Ind. Eng. Chem. Fundam.
1980, 19, 385-389
385
Mass Transfer and Flooding in Wetted-Wall and Packed Columns Gordon A. Hughmark €thy/ Corporation, Baton Rouge, Louisiana 7082 1
Mass transfer coefficients for the gas or vapor phase in wetted-wall and packed columns is shown to be represented by the equation for mass transfer in turbulent pipe flow without the boundary layer resistance. Shear velocity for packed columns appears to correspond to 20 to 50% of the total pressure drop depending upon the packing. Interfacial areas in large beds for packed columns appear to be less than for small beds with optimum liquid loading for some of the types of packing. A model is also presented for flooding velocities with countercurrent flow in wetted-wall columns and for packing.
Mass transfer in wetted-wall columns and columns with packing were the subject of intensive experimental programs about 40 years ago. Packed column use in the United States was limited for many years to applications in which it was inconvenient to install trays. Ceramic packing for corrosive fluid systems and column diameters too small for trays represented the primary applications. Extensive experimental programs by Fractionation Research, Inc., and by packing manufacturers have resulted in the use of packing for many applications where trays were formerly used. An excellent analysis of packed column design methods was presented by Bolles and Fair (1979). This paper concludes that the reliability of the best of the existing packed column design models leaves a good deal more to be desired. Hughmark has demonstrated the correlation of heat and mass turbulent fluid fields (1980) with the shear velocity rather than a Reynolds number. This paper considers wetted-wall and packed column data with turbulent gas or vapor flow with the shear velocity concept. Wetted-Wall Columns Gilliland and Sherwood (1934) reported data for vaporization of water and eight organic liquids into air flowing in a 2.67 cm wetted-wall column. The Schmidt number range was 0.60 to 2.26. Correlation of the Sherwood number for the gas phase with the Reynolds and Schmidt numbers shows a 0.44 exponent for the Schmidt number. Data are reported for cocurrent and countercurrent flow. Barnet and Kobe (1941) reported data for heat and mass transfer with water and air and heat transfer data with air and low viscosity oils for countercurrent flow in a 2.54-cm column. Johnstone and Pigford (1941) presented data for distillation for five systems in a 2.98-cm wetted-wall column. Transfer coefficients are observed to be greater than for single phase fluid flow in a pipe. Hughmark (1979) showed that transfer data for turbulent pipe flow with a wide range of Schmidt or Prandtl numbers and Reynolds numbers are represented by the model 1 1 1 1 - =--+-+(1) k+ k B + kT+ kc+ The transport coefficient for the transition region from y+ = 5.5 to y+ = 34.6 is kT+ = (0.0094/N~c)1/2[N~~1~2/u tan [34.6(0.0094Nsc)1~2] u tan [5.5(0.0094N~,)'~2]) (2) The approximate transport coefficient (Hughmark, 1975) for the core is 0196-4313/80/1019-0385$01.00/0
Gas phase mass transfer for a wetted-wall column can be represented by the model from eq 1without the boundary layer resistance because of the liquid film-turbulent gas interface. The Gilliland and Sherwood data for humidification represent no resistance in the liquid phase, so they can be compared with this model. Combination of eq 1, 2, and 3 without the kB+ term shows a 13% average absolute deviation between calculated and experimental values for 38 data sets for water and five organic liquids with countercurrent flow. Velocities were calculated as the air velocity plus the average liquid film velocity corresponding to the film thickness. Friction factors were the experimental values reported in the paper. Positive and negative deviations are approximately equal, so this model provides an excellent representation of the experimental data. The Schmidt number exponent of 0.44 reported by Gilliland and Sherwood is explained by the combination of the transition and core region responses according to eq 2 and 3. The heat transfer data of Barnet and Kobe for mineral seal oil and the distillation data of Johnstone and Pigford include a liquid phase resistance. Hughmark (1973) suggested that liquid phase transfer for a falling film is represented by the equation kL+NscL112= 0.036
