ETBE Synthesis via Reactive Distillation. 2. Dynamic Simulation and

Mar 1, 1997 - Some general recommendations for the control of reactive ETBE columns are made ... capital cost is also lower than the conventional proc...
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Ind. Eng. Chem. Res. 1997, 36, 1870-1881

ETBE Synthesis via Reactive Distillation. 2. Dynamic Simulation and Control Aspects Martin G. Sneesby,*,† Moses O. Tade´ ,† Ravindra Datta,‡ and Terence N. Smith† School of Chemical Engineering, Curtin University of Technology, Perth, Western Australia, and Department of Chemical and Biochemical Engineering, University of Iowa, Iowa City, Iowa 52242

Ethyl tert-butyl ether (ETBE) is growing in importance as a gasoline oxygenate and octane enhancer. Its gasoline blending properties are superior to methyl tert-butyl ether (MTBE), and its semirenewability is attracting subsidies from many governments. Synthesis of ETBE via reactive distillation offers advantages of higher conversion, improved energy efficiency, and lower capital costs. A dynamic simulation, based on the MESH equations with supplementary equations to model the main chemical reaction, was developed using SpeedUp. The simulations were then utilized for the study of transient open-loop responses and for control system design. The control of a reactive distillation column presents several difficulties not normally associated with distillation, and dynamic simulation proved to be the ideal tool for the study and resolution of these problems. Some general recommendations for the control of reactive ETBE columns are made, including the need to address control issues early in the design process to recognize implications on process equipment design. Introduction Gasoline oxygenates are becoming increasingly important as more and more countries follow the U.S.A. in introducing legislation requiring a minimum percentage of oxygen to be included in gasoline solid in areas with low or marginal air quality. Although methyl tertbutyl ether (MTBE) remains the market leading oxygenate, ethyl tert-butyl ether (ETBE) is becoming increasingly important and is a viable alternative to MTBE where ethanol subsidies exist. ETBE has superior properties for oxygenating gasoline (especially higher octane and much lower volatility) and is classified as semirenewable when the ethanol reactant is derived from biomass. Both MTBE and ETBE can also be used to replace lead-based octane enhancers (tetramethyllead and tetraethyllead) and are, therefore, viewed as environmentally friendly gasoline additives. The reactive distillation (also called catalytic distillation where a catalyst is present) process for MTBE synthesis can increase reactant conversion and energy efficiency compared with the conventional process. The capital cost is also lower than the conventional process as the functionalities of two process elements (reaction plus separation) are combined in a single item of equipment. This technology can be extended to ETBE synthesis with similar benefits. A previous paper (Sneesby et al., 1996) discussed the steady-state simulation of reactive distillation columns for ETBE synthesis. Here, the model will be extended to the dynamic case for the study of transient responses, process control, and hysteresis. The ETBE synthesis reaction is the reversible etherification of ethanol and isobutylene on an acid catalyst, such as the acidic ion-exchange resin, Amberlyst 15. The reaction is equilibrium limited at high temperatures (above 80 °C) and very slow at low temperatures (below 60 °C). The main side reaction is the dimerization of isobutylene to form diisobutylene (DIB), but this reac* Author to whom correspondence should be addressed. Telephone: 619-351-3776. Fax: 619-351-3554. Email: [email protected]. † Curtin University of Technology. ‡ University of Iowa. S0888-5885(97)00053-5 CCC: $14.00

tion can be restricted by maintaining the ethanol concentration above 4 mol % as then ensures that the catalyst surface is essentially covered with ethanol (Kitchaiya and Datta, 1996). A secondary side reaction occurs between isobutylene and watersthe hydration of isobutylene to form isobutyl alcohol. This reaction can be essentially eliminated by preventing water from entering the system. The reaction chemistry is discussed more fully in Sneesby et al. (1997) and Jensen and Datta (1995, 1996). Reactive Distillation Process for ETBE Synthesis Schemes utilizing reactive distillation for ETBE synthesis are comprised of at least three basic stages: first, pretreatment to remove water and salts that would potentially deactivate the catalyst; second, primary reaction to convert around 80% of the reactants in economical conditions, with effective temperature control to remove the substantial heat which is liberated; and, third, reactive distillation to purify the ether product and remove unreacted hydrocarbons (mostly n-butylenes) from the system. This process is depicted in the simplified process flow diagram (PFD) shown in Figure 1. A fourth stage, the recovery of unreacted ethanol from the distillate product, can be added, but in many cases this is not required. Depending on the overall system requirements and refinery configuration, the reactive distillation column can be designed to produce a very high-purity ether product with little ethanol and no light hydrocarbons or a lower purity product that contains some ethanol and a small amount of light hydrocarbons. The second alternative can be achieved at a lower capital cost, with no loss in isobutylene conversion, but the inclusion of light components is often sufficient to suppress the initial boiling point and flash point of the ether product. The process specification for the ethanol content of the distillate product can also vary between installations. Where an alkylation unit is present downstream, there is an incentive to keep ethanol in the distillate to very low levels. However, if the distillate was to be used © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1871

Figure 1. ETBE synthesis via reactive distillation.

