Ind. Eng. Chem. Res. 1993,32, 2767-2774
2767
Multiple Steady States during Reactive Distillation of Methyl tert-Butyl Ether S.A. Nijhuist Chemical Engineering Department, University of Amterdam, Nieuwe Achtergracht 166, The Netherlands
1018 WV Amsterdam,
F,P. J. M. Kerkhof and A. N. S. Mak' Comprimo Engineers & Contractors, P.O.Box 58026, 1040 HA Amsterdam, The Netherlands This paper presents results of computer simulations of the synthesis of methyl tert-butyl ether (MTBE) in a fixed-bed reactor and in a reactive distillation column. These calculations clearly showed the advantages of MTBE synthesis in a catalytic distillation tower. Furthermore, the computer simulations showed that multiple steady states may occur in the reactive distillation column during MTBE synthesis in a broad range of operating conditions. An analysis of some sensitivity studies is presented. 1. Introduction Gasoline lead phase-out has stimulated the production of ethers like MTBE (methyl tert-butyl ether), TAME (tert-amyl methyl ether), and others (e.g., Short, 1986; Unzelman, 1989). Blended in the gasoline pool, these socalled octane boosters increase the octane number of gasoline and decrease carbon monoxide emissions. At present, the world MTBE production capacity is sharply increasing and it is expected that in 1993 17 X 106 tons will be produced worldwide, which is almost twice as much as the 1990 MTBE production capacity. The most commonly used production for MTBE is based on the liquid-phase chemical reaction between methanol and isobutene in a fixed-bed reactor. The above-mentioned reaction is acid catalyzed, and the majority of the production processes use a strong-acid ion-exchange resin as a catalyst. The catalytic reaction CH,OH methanol
+ (CH,),C=CH, isobutene
-
H+
(CH,)COCH, MTBE
between methanol and isobutene to MTBE has the following characteristics: 1. The reaction is exothermic (A",= -37.7 kJ/mol) and the maximum conversion is determined by a thermodynamic equilibrium value. 2. The reaction is selective to isobutene; i.e., other butenes are not converted and almost no byproducts are formed. 3. The vapor-liquid equilibrium behaves nonideally; i.e., relatively large activity coefficients can be obtained. Liquid-phase separations, however, do not occur. In a conventional MTBE production process (e.g., Ancillotti et al., 19871, methanol, a mixture of butenes, and a cooled recycle stream are fed to a fixed-bed reactor consisting of a strong-acid ion-exchange resin. The net product stream of this reactor consists of unconverted methanol and isobutene, MTBE, and the inert other butenes which are separated by distillation and extraction. The isobutene from the distillation column and the methanol from the extraction column are recycled to the
* To whom correspondence should be addressed.
+ Present address: University of Twente,Faculty of Chemical
Technology,P.O. Box 217,7500 AE Enschede,The Netherlands.
reactor feed stream. In a catalytic distillation unit both the chemical reaction and distillation occur simultaneously in a packed or tray column (see Figure 1). This combination offers potential advantages over the above-mentioned fixed-bed and subsequent distillation system, including the following: use of the heat of reaction for product separation; a relatively easy controllable temperature profile in the catalytic section, i.e., no cooling required and no occurrence of hot spots; lower operating costs due to higher obtainable conversions (see, e.g, Kerkhof et al., 1991), because thermodynamic equilibrium limitations are avoided due to in situ product separation; lower capital cost due to less equipment. At present some commercial catalytic distillation processes are operated using a distillation tower packed with bales of glass wool in which the catalyst is embedded (Lander et tal., 1983). Other kinds of packing, like acid resins embedded in structured packing (DeGarmo et al., 1992) can also be used as a suitable material. Reactive distillation is the subject of an increasing number of theoretical and experimental studies. The following applications of this new unit operation can also be considered hydrolysis reactions (e.g., deesterifications), heterogeneous catalytic systems (e.g., etherification, alkylation), and metathesis reactions. The combination of reaction and distillation in a single process step may be hampered by a number of complex interactions. Simulation studies may help to determine the influence of feed locations, the reflux ratio, and the amount of catalyst on the overall conversion and product purities and to optimize column performance. In the following, results will be presented of computer simulations of MTBE synthesis in a fixed bed and in a reactive distillation column. 2. Simulation Basis 2.1. Feed Specifications and Physical Properties. The simulations of the catalytic distillation column (CDC) and the fixed-bed reactor (FBR) were executed using the commercially available flowsheeting package ASPEN PLUS licensed by ASPEN TECH (ASPEN, 1988). As a basis for the simulations of the catalytic distillation column (CDC) and the fixed-bed reactor (FBR), it will be assumed that 197 mol/s (500 000 metric tons/year) MTBE is produced. Furthermore, it will be assumed that the
0SSS-5SS5/93/2632-2767~04.00/00 1993 American Chemical Society
2768 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 Table I. Feed and Operating Conditions (Design Cases) Used for the Computer Simulations of the Catalytic Distillation Column (see Figure 1) and the Fixed-Bed Reactor (FBR) CDC FBR feed methanol methanol quantity (liq) C 4 O (vap) (liq) C4 (liq) units Fi 206 549 206 549 mol/s T 320 350 343/353 343/353 K P 11 11 50 50 bar feed stage 10 9/10/11b W 6400 6400 kg R, 7 B 197 mol/s a
*
35.6% isobutene, balance n-butene. Split: 30-30-40.