(4)
where u* = ( g ~ ) ' for / ~ a vertical falling film. Calculation of liquid film resistances showed these to be less than 1% of the total resistance for the heat transfer data and less than 10% for the distillation data. Average absolute deviation between calculated and experimental values for the air-mineral seal oil were 14.9% for 14 data sets. All experimental values are greater than the calculated values. Representative data for the Johnstone and Pigford toluene-EDC system and the data for the benzene-toluene system provide 26 data sets with an average absolute deviation of 8.1 % between calculated and experimental values for the vapor phase coefficients corrected for the liquid phase resistance. It is apparent that this is an excellent representation of the gas or vapor phase coefficients for wetted-wall columns. Packed Columns-Liquid Phase Most of the mass transfer data for packed columns include a liquid phase resistance. Hughmark (1973) suggested that the liquid phase transfer model for falling films may also apply to the liquid films on packing. Portalski (1963) reported film thickness data for 13 fluids on a flat vertical plate. Portalski concluded that Kapitsa's theory 0 1980 American Chemical Society
386 Ind. Eng. Chem. Fundam., Vol. 19, No. 4, 1980
(1948) approximates the experimental results better then Nusselt's theory (1916). The film thickness for a liquid flowing on packing is then =
(
2.4uL g sin 0 a
)'"
Table I. Gas Phase Mass Transfer Coefficients source
Nsc
Houston and Walker ( 1 9 5 0 ) 0.87
(5)
Shulman et al. (1955) report operating hold-up data for 2.54-cm Raschig rings with water, methanol, benzene, and calcium chloride solutions. Danckwerts and Sharma (1966) show interfacial areas for 2.54-cm Raschig rings with water. The holdup with the interfacial area provides an average film thickness. The film thickness with eq 5 provides sin 0 which represents an average effective angle for liquid flow on the packing. Values of sin 8 are about 0.18 for the four liquids with viscosities up to 1.21 cP. Interfacial areas for the liquids other than water were those for the volumetric flow rate of the liquid. Calculnted holdups from eq 5 with sin 0 = 0.18 show an average absolute deviation of 5.3% for the 20 data sets for the four fluids. This indicates that this is an excellent representation of film thickness with packing. Shulman et al. also show operating holdup data for 2.54-cm Berl saddles with water. Danckwerts and Sharma show interfacial areas with water for this packing. These holdups are also consistent with cos 8 = 0.18 for eq 5. The Shulman data for 4.5 CPand higher viscosity liquids show sin 8 increasing with viscosity, which indicates a different film mechanism with the more viscous fluids. Calculation of an average film thickness with sin 0 provides an estimate of the shear velocity for the liquid film from u* = (g sin 0 y)1/2. Sherwood and Holloway (1940) present data for the desorption of oxygen from water with air for 2.54,3.81, and 5.08-cm Raschig rings and 2.54-cm Berl saddles. Interfacial areas are available for 2.54 and 3.81-cm Raschig rings and 2.54-cm Berl saddles from Danckwerts and Sharma. Chung and Mills (1975) report COSabsorption into falling films of ethylene glycol water mixtures which provide data with liquid physical properties that were not available a t the time of the Hughmark (1973) paper. Correlation of the Chung and Mills (19761, Lamourelle and Sandal1 (1972), and Miller (1948) data with the Emmett and Pigford (1954) data provide
