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Experimental and Theoretical Study of Reactive Stripping in Monolith Reactors Ivo Mueller,† Tilman J. Schildhauer,‡,§ Anis Madrane,† Freek Kapteijn,‡ Jacob A. Moulijn,‡ and Eugeny Y. Kenig*,† Department of Biochemical and Chemical Engineering, UniVersity of Dortmund, Emil-Figge-Strasse 70, 44227 Dortmund, Germany, and DelftChemTech, Technical UniVersity Delft, Julianalaan 136, 2628 BL Delft, The Netherlands
In this paper, reactive stripping in monolithic reactors is studied experimentally and theoretically. For the experiments, different monolith types are coated with a catalyst and operated in cocurrent and countercurrent mode. The esterification of 1-octanol and hexanoic acid is investigated in a batch-recycle mode; the liquid phase is recirculated, whereas the stripping gas nitrogen with the stripped water is vented after each pass through the column. The experimental results show that the conversion of equilibrium-limited esterifications can be increased using reactive stripping, the process performance being influenced by the monolith type and operating mode. The theoretical description is given by a rate-based model, which is successfully validated against the experimental data and used to conduct sensitivity studies, with regard to operating parameters and different reactive zone arrangements within the monoliths. 1. Introduction One of the promising ways for process intensification is to integrate reaction and separation in one single unit. In recent decades, the chemical process industries have shown an increasing interest in the development of such integrated processes. In this respect, reactive distillation represents undoubtedly one of the most popular examples. However, reactive distillation is only advantageous for processes in which the temperature windows for distillation and reaction coincide. Otherwise, reactive stripping may be an interesting alternative. The removal of reaction (by)products from the liquid phase by means of a sweep gas offers flexibility in process conditions, in regard to pressure and temperature. In contrast to reactive distillation, reactive stripping can be performed in both cocurrent and countercurrent operating modes. The feasibility of reactive stripping in monolithic catalyst supports was successfully demonstrated at the pilot scale by applying the so-called film-flow monoliths with wide channels.1,2 The investigated process was the esterification of hexanoic acid with 1-octanol, accompanied by the etherification of the alcohol (Figure 1). In the present work, this process has been studied both experimentally and theoretically for different monolith types and operating modes. The experimental results are used for a thorough validation and further development of a rate-based model, which has been recently created at the University of Dortmund.3 In this work, special consideration is given to the description of the interfacial mass transfer and reaction kinetics. The validated model is used to perform sensitivity studies regarding operating parameters and different reactive zone arrangements within the monolith. * To whom correspondence should be addressed. Tel.: +49 231/755-2357. Fax: +49 231/755-3035. E-mail: e.kenig@ bci.uni-dortmund.de. † Department of Biochemical and Chemical Engineering, University of Dortmund. ‡ DelftChemTech, Technical University Delft. § Present address: Laboratory for Energy and Materials Cycles, PaulScherrer-Institut, CH-5232 Villigen PSI, Switzerland.
Figure 1. First (main) reaction: esterification of hexanoic acid with 1-octanol to octyl hexanoate (ester) and water; second (side) reaction: etherification of 1-octanol to dioctyl ether and water.
Figure 2. Monolithic catalyst supports for film flow operation with a diameter of 43 mm (from left to right): squared channel, 50 cpsi (SQ, specific surface area ) 920 m2/m3); squared channel, 25 cpsi (SQ, surface area ) 640 m2/m3); internally finned monoliths, 25 cpsi (IFM, surface area ) 1040 m2/m3); and more rounded channel, 25 cpsi (MRC, surface area ) 546 m2/m3).