Figure 2. Reactive distillation column configuration for ETBE synthesis.

directly for gasoline blending, the process requirements are somewhat less stringent and a shorter column could be used. The dynamic simulations presented here are for a relatively short column (Figure 2) which could be suitable for an installation requiring high isobutylene conversion but without overly tight restrictions on either the ether volatility/flash point or the distillate ethanol content. This column is based on the MTBE reactive distillation column used in the first patent for the MTBE catalytic distillation process (Smith, 1980) and has been the basis of previous simulation studies (Sneesby et al., 1997; Abufares and Douglas, 1995). Additional stripping stages would be required for this column to meet more stringent specifications on the product compositions. Reactive Distillation Dynamic Model The MESH (Material balance, vapor-liquid Equilibria equations, mole fraction Summations and Heat

balance) equations for distillation were used as the basis for the dynamic reactive distillation model developed here. Equations describing the chemical reaction were added to the material balances where appropriate. To simplify the model from the steady-state case (Sneesby et al., 1997), the following assumptions were introduced: (1) chemical equilibrium is attained on all reactive stages, (2) DIB formation is negligible, (3) constant enthalpy per stage (negligible heat losses), and (4) ideal vapor phase. The assumption of chemical equilibrium allows the reaction kinetics to be neglected, simplifying the modeling of the reactive stages of the column. Negligible DIB formation allows the number of components to be reduced from five to four and the elimination of equations describing the DIB reaction. Negligible heat losses allow enthalpy derivatives to be effectively excluded from the model, and, finally, an ideal vapor phase allows fugacity coefficients to be neglected. These assumptions slightly reduce the absolute accuracy of the model but make it a more effective

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dynamic simulation tool by improving the ratio of real time to simulation time. Dynamic distillation models are susceptible to index problems in the solution of the global set of differential and algebraic equations (DAEs) (Ponton and Gawthrop, 1991; Unger et al., 1995). An index problem arises when the global set of DAEs must be differentiated more than once to reach the solution. To avoid such a problem, the overall model must be fully closed (Moe et al., 1995), requiring relationships between stage-to-stage pressure drop, stage-to-stage holdup, and vapor and liquid internal flows. The full set of reactive distillation dynamic equations is shown below. As with the steady-state model, the heat of reaction is calculated implicitly and does not need to be separately specified.

component balance d(Mxi) ) Linxi,in + Vinxi,in - Loutxi,out - Voutxi,out + ri dt (16) energy balance d(MH) L V L V ) LinHi,in + VinHi,in - LoutHi,out - VoutHi,out dt (17) dH )0 dt Pyi ) γixiPvap i

equilibrium

Separation Stage material balance

dM ) Lin + Vin - Lout - Vout dt (1)

component balance d(Mxi) ) Linxi,in + Vinxi,in - Loutxi,out - Voutxi,out (2) dt energy balance d(MH) L V L V ) LinHi,in + VinHi,in - LoutHi,out - VoutHi,out dt (3) dH )0 dt equilibrium

Pyi ) V

holdup

(4) γixiPvap i

hydraulics

L

(20)

∑yi ) 1

(21)

∆P ) f(M,V)

(22) (23)

Total Condenser material balance

component balance

dM )V-L dt d(Mxi) ) Vyi - Lxi dt d(MH) ) VHV - LHL - Qc dt

energy balance

dH )0 dt

T )T

(6)

∑yi ) 1

(7)

equilibrium

(8)

holdup

(9)

hydraulics

∆P ) f(M,V)

(19)

TV ) TL

M ) f(L,F,vol)

(5)

M ) f(L,F,vol)

hydraulics

holdup

(18)

P)

∑γiyiPvap i

(24)

(25)

(26) (27) (28)

M ) f(L,F,vol)

(29)

∆P ) Pi - P ) f(V)

(30)

Partial Reboiler Reactive Stage material balance material balance dM ) Lin + Vin - Lout - Vout + dt rETBE ) -rEtOH ) -rBut rnBut ) 0 Keq )

aETBE aEtOHaiBut

∑ri

(10)

(11, 12) (13)

(31)

component balance d(Mxi) ) Linxi,in - Loutxi,out - Vyi (32) dt energy balance d(MH) L ) LinHin - LoutHLout - VHV + Qr (33) dt

(14)

4060.59 - 2.89055 ln T T 0.0191544T + 5.28586 × 10-5T2 - 5.32977 × 10-8T3 (15)

ln Keq ) 10.387 +

dM ) Lin - Lout - Vt dt

dH )0 dt equilibrium

Pyi ) γixiPvap i TV ) TL

(34) (35) (36)