K+N~c'"2 = 0.0042(N~,,)''3 (6) The t value for the one-third exponent on the Reynolds number is 6.74 so this is shown to be a highly significant variable. Average absolute deviation between calculated and experimental mass transfer coefficients is 21.4% for the 66 data sets used in the correlation. Correlation of the liquid phase mass transfer data for packing results in the equation (7) The t value for the one-third exponent on the liquid Reynolds number is 6.43 so this is also a highly significant variable. Average absolute deviation between calculated and experimental mass transfer coefficients is 14.9% for the 31 data sets used in the correlation. Thus, the equations for liquid phase mass transfer with a falling film and with packing are both of the same form. Packed Columns-Gas Phase Hughmark (197313) showed that 2.54-cm packing gives a different gas phase coefficient response than smaller packing, probably because turbulent flow occurs in the larger packing but not in small packing. Therefore, this analysis is limited to 2.54-cm and larger packing to restrict the data to a turbulent regime. Houston and Walker
1.02
1.3 1.71 Yoshida and Tanaka ( 1 9 5 1 ) 0.80
kl klu
0.37~
0.113 0.037 0.100 0.035 0.095 0.028 0.076 0.042 0.113 0.042
eq8, k+ 0.118 0.105 0.088
0.076 0.128
(1950) presented absorption data for ammonia, acetone, methanol, and ethanol in water from air with 2.54-cm Raschig rings. Column diameter was 30.5 cm with 61 cm bed depth. Gas phase Schmidt numbers for these systems are from 0.87 to 1.7. Data were obtained for a range of air rates and liquid rates. Gas phase mass transfer coefficients were calculated from the data with a liquid rate of 0.27 g/cm2 s. Gas velocities were calculated from the packing void fraction. Gas velocities relative to the liquid phase were assumed to be the sum of the gas and liquid velocities. Mass transfer coefficients divided by the gas velocity relative to the liquid phase were observed to be nearly constant for a specific system. If gas phase mass transfer for packing is consistent with that for wetted-wall columns, eq 8 should apply. Pressure drop for packing represents shear drag and form drag with mass transfer related only to shear drag. 1 _1 --- 1 (8) kc+ kT+ kc+
+-
Yoshida and Tanaka (1951) report heat and mass transfer for air humidification with water for 2.54-cm Raschig rings in a 25-cm column with 32 cm depth. The heat transfer data for air and water rates comparable to that from Houston and Walker were also used with eq 8. Table I shows the values of k/u (f/2)'I2 with Cf/2)'i2 = 0.37 compared to values from eq 8 with Cf/2)'i2 = 0.37. Good agreement is observed. Packing pressure drop data can be used to calculate a friction factor for gas flow in the packing. If the wetted area is assumed as the surface area, the hydraulic radius is € / a where a is the wetted surface area per volume of packed column. Friction factors calculated from the pressure drop data of Fellinger (1941) for comparable gas and liquid rates with 2.54-cm Raschig rings show (f/2)'/2 = 1.85. Thus, shear drag is indicated to be about 20% of the total drag. Hughmark (1972) showed that the shear drag fraction is 28% for heat transfer in the shell side of tube bundles. Thus, the shear drag fraction appears to be reasonable. Bolles and Fair (1979) present a bibliography of the packed column data for Raschig rings, Pall rings, and Berl saddles with 2.54 cm and larger packing. These data represent a wide range of column diameters and packing depths. Billet (1967,1969), Cornel1 et al. (1960), Fellinger (1941), Kirschbaum (1948), Silvey and Keller (1969), and Yanagi (1975) are listed in this bibliography. All but Cornel1 et al. and Kirschbaum include pressure drop data with the efficiency data. These data represent the major resistance in the gas or vapor phase. The data have been analyzed by estimating the liquid phase resistance from kL+using eq 7. Danckwerts and Sharma show interfacial areas as a function of water superficial velocity for 2.54 and 3.81-cm Raschig rings, 2.54-cm Berl saddles, and 2.54-cm Pall rings. Interfacial areas for 5.08-cm Raschig rings were estimated from the Sherwood and Holloway data with the assumption that eq 7 is applicable. Interfacial areas for 5.08-cm Pall rings were assumed to be that for 2.54-cm Pall rings multiplied by the dry surface area ratio of the 5.08