Table 11. Coefficients Which Can Be Used To Calculate the Binary UNIQUAC (Reid et aL, 1977) Interaction Parameters 7u = exp(Au/T) (from Rehfinger et ab, 1991) Ai? value Ai? value A12 35.38 K A23 -52.20 K A13 88.04 K A31 -468.76 K A21 -706.34 K A32 24.63 K MeOH = 1; isobutene = 2; MTBE = 3.
reactor feed streams consist of a slight stoichiometricexcess of pure methanol and a binary mixture of isobutene (35.6 mol 5%) and 1-butene. This butene mixture can be regarded as a simplification of a FCC butene stream assuming that the C i s like trans-2-butene, cis-2-butene, and butanes do not significantly change the physical and chemical behavior of the isobutene and 1-butene mixture. This also implies that the methanol, isobutene, 1-butene mixture can be regarded as a pseudobinary system. In Table I a summary is presented of the input variables, i.e., amount of catalyst, feed streams, temperature, pressure, and feed stage, which were provided to the program package. As mentioned in section 1,a liquid mixture of butenes, methanol, and MTBE behaves strongly nonideally (see, e.g., Alm and Ciprian (1980) and Colombo (1983)). As a result of this nonideality, a minimum boiling azeotrope occurs for the binary methanol/MTBE and the pseudobinary methanollbutenes system. The azeotropic compositions also depend on the system pressure. For the description of liquid-phase and gas-liquid interactions, the UNIQUAC (Reid et al., 1977) method was used while gas-phase interactions were modeled using the well-known Redlich-Kwong equations (property set Sysop 11of the ASPEN PLUS program package). In Table I1 the UNIQUAC parameters are presented which were used by Rehfinger and Hoffmann (1990) to describe the kinetics of the MTBE reaction (see section 2.2). These kinetics were used in our simulations, and it will be obvious that we applied, therefore, the same interaction model as the above-mentioned authors. General thermodynamic data were obtained from the DIPPR data bank (ASPEN, 1988). 2.2. Reaction Kinetics and Diffusion Limitations. During the computer simulations, the reaction kinetics of the liquid-phase reaction between methanol and isobutene dissolved in 1-butene, presented by Rehfinger and Hoffmann (1990) were applied:
where r represents the reaction rate per unit catalyst mass, q is the amount of acid groups on the resin per unit mass (4.9 equiv/kg), and a is the activity of a component.
Table 111. Thermodynamic Equilibrium Constant K. and Reaction Rate Constant k. as a Function of Temperature T k, = 3.67 X 10l2 e-lllloITmol/@equiv) K, = 284 exp[f(T)I
($- $)+ c2 log( i)+
f(T) = c1
+
c3(T - To) c , ( p
c,(P- 2';)
- T:) +
+ c,(P- Tt)
To = 298.15 K ~1
= -1493K; ~2 = -77.4; ~3 = 0.508K-l; ~4 = -0.913 X 1 W P ,cs = 1.11X 10-BK4; cg -0.628 X IO%-'
In Table I11 the temperature dependencies of the reaction rate constant k, and the thermodynamic equilibrium constant K, are presented. In section 1it was stated that the acid-catalyzed reaction between methanol and isobutene is selective and that almost no byproducts are formed. This is only valid if mass-transfer rates are determined by the reaction rate itself. If the rate of methanol transfer inside the pores of the particles to the acid sites of the resin is the ratedetermining step, large MTBE formation rates can be obtained but the byproduct diisobutene will also be formed. If the transfer rate of isobutene is rate limiting, low reaction rates will be obtained. Rehfinger and Hoffmann (1990) defined two parameters 4 and 4~ which determine the influence of diffusion limitations on the effective reaction rate:
(3) In eqs 2 and 3 d, is the particle diameter, p, is the density of the of catalyst particles, ct is the total concentration of e ~effective ~ diffusion coefficient of the liquid, D e ~is the methanol inside the pores of the particles, and Deois the limiting diffusion coefficient of methanol in isobutene. It should be noted that the effective diffusion coefficient depends on liquid composition and pore sizes as was shown by Rehfinger and Hoffmann (1990). If in eqs 2 and 3 the value of 4 < 0.5 and the value of 4~ > 0.001, the reaction rate will not be limited by particle diffusion. 2.3. Simulationof the Fixed-BedReactor. Assuming plug flow, a mass balance of the reactants over a differential slice of the reactor results in
ax,
w
(4)
where L is the reactor length, r is the reaction rate per unit of catalyst mass, W is the catalyst weight and Fi is the molar feed rate of component i. With eq 4 the conversion Xi of reactant i can be calculated as a function of the distance z from the reactor inlet if this reactor is operated isothermally. If a heat balance is applied to a differential slice of the reactor, one obtains
where U denotes the overall heat-transfer coefficient, A is the heat-transfer area, T is the temperature in the reactor, and T , is the reactor wall temperature. If in eq 5 the heat-transfer term UA(T - T,) is considered, the following equalities are valid in case the reactor is operated:
