forcing the transition to the most desirable steady state is required.
Perfect level control is not always practically possible. Does the steady-state transition still occur if the level control is imperfect? Steady-state simulations can be used to generate the continuation curve for the reboiler duty as the bottoms rate is varied from 0.0935 to 0.1181 m3/h. This was done and is shown in Fig. 13. The continuation path moving from the low conversion steady state (point A) through the medium conversion steady state (point B) to the high-conversion steady state (point C). The shape of the path resembles the reboiler duty responses shown in Fig. 12.
6. Programmed transitions If a column is found to be operating at an undesirable steady state after start-up or some other period of open-loop operation, the transition back to the desirable steady state must be made using the available manipulated variables. This should be done without destabilising the column which could occur via rapid changes in the internal flow rates or via detrimental interactions with the inventory controllers. Ideally, the transition would be achieved quickly and smoothly with minimal operator intervention. Possible means of achieving this objective include: 1. perturbating the column in a controlled manner in order to cause a transition to the desirable steady state (e.g. Fig. 4); 2. confining the column operation to a single steady state by initiating closed-loop control of a suitable temperature; 3. forcing a change in the column material balance by manipulating a product draw rate;
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Fig. 12. Reboiler duty response during a programmed transition.
Fig. 13. Reboiler duty continuation path.
4. adjusting the primary manipulated variable until a catastrophic shift occurs. Each of these alternatives is evaluated below. 6.1. Controlled perturbation A suitable perturbation in the feed rate, feed composition or either of the manipulated variables being used for composition control (the other manipulated variables should be retained in closed-loop control of the column inventory) might be effective in producing the desired steady state transition. However, the feed rate and composition are normally determined by
external factors (e.g. product demand and upstream processes) so that it is preferable to use one of the manipulated variable to force the transition. The previous open-loop simulations did not identify a reboiler duty perturbation that produced a steady state transition from the low conversion steady state so that a solution is not immediately evident. However, the simulation results can be used to calculate the net amount of heat contained within the column to determine whether differences between the steady states might be offset by an energy impulse (i.e. reboiler duty perturbation). The required relationship is shown in (1), where H is the
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total energy contained within the column, M is the hold-up on each stage, H is the specific enthalpy on each stage and n is the number of stages (including the condenser and reflux accumulator, and the reboiler sump): n H" + M H . (1) i i i/1 Evaluation of (1) for each of the steady states shown in Table 2 indicates that the low-conversion solution contains the most energy while the high-conversion solution contains the least energy. This suggests that a temporary decrease in the energy input to the column might initiate a transition to the high-conversion steady state. The difference in heat content is approximately 110 MJ, which is equivalent to a perturbation of 5 kW (approximately 10%) for 360 min at the base case feed rate of 2.75 kol/h. Unfortunately, such a large perturbation produced very rapid changes in column properties which prevented a complete solution during simulation and would probably quickly result in instability in practice. Even comparatively small perturbations (e.g. 2.8 kW over 60 min, equivalent to an energy impulse of !10 MJ) prevented the simulation from converging. This testifies to the sensitivity of the column operation and suggests that manual control of this column would be difficult. The observed sensitivity is a result of a domino effect which is initiated by an energy impulse. The reactive section is affected most significantly: the initial change in the heat input produces a change in the composition profile which then affects the reaction and changes the heat balance (via a change in the net heat of reaction) which has a further effect on the composition profile. Simulations indicated that, generally, imparting a small perturbation allows the column to return to the original operating conditions while a larger perturbation produced instability caused by the formation of a dry stage(s) within the column. Although a suitable perturbation might exist, this method of forcing a transition was considered impractical due to the degree of precision required and the risk of destabilising the column operation. Reflux rate perturbations were also found to be ineffective in forcing a steady state transition. As with the reboiler duty, small perturbations resulted in the column returning to the original steady state after the transient response or produced very rapid changes in the column properties which prevented a complete dynamic solution. The simulation results suggest that a controlled perturbation in a manipulated variable is not a practical method of forcing a steady state transition. 6.2. Closed-loop control The possibility of using closed-loop operation to manage a transition between parallel steady states appears to have some potential. Theoretically, the column inputs could be manipulated in order to achieve a specified output condition which was only
found in the desirable steady state. For example, a high reboiler temperature and moderate stripping section temperature are characteristics of the highconversion solution (see Fig. 9) so that either of these variables could potentially be controlled to force a transition. However, as described above, the relationships between potential manipulated and controlled variables place restrictions on the performance of linear controllers. Robust control of the reboiler temperature is not possible as the process gain changes sign in the interval around the normal operating point. Although an effective controller for ¹ is easier to develop, 12 stability is not possible for the medium conversion solution unless the controller gain changes sign at the singular points (i.e. A/B, A@/B@). Thus, a finely tuned adaptive controller is required. Finally, the controller must be capable of both increasing and decreasing the manipulated variable in the course of a single setpoint update in order to return the column inputs to the original values after the steady state transition has been completed. An adaptive controller is a technically feasible method of programming a steady-state transition but is unlikely to be a practical solution due to the required accuracy of the model and complexity of the continuation path (via an unstable, medium-conversion steady state) which must be followed. 6.3. Material balance manipulation The manipulation the column material balance via a product draw rate was also considered as a method of programming a transition. A temporary reassignment of manipulated variables is required if the LV configuration (the preferred control structure) is being used as neither the reflux rate nor the reboiler duty can affect the material balance directly. If the material balance change is to be affected using the bottoms draw rate, the reboiler sump level must be temporarily controlled via the reboiler duty. Tight level control is also required to ensure that the changes in the bottoms rate are transmitted directly to the column and are not absorbed by inventory changes. Whereas previously a perturbation in a manipulated variable was required, here the shift must be permanent as the bottoms rate is different for each steady state. The bottoms rate was ramped over a period of 60 min from the low conversion steady state value (0.0935 m3/h) to the high-conversion steady state value (0.1181 m3/h). The column responded in the desired manner and a transition to the high conversion steady state was completed after about eight hours, as shown in Fig. 11. The reboiler duty (for perfect level control of the reboiler sump) varied both above and below the steady-state value during the transition, as shown in Fig. 12. A fourth-order polynomial regression was found to produce a good fit with the continuation path (R2'0.99). If the reboiler duty is programmed to respond according to regression function over a period of 240 min, ¹ responds as shown in Fig. 14. The "
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Fig. 14. Programmed transition using reboiler duty.
