Simultaneous production of diacetone alcohol and mesityl oxide from acetone using reactive distillation

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1 Simultaneous production of diacetone alcohol and mesityl oxide from acetone using reactive distillation Suman Thotla, Vishal Agarwal, Sanjay M. Mahajani Department of Chemical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai , India Abstract Dimerization of acetone (Ac) yields diacetone alcohol (DAA), which on further dehydration gives mesityl oxide (M) along with various side-products. The reacting system is a combination of various series and parallel reactions. In the present work, the reaction is studied using a cation exchange resin (Amberlyst 15 ) as catalyst. The effect of catalyst loading and temperature on reaction kinetics was evaluated and three models based on simplified Langmuir Hinselwood mechanism are proposed. Aim of the work is to minimize undesired side-products and understand the effect of different parameters and operating modes on DAA:M product ratio in reactive distillation (RD). It has been shown that the reaction when operated in a reactive rectification mode offers flexibility in the relative production rates of DAA and M. The experimental results obtained are explained by simulation. Keywords: Acetone; Diacetone alcohol; Mesityl oxide; Reactive distillation; Cation exchange resin; Kinetics; Selectivity 1. Introduction Diacetone Alcohol (DAA) and mesityl oxide (M) are industrially useful products derived from acetone. DAA is produced by selective aldol condensation of acetone. It is an industrially important compound which is mainly used as a solvent in purification processes. It is also used as a component of solvent blends for nitrocellulose, acrylic, and cellulose acetate lacquers and thinners. ther applications of DAA include metal cleaning compounds, degreasers, stripping aids for textiles, gum and resin removers in automobile carburetor cleaners. Dehydration of DAA produces 4-methyl-3-penten-2-one, commonly known as M. M is a useful compound with various applications, the most important being the precursor for the production of a popular solvent methyl isobutyl ketone (MIBK). Hydrogenation of M under suitable conditions gives MIBK in high yields ( Keefe et al., 2005). Aldol condensation of M and acetone further produces heavier products, such as isophorone. Fig. 1 shows the reactions of interest. In the present study, we explore the possibility of using reactive distillation (RD) to conveniently manipulate DAA:M ratio. RD is a popular multifunctional reactor that has been used successfully for many commercial processes in the last two decades (Sharma and Mahajani, 2002). There are various motives behind its several applications and selectivity engineering to manipulate the product composition is one of them (Agarwal et al., 2006). With judicious choice of operating parameters, one can manipulate the composition profiles in the reactive zone of the column and obtain enhanced selectivity towards the desired product(s). Various kinetic studies on this reaction using different catalysts have been performed in the past. The aldol condensation of acetone is commonly conducted in the presence of base catalyst such as NaH, KH, Ca(H) 2 and Ba(H) 2. Many other alternative catalysts such as metal oxides and hydroxides, which exhibit both acidic and basic properties, were found to offer less selectivity towards DAA as compared to that obtained by the homogeneous catalyst (Lippert et al., 1991). A detailed kinetic study of aldol condensation of acetone using

2 5568 H K 1 1) 2 H 3 C CH 3 (H 3 C) 2 C H 2 C K 2 Acetone Diacetone alcohol CH 3 Table 1 Properties of Amberlyst 15 Property Units Value 2) 3) 4) (H 3 C) 2 H 3 C H K 3 C H 2 C CH 3 (H 3 C) 2 C HC CH 3 + H 2 Diacetone alcohol Acetone CH 3 + (H 3 C) 2 Mesityl xide K (H 3 C) 2 C HC CH 3 + H 5 2 (H 3 C) 2 CH HC CH 3 Mesityl xide C HC Mesityl xide CH 3 K 4 MIBK Heavier products Fig. 1. Reaction scheme for aldol condensation of acetone and related reactions. anion exchange resin (Amberlite IRA-900) has also been reported in the literature (Podrebarac et al., 1997). This reaction is also catalyzed by acid catalyst, however, the rapid dehydration of DAA to M usually follows and DAA:M ratio reduces to a vanishing level (March, 1985; Panov and Fripiat, 1998; Flego and Perego, 2000; Kim and Hatfield, 1985). It is for this reason that the cation exchangers, as acid catalyst, have not attracted much attention when the objective is to selectively produce DAA. To the best of our knowledge, barring few studies (Klein and Banchero, 1956), there is not much information available on this reaction with cation exchange