Ind. Eng. Chem. Res. 2005, 44, 6171-6180
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Comparison of a Pseudo-homogeneous Nonequilibrium Dynamic Model and a Three-phase Nonequilibrium Dynamic Model for Catalytic Distillation Yongqiang Xu, Flora T. T. Ng,* and Garry L. Rempel Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
A comparison of a pseudo-homogeneous nonequilibrium (NEQ) dynamic model and a threephase NEQ dynamic model was studied for the simulation of both a batch catalytic distillation (CD) process and a continuous CD process for the aldol condensation of acetone. The models were implemented in gPROMS and C++. The simulation results show that most of the dynamic responses of both the batch and continuous CD columns are either close to zero order or first order; however, the responses of temperatures in and below the reaction zone of the batch CD column predicted by the pseudo-homogeneous NEQ dynamic model are highly nonlinear. The formation rate of diacetone alcohol (DAA) and the liquid phase temperatures predicted by the pseudo-homogeneous NEQ dynamic model were found to be much higher than those predicted by the three-phase NEQ dynamic model for both the CD columns. Through a comparison with the experimental data, it was found that the three-phase NEQ dynamic model can adequately describe this CD process, while the simpler pseudo-homogeneous NEQ dynamic model overly predicts the formation rate of DAA and the liquid phase temperatures because the mass- and heat-transfer resistances between the liquid and solid phases are ignored. Since the computation time for the two NEQ dynamic models is very similar, it is recommended that the three-phase NEQ dynamic model should be used in the simulation of the CD process unless it is known a priori that the CD process is kinetically controlled. 1. Introduction Catalytic distillation (CD) combines distillation and a heterogeneous catalyzed reaction in a single vessel. This combination can lead to many advantages, such as increasing conversion for an equilibrium-controlled reaction, enhancing selectivity of an intermediate product for a consecutive reaction, reducing energy consumption by utilizing reaction heats, as well as saving capital costs by carrying out two unit operations in one piece of equipment. Due to its advantages, many CD applications such as aldol condensation, etherification, esterification, and hydrogenation have been studied. Thus far, a few comprehensive reviews of CD applications have been published.1-3 Most of the CD processes reported have been continuous processes, which are suitable for producing bulk chemicals. To date, very few papers on batch CD processes have been published,4,5 even though they are very important because of their operation flexibility and, hence, suitability for the manufacture of high-value-added pharmaceutical products and fine chemicals normally produced in small quantities. For the purpose of design, optimization, and control of a CD process, a rigorous theoretical dynamic model is required. Currently, there are two types of dynamic CD models existing in the literature. The first type is a two-phase equilibrium (EQ) dynamic model in which the vapor phase and liquid phase are assumed to be in equilibrium.6,7 However, CD is rarely operated at or near the equilibrium. As a result, concepts of either stage efficiencies for a tray column or HETP (height * Corresponding author. Tel.: (519) 888-4567 ext. 3979. Fax: (519) 746-4979. E-mail:
[email protected].