column restabilises to the low conversion steady state. Therefore, while a planned manipulated of the column material balance can be used to transfer the operating point between parallel steady states, perfect level control is a prerequisite of a successful transition. Thus, manipulation of the bottoms rate is also not a practical method of promoting a steady-state transition. Material balance manipulation via the distillate product draw is also unviable due to the difficulties in maintaining perfect level control of the reflux accumulator. Once again, a linear controller is incapable of providing perfect level control as the manipulated variable (the reflux rate) must be both increased and decreased during the steady-state transition. 6.4. Catastrophic shift Multiple steady states only exist for this column for finite ranges of the column inputs. For example, Fig. 9 shows three steady states for reboiler duties between 49.6 and 51.8 kW but only one steady state for reboiler duties outside this interval. Therefore, if the column is operating at the low-conversion steady state with a reboiler duty of, say, 50.6 kW, decreasing the duty to a value below 49.6 kW without changing any other input will force a catastrophic shift in the column operating point. Increasing the reboiler duty again should move the operating point along the continuation path to the high conversion steady state, regardless of the starting point. Note that the reboiler temperature will only change slightly during the catastrophic shift but that other temperatures, the internal flow rates and the stage-to-stage compositions will all change dramatically. Other column inputs can also be manipulated in this manner to affect catastrophic shifts. For example, from the low conversion initial state described above,
increasing the reflux rate to 1.25 m3/h would have a similar affect to decreasing the reboiler duty. Reversing this change should complete a steady-state transition to the high-conversion steady state. Similarly, a transition in the opposite direction could be enforced by increasing the reboiler duty to affect a catastrophic shift and then reversing the change to allow the column to move along the continuation path and restabilise at the low-conversion steady state. Unfortunately, as the name suggests, the catastrophic shift might temporarily destabilise the column due to the rapid changes in the internal flow rates. However, this appears to be the only effective method of guaranteeing a transition between parallel steady states. 7. Conclusions A dynamic simulation model of a MTBE reactive distillation column was built in the SpeedUpTM simulation environment to study the effect of various disturbances on the column operating conditions. Multiple steady states were found when the column was operated with the LV control structure while the material-balance configurations were found to yield only a single, unique steady state solution. Three steady states occur in the industrially significant operating range for this column but up to five separate and distinct steady-state solutions are possible for some combinations of reboiler duty and reflux rate. Some disturbances were found to produce transitions between the parallel steady states. The medium-conversion steady state was found to be particularly unstable and transitions resulted from every disturbance considered, including very minor per-
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turbations in the feed composition or a manipulated variable. The magnitude and duration of the perturbation and the initial operating point were all found to significantly affect the column response, and it was difficult to predict whether the column would finally settle to the high- or low-conversion steady state. The high- and low-conversion steady states were found to be generally stable although a transition occurred from the low steady state to the high steady state following a perturbation in the methanol feed rate. The extreme process non-linearities and input and output multiplicities act together to make closed-loop control of a MTBE reactive distillation column technically challenging. A suitable linear control scheme was suggested to constrain the column to a single steady state. The LV control structure was determined to outperform other alternatives and the use of a temperature near the top of the stripping section to infer the current operating condition was found to be effective in minimising the risk of controller instability caused by reversing process gains. Although the high-conversion steady state was found to be stable and closed-loop control was found to effectively prevent steady-state transitions, the possibility of a column reaching an undesirable steady state during a start-up sequence could not be eliminated. Therefore, a means of programming a transition from an undesirable (low conversion) steady state to a desirable (high conversion) steady state is required. Several alternatives were evaluated: using a controlled perturbation; implementing closed-loop operation; manipulating the material balance; and initiating a catastrophic shift. Of these, only the catastrophic shift was found to be both effective and practical. However, large changes in the internal flow rates, temperatures and compositions are associated with a catastrophic shift and these could temporarily destabilise the column. References Aspen Technology Inc. (1993) ¹he SpeedºpTM ºser’s Manual. Cambridge, Massachusetts, USA. Bekiaris, N. and Morari, M. (1993) Multiple steady states in homogeneous azeotropic distillation. Ind. Engng Chem. Res. 32, 2023—2038. Bekiaris, N. and Morari, M. (1996) Multiple steady states in distillation: R/R predictions, extensions and implications for design, synthesis and simulation. Ind. Engng Chem. Res. 35, 4264—4280.
Gu¨ttinger, T.E., Dorn, C. and Morari, M. (1997a) Experimental study of multiple steady states in homogeneous azeotropic distillation. Ind. Engng Chem. Res. 36, 794—802. Gu¨ttinger, T.E. and Morari, M. (1997b) Predicting multiple steady states in distillation: singularity analysis and reactive systems. Computers Chem. Engng. 21(Suppl), S995—S1000. Jacobs, R. and Krishna, R. (1993) Multiple solutions in reactive distillation for methyl tert-butyl ether synthesis. Ind. Engng Chem. Res. 32, 1706—1709. Jacobsen, E.W. and Skogestad, S. (1991) Multiple steady states in ideal two-product distillation. AIChE. J. 37(4), 499—511. Hauan, S., Hertzberg, T. and Lien, K. M. (1995) Why methyl tert-butyl ether production by reactive distillation may yield multiple solutions. Ind. Engng Chem. Res. 34, 987—991. Mohl, K.D., Kienle, A., Gilles, E.D., Rapmund, P., Sundmacher, K. and Hoffman, U. (1997) Nonlinear dynamics of reactive distillation for the production of fuel ethers. Computers Chem. Engng. 21(Suppl), S989—S994. Riddle, L. (1996) HPI Construction Boxscore. Hydrocarbon Process, 75(10B). Schrans, S., de Wolf, S. and Baur, R. (1996) Dynamic simulation of reactive distillation: An MTBE Case Study. Comput. Chem. Engng. 20(Suppl), S1619—S1624. Smith, L.A. (1980) Catalytic distillation process and catalyst. Eur. Pat. Appl. EP8860. Smith, L. A. and Huddleston, M.N. (1982). New MTBE design now commercial. Hydrocarbon Process 61(3), 121. Sneesby, M.G., Tade´, M.O. and Smith, T.N. (1997a) Implications of reactive distillation multiplicity for operation and control of etherification columns. Distillation and Absorption ‘97, Maastricht. Sneesby, M.G., Tade´, M.O. and Smith, T.N. (1997b) Multiplicity and pseudo-multiplicity in MTBE and ETBE reactive distillation. ¹rans. I. Chem. Engng, submitted. Sneesby, M.G., Tade´, M.O., Datta, R. and Smith, T.N. (1997c) ETBE Synthesis by reactive distillation. 1. Steady-state simulation and design aspects. Ind. Engng Chem. Res. 36(5), 1855—1869. Sneesby, M.G., Tade´, M.O., Datta, R. and Smith, T.N. (1997d) ETBE synthesis by reactive distillation. 2. Dynamic simulation and control aspects. Ind. Engng Chem. Res. 36(5), 1870—1881. Sundmacher, K. and Hoffman, U. (1995) Oscillatory vapor—liquid transport phenomena in a packed reactive distillation column for fuel ether production. Chem. Engng. J., 57, 219—228. Zhang, T. and Datta, R. (1995) Integral analysis of methyl tert-butyl ether synthesis kinetics. Ind. Engng Chem. Res. 34, 730—740.