resin as catalyst. Podrebarac et al. (1998) used RD for this reaction with an objective of selectively producing DAA from acetone, in the presence of anion exchange resins. In the present study we address the simultaneous production of DAA and M from acetone in RD using cation exchange resin (Amberlyst 15 ) which has not been explored till date. The aim is to manipulate DAA:M ratio by conducting the reaction in a RD column, which operates close to or above the boiling point of acetone. To predict the performance of a catalytic distillation column, liquid phase kinetic data for DAA and M formation at temperatures near the boiling point of acetone is required. The kinetic data was obtained in a laboratory batch reactor and a kinetic model has been developed. Batch reactive distillation (BRD) and continuous reactive distillation (CRD) studies have been performed to demonstrate the potential of reactive distillation to enhance the selectivity towards the intermediate product(s). The results of BRD and CRD are validated independently using simulation studies based on the kinetics developed in the present work. 2. Kinetic model development 2.1. Experimental Materials and catalyst Acetone (AR grade, moisture < 0.02%) was supplied by Merck Ltd. The catalyst used in the experiments is commercial strong-cation exchange resin, Amberlyst 15 and was obtained from Rohm and Hass, Philadelphia, PA. The physical proper- Minimum exchange capacity (dry basis) eq/kg 4.7 Internal surface area m 2 /gm 50 Particle size mm 0.5( 90%) Density gm/lit 780 Shape Bead Maximum operating temperature C 120 ties of the catalyst are listed in Table 1. Before its use, the fresh catalyst was carefully washed with pure water, isopropyl alcohol, dilute hydrochloric acid and then again with pure water sequentially. It was then dried at 70 C under vacuum for about 12 h to remove moisture present in it Apparatus and procedure The reaction was performed in a 300 ml stainless steel batch autoclave (Parr, USA) equipped with temperature and speed monitoring facility. The desired quantities of acetone (i.e. 190 gm) and the catalyst were charged before the heating was started. The agitation was started, typically after 5 min, when the desired reaction temperature was attained. This time was considered as the zero reaction time. The samples were removed after specific time intervals and were cooled through a coil immersed in chilled water to prevent acetone evaporation during the sampling. Various experiments were carried out to study the effect of different parameters like temperature and catalyst loading on the kinetics of the reaction Analysis A gas chromatograph (GC-911; Mak Anlytica India Ltd.) equipped with flame ionization detector (FID) was used to analyze the reaction mixture of acetone, M and DAA. The analysis was carried out in a 30 m long BP-5 column (SGE, Australia) with an inner diameter of 0.55 mm. Elution was established by nitrogen as a carrier gas at a flow rate of 0.5 ml/min. Methyl ethyl ketone (MEK) was used as an external standard. The water concentration was calculated based on the material balance. The molar amount of water formed was assumed to be same as that of M because the formation of heavier side-products was negligible compared to the amount of acetone converted or M formed. Klein and Banchero (1956) proved that this method of analysis is sufficiently accurate over a temperature range of C Calculations for selectivity and conversion Conversion of acetone is calculated on the basis of initial moles of acetone moles of acetone present X = 1 initial moles of acetone taken. (1) Selectivity towards DAA is calculated as 2 moles of DAA formed S = moles of acetone converted. (2)

3 5569 Conversion of acetone 0.07 Total 0.06 Towards M 0.05 Towards DAA Table 2 UNIQUAC model binary interaction parameters (Aspen Technology Inc., 2001) Acetone DAA M Water Acetone DAA M Water Time (min) water concentration may be different for the two different reactions taking place simultaneously. Such an observation has also been reported by Lemcoff and Cunningham (1971). The models considered for reactions (3) and (4) are as follows: Model A: Fig. 2. Conversion vs time at 55 C and 3.5% (w/w) of catalyst loading General course of the reaction Fig. 2 shows the general course of reaction with respect to time in the batch reactor. Since the equilibrium conversion of acetone to DAA is very low, DAA concentration does not rise beyond a particular limit. The total amount of acetone consumed at any time is approximately equal to the amount of acetone converted to DAA and M indicating negligible conversion towards the heavies. However, it must be noted that at relatively large