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1873 Table 1. Physical Property Routines and Sources property

method and source

reaction equilibrium vapor pressures liquid activity coefficients vapor fugacity coefficients enthalpy density

activities (Jensen and Datta, 1995) Antoinne equations (Krahenbu¨hl and Gmehling, 1994) UNIFAC model ideal vapor phase Soave-Redlich-Kwong equation of state Soave-Redlich-Kwong equation of state

Table 2. ETBE Reactive Distillation Column Simulation Input feed conditions

column specification

temperature (°C) rates (L/min) composition (mole basis)

30 0.76 29.1% ETBE, 9.1% ethanol, 7.3% isobutylene, 54.5% n-butylenes

composition (weight basis)

43.3% ETBE, 6.1% ethanol, 6.0% isobutylene, 44.6% n-butylenes

overall excess ethanol (mol %)

5.0

rectification stages reaction stages stripping stages total stages overhead pressure (kPa) condenser reflux ratio reboiler

2 3 5 10 950 total 5.0 partial

Table 3. Comparison of Steady-State and Dynamic Model Simulation Outputs property

steady-state model

dynamic model

condenser temp (°C) reaction zone temp (°C) reboiler temp (°C) isobutylene conversion (mol %) bottoms composition (wt %) distillate composition (wt %) condenser duty (kW) reboiler duty (kW) reaction rates (mol/min)

79 80-84 160 97.5 96.5% ETBE, 2.7% ethanol, 0.7% butylenes, 0.04% DIB 97.7% n-butylenes, 1.6% isobutylene, 0.7% ethanol 6.73 8.33 0.18 (stage 3), 0.19 (stage 4), 0.11 (stage 5)

79 80-84 160 97.7 96.6% ETBE, 2.6% ethanol, 0.8% butylenes 97.8% n-butylenes, 1.5% isobutylene, 0.7% ethanol 6.71 8.31 0.17 (stage 3), 0.18 (stage 4), 0.13 (stage 5)

holdup

∑yi ) 1

(37)

M ) f(L,F,vol)

(38)

The various physical property routines that were used are indicated in Table 1 and are identical to those used for the steady-state simulation (Sneesby et al., 1997). A recently published reaction equilibrium expression, specifically derived for ETBE, was used (Jensen and Datta, 1995) in preference to older information or equations based on MTBE synthesis. Similarly, the latest vapor pressure data was used (Krahenbu¨l and Gmehling, 1994). The numerical constants and equation structure for eqs 8, 9, 22, 23, 29, 30, and 38 were determined semiempirically for the column being simulated. Although fully rigorous equations are available, they do not contribute significantly to the accuracy of the solution but unnecessarily add to the complexity of the model. The variables relating to physical dimensions of the equipment (eqs 8, 22, 30, and 38) were estimated based on the flow rates and duties specified for a pilot-scale laboratory system (154 mm diameter column) which was recently constructed at Curtin University, Western Australia. The pilot-plant column will be used to provide further verification of the steady-state simulation model and to assess the accuracy of the dynamic model before testing a range of distillation control configurations and various advanced control strategies for reactive distillation. The column has been designed to operate in the industrially significant range of product purities and isobutylene conversions and will process a hydrocarbon feed stream supplied by a local refinery. The global system of DAEs for the simplified dynamic model comprised 568 algebraic variables, 505 linear and nonlinear equations, and 50 unknown derivatives. By

comparison, the full steady-state model (with five components but excluding equations for dynamics, stage-to-stage pressure drops, etc.) contained 578 variables and 504 equations. Steady-State Solution The simulation input (feed conditions and column specification) that was used previously for steady-state analysis was used again here (see Table 2). Results obtained from the simplified dynamic case are compared with previously published results for the full steadystate model in Table 3, using the dynamic process simulator, SpeedUp (Aspen Technology, 1993) for both simulations. The two sets of results are almost identical and validate the use of simplifying assumptions in the development of the dynamic model. Probably the most significant shortcoming of the dynamic model is its inability to estimate the extent of DIB formation or identify transient effects on the side-reaction rate. However, the model remains valid for most simulation studies and could be readily extended to model the side reaction but only with a penalty to the ratio of real time to simulation time. Open-Loop Transient Responses It is becoming increasingly important to consider dynamic responses in the design phase of major engineering projects to realize the benefits of integrating control system design with process design. Process control considerations can influence equipment requirements (especially instrumentation) and can, in exceptional cases, negate the effectiveness of a design that is satisfactory at steady state but difficult to control. This is particularly true for processes such as MTBE and ETBE reactive distillation, where instability and/or hysteresis effects may be present (Jacobs and Krishna, 1993; Nijhuis et al., 1993).