Computers Chem. Engng Vol. 22, No. 7—8, pp. 879—892, 1998 ( 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain S0021-9290(97)00273-1 0098—1354/98 $19.00#0.00
Steady-state transitions in the reactive distillation of MTBE M.G. Sneesby,* M.O. Tade´ and T.N. Smith School of Chemical Engineering, Curtin University of Technology, Perth, Western Australia (Received 2 April 1997; revised 29 October 1997) Abstract The reactive distillation process for MTBE synthesis can produce multiple steady states which reduce column operability and controllability, particularly during start-up. A rigorous dynamic simulation of a MTBE reactive distillation column has been developed for a column which was suspected to exhibit multiplicity. Three distinct steady states were found at the nominal design point. Certain perturbations in the feed composition or the manipulated variables were found to cause transitions between parallel steady states and these were plotted using the dynamic capabilities of the column model. Steady-state transitions were only found when neither product flow rate was used as a column input (i.e. when an energy balance control configuration was used). Appropriate closed-loop control was also found to essentially prevent steady-state transitions. No practical mechanism of controlling a transition from an undesirable steady state to a desirable steady state was found: the controlled perturbations of a manipulated variable, the initiation of closed-loop control and the direct manipulation of the column material balance were all found to be either ineffective or impractical. A catastrophic shift can be contrived by manipulating an input variable but destabilisation of the column operation is a potential consequence of the rapid change in internal flows which occurs during the transition. ( 1998 Elsevier Science Ltd. All rights reserved Keywords: steady-state transitions; reactive distillation of MTBE 1. Introduction Reactive distillation is an important technology which has been developed substantially since it was first patented for MTBE synthesis (Smith, 1980). Prior to 1980, reactive distillation had been used for esterification (particularly for methyl and ethyl acetate) but was under utilisation in other areas. It was commercialised for MTBE synthesis in 1982 (Smith and Huddleston, 1982) and MTBE production is now its most important area of application. It offers several significant advantages compared with the conventional process where the reaction and distillation stages are completed sequentially rather than concurrently: (a) reduced capital costs resulting from the combination of two unit operations into a single item of equipment; (b) increased reactant conversion via the continuous recycling of reactants to the reaction zone and removal of products from the reaction zone which improves the reaction stoichiometry; and (c) increased energy efficiency through direct utilis-
* Corresponding curtin.edu.au.
author.
E-mail:
sneesbym@che.
ation of the heat of reaction for separation. Of the many new MTBE plants that are currently in either the planning or construction phases, most will use processes based around reactive distillation (Hydrocarbon Processing, 1996). Research on reactive distillation, especially for MTBE synthesis, has also been prevalent in the last decade. Active areas have included simulation, design methods, reactive azeotropy and, more recently, the phenomenon of multiplicity of steady states. Since 1993, various researchers have proposed explanations for the existence of multiple steady states in the reactive distillation of MTBE (e.g. Jacobs and Krishna, 1993; Hauan et al., 1995; Gu¨ttinger et al., 1997a), demonstrated the existence of multiple steady states experimentally (e.g. Sundmacher and Hoffman, 1994) and discussed the implications this phenomenon has for the design and control of reactive distillation columns (e.g. Sneesby et al., 1997a). The importance of using the correct frames of reference and simulation basis have also been discussed (e.g. Sneesby et al., 1997b). There are parallels between observations of multiple steady states in reactive distillation and the behaviour of some azeotropic distillation columns. Related research at both an experimental
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(Gu¨ttinger et al., 1997b) and theoretical level (Bekiaris and Morari, 1993, 1996) has provided additional insights into this phenomenon. This paper utilises previously developed simulation models (Sneesby et al., 1997c,d) to further investigate multiple steady states in reactive distillation. In particular, the transitions between parallel steady states are examined. Here, we define parallel steady states to be the different steady-state solutions to a unique set of operating conditions (process inputs). The synthesis of ETBE has been considered in previous contributions but no evidence of multiple steady states was found for the column studied, and a MTBE reactive distillation column has been used as the basis for the current study. Steady-state simulations can be used to adequately identify multiple steady states but dynamic simulations are required to reveal the transition path. If no readily accessible path exists, the presence of multiple steady states has less significance compared with the case where minor perturbations in feed conditions or process disturbances produce a transition to a less desirable steady state. Transition paths have been plotted previously (Schrans et al., 1997; Mohl et al., 1997) but these results rely on physically unrealisable molar flow control of a product stream. Physically realisable transitions are shown in this paper. Multiplicity has obvious implications for the operability and controllability of a column and these issues are briefly addressed. Both open-loop operation and closed-loop control are considered to clarify the potential for steady-state transitions in an operating environment. The problem of “programming” a transition from an undesirable steady state to a desirable steady state by manipulating the column operating conditions is also discussed. This issue has practical relevance in maximising the profitability of a column which is susceptible to steady-state transitions. 2. Dynamic simulation There are essentially two main modelling techniques in use for distillation simulation: the equilibrium stage model, and the rate-based mass transfer model. The equilibrium stage model uses the MESH (material balances, vapour—liquid equilibrium, sum of component fractions and heat balance) equations and can readily be extended to reactive distillation with the inclusion of appropriate equations to model the relevant chemical reactions. Chemical equilibrium can be assumed or kinetic expressions can be incorporated into the model. This modelling method has previously been successfully applied to produce a rigorous equilibrium model of a reactive distillation column for ETBE synthesis (Sneesby et al., 1997c), and then extended to the dynamic case (Sneesby et al., 1997d). This model was found to produce accurate estimates of operating conditions and product composi-