conversion (> 10%), the formation of high molecular weight compounds is significant Kinetic modeling The proposed reaction mechanism by Lemcoff and Cunningham (1971) for the dehydration of DAA reaction over acid catalyst (Amberlite IR-200) involves three parallel reactions (1) (3) given in Fig. 1. They proved that the sequence of steps of aldol condensation of acetone is Acetone DAA M+Water. This was also verified in the present work by performing independent experiments with various combinations of DAA, M, water and acetone as feed to the batch reactor. From the batch kinetic experiment with M, water and isopropyl alcohol added as a co-solvent to homogenize the reaction mixture, it can be concluded that backward reaction of M to DAA is very slow compared to the forward reaction and can easily be neglected while developing the kinetic model. Hence, the reaction scheme considered for the kinetic modeling is 2 Acetone Diacetone alcohol, (3) Diacetone alcohol Mesityl oxide + Water. (4) The heterogeneous reaction may be described by many models such as Langmuir Hinselwood, Eley Rideal and pseudohomogeneous models. The modified versions of these models are also known to work well for many reactions. In this work we considered three different representative rate equations (models A, B, C) and evaluated the applicability based on the quality of fit obtained. It should be noted that the effect of r DAA = dn DAA r M = dn M Model B: r DAA = dn DAA r M = dn M Model C: r DAA = dn DAA r M = dn M = M cat(k f a 2 Ac k ba DAA k M a DAA ) (1 + K W a W ) 2, (5) = M catk M a DAA (1 + K W a W ) 2. (6) = M cat(k f a 2 Ac k ba DAA ) (1 + K W a W ) r M, (7) = M catk M a DAA (1 + K W a W ) 2. (8) = M cat (k f a 2 Ac k ba DAA ) r M, (9) = M catk M a DAA (1 + K W a W ) 2, (10) where, M cat is the weight of catalyst and K W is the adsorption constant for water. Water being the most polar component has highest affinity towards the catalytic sites so adsorption of acetone, M, DAA were assumed to be negligible compared to K W. This assumption is in concurrence with the earlier studies by Du Toit and Nicol (2003). The UNIQUAC model was used to determine the activities of the components and the UNI- QUAC binary interaction parameters were determined by UNI- FAC method using Aspen property plus. The binary interaction parameters of UNIQUAC model are given in Table 2. The Aspen custom modeler (ACM) was used to estimate the kinetic parameters by regression. The program in ACM uses the least square method to minimize weighted absolute square error between the observed and predicted values of the measurements. It determines the values of the parameters by solving the following minimization problem: ND N M ij min (Z j (t ij k ) Z ikj ) 2, (11) i=1 j=1 k=1

4 5570 Table 3 Estimated values of parameters for activity based kinetic models with 95% confidence limit Model A Model B Model C E f (j/mol) ± ± ± E b (j/mol) ± ± ± E M (j/mol) ± ± ± k f 0 (mol/kg/h) ± ± ± k b0 (mol/kg/h) ± ± ± k M0 (mol/kg/h) ± ± ± K W 1.66 ± ± ± SRS at 55 C, 2% wwcat 0.1 at 55 C, 2% wwcat 0.04 at 55 C, 3.5% cat at 55 C, 5% wwcat 0.08 at 55 C, 3.5% wwcat at 55 C, 5% wwcat r DAAcal at 70 C, 3.5% wwcat at 85 C, 3.5% wwcat r Mcal at 70 C, 3.5% cat at 85 C, 3.5% wwcat r Mobs r DAAobs Fig. 3. Calculated vs observed reaction rates for DAA formation. Fig. 4. Calculated vs observed reaction rates for M formation. where, ND is the total number of dynamic experiments performed; z j are the number of variables (i.e. concentrations of various species) measured over all the experiments and M ij is the number of measurements made in the experiment i. The regression results are summarized in Table 3, which includes the values of the regression parameters, square of residual error (SRS) with 95% confidence limit. The three kinetic models when compared based on the values of SRS, indicate that the rate equation given by model C explains the experimental data more accurately than models A and B. The calculated reaction rates for the model C at different batch times were plotted against the observed rates of DAA and M formation in Figs. 3 and 4, respectively, for all temperatures and catalyst loadings. The plot shows a good agreement between the experimental and predicted results. According to model C, the first step (i.e. dimerization of acetone to DAA) is insensitive to the water content and can be best explained using a pseudo-homogeneous type model whereas, the second step (i.e. dehydration of DAA to M) is explained using the Langmuir Hinselwood type model as it is strongly influenced by the adsorption of water on the resin. This observation that the water content makes a favorable impact on the DAA formation can be