equivalent to a theoretical plate) for a packed column are usually introduced into the model for correcting the difference between the ideal equilibrium and actual nonequilibrium (NEQ) of the real column. The second type is a pseudo-homogeneous (two-phase) NEQ dynamic model,5,8-12 in which the actual mass- and heattransfer rates between the vapor and liquid phases are considered. A comparison between a two-phase EQ dynamic model and a pseudo-homogeneous NEQ dynamic model for the simulation of the CD process for the production of tert-amyl methyl ether was presented by Peng et al.11 It was found that the dynamic behaviors predicted by the two models were similar in general; however, some differences in steady-state values were observed. Unfortunately, no experimental data were provided to clearly ascertain whether the pseudohomogeneous NEQ dynamic model was better than the two-phase EQ dynamic model. Dynamic simulations of batch CD columns are rarely found in the literature despite their significance, except that Schneider et al.5 studied an application of a pseudo-homogeneous NEQ model on the dynamic simulation of a batch CD process for the production of methyl acetate. The model was found to be in a good agreement with the experimental data. A comparison between a two-phase EQ dynamic model and the pseudo-homogeneous NEQ dynamic model was also carried out for this process. The results showed that the pseudo-homogeneous NEQ dynamic model was more accurate than the two-phase EQ dynamic model. In the pseudo-homogeneous NEQ dynamic models, however, mass-transfer and heat-transfer resistances between the liquid phase and solid (catalyst) phase are not considered. Therefore, a three-phase NEQ dynamic
10.1021/ie049100u CCC: $30.25 © 2005 American Chemical Society Published on Web 06/09/2005
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model is more appropriate for the simulation of CD than a pseudo-homogeneous NEQ dynamic model because, in general, a temperature gradient for a highly exothermic reaction and a concentration gradient for a fast reaction exist between the liquid phase and the solid phase. In our group, a three-phase NEQ model (MECRES equations) for the simulation of a steady-state CD process using empirical overall vapor-liquid and liquidsolid mass-transfer coefficients was developed.12,13 The model was validated for the CD process for the aldol condensation of acetone (Ac) to selectively produce diacetone alcohol (DAA), which was developed in our laboratory.4 The reaction from acetone to DAA is a reversible reaction and DAA can undergo a further dehydration to produce mesityl oxide (MO), as shown in eq 1. k1
k3
Ac w\ x DAA 98 MO + H2O k 2
(1)
The desired product is DAA, which is considered as an environmentally friendly solvent due to its low volatility. The heterogeneous catalyst Amberlite IRA900 anion-exchange resin was used for this process. The catalyst was placed in fiberglass bags which were wrapped with demister wire and then packed in the column. Unfortunately this type of packing method usually encounters a quite severe mass-transfer limitation due to the diffusion through the catalyst bag. The effect of the mass transfer and kinetics on the formation rate of DAA and MO in the CD column was examined.13 It was found that DAA is limited by the external liquidsolid mass transfer through the catalyst bag while MO is controlled by the kinetic rate. We have improved the MECRES model by computing the mass and heat transfers among different phases using the Maxwell-Stefan theory.14-17 An interesting comparison between a pseudo-homogeneous NEQ steadystate model and a three-phase NEQ steady-state model was reported.17 It was found that a pseudo-homogeneous NEQ steady state model could adequately simulate the temperature profile, yield, and selectivity for a CD process that is kinetically controlled. However, a threephase NEQ steady-state model is required for the simulation of a CD process that is liquid-solid masstransfer controlled. Recently, a three-phase NEQ dynamic model was reported for the simulation of CD for the production of methyl acetate by Noeres et al.18 It appears that the same approach proposed by our group12-17 may have been used to describe the liquid-solid mass and heat transfer in their model, that is, the reaction rate