tions when compared with published experimental results (Smith, 1980). The model was also used to validate the assumption of chemical equilibrium for MTBE (and ETBE) which simplifies the overall model and increases the speed of dynamic simulations. Similarly, the dimerisation side reaction, which produces di-isobutylene from isobutylene, was assumed to be negligible but it can be shown that this does not affect the existence of multiplicity or significantly affect the results (Sneesby et al., 1997a). Consequently, these is considerable confidence that the simulation results presented here reflect actual processes and that steady-state transitions are possible at an experimental or industrial scale. The MTBE reaction system includes hydrocarbons (isobutylene and other, non-reactive, C components), 4 an alcohol (methanol) and an ether (MTBE), and is, therefore, highly non-ideal. It is necessary to use component activities in all calculations rather than concentrations. The UNIFAC model was used to provide the required activity coefficient data. Published vapour pressure data was used in the VLE calculations and the Soave—Redlich—Kwong method was used to estimate other required properties. The MTBE reaction model of Zhang and Datta (1995) was used to provide the necessary chemical equilibrium data. The full simulation model was implemented within the SpeedUpTM simulation environment (Aspen Tech, 1993). It is important to recognise that the reactive distillation system which is used to synthesise MTBE is actually a hybrid column consisting of one reactive section and two non-reactive sections. The reaction only occurs on the surface of the catalyst (Amberlyst 15TM or a similar protonated ion-exchange resin) and can, therefore, be easily constrained within a column environment. The interaction between the reactive and non-reactive sections allows favourable reaction conditions to be maintained in the column despite the equilibrium limitations of the synthesis reaction. A 17-stage column, shown in Fig. 1, was used as the basis of the simulation results presented here. A similar column has previously been simulated by Schrans et al. (1996). This column is possibly smaller than would be found in a commercial process but Bekiaris and Morari (1996) have suggested that an increase in the number of stages only makes multiplicity more likely. A reflux ratio of approximately 5.0 is used to produce industrially significant isobutylene conversion and MTBE product purity. In industrial situations, a lower reflux ratio might be more practical to minimise the utility demand. Lower reflux ratios decrease the column internal vapour—liquid traffic and, thereby, reduce the likelihood of multiplicity (Jacobsen and Skogestad, 1991) but there is no evidence to suggest that multiplicity is not possible in many commercial reactive distillation columns. The feed conditions and key operating conditions (inputs) are given in Table 1. The dynamic behaviour of the column is based on stage-to-stage
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Fig. 1. MTBE reactive distillation column configuration. Table 1. Operating conditions for MTBE reactive distillation column Feed conditions Temperature Total feed rate Composition (mol%)
Excess MeOH
Column specification 70°C 2.75 kmol/h 28.2%MeOH, 25.6% iBut, 46.2%nC 4 10.0 mol%
hold-up times of approximately 20—4 s and approximately 4—5 min in the reboiler sump and reflux accumulator. 3. Multiplicity As indicated above, the output conditions (i.e. the temperature profile, product flow rates and compositions, etc.) for this MTBE column are ambiguous for the set of inputs given in Table 1. Each set of output conditions shown in Table 2 corresponds to a separate and distinct steady state and each set is an acceptable solution. These solutions will, henceforth, be denoted as high, medium and low conversion steady states. The high conversion steady state is the desirable state and the “normal” operating condition. The low conversion steady-state is associated with much higher temperatures, particularly in the stripping section, and high concentrations of methanol throughout the column. The medium conversion steady-state operating conditions are all between the high conversion and low conversion solutions.
Rectification stages Reaction stages Stripping stages Total stages Feed stage Overhead pressure Reflux rate Reboiler duty
3 8 6 17 11 1100 kPa 1.20 m3/h 50.6 kW
A simple single-feed, dual-product distillation column has five degrees of freedom: the distillate product draw rate, the bottoms product draw rate, the reflux rate, the reboiler duty and the condenser duty. Three degrees of freedom must be used to control the column inventory (i.e. the reboiler sump level, reflux accumulator level and the pressure). The remaining two degrees of freedom can be specified independently and determine the operation of the column. In this case, the reflux rate and the reboiler duty have been specified. This mode of operation is described as the LV control structure where the following nomenclature is employed: f distillate product draw rate D; f bottoms product draw rate B; f reflux rate ¸ (indicating equivalence to the internal liquid rate); f reboiler duty » (indicating equivalence to the internal vapour rate); f condenser duty Q (normally reserved for pressure # control).