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2769 isothermally
aTia(ziL)= o
countercurrently cooled
d(F C T aziL
)
= AU(T - T,) (6)
where F,and C, denote the coolant flow and heat capacity, respectively. Assuming plug flow and countercurrent separate flow of coolant and reactants, the concentration and temperature profile in the reactor can be obtained if eqs 4-6 are solved simultaneously using the appropriate reaction kinetics. 2.4. Simulationof the Catalytic Distillation Tower. In order to calculate the concentration profile, reaction rates, and the temperature profile in the CDC column, it was assumed that the column consisted of 17 equilibrium stages. A schematic representation of the column used for the simulations is plotted in Figure 1. Figure 1shows the following three sections of the catalytic distillation unit: a rectification zone in the top section, stages 1-3; a reactive distillation zone in the middle section, stages 4-11; a stripping zone in the bottom, stages 12-17 (including reboiler). The simulations of the CDC were performed using the RADFRAC block with user-supplied reaction kinetics. This program block solves the following set of equations (Venkataraman et al. 1990) associated to any stage j in the distillation column:
methanol
2 3 4
-+
methanol -
Cpix
13 14 15 16
Figure 1. Schematic representation of the configuration of the CDC used during the computer simulations. The stage numbers in this figure refer to the rectification zone, stages 1-3; reactive distillation zone, stages 4-11; and stripping zone, stages 12-17.
component material balances
1
1-00 I
virjwj3 = 0 (7) where Lj denotes the molar liquid flow rate, Gj is the molar gas flow rate, Jj is the amount of catalyst on stage j (W = 0 outside reactive section of the column) and vi is the stoichiometric coefficient of component i; phase equilibrium equations I
0.00
0.00
0.20
0.40
0.60
0.80
-
1.00
L
where Kij denotes the phase equilibrium ratio of component i at stage j ; enthalpy balances
Figure 2. Isobutene conversion X plotted against dimensionless length z/L at two different temperatures in an isothermally operated fixed-bed reactor. The lines in this figure were calculated by the ASPEN PLUS program package using the RPLUG block with user supplied kinetics (eq 1). The reactor operating and feed conditions used for the simulations are presented in Table I.
estimated and calculated values of the unknown physical quantities had a value lower than 10-4. where Jij and H G j denote the enthalpy of the liquid and gas mixture on stage j , respectively. The elemental reference state is used for the calibration of the enthalpies of the mixtures, and thus the heat generated by the chemical reaction does not appear in eq 9. Equations 7-9 are equal to the basic equations used for the calculation of the temperature and concentration profile in a distillation column except for the fifth term in eq 7, which is a consumption/production term resembling the chemical reaction occurring on stage j . The set of equations represented in eqs 7-9 combined with eq 1, the reaction rate equation, are solved iteratively by the ASPEN PLUS program package. During our calculations, convergence was assumed if the relative error between
3. Fixed Bed Reactor Simulation Results
In Figure 2 the isobutene conversion X is plotted against the dimensionless reactor length zJL at two different temperatures T. The lines in Figure 2 were calculated by the ASPEN PLUS program package assuming isothermal operation of a FBR and using the RPLUG block with user-supplied kinetics (eq 1). The reactor operating and feed conditions are represented in Table I. A reactor operating pressure of 50 bar is used in order to stay below the boiling point of the reaction mixture at any condition. Figure 2 clearly shows that, in a fixed-bed reactor, the isobutene conversion X is limited by its thermodynamic
2770 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
r
1.00
[mrnol/s kg]
X 0.75
0.50
1
1
-
CASE A
I '
,
4, C A S E B
0.25
0.0ot " ' I " " I ' ' ' " " 0 1 2 3 4 5 6 7 8 9 1011121314151617 0.00
0.00
b.20
b.10
b.38
0.40
-
0.5b
L
4b8
I
1
0.00
I
~~
49-
0.20
b.40
b.68
8.8b
2 -
1.W
L Figure 3. (a, top) Isobutene conversion X and reaction rate r againat dimensionlees reactor length z/L. The lines in this f i e were calculated by the ASPEN PLUS program package using the RPLUG block with user supplied kinetics (eq 1). The reactor operating and feed conditions used for the simulations are represented in Table I. Furthermore, it was assumed for the calculations of the abovementioned profies that the reactor was countercurrently cooled with cooling water (cooling water flow 10 kmol/s, UA = 600 kW/K). (b, bottom) Reactor temperature and cooling water temperature profile against z/L. The lines in this figure correspond to the case described in the caption of part a.