and mass-transfer rate through the liquid-solid interface was assumed to be equal and the macrokinetics was used in the calculation of the reaction rate. In their model, only the liquid holdups were considered while the vapor holdups were ignored. The model was quite complex because of its partial differential equations approach. It was reported that no significant difference between the three-phase NEQ dynamic model and a two-phase EQ dynamic model was found and, hence, the simpler two-phase EQ dynamic model was recommended for control and optimization purposes. However, no clear explanation was provided as to why these two models predicted similar results. We have recently developed a detailed three-phase NEQ dynamic CD model19 based on our three-phase NEQ steady-state model.14-17 In our models, both the
vapor and liquid holdups were considered and the column was divided into a series of NEQ sections. The model was successfully validated for both a batch and a continuous CD process for the aldol condensation of acetone. The purpose of the present paper is to develop a simpler pseudo-homogeneous NEQ dynamic model and compare it with the three-phase NEQ dynamic model to ascertain which model should be chosen for the simulation of CD processes. 2. Models In both the pseudo-homogeneous NEQ and threephase NEQ dynamic models developed, all bulk phases are assumed to be perfectly mixed, the mass- and heattransfer resistances are assumed to occur in the films adjacent to the bulk phases, and the vapor-liquid equilibrium is assumed to take place at the vaporliquid interface. The condenser and reboiler are assumed to be at equilibrium. The whole column is assumed to be at constant pressure, because the differential pressure between the condenser and the reboiler was found to be negligible during all the CD experiments. The main difference between these two models is that the three-phase NEQ dynamic model considers the mass- and heat-transfer resistances between the liquid and solid phases and the heterogeneous catalyzed reaction happens on the surface of the catalyst while the pseudo-homogeneous NEQ dynamic model ignores these resistances and assumes the catalyzed reaction happens in the liquid phase. The mathematic equations of the two models based on the above assumptions are summarized in Table 1. 2.1. Submodel. In both of the models, the liquid molar holdup for the structure packings used to hold the catalyst is calculated using the correlation developed by Xu et al.20 and that for the random packing in the nonreaction zone is based on the correlation developed by Billet and Schultes.21 The binary mass-transfer coefficients for the nonreaction zone are computed based on the model proposed by Onda et al.,22 and those for the catalyst packing are calculated with the correlation developed by Zheng and Xu.23 The multicomponent mass-transfer coefficients are evaluated with the Maxwell-Stefan theory.24 The heat-transfer coefficients are calculated with the Chilton-Colburn analogy.25 The thermodynamic factor Vj in the heat-transfer rate equation of the vapor phase is defined by Vj ) C (NVij CpVij/hVj aj), and the function Vj /(Vj - 1) in the ∑i)1 equation serves to correct the vapor heat-transfer coefficient hVj for the influence of nonzero mass-transfer rates.26 The liquid activity coefficient is computed with the modified UNIQUAC model.27 Physical properties such as density, diffusivity, enthalpy, conductivity, and vapor pressure are calculated using models recommended by Reid et al.28 and by Danbert and Danner.29 The reaction rate is calculated with the kinetics developed by Podrebarac et al.:30
RDAA ) k1CAc2 - (k2 + k3)CDAA
(2)
RMO ) RH2O ) k3CDAA
(3)
where R is the reaction rate, k1, k2, and k3 are the reaction rate constants of the associated reaction steps, and C is the molar concentration.
Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 6173 Table 1. Comparison between the Pseudo-Homogeneous NEQ Dynamic CD Model and the Three-Phase NEQ Dynamic CD Model Equations pseudo-homogeneous NEQ dynamic CD model
three-phase NEQ dynamic CD model
for the vapor phase: mass balance
dM Vij dt
heat balance
∑
C
M Vij H Vj
i)1
d
c
) dt
∑
vij H Vj -
∑
k)1
eVj ) hVj aj
∑
-
∑
∑
∑N
kVikjaj(ykj - yIkj) + yij
+ eVj
V kj
k)1
eVj ) hVj aj
k)1
C
VF i,j H j
i)1
k)1
N Vkj HVkj
∑f c