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Table 2. Multiple steady-states for MTBE reactive distillation column
Isobutylene conversion (mol%) Bottoms ether purity (wt%) Distillate methanol purity (wt%) Bottoms rate (m3/h) Temperatures (°C): Condenser Bottom rectification section Middle reactive section Bottom reactive section Top stripping section Middle stripping section Reboiler
High-conversion steady state
Medium-conversion steady state
Low-conversion steady state
97.0 99.9 5.3 0.118 81.0 83.4 84.6 92.3 108.5 144.5 152.2
90.9 96.8 4.9 0.108 80.8 83.5 88.3 109.6 124.8 131.7 143.8
67.1 80.6 2.5 0.093 80.7 83.3 95.2 111.7 126.1 131.4 133.1
If the reflux rate and the bottoms rate were specified independently, the control structure would be designated LB. With either of the product draw rates (D or B) specified, the material balance of the column is effectively set and the control structure is described as a material-balance configuration. Otherwise, the control configuration is described as an energy-balance configuration. The definitions of control strcutures apply equally to both open- and closed-loop operation. In each case, the designation indicates the manipulated variables or column inputs. The control structure is a crucial consideration in ascertaining multiplicity. In this column, the LV structure produces mutliple steady states but the LB structure results in an unique set of output conditions for all possible inputs, unless a molar basis is used, in which case multiple steady states can again be found. This difference highlights a second crucial consideration in ascertaining multiplicity: the unit basis. A molar basis has traditionally been used for distillation simulations as it simplifies the calculations required. However, it is not physically possible to control a molar flow rate so that the results of simulations based on the assumption of constant molar flow do not correspond to physically realisable conditions. This distinction has been described previously (Sneesby et al., 1997b) and multiplicity that occurs only when considering constant molar flows has been referred to as pseudo-multiplicity to indicate its lack of practical significance. The difference between a molar basis and a mass or volume basis arises as the product compositions change across the spectrum of operating conditions. The simulation results presented here use physically realisable units only (e.g. power or heat duty, and volumetric flows) except for feed streams where the composition is constant so that all bases are equivalent. Thus, all of the steady-state transitions shown are physically realisable. 4. Open-loop transitions A series of dynamic simulations were performed with the column operating in open-loop mode using
the LV control structure. Three different initial conditions were considered: (a) the high-conversion steady state; (b) the low-conversion steady state; and (c) the medium-conversion steady state. In each case, the column bottom temperature was used to determine how the column responded to various perturbations. 4.1. Transitions from the high-conversion steady state Initially, the effect of pertrubations in the feed composition was investigated. Starting with stable operation at the high-conversion steady state, various increases and decreases in the methanol feed rate of 10% and 15% over 30, 60 and 120 min were considered. The column returned to the initial operating point without significant perturbation from the original condition in most cases. Numerical errors associated with rapid changes in state variables produced incomplete solutions in the other cases, possibly indicating an instability caused by a depletion of liquid in one part of the column. There was no evidence of a transition to another steady state for any of the perturbations considered. Figure 2 plots the column responses for a 10% increase in the methanol feed rate over 120 min and a 10% decrease over 60 min. Interestingly, a 10% decrease in the methanol feed rate for 60 min had almost no effect on the column, while a 10% increase for 120 min substantially changed the bottoms temperature for a considerable period. Disturbances in the reboiler duty were also considered. In these simulations, the feed rate, feed composition and reflux rate were all fixed, while the reboiler duty was varied by $5% over 30 and 120 min (four different cases). In three of the four cases, the column returned to the initial operating point quickly and smoothly, while a 5% increase over 120 min caused the column flows and temperature to oscillate divergently. The response to a 30 min increase and decrease is shown in Fig. 3. As would be expected, a much greater deviation from the initial conditions is observed for longer perturbations in the reboiler duty. The results presented above suggest that the highconversion steady state is locally stable. Neither per-
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Fig. 2. 10% methanol feed rate increase/decrease from the high-conversion steady-state.
Fig. 3. 5% Reboiler duty increase/decrease from the high-conversion steady-state.
turbations in the feed nor in a primary manipulated variable (i.e. reboiler duty) produced a steady-state transition. This result is important as it implies that column operation should be stable once the highconversion steady state has been attained. This reduces the implications of steady-state multiplicity for the operation of this MTBE column. However, it does not eliminate the possibility of a start-up sequence ending with the column in an undesirable steady state nor does it eliminate the possibility of an unstable highconversion steady state in other columns.
4.2. Transitions from the low-conversion steady state A similar series of tests was simulated starting from the low-conversion steady state. The methanol feed rate was increased and decreased by 10% over 120 min. In both cases, the column settled to the original operating point. However, if the methanol feed rate was temporarily increased or decreased by 15% over the same period, the column jumped to the high-conversion solution! The response to a 15% increase is shown in Fig. 4. Steady-state transitions were not detected for perturbations in the reboiler
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Fig. 4. 10% and 15% methanol feed rate increase from the low-conversion steady-state.
Fig. 5. 1% reboiler duty increase (30 min) from the medium-conversion steady state.
duty although relatively small increases (e.g. #3% over 30 min) caused the reboiler sump to run dry and destabilise the column. Similarly, relatively small decreases in the reboiler duty increased the internal column liquid rate significantly and induce flooding. 4.3. Transitions from the medium-conversion steady state Starting from the medium-conversion steady state, several unusual results were found. Firstly, every perturbation which was considered produced a steadystate transition. This is emphasised in Fig. 5 which
indicates that a steady-state transition occurs after a short, temporary increase of only 1% in the reboiler duty. Second, the column could shift to either the high- or low-conversion steady state. Figure 6 indicates the effect of a 10% and a 15% increase in the methanol feed rate and shows that the column stabilised to the low-conversion steady-state in the first case (10% perturbation) and the high-conversion steady state in the second case (15% perturbation). Third, some transitions were very smooth and had been fully manifested within 120 min, while some transitions took more than 15 h. An example of this is
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Fig. 6. 10% and 15% methanol feed rate increase from the medium-conversion steady state.
Fig. 7. 5% methanol feed rate decrease/increase from the medium-conversion steady state.
given by Fig. 7 which indicates the response to a perturbation of $5% in the methanol feed rate. The response to a 5% decrease was rapid, while a 5% increase initiated a transient response which lasted for several hours. Fourth, slight changes in the initial operating point sometimes resulted in completely different column responses. Figure 8 compares the response to a 10% increase in the methanol feed rate from two slightly different initial conditions. In Fig. 8, the solid line corresponds to the same base case as used for all the
previous simulations (reboiler duty of 50.6 kW), while the dashed line shows the response for a reboiler duty of 50.0 kW with all other variables equal. Note that the initial bottoms temperature shifts from 144°C to 141°C due to the difference in the column energy balance. The column shifted from the medium-conversion steady state to the high-conversion steady state when the reboiler duty was 50.0 kW, whereas it shifted to the low-conversion steady state when the initial operating point equated to the original base case (50.6 kW).
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Fig. 8. 10% methanol feed rate increase from two similar medium-conversion steady states.
