Ind. Eng. Chem. Res. 1995,34, 987-991
987
Why Methyl tert-Butyl Ether Production by Reactive Distillation May Yield Multiple Solutions Steinar Hauan, Terje Hertzberg, and Kristian M. Lien* Laboratory of Chemical Engineering, The Norwegian Institute of Technology, The University of Trondheim, N-7034 Trondheim, Norway
This paper presents a n explanation of why methyl tert-butyl ether (MTBE)production by reactive distillation may yield multiple solutions. Widely different composition profiles and conversions may, as already reported by Krishna and others, result with identical column specifications, depending on the initial estimates provided. A hypothesis yielding a qualitative understanding of this phenomenon has been developed. The inert n-butene plays a key role in the proposed explanation: As the reaction mixture is diluted with n-butene, the activity coefficient of methanol increases substantially and the temperature decreases. This dilution has a profound effect on the equilibrium conversion, enabling MTBE to escape from the reactive zone without decomposition. When methanol is fed below or in the lower part of the reactive zone of the column, the “lifting capacity” of the minimum boiling point MTBE-methanol azeotrope will also be important.
Introduction
Reflux ratio: U D = 7.0
Figure 1 shows a reactive distillation column that may be used for production of MTBE (methyl tert-butyl ether) from methanol and isobutene. Inert n-butene is fed along with the isobutene. The column is divided into three zones, and the chemical conversion occurs in the middle reactive zone, which is packed with catalyst material. The 17 stages include a partial reboiler and a total condenser. The butenes are fed to the column on stage 11. The methanol feed location is varied between stages 2 and 16. Catalyst material is present on stages 4-11, and chemical reaction equilibrium is assumed to be reached on each of these stages. This column configuration has previously been analyzed by Jacobs and Krishna [I], who were able to demonstrate that widely different converged solutions could be obtained for certain sets of column specification. They examined why they would get multiple solutions, considering several alternative hypotheses. After having discarded both crossing of nonreactive distillation boundaries and “CSTR-like” multiplicity behavior as possible explanations, they concluded that simultaneous reaction and phase equilibrium could explain the observed behavior: By tracing residue curve maps for simultaneous chemical and phase equilibrium, they were able to identify two distinctly different families of curves, depending the curves’ origin in composition space. In order to reproduce Jacobs and Krishna’s results, we have carried out steady state simulations using the same model and parameters: the model described by Venkataraman [3] and implemented in ASPEN Plus as the rigorous distillation module RADFRAC. The liquid phase activities have been calculated using UNIQUAC, with the binary interaction parameters reported by Rehfinger [2].The ASPEN Plus property set Sysop11 defines the various thermodynamic models in use, Redlich-Kwong for equation of state calculations and UNIQUAC for liquid activity and flash calculations. The polynomial given by Rehfinger [2]has been used to represent the temperature dependence of the reaction equilibrium constant.
* Author to whom correspondence should be addressed. E-mail: 1ienOkjemi.unit.no.
Methanol feed F = 215.5 molls
v n-Butene feed T=350K P = 11.0 atm F = 200-600 m l / S
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B Bottoms flow: B = 197 moYs
Figure 1. Column configuration and specifications.
Results The multiplicities reported by Krishna [I]are reproduced with the assumption of reaction equilibrium on all stages, as illustrated in Figure 2. In this and subsequent .figures,fully drawn lines correspond to the solution where low conversion of methanol is achieved. Dash-dotted lines represent the corresponding highconversion solution. Resulting composition profiles for the case where methanol is fed to stage 10 are shown in Figures 3-6. Formation rates for the same case (methanol feed on stage lo), defined as the rate of formation for MTBE on each stage in the reactive zone, are illustrated in Figure 7. The temperature profiles are given in Figure 8. Figure 9 shows how the multiplicity region grows
0888-5885/95/2634-0987$09.00/00 1995 American Chemical Society
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Figure 4. Mole fraction methanol, F(n-butene) = 350 molls, MEOH feed on stage 10. ...................................................................................................
