Study on Catalytic Distillation Processes

0263±8762/99/$10.00+0.00 € Institution of Chemical Engineers Trans IChemE, Vol. 77, Part A, January 1999

STUDY ON CATALYTIC DISTILLATION PROCESSES Part IV: Axial Dispersion of Liquid in Catalyst Bed of Catalytic Distillation Column XIEN XU*, ZHIHAI ZHAO² and SONGJIANG TIAN* *Department of Chemical Engineering, Tianjin University, Tianjin, China ² Department of Chemical Engineering, University of Petroleum, Beijing, China

T

he backmixing characteristics of the liquid in a countercurrent two-phase ¯ ow catalytic distillation column was examined. The residence time distribution (RTD) curves were interpreted using the axial dispersion model. The axial Peclet number was obtained by the least-squares ® tting method in the entire time domain, and the correlation, Pea 10.487 ReL 0.224 ReG 0.0765 , was obtained. An example is given to show the effect of axial dispersion on the yield of Methyl Tert-Butyl Ether (MTBE) synthesized using catalytic distillation. Keywords: catalytic distillation column; axial dispersion; least-squares ® tting method; axial Peclet number

INTRODUCTION

models to these data. Many models for backmixing have been proposed but the axial dispersion model has been the most widely used, due to its simplicity. There are several methods used to estimate axial dispersion coef® cient14 : moment method, weighted moment method, transfer function method and the least-squares ® tting method in the time domain. The least-squares ® tting method in the time domain can ® t calculated curves to experimental ones better than the other methods, so it is a better method to use to estimate axial dispersion coef® cient. In this paper, the backmixing characteristics of a catalytic distillation column were investigated in which the catalyst bed was packed in the same way that has been used in an industrial unit15 . The imperfect pulse injection technique was employed to obtain the RTD curves, the axial dispersion model was used to describe backmixing of the liquid phase, and the least-squares ® tting method in the time domain was used to calculate the axial dispersion coef® cient. As an example, the effect of axial dispersion on the yield of MTBE was studied.

Catalytic distillation has been paid more and more attention by virtue of its advantages, such as high selectivity, high yield, energy-saving, easy control and low investment. So it is widely used in many chemical engineering processes, for example, etheri® cation1 , decomposition of ether2 , esteri® cation3 , alkylation4 , dipolymerization5 , hydrogenation6 , isomerization7 , dehydration8 , hydrolization9 , etc. In the ® rst three of this series of papers, the mass transfer characteristics in the catalyst bed10 , process simulation with a rate-based model11 and the pressure drop and liquid holdup12 were investigated. Backmixing in various phases in reaction processes can have signi® cant effects on the reaction rates and product selectivity, due to the reduction in the effective concentration of the species which affect the rate also, via a reduction in the effective driving force. If backmixing in the phases is ignored, overestimation of separation effectiveness may be obtained and sometimes it will lead to failure in design or scale-up of the reactor. Thus it is important to investigate backmixing characteristics of the phases in the reaction processes. The catalytic distillation column possesses the features of both a ® xed bed reactor and a packed column, and it is necessary to investigate its backmixing characteristics for design or scale-up requirements. The backmixing characteristics of various phases are evaluated from the RTD curves of a tracer injected into the phase of interest. These tracer techniques usually involve the injection of a tracer at one or more locations in the system and detection of its concentration as a function of time at one or more downstream positions. Various types of tracer inputs such as step, pulse, imperfect pulse, sinusoidal, ramp and parabolic have been employed13 . Once the data for RTD are obtained, the backmixing characteristic for each phase can be quantitatively evaluated by ® tting appropriate

EXPERIMENTAL APPARATUS AND METHOD A schematic drawing of the experimental apparatus is shown in Figure 1. The column was a plexiglass tube 9 ´ 10 2 m i.d. Air and water at normal temperature and pressure were employed as test ¯ uids. Deionized water was used to ensure accuracy of the experiments at all times. The gas and liquid ¯ ow rates were measured by rotameters, and their ranges were 4.0±12.0 m3 h 1 and 3.18 ´ 10 2 19.08 ´ 10 2 m3 h 1 , respectively. The packed bed consisted of six layers of catalyst bundles. The upper two layers made up the calming section, and the other four layers comprised the test section. The catalyst bundles were made from catalyst particles wrapped 16

STUDY ON CATALYTIC DISTILLATION PROCESSES: PART IV

17

then equation (1) becomes 1 ¶2 C Pea ¶x2

¶C ¶x

¶C ¶h

2

through Laplace transformation, the solution to equation (2) is t

C t, 1

f t

j C j, 0 dj

3

0

where f t Figure 1. Schematic diagram of experimental apparatus. 1. Valve; 2. Rotameter for liquid ¯ ow rate; 3. Injector; 4. Liquid distributor; 5. Conductivity probe; 6. Conductometer; 7. Recorder; 8. Catalyst bed; 9. Column; 10. Rotameter for gas ¯ ow rate; 11. Air blower; 12. Thermometer.

