Computers chem. Engng Vol. 20. Suppl.. pp. $267-$272. 1996 ~ ) Copyright © 1996 Elsevier Science Ltd

Pergamon S0098-1354(96)00055-5 Printed in Great Britain. All rights reserved 0098-1354196 $15.00+0.00

A S P E C T S OF S I M U L A T I O N , D E S I G N A N D A N A L Y S I S OF R E A C T I V E D I S T I L L A T I O N

O P E R A T I O N S

E. PEREZ-CISNEROS, M. SCHENK, R. GANI Department of Chemical Engineering, Technical University of Denmark, 2800 Lyngby, Denmark

P.A. PILAVACHI European Commission, DGXII-Science, Research and Development, 1049 Brussels, Belgium

Abstract -Various aspects related to simulation, design and operation of reactive distillation processes are presented through a systematic analysis of the model parameters and the important design/operational variables. The need for reliable, versatile and consistent simulation tools that allow the analysis of design/operation of reactive distillation processes are highlighted through two well known examples. The model parameters for the estimation of the properties related to physical and chemical equilibrium have been found to be highly sensitive to the design and operation of the two systems studied. The reactive phase diagrams and the existence of reactive azeotropes have been found to influence the choice of the condition of operation and the existence of multiple solutions.

INTRODUCTION In recent years, reactive distillation has received increased attention since it has the potential of separating liquid mixtures involving azeotropes or isomers. Separation of these mixtures by conventional distillation requires high energy costs while separation with solvent based distillation requires a suitable solvent, which in some cases, may not be available. Another important advantage of reactive distillation is that, by allowing separation of the reaction products from the reactants in the same unit operation, it is able to increase the product yield. Examples of application of reactive distillation can be found in esterification processes (Agreda et al, 1990, Sawistowski and Pilavachi, 1988), separation of isomers (Saito et al., 1971), and, in the manufacture of "anti-knock" enhances such as MTBE and TAME (e.g., DeGarmo et al. 1992, Ignatius et al. 1995).

Although the use of reactive distillation as a separation technique has been known for a long time, it has only been shown recently to be able to solve separation problems which were previously considered difficult or unsolvable. Despite the recent advances by Doherty and co-workers (Barbosa and Doherty, 1988, Ung and Doherty, 1995), it can be claimed that there are still no generally accepted design methods for these processes. One important reason is the difficulty associated with the modelling of these processes. As a result, reliable and consistent models (for properties prediction, reaction kinetics and process simulation) are not available, and, the dependence of the model parameters are unknown. It is obvious that without appropriate "tools", the design and operation of any new process would be subject to unacceptable uncertainties.

The objective of this paper is to present a systematic approach to the analysis of design and operation of reactive distillation processes. First, appropriate models and their parameters are validated. Second, the validated models are employed to generate relationships between variables that have a large impact on the design and operation of the process. Finally, the generated relationships are employed to analyse the reliability and efficiency of design and operation of the reactive distillation columns.

DESCRIPTION OF THE SYSTEMATIC ANALYSIS The analysis is performed in three levels. In the first (model validation) level, the reliability and consistency of the "tools" to be employed are established. Through a systematic analysis of the applicability of the models (and their parameters) for the estimation of the relevant pure component and mixture properties. The prediction of chemical- physical equilibrium (CPE), as well as, steady state and dynamic simulations need to be validated before a design/analysis study can be initiated. The objective of level 1 is to identify the set of sensitive properties for any reactive distillation problem, to select the appropriate models, and finally, to validate the models and their parameters. In the second (relationships) level, the relationships between model parameters and design objectives, and, the relationships between reaction kinetics, physical properties, steady state operation, transient behaviour are established. For example, how are the chemical equilibrium constants and the activity coefficient model parameters related to the conditions of operation of reactive distillation columns ? The objective of level 2 is to determine the sensitivities of the selected model parameters to the prediction of CPE and the variables related to the condition of operation of the process. Also, the influence of the phase diagrams and the location of the reactive azeotropes on the design and operation of reactive distillation columns are established. In the third and final level, the determined relationships from the lower levels are employed to analyse their effect in design and operation of reactive distillation operations.