Ind. Eng. Chem. Fundam., Vol. 19, No. 4, 1980
387
Table 11. Summary of Vapor Phase Mass Transfer Coefficient Data source
pressure, a t m
packed vol, m 3
NSCC
calcd
0.69 0.77 0.44
klu 2.54-cm Raschig Rings
total (f/2)'l2
% shear drag
0.44 0.27 0.48
2.9 2.0 2.2
15 13.5 22
0.29 0.19 0.26
2.0 1.48 1.23
14.5 13 21
(f/2)'/*
Billet (1969) Fellinger Kirschbaum
0.131 1.0 1.0
0.39 0.104 0.126
Fellinger Silvey, Keller Yanagi
1.0 1.63 1.36
0.104 3.53 6.4
Billet (1969) Billet (1969) Billet (1969) Fellinger
0.066 0.131 1.0 1.0
0.39 0.39 0.39 0.098
0.089 0.098 0.067 0.031
0.54 0.59 0.50 0.25
2.64 2.44 1.9 1.4
20.5 24 26
Cornel1 e t al. Fellinger Kirsch baum
1.0 1.0 1.0
2.54-cm Berl Saddles 0.72 0.019 1.78 0.091 0.77 0.032 0.126 0.44 0.065
0.15 0.25 0.34
1.3 1.3 1.3
12 19 26
Billet (1969) Billet (1969)
0.131 1.0
0.39 0.39
2.54-cm Pall Rings 0.69 0.028 0.80 0.031
0.21 0.25
1.02 0.92
27.5 27
0.131 1.0 0.32 1.0 1.63 11.2
0.26 0.39 6.4 6.4 6.4 6.4
0.046 0.040 0.021 0.0166 0.016 0.0066
0.31 0.32 0.17 0.12 0.15 0.075
1.03 0.83 0.85 0.82 0.70 0.49
30 39 20 14.5 21.5 15
Meier e t al. Meier e t al. Meier et al.
0.025 1.0 1.0
6.2" 6.2" 6.2"
0.0118 0.0125 0.0138
0.11 0.12 0.15
0.30 0.35 0.39
37 34 38
Bulletin KS-1 Bulletin KS-1
0.026 0.131
a a
0.012 0.009
0.12 0.10
0.22 0.22
54 45
0.067 0.034 0.113
3.81-cm Raschig Rings 0.77 0.72 0.66
0.036 0.022 0.037
5.08-cm Raschig Rings 0.67 0.69 0.80 0.77
18
5.08-cm Pall Rings Billet Billet Billet Billet Billet Billet
(1969) (1969) (1967) (1967) (1967) (1967)
0.69 0.80 0.65 0.39 0.79 0.61
Flexipac 2 0.80 0.80 0.87
Koch Sulzer 0.73 0.80
" HETP stated t o be independent of column diameter. t o 2.54 cm rings. Table I1 shows a summary of the gas or vapor phase coefficients divided by the velocity based upon the void fraction for the dry packing. Gas velocity relative to the liquid phase was assumed to be the sum of the gas and liquid velocities. Data are limited to less than 70% of the flood point. The values of (f/2)1/2 are shown that are required to fit the mass transfer coefficients to eq 8. Values of (f/2)1/2calculated from pressure drop data at equivalent flow rates are shown which provide an indication of the percent shear drag. The Billet (1967), Cornell, and Silvey and Keller data represent large packing volumes and are observed to show about one-half of the percent shear for other data with that packing. The lower values probably are a result of reduced interfacial areas in the large beds rather than lower shear fractions or mass transfer coefficients. Pressure drop and HETP data have been published for two proprietary packings of interest. Meier et al. (1977) report data for chlorobenzene-ethylbenzene with Flexipac 2 for the pressure range of 19 to 760 mmHg and for ammonia absorption in water. Koch Engineering Bulletin KS-1 provides pressure drop and HETP data for ethylbenzene-styrene at 100 mmHg and cis,trans-decalin at 20 mmHg for Koch Sulzer packing. Liquid phase coefficients were calculated with the assumption that the entire dry surface areas were wet with liquid and that the wetted area did not change with liquid rate. Table I1 summarizes the calculated mass transfer coefficients and percent shear
Table I11 packing Raschig rings Raschigrings Raschigrings Pall rings Pall rings Berl saddles
size, cm ap, cm-' 2.54 3.81 5.08 2.54 5.08 2.54
1.9 1.18 0.95 2.06 1.02 2.59
A 1.28 x 1.71 x 1.03 x 2.25 X 5.6 x loT5 1.82 x
o/
0.4 0.7 0.8 0.37 0.37 0.4
drags which correspond to the reported pressure drops. Interfacial Area Interfacial area can be represented by the equation of the form (9)
Values for the various packings are listed in Table 111. Interfacial areas for 2.54-cm, 3.81-cm Raschig rings, 2.54cm Pall rings, and Berl saddles are those reported by Danckwerts and Sharma. All of these areas appear to represent the optimum liquid loading conditions for the packing. These conditions do not appear to be realized in large packed beds as indicated from the results shown in Table 11. Pressure Drop The values of total (f/2)'I2 indicate that these values are relatively constant for a specific packing. Correlations with
388
Ind. Eng.