2. Experimental Section 2.1. Setup. Squared channel (SQ) monoliths of 25 cpsi and 50 cpsi size (see Figure 2) were coated with zeolite BEA (CP811 E-75, from Zeolyst, with an Si/Al ratio of 150). Following the procedure described elsewhere,4 a slurry of BEA powder, colloidal silica, and a small amount of surfactant in water was prepared. Compared to the original procedure,4 the double amount of water was used to obtain very thin (yet uniform and stable) catalyst layers in the wide channels. The monoliths were dipped into the slurry, dried, and calcined. To increase the catalyst loading, they were again coated, dried, and calcined. An ion exchange with ammonium nitrate solution and subsequent calcination was conducted to obtain the H-BEA form reliably. This leads to stable catalyst coatings with an average loading of 25 g BEA on each 50-cm-long monolith piece. The experiments were performed in a pilot-scale plant (Figure 3). For each experiment, four pieces of coated monoliths are stacked carefully in line and mounted in a 2-m-high heated column with a diameter of 50 mm. The preheated liquid feed (25 kg/h), which consists of the reactants and the solvent cumene, is distributed through a spray nozzle. After each pass, the liquid is collected in the liquid-supply vessel and circulated
10.1021/ie061111v CCC: $37.00 © 2007 American Chemical Society Published on Web 02/02/2007
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Figure 5. Increase in ester concentration during one pass through the column in countercurrent operation for different monolith types. Figure 3. Experimental pilot-plant setup.
Figure 4. Ester molar fractions in countercurrent operation for 25-cpsi SQ monoliths (data taken from Schildhauer et al.1) and 50-cpsi SQ monoliths (closed symbols represent data from the reactor outlet, and open symbols represent data from the reactor inlet).
continuously through the reactor (batch-recycle mode). The nitrogen stream (500 NL/h) is preheated before entering the column. After one pass, the gas is entered into the condenser, where it is separated from the liquid phase and then vented. The condensate is collected in a phase separator, from which water can be tapped off, whereas the organics (mostly cumene) are recycled back to the liquid vessel via the overflow. During the experiments, liquid samples are taken from the liquid reactor inlet and outlet; the setup does not allow taking samples along the column. Samples are analyzed using gas chromatography (GC) and Karl Fischer coulometry, to determine the concentrations and water content. For reactive stripping experiments, ∼13 L of liquid was used, containing cumene as solvent, tetradecane as internal standard for the chromatography study, and ∼12 mol % of both hexanoic acid and 1-octanol. All experiments were conducted at a temperature of 160 °C and an absolute pressure of 5 bar. The total BEA catalyst amount in the reactor ranged between 90 g for the 50 cpsi and 115 g for the 25 cpsi monolith sets, which corresponds to 12.5 and 22.8 gBEA/m2, respectively. The total mass balance error for the experiments did not exceed 0.9%, whereas water balance errors did not exceed 10%, thus giving sufficient confidence in the results of the GC and Karl Fischer analyses. 2.2. Results. Figure 4 shows the molar fractions of the reaction product ester for the experiments with squared channel monoliths 25 and 50 cpsi in size. Because the samples have
Figure 6. Molar fractions of the main product ester and the byproduct ether for countercurrent and cocurrent operations in 25 cpsi SQ monoliths (closed symbols represent data from the reactor outlet, and open symbols represent data from the reactor inlet).
