Effect of Adsorption on Residue Curve Maps for Heterogeneous

3242

Ind. Eng. Chem. Res. 2004, 43, 3242-3250

Effect of Adsorption on Residue Curve Maps for Heterogeneous Catalytic Distillation Systems Carlos Duarte and Jose´ M. Loureiro* Laboratory of Separation and Reaction Engineering, Department of Chemical Engineering, University of Porto, 4200-465 Porto, Portugal

Heterogeneous catalytic distallation has seen in the last few years an increase in interest from both academic and industrial researchers as a means of obtaining higher product yields in otherwise equilibrium-limited processes. One of the first steps toward the design of a reactive distillation column is the study of the system’s residue curve maps (RCMs), which are normally obtained through simulation of a simple batch distillation in a heated still. Although this process always works in an unsteady state, unsteady-state phenomena, such as adsorption, are usually not considered when deriving a model. In this paper, a four-component reactive system, comprised of 2-methyl-1-butene, 2-methyl-2-butene, methanol, and tert-amyl methyl ether, is studied to determine the effects of adsorption in the RCMs. To do so, two new models that take into account Langmuir mono- and multicomponent isotherms were derived and used for the construction of the RCMs. These RCMs were then compared to those of the nonadsorptive model, and it was found that adsorption can play an important role in the process. Also, a study of the influence of two parameters and one variable, the Damko¨hler number (Da), the ratio of vapor flow rate to liquid holdup (RV/L), and the temperature, on the adsorptive models was carried out, and it was found that the effects of adsorption increase for systems operating at higher Da, RV/L, and temperature. Introduction Reactive distillation (also known as catalytic distillation) has seen in the past few years renewed interest from both academic and industrial researchers. This intensified type of operation can be advantageous over normal, nonintegrated processes. Several successful examples are readily available from the existing literature.1 The first step usually taken toward the design of a distillation column is the analysis and evaluation of the system’s residue curve maps (RCMs). RCMs consist of a graphical representation (on a two-dimensional ternary graph) of the system’s composition over time, where distillation zones are determined in accordance with the system’s stationary points.2 This concept was also applied successfully to reactive distillation systems by Barbosa and Doherty,3 Venimadhavan et al.,4 and Ung and Doherty,5 with the inclusion of the chemical reaction in the model’s formulation. Unfortunately, this direct application might not be correct at all times: batch reactive distillation is an unsteady-state process, and therefore it is affected by unsteady-state phenomena, such as adsorption. Adsorption, according to IUPAC,6 is defined as “...the enrichment (positive adsorption, or briefly, adsorption) or depletion (negative adsorption) of one or more components in an interfacial layer.” Depending on the strength of the bond between the adsorbed compound and the adsorbent, adsorption can be of either a chemical (chemisorption) or physical nature.7 For the large majority of processes, only physical adsorption is useful and considered, and so in this * To whom correspondence should be addressed. Tel.: (+351) 22 508 1672. Fax: (+351) 22 508 1674. E-mail: [email protected].

study the term adsorption will be used to designate physical adsorption only. A far more complete introduction to the phenomenon of adsorption is given by Rouquerol et al.8 In this work, the reactive system under study is the tert-amyl methyl ether (TAME) synthesis system, which consists of four components, 2-methyl1-butene (2M1B), 2-methyl-2-butene (2M2B), methanol (MeOH), and TAME, and three reversible chemical reactions (2M1B and MeOH to TAME, 2M2B and MeOH to TAME, and the isomerization of 2M1B to 2M2B). A previous study of this system was conducted by Thiel et al.,9 but the adsorptive effects were not taken into account and different kinetics were used. Nonetheless, that work will be used as a basis for comparison with the results obtained in this study. Two new models were developed, each one accounting for one of the following types of adsorption isothermal models: noncompetitive Langmuir and competitive Langmuir. These two models and a third, the nonadsorptive model, were then computer simulated at different parameter values in order to obtain a first comparison among them. Afterward, an adsorption-specific parameter (the vapor flow rate/liquid holdup ratio) was further analyzed in order to assess its influence on the process models behaviors. Formulation of the Models Batch reactive distillation is a simple distillation, carried out in a heated still that contains catalyst, from which the vapor phase is removed and the liquid phase analyzed as a function of time. In more detail, a liquid solution is placed inside a still (liquid holdup H), which is then heated at a variable heat input Q to vaporize part of the solution (with a vapor flow rate V˙ ). The reaction occurs in the liquid phase between the species