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when the amount of n-butene fed to the column is increased. As the amount of n-butene fed to the column increases, multiplicity is obtained with methanol fed further down in the column. This corresponds to the dash-dotted conversion lines moving t o the right. If the amount of n-butene is larger than 600 mob, only high conversion is possible for all methanol feed locations. On the other hand, if the column feed contains less than 200 mol of n-butene per second, only low conversion is possible. Note that in Figure 9 there is only one fully drawn line, representing all the low-conversion cases. This is an approximation, made in order to improve the appearance of the figure: This line shows the average conversions for all the low-conversion cases. These were very close to one another. Dependence on Initial Estimates. In all the above cases, the initial composition and temperature profiles decided whether a simulation converged toward the high- and low-conversion solution. Knowing this, we
w e Figure 5. Mole fraction isobutene, F(n-butene) = 350 molls, MEOH feed on stage 10.
conducted a systematic study into the case where methanol is fed to stage 10 and the amount of inert n-butene feed is 350 mol/s. Could we identify a surface in composition space where small perturbations in the initial estimates would yield widely different solutions? Specification of the initial estimate of the composition on tray 11did here turn out to be sufficientto determine whether an estimate would yield the high- or the lowconversion solution. This surface (with isobutene mole fraction estimated to be zero) is described in Table 1.
Mechanisms Our initial hypothesis, which later turned out to be incomplete, was based on methanol and MTBE alone. When methanol was fed below the reactive zone, high or low conversion would depend on whether there already were sufficient amounts of the MTBE product to "lift" all the methanol into the reaction zone, where
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 989
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Figure 6. Mole fraction n-butene, F(n-butene) = 350 molls, MEOH feed on stage 10.
Figure 8. Temperature profiles, F(n-butene) = 350 moVs, MEOH feed on stage 10.
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it would meet isobutene and react to MTBE. Viewed in isolation, methanol is the heaviest of all the components and would consequently tend t o go down the column. However, MTBE and methanol form a minimum-boiling azeotrope, and therefore, we assumed that high conversion would be caused by an internal MTBE recirculation in the column, transporting methanol upward into the reactive zone. This hypothesis had to be abandoned as the entire explanation. In low-conversion cases, there was still plenty of methanol on the reactive trays. Instead, it was discovered from the plot of formation rates (Figure 7) that when the low-conversion solution was obtained, MTBE was being formed in the upper part of the reaction zone. In the lower part of the reaction zone, the reaction was reversed; MTBE was decomposed. In other words, in the low-conversion solution there is a counterproductive internal “recycle”of MTBE such that
Figure 9. Multiplicity region, F(n-butene) = 200, 225, 250, 350, 500, 575, 600 molls. Table 1. Composition Estimates at Tray 11 high conversion low conversion
XMTBE
XMEOH
0.150 0.175 0.200 0.225 0.250 0.275
0.675 0.625 0.618 0.565 0.560 0.530
XNBUT
XMEOH
XNBUT
0.175 0.200 0.182 0.210 0.190 0.195
0.680 0.630 0.619 0.570 0.565 0.535
0.170 0.195 0.181 0.205 0.185 0.190
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MTBE cannot escape from the reactive zone without decomposition. Further simulations made it clear that as the amount of n-butene increased, the amount of MTBE decomposition decreased. As the components leaving the lower reactive tray are in equilibrium, the inert “dilution” of the reaction mixture introduces a shift in the reaction toward MTBE. The temperature profiles in the reactive zone, shown
990 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 Table 2. Azeotropic Compositions for Different Pressures