1

L

Fs

1 2

Pea t3 4pt 3

1 t

exp

Pea t 1 4t

t t

2

4 The least-squares ® tting method in the time domain was used to estimate the coef® cients Pea and t. The objective function is as follows t2

with inert material and its structure is shown in Figure 215 . The outer diameter of each bundle was equal to the inner diameter of the column, and the height was 150 mm. The bed porosity, e, was 0.72. The tracer solution employed was 1N KCl aqueous solution. The imperfect pulse injection technique was employed to obtain the RTD curves, the tracer was injected into the column from the top by use of an injector and was mixed with the liquid ¯ ow before the liquid distributor. The tracer concentration was detected at two points along the centre line of the bed, one at the top of the test section and the other at the bottom.

RESULTS AND DISCUSSION Estimation of Axial Dispersion Coef® cient

2 ¶ CA ¶C ¶CA uz A 2 z z ¶ ¶ ¶t Introducing the following dimensionless variables uz L z t tuz Pea x C h Ea L L t

Ci ti , 1

1

CA CA0

2

Min

5

Ci ti , 1 and Ci ti , 1 are experimental and calculated dimensionless concentrations. The least-squares ® tting can be divided into three types according to time domain: one point ® tting method, partial time domain ® tting method, and entire time domain ® tting method. In this paper, the leastsquares ® tting method in the entire time domain was used. The initial values of Pea and t were given by the transfer function method. The transfer function in the bed can be de® ned as Fs

¥ 0 ¥ 0

b Cexp e st dt a Cexp e st dt

Pea 1 2

6 1

equation (7) can be expressed as 1 Y s tsY s 2 Pea

4ts Pea

7

8

where, Y s is ±[lnF s 1 . When Y s was plotted versus sY s 2 , a straight line was obtained. From the slope and intersection of the line, t and Pea were obtained. The range of 2 # st # 5 pointed out by Hopkins et al.16 was used. An example is given in Figure 3.

Figure 2. The structure of the catalyst bundle.

Trans IChemE, Vol 77, Part A, January 1999

Ci ti , 1

t i t1

exp

The mass balance of tracer in the interparticle space may be written as Ea

J

18

XU et al.

Figure 3. Transfer function method used to determine coef® cients. QG 4.0 m3 h ±1; QL 3.18 ´ 10 2 m 3 h 1 ; s 0.025, 0.030, 0.035, 0.040, 0.045, 0.050, 0.055, 0.160, 0.205, 0.330.

The typical response curves of dimensionless tracer concentration are shown in Figure 4. Using the method outlined above, for each liquid and gas ¯ ow rate, values of the liquid phase Pea were obtained, as shown in Figure 5. It can be seen that, with ReL and ReG increasing, the Pea values decrease, and that ReL affects Pea more than ReG does. Fitting the experimental data, the following correlation was obtained Pea

aRebL RecG

9

where a 10.487, b 0.224, c 0.0765. A comparison between Pea calculated from equation (9) and experimental data is shown in Figure 6. The dimensionless experimental concentration data Ci ti , 1 were compared to Ci ti , 1 calculated, and the typical result is shown in Figure 7. From the ® gure, it can be seen that the calculated concentrations give a good ® t to the experimental ones.

Figure 5. Pea as a function of ReL for various ReG .

synthesize MTBE was investigated, and the effect of axial dispersion on the yield of MTBE was studied. The structure of the column and the operational parameters are listed in Table 1. The column consists of three sections: rectifying section, reacting section and stripping section. The rectifying section and stripping section comprise distillation trays, and the reacting section, the height of which is 16 metres, comprises catalyst bundles. The structure of the catalyst bundles with Amblyst-15 is the same as that used by the authors. The chemical equation of the reaction which synthesizes MTBE is CH3 OH

CH3 2 C

MeOH

CH2

CH3 3 COCH3

IB

MTBE

and the dynamic equation under catalytic distillation conditions is20 RMTBE

k CIB

k CMTBE

10

where 42000 Rg T

Effects of Axial Dispersion on the Yield of Reaction Product

k

36.34 exp

It is usual to measure dispersion coef® cients in the absence of chemical reaction, simply because such experiments can be more easily carried out. The question of whether dispersion coef® cients are changed with the occurrence of a chemical reaction has been raised, but not well resolved by several authors including Aris17 , Wakao et al.18 , and Gunn et al.19 . The industrial process using catalytic distillation to

k

4.061 ´ 1011 exp

In the industrial column, methanol and isobutene are fed to the top and bottom of the reacting section separately. The feed ¯ owrate for methanol is 3.74 mol s ± 1 , and that for the mixture containing isobutene 3.97% is 42.57 mol s ± 1 . If three simplifying assumptions are made; the reaction occurs only in the reacting section; the liquid phase has a constant

Figure 4. Typical stimulus-response curve.