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Figure 3. Open-loop response to step increase in feed rate.

Figure 4. Open-loop response to step change in feed composition.

The dynamic capability of SpeedUp was initially utilized to analyze open-loop dynamic responses for some key disturbances to the system: (1) feed rate step increase, (2) feed composition step increase, and (3) reflux rate step increase. The magnitudes of the step changes were sufficient to have a significant affect on the column operation but were not so large that the column stability was compromised. In each of the above cases, the overhead pressure, reboiler duty, and reflux rate were assumed to be constant. Effects of a Step Change in Feed Rate. The transient response to a 5% increase in feed rate with pressure, reboiler duty, and reflux rate held constant is shown in Figure 3. Without an increase in heat input, there was a significant increase in the bottoms flow rate as the extra feed material left the column almost entirely with the ether product. The composition of the bottom product shifted to include the additional light material and the temperature decreased accordingly as the reboiler remained in phase equilibrium. Less ethanol was returned to the reaction zone which subsequently reduced the isobutylene conversion. Effects of a Step Change in Feed Composition. Figure 4 shows the transient response of the same column after the feed composition was adjusted to increase the ratio of ethanol to isobutylene by 2%. The total molar feed rate was fixed as were the pressure, reboiler duty, and reflux rate. The responses were essentially first order under this scenario, and the permanent responses became fully evident after about 40 min. The isobutylene conversion increased slightly by the additional driving force for the reaction, but ether purity decreased as the ethanol content of the bottoms product increased without additional heat input. The bottoms temperature followed the composition changes as phase equilibrium was maintained. Effects of a Step Change in Reflux Rate. The transient response to a 5% increase in reflux rate is

Figure 5. Open-loop response to step increase in reflux rate.

shown in Figure 5. The same column was used (Figure 2), and pressure and reboiler duty were again held constant. There was a fast initial response which then disappeared as the permanent changes were asserted. Without an increase in reboiler duty, the column was effectively quenched by the extra reflux and ethanol was shifted to the reboiler. The temporary increase in separation efficiency in the rectification section (due to increased vapor and liquid flows) reduced the amount of ethanol lost in the distillate and had a very short positive effect on the overall conversion. However, this effect was quickly overshadowed by the loss of ethanol from the reaction zone. Both conversion and ether purity moved quickly away from acceptable values, indicating the importance of maintaining the reboiler duty close to the optimum. Changes in the distillate product became evident more quickly than in the bottoms product, indicating the damping effect of column holdup. Other Transient Responses The basic dynamic model was modified to simulate two other disturbances to the reactive distillation system. First, catalyst aging was simulated by reextending the model to incorporate reaction kinetics and decreasing the amount of active catalyst present according to a simple ramp function. Second, changing ambient temperature was simulated by modifying the reflux rate according to a pattern that might result if an air cooler operated at its duty limit with a control configuration that manipulated the reflux drum level with the condenser duty. Catalyst Aging. Amberlyst 15 is susceptible to both short-term poisoning and long-term deactivation. A time frame of 15 h was assumed here for the amount of active catalyst to linearly decrease to 10% of the initial catalyst load, mcat (equivalent to 1% deactivation every 10 min), to simulate severe short-term poisoning. The initial catalyst load was estimated based on the dimensions of the pilot-scale column. The full reaction rate equation, proposed for conditions where the ethanol concentration is below 4.0 mol % (Jensen and Datta, 1996), was used to provide the required kinetic information. However, the ethanol adsorption equilibrium constant (KA) was assumed to be constant over the reaction zone temperatures to reduce the total number of equations to be solved. The additional equations, given below, replace eq 14 in the basic dynamic model (eqs 1-38).

(

aETBE KeqaEtOH

mcatkrateaEtOH2 aiBut rETBE )

3

(1 + KAaEtOH)

(

krate ) 7.418 × 1012 exp KA ) 15

60.4 RT

)

)

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1875

(39)

(40) (41)