∑
NVij )
Vj
c
(T Vj - T Ij ) +
c
V vi,j+1 H j+1 -
c-1
N Vkj
k)1
exp Vj - 1
V ij H j
i)1
c
kVikj aj (ykj - yIkj) + yij
∑v
c
V fi,j H VF j + ej
i)1
Vj
c
i)1
c
c-1
heat-transfer rate
H Vj
dt
V vi,j+1 H j+1 -
i)1
∑
V ij
)
i)1
∑ N Vij )
∑M i)1
c
summation equation
) vij - vi,j+1 - f Vij + N Vij
dt
C
d
mass-transfer rate
dM Vij
) vij - vi,j+1 - f Vij + N Vij
c
exp Vj - 1
(T Vj - T Ij ) +
∑N
V V kj H kj
k)1
C
∑y
I ij
∑y
-1)0
i)1
I ij
-1)0
i)1
for the liquid phase: mass balance
dM Lij dt
) lij - li,j-1 - f Lij - N Lij + νi Rij Gj
heat balance
) lij - li,j-1 - f Lij - N Lij + N Sij
∑
C
M Lij H Lj
i)1
d
c
) dt
∑
i)1
∑
c
∑l
ij
∑
i)1
c
c
kLikj aj (xIkj - xkj) + xij
∑
N Lij )
L S H LF j - e j + ej
∑
c
kLikj aj (xIkj - xkj) + xij
k)1
∑N
L kj
k)1
c
∑N
L ij
i)1
c-1
N Lkj
k)1
eLj ) hLj aj (T Ij - T Lj ) +
∑f
L li,j-1 H j-1 -
i)1
k)1
c
L kj
H Lkj
eLj ) hLj aj (T Ij - T Lj ) +
k)1
summation equation
H Lj -
i)1
c
L r f Lij H LF j - ej + Q j
c-1
∑
H Lj )
c
L li,j-1 H j-1 -
L ij
dt
i)1
∑ N Lij )
∑M i)1
lij H Lj -
c
heat-transfer rate
dt
C
d
mass-transfer rate
dM Lij
∑N
L kj
H Lkj
k)1
C
∑x
C
I ij
∑x
-1)0
i)1
I ij
-1)0
i)1
for the vapor-liquid interface: continuity equations
vapor-liquid equilibrium
N Vij ) N Lij
N Vij ) N Lij
eVj ) eLj
eVj ) eLj
yIij
)
K Iij
xIij
yIij ) K Iij xIij for the liquid-solid interface:
mass balance
N Sij - νi Rij Gj ) 0
heat balance
eSj - Qrj ) 0
mass-transfer rate
c-1
N Sij )
∑k
c
S S ikj aj (xkj
- xSkj) + xij
k)1
heat-transfer rate
∑N
S kj
k)1
c
eSj ) hSj aSj (T Lj - T Sj ) +
∑N
S kj
H Lkj
k)1
summation equation
C
∑x
S ij
-1)0
i)1
3. Numerical Methods The model equations listed in Table 1 are implemented in an equation-oriented software package called gPROMS.31,32 Compared to a sequential, modular software package such as AspenPlus, equation-oriented software like gPROMS has one distinct advantage of a
higher computational efficiency by solving all the model equations simultaneously instead of solving each simulation block sequentially. One exception is the implementation of the submodel equations. This type of equation is very cumbersome to be written in gPROMS because it involves many intermediate variables. The
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Figure 1. Schematic diagram of the batch and pilot-plant CD columns.
introduction of these intermediate variables will increase the size of the program significantly and, hence, make the program very difficult to be solved. Therefore, a better approach is to implement these submodel equations in a procedural programming language, such as FORTRAN, C, or C++, as foreign objects. The foreign objects are simultaneously linked to gPROMS during the computation. Considering that each NEQ section in the models requires an instance of the foreign object class, the object-oriented language C++ is chosen for implementing all submodel equations because it can easily handle multiple instances of the same class. 4. Results and Discussions 4.1. Batch Bench-Scale CD Column. The batch CD experiments were carried out in a 2.54 cm bench-scale glass column with a total reflux. For a typical run, 750 mL of acetone was first charged into the reboiler and then the heater of the reboiler duty was turned on to start the run. The column was operated at total reflux. The detailed column configuration and operating parameters were given by Podrebarac et al.4 In this simulation, the column was divided into 50 NEQ sections with 10 stions in the upper nonreaction zone, 4 stions in the reaction zone, and 36 stions in the lower nonreaction zone (see Figure 1). This number of NEQ sections was found to be sufficient for both the pseudohomogeneous NEQ dynamic model and the three-phase NEQ dynamic model regarding the modeling accuracy, that is, almost no change in the prediction results was observed with a further increase in the number of NEQ sections. The computational time required for solving the three-phase NEQ dynamic model and the pseudohomogeneous NEQ dynamic model was found to be very similar, since the two models have almost the same number of equations, except that the three-phase NEQ dynamic model includes extra equations for describing
Figure 2. Comparison of dynamic responses of the liquid composition in the reboiler of the batch CD column between the pseudo-homogeneous and the three-phase NEQ dynamic models.