Chem. Fundam., Vol. 19, No. 4, 1980
Table IV
packing Raschig rings Raschig rings Raschig rings Pall rings Pall rings
size, cm
2.54 3.81 5.08 2.54 5.08
C 0.070 0.050 0.050 0.040 0.020
the pressure drop data for Raschig and Pall rings showed that these data are correlated by the following equations (f/2€)1'2 = 1 - Y L/YG for 2.54 and 5.08 cm Pall rings, and (f/2t)'i2 = 2.24 - 2 . 2 4 ~ ~ / ~ c for 2.54, 3.81, and 5.08-cm Raschig rings. The average absolute deviation between calculated and experimental pressure drop is 30% for 53 data sets for Pall rings. Average absolute deviation between calculated and experimental pressure drop is 44% for 69 data sets for Raschig rings. Gas velocity for friction factor, drag coefficient, and pressure drop calculations was assumed to be the sum of the gas velocity relative to the packing and the liquid velocity.
Flooding Successful correlation of gas phase mass transfer for wetted wall columns and for packing with a gas velocity represented by the sum of the gas velocity relative to the wall or packing and the liquid velocity indicated that this could also be useful in flooding correlations. Kraybill (1953) reported extensive experimental data for flooding with countercurrent flow in vertical tubes of 0.95, 1.9, 3.8, and 7.6 cm diameter. Ten different gas-liquid systems were used including hydrogen, helium, air, carbon dioxide, propane, and Freon-12 as gasses and butanol, water, and sucrose solutions as liquids. Pressure drop data are also reported. Data were selected to represent the range of flow conditions for each tube diameter and system for which data are reported. The data were found to be correlated with a Froude number representing the velocity between the gas and liquid phases and the gas core diameter, the friction factor, the ratio of the liquid film thickness to the tube radius, and the phase density ratio.
Average absolute deviation between calculated and experimental flooding velocities is 16.8% for 34 data sets. Data for flooding with Raschig and Pall ring packing are reported by Billet (1967,1969), Schoenborn and Dougherty (1944), Silvey and Keller (1969), and Yanagi (1975). Correlation of these data with the form of eq 10
provide the values of C as listed in Table IV. Ten data sets are available for 5.08-cm Pall rings which is the greatest amount of data available for any of the packingsize combinations. Average absolute deviation between calculated and experimental flooding velocities is 10.5% for these ten data sets. It is interesting that the value of C for 5.08-cm Pall rings multiplied by the square root of the shear drag of 0.20 results in a coefficient of 0.0089 which is approximately the same value as eq 10 shows for
wetted-wall column flooding. Thus, the shear drag contribution with 5.08-cm Pall rings appears consistent with wetted-wall flooding. Conclusions Conclusions from analysis of gas or vapor phase mass transfer for wetted-wall columns and packed columns are as follows. 1. Mass transfer coefficients for countercurrent flow in wetted-wall columns are predicted by the turbulent pipe flow model without the boundary layer resistance. 2. Mass transfer coefficients for packed columns are also predicted by the turbulent pipe flow model without boundary layer resistance and with the appropriate shear drag for the packing. Gas velocity is assumed as the sum of the gas velocity relative to the packing and the liquid velocity. 