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Computational "Tools" Required The proposed analysis approach is largely dependent on computational "tools" such as, estimation methods for pure component properties (heats of formation, vapour pressures, enthalpies, etc.), mixture properties (fugacity coefficients, activity coefficients, densities, etc.), physical and/or chemical equilibria. These estimation methods need to be employed in calculation procedures that generate phase diagrams, locate the existence of reactive/non- reactive azeotropes, and, in process simulation models (steady state and dynamic). In this work, for the analysis of CPE and its relation to design/analysis, a new computational procedure based on the elemental balance approach (P6rez-Cisneros et al, 1995) has been employed. The advantage of this approach over other approaches (e.g., Ung and Doherty, 1995) is that the method of solution is similar to the well known non-reactive physical equilibrium problems. Also, the model variables (elemental fractions) can be directly employed in phase diagrams, and, for design/analysis. Finally, this approach reduces the dimension of the problem, thereby, allowing the representation of multi-component reactive systems in two- or three-dimensional phase diagrams.

Elemental Mass Fractions: The elemental mass fractions (WkP), is the ratio of mass of element k to the total elemental mass (in the phase p) and is defined as follows:

NC Xak,ib~,i (1)

W~ = i=1 M"NC k = 1,2..., M

XXAj , ibP , i j=li=l

In Eq. (1), bk.~ is the mass of element k contained in species i and Ak.~, an element of the atomic matrix, is defined as the number of times element k appears in species i Note that the composition variables (elemental mass fractions) used for the reactive phase diagrams are based on the atomic matrix and the elemental mass. In terms of mole fractions, Eq. (1) becomes,

NC NC ~ Ak.i Xi mk ZAk, iYimk (2)

i=1 k =I,2, . . ,M Wl= i=l k = l , 2 , . . , M ; W~= MNC M NC E E A j . i x i m j Z Z A j , iYimj j=li=l j=li=l

where, x and v are the liquid and vapour mole fractions respectively, and, m are the element masses. Elemental Separation Factor: The Elemental Separation Factor (Kv.) for element k is defined as:

w[ (3) K k = W--~k

Reactive Azeotrope. A reactive azeotrope as defined by Ung and Doherty (1995) requires the equality of their transformed compositions. The transformed variables, are however, functions of more than one component compositions. Therefore, the behaviour of a single component in the system cannot be visualized in the transformed variables based diagrams. In this work, the reactive azeotrope is defined in terms of the reactive relative volatility (Ok.M) and the elemental mass fractions. The reactive relative volatilty of element k with respect to reference element M is defined as,

M

ZW~ Kk (4) j=l where j ~ k Ctk,M- M

Xw Kj j=l

The necessary and sufficient conditions for the existence of reactive azeotropes are, i) the equality of the elemental mass fractions (Wk I = Wk v ), and, ii) Ok.M=I. Note that these conditions are similar to the non-reactive case.

RESULTS/DISCUSSION OF THE TWO ANALYSES In this paper, the application of the proposed analysis approach is highlighted through two well known reactive systems, the M T B E Process (the production of Methyl Tert-Butyl Ether from the reaction of iso-butene and methanol with the presence of one inert component) and an esterification process (the production of ethyl acetate and water from ethanol and acetic acid). Only a sub-set of the results are highlighted. Due to page limitations, problem details are also not provided. However, upon request the interested reader will be provided with the full details of the problem specifications and the corresponding results so that what is presented below can be reproduced by others.

Level 1 : Validation of the Computational Tools Steady state simulation results for both reactive systems have been reported in the literature. For the MTBE process, it was tried to reproduce the results of Jacobs and Krishna (1993) and Hauan et al. (1995). Both sets of authors have reported the existence of multiple solutions. For the esterification process, experimental data reported by Suzuki et al. (1971) have been successfully reproduced by steady state and dynamic simulation.