been taken from the reactor inlet and outlet simultaneously, both the inlet and outlet molar fractions are represented. From this figure, no significant difference in the performance for both channel sizes can be observed. The reaction proceeds fast initially and slowly approaches full conversion of the reactants. This demonstrates the positive stripping effect, because, without water removal, the chemical equilibrium would limit the ester molar fraction by ∼8%. The similar performance for both sizes is consistent with earlier findings1 in which different channel geometries did not result in significant differences, despite the fact that different channel shapes also mean different specific surface areas. Figure 5 compares ester concentration changes achieved during one pass through the column (i.e., the difference between inlet and outlet values at the same time). All monolith types show the same behavior: as the water content decreases from the initial level, because of stripping, the reaction is less and less inhibited by water adsorbed on the active sites of the zeolite. Therefore, the reaction rate can still increase while the reactant concentration decreases. Within ∼60 min, this effect ceases, the decrease in the reactant concentration becomes dominant, and the reaction rate decreases as a consequence of the decreasing driving force, finally approaching zero. Figure 6 shows ester and ether concentrations for both operating modes for monolith SQ (25 cpsi). The difference between the outlet and inlet concentrations reflects the formation rate of ester and ether. The countercurrent operating mode has a higher ester formation rate, compared to the cocurrent operation (especially between 60 min and 90 min). However, the formation rate of ether is also increased, which reduces the
Ind. Eng. Chem. Res., Vol. 46, No. 12, 2007 4151 Table 1. Kinetic Parameters for the Zeolite BEA Catalyst parameter
value
kester kether Keq Kalcohol Kwater
1.98 × 10-7 m3/(gcat s) 2.27 × 10-5 mol/(gcat s) 2.65 3.19 × 10-3 m3/mol 1.23 × 10-1 m3/mol
Table 2. Vapor Pressures of Pure Components at 150 °C
Figure 7. Water contents at the reactor inlet and outlet for countercurrent and cocurrent operation in 25 cpsi SQ monoliths.
selectivity. Both effects are related to the better stripping of water in the countercurrent operating mode. The lower water concentration increases the formation rate of ester. Because the etherification is more strongly inhibited by water,2,5 it benefits significantly more from the water removal. The better stripping of water in the countercurrent operating mode is illustrated in Figure 7. The inlet and outlet water concentrations are almost always lower for the countercurrent operation. This supports the conclusion that countercurrent reactive stripping is more effective under the conditions of these experiments. Similar results were obtained for the same reaction system with catalytically coated Sulzer DX packings.6 Still, it should be noticed that the overall water concentration in the column might differ from the inlet and outlet concentrations. As discussed in Schildhauer et al.,6,7 an internal water loop might occur when the gas stream saturated with water contacts the liquid stream at the top of the column. In this part, the liquid has a low water concentration, and hence, water is (re)absorbed by the liquid, thus increasing the overall holdup of the undesired byproduct in the reactor. 3. Modeling 3.1. Modeling Basis. In integrated processes, the interfacial mass transfer, vapor-liquid equilibrium, and reaction are interdependent, and their interactions strongly influence both the conversion and selectivity. For such complex processes, ratebased models are preferable to equilibrium models (see, e.g., Baur et al.,8 Kenig et al.9). Because the changes in the process variables with time are small and the residence time (τ) of both phases within the column is short (τliquid is approximately a minute, τgas is 1.5 Vi
(10)
For the adjustment to concentrated solutions, the method by Vignes18 and the method by Wesselingh and Krishna19 are compared. The method by Vignes18 yields very high diffusivities for components with low concentrations, which lie beyond physically significant limits. Therefore, the approach by Wesselingh and Krishna19 is preferred, which estimates the Maxwell-Stefan diffusion coefficients using the following equation:
Dij ) (D∞ij )(1+xj-xi)/2 × (D∞ji )(1+xi-xj)/2
with
ShL ) ReL )
k Ld h D
The obtained binary diffusion coefficients are used to adapt the binary mass-transfer coefficients, according to eq 9:
L
uL,sdh
κLij
νL
κLoxygen/water
νL DL
4. Simulations
ScL )
Because the monolith geometry is the same for both systems, the constant C is equal for both correlations:
ShL,1 RemL,1ScnL,1
) C1 ) C2 )
ShL,2 RemL,2ScnL,2
(8)
This condition leads to the following relationship between the mass-transfer coefficients:
kLl
() () ( )
DLl ) kL2 DL2
1-n
νLl
νL2
n-m
(11)
uL,s 1
uL,s 2
m
(9)
The m value of 0.35 is determined from the experimental data,7 whereas n is assigned a value of 0.333. Thus, the mass-transfer coefficient is related to the diffusion coefficient as kL ∝ (DL)2/3. This is in accordance with the analytical solution of the
)
(
DLij
DLoxygen/water
)( )( ) 1-n
νLmixture νLwater
n-m
uL,s mixture uL,s water
m
(12)
For reliable simulation results, a reasonable number of the column discretes must be chosen. For the investigated test case, this number was determined to be 40 elements, each with a height of 5 cm. With higher discrete numbers, no change in the results was observed. 4.1. Validation. The developed model is validated for different monoliths (IFM, MRC, and SQ (25 cpsi)) and operating modes (cocurrent and countercurrent). The calculations are performed without any adjusting parameters. In Figure 8, two concentration profiles for the IFM at different run times are presented. After 35 min (Figure 8, left), a clear maximum can be observed in the water concentration profile. The appearance of such a maximum was discussed by Schildhauer et al.6,7 The concentration profiles of the other components are almost linear. At the end of the experiment (after 261 min; Figure 8, right), the water concentration maximum decreases, because less water is produced by the reaction. Furthermore, ester and ether concentrations become
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Figure 8. Simulated liquid concentration profiles and experimental data for IFM (countercurrent mode) after run times of 35 min (left) and 261 min (right).