Figure 6. Comparison of calculated Pea data with experimental ones.

116500 Rg T

Trans IChemE, Vol 77, Part A, January 1999

STUDY ON CATALYTIC DISTILLATION PROCESSES: PART IV

19

Table 1. Structure of the column and operational parameters. Reacting section height, m 16.0 Column diameter, m 0.95 Outlet weir height, m 0.045 Length of the tray for liquid ¯ ow through, m 0.75 Catalyst diameter, mm 0.3~1.2 speci® c surface area, m2 m ±3 1545.6

Operation pressure, kPa 950 Re¯ ux ratio 2 Temperature C top bottom feed

66 142 45

¯ ow rate; and side reactions are ignored, then the concentration of isobutene within the liquid stream at a given cross-section of the reacting section can be expressed as follows 0 CIB

CIB

CMTBE,out

CMTBE

RMTBE

k C k

CMTBE,out k CMTBE

cMTBE

d2 CM dx2 where

k CMTBE 0 k CIB

k CMTBE,out

12

a

For steady state, using the pseudo-homogeneous model, the following differential equation is obtained, where each term has units of kmol s ± 1 , d2 CMTBE dC uz MTBE Ge RMTBE 2 dz dz and its dimensionless form is

Ea

d2 CM dx2

Pea

dCM dx

Pea tGe k

k CM

0

13

k Cout

k

0 14

where Pea Cout

uz L x Ea CMTBE,out 0 CIB

Z L Ge

t

L uz

CM

CMTBE 0 CIB

ggext Greal

g is the catalyst effectiveness factor which was given by Xu Xien et al.20 . gext is the external liquid-solid contacting ef® ciency which was determined by experiments using the method pointed out by Colombo et al.21 , and a correlation was obtained as follows gext

0.265u0.681 u0.090 L G

15

Figure 7. Comparison of experimental data with that calculated. ReL 3.32, ReG 32.20.

Trans IChemE, Vol 77, Part A, January 1999

78.0 min.

Equation (14) can be rewritten as

11

then 0 IB

Figure 8. The yield of MTBE along the bed. t

Pea

dCM dx

Pea tGe k

aCM

0

16

0

17

k

Pea tGe k Cout

b

b

Pea tGe k

The initial boundary conditions are t

0,

x

0,

0
CM

CM 0 18 dCM x 1, 0 19 dx The ® nite-difference method was used to solve equations (16) to (19). Cout in the parameter b is the yield of MTBE at the outlet of the bed, which has to be determined by iteration. For different Pea values and a given average residence time, which was determined according to the catalyst bed and liquid ¯ ow rate in the column investigated, the yield of MTBE along the catalyst bed was calculated. The results are shown in Figure 8. When Pea is low, though a higher yield of MTBE can be obtained in the upper part of the bed, the yield at the outlet is lower. When Pea is high, the reverse result is evident. Figure 9 shows the yield of MTBE at the outlet as a function of Pea for different t. For a given value of t, when Pea is below a certain value which is about 4.0, Cout increases rapidly with Pea , and it reaches a maximum when Pea is about 4.0, then it decreases a little while Pea is

Figure 9. Variation of Cout vs Pea .

20

XU et al.

increasing. When Pea is very high or axial dispersion can be ignored, Cout becomes a constant. For this industrial catalytic column, t is 78.0 min and Pea is 6.11, the calculated Cout shown on point A in Figure 8 is 0.9094 which is about the same as that in the reference11 . Once the dynamic equation of a reaction is available, the effect of axial dispersion on the yield of a product is easy to obtain for other catalytic processes. From the discussion above, it can be concluded that, in a countercurrent twophase ¯ ow catalytic distillation column, very high axial dispersion is detrimental to the yield of the product, and that when the axial dispersion is low, the effect of axial dispersion can be ignored, and that, for a given average residence time, the yield of the product can reach a maximum at a certain Pea . When the Peclet number is low, axial dispersion must be taken into account in order to succeed in design or scale-up of a catalytic distillation column. CONCLUSIONS The axial dispersion characteristics of the liquid in a catalytic distillation column with an internal diameter of 90 mm was studied in this work. The RTD curves were obtained by the imperfect pulse tracer technique, then the axial dispersion model and the least-squares ® tting method was used to ® t experimental data and calculate axial Peclet number. The results showed that this model produced a good ® t for the experimental response curves. The correlation which can be used to predict axial Peclet number according to the operational conditions, Pea 10.487 ReL 0.224 ReG 0.0765 , was obtained. The values of Pea were affected by ReL more than by ReG . An example of an industrial catalytic process was given, and the effect of axial dispersion on the yield of the product was discussed. For a given average residence time, the yield of the product can reach a maximum while the Pea values vary, as shown in Figure 9. It can be concluded that the effect of axial dispersion must be taken into account when the Peclet number is low. NOMENCLATURE at C CA CA0 a Cexp b Cexp CIB 0 CIB CM CMTBE Cout dp Ea Fs Ge Greal k k L Pea QG QL Rg