Figure 6 shows the column response. Until the amount of active catalyst falls to around 20% of the starting load, the reductions in conversion and product purity are only slight and would probably go undetected in an industrial environment. However, after that point effects become more exaggerated and would necessitate a unit shutdown after only a few more hours if the poisoning were allowed to continue unabated. Longer term catalyst aging (deactivation) would probably follow a similar path on a different time scale. Ambient Temperature Rise. The reflux rate was varied in a sinusoidal pattern over a period of 6 h to simulate an ambient temperature rise in the morning followed by a temperature fall in the afternoon. The initial and final conditions are equivalent to the steadystate conditions given in Tables 2 and 3, while the reflux rate reached a minimum of 80% of the steady-state value after 3 h (corresponding to the daily maximum temperature). The reboiler duty was constant throughout the simulation. This scenario corresponds to a system where the reflux drum level is controlled by manipulating the condenser duty and the condenser is directly affected by ambient conditions (e.g., an air cooler operating at its maximum speed). In practice, the reflux drum would essentially run dry and the reflux flow control valve would saturate during periods of high ambient temperature, causing the reflux rate to fall as the ambient temperature rises. The simulation output reflects the changes to operation that would occur if the reboiler duty was not manipulated to compensate for the fall in reflux rate. The column response is shown in Figure 7. Changes are dramatic and clearly show the need to constantly monitor and adjust the reboiler duty to maintain acceptable operating conditions. The hiccup in the response which occurs between 80 and 90 min after the start of the simulation appears to be a result of the column readjusting itself to the relatively fast changes that occur. The reaction conditions are temporarily stabilized due to interactions between the changing composition and reaction equilibrium. The shape of the response was not affected by rounding errors in the simulation. The response is not symmetrical due to the lags and dynamics present in the system. Process Control The controllability of a reactive distillation column is an important consideration in the design phase. More so than many other processes, reactive distillation requires tight process control to ensure that deviations from the optimum operating point can be handled adequately to minimize any yield or production losses. A column that appears satisfactory in the steady state may be uncontrollable in dynamic operation if the operating point is unstable or relies on overly tight control of one or more operating variables. The development of a successful process control scheme requires

Figure 6. Transient response to catalyst aging.

Figure 7. Transient response to variation in ambient temperature.

the identification of the key process objectives, translation of these objectives into achievable control objectives, and integration of the control objectives within an overall control strategy. For ETBE columns, coupling the process objectives with achievable control objectives presents some difficulties, while the control strategy itself requires some significant intricacies to maximize its effectiveness. An accurate dynamic simulation of the reactive distillation column can be of great benefit in this process. Process Objectives. The final, overall objective of any process should always be to maximize profitability. This is normally achieved via a rationalization of energy consumption with the value added by the process. For example, in a conventional distillation column, increasing the reflux rate and reboiler duty nearly always increases the fractionation achieved and, subsequently, increases the product value or its yield. With most reactors and many other unit operations, this principle often manifests itself with respect to heating or cooling requirements. In many cases, the value added by the process coupled with a high demand for the product if more significant than energy costs, and the incentive is to operate the system up to equipment constraints while maintaining product quality. Reactive distillation combines the functionality of both the reaction and purification stages of a process, and the main operating objective for a reactive distillation column should reflect both roles. In a reactor, the principal process objective which maximizes profitability is conversion of the limiting reactant, while in distillation it is separation (or fractionation) which is normally measured by the product purity. For an ETBE column, the combination of the two objectives can be expressed as “meeting a target specification for the ETBE product purity while maximizing isobutylene conversion”.

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Figure 8. Nonlinear relationship between reboiler temperature and bottoms composition in an ETBE column.

Figure 9. Relationship between stripping section temperature and bottoms composition in an ETBE column.

There are also several secondary process objectives for reactive distillation ETBE columns. ETBE appearing in the distillate is essentially lost from the product and should, therefore, be minimized. Contamination of the ether product with ethanol has the potential to impact on the profitability of some downstream units and should, again, be minimized. The catalyst life should be maximized to avoid the significant costs associated with shutting down a unit to replace spent catalyst. Control Objectives. Once the process objectives have been defined, a means of determining whether the objectives are being met (monitoring the process) must be established. There are three basic methods for monitoring product composition: (a) directly, with one or more online analyzers; (b) indirectly, using a temperature or pressure corrected temperature to infer composition; and (c) externally, using process samples taken at regular intervals and appropriate laboratory equipment. Analyzers have many advantages but are costly, require regular maintenance, and usually introduce a significant time delay into the process. Inferential control is cheaper and, often, more reliable but can also be less accurate. The use of external measuring equipment limits the frequency of measurements and cannot be used directly for closed-loop control. If some form of inferential controller is to be used (either in a closed-loop or open-loop system) to monitor product composition, the temperature sensor must be located carefully to ensure that changes in the composition are accurately reflected and good sensitivity to setpoint changes is provided. The reboiler sump is commonly used as a sensing location as it minimizes process dead time and sensitivity is usually high (except with very high product purities). Variations in the reboiler temperature (at constant pressure) directly relate to changes in the product composition, whereas other locations are susceptible to interference from other sources. However, in an ETBE reactive distillation column, the relationship between reboiler temperature and bottoms composition is neither linear nor even monotonic, as indicated by Figure 8, which was produced using simulation data. The nonmonotonic relationship prevents the reboiler temperature from being used to infer composition. The optimum operating point for reboiler duty (and bottoms rate) occurs near an inflection point so that, essentially, the bottoms temperature should be maximized. If the ether purity is below its desired value, the reboiler duty (or bottoms rate) may need to be increased or decreased. In an ETBE column, the best location for the temperature sensor is toward the middle of the stripping section.