10.1021/ie034315+ CCC: $27.50 © 2004 American Chemical Society Published on Web 05/27/2004

Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3243

present there, with a molar fraction xi (in which i represents the species). The vapor-phase composition, yi, is obtained through phase equilibrium with the liquid holdup at each temperature. A simple schematic representation of the still is shown in Figure 1. Liquid samples are then collected at given times and their compositions analyzed and plotted in a twodimensional ternary graph. Nonadsorptive Model. From the scheme in Figure 1, a simple mass balance to a generic component i can be derived:4

d(Hxi) dt

Vcat M H (νi,jrj) ) -V˙ yi + F H0 j)1

∑

Figure 1. Schematic representation of a generic reactive batch distillation system.

(1)

in which the variation of species i in the still liquid is a function of its amount present in the vapor phase and of the chemical reactions occurring in the wet catalyst. By summation of the mass balances for each component in the system, an overall mass balance can be obtained:

Vcat N M H (νi,jrj) ) -V˙ + F dt H0 i)1j)1

dH

∑∑

(2)

Expanding the differential term of eq 1, substituting the differential term dH/dt with eq 2, dividing the whole equation by H, and rearranging give the following species-dependent differential equation:

dxi dt

)

N M Vcat M [ (νi,jrj) - xi (νi,jrj)] (3) (xi - yi) + F H i)1 j)1 H0 j)1

V˙

∑

∑∑

To simplify the model even further, it is commonly assumed that the liquid holdup in the still and the vapor flow rate have a constant ratio at start-up (time 0) and during operation; thus

V˙ V˙ 0 ) ) RV/L 0 H H

(4)

As is obvious by inspection, RV/L has dimensions of reciprocal time, so we can also use it to obtain a dimensionless time (τ), defined as

τ)

V˙ 0 t H0

(5)

By substitution of eq 5 into eq 3 and also application of the equalities defined by eq 4, the expression can be simplified. Introducing the Damko¨hler number, defined as

Vcat Da ) F 0 kcinref V˙

(6)

dτ

) (xi - yi) +

Da kcinref

M

[

θi )

N M

(νi,jrj) - xi∑∑(νi,jrj)] ∑ j)1 i)1 j)1

(7)

Kiai 1 + Kiai

(8)

where θi quantifies the fraction of sites occupied by compound i. The simplest situation, as described by eq 8, is one for a pure-component system (i.e., a system with only one component). For multicomponent systems, a fourth assumption (or simplification) can be made. 4. Each one of the system components adsorbs only in a specific site, with no competition existing for the occupation of active sites. This allows the use of eq 8 in multicomponent systems. Using eq 8, the material balance to a single component on the still can be rewritten, to include the transient adsorption of the component on the catalyst, as

d(Hxi) dt

Vcat M Vcat dΘi H H (νi,jrj) +F ) -V˙ yi + F dt H0 H0 j)1

∑

(9)

and the respective overall mass balance as

( )

Vcat N dΘi Vcat N M H (νi,jrj) - F H ) -V˙ + F dt H0 i)1j)1 H0 i)1 dt

dH

a new substitution can be made, thus obtaining a final, generic, nonadsorptive batch reactive distillation model.

dxi

Noncompetitive Langmuir Adsorptive Model. The Langmuir adsorption model, first presented by Langmuir,10 starts from three assumptions to derive a thermodynamic model for adsorption:11 1. The surface is homogeneous; that is, the adsorption energy is constant over all sites. 2. Adsorption on the surface is localized; that is, adsorbed atoms or molecules are adsorbed at definite, localized sites. 3. Each site can accommodate only one molecule or atom. From these considerations, it is possible to obtain a mathematical model11 that describes the adsorption of compounds on the surface of the adsorbent. Expressed in dimensionless form and with the species liquid-phase activity

∑∑

∑

(10)

Expanding the differential term that refers to the species concentration on the still, applying the overall mass balance, and then using the time constant and RV/L, as defined in eqs 4 and 5, respectively, give the

3244 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004

following simplified expression:

occupied by compound i is slightly different and takes into account all of the adsorbed competing species