Set of sensitive oronerties: For both reactive systems, the identified set of sensitive properties are the pure component Gibbs Free Energies, the temperature dependence of the chemical equilibrium constant , and, the

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liquid phase activity coefficients (because the reactions are assumed to occur only in the liquid phase which represents a non-ideal mixture). In addition, for the esterification process, the effect of dimerization in the vapor phase fugacity coefficients has also been found to have importance.

Selection/validation of models: The MTBE process simulations have been performed with ASPEN-PLUS (1995) using various model combinations. With the combination of the UNIQUAC model for the liquid phase activity coefficients, the Redlich-Kwong EOS for the vapour phase, the Rehfinger-Hoffmann expression (1990) for the temperature dependent equilibrium constant term, and, the non-ideal expression for the stoichiometry based equilibrium constant term, it was possible to match the results reported by Jacobs and Krishna (1993) and those of Hauan et al. (1995). Figure 1 shows the variation of fractional conversion of iso-butene as a function of the methanol feed location. With the UNIFAC model (for the liquid phase activity coefficient), although the high conversion solutions were found to be approximately similar, the low conversion solutions (between feed stages 8 to 10) were found to be somewhat different (not shown in Fig. 1). Figure I also shows that using the Colombo et

al. (1983) expression for the temperature dependent equilibrium constant term, multiple solutions are not obtained and the fractional conversion of iso-butene is different for methanol feed stages 11 to 14 (Curve B in Fig. 1). The phase diagrams shown in Fig. 2 (Rehfinger-Hoffmann expression used) confirm the existence of reactive azeotropes for inert compositions (1-butene mole fraction) greater than 0.0155. Using the Colombo expression, however, the reactive azeotrope could not be found. Therefore, for the MTBE process, the choice of the temperature dependent equilibrium constant expression is very important

The esterification simulations have been performed with ASPEN-PLUS and READYS (Ruiz et al., 1995) using various model combinations. The simulation results obtained with ASPEN-PLUS are shown in Figures 3a- 3c, and, the corresponding steady states obtained through dynamic simulations with READYS are shown in Fig. 4. From these figures, an important point to note is that the experimental data of Suzuki et al. (1971) are quite difficult to match unless the "fitted" activity coefficient model (modified Margules in Figure 4) proposed by Suzuki et al. is employed together with the expressions for the reaction kinetics. With ASPEN PLUS, the best match of the Suzuki et al. data could be achieved with the combination of UNIFAC for the liquid phase, the Virial equation for the vapour phase (taking into account, association and dimerization) and the Venkataraman et al. (1990) rate of reaction expression. The CPE program package did not find any reactive azeotrope for this system.

Level 2 : Relationships Model/parameter Sensitivities: For the MTBE process, the activity coefficient model parameters have been found to be sensitive to the low conversion solution. It was possible even to obtain UNIQUAC model parameters which gave only the high conversion solutions (for the reactive zone). The choice of the temperature dependent expression (or the parameters for this expression) also appears to be important for the low conversion region. Note that the low conversion corresponds to higher temperatures and that the deviation between the Rehfinger- Hoffmann and the Colombo et al expressions increase as the temperature increases. For this reason, only the low conversion solutions are affected by use of the Colombo et al. expression. Neglecting the non-ideal term (not recommended in this paper) of the stoichiometry based equilibrium constant expression, also produces the high and low conversion solutions (which are different from the reported solutions of Hauan et al.).

For the esterification process, the sensitivity of the model parameters is also very high. If the reaction is described by a correlated reaction kinetic expression, then the corresponding activity coefficient model parameters used together with this correlation must be employed in the simulations. That is, activity coefficient model parameters estimated from purely vapour-liquid equilibrium data, when employed in process simulations will not produce acceptable results. The ASPEN-PLUS results show that the physical equilibrium based activity coefficient model parameters can be used, when the association and dimerization of acetic acid in the vapour phase are also considered. It can be noted from Fig. 3b, that the rate of generation of ethyl acetate is approximately zero. Therefore, it is likely that these stages are in chemical equilibrium. Subsequent computations of the rate of change of Gibbs energy (from the known liquid phase compositions) also show that equilibrium has indeed been attained.