Figure 9 shows the relationship between a temperature in the middle of the stripping section and the bottoms composition and was again generated using simulation data from the SpeedUp model. The shape of the curve clearly contrasts with the relationship shown in Figure 8. Although the relationship between the stripping section temperature and bottoms composition is still highly nonlinear, and a bottoms composition of, say 90 mol %, is obtained at two temperatures (approximately 99 and 132 °C), every temperature corresponds to one, and only one, composition. Therefore, the stripping section temperature uniquely defines the operating point of the column. The sensitivity is also high, with a change of 5 °C representing only a small change in ether purity near the optimum operating point. The stripping section temperature is, therefore, suitable to be used in an inferential controller. Shifting the sensing point away from the reboiler increases the system dead time, but this cannot be avoided if a stable inferential controller is to be implemented. Measuring the product composition, via an analyzer, inferential control, or laboratory results, allows the ether purity to be monitored with respect to the process objective but does not determine the isobutylene conversion which is also of importance. Direct measurement of the conversion would require complex, synchronized analyzers on the feed, distillate, and bottoms products plus a calculation module. Fortunately, high ether purity implies satisfactory conversion, as it indicates that ETBE formation in the column is also high. However, the purity and conversion curves do not correspond exactly, and maximum conversion is normally achieved at an ether purity just less than the maximum (Sneesby et al., 1997). The simulation data presented in Figure 10 indicate that the maximum conversion is achieved at an ether purity of around 88 mol %, while the maximum purity is approximately 91 mol % (96 wt %) for this column. The optimal operating point would probably be between the two maxima but would need to be determined for the specific column installation with respect to raw material costs and product values. The difference between ether purity and isobutylene conversion creates an incentive to monitor the conversion online to guarantee that both key process objectives (purity and conversion) are met satisfactorily. Another inferential controller is suggested, utilizing available process data such as the temperature profile, product rates, and prereactor temperatures. Regular laboratory tests should be used to monitor the performance of the inferential controller and update any bias, as necessary.

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1877 Table 4. Basic Distillation Control Configurations composition control

level control

configuration

primary manipulated variable

secondary manipulated variable

reflux drum level

reboiler sump level

LV LB LD DV DB VB

reflux rate or reboiler duty bottoms rate distillate rate distillate rate distillate rate bottoms rate

reboiler duty or reflux rate reflux rate reflux rate reboiler duty bottoms rate reboiler duty

distillate rate distillate rate reboiler duty reflux rate reflux rate distillate rate

bottoms rate reboiler duty bottoms rate bottoms rate reboiler duty reflux rate

Figure 10. Ether purity and isobutylene conversion in an ETBE column.

Control Configurations for Reactive Distillation. The degrees of freedom for a reactive distillation column are essentially the same as those for a conventional binary distillation column: distillate rate (D), bottoms rate (B), reflux rate (L or R), reboiler duty (V or Qr), and condenser duty (Qc). Three of these streams must be used to control the state of the column (pressure, reboiler sump level, and reflux drum level), leaving two streams to control the operation of the column. Where the column has two feed streams, an additional stream is available to be manipulated. However, in an industrial situation, ethanol is generally added upstream of the prereactor so that there is only a single feed to the ETBE column (Figure 1). The operating pressure of a reactive distillation column can be controlled by any of the methods used in conventional distillation (Neisenfeld and Seeman, 1981) and generally involves some type of manipulation of the condenser duty or distillate product rate. To ensure an effective dynamic response, the reboiler (sump) level is usually controlled via the bottoms flow or the reboiler duty, while the reflux drum (accumulator) level is usually controlled via the reflux or distillate flow (assuming that the condenser duty is already being used to control pressure). Two degrees of freedom remain to control product compositions. Excluding the condenser duty as a manipulated variable for composition control, there are six possible combinations of the remaining variables, as indicated by Table 4. The configurations are described by the two manipulated variables used for composition control. The DB configuration violates steady-state material balance integrity and is generally not considered although its effectiveness has been demonstrated experimentally for some columns (Skogestad et al., 1990). Both the LD and VB configurations are feasible but lead to sluggish level control which subsequently affects composition control via the overall column material balance and reduces the maximum achievable control response. Therefore, three principal control configurations remainsLV, LB, and DV. For the LB and DV schemes, the primary manipu-