equilibrium value. Furthermore, Figure 2 shows that this equilibrium value decreases with increasing values of the reactor temperature T. In Figure 3a the isobutene conversionX and the reaction rater are plotted against zlL in the case where the reactor is cooled countercurrently. The lines in Figure 3a were calculated by the ASPEN PLUS program package using the RPLUG block with user-supplied kinetics (eq l),and the operating data are presented in Table I and in the caption of Figure 3a. In Figure 3b the corresponding profiles of the reactor temperature and the cooling medium temperature are presented. Figure 3 shows that in a countercurrently cooled reactor hot spots may occur which result in a relatively low value of the isobutene conversion and in a decrease of the selectivity of the reaction (see section 2.3). In practice, therefore, MTBE reactors are operated with a recycle flow causing smooth temperature and reaction rate profiles. However, the obtainable isobutene conversion value in a recycle reactor is limited. Clearly, the above-mentioned simulation results show the benefits of the use of a catalytic distillation column for the synthesis of MTBE, i.e., high obtainable conversions and smooth operation. 4. Catalytic Distillation Column Simulation Rasults As mentioned in section 1, the intention of this study was to investigate the influence of reflux ratio, catalyst
STAGE NUMBER
Figure 4. Isobutene conversion X as a function of location of methanol feed stage. The solid line in this f i e refers to the highconversion case (case A). The dashed line in thie f i e refera to the low-conversion case (case B). Both cases were obtained with equal feed conditions but with different initial Conditions (seesection 4.1). The dots in this figure refer to the design case (see Figures 6 and 6 andTable1). BothlinesinthiefiiewerecalculatedwiththeASPEN PLUS program package and usingeq 1as a user-supplied production/ consumption term on an equilibrium stage.
weight, and location of the methanol feed stream upon the column operating temperture and isobutene conversion. The location of the butene feed stream at the bottom trays is determined by ita relatively low volatility. The followinginitial values were supplied to the ASPEN PLUSprogram package: composition bottom stage, X ~ = 0.95 and X M ~ O H= 0.05; bottom temperature 420 K; top temperature 350 K. The compositions of the intermediate stages are set by the program and are equal to the composition of the bottom stage. The temperatures of the intermediate stages are calculated by the program by linear interpolation between the top stage and the bottom stage. With these initial values, the program starts the iteration procedure and proceeds until convergence (see section 2.4) is obtained. 4.1. Influence of Methanol Feed Stage Location. When the influence of the location of the methanol feed stage on isobutene conversion was investigated, no convergence was obtained using the above-mentioned initial values if methanol was fed to stage 10. Therefore, we decided to use the following iterative procedure. First the column temperature and concentration profile were calculated with the methanol feed point located at stage 1. Then the values obtained from this simulation were used as initial values for the calculations with the methanol feed point located at stage 2 using the same operating and feed conditions as in the previous simulation. The concentration and temperature profile thus obtained were used for the simulation with the methanol feed point at stage 3 and so on until stage 10. This procedure will be referred toas case A. Avery interestingresult wasobtained when the above-mentioned procedure was reversed, i.e., the column concentration and temperature profile were calculated with the methanol feed located at stage 17which were then used to calculate the concentration and column profile with the methanol feed at stage 16 and so on. With this procedure, steady-state concentration and temperature profiles totally different from the profiles of case A were found. These steady-state profiles will, therefore, be referred to as case B. The resulting isobutene conversions obtained by the above-mentioned procedures are plotted as a function of the methanol feed location in Figure 4. Figure 4 shows that, a t least, two steady states can exist in a CDC column, i.e., a high-conversion steady state (case A, solid line) and a low-conversion steady state (case B, dashed line).