( )

Vcat dΘi Vcat N dΘi H H xi ) +F -F dτ dτ H0 H0 i)1 dt N M Vcat M (xi - yi) + F [ (νi,jrj) - xi (νi,jrj)] (11) i)1 j)1 V˙ 0 j)1

dxi

∑

∑

∑∑

Θi )

+

dτ

Da

dΘi

RV/L

kcinref

-

dτ

(xi - yi) +

N

Da

∑

( ) dΘi

RV/L kcinref i)1 dt M

Da kcinref

[

Θi ) Kiai/DEN

xi ) (12)

(13)

eq 8 can be rewritten as

(14)

dΘi dxi Kiγi ) 2 dτ dτ (1 + K a )

(15)

i i

N

Θi ) ∑ i)1

Da

N

∑ i)1

RV/L

kcinref

[

K iγi

(

(1 + Kiai)2 dτ Da

kcinref

M

[

)

dxi dΘi dDEN 1 ) DEN - Kiγixi Kiγi (21) 2 dτ dτ dτ DEN or summing up to the N components

dτ

N

d

Θ i) ) ∑ dτ i)1

(

(

1-

)

1

)-

DEN

d(1/DEN) dτ 1 DEN2

) dDEN dτ

(22)

Substituting into eq 12 and expressing DEN with the molar fractions lead to the model equation for a competitive Langmuir adsorptive batch reactive distillation system.

]

dxi

∑Kiγixi 1 1 )1)1DEN 1 + ∑Kiγixi 1 + ∑Kiγixi

Differentiating Θi with time

d

Replacing dΘi/dτ in eq 12 and rearranging with the differential term produce a new equation, or model, for a noncompetitive Langmuir adsorptive reactive distillation system.

]

(19)

is the ratio between the total concentration of active sites and the concentration of free (not covered) active sites. The formulation of the competitive model is equal to that of the noncompetitive model, up to eq 12, because it does not depend on the adsorption model used. However, as for competitive Langmuir adsorption, the substitution made in eq 12 will yield a different result. Also, the following relation can be derived:

Differentiating this equation with the dimensionless time

[

(Kiai) ∑ i)1

(20)

Kiγixi Θi ) 1 + Kiγixi

Kiγi dxi RV/L kcinref (1 + Kiai)2 dτ

(18)

N

DEN ) 1 +

N M


ai ) xiγi

Da

(17)

∑(Kiai)

in which

As mentioned before, the Langmuir adsorption model relates the amount of each species that is adsorbed on the catalyst to the same species concentration in the bulk. Using the dimensionless version presented in eq 8 and taking into account that the liquid-phase activity of each component is a function of the species molar fractions and liquid-phase activity coefficient

1+

1+

or

Finally, considering the Damko¨hler number defined by eq 6, an expression equivalent to eq 7 is obtained.

dxi

Kiai

xi ) (xi - yi) + N M


(

)

K iγi dxi 1 + DaRV/L kcinrefDEN dτ

(16)

Competitive Langmuir Adsorptive Model. The competitive Langmuir model is derived from the exact same assumptions that were used to derive the noncompetitive Langmuir model, with the exception of assumption number 4. In the competitive Langmuir model, no simplification regarding the specificity of active sites is made, and it considers that all species adsorb on the same type of active site, thus competing among themselves.11 As such, the mathematical equation used to represent the fraction of active sites

( )

dxi Da RV/L N K iγi ) (xi - yi) + (1 + Kiγixi) kcinref DEN2i)1 dτ

∑

Da kcinref

M

[

N M


(23)

Heterogeneously Catalyzed TAME Synthesis Model. TAME is usually synthesized from a liquidphase mixture of two isoamylenes (2M1B and 2M2B) and methanol (MeOH), using as the catalyst a sulfonic acid ion-exchange resin. The stoichiometry of these


(eqs 33-35)15 and equilibrium (eqs 36-38) constants.16

Table 1. Stoichiometric Coefficients νi,j 1 2 3

1 -1 0 -1

2 0 -1 1

3 -1 -1 0

4 1 1 0

∑ -1 -1 0

kcin1 ) 3.2870 × 1010e-76.8×10 /RT

(33)

kcin2 ) 3.6382 × 1013e-99.7×10 /RT

(34)

kcin3 ) 7.4767 × 1010e-81.7×10 /RT

(35)