advantageously exploited to further increase the selectivity of DAA. 3. Reactive distillation The kinetic experiments conducted in batch reactor using cation exchange resin showed that the selectivity of DAA is quite low. Podrebarac et al. (1997) have reported that an equilibrium conversion of acetone to DAA is as low as 4.3% at 54 C. Further the same group has demonstrated the use of RD to increase the selectivity towards DAA in the presence of anion exchange catalyst (Podrebarac et al., 1998). Here, we propose use of RD for the acid catalyst, i.e. cation exchange resin, to increase the selectivity of DAA. This may allow one to achieve the DAA:M ratio over a wide range by manipulating the design and operating parameters. By using RD, the chemical equilibrium can be shifted towards the production of DAA through continuous removal of DAA from the reactive zone. Also the consecutive dehydration of DAA to M may be controlled by manipulating the extent of insitu separation of DAA from the reactive zone thereby maintaining sufficiently low concentration of DAA in the reactive zone. The overall yield towards DAA and M is also expected to be high due to reduced side-product formation. As acetone (boiling point of 56.3 C) is the lightest compound compared to water (bp: 100 C), M (bp:129.5 C) and DAA (bp: C), the reactive zone is placed in the rectifying section

5 5571 Fig. 5. Reactive Distillation Setup: Shaded region indicates the reactive zone. (Agarwal et al., 2006). It should be noted that M and water form a minimum boiling azeotrope at atmospheric pressure. However, in the present case, both M and water will be removed as bottom products, this azeotrope is not relevant in context to the process feasibility. Except for the M water mixture, all the other binaries are non-azeotropic. In RD experiments, acetone is present on all the stages which helps homogenizing the reaction mixture and avoids a possible liquid liquid split due to the miscibility gap between water and M Apparatus RD setup shown in Fig. 5 consists of a reactive section (0.7 or 1.4 m) and a non-reactive section (0.6m). Reactive section is packed with Sulzer Katapak packing filled with cation exchange resin Amberlyst 15 and the non-reactive section is packed with HYFLUX packing from Evergreen India Ltd. Temperature sensors and sampling ports are provided on each stage for monitoring the performance of RD run periodically Batch reactive distillation (BRD) As the first step to evaluate the feasibility of RD, BRD runs were conducted by varying re-boiler duty and catalyst concentration under total reflux. BRD runs are less time consuming and use less amount of chemicals. Hence, these experiments can be performed as the first step in process development to quickly ascertain the potential of RD. The setup shown in Fig. 5 was used to conduct the experiments by feeding acetone into the re-boiler initially and removing samples at different time intervals from the re-boiler to monitor the performance. The equilibrium stage model based simulations were performed using Aspen plus simulator (ASPENDYNAMICS). The heat losses from the column wall and reboiler were calibrated and were considered while giving input to the simulator. Similarly, the number of theoretical stages for the reactive and non-reactive sections were independently determined by performing simple distillation of the standard methanol water mixture (NTSM for the reactive zone: 3; NTSM for the nonreactive zone: 6). The equations involved in a BRD model are

6 5572 Mole fraction Time (hr) Acetone DAA M Simuation Temperature Fig. 6. Variation of composition and temperature of reboiler with time for heat duty of 0.6 kw and catalyst concentration of 0.02 kg/m. Temperature (K) Selectivity Conversion 0.02 Kg/m of catalyst conc Kg/m of catalyst conc. Batch Reactor Simulation Fig. 8. Effect of catalyst concentration (kg/m) on selectivity for 0.6KW of re-boiler duty. Selectivity KW 0.6 KW 1 KW Batch Reactor Simulation ing one can considerably increase the selectivity of DAA formation for the same conversion. Selectivity towards DAA increases from 40% to 60% by increasing the reboiler duty from 0.32 to1 KW at 40% conversion and catalyst concentration of 0.04 kg/m whereas, the selectivity in the batch reactor is 2% at the same conversion. Both Figs. 7 and 8 show that, under otherwise similar conditions, increase in reboiler duty or increase in the number of reactive stages with the overall catalyst loading being same has a favorable effect on the selectivity of the intermediate compound (DAA), which is in concurrence with the theory put forth by Agarwal et al. (2006) Continuous reactive distillation (CRD) Conversion Fig. 7. Effect