lated variable for composition control must be one of the products flows as material balance effects (feed split) predominate over energy balance effects (fractionation) (Neisenfeld and Seeman, 1981). The LV configuration is feasible with either reflux rate or reboiler duty as the primary manipulated variable for composition control. Figure 11 shows the control connections implied by the LV configuration. Other configurations can be set up similarly. Each of the control configurations indicated in Table 4 can be implemented in one of three ways: (a) manual control; (b) single composition control; or (c) double composition control. Manual control implies no closedloop controllers except for column state variables (pressure and level control). Single composition control allows one closed-loop controller on the primary product using either a process analyzer or inferential composition calculations. Double composition control allows for both the distillate and bottoms product compositions to be simultaneously regulated by closed-loop controllers using process measurements. In an ETBE column, the bottoms product (ether) is clearly more important than the overhead product and single composition control should suffice. This keeps the control system simple and avoids the possibility of columns instability caused by control loop interactions. The remaining variable not being used for composition control would then be used to maximize the value added by the process up to the equipment constraints (e.g., fix the reflux rate at a level just below the column flooding limit or condenser duty limit). For single composition control using inferential control to monitor the ether product purity, three control configurations warrant further investigationsLV, LB, and DV. Some general process control rules can expedite the selection of a single scheme. First, the best control scheme should combine steady-state sensitivity and dynamic responsiveness (Neisenfeld and Seeman, 1981). Since the sensing point is likely to be near the middle of the stripping section, the reboiler duty (V) and bottoms rate (B) are favored as the principal manipulated variables, although all three candidates show good sensitivity for the controlled variable. Second, level controllers should preferentially use the largest outlet stream (Luyben, 1992). This implies using reflux rate to control the reflux drum level on columns where the reflux ratio is much higher than unity. This consideration favors the DV configuration for columns with high reflux ratio and the LV and LB configurations for columns with low reflux ratio. No clear preference for any control configuration is evident. However, dynamic simulation provides a means of quickly assessing each scheme. Control performance was tested against two common disturbances (a feed rate step increase and a feed composition step increase) and a set-point change. Simple PI controllers were used in all cases, with control constants determined empiri-

1878 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997

Figure 11. LV composition control configuration (manual operation).

Figure 12. Step increase in feed with the LV configuration.

Figure 13. Step change in feed composition with the LV configuration.

cally. A temperature at the middle of the stripping section was used as the controlled variable. The results are presented in Figures 12-20 and summarized in Table 5 in terms of the integrated absolute error (IAE) and the integrated time-weighted absolute error (ITAE) of the controlled variable. Table 5 clearly suggests that the LV and LB schemes are more effective than the DV configuration, but this is much less evident from the simulation responses shown in Figures 12-20. The LV and LB configurations produce a faster response to feed rate changes than the DV scheme. The deviation from the initial conditions is another applicable point of comparison, since the product composition is not being measured or controlled directly, and the LV and LB configurations again outperform the DV scheme for a change in the feed rate. However, the dynamic responses of the ether product to changes in the feed composition and set point were

similar for all configurations, despite the much higher IAE and ITAE for the DV configuration. Overall, the LV and LB configurations were still preferred. These results indicate that the presence of a reaction has a significant influence on the performance of a control system. The DV configuration is very widely used in industry for conventional distillation columns, including those where the primary product is the column bottoms, and normally yields very satisfactory results based on controlling the feed split. However, in reactive distillation columns, manipulating the feed split does not necessarily ensure that satisfactory reaction conditions are maintained and a control configuration manipulating the reboiler energy input (either directly with the LV configuration or indirectly with the LB configuration) is preferred. In addition to the basic control configurations shown in Table 4, ratio control schemes are widely used for

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1879

Figure 14. Step change in set point with the LV configuration.

Figure 18. Step increase in feed with the DV configuration.

Figure 15. Step increase in feed with the LB configuration.

Figure 19. Step change in feed composition with the DV configuration.

Figure 16. Step change in feed composition with the LB configuration.

Figure 20. Step change in set point with the DV configuration.

Figure 17. Step change in set point with the LB configuration.

distillation control. Many combinations are possible, but three of the more commonly used schemes are shown in Table 6. The (L/D)V scheme is also known as Ryskamp’s scheme, while the (L/D)(V/B) is known as the double ratio scheme and has been widely recommended (Skogestad and Morari, 1987; Shinskey, 1984).

Ratio schemes create implicit decoupling (Waller, 1992) which is highly advantageous for double composition control but less useful for single composition control where the control scheme makes it more difficult to sustain operation at an equipment constraint. The performance of the ratio schemes can also be assessed using dynamic simulations. Considering only single composition control and utilizing a temperature from the middle of the stripping section to infer bottoms composition, the configurations listed in Table 6 were tested. Table 7 gives the IAE and ITAE for the same three tests used on the LV, LB, and DV configurations and indicates that the performances of the ratio schemes were generally slightly inferior to the LV and LB configurations (cf. Table 5). The dynamic simulation responses are similar to those shown in Figures 12-17 but have not been included here due to space limitations. Overall Control Strategy. A successful control system for an ETBE reactive distillation column should incorporate the following features: (1) recognize both