3

3

reactions (Table 1) can be described by the following three equations:

3

2M1B + MeOH h TAME

(24)

2M2B + MeOH h TAME

(25)

2M1B h 2M2B

(26)

3

Keq1 ) e(5.0166×10 /T)-10.839 3

Other side reactions are known to occur, but they usually are of far less importance, and for this work they will then be neglected. To model this system, on the liquid phase, reaction equilibria, reaction rates, and adsorption equilibria must be considered. For the vapor phase, only the vapor-liquid equilibrium (VLE) of the system is considered because, although chemical reactions probably occur in the vapor phase, their extent is very small (because of volume differences between the liquid and vapor phases) and can be neglected. VLE, Adsorption, and Chemical Reaction Data

Keq2 ) e(3.7264×10 /T)-9.6367

(37)

Keq3 ) Keq1/Keq2

(38)

Adsorption Data. Adsorption data for this work (eqs 39-42) were extracted from work by Oktar et al.,17 who conducted an experimental study on the adsorption of the TAME system components on a sulfonic acid ionexchange resin. The data were validated for a noncompetitive Langmuir model but, because of the lack of more adequate data, will also be used in the competitive Langmuir model.

VLE Data. VLE relations can be easily established through the use of Raoult’s law

K1 ) e(4.6825×10 /T)-10.157

yiP ) Psat i γixi

K2 ) e(3.4420×10 /T)-6.5849

(27)

because P is known, xi is known or iterated, Psat i can be calculated using a vapor-pressure correlation (eq 28) taken from DIPPR,12 and γi can also be calculated using, e.g., a modified (Dortmund) UNIFAC method.13

ln(Psat i ) ) Ai +

Bi + Ci ln(T) + DiTEi T

(

r1 )

DEN2

(

kcin2K2K3 a2a3 r2 )

DEN2

(

kcin3K1 a1 r3 )

(29)

)

(30)

a4 Keq2

a2 Keq3

DEN

)

(31)

4

DEN ) 1 +

(Kiai) ∑ i)1

3

3

K3 ) e(1.0014×10 /T)+4.7496 3

K4 ) e(2.3934×10 /T)-3.5736

(39) (40) (41) (42)

Model-Specific Mass Balance Equations

)

a4 Keq1

3

(28)

Chemical Reaction Data. The system under analysis consists of three reversible simultaneous chemical reactions. As such, both chemical reaction rates (including kinetic constants) and chemical equilibria data must be considered. For this work, a multiparametric reaction rate model, obtained from experimental data, was used (eqs 29-32)14 in conjunction with the necessary kinetic

kcin1K1K3 a1a3 -

(36)

(32)

For the derivation of the TAME system specific mass balances, the reference kinetic constant (kcinref) was taken to be the kinetic constant of reaction 1 (eq 33) at 298 K [kcin1(298 K)]. Nonadsorptive Model. From eq 7, using subscripts 1-4 to designate 2M1B, 2M2B, MeOH, and TAME, respectively, the mass balance for each component becomes

d(x1) Da ) (x1 - y1) + [-r1(1 - x1) - r3 + r2x1] dτ kcinref (43) d(x2) Da [-r2(1 - x2) + r3 + r1x2] ) (x2 - y2) + dτ kcinref (44) d(x3) Da ) (x3 - y3) + [-r1(1 - x3) - r2(1 - x3)] dτ kcinref (45) d(x4) Da [r (1 + x4) + r2(1 + x4)] ) (x4 - y4) + dτ kcinref 1 (46)


Noncompetitive Langmuir Adsorptive Model. Using the same subscript notation as that in the nonadsorptive model, eq 16 can be rewritten for each of the system components:

[

1+

]

K1γ1

Da

kcinref

4

RV/L

∑ i)1

∑

dx1

[

K iγi

]

dxi

(1 + Kiai)2 dτ

x1 ) (x1 - y1) +

Da

[-r1(1 - x1) - r3 + r2x1] (47) kcinref

[

∑

[

1+

]

K2γ2 dx2 RV/L kcinref (1 + K2a2)2 dτ 4 K iγi dxi Da RV/L x2 ) (x2 - y2) + 2 kcinref i)1 (1 + K a ) dτ i i Da [-r2(1 - x2) + r3 + r1x2] (48) kcinref Da