of re-boiler duty on selectivity of DAA for catalyst concentration of 0.04 kg/m. well known and one may refer our earlier work for the details (Kumar et al., 2006). The kinetics used for simulations is the one developed in the present work. The UNIQUAC binary interaction parameters used for the prediction of VLE are given in Table 2. The experimental and simulation results of BRD are shown in Figs. 6 8 and are found to be in good agreement. Fig. 6 shows the concentration and temperature profiles in a typical BRD run with respect to time. As anticipated, the temperature of the reboiler increases over a period due to accumulation of high boiling products. After 6 h of BRD run, for 0.6kW reboiler duty and 1.4kg/m of catalyst concentration, typical composition and temperature of the reboiler are x Ac = 0.732, x DAA = 0.109, x M = 0.083, x W = and 63 C, respectively. Fig. 7 shows the effect of boil up rate. By increasing the boil up rate (i.e. reboiler duty) for the same catalyst load- The setup shown in Fig. 5 was used to conduct the experiments under total reflux condition by feeding acetone continuously at the bottom of the reactive section and by continuously withdrawing the bottom product stream. Samples at several locations in the column were analyzed at different time intervals to monitor the performance. The attainment of steady state was ensured by constancy in temperature and concentration profiles. Typically, it takes 6.8 h to obtain the steady state. An equilibrium stage model, considering the heat losses from the column and reboiler to the surrounding, was solved using Aspen plus simulator (RADFRAC). The relevant model equations and underlying assumption may be found elsewhere (Taylor and Krishna, 2000). It should be noted that the external mass transfer resistance at the solid liquid interface is not considered here. An exhaustive three-phase model (Xu et al., 2005) is required to be solved to consider these effects, which is out of the scope of the present work. Nevertheless the simplified model used here is able to explain the results over the conditions of interest. The experimental and simulation results of CRD are shown in Figs. 9 and 10. Figs. 9a and b show the steady state concentration and temperature profiles along the length of the column, obtained by experiments and simulation, in a representative CRD run. The height of the column being constant, the

7 5573 a 8 b Stage number Acetone DAA M Water Simulation Stage number Simulation Experimental Mole fraction Temperature (K) Fig. 9. (a) Steady state experimental and simulated composition profiles along length of column for 0.65 KW of re-boiler duty and 150 gm catalyst loading. (b) Steady state experimental and simulated temperature profile along length of column for 0.65 KW of re-boiler duty and 150 gm catalyst loading kilow att 1.5 kilow att 1 kilow att Selectivity for DAA watts 650 watts 850 watts simulation Selectivity for DAA kilow att 3 kilow att 4 kilow att Conversion Fig. 10. Effect of re-boiler duty on selectivity of DAA at various conversion levels Number of reactive stages Fig. 11. Effect of re-boiler duty on DAA selectivity for conversion close to 100%. total catalyst loading and reboiler duty were the two adjustable parameters. Under otherwise similar conditions, catalyst loading may be increased to increase the conversion. Fig. 10 shows the relation between conversion and selectivity of DAA thus obtained at different reboiler duties. As anticipated, the CRD runs show similar trends in selectivity as that of BRD i.e., at the same conversion the selectivity increases with the increase in reboiler duty. The agreement between experimental data and the predicted results is satisfactory. The validated model is further used to predict the performance of CRD over a wide range of different parameters including number of reactive stages. Fig. 11 summarizes the CRD simulation results performed by varying the re-boiler duty and the number of reactive stages. In all the runs the number of non-reactive stages is same and the catalyst loading is varied so as to obtain the same conversion. It can be seen that the selectivity is very sensitive to the change in reboiler duty. The effect of number of reactive stages becomes insignificant beyond a particular limit and theoretically very large number of stages is required to achieve selectivity close to 100%. This is because of the dehydration of DAA (second step) being intrinsically very fast compared to aldol condensation (first step), which has been experimentally