5. Closed-loop transitions Steady-state transitions are clearly possible for a range of realistic disturbances when open-loop operation is considered. Are transitions still possible if closed-loop control is used? Output multiplicity implies that there is more than one set of output variables which satisfy a single set of inputs. If each set of outputs are separate and distinct, perfect control of any output variable will confine the column to a single steady state for any known set of inputs. However, if the parallel output sets have common elements, control of one of those common elements might not be sufficient to prevent a transition to a parallel steady state. Thus, the choice of controlled variable(s) within the control scheme is critical. The usual criteria for selecting a controlled variable are the set-point sensitivity and the correlation with the principal operating objective. In this case, the most important product is the bottoms and the primary objective is the MTBE purity. Therefore, potential controlled variables include the MTBE purity (measured directly via an on-line process analyser), the reboiler temperature (used to infer the MTBE purity) and temperatures from the stripping section (also used to infer the bottoms product composition but, perhaps, providing increased set-point sensitivity). The manipulated variables (i.e. the control structure) should be chosen to ensure good dynamic responsiveness. The reboiler duty, Q , or the bottoms 3 product draw rate, B, are preferred choices for the primary manipulated variable in order to minimise the process lags since the controlled variable is likely to be located close to the reboiler. This implies that either the LV or the LB control structure will be used. This is consistent with previous studies of an ETBE
reactive distillation column which identified the LV and LB control structures as the best choices in that instance via rigorous dynamic simulations of various linear control systems (Sneesby et al., 1997d). The inherent similarities between the ETBE column and the current MTBE column generate further confidence in this result. It is not feasible to consider all combinations of controlled and manipulated variables but the importance of making appropriate choices when steady-state transitions must be avoided can be demonstrated by considering four combinations of variables for this MTBE column. Figure 9 shows the relationships between the reboiler temperature, ¹ , and the temper" ature on stage 12 (i.e. top of the stripping section), ¹ , and the reboiler duty, Q . Figure 10 examines the 12 3 relationships between ¹ and ¹ and the bottoms " 12 draw rate, B. The relationships between the MTBE purity and Q and B are very similar to the ¹ !Q 3 " 3 and ¹ !B relations shown in Figs 9 and 10, respec" tively. The upper part of Fig. 9 indicates the variation in ¹ with the reboiler duty. The important aspect of this " plot is that most values of ¹ correspond to two " separate values of Q . In contrast, the lower part of 3 Fig. 9 shows that each value of ¹ corresponds to 12 one (and only one) value of Q . Thus, the perfect 3 control of ¹ will confine the column to a single 12 operating point (i.e. a single steady state) but control of ¹ will not. Figure 10 shows that either ¹ or " " ¹ could be used in conjunction with B without 12 risking an unwanted steady-state transition. In fact, open-loop operation is sufficient with the LB control structure as only one steady state exists for all values of B. However, this analysis conceals that a linear controller for the reboiler sump level would be unsta-
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Fig. 9. Relationships between reboiler duty and column temperatures.
Fig. 10. Relationships between reboiler duty and column temperatures.
ble as the sign of the gain is indeterminate between A and A@ (or B and B@). This can be inferred from Figs 9 and 10 together which shows that some values of B correspond to multiple values of Q . 3 Therefore, the only acceptable combination of controlled and manipulated variables for a linear controller is ¹ !Q . Such a controller will prevent 12 3
unwanted steady-state transitions and simplify the associated inventory control system. However, a linear controller will be unstable for 124.5(¹ (125.5°C as the process gain is negative 12 in this interval and positive elsewhere. The controller may also be inefficient for ¹ '125.5°C (i.e. the low 12 conversion steady state) because of tuning as the
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Fig. 11. Steady-state transition by material balance manipulation.
process gain is approximately 50 times lower than for ¹ (124.5°C (i.e. the high-conversion steady state 12 and normal operating region). So far, only linear controllers and one-point control systems have been considered. With respect to multiplicity, there is essentially no difference between a linear controller and a more complex, multivariable controller. In either case, steady-state transitions are only possible where the controlled variables are common to multiple steady states. Two-point control makes steady-state transitions less likely as two elements (i.e. the values of both controlled variables) of each output set must be common. In practice, reasonably tight control (but not necessarily perfect control) of almost any temperature within the column should be sufficient to prevent a steady-state transition. This ensues from the differences between the temperature profile of the different steady states, particularly in the stripping section where the controlled variable is most likely to be (see Table 2). Note that although tight control of any temperature is adequate, this might only be realisable for some temperatures. For example, the process gain, ¹ !Q , " 3 is both positive and negative in the normal operating region (i.e. the high-conversion steady state) so that a linear controller would not be globally stable. This result provides further encouragement that once the high-conversion steady state is reached, the column operation should be stable, especially if closed-loop control is used. However, the possibility of a start-up sequence ending at an undesirable steady state still remains as start-up is almost always conducted in open loop. If this situation arises, a means of forcing the transition to the most desirable steady state is required.
Perfect level control is not always practically possible. Does the steady-state transition still occur if the level control is imperfect? Steady-state simulations can be used to generate the continuation curve for the reboiler duty as the bottoms rate is varied from 0.0935 to 0.1181 m3/h. This was done and is shown in Fig. 13. The continuation path moving from the low conversion steady state (point A) through the medium conversion steady state (point B) to the high-conversion steady state (point C). The shape of the path resembles the reboiler duty responses shown in Fig. 12.
6. Programmed transitions If a column is found to be operating at an undesirable steady state after start-up or some other period of open-loop operation, the transition back to the desirable steady state must be made using the available manipulated variables. This should be done without destabilising the column which could occur via rapid changes in the internal flow rates or via detrimental interactions with the inventory controllers. Ideally, the transition would be achieved quickly and smoothly with minimal operator intervention. Possible means of achieving this objective include: 1. perturbating the column in a controlled manner in order to cause a transition to the desirable steady state (e.g. Fig. 4); 2. confining the column operation to a single steady state by initiating closed-loop control of a suitable temperature; 3. forcing a change in the column material balance by manipulating a product draw rate;
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Fig. 12. Reboiler duty response during a programmed transition.
Fig. 13. Reboiler duty continuation path.