[

]

]

Da kcinref

4

RV/L

∑ i)1

[

K iγi

]

dxi

(1 + Kiai) dτ 2

x3 ) (x3 - y3) +

Da

[-r1(1 - x3) - r2(1 - x3)] (49) kcinref

[

1+

]

K4γ4 dx4 RV/L kcinref (1 + K4a4)2 dτ Da

Da kcinref

4

RV/L

∑ i)1

[

K iγi

kcinref

]

dxi

(1 + Kiai)2 dτ Da

x4 ) (x4 - y4) +

[r1(1 + x4) + r2(1 + x4)] (50)

Competitive Langmuir Adsorptive Model. From eq 23 and using the same notation as before, each component mass balance for competitive Langmuir adsorption can be written as

(

)

K1γ1 dx1 1 + DaRV/L kcinrefDEN dτ

( )

dxi Da RV/L 4 Kiγi ) (x1 - y1) + (1 + K1γ1x1) kcinref DEN2i)1 dτ

∑

Da

( )

Da

[-r2(1 - x2) + r3 + r1x2] (52) kcinref

(

)

K3γ3 dx3 1 + DaRV/L kcinrefDEN dτ RV/L

( )

dxi Kiγi ) (x3 - y3) + (1 + K3γ3x3) kcinref DEN2i)1 dτ Da

4

∑

Da

[-r1(1 - x3) - r2(1 - x3)] (53) kcinref

(

)


( )


∑

Da

K3γ3 dx3 RV/L kcinref (1 + K3a3)2 dτ Da

)


RV/L kcinref (1 + K1a1)2 dτ Da

1+

(


[-r1(1 - x1) - r3 + r2x1] (51) kcinref

[r1(1 + x4) + r2(1 + x4)] (54) kcinref Simulation The models for the batch reactive distillation of TAME (eqs 43-54) were programmed in FORTRAN 90, together with subroutines for VLE and activity coefficients calculation, and then integrated with a double-precision subroutine appropriate for the solution of differentialalgebraic problems (DDASPK) to simulate the models’ behaviors. To calculate the system stationary points, steady-state equations were derived from eqs 43-46, and then points were taken using a FORTRAN 90 implementation of Broyden’s method.18 Simulation Results. Simulations were run for five different reaction rate vs vapor flow rate parameters (Damko¨hler numbers equal to 1, 10-1, 10-2, 10-3, and 10-4) and at two different pressures (0.1 and 1 MPa) and for the three cases under analysis: no adsorption, Langmuir noncompetitive model, and Langmuir competitive model. Also, for the adsorptive models, the time constant (RV/L, vapor flow rate/liquid holdup ratio) was considered to be equal to 0.1 in all simulations. To assess the effect of adsorption in the system, RCMs were plotted for each Damko¨hler/pressure pair (Figures 2 and 3). Curve starting points were either chosen because of their proximity to a node or taken at molar fraction intervals (for component pairs), to best represent the evolution of the system. For each starting point, curves for all three adsorption cases were computed. Each curve will then go from its starting point toward the zone stable node (with the different zones being divided by sepatrixes).2 No direction arrows or temperature information is given in order to unclutter the graph. Inspection of eqs 16 and 23 shows that the adsorptionspecific differential terms are directly dependent on two constants, Da and RV/L, and indirectly dependent on two variables, composition and temperature. The effect of


Figure 2. RCMs for the batch reactive distillation of TAME at an operating pressure of 0.1 MPa and Damko¨hler numbers of 10-4, 10-3, 10-2, 10-1, and 1.

the Damko¨hler number can be easily assessed just by looking at eqs 16 and 23: as it increases, so does the adsorptive term. The same is true for the influence of RV/L in eq 23: as it increases in value, so does the adsorptive term. The influence of both temperature and composition is not so easily quantified. Temperature is a wide-variation variable in each system, ranging from the lowest boiling point in the system to the highest. The order of magnitude of those values is only dependent, through VLE calculations, on pressure, and so it can be adjusted in magnitude through it. The influence of temperature in the system is a major one, both in VLE and UNIFAC parameter

calculation and in the reaction, equilibrium, and adsorption constants, these last being dependent only on temperature and not on composition. Higher temperatures favor strongly reactions rates but disfavor, although to a much smaller extent, both chemical equilibria and adsorption. Composition (in molar fractions) has a twofold influence. It influences VLE (for obvious reasons) and the activity coefficient of the species, determined through UNIFAC. These parameters influence the adsorptive term indirectly (temperature on the adsorption constants and both on activity coefficients) and directly (composition in the activity of each species), the effects