the solid phase (see Table 1). A comparison of the dynamic responses of the liquid mole fractions of components in the reboiler predicted by the three-phase NEQ dynamic model and by the pseudo-homogeneous NEQ dynamic model, together with the experimental data, is shown in Figure 2. It can be seen that the dynamic responses of the liquid mole fractions in the reboiler can be approximated with a simple zero-order differential equation. The liquid mole fractions predicted by the three-phase NEQ dynamic model (e.g., 79.45 mol % Ac, 10.27 mol % DAA, 5.68 mol % MO, and 4.61 mol % water at 7.5 h) are in good agreement with the experimental data (78.84 mol % Ac, 9.56 mol % DAA, 4.79 mol % MO, and 6.80 mol % water at 7.5 h). The liquid mole fractions of MO and water predicted by the pseudo-homogeneous NEQ dynamic model (6.47 mol % MO and 5.31 mol % water at 7.5 h) are also close to the experimental data. However, the DAA mole fraction predicted by the pseudo-homogeneous NEQ dynamic model (22.28 mol % DAA at 7.5 h) is much higher than the measured data due to the fact that the liquid-solid mass-transfer resistances are ignored in the model. This indicates that a kinetically controlled reaction such as the production of MO13 can be adequately described with the pseudo-homogeneous NEQ dynamic model, while, for a mass-transfer-controlled reaction such as the production of DAA,13 a three-phase NEQ dynamic model is required in a batch CD column. Deviation between the measured data and the result predicted by the threephase NEQ dynamic model is noticeable with time (see Figure 2), probably due to the fact that, in modeling a batch CD process, the deviation between the measured data and predicted result is integrated with time. Another possible reason could be due to the slow deactivation of the catalyst over time, which was discussed in a previous paper.4 The dynamic behaviors of the liquid temperatures predicted by the pseudo-homogeneous NEQ dynamic
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Figure 3. Comparison of dynamic responses of the liquid temperature along the batch CD column between the pseudohomogeneous and three-phase NEQ dynamic model (i in TL(i) means the section number, RXT means the reaction zone temperature, and NRXT means the nonreaction temperature).
model and the three-phase NEQ dynamic model along the column are shown in Figure 3. It can be seen that the nonreaction zone temperature TL30 and the reboiler temperature TL52 are constant and identical for the two models before approximately 30 and 400 s, respectively. After 30 and 400 s, respectively, TL30 and TL52 increase monotonically in both models, and these two temperatures predicted by the pseudo-homogeneous NEQ dynamic model are higher than those predicted by the three-phase NEQ dynamic model. Since TL52 is further down in the column, the onset of its dynamic response is a little later than TL30, because the high boiling point products take a little longer to reach TL52 than TL30. It can be seen from Figure 3 that the absolute changes of the temperatures in the sections above the reboiler are not significant while the reboiler temperature TL52 increases quite rapidly. The reason is that the high boiling point products (DAA and MO) are quite easy to be separated from the reactant (Ac) due to the large difference in their boiling points and, therefore, most of the high boiling point products are accumulated in the reboiler. It was also surprisingly found that the responses of the reaction zone temperature (T13) and the nonreaction zone temperature (T16) just below the reaction zone predicted by the pseudohomogeneous NEQ dynamic model are highly nonlinear within the first 20 s. The temperatures of T13 and T16 predicted by the pseudo-homogeneous NEQ dynamic model initially rise to a maximum, then decrease, and then increase slowly, while the temperatures predicted by the three-phase NEQ dynamic model increase monotonically. It is likely that, since the liquid-solid masstransfer resistance is ignored in the pseudo-homogeneous NEQ dynamic model, the predicted reaction rate of the exothermic condensation reaction of Ac to DAA (-27 kJ/mol)33 is much higher than that in the threephase NEQ dynamic model. In addition, the heattransfer resistance between the liquid and solid phases is also ignored in the pseudo-homogeneous NEQ dy-
Figure 4. Comparison of dynamic responses of the liquid composition in the reboiler of the pilot-plant CD column between the pseudo-homogeneous and three-phase NEQ dynamic models for a negative step change in reboiler duty from 280 to 190 W.