3. Interfacial areas in large beds for packed columns appear to be less than the areas with optimum liquid loading in small beds. Flooding velocities for countercurrent flow in wetted-wall columns and for packing are also correlated with a model with the gas velocity assumed as the sum of the gas velocity relative to the tube wall or packing and the liquid velocity. Nomenclature a = interfacial area between gas or vapor and liquid phases up = surface area of dry packing D = tube diameter De = packing equivalent diameter, 4t/ap f = friction factor g = acceleration due to gravity k = mass transfer coefficient k+ = k / u * L = superficial liquid velocity NRe= Reynolds number Nsc = Schmidt number r = tube radius u = phase velocity u* = shear velocity y = liquid film thickness yf = y u * / v Greek Letters t = dry packing void fraction v = kinematic viscosity p = density Subscripts B = boundary layer C = core G = gas or vapor phase L = liquid phase T = transition region W = water at 20 "C Literature Cited Barnet, W. I., Kobe, K. A., Ind. Eng. Chem., 33, 436 (1941). Billet, R., Chem. Eng. Prog., 63, 53 (Sept 1967). Billet, R., Roc. Int. Symp. Dist. (Brighton), Int. Chem. Eng. Symp. Ser. (London), No. 32,4, 42 (1969). B o k , W. L., Falr, J. R., paper presented at Third International Symposium on Distillation, London, April 1979. Chung, D. K., Mills, A. F., Int. J. Heat Mass Transfer, 19, 51 (1976). Cornell, D., Knapp, W. G., Fair, J. R., Chem. Eng. Prog., 56, 48 (Aug 1960). Danckwerts, P. V., Sharma, M. M., Trans. Inst. Chem. Eng., 44, CE 244 (1966). Fellinger, L., D.Sc. Dissertation, Massachusetts Institute of Technology, Cambridge, Mass., 1941. Gilliland, E. R., Sherwood, T. K., Ind. Eng. Chem., 26, 516 (1934). Houston, R. W., Walker, C. A., Ind. Eng. Chem., 42, 1105 (1950). Hughmark, G. A., AIChE J., 18, 1020 (1972). Hughmark, G. A,, AIChE J., 19, 856 (1973). Hughmark, G. A,, AIChE J., 19, 1258 (1973b). Hughmark, G. A., AIChE J., 21, 1033 (1975). Hughmark, G. A,, AIChE J., 25, 555 (1979). Hughmark, G. A,, Ind. Eng. Chem. fundam., 19, 198 (1980). Johnstone, H. F., Pigford, R. L., Trans. AIChE, 37, 25 (1941). Kapitsa, P. L., Z . Eksper. Teoret. Fir. SSSR, 18, 3 (1948).
Ind. Eng. Chem. Fundam. Kirschbaum, F.. "Distillation and Rectification", Chemical Publishing Co., Inc., New York, 1948. Koch Engineering Co., "Koch Sulzer Rectification Columns", Bulletin KS-1, Wichita, KanL Kraybill, R. R., Ph.D. Dissertation, University of Michigan, 1953. Lamourelle, A. P., Sandall, 0. C., Chem. f n g . Sci., 27, 1035 (1972). M e r , W. D., Stoecker, W. D., Weinstein, B., Chem. Eng. Prcg.,71 (Nov 1977). Miller, E. G.,S.B. Thesis in Chemical Engineering, University of Delaware, 1948. Nusselt. W.. 2. Ver. Deut. Ina.. 60. 541 (1916). Portalski, S:, Chem. Eng. Sci: IS,787 (1$63).' Schoenborn, E. M.. Dougherty, W. J., Trans. AIChE, 51, 40 (1944)
1980, 19, 389-396
389
Sherwood, T. K., Holloway, F. A. L., Trans. AIChE, 36, 39 (1940). Shulman, H. L., Ullrich, C. F., Wells, N., Proulx, A. Z.,AIChE J . , 1, 259 (1955). Silvey, F. C., Keller, G. J., Proc. Int. Symp. Dist. (Brighton),Ind. Chem. Eng. Symp. Ser., London, No. 32, 4, 18 (1969). Yanagi, T., paper presented at 1975 International Chemical Plant Engineering Congress, Tokyo, 1975. Yoshida, T., Tanaka, T.. Ind. Eng. Chem., 43, 1467 (1951).