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in Figure 8, are affected by dilution. The more inert n-butene, the lower temperature in the catalyst section. As the reaction equilibrium constant increases exponentially with decreasing temperature, the equilibrium is shifted toward MTBE. The effect of dilution on activity coefficients is an additional positive factor. For mole fractions above 0.3, all three reactive components have activity coefficients not too far from 1.0, but as the reactive mixture is diluted with the inert n-butene, the activity coefficient of methanol increases substantially. This implies a shift in reaction equilibrium toward MTBE, and consequently less decomposition. The activity coefficients of methanol, isobutene and MTBE on all stages through the reactive zone are displayed in Figure 10 for both the high- and the low-conversion solutions. Figure 11shows how YMTB~((YIBUTYMEOH)(the nonideal part of the equilibrium expression) varies along the reactive zone for both the high- and low-conversion cases. A factor of 7 in the difference between the two cases at the lowest reactive stage demonstrates that
pressure (atm) 9.0 10.0 11.0 12.0
MEOH-MTBE Azeotrope temperature (“0 XMEOH 124.7 129.0 132.9 136.6
0.555 0.565 0.575 0.580
XMTBE 0.445 0.435 0.425 0.420
MEOH-n-Butene Azeotrope pressure (atm) temperature (“C) XMEOH XNBUT 9.0 10.0 11.0 12.0
66.4 70.7 74.9 78.5
0.076 0.084 0.091 0.098
0.924 0.916 0.909 0.902
there will be a profound difference in the amount of MTBE decomposition on this stage. Figure 7 confirms this observation. In order to achieve high conversion of methanol, it is thus clear that two conditions must be met: The reaction mixture in the lower part of the reactive zone must be sufficiently diluted, so that MTBE is not decomposed before it escapes the reactive zone. Furthermore, when methanol is fed below the reactive zone, sufficient amounts of other components forming minimum-boiling azeotropes must be present in this section of the column that all the methanol is lifted up to the reaction zone. MTBE, isobutene, and n-butene may in principle perform such a task, but the butenes only to a limited extent: The butene-methanol azeotropes contain a modest amount of methanol (see Table 2) so their ‘lifting capacity” is limited. It should be noted that the compositions of the azeotropes are sensitive to pressure. ”Lift” of methanol by MTBE (azeotropic behavior), together with “dilution” of the reaction mixture by n-butene to prevent MTBE decomposition in the lower part of the reactive zone, are thus conjectured to be the major underlying mechanisms necessary to obtain highconversion solutions in the kind of MTBE reactive distillation column which has been examined here. If too little MTBE is present in the lower section of the column, or if too little n-butene is present in the lower part of the reactive zone, then unreacted methanol will have to leave the column in the bottoms product, and a low-conversion solution is obtained. These phenomena are linked through the composition on the lowest stage in the reactive zone. This may be the explanation why we were able to identify the borderline in initial estimates between the high- and the low-conversion solution using compositions on this stage alone. Conclusion
For a reactive distillation column, multiple solutions are possible. The initial estimates for temperature and composition profiles decide whether a steady state simulation will converge to a high-conversion or a lowconversion solution. In order t o obtain the high-conversion solution, the lower section of the column must contain sufficient MTBE to lift all the methanol to the reactive zone, and in the reactive zone, the reaction mixture must be sufficiently diluted to avoid a substantial amount of MTBE decomposition. It has been demonstrated that the borderline in initial estimates between high- and low-conversion solutions
Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 991 may be described using the composition on the lowest stage in the reactive zone only, and this is expected to be due t o the inherent coupling between ''lift" and "dilution" effects which take place on this stage.
Acknowledgment This work has been funded in part by the Nordic Petroleum Research Programme and Statoil. Helpful input from Dr. R. Krishna regarding the use of UNIQUAC binary interaction parameters is acknowledged.
Literature Cited (1) Jacobs, R.; Krishna, R. Multiple solutions in reactive distillation for Methyl tert-Butyl Ether synthesis. Znd. Eng. Chem. Res. 1993,32, 1706-1709. (2) Rehfinger, A.; Hoffman,U. Kinetics of methyl tertiary butyl ether liquid phase synthesis catalyzed by ion exchanged resin-I. Intrinsic rate expression in liquid phase activities. Chem. Eng. Sci. 1990,45, (6), 1605-1617. (3) Venkataraman, S.; Chan, W. K.; Boston, J. F. Reactive distillation using ASPEN PLUS. Chem. Eng. Prog. 1990, Aug, 45-54.
Received for review July 7, 1994 Revised manuscript received November 16, 1994 Accepted December 13, 1994@
Nomenclature
IE940427C
Fi = formation rate for component i, mol/s
Xi = mole fraction for component i, liquid phase Yi = mole fraction for component i , vapor phase yi = activity coefficient for component i
Abstract published in Advance ACS Abstracts, January 15, 1995. @