Figure 3. RCMs for the batch reactive distillation of TAME at an operating pressure of 1 MPa and Damko¨hler numbers of 10-4, 10-3, 10-2, 10-1, and 1.

of which are not easily apprehended. Lower compositions seem to favor the adsorptive term, but because they are dependent on one another, their effect is much less evident, with the exception being made for low quantities of methanol, which affect to a greater extent the adsorptive balance. Temperature shows its effect mainly through adsorption constants, with higher temperatures increasing the adsorptive term. Nonetheless, exceptions do exist (e.g., K2M1B at low molar fractions), and a more thorough study of each system is needed, although from a purely empirical analysis an increase in pressure (and subsequently in the order of magnitude

for the temperature) seems to favor the appearance of adsorptive effects on the RCMs. Looking at Figure 2, few curves can be easily spotted. This is due mainly to the chemical equilibrium curve, which is not represented, being very close to the TAME axis because of the higher equilibrium constants at this operating pressure. A far more complete and thorough analysis of this effect in the TAME synthesis system is done by Thiel et al.9 and as such will not be repeated here. Despite the lack of more interesting data, a small effect can be seen in Figure 2a near the separatrix. At higher Damko¨hler numbers and because of the higher


reactive effect, no curves were obtained near the separatrix, so the effects are not shown but expected to exist. Also, a strong effect on the highest Damko¨hler number RCM (Figure 2e) exists near the 2MxB axis. This effect is more evident mainly because of the higher Damko¨hler, as predicted and explained before. At a higher operating pressure of 1 MPa, the results gain far more interest because of both a more “central” chemical equilibrium line9 and higher adsorptive effects, as explained previously. Looking at Figure 3, it can be easily observed that, as the chemical reaction gains importance (higher Da’s), so do the adsorptive effects. As expected, the effects are stronger at lower methanol concentrations, with linear curves, with sharp inflections, toward the 2MxB stable nodes (Figure 3d,e). The effect is more notorious on the competitive Langmuir model as, because of competition for the active sites, methanol influences the adsorption of every component in the system.

Q ) heat input in the still, J/s rj ) rate of reaction j, mol/kgcat‚s R ) universal gas constant ) 8.314 J/mol‚K RV/L ) time constant, s-1 t ) time, s T ) temperature, K V˙ ) vapor flow rate, mol/s Vcat ) catalyst volume, m3 xi ) liquid-phase mole fraction of component i yi ) vapor-phase mole fraction of component i

Conclusions

0 ) initial condition L ) in the liquid phase M ) total number of reactions N ) total number of components V ) in the vapor phase

The main conclusion that should be derived from this work is that adsorption can play a major role in explaining the behavior of reactive distillation systems. Although its effect has been traditionally neglected, because of adsorption only being felt at unsteady-state operation, when considering unsteady-state operations, adsorption must be considered a part of the problem and analyzed as such. In the specific case of the TAME synthesis system, the RCMs show that at higher Damko¨hler numbers adsorption becomes an integral and important part of the system. Damko¨hler numbers and time constants higher than those used in this work will most likely amplify even further the effects of adsorption. With regards to the effect of temperature on adsorption, a more thorough study of the behavior of the adsorptive term as a function of the system composition and temperature can lead to a deeper understanding of their effect on the system and even adsorption in general. Finally, it should be noted that the effects of adsorption on RCMs and in reactive distillation systems in general, shown in this work for the TAME synthesis system, are likely to occur in every heterogeneous catalytic reactive distillation system. This means that, when modeling other heterogeneous catalytic distillation systems, the models must include adsorption, and its effects should be quantified and taken into account when dealing with real industrial applications. Acknowledgment The authors thank the Fundaç aõ para a Cieˆncia e Tecnologia (FCT) for the financial support given to this project under Grant POCTI/EQU/41406/2001. Nomenclature ai ) liquid-phase activity of component i Ai-Ei ) DIPPR correlation coefficients Da ) Damko¨hler number H ) liquid holdup in the still, mol kcinj ) kinetic constant of reaction j, mol/kgcat‚s Ki ) Langmuir adsorption constant of component i, m3/mol Keqj ) chemical equilibrium constant of reaction j P ) pressure, Pa Psat ) saturation pressure of component i, Pa i