namic model, which means that the liquid phase immediately absorbs all the reaction heat. Therefore, the reaction zone temperature initially increases to a maximum value. After DAA is formed, the endothermic dehydration of DAA to MO (25 kJ/mol)33 occurs. As a result, the reaction zone temperature decreases. Since the nonreaction zone temperature (T16) is just below the reaction zone, a similar dynamic pattern is expected. In the three-phase NEQ dynamic model, however, the unusual inverse responses of the temperatures predicted by the pseudo-homogeneous NEQ dynamic model are not observed since the mass- and heat-transfer resistances between the liquid and solid phases have been taken into account. 4.2. Continuous Pilot-Plant CD Column. Continuous CD experiments were carried out in a pilot-plant column with total reflux. The column was divided into a nonreaction zone, a reaction zone, and a nonreaction zone from the top to the bottom. The acetone was fed in the middle of the column, and its feed rate was 152 mL/ h. Previously in our group, the dynamic behavior of the column was studied experimentally by a step change in the reboiler duty from 280 to 190 W. The column was operated under total reflux. The bottom flow rate was adjusted so that the liquid level in the reboiler remained constant. The detailed column configuration and operating parameters were given by Podrebarac et al.4 In the simulation, the column was divided into 50 NEQ sections with 10 stions in the upper nonreaction zone, 2 stions in the reaction zone, and 38 stions in the lower nonreaction zone (see Figure 1). This number of NEQ sections was found to be sufficient for both the pseudohomogeneous NEQ dynamic model and the three-phase NEQ dynamic model in terms of modeling accuracy for the simulation of this CD process. The dynamic responses of the predicted composition in the reboiler by the three-phase NEQ dynamic model and the pseudo-homogeneous NEQ dynamic model are shown in Figure 4. The results show that dynamic responses of the liquid compositions in the reboiler are approximately first order when the reboiler duty un-
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Figure 5. Comparison of dynamic responses of the liquid temperature in the reboiler of the pilot-plant CD column between the pseudo-homogeneous and three-phase NEQ dynamic models for a negative step change in reboiler duty from 280 to 190 W.
dergoes a step decrease from 280 to 190 W. The predicted results by the three-phase NEQ dynamic model (e.g., 74.74 mol % Ac, 11.50 mol % DAA, and 7.59 mol % MO at 3 h) are in good agreement with the experimental data (74.07 mol % Ac, 12.54 mol % DAA, and 5.01 mol % MO at 3 h). The predicted liquid mole fraction of MO by the pseudo-homogeneous NEQ dynamic model (6.90 mol % MO at 3 h) is also close to the experimental data. However, the liquid mole fraction of DAA predicted by the pseudo-homogeneous NEQ dynamic model (20.50 mol % DAA at 3 h) is much higher than the measured data. The results show that the pseudo-homogeneous NEQ dynamic model can adequately describe a kinetically controlled reaction such as the production of MO;13 however, a three-phase NEQ dynamic model is required for the simulation of a masstransfer-controlled reaction such as the production of DAA13 in a continuous CD column. The dynamic responses of the reboiler temperature predicted by the pseudo-homogeneous NEQ dynamic model and the three-phase NEQ dynamic model are shown in Figure 5. It was found that the dynamic response of the reboiler temperature can be approximated with a first-order differential equation for both models. The reboiler temperature predicted by the three-phase NEQ dynamic model (e.g., 335.62 K at 3 h) is in much better agreement with the measured temperature (335.55 K at 3 h) than the temperature predicted by the pseudo-homogeneous NEQ dynamic model (339.59 K at 3 h) (see Figure 5). Figure 6 shows the dynamic responses of the predicted liquid-phase temperatures along the column predicted by the two models. It can be seen that the reaction zone temperatures (sections 12 and 13) predicted by the pseudo-homogeneous NEQ dynamic model and the three-phase NEQ dynamic model are quite different. In the three-phase NEQ dynamic model, the temperature increases as expected from sections 12 to 13 because of a higher concentration of the products in the lower section 13 than in the upper section 12 (see Figure 7). It is interesting to note that in the pseudo-
Figure 6. Comparison of dynamic responses of the liquid temperature along the pilot-plant CD column between the pseudohomogeneous and three-phase NEQ dynamic models for a negative step change in reboiler duty from 280 to 190 W.