E
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2771
m methsnol 0I-butene
MTBE
=
0n-butene
1.00
methanol
0I-butene
0n-butene
MTBE
1.00
X
X
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.00
0 1 2 3 4 5 6 7 8 9 1011121314151617
0
1 2 3 4 5 6 7 8 9 1011121314151617
STAGE NUMBER
STAGE NUMBER
T K
440 420 400
400
t
I
I
/
STAGENUMBER
380 360
340' " ' ' ' ' ' ' ' ' ' " 0 1 2 3 4 5 6 7 8 91011121314151617 I
'
I
'
STAGE NUMBER
340' I ' ' " " ' ' ' 0 1 2 3 4 5 6 7 8 91011121314151617 I
'
I
'
I
'
STAGE NUMBER
Figure 5. (a, top) Mole fractions of the different components in the catalytic distillation column against the columnstage number. Each bar pattern in this figure represents a calculated value of the mole fraction x of a component at steady state, and refers to design case A (see Table I for operating conditions). (b,bottom) temperature Tand reaction rate r in the catalytic distillation column corresponding to the tray compositions represented in part a.
Figure 6. (a, top) Mole fractions of the different components in the catalytic distillation columnagainst the columnstage number. Each bar pattern in this figure represents a calculated value of the mole fraction x of a component at steady state, and refers to case B (see Table I for operating conditions). (b, bottom) Temperature T and reaction rate r in the catalytic distillation column correspondingto the tray compositions represented in part a.
Furthermore, by following the arrows, it can be obtained from Figure 4 that by varying the methanol feed location (with very small nondiscrete steps) hysteresis occurs; i.e., case A disappears and only case B is obtained if the feed location is lowered to below stage 11 while the opposite happens if the feed location is heighten to above stage 9. Again it should be noted that both cases were obtained using the feed and operating conditions presented in Table I. Also note that the isobutene conversion X in Figure 4 is practically equal to the MTBE mole fraction in the column bottom product since there is a negligible amount of MTBE present in the top of the column. In Figure 5a the composition of the liquid on each tray resulting from the simulation of the reactive distillation between methanol and isobutene is plotted. The values of the mole fractions x of the four different components in the liquid phase presented in this figure refer to the high-conversion case (case A) and were calculated with the methanol feed located at stage 10. Figure 5a shows that the major part of the top and the reactive section of the column consists of n-butene and that the bottom part consists of MTBE. In Figure 5b the temperature profile and the reaction rate in the CDC column are plotted, which correspond with the concentration profile presented in Figure 5a. This figure shows that the temperature of the reactive zone has a relatively low value which results in a relatively large obtainable equilibrium conversion value of isobutene. Furthermore, it can be seen in Figure 5b that the values of the reaction rate in the reaction section are always positive. In Figure 6, the low-conversion (case B) con-
centration, temperature, and reaction rate profiles are plotted. Figure 6a shows that in this case the major part of the reaction zone consists of methanol and MTBE. As a consequence, the temperature of the reaction section in the column is much higher compared to case A (Figure 5a) and as a result lower equilibrium conversion values are obtained (Figure 4). Figure 6a also shows that no separation of methanol and MTBE occurs in the bottom section. 4.2. Influence of Reflux Ratio. The influence of the reflux ratio R, upon the isobutene conversion X in the CDC column was determined by varying this ratio in the domain 0.2 IRr I10. For each value of R, the steadystate column concentration and temperature profiles were calculated using, as initial values, the concentration and temperature profiles of case A and case B, respectively. In Figure 7 the overall isobutene conversion X is plotted against the reflux ratio Rp Figure 7 shows that both the high-conversion case (case A indicated by the solid line) and a low-conversion case (case B indicated by a dashed line) still occur in a large range of Rr values. For case A the conversion to isobutene is large and practically independent of the reflux ratio, provided R , exceeds a minimum value 4. If R, < 4 only case B was obtained. For the low-conversion case, Figure 7 shows that X first increases and then decreases with increasing values of R,. In Figure 8, concentration, temperature, and reaction rate profiles in the CDC column are presented, which were obtained with a value of R, = 10 and which refer to case B. Figure 8a showsthat in spite of the low overallisobutene conversionvalue which was obtained in the column, MTBE
2772 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 100
/
X
X
-
CASE A
75
50
25
0 '
'
0.0
I "
"
2.5
'
'
"
I
'
"
5.0
'
I
"
'
'
7.5
' 10.0
0.25
CASE B
ti
o . o o " " " " " " ' " ' ' ' " ' ' ' ' ~ 0
2
R,
methanol
0isobutene
MTBE
0n-bulene
0.40 0.20 0.00 0 1 2 3 4 5 6 7 8 9 1011121314151617 STAGE NUMBER
T K
380
360 340
4
6
w
S
10
10' kg
Figure 7. Isobutene conversion X as a function of reflux ratio R,. The solid line in this figure refers to the high-conversion case, case A, and the dashed line in this figure refers to the low-conversioncase, case B. The lines in this figure were calculated by the ASPEN PLUS program package using the RADFRAC block option with usersupplied production terms (eq 1)on catalyst containing equilibrium stages. Other operating and feed conditions used during the simulation are presented in Table I. The dots in this figure refer to the design cases A and B (see Figures 5 and 6) which were taken as a start of the parameter sensitivity study.