Figure 9. Simulated liquid concentration profiles and experimental data for SQ (25 cpsi, cocurrent mode) after run times of 53 min (left) and 240 min (right).
water concentration also suppresses the side reaction, which increases the selectivity. This behavior is consistent with the experimental observations (cf. Figure 6). The water concentration at the monolith outlet represents an interesting and sensitive process parameter, as it is dependent both on the kinetics and, because of high volatility (cf. Table 2), on mass transfer. Nevertheless, a good agreement between the simulated and measured data for all studied monoliths and operating modes is achieved (Figure 10). The simulated outlet concentrations of the other components also agree well with the experimental values. Along with water concentration, the comparison of simulated and experimentally determined conversion and selectivity is important. The single-pass conversion for the hexanoic acid is defined as Figure 10. Parity plot of the water outlet concentration for different monoliths and operating modes.
significantly higher, while their profiles remain linear. The simulated results show very good agreement with the experimental data. In Figure 9, the concentration profiles for SQ in the cocurrent mode are presented. The experimental outlet concentrations are reproduced very well by the simulations. It can be further observed, that, contrary to the countercurrent flow regime, the profile of the water concentration does not show any maximum. Because the water concentration is almost constant at a high value, the conversion in cocurrent mode is lower. This high
Xsingle pass,acid (%) ) L V L V + Nacid,inlet ) - (Nacid,outlet + Nacid,outlet ) (Nacid,inlet L Nacid,start
× 100 (13)
and the single-pass selectivity of 1-octanol is defined as
Ssingle pass,alcohol (%) ) L V L V + Nester,outlet ) - (Nester,inlet + Nester,inlet ) (Nester,outlet
× L V L V (Nalcohol,inlet + Nalcohol,inlet ) - (Nalcohol,outlet + Nalcohol,outlet ) 100 (14)
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Figure 11. Acid conversion and alcohol selectivity for countercurrent mode: IFM (left) and MRC (right).
Figure 12. Acid conversion and alcohol selectivity for the SQ monolith (25 cpsi) for countercurrent mode (left) and cocurrent mode (right).
Because pure nitrogen is used as stripping gas, no reactant enters the column with the vapor flow. Thus, the reactants flow rates in the inlet vapor stream are equal to zero in eqs 13 and 14: V V V Nalcohol,inlet ) Nester,inlet ) Nacid,inlet )0
(15)
If a constant molar flow rate through the column is assumed and the transport of acid and alcohol to the vapor phase is neglected, conversion and selectivity can be obtained from the measured liquid-phase concentrations,
Xsingle pass,acid (%) ≈ Xsingle pass,alcohol (%) ≈
xacid,inlet - xacid,outlet × 100 (16a) xacid,start
xalcohol,inlet - xalcohol,outlet × 100 (16b) xalcohol,start
and
Ssingle pass,alcohol (%) ≈
xester,outlet - xester,inlet × 100 (17) xalcohol,inlet - xalcohol,outlet
Equations 16 and 17 are also used for the simulated conversion and selectivity. Figure 11 shows the single-pass conversion and selectivity for the experiments with IFM and MRC under countercurrent flow conditions. In the beginning, the acid conversion has a value of ∼12% and decreases to 80%) are reached for almost the entire period of time, whereas the selectivity in the countercurrent operating mode decreases after 100 min. This can be explained by higher water concentration in the cocurrent mode (cf. Figure 7), which hinders the etherification and leads to high selectivities. The experimental selectivity profiles can be well-reproduced by the simulations.