1880 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 Table 5. Control Scheme Performance feed rate step increase (+8%)

feed composition step increase (+2% to ratio)

set-point change (+5 °C)

scheme

IAE

ITAE

IAE

ITAE

IAE

ITAE

LV LB DV

0.3 0.4 42

0.6 0.8 430

0.05 0.05 1.4

0.3 0.1 7.8

1.3 0.6 15

2.2 1.0 73

Table 6. Ratio Control Configurations for Distillation composition control

level control

configuration

primary manipulated variable

secondary manipulated variable

reflux drum level

reboiler sump level

(L/D)V (L/D)(V/B) (V/B)L

reboiler duty reflux ratio or boilup ratio reflux rate

reflux ratio boilup ratio or reflux ratio boilup ratio

distillate rate distillate rate distillate rate

bottoms rate bottoms rate bottoms rate

Table 7. Ratio Control Scheme Performance feed rate step increase (+8%)

feed composition step increase (+2% to ratio)

set-point change (+5 °C)

scheme

IAE

ITAE

IAE

ITAE

IAE

ITAE

(L/D)V (L/D)(V/B) (V/B)L

0.8 0.1 0.4

2.3 0.6 1.0

0.07 0.1 0.1

0.6 0.6 0.7

1.6 1.5 1.5

3.4 2.5 2.5

ether purity and isobutylene conversion as process objectives, (2) use a temperature from the middle of the stripping section rather than the reboiler to infer bottoms composition, (3) generally use single composition control, (4) use only control configurations that manipulate the reboiler (either the LV or LB are recommended). Other features should also be developed into more complex controllers. For example, inferential conversion control and catalyst monitoring. The multiplicity phenomenon (Jacobs and Krishna, 1993; Nijhuis et al., 1993) also has implications for control system design. These aspects will be discussed in a later paper. It is also important to acknowledge the implications the control system has for the process design. For example, the reboiler design may be influenced by the need to provide high-precision control for either the LV (where the reboiler duty is manipulated directly) or LB (where tight sump level control is required to maintain the integrity of the material balance and ensure that changes in the bottoms rate directly affect the column) configurations. The choice of reflux ratio also influences the control configuration and indirectly affects the dynamic performance of the column as the reflux rate (the larger outlet stream from the reflux drum in many cases) is unlikely to be available for level control. Conclusions Process simulation of ETBE reactive distillation columns can be performed in a way similar to that for MTBE columns, using either the MESH or MERQ distillation equations and appropriate additional equations to model the chemical reaction(s). The MESH method was previously shown to be accurate for an MTBE column and was extended to ETBE columns using both Pro/II (Simuation Sciences, 1994) and SpeedUp (Aspen Technology, 1993). The SpeedUp model has subsequently been extended to the dynamic case using a pilot-scale column to provide system lags and dimensions. The dynamic model was used to determine transient open-loop responses and test several closed-loop controller configurations. The interactions between the chemical and phase equilibrium which are present in reactive

distillation create several unusual control problems which do not generally occur with conventional distillation. Dynamic simulation is the ideal tool for studying these responses. The presence of dual operating objectives in reactive distillation also influences the operation and control of the column. It is important to identify these issues early in the process design phase as some aspects of the control system design also have implications for the process design. Dynamic simulations were used to evaluate a range of standard and ratio control configurations for ETBE reactive distillation columns. Several control configurations were found to be feasible, but two are recommended: the LV and LB configurations, both set up for single composition control. The location of the temperature sensor is critical and can dramatically affect the stability of the control schemesa location near the middle of the stripping section is preferred. Additional controller complexities can be added to monitor (and control) isobutylene conversion, monitor catalyst aging, and detect multiplicity where these issues are important. Nomenclature ai ) activity of component i HL ) molar liquid enthalpy HV ) molar vapor enthalpy krate ) reaction rate constant Keq ) ETBE reaction equilibrium constant mcat ) catalyst load per stage L ) molar liquid flow M ) molar holdup P ) pressure Pvap ) vapor pressure Qc ) condenser duty Qr ) reboiler duty ri ) reaction rate of component i TL ) liquid temperature TV ) vapor temperature V ) molar vapor flow vol ) volume of stage/condenser/reboiler xi ) molar liquid concentration of component i yi ) molar vapor concentration of component i F ) density

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1881 γi ) activity coefficient of component i Abbreviations DIB ) diisobutylene ETBE ) ethyl tert-butyl ether EtOH ) ethanol iBut ) isobutylene MTBE ) methyl tert-butyl ether nBut ) normal butylenes (1-butylene and 2-butylene)

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Received for review January 15, 1997 Accepted January 16, 1997X IE970053Y

X Abstract published in Advance ACS Abstracts, March 1, 1997.