homogeneous NEQ dynamic model, the temperature of section 12 was surprisingly found to be higher than the temperature of section 13. A plausible explanation is that, in section 12, the reaction rate of the exothermic condensation of acetone to DAA predicted by the pseudohomogeneous NEQ dynamic model is much higher and, thus, releases more heat than in section 13 due to a higher concentration of acetone in section 12 than in section 13 (see Figure 8). In the three-phase NEQ dynamic model, the reaction rate of the condensation of acetone to DAA is limited by the liquid-solid masstransfer resistance and, therefore, the reaction heat released is lower than that in the pseudo-homogeneous NEQ dynamic model. The temperatures starting from the reaction zone and further down the column (sections 12-51) predicted by the pseudo-homogeneous NEQ dynamic model are higher than those predicted by the three-phase NEQ dynamic model (see Figure 6). This is likely due to the over prediction of the reaction rates in the pseudo-homogeneous NEQ dynamic model. It can also be seen from Figure 6 that, between 0 and 10 000 s, overall, the liquid temperatures of the upper part of the column from sections 1-43 predicted by the pseudo-homogeneous NEQ dynamic model and from sections 1-48 predicted by the three-phase NEQ dynamic model increase, while in the corresponding remaining lower part of the column, overall, the temperatures decreased from 0 to 10 000 s when the reboiler duty was decreased. It is known that, with a decrease in the reboiler duty, the separation efficiency is decreased because of the lower liquid-vapor mass transfer, and hence, it is expected that the concentration of products, especially water, which is relatively more difficult than DAA and MO to be separated from acetone, increases in the upper section of the column (see Figures 7 and 8). With a decrease in the reboiler duty, the liquid-solid mass transfer decreases and, hence, the reaction rate also decreases, resulting in a lower concentration of products in the lower part of the
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Figure 7. (a) Dynamic responses of the liquid composition of Ac and water along the pilot-plant CD column predicted by the threephase NEQ dynamic model for a negative step change in reboiler duty from 280 to 190 W. (b) Dynamic responses of the liquid composition of DAA and MO along the pilot-plant CD column predicted by the three-phase NEQ dynamic model for a negative step change in reboiler duty from 280 to 190 W.
column (see Figures 7 and 8). As a result, the liquid temperatures in the upper part of the column increase while the temperatures in the lower part of the column decrease. It is also interesting to note that the liquid temperatures below the feed point do not change monotonically; instead, they all initially decrease from
Figure 8. (a) Dynamic responses of the liquid composition of Ac and water along the pilot-plant CD column predicted by the pseudo-homogeneous NEQ dynamic model for a negative step change in reboiler duty from 280 to 190 W. (b) Dynamic responses of the liquid composition of DAA and MO along the pilot-plant CD column predicted by the pseudo-homogeneous NEQ dynamic model for a negative step change in reboiler duty from 280 to 190 W.
0 to 100 s in both models. Since acetone is being fed into the column, it is likely that the dynamic change of the acetone flow rate may be a little slower than the dynamic decrease of the flow rates of the other components below the feed point. Since acetone is being fed at room temperature and also has the lowest boiling point among the components, the dynamic increase in the acetone concentration below the feed point (see Figures 7 and 8) resulted in a decrease of the temperatures in the lower section of the column from 0 to 100 s.
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Figure 9. Comparison of dynamic responses of the liquid composition in the reboiler of the pilot-plant CD column between the pseudo-homogeneous and three-phase NEQ dynamic models for a negative step change in the feed rate from 152.00 to 103.36 mL/h.
Figure 11. Comparison of dynamic responses of the liquid temperature along the pilot-plant CD column between the pseudohomogeneous and three-phase NEQ dynamic models for a negative step change in the feed rate from 152.00 to 103.36 mL/h.
three-phase dynamic model. These dynamic behaviors are similar to those observed when the reboiler duty was reduced. The dynamic responses of the temperatures along the column predicted by the two models are shown in Figure 11. It shows that the temperatures along the column increase with a decrease in the feed rate, as one would expect. 5. Conclusions
Figure 10. Comparison of dynamic responses of the liquid temperature in the reboiler of the pilot-plant CD column between the pseudo-homogeneous and three-phase NEQ dynamic models for a negative step change in the feed rate from 152.00 to 103.36 mL/h.