Influence of Phase Diagrams: The phase diagrams of the type shown in Fig. 2 (temperature-composition diagrams) provides information related to the location of the feed and the influence of the inert composition (e.g., for the MTBE process). The existence of reactive azeotropes increases the importance of these phase diagrams. Figure 5a shows the location of the stage compositions (elemental mass fractions calculated with Eq. 2) for the high and low conversion solutions when the methanol feed stage is 10. It can be noted that the high conversion solution stage compositions are located in one end of the phase diagram while the low conversion solution is located at the other end. A magnification of the diagram between 0.4 and 0.6 would show that at stage 10, the composition is exactly on the reactive azeotrope point.

The location of the reactive azeotrope is closely related to multiple solutions. For the MTBE process, Fig. 5b shows the distribution of the calculated reactive relative volatilities (using Eq. 4) for reactive stage 10 as a function of methanol feed location. It can be noted that for methanol feed at stage 10 or above, the conditions for reactive azeotrope is satisfied on reactive stage 10. From the phase diagrams in Fig. 2 and considering the 1- butene stage compositions (for the low conversion solution), it can also be noted that the value of Xa for stage 4 lie after the corresponding reactive azeotrope, and, outside the zone corresponding to the high conversion solution.

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Therefore, in this case, the higher conversion solution is not obtained (implying that a relationship exists between the two multiple solutions, the location of the reactive azeotrope and the choice of the initial condition).

Level 3 : Analysis for Design and Operation Models/parameters and design: Since the activity coefficient model parameters are sensitive, they have also significance with respect to design. For example, for the esterification process, the reboiler heat duties needed to obtain the same product specification (amount of ethyl acetate in the top product) using two different model combinations (UNIFAC with RK EOS for the vapour phase as opposed to UNIFAC with the Virial equation for the vapour phase) differ by more than 50 %. Depending on which combination is correct and which combination is used, the design results may lead to wasted energy, or, off-specification products. The same behaviour was also found with READYS when the corresponding activity coefficient model parameters were not used together with the known kinetic expression. Since some stages (1 to 5) are in chemical equilibrium (see level 2), dividing the column into two reactive zones (a chemical equilibrium zone and a kineticaily controlled zone) and repeating the simulation should give approximately the same results as those shown in Fig. 3b. Therefore, it is possible to identify the equilibrium behaviour of a section of the reactive column through the proposed analysis.

CPE and design/operation: The existence of reactive azeotropes is closely related to the final steady state condition of operation. If reactive azeotropes are present (as in the case of the MTBE process), the initial condition of the column stage compositions and the feed location determine which of the multiple solutions the column will arrive at. If reactive azeotropes are not present (as in the case of the esterification process), it is the feed location and not the initial condition that determines the final steady state condition of operation. In this work, we have only investigated the effects of feed location and initial conditions. Other variables may also lead to the same observations described above. In the case of systems with reactive azeotropes, however, the feed location and initial condition must match (i.e., they lie on the correct side of the phase diagram) for the corresponding steady state solution.

The two multiple solutions for the MTBE case, show large differences in the total liquid and vapour flowrates (9302.4 as opposed to 13910.4 kmol/hr). Thus, it may be possible to obtain these multiple solutions with steady state simulation models which do not consider equipment sizing parameters. With dynamic simulation, however, only one solution may be obtained (either the high or the low conversion). This indicates that even if multiple solutions exist, the equipment design may exclude some of these solutions. The opposite, equipment design introducing new solutions, has not been investigated in this work.