speci® c surface area of the particles in a catalyst bundle, m2 dimensionless concentration concentration of A, kmol m ±3 initial concentration of A, kmol m ±3 input experimental tracer concentration output experimental tracer concentration concentration of isobutene, kmol m ±3 initial concentration of isobutene, kmol m ±3 dimensionless concentration of MTBE concentration of MTBE, kmol m ±3 dimensionless concentration of MTBE at outlet equivalent diameter of the catalyst bundle, 4e at , m axial dispersion coef® cient, m2 s ±1 transfer function effective weight of catalyst per unit volume, kg m ±3 real weight of catalyst per unit volume, kg m 3 positive reaction rate constant, m ±3 kg ±1 mol ±1 back reaction rate constant, m ±3 kg ±1 mol ±1 reactor length, m uL axial Peclet number, z , dimensionless Ea volume ¯ ow rate of gas, m ±3 h ±1 volume ¯ ow rate of liquid, m ±3 h ±1 gas constant, kJ kmol ±1 K ±1

reaction rate of A, kmol kg ±1 s ±1 du r gas Reynolds number, p mG G , dimensionless G du r liquid Reynolds number, p mL L dimensionless

RA ReG ReL

L

RMTBE s t T uz uG uL x z

reaction rate of MTBE, kmol kg ±1 s ±1 Laplace parameter time, s temperature in the bed, K actual liquid velocity, m s ±1 gas super® cial velocity, m s ±1 liquid super® cial velocity, m s ±1 dimensionless axial coordinate axial coordinate, m

Greek letters e bed porosity g catalyst effectiveness factor gext external liquid±solid contacting ef® ciency mG gas viscosity, Pa s mL liquid viscosity, Pa s h dimensionless time rG gas density, kg m ±3 rL liquid density, kg m ±3 t mean residence time of liquid in the bed, s Subscripts a axial cal calculated exp experimental G gas L liquid

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Smith, L. A. Jr., 1990, US Patent 4978807. Smith, L. A. Jr., Jones, E. M. Jr., and Hearn, D., 1984, US Patent 4447668. Arganbright, R. P., 1982, US Patent 5087780. Smith, L. A. Jr., 1995, US Patent 5446223. Smith, L. A. Jr., Hearn, D. and Jones, E. M. Jr., 1984, US Patent 5003124. Hearn, D., 1996, US Patent 5510568. Arganbright, R. P., 1982, US Patent 5087780. Arganbright, R. P. and Hearn, B. S., 1993, US Patent 5231234. Palmer, D. A., Larson, K. D. and Fjare, K. A., 1992, US Patent 5113015. Zheng, Y. and Xu, X., 1992, TransIChemE, Chem Eng Res Des, 70(A5): 459. Zheng, Y. and Xu, X., 1992, TransIChemE, Chem Eng Res Des, 70(A5): 465. Xu, X., Zhao, Z. and Tian, S., 1997, TransIChemE, Chem Eng Res Des, 75(A6): 625. Shan, Y. T., Stiegel, G. J. and Sharma, M. M., 1978, AIChE J, 24(3): 369. Wakao, N. and Kaguei, S., 1982, Heat and Mass Transfer in Packed Beds (Gordon and Breach, Science Publishers, Inc). Smith, L. A. Jr., 1980, US Patent 4242530. Hopkins, M. J., Sheppard, A. J. and Eisenklam, P., 1969, Chem Eng Sci, 24(9): 1131. Aris, R., 1965, Introduction to the Analysis of Chemical Reactors, (Academic Press, New York). Wakao, N., Kagui, S. and Nagai, M., 1978, Chem Eng Sci, 33(2): 183. Gunn, D. J. and Vortmeyer, D., 1990, AIChE J, 36(9): 1449. Xu, X. and Zheng, Y., 1995, Ind Eng Chem Res, 34(7): 2232. Colombo, A. J., Bald, G. and Sicardi, S., 1976, Chem Eng Sci 31(12): 1101.

ACKNOWLEDGEMENT The authors are grateful to SINOPEC for ® nancial support of this work.

ADDRESS Correspondence concerning this paper should be addressed to Professor Xu, Xi-en, Department of Chemical Engineering, Tianjin University, Tianjin 300072, People’ s Republic of China. The manuscript was received 25 July 1997 and accepted for publication after revision 11 September 1998.

Trans IChemE, Vol 77, Part A, January 1999