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Figure 13. Influence of pressure and temperature on conversion (left) and selectivity (right) for IFM monolith (countercurrent mode). Table 3. Simulation Results for Different Arrangements of the Reactive Zone (cf. Figure 14) Configuration 1
Configuration 2
Configuration 3
Configuration 4
Configuration 5
parameter
CoC
CC
CoC
CC
CoC
CC
CoC
CC
CoC
CC
Xsingle pass,acid [%] Xsingle pass,alcohol [%] Ssingle pass,alcohol [%] Ysingle pass, ester [%] xwater,outlet [10-2 mol/mol]
15.59 16.50 92.72 15.30 1.35
11.89 12.37 94.31 11.67 0.86
14.98 15.79 93.04 14.69 1.25
10.53 10.89 94.85 10.33 0.43
15.22 16.09 92.80 14.93 1.38
10.86 11.22 94.92 10.65 1.14
15.09 15.92 93.00 14.80 1.37
13.15 13.75 93.82 12.90 0.99
15.09 15.91 93.00 14.80 1.27
11.22 11.64 94.60 11.01 0.60
a
Abbreviations for operating modes: CoC ) cocurrent; CC ) countercurrent.
The conversion for the cocurrent mode is also well-described by the model; yet, for the countercurrent mode, deviations appear in the beginning (for run times of 160 °C). This behavior is caused by the enhanced stripping of water, due to higher temperatures and lower pressures, which shifts the chemical equilibrium toward the product side. The influence on selectivity is small under all investigated operating conditions (Figure 13, right). 4.3. Arrangement of the Reactive Zone. The experiments and simulations show that the presence of water inhibits the reaction and limits conversion. Thus, it seems reasonable to locate the reactive zone in the monolith section with low water concentrations, via a suitable combination of reactive and nonreactive sections. In practice, these configurations can be easily realized using coated (reactive) and uncoated (nonreactive) monolith segments. In Figure 14, five investigated arrangements are presented. The liquid inlet is always fixed at the top of the monolith reactor, whereas the inlet of the stripping gas is dependent on the operating mode (top for cocurrent flow and bottom for countercurrent flow). To enable a simple comparison of the reactor performance, the total catalyst mass for the column is kept constant. Thus, for configurations 2-5 the catalyst loading
Figure 14. Investigated arrangements of the reactive zone (denoted by the gray shading).