CONCLUSIONS Through two well known reactive distillation processes, we have highlighted the results from a systematic analysis related to design and operation of these processes. Because the reactive systems are highly system specific, it is not feasible to propose a generalized methodology. The analysis, however, show that there exists a set of sensitive properties and that the selected models for their predictions play an important role in the design/operation of the distillation columns. The analysis also illustrate how design decisions related to feed location, product specification and initial conditions can be made, and, points out the dangers related to design/operation of the reactive distillation columns due to incorrect choices of the models/parameters. Therefore, the basic steps of the proposed analysis approach are also valid for other reactive systems. Multiple solutions appear to be related to the existence of reactive azeotropes, and, the design/operation of the reactive distillation columns are closely related to the phase diagrams of the reactive system. Current and future work is focussing on the development of a general reactive distillation model and the development of an algorithm which combines design and operation through the elemental mass fraction based phase diagrams. Finally, compared to the transformation variables based approach, the elemental mass balance based approach to simulation, design and analysis provides a promising alternative that deserves further attention.

REFERENCES Agreda, V.H., Partin, L.R., and Heise, W.H., 1990, High-purity Methyl Acetate via Reactive Distillation, Chem.

Eng. Prog., 86, 40. Aspen Technology Inc., 1995, The ASPEN PLUS User "s Manual. Ver.8.5-6. Barbosa, D., and Doherty, M.F., 1988, Design of Multicomponent Reactive Distillation Columns, IChem. Eng.

Symposium Series No. 194, B369. Colombo, F., Cori, L., Dalloro, L., and Delogu, P., 1983, Equilibrium Constant for the Methyl tert-butyl ether

Liquid Phase Synthesis by use UNIFAC, Ind. Eng. Chem. Fundam., 22, 219. De Garmo, J.L., Parulekar, V.N., and Pinjala, V.,1992, Consider Reactive Distillation, Chem. Eng. Prog. 88,43. Hauan, S., Hertzberg, T., and Lien, K.M., 1995, Why methyl tert-butyl ether Production by Reactive Distillation

May Yield Multiple Solutions, Ind. Eng. Chem. Res., 34, 987. Ignatius, J., J~irvelin, H., and Lindquist, P., 1995, Use TAME and Heavier Ethers to improve Gasoline Properties,

Hydrocarbon Processing, 2, 51.

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Jacobs, R., and Krishna, R., 1993, Multiple Solutions in Reactive Distillation for Methyl tert-butyl ether Synthesis, Ind. Eng. Chem. Res., 32, 1706.

Ptrez-Cisneros, E. S., Gani, R., and Michelsen, M.L., 1995, Reactive Separation Systems. Part I: Computation of Physical and Chemical Equilibrium, SEP 9547, IVC-SEP Report, DTU, Denmark.

Rehfinger, A., and Hoffmann, U., 1990, Kinetics of the Methyl tertiary butyl ether Liquid Phase Synthesis Catalysed by Ion Exchange Resin-I. Intrinsic Rate Expression in the Liquid Phase Activities, Chem. Eng. Sci., 45, 1605.

Ruiz, C.A., Basuaido, M S., and Scenna, N.J., 1995, Reactive Distillation Dynamic Simulator, Trans IChem. Engrs., Part A, 73, 363.

Saito, S., Michishta, T., and Maeda, S., 1971, Separation of Meta- and Para-xylene Mixture by Distillation accompanied by Chemical Reactions, J. Chem. Eng. Japan, 4, 37.

Sawistowski, H., and Pilavachi, P., 1988, Performance of Esterification in a Reaction-Distillation Column, Chem. Eng. Sci., 43, 355.

Suzuki, I., Yagi, H., Komatsu, H., and Hirata, M., 1971, Calculation of Multicomponent Distillation accompanied by a Chemical Reaction, J. Chem. Eng. Japan, 4, 26.

Ung, S., and Doherty M.F., 1995, Vapour-liquid Phase Equilibrium in System with Multiple Chemical Reactions, Chem. Eng. Sci., 50, 23.

Venkataraman, S., Chan, W.K., and Boston, J.F., 1990, Reactive Distillation using ASPEN PLUS, Chem. Eng. Prog., 86 (8), 45.

ABBREVIATIONS CPE: Chemical-Physical Equilibrium; MTBE: Methyl-tert-butyl ether; TAME: Tert-amyl methyl ether.