8 5574 verified in the present study. Hence, though RD offers a significant rise in selectivity of DAA as compared to conventional reactors, a quantitative conversion towards only DAA is practically impossible with this catalyst. The results showed that one can vary the selectivity of DAA with judicious choice of operating and design parameters. It should also be noted that the number of non-reactive stages also plays an important role and needs special attention to arrive at the economically viable column design. 4. Conclusion Different activity based models for the reactions system involving aldol condensation and dehydration of acetone in the presence of cation exchange resin (Amberlyst 15 ) have been proposed and compared. The experiments show that reactive distillation (RD), due to its ability to remove the product offers significantly high selectivities towards useful intermediates such as DAA and M which are otherwise not attainable in any conventional reactor with acid catalyst. The formation of high molecular weight undesired side-products is significantly low. Moreover, RD may be considered as a promising multifunctional reactor system when both the products are desired. ne can manipulate the design and operating parameters, such as boil up rate, catalyst concentration etc. to achieve the flexibility in product distributation. High reboiler duty or small per stage Damkohler number allows one to enhance the DAA formation. Notation a i E b E f E M k b0 k f k f 0 k M k M0 K b K i M M ij n i ND r i t x z j activity coefficient of component i activation energy for DAA decomposition activation energy for DAA formation activation energy for DAA dehydration frequency factor for DAA decomposition second order rate constant for DAA formation frequency factor for DAA formation first order rate constant for DAA dehydration or M formation frequency factor for DAA dehydration first order rate constant for DAA decomposition adsorption equilibrium constant of component i mass of catalyst, gm number of measurements made in the experiment i number of moles (g-mol) of component i total number of dynamic experiments performed reaction rate (g-mol/min) of component i time mole fraction number of variables measured over all the experiments Subscripts Ac acetone cat catalyst DAA diacetone alcohol i general component M mesityl oxide t time T temperature W water References Agarwal, V., Thotla, S., Mahajani S.M., Selectivity with reactive distillation determination of attainable regions, Distillation and Absorption Aspen Technology Inc., ASPEN Process Manual. Du Toit, E.L., Nicol, W., The rate inhibiting effect of water as a product on reactions catalyzed by cation exchange resins: formation of mesityl oxide from acetone as a case study. M.Sc. Thesis, University of Pretoria, South Africa. (last visited on 26/01/2006). Flego, C., Perego, C., Acetone condensation as a model reaction for the catalytic behaviour of acidic molecular sieves: a UV Vis study. Applied Catalysis A 192, Kim, Y.K., Hatfield, J.D., Kinetics and equilibrium data of the dehydration-hydration reaction between diacetone alcohol and mesityl oxide in phosphoric acid. Journal of Chemical and Engineering Data 30, Klein, K.G., Banchero, J.T., Aldol condensation of acetone to mesityl oxide. Industrial & Engineering Chemistry 48, Kumar, R., Mahajani, S.M., Nanavati, H., Noronha, S., Recovery of lactic acid by batch reactive distillation. Journal of Chemical Technology and Biotechnology 81, Lemcoff, N.., Cunningham, R.E., Kinetics of diacetone alcohol conversion to mesityl oxide catalyzed by ion exchange resin. Journal of Catalysis 23, Lippert, S., Baumann, W., Thomke, K., Secondary reactions of the base-catalyzed aldol condensation of acetone. Journal Molecular Catalysis 69, March, J., Advanced rganic Chemistry. Wiley, Toronto, Canada. pp Keefe, W.K., Jiang, M., Ng, F.T.T., Rempel, G.L., Liquid phase kinetics for the selective hydrogenation of mesityl oxide to methyl isobutyl ketone in acetone over a Pd/Al 2 3 catalyst. Chemical Engineering Science 60, Panov, A.G., Fripiat, J.J., Acetone condensation reaction on acid catalysts. Journal of Catalysis 178, Podrebarac, G.G., Ng, F.T.T., Rempel, G.L., A kinetic study of the aldol condensation of acetone using an anion exchange resin catalyst. Chemical Engineering Science 52, Podrebarac, G.G., Ng, F.T.T., Rempel, G.L., The production of diacetone alcohol with catalytic distillation. Part-I. Catalytic distillation experiments. Chemical Engineering Science 53 (5), Sharma, M.M., Mahajani, S.M., Reactive Distillation: Status and Future Directions. Wiley- VCH, Weinheim. pp Taylor, R., Krishna, R., Modelling reactive distillation. Chemical Engineering Science 55, Xu, Y., Zheng, Y., Ng, F.T.T., Rempel, G.L., A three-phase nonequilibrium model for catalytic distillation. Chemical Engineering Science 60,