of the reactive segments is twice the loading of the reactive segments of configuration 1. The investigation is performed with the IFM monolith, with the liquid inlet concentrations kept constant at the experimental values achieved after 20 min. The results are presented in Table 3. It can be seen that, generally, the cocurrent mode reveals higher conversion, whereas the countercurrent mode offers higher selectivity. In the experimental investigation, an opposite effect is observed. This is attributed to the fact that, in the batch-recycle mode, the water inlet concentration is lower in the countercurrent operating mode than in the cocurrent operating mode (cf. Figure 7), because of the better water stripping performance at the bottom of the column. Thus, the water holdup in the column is smaller for the countercurrent operating mode. In this parameter variation study, the same water inlet concentration is chosen for both operating modes. As the result, the countercurrent operating mode is handicapped by the water concentration maximum, which leads to a higher water holdup, compared to the cocurrent operating mode, with an almost
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constant water concentration (cf. Figure 9). Therefore, the countercurrent operating mode provides less conversion and higher selectivity than the cocurrent mode for the same feed concentration. The different configurations were evaluated by a yield comparison. The highest yield can be obtained for the experimentally investigated configuration (configuration 1) in cocurrent operating mode. If low water concentration in the liquid outlet is more important than high yield, configuration 2 in countercurrent operating mode represents an interesting alternative. A combination of high yield and low water concentration can be achieved with configuration 4 in countercurrent operating mode. 5. Conclusions The reactive stripping is studied experimentally and theoretically for monolith reactors with different geometry under cocurrent and countercurrent operating conditions. The experiments are realized as a batch-recycle operation for the esterification of 1-octanol with hexanoic acid. It is shown that the integration of reaction and separation enhances conversion, compared to traditional reactor performance (equilibrium limited). The change in conversion with time is similar for all monolith types studied. A more clear influence is exhibited by the operating mode (cocurrent and countercurrent), with regard to the conversion, selectivity, and water concentration profile. A rate-based model is developed, with special consideration given to the description of the mass transfer. In particular, an adjustment of the mass-transfer coefficient from the nonreactive system to the reactive system and the study of diffusivity calculation methods are performed. A successful model validation against experimental results obtained for three different monoliths and both operating modes is demonstrated. For all investigated process variables (including concentrations, selectivity, and conversion), good agreement is achieved. The parametric study of the system pressure and liquid-phase temperature shows that both parameters can be used to shift the reaction conversion favorably, whereas the selectivity is hardly influenced. It is also shown that the proper choice of the operating mode (cocurrent or countercurrent), as well as a suitable arrangement of the reactive zone, can contribute to improving the conversion and selectivity and to achieving high yield and low water concentrations in the liquid outlet stream. Acknowledgment The support of the European Commission in the context of the Fifth Framework Programme (INTINT, Contract No. G1RDCT-1999-00048) is greatly acknowledged. Nomenclature A ) kinetic parameter C ) Sherwood correlation constant c ) molar concentration [mol/m3] D ) binary diffusion coefficient in concentrated mixtures [m2/s] ∞ D ) binary diffusion coefficient for diluted mixtures [m2/s] dh ) hydraulic diameter of the monolith channel [m] H ) height [m] (J) ) vector of diffusional fluxes [mol/(m2 s)] k ) reaction rate constant [m3/(gcat s), mol/(gcat s)] [k] ) matrix of mass transfer coefficients [m/s] K ) adsorption constant [m3/mol] Keq ) reaction equilibrium constant