ACKNOWLEDGEMENT The authors would like to acknowledge the useful information received from Professor K. Lien and Mr. S.

Hauan with respect to the MTBE steady state results with ASPEN PLUS.

1,0- ~ --~, 1,0 Keq J " f~ (Rehfinger and Hoffman) 0,9 B 0,9 - (Low conversion profile)

0,8 . / 0,8

. 0'7 /f "~ 0,6 0,6 ~ ' ~ / / f " ~ ' - ~

' "~'~ ~"~ ~ J Reactive "~0,5~ 0,4 ~ 0,40'5 / J Azeotrope Zone

"~0,3 0,3

~, 0,2 0,2 .% ~,

0,1 • 0,1

0,0 - - ~ ~ 0,0 I I l I I I I I I

2 3 4 5 6 7 8 9 10111213 14 0 ,00 ,10 ,20 ,30 ,40 ,50 ,60 ,70 ,80 ,91 ,0 Methanol Feed Stage WA l (Iso-butene-MTBE)

Fig 1. Fractional conversion of isobutene as a function of the Fig 2. Reactive Phase diagrams corresponding methanol feed location using two different expressions for K(T). to the MTBE process. Methanol Feed at stage 10.

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0,6 ~, UNIFAC/RK ~,12o UNIFAC/RK ..q Wilson/RK E Wilson/RK

0,5 - o"--. = ~ 1 ° - ~= e ~ UNIFAC/Virial - UNIFAC/Virial

• E x p e r i m e n t a l ~ E x p e r i m e n t a l 0,4 e \ . ~ 8 -

= \ \ < o ~ "= .,\ e ' \ 6 - ~0,3 - ....\ .\ ~ ,

{ 0 , 2 - - "~\ . ~ 4 - - , /

o ...\ u ~-... . . ~o,1 - '..k °--Q... o ~ / - - - - - = ~ " - ~ ~ 0 - ~ - - ~ - - 4 ~ " : ° - ' ° - ' ~ ' t - ' t - -= "'-'>- "-4). o

0,0 I I I I I I ~ " ~ -2 . I I I I I I 0 2 4 6Stage8 10 12 14 0 2 4 6Stage8 10 12 14

Fig. 3a. Liquid composition profiles of Ethyl Acetate Fig. 3b. Rate of Generation of Ethyl Acetate using using different thermodynamic models, different thermodynamic models.

3,0 200 [ • Experimental • [ - - - - - UNIFAC/RK 195-1 - - READYS [

[ ........ Wilson/RK I ~ 2 5 ~ . sx, .r ,m.. t . , I 190-~ / ]

- I .-, / / - \ l ~ l S ' - l " / I

/ / \ . . . . . . - " \ [ ~ 1 8 o - t • / I ~2,0 ~ //" " \ I ~ - 7 5 / • • ° • / I • ~ i ,, "... . ' . " • . / I / '~] e ` ' ' 'e' 'e' ' 'e" ........ "'" f"170--[ ~ " 1 1

"1 '5 - - I '/ • "',.e 1165- o_to " e ~ / ' ] "-~ / • • I ~, / e [ 1 6 0 - t I

i Profile at t=50h. [ l,o ~l i I i I i i I 155 / I ~ i i i i I

0 2 4 6Stage8 10 12 14 0 2 4 6- 8 10 12 14 Stage Fig. 3c. Activity Coefficients of Ethyl Acetate Fig.4. Computed profiles of Temperature at each stage, with READYS.

0,6 ~ 1,1

i i0,1 •

/ J/ I I / . . 3 / , , / I

~ o , 2 - 1 / . / / " " ~ I

°,° F i i I i i I , i i i I I I i I I i I i 0,0 0,l 0,2 0,3 0,4 0,5 0,6 2 3 4 5 6 7 8 9 10 11 12 13 14

WAl(isobutene_MluE)~ , . , Methanol Feed Stage Fig 5a. Phase diagrams and location ot stage eiementat Fig 5b. Reactive relative volatilities at stage i 0 as mass fractions for two inert compositions, a function of Methanol feed location.