4. adjusting the primary manipulated variable until a catastrophic shift occurs. Each of these alternatives is evaluated below. 6.1. Controlled perturbation A suitable perturbation in the feed rate, feed composition or either of the manipulated variables being used for composition control (the other manipulated variables should be retained in closed-loop control of the column inventory) might be effective in producing the desired steady state transition. However, the feed rate and composition are normally determined by
external factors (e.g. product demand and upstream processes) so that it is preferable to use one of the manipulated variable to force the transition. The previous open-loop simulations did not identify a reboiler duty perturbation that produced a steady state transition from the low conversion steady state so that a solution is not immediately evident. However, the simulation results can be used to calculate the net amount of heat contained within the column to determine whether differences between the steady states might be offset by an energy impulse (i.e. reboiler duty perturbation). The required relationship is shown in (1), where H is the
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total energy contained within the column, M is the hold-up on each stage, H is the specific enthalpy on each stage and n is the number of stages (including the condenser and reflux accumulator, and the reboiler sump): n H" + M H . (1) i i i/1 Evaluation of (1) for each of the steady states shown in Table 2 indicates that the low-conversion solution contains the most energy while the high-conversion solution contains the least energy. This suggests that a temporary decrease in the energy input to the column might initiate a transition to the high-conversion steady state. The difference in heat content is approximately 110 MJ, which is equivalent to a perturbation of 5 kW (approximately 10%) for 360 min at the base case feed rate of 2.75 kol/h. Unfortunately, such a large perturbation produced very rapid changes in column properties which prevented a complete solution during simulation and would probably quickly result in instability in practice. Even comparatively small perturbations (e.g. 2.8 kW over 60 min, equivalent to an energy impulse of !10 MJ) prevented the simulation from converging. This testifies to the sensitivity of the column operation and suggests that manual control of this column would be difficult. The observed sensitivity is a result of a domino effect which is initiated by an energy impulse. The reactive section is affected most significantly: the initial change in the heat input produces a change in the composition profile which then affects the reaction and changes the heat balance (via a change in the net heat of reaction) which has a further effect on the composition profile. Simulations indicated that, generally, imparting a small perturbation allows the column to return to the original operating conditions while a larger perturbation produced instability caused by the formation of a dry stage(s) within the column. Although a suitable perturbation might exist, this method of forcing a transition was considered impractical due to the degree of precision required and the risk of destabilising the column operation. Reflux rate perturbations were also found to be ineffective in forcing a steady state transition. As with the reboiler duty, small perturbations resulted in the column returning to the original steady state after the transient response or produced very rapid changes in the column properties which prevented a complete dynamic solution. The simulation results suggest that a controlled perturbation in a manipulated variable is not a practical method of forcing a steady state transition. 6.2. Closed-loop control The possibility of using closed-loop operation to manage a transition between parallel steady states appears to have some potential. Theoretically, the column inputs could be manipulated in order to achieve a specified output condition which was only
found in the desirable steady state. For example, a high reboiler temperature and moderate stripping section temperature are characteristics of the highconversion solution (see Fig. 9) so that either of these variables could potentially be controlled to force a transition. However, as described above, the relationships between potential manipulated and controlled variables place restrictions on the performance of linear controllers. Robust control of the reboiler temperature is not possible as the process gain changes sign in the interval around the normal operating point. Although an effective controller for ¹ is easier to develop, 12 stability is not possible for the medium conversion solution unless the controller gain changes sign at the singular points (i.e. A/B, A@/B@). Thus, a finely tuned adaptive controller is required. Finally, the controller must be capable of both increasing and decreasing the manipulated variable in the course of a single setpoint update in order to return the column inputs to the original values after the steady state transition has been completed. An adaptive controller is a technically feasible method of programming a steady-state transition but is unlikely to be a practical solution due to the required accuracy of the model and complexity of the continuation path (via an unstable, medium-conversion steady state) which must be followed. 6.3. Material balance manipulation The manipulation the column material balance via a product draw rate was also considered as a method of programming a transition. A temporary reassignment of manipulated variables is required if the LV configuration (the preferred control structure) is being used as neither the reflux rate nor the reboiler duty can affect the material balance directly. If the material balance change is to be affected using the bottoms draw rate, the reboiler sump level must be temporarily controlled via the reboiler duty. Tight level control is also required to ensure that the changes in the bottoms rate are transmitted directly to the column and are not absorbed by inventory changes. Whereas previously a perturbation in a manipulated variable was required, here the shift must be permanent as the bottoms rate is different for each steady state. The bottoms rate was ramped over a period of 60 min from the low conversion steady state value (0.0935 m3/h) to the high-conversion steady state value (0.1181 m3/h). The column responded in the desired manner and a transition to the high conversion steady state was completed after about eight hours, as shown in Fig. 11. The reboiler duty (for perfect level control of the reboiler sump) varied both above and below the steady-state value during the transition, as shown in Fig. 12. A fourth-order polynomial regression was found to produce a good fit with the continuation path (R2'0.99). If the reboiler duty is programmed to respond according to regression function over a period of 240 min, ¹ responds as shown in Fig. 14. The "
The reactive distillation of MTBE
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Fig. 14. Programmed transition using reboiler duty.