=
I
Figure 9. Isobutene conversion X as a function of total amount of catalyst Win the column. The solid line in this figure refers to the high-conversioncase, case A, and the dashed line in this figure refers to the low-conversion case, case B. Both lines in this figure were calculated with the methanol feed at stage 10. The dots in this figure refer to the design cases A and B (see Figures 5 and 6) which were taken as a start of the parameter sensitivity study.
4.3. Influenceof Amount of Catalyst. The influence of the amount of catalyst Won the trays in the CDC column upon isobutene conversion was determined using a procedure similar to that described in section 4.2. In Figure 9 X is plotted as a function of the total catalyst weight Win the CDC. Figure 9 shows that starting from the base case (W = 6400 kg), increasing the amount of catalyst does have a small effect on the conversion of both case A (solid line) and case B (dashed line). If one follows the arrows in the direction of decreasing values of W, the conversion of case B first increases until W = 800 kg after which the conversion decreases until a zero conversion at W = 0. Figure 9 also shows that multiplicity starts to occur at W 700 kg. This rules out that multiplicities are a result from vapor-liquid nonidealities alone. It should be noted that if the value of W is relatively low ( 0.001 (eq 3). Using eqs 2 and 3, we found that if the CDC column contained 6400 kg (case A, Figure 5 ) of catalyst (800 kg/tray), the maximum particle diameter was calculated to be 280pmin order to avoid particle diffusion limitations and thus the formation of byproducb. This is already a relatively small diameter considering that a commercially available ionexchange resin has particle diameters ranging from 100 to 1200 pm. The maximum value of the particle diameter in a CDC containing 1500 kg of catalyst was calculated to be 75 pm. The dashed line in Figure 9, which refers to case B, shows that X decreases if the amount of catalyst in the column is increased. This phenomenon is due to the fact that a small amount of catalyst causes low decomposition rates of MTBE and thus higher conversion values. In general, the influence of the amount of catalyst in the column is almost negligible if W > 2000 kg and if particle diffusion limitations are not considered.
1 0 1 2 3 4 5 6 7 8 9 1011121314151617
STAGE NUMBER
Figure 8. (a, top) Mole fractions of the different components in the catalytic distillation column against the column stage number. Each bar pattern in this figure represents a calculated value of the mole fraction r of a component at steady stateand refers to case B. During the calculations a reflux ratio value of 10 was assumed, keeping the other design conditions constant (see Table I). (b, bottom) Temperature 5" and reaction rate r in the catalytic distillation column. The lines in this figure refer to case B at a reflux ratio value of 10.
is present in substantial amounb on the upper trays. This low-conversion value is caused by the relatively large temperature of the bottom trays which causes the formed MTBE to decompose. This can also be seen in Figure ab, which shows that the positive area of the reaction rate curve almost equals the negative (decomposition) area. The net result is an almost zero conversion.
5. Discussion
The results of the simulations show that, for identical column feed flows, reflux ratios, and catalyst weights, two different steady states can exist during reactive distillation of MTBE, i.e., a high (caseA) and a low (case B) conversion state. Furthermore, it was shown in the previous section
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2773 T K
420
415
410
405
0.00
0.25
0.50
0.75 4
1.00 m
E
Figure 10. Gas-liquid equilibrium of the methanoVMTBE mixture as a function of temperature T a t a pressure of 11bar. The lines in this f i e are calculated using the UNIQUAC group contribution method (see Table 11) for liquid-phase activities and the Antoine formula for vapor pressures. Table IV. Operating Conditions and Feed and Product Flow Compositions of Case A and Case B, Calculated Using the Feed and Operating Conditions Presented in Table I case A case B 'cold state" 'hot state" property top bottom top bottom units 0.04 0.00 0.02 0.56 X W H 0.01 0.00 0.25 0.00 xm XbslgE ~*but.o.