Received f o r review March 3, 1980 Accepted August 4, 1980
Control of Temperature Peaks in Adiabatic Fixed-Bed Tubular Reactors Gerhard K. Giger,' Rajakkannu Mutharasan, and Donald R. Coughanowr Department of Chemical Engineering, Drexei University, Philadelphia, Pennsylvania 19 104
Catalytic fixed-bed tubular reactors can undergo severe temperature excursions, particularly when there is a drop in feed temperature. Several control strategies have been studied which attenuate temperature peaks that would occur in an uncontrolled reactor. A practical strategy is recommended which requires feeding a fraction of the reactants at an intermediate point along the reactor bed. A cantrol algorithm which enables the calculation of the secondary flow is proposed and its performance characteristics are evaluated by dynamic simulations. The proposed method is very effective in attenuating the temperature peaks, thus preventing catalyst deactivation and structural damage to the reactor.
Introduction Temperature control of fixed-bed tubular reactors, which has been the subject of several investigators, presents several complex problems involving temperature and composition wave phenomena. Reactant gases have low thermal capacity compared with the catalyst bed. When the feed temperature decreases, the catalyst a t the entrance which is a t a temperature higher than the feed is cooled by the incoming gas, thus causing less reaction to take place in the entrance section of the reactor. As the reactants move further down the reactor, they gain heat as they come in contact with the hot catalyst bed. Since the gas stream has a higher concentration of reactants (because in the entrance section of the bed less reaction took place as compared to the initial steady state) more reaction takes place than occurred during the initial steady state. Thus, for an exothermic reaction, heat is released in an amount greater than that for the initial steady state and causes the occurrence of a temperature peak. For adiabatic reactors, the peak of the temperature wave increases as the wave moves down the reactor. When external cooling is used for the entire section of the reactor, the peak of the temperature wave can be attenuated to some extent; however, total elimination of the wave is difficult. The magnitude of the temperature peak is a function of heat of reaction, thermal capacities of the bed and the reactant gases, and the interphase heat transfer coefficient between the reactant gas apd the catalyst bed. In several industrial reactors, such temperature peaks are high enough to deactivate the catalyst or cause structural damage to the reactor. In industrial situations, the problem of high temperature peaks is handled by stoppage of reactant flow to the reactor. Current industrial practice Ciba-Geigy, Basel, Switzerland. 0196-4313/80/1019-0389$01.OO/O
is overly cautious and in this paper we present several alternative control strategies which do not require reactor shut-down. The main objective of this paper is to present a practical solution to the important problem of control of temperature peaks, with special emphasis on hydrodealkylation reactors. Several papers have appeared in the past on the temperature control of packed bed reactors. Most of these publications treat the design of control algorithms to mqintain exit temperature and/or concentration a t some desired level. It should be pointed out that controlling the exit temperature need not imply that the temperature within the reactor is maintained within safe limits. For example, in the paper by Strangeland and Foss (1970), their algorithm controls the outlet temperature very closely, but large temperature peaks occur within the reactor. In this paper, the primary goal is to solve the problem of controlling the temperature peaks which occur within the reactor. Previous Literature Dynamics of packed bed heat regenerators were first analyzed by Anzelius (1926) and were later extended to packed bed reactors by Brinkley (1947). Amundson (1956) also studied the dynamics of a packed adiabatic reactor in which radial gradients were included. The temperature and concentration interactions were first included in a model for systematic study of the dynamics of such a reactor by Bilous and Amundson (1956). Strangeland and Foss (1970) used the heterogeneous plug-flow reactor model to simulate the control of an adiabatic reactor. They linearized the equations describing the dynamics about the desired steady state to obtain tbe transfer functions relating the deviations in composition and temperature to the inlet condition of the reactor. They also investigated the feasibility of controlling the outlet 0 1980 American Chemical Society