Dynamic behaviors of the CD column are also simulated for a negative step change of the feed rate from 152.00 to 103.36 mL/h with the pseudo-homogeneous dynamic NEQ model and the three-phase NEQ dynamic model. The results are shown in Figures 9 and 10. It was found that dynamic responses of the liquid composition and temperature in the reboiler are close to first order for both models. The liquid compositions of the products and the temperature in the reboiler increase with a decrease in the feed rate, as predicted by both models. The pseudo-homogeneous NEQ dynamic model predicts a much higher formation rate of DAA and a higher reboiler temperature than those predicted by the
A comparison of a pseudo-homogeneous NEQ dynamic model and a three-phase NEQ dynamic model has been studied for both batch and continuous CD processes for the aldol condensation of acetone. The simulation results show that the dynamic behaviors of the composition and temperatures predicted by the two models are, in general, close to either zero order or first order for both models. However, highly nonlinear responses of the temperatures in the reaction zone as well as in the nonreaction zone immediately below the reaction zone in the batch CD column are observed in the pseudohomogeneous NEQ dynamic model, since the heat- and mass-transfer resistances between the solid and liquid phases are not considered for a CD process which is mass-transfer controlled. On the basis of a comparison with the experimental data, it was found that the pseudo-homogeneous NEQ dynamic model may adequately describe the production of MO, which is kinetically controlled, while the threephase NEQ dynamic model is required to describe the production of DAA, which is liquid-solid mass-transfer controlled, in the CD process for the aldol condensation of acetone. It was also found that the computational time for solving the pseudo-homogeneous NEQ dynamic model and the three-phase NEQ dynamic model is very similar. Therefore, we propose that a three-phase NEQ dynamic model should be used for the simulation of the CD process instead of the simpler two-phase NEQ
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dynamic model unless it is known a priori that the CD process is kinetically controlled. Further comparison of the pseudo-homogeneous NEQ dynamic model and the three-phase NEQ dynamic model will be carried out on other CD processes, such as the oligomerization of butenes, that have been developed in our laboratory. Acknowledgment The financial support from Natural Sciences and Engineering Research Council of Canada, Strategic Project Research Program, is gratefully acknowledged. Notation a ) effective interfacial area, m2 section-1 c ) total number of components C ) molar concentration, kmol m-3 Cp ) molar specific heat, kJ kmol-1 K-1 e ) heat-transfer rate, kJ s-1 f ) feed rate of component, kmol s-1 G ) amount of catalyst, mL section-1 h ) heat-transfer coefficient, kJ m-2 s-1 K-1 H ) mole enthalpy, kJ kmol-1 k1 ) DAA formation forward rate constant, kmol-1 m6 (mL of catalyst)-1 s-1 k2 ) DAA formation reversible rate constant, m3 (mL of catalyst)-1 s-1 k3 ) MO and water formation rate constant, m3 (mL of catalyst)-1 s-1 k ) multicomponent mass-transfer coefficient, kmol m-2 s-1 K ) equilibrium ratio l ) liquid flow rate for components, kmol s-1 M ) section holdup, kmol N ) mass-transfer rate, kmol s-1 Q ) heat duty, kJ s-1 R ) macro kinetic rate, kmol (ml of catalyst)-1 s-1 T ) absolute temperature, K v ) vapor flow rate for components, kmol s-1 x ) liquid composition, mole fraction y ) vapor composition, mole fraction Greek Letters ) thermodynamic factors Subscripts i ) component index j ) section index k ) alternative component index m ) property of mixture Superscripts I ) vapor-liquid interface L ) liquid phase LF ) liquid feed r ) reaction S ) catalyst phase V ) vapor phase VF ) vapor feed
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Received for review September 15, 2004 Revised manuscript received April 20, 2005 Accepted April 25, 2005 IE049100U