T product flows Q (duties)
X T (range in reactive zone) T (mean in reactive zone) K. (at mean 27 Lo(reflux flow)
0.00 0.95 348 366 49.7
0.98 0.02 424 197 35.1
98.5 350-357 352 24.4 2.6
0.00 0.41 0.73 349 478 64.1
0.03 406 197 53.7
41.4 354-391 375 9.9 3.3
K moUs
MW %
K K km0VS
that the occurrence of either case depends on the initial state of the column and that by changing operating conditions it is possible to jump from one state to another. In Table IV, operating conditions and feed and product flow compositions of case A and case B are presented, which were calculated using the feed and operating conditions presented in Table I. Table IV shows that in case A relatively large values of the isobutene conversion X (and thus the MTBE bottom mole fraction XMTBE) are obtained and that the temperature of the reactive section is relatively low. Case B in Table IV shows the opposite characteristics, Le., relatively low conversion and high temperatures in the reactive zone. Table IV also shows that the equilibrium constant Ka drops 40% due to a temperature increase of 23 "C. Possible phenomena responsible for the multiple steady states can be the nonideality of the liquid mixtures or the presence of a chemical equilibrium reaction in the column. In Figure 10the T-x-y diagram of the methanol/MTBE system is presented. Figure 10clearly shows the methanol/ ~ = 0.57. E The case B column MTBE azeotrope at X concentration profile presented in Figure 6a shows that, indeed, the column bottom section operates at this azeotropic composition. However, from the dashed line (case B) in Figure 4 it can be seen that by increasing the location of the methanol feed tray, the conversion X and thus the bottom MTBE mole fraction increases to values
far beyond the azeotropic methanol/MTBE composition. This means that the above-mentioned azeotrope is not an explanation for the existence of multiple steady states in a CDC. Figure 9 shows that, for both case A and case B, the isobutene conversion X becomes almost independent of the catalyst weight W, if the amount of catalyst exceeds a minimum value. This means that the CDC operates close to chemical equilibrium for both cases and that the multiple steady states are not caused by the presence of a chemical reaction, i.e., kinetic limitations. A much better explanation of the existence of multiple steady states is that this phenomenon is caused by a combination of physical separation and the presence of a exothermic chemical equilibrium reaction inside the column. This can be seen from Figures 4-6. Figure 5 shows that, at the high-conversion state, butenes are present throughout the column resulting in relatively low temperatures on the reactive stages. Figure 6 shows that, a t the low-conversion state, methanol and MTBE are present on the reactive stages resulting in relatively high temperatures on these stages. As the reaction of methanol and isobutene to MTBE is exothermic and conversion is limited by thermodynamic equilibrium, high temperatures on the reactive stages will lead to low Ka values (see Table IV) and thus to lowconversion values whereas low temperatures will result in high values of X which explains the occurrence of a lowconversion state and a high-conversion state. Figure 4 can also be explained by the above-mentioned assumption, i.e., that the exothermicity of the reaction is responsible for the existence of multiple steady states. If the arrows on the solid line (case A) are followed, it can be seen that if methanol is fed below stage 11, the last reactive stage, conversion drops immediately. The reason for this jump is that methanol displaces the butenes in the column bottom section, causing a temperature increase. The opposite effect is encountered for case B when the location of the methanol feed stage is moved upward. Now the butenes start to displace the methanol in the column bottom section, thereby lowering the temperature and increasing conversion. The jump to case A is made when all the methanol in the bottom of the column is replaced by butenes. A further understanding of the multiple steady states during reactive distillation of MTBE might be obtained if so-called residue curves (see, e.g., Barbosa and Doherty (1988))are made. A final remark has to be made about the values of the reflux and reboiler duties presented in Table IV. It may be expected that the difference between these two duties will be equal to the sum of the heat released by the chemical reaction and the heat of vaporization of the butene feed as this is completely vaporized. For this reason, it may also be expected that for the high-conversion case A the reflux duty will be larger than that for case B as in case A muchmore heat will be released by the chemical reaction. As can be seen in Table IV the opposite is true; Le., case B has larger reflux duties than case A. This can be explained if the stoichiometry of the chemical reaction is considered. As 1mol of methanol and 1mol of isobutene form 1 mol of MTBE, lower conversion values on the reactive stages will lead to larger vapor flows inside the column (bottom molar flow rate was fixed during the simulations). This means that reflux and reboiler duties can be larger at low isobutene conversions although less heat is generated by the chemical reaction compared to the high-conversion case.
2774 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
6. Conclusions
Calculations of the concentration profiles and the temperature profile at reactive distillation of MTBE showed that at least two types of steady states may occur: a high isobutene conversion state with a relatively low temperature in the reactive section; a low isobutene conversion state with a relatively high temperature in the reactive section. At the high-conversion state the isobutene conversion X increases with increasing amounts of catalyst in the column until a limiting value is reached and is independent of the reflux ratio R, provided R, > 4. At the low-conversion state the isobutene conversion X decreases with increasing amounts of catalyst and initially increases and then decreases with increasing values of R,. The existence of the two steady states can be explained by the simultaneous occurrence of physical equilibrium of a multiphase mixture and an exothermic chemical equilibrium reaction in the catalytic distillation column. The simulations show that it might be feasible to install more than one methanol feed location on a CDC in order to avoid or to overcome an unwanted steady state caused by, e.g., column misoperation.