column restabilises to the low conversion steady state. Therefore, while a planned manipulated of the column material balance can be used to transfer the operating point between parallel steady states, perfect level control is a prerequisite of a successful transition. Thus, manipulation of the bottoms rate is also not a practical method of promoting a steady-state transition. Material balance manipulation via the distillate product draw is also unviable due to the difficulties in maintaining perfect level control of the reflux accumulator. Once again, a linear controller is incapable of providing perfect level control as the manipulated variable (the reflux rate) must be both increased and decreased during the steady-state transition. 6.4. Catastrophic shift Multiple steady states only exist for this column for finite ranges of the column inputs. For example, Fig. 9 shows three steady states for reboiler duties between 49.6 and 51.8 kW but only one steady state for reboiler duties outside this interval. Therefore, if the column is operating at the low-conversion steady state with a reboiler duty of, say, 50.6 kW, decreasing the duty to a value below 49.6 kW without changing any other input will force a catastrophic shift in the column operating point. Increasing the reboiler duty again should move the operating point along the continuation path to the high conversion steady state, regardless of the starting point. Note that the reboiler temperature will only change slightly during the catastrophic shift but that other temperatures, the internal flow rates and the stage-to-stage compositions will all change dramatically. Other column inputs can also be manipulated in this manner to affect catastrophic shifts. For example, from the low conversion initial state described above,
increasing the reflux rate to 1.25 m3/h would have a similar affect to decreasing the reboiler duty. Reversing this change should complete a steady-state transition to the high-conversion steady state. Similarly, a transition in the opposite direction could be enforced by increasing the reboiler duty to affect a catastrophic shift and then reversing the change to allow the column to move along the continuation path and restabilise at the low-conversion steady state. Unfortunately, as the name suggests, the catastrophic shift might temporarily destabilise the column due to the rapid changes in the internal flow rates. However, this appears to be the only effective method of guaranteeing a transition between parallel steady states. 7. Conclusions A dynamic simulation model of a MTBE reactive distillation column was built in the SpeedUpTM simulation environment to study the effect of various disturbances on the column operating conditions. Multiple steady states were found when the column was operated with the LV control structure while the material-balance configurations were found to yield only a single, unique steady state solution. Three steady states occur in the industrially significant operating range for this column but up to five separate and distinct steady-state solutions are possible for some combinations of reboiler duty and reflux rate. Some disturbances were found to produce transitions between the parallel steady states. The medium-conversion steady state was found to be particularly unstable and transitions resulted from every disturbance considered, including very minor per-
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turbations in the feed composition or a manipulated variable. The magnitude and duration of the perturbation and the initial operating point were all found to significantly affect the column response, and it was difficult to predict whether the column would finally settle to the high- or low-conversion steady state. The high- and low-conversion steady states were found to be generally stable although a transition occurred from the low steady state to the high steady state following a perturbation in the methanol feed rate. The extreme process non-linearities and input and output multiplicities act together to make closed-loop control of a MTBE reactive distillation column technically challenging. A suitable linear control scheme was suggested to constrain the column to a single steady state. The LV control structure was determined to outperform other alternatives and the use of a temperature near the top of the stripping section to infer the current operating condition was found to be effective in minimising the risk of controller instability caused by reversing process gains. Although the high-conversion steady state was found to be stable and closed-loop control was found to effectively prevent steady-state transitions, the possibility of a column reaching an undesirable steady state during a start-up sequence could not be eliminated. Therefore, a means of programming a transition from an undesirable (low conversion) steady state to a desirable (high conversion) steady state is required. Several alternatives were evaluated: using a controlled perturbation; implementing closed-loop operation; manipulating the material balance; and initiating a catastrophic shift. Of these, only the catastrophic shift was found to be both effective and practical. However, large changes in the internal flow rates, temperatures and compositions are associated with a catastrophic shift and these could temporarily destabilise the column. References Aspen Technology Inc. (1993) ¹he SpeedºpTM ºser’s Manual. Cambridge, Massachusetts, USA. Bekiaris, N. and Morari, M. (1993) Multiple steady states in homogeneous azeotropic distillation. Ind. Engng Chem. Res. 32, 2023—2038. Bekiaris, N. and Morari, M. (1996) Multiple steady states in distillation: R/R predictions, extensions and implications for design, synthesis and simulation. Ind. Engng Chem. Res. 35, 4264—4280.
Gu¨ttinger, T.E., Dorn, C. and Morari, M. (1997a) Experimental study of multiple steady states in homogeneous azeotropic distillation. Ind. Engng Chem. Res. 36, 794—802. Gu¨ttinger, T.E. and Morari, M. (1997b) Predicting multiple steady states in distillation: singularity analysis and reactive systems. Computers Chem. Engng. 21(Suppl), S995—S1000. Jacobs, R. and Krishna, R. (1993) Multiple solutions in reactive distillation for methyl tert-butyl ether synthesis. Ind. Engng Chem. Res. 32, 1706—1709. Jacobsen, E.W. and Skogestad, S. (1991) Multiple steady states in ideal two-product distillation. AIChE. J. 37(4), 499—511. Hauan, S., Hertzberg, T. and Lien, K. M. (1995) Why methyl tert-butyl ether production by reactive distillation may yield multiple solutions. Ind. Engng Chem. Res. 34, 987—991. Mohl, K.D., Kienle, A., Gilles, E.D., Rapmund, P., Sundmacher, K. and Hoffman, U. (1997) Nonlinear dynamics of reactive distillation for the production of fuel ethers. Computers Chem. Engng. 21(Suppl), S989—S994. Riddle, L. (1996) HPI Construction Boxscore. Hydrocarbon Process, 75(10B). Schrans, S., de Wolf, S. and Baur, R. (1996) Dynamic simulation of reactive distillation: An MTBE Case Study. Comput. Chem. Engng. 20(Suppl), S1619—S1624. Smith, L.A. (1980) Catalytic distillation process and catalyst. Eur. Pat. Appl. EP8860. Smith, L. A. and Huddleston, M.N. (1982). New MTBE design now commercial. Hydrocarbon Process 61(3), 121. Sneesby, M.G., Tade´, M.O. and Smith, T.N. (1997a) Implications of reactive distillation multiplicity for operation and control of etherification columns. Distillation and Absorption ‘97, Maastricht. Sneesby, M.G., Tade´, M.O. and Smith, T.N. (1997b) Multiplicity and pseudo-multiplicity in MTBE and ETBE reactive distillation. ¹rans. I. Chem. Engng, submitted. Sneesby, M.G., Tade´, M.O., Datta, R. and Smith, T.N. (1997c) ETBE Synthesis by reactive distillation. 1. Steady-state simulation and design aspects. Ind. Engng Chem. Res. 36(5), 1855—1869. Sneesby, M.G., Tade´, M.O., Datta, R. and Smith, T.N. (1997d) ETBE synthesis by reactive distillation. 2. Dynamic simulation and control aspects. Ind. Engng Chem. Res. 36(5), 1870—1881. Sundmacher, K. and Hoffman, U. (1995) Oscillatory vapor—liquid transport phenomena in a packed reactive distillation column for fuel ether production. Chem. Engng. J., 57, 219—228. Zhang, T. and Datta, R. (1995) Integral analysis of methyl tert-butyl ether synthesis kinetics. Ind. Engng Chem. Res. 34, 730—740.