M ) molar weight [g/mol] N ) molar flow rate [mol/s] n ) number of components [R] ) matrix defined by eqs 4 and 5 [s/m] Re ) Reynolds number r ) reaction rate [mol/(gcat s)] Sc ) Schmidt number Sh ) Sherwood number Ssingle pass ) single-pass selectivity T ) temperature [K] us ) superficial velocity [m/s] V ) molar volume at the normal boiling point [cm3/mol] Xsingle pass ) single-pass conversion x ) liquid-phase molar concentration [mol/mol] Ysingle pass ) single-pass yield Greek Letters [Γ] ) matrix of thermodynamic correction factors κ ) binary mass-transfer coefficient [m/s] µ ) dynamic viscosity [kg/(m s)] ν ) kinematic viscosity [m2/s] τ ) residence time [s] Subscripts acid ) hexanoic acid alcohol ) octanol ester ) octyl hexanoate ether ) dioctyl ether i, j, k ) component indices inlet ) concentration of the liquid inlet stream L ) liquid phase outlet ) concentration of the liquid outlet stream start ) concentration at t ) 0 t ) total Superscripts B ) bulk phase I ) Interface L ) liquid phase AbbreViations CC ) countercurrent CoC ) cocurrent cpsi ) cells per square inch IFM ) internally finned monolith MRC ) more rounded channel SQ ) squared channel Literature Cited (1) Schildhauer, T. J.; Kapteijn, F.; Moulijn, J. A. Reactive stripping in pilot scale monolith reactorssapplication to esterification. Chem. Eng. Process. 2005, 44, 695-699. (2) Beers, A. E. W.; Spruijt, R. A.; Nijhuis, T. A.; Kapteijn, F.; Moulijn, J. A. Esterification in a structured catalytic reactor with counter-current water removal. Catal. Today 2001, 66, 175-181. (3) Klo¨ker, M.; Kenig, E. Y.; Hoffmann, A.; Kreis, P.; Go´rak, A. Ratebased modelling and simulation of reactive separations in gas/vapour-liquid systems. Chem. Eng. Process. 2005, 44, 617-629. (4) Nijhuis, T. A.; Beers, A. E. W.; Vergunst, T.; Hoek, I.; Kapteijn, F.; Moulijn, J. A. Preparation of monolithic catalysts. Cat. ReV.-Sci. Eng. 2001, 43, 345-380. (5) Nijhuis, T. A.; Beers, A. E. W.; Kapteijn, F.; Moulijn, J. A. Water removal by reactive stripping for a solid-acid catalyzed esterification in a monolithic reactor. Chem. Eng. Sci. 2002, 57, 1627-1632. (6) Schildhauer, T. J.; Kapteijn, F.; Moulijn, J. A. Reactive stripping in structured catalytic reactors. In Proceedings of 7th World Congress of Chemical Engineering, Glasgow, July 2005.
Ind. Eng. Chem. Res., Vol. 46, No. 12, 2007 4157 (7) Schildhauer, T. J.; Heibel, A. K.; Yawalkar A.; Kapteijn, F.; Moulijn, J. A. Reactive stripping in structured catalytic reactorsshydrodynamics and reaction performance. In Integrated Chemical Processes; Sundmacher, K., Kienle, A., Seidel-Morgenstern, A., Eds.; Wiley-VCH: Weinheim, Germany, 2005. (8) Baur, R.; Higler, A. P.; Taylor, R.; Krishna, R. Comparison of equilibrium stage and nonequilibrium stage models for reactive distillation. Chem. Eng. J. 2000, 76, 33-47. (9) Kenig, E. Y.; Schneider, R.; Go´rak, A. Reactive absorption: optimal process design via optimal modeling. Chem. Eng. Sci. 2001, 56, 343-350. (10) Krishna, R.; Standart, G. L. Mass and energy transfer in multicomponent systems. Chem. Eng. Commun. 1979, 3, 201. (11) Schildhauer, T. J.; Tromp, S.; Mu¨ller, I.; Schilkin, A.; Kenig, E. Y.; Kapteijn, F.; Moulijn, J. A. Modelling of reactive stripping in monolith reactors. Catal. Today 2005, 105, 414-420. (12) Kramers, H.; Kreyger, P. J. Mass transfer between a flat surface and a falling liquid film. Chem. Eng. Sci. 1956, 6, 42-48. (13) Olander, D. R. The diffusivity of water in organic solvents. AIChE J. 1961, 7, 175-176.
(14) Reddy, K. A.; Doraiswamy, L. K. Estimating liquid diffusivity. Ind. Eng. Chem. Fundam. 1967, 6, 77-79. (15) Lusis, M. A.; Ratcliff, G. A. Diffusion in binary liquid mixtures at infinite dilution. Can. J. Chem. Eng. 1968, 46, 385-387. (16) Tyn, T. M.; Calus, F. W. Diffusion coefficients in dilute binary liquid mixtures. J. Chem. Eng. Data 1975, 20, 106-109. (17) Hayduk, W.; Minhas, B. S. Correlations for prediction of molecular diffusivities in liquids. Can. J. Chem. Eng. 1982, 60, 295-299. (18) Vignes, A. Diffusion in Binary Solutions. Variation of diffusion coefficient with composition. Ind. Eng. Chem. Fundam. 1966, 5, 189199. (19) Wesselingh, J. A.; Krishna, R. Mass Transfer; Ellis Horwood: Chichester, U.K., 1990.
ReceiVed for reView August 22, 2006 ReVised manuscript receiVed December 8, 2006 Accepted December 12, 2006 IE061111V