Acknowledgment The authors would like to thank Prof. R. Krishna for his valuable advice. Nomenclature ai = liquid-phase activity of component i A = heat-transfer area, m2 B = product flow rate at the bottom of the column, mol/s ci = liquid concentration of component i, mol/m3 ct = total liquid concentration, mol/m3 C, = heat capacity, J/(mol K) E, = activation energy, J/mol d, = particle diameter, m De,MeOH = effective binary diffusion coefficient of methanol inside the pores of the resin, m2/s Deo = effective limiting diffusion coefficient of methanol in isobutene, m2/s Fi = molar flow rate of component i, mol/s F, = molar flow rate of coolant, m o b Gj = molar gas flow rate from stage j , mol/s H = enthalpy, J/mol AH, = reaction enthalpy, J/mol k = first-order reaction rate constant, m3/(s kg of catalyst) k, = reaction rate constant, mol/@equiv) K = phase equilibrium ratio K, = thermodynamic equilibrium constant L = reactor length, m Lj = molar liquid flow rate from stage j , m o b q = moles of acid groups per unit mass of ion-exchangeresin, equiv/kg Q = duty, W r = reaction rate, mol/(s kg) R = gas constant, J/(mol K) R, = reflux ratio T = temperature, K T, = reactor wall temperature, K T,= critical temperature, K
U = heat-transfer coefficient, W/(m2 K) W = catalyst weight, kg = mole fraction of component i in the liquid phase X = isobutene conversion yi = mole fraction of component i in the gas phase z = axial distance from reactor inlet, m xi
Greek Letters
v = stoichiometric coefficient pp =
density of the catalyst, kg/m3 9 = dimensionless parameter defined in eq 2 $A = dimensionless parameter defined in eq 3 Subscripts
G = gas phase i = component number IB = isobutene j = stage number L = liquid phase MeOH = methanol MTBE = methyl tert-butyl ether
Literature Cited Alm, K.; Ciprian, M. Vapour Pressures, Refractive Index at 20 'C, and Vapour-Liquid Equilibrium at 101.325 kPa in the Methyl Tert-Butyl Ether-Methanol System. J. Chem. Eng. Data 1980, 25, 100-103. Ancillotti, F.; Pescarollo, E.; Szatmari, E.; Lazar, L. MTBE from butadiene-rich Cds, Hydrocarbon Process. 1987,66,50-53. ASPEN PLUS User Guide; Manual for ASPEN PLUS Release 8; Aspen Technology Inc.: Cambridge (USA), 1988. Barbosa, D.; Doherty, M. F. The simple distillation of homogeneous reactive distillation systems. Chem. Eng. Sci. 1988,43,541-550. Colombo, F.; Cori, L.; Dalloro, L.; Delogu, P. Equilibrium constant for the Methyl tert-Butyl Ether Liquid-Phase Synthesis by Use of UNIFAC. Znd. Eng. Chem. Fundam. 1983,22,219-223. DeGarmo, J. L.; Parulekar, V. N.; Pinjala, V. Consider reactive distillation. Chem. Eng. Prog. 1992,88 (March), 43-50. Kerkhof, F. P. J. M.; Mak, A. N. S.; Krishna, R.Formation of MTBE by reactive distillation. Procestechnologie 1991,6/91,59-64. Lander, E. P.; Hubbard, N. J.; Smith, L. A. Revving-up refining profits with catalytic distillation. Chem. Eng. 1983,90 (April), 36-39. Rehfinger, A.; Hoffmann, U. Kinetics of methyl tertiary-butyl ether liquid phase synthesis catalyaedby ion exchangeresin-I. Intrinsic rate expression in liquid phase activities. Chem. Eng. Sci. 1990a, 45, 1605-1617. Rehfhger, A.; Hoffmann, U. Kinetics of methyl tertiary-butyl ether liquid phase synthesis catalysed by ion exchange resin-11. Macropore diffusion of methanol as rate-controlling step. Chem. Eng. Sei. 1990b,45,1619-1626. Reid, R.C.; Prausnitz, J. M.; Sherwood, T. K. Properties of gases and liquids, 3rd ed.; McGraw-Hill: New York, 1977;pp 347-350. Short, H. Multi-ether processes boost gasoline octane. Chem. Eng. 1986,93,June, 34-35. Unzelman, G. H.Ethers have good gasoline blending attributes. Oil Gas J. (April), 32-37. Venkataraman, S.; Chan, W. K.; Boston, J. F. Reactive distillation using ASPEN PLUS. Chem. Engng Progr. 1990, 86 (August), 45-54. Received for review November 20, 1992 Revised manuscript received July 12, 1993 Accepted July 27, 1993. Abstract published in Advance ACS Abstracts, October 1, 1993. @