Greek Symbols γi ) liquid-phase activity coefficient of component i θi ) fraction of active sites occupied by component i νi,j ) stoichiometric coefficient of component i in reaction j F ) density of catalyst, kg/m3 τ ) dimensionless time Superscripts

Subscripts i ) component (number) j ) reaction number Abbreviations 2M1B ) 2-methyl-1-butene 2M2B ) 2-methyl-2-butene 2MxB ) isoamylenes (2M1B and 2M2B) DEN ) denominator of the competitive Langmuir model N ) 1 + ∑i)1 (Kiai) MeOH ) methanol RCM ) residue curve map TAME ) tert-amyl methyl ether

Literature Cited (1) Sharma, M. M.; Mahajani, S. M. Industrial Applications of Reactive Distillation. In Reactive DistillationsStatus and Future Directions; Sundmacher, K., Kienle, A., Eds.; Wiley-VCH: Weinheim, Germany, 2003; Chapter 1, pp 3-29. (2) Foucher, E. R.; Doherty, M. F.; Malone, M. F. Ind. Eng. Chem. Res. 1991, 30, 760-772, 2364. (3) Barbosa, D.; Doherty, M. F. Chem. Eng. Sci. 1988, 43, 541550. (4) Venimadhavan, G.; Buzad, G.; Doherty, M. F.; Malone, M. F. AIChE J. 1994, 40, 1814-1824. (5) Ung, S.; Doherty, M. F. Ind. Eng. Chem. Res. 1995, 34, 3195-3202. (6) International Union of Pure and Applied Chemistrys Division of Physical Chemistry. Manual of symbols and terminology for physicochemical quantities and unitssAppendix II: definitions, terminology and symbols in colloid and surface chemistrys Part I; Internet ed.: Washington, DC, 2001. (7) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons: New York, 1984; Chapter 2, pp 29-30. (8) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by Powders & Porous Solids; Academic Press: London, 1999; Chapter 1, pp 1-25. (9) Thiel, C.; Sundmacher, K.; Hoffmann, U. Chem. Eng. Sci. 1997, 52, 993-1005. (10) Langmuir, I. J. Am. Chem. Soc. 1918, 1361. (11) Do, D. D. Adsorption Analysis: Equilibria and Kinetics; Imperial College Press: London, 1998.

3250 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 (12) Rowley, R. L.; Wilding, W. V.; Oscarson, L. J.; Yang, Y.; Zundel, N. A.; Daubert, T. E.; Danner, P. R. DIPPR Data Compilation of Pure Compound Properties; Technical Report; Design Institute for Physical Properties, AIChE: New York, 2001. (13) Gmehling, J.; Li, J.; Schiller, M. Ind. Eng. Chem. Res. 1993, 32, 178-193. (14) Ferreira, M. M. V.; Loureiro, J. M. Sıńtese de TAME: Equı´librio Quı´mico e Cine´tica em Reactor Fechado. In Proceedings of the 8th International Chemical Engineering Conference CHEMPOR 2001; Ramoâ Ribeiro, F. J., Cruz Pinto, J. C., Eds.; CHEMPOR: Aveiro, Portugal, 2001. (15) Kiviranta-Paä¨kko¨nen, P.; Struckmann, L.; Krause, A. O. I. Chem. Eng. Technol. 1998, 4, 321-326.

(16) Ferreira, M. M. V.; Loureiro, J. M. Chem. Ing. Tech. 2001, 6, 684. (17) Oktar, N.; Mu¨rtezaoglu, K.; Dogu, T.; Dogu, G. Can. J. Chem. Eng. 1999, 77, 406-412. (18) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1992; pp 382-385.

Received for review December 16, 2003 Revised manuscript received April 16, 2004 Accepted April 26, 2004 IE034315+

Effect of Adsorption on Residue Curve Maps for Heterogeneous

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