Ind. Eng. Chem. Res. 1997, 36, 1637-1643
1637
PROCESS DESIGN AND CONTROL Design and Operation of a Catalytic Polymerization Reactor in a Dilute Spouted Bed Regime Martin Olazar,* Jose´ M. Arandes, Gorka Zabala, Andre´ s T. Aguayo, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain
A simulation model for a catalytic polymerization reactor in a dilute spouted bed regime is described. The model, which is of dispersed plug flow, is based on solving the mass conservation equation for the monomer. The input parameters in the simulation program are the geometric factors of the contactor, the kinetic equations of polymerization and of catalyst deactivation, reaction temperature, monomer concentration in the feed, mean residence time of the catalyst in the reactor, and bed voidage. The following are calculated: (a) parameters that describe the state of the catalyst in the reactor (particle size distribution of the catalyst coated with polymer, catalyst amount, activity distribution); (b) hydrodynamic conditions of the bed (feed flow, dispersion coefficient, radial and longitudinal distribution of gas velocities, and alcohol concentration profiles); (c) catalyst flow required in the feed; (d) polymer yield. The simulation model has been verified with results from a pilot plant using, as test reaction, the polymerization of benzyl alcohol on a silica/alumina catalyst in order to obtain thermally stable polybenzyls. 1. Introduction Catalytic polymerizations have peculiar characteristics that condition the design of the reactor: high exothermicity, particle fusion (the catalyst is coated with polymer), wide particle size distribution, and the need for continuous catalyst circulation (imposed by production requirements). These circumstances hinder the use of conventional gas-solid contact reactors, in either a fixed or fluidized bed. The conventional applications of the spouted beds (drying, granulation, coating, etc.) have been restricted to the handling of large particles (of diameter greater than 1 mm) and show the suitability of this contact method for carrying out the operation with wide particle size distributions and with catalyst circulation (Mathur and Epstein, 1974; Kalwar et al., 1990). The development of the spouted bed of totally conical geometry has extended the application possibilities of this contact method (Markowski and Kaminski, 1983; Olazar et al., 1992). Two peculiarities of conical spouted beds are worth mentioning as they are important for their application as a polymerization reactor: (a) the ability to handle fine particles by properly designing the contactor (Olazar et al., 1996a); (b) the bed capacity for expansion up to the regime of jet spouted bed (San Jose´ et al., 1993), which was called dilute spouted bed by Epstein (1992). While the first peculiarity allows for carrying out the operation with solid catalysts (generally of particle diameter lower than 1 mm in order to avoid diffusional limitations), the second peculiarity gives a high velocity to the particles. This vigorous movement, by maintaining well-defined particle trajectories, is needed for avoiding fusion of particles and for attaining the desired isothermicity. * To whom correspondence should be addressed. Telephone: 34-4-4647700 ext. 2575. Fax: 34-4-4648500. E-mail:
[email protected]. S0888-5885(96)00616-1 CCC: $14.00
In previous papers, the good performance of the dilute spouted bed for catalytic polymerizations has been shown in studies carried out at laboratory scale (Bilbao et al., 1997a; 1989) and at pilot plant (Olazar et al., 1994a), where the obtaining of thermally stable polybenzyls by gaseous benzyl alcohol polymerization on acidic catalysts (silica/aluminas and Y zeolites) was carried out. The aim of this paper is to establish a program for simulation of reactors with the aforementioned characteristics and which takes into account the following general design aspects: (a) the use of a polymerization kinetics that takes into account the catalyst deactivation; (b) the consideration of a gas flow model in the reactor; (c) the consideration of catalyst circulation and, consequently, that the reactor inventory is made up of catalyst particles of wide residence time distribution, which gives way to particle size distribution (catalyst coated with different polymer amounts) and to activity distribution. The simulation program has been verified in a wide experimental basis of results, obtained in a pilot plant in which the polymerization of benzyl alcohol has been studied on silica/alumina catalyst in a wide range of operating conditions: catalyst residence time and monomer concentration at the reactor inlet. In previous papers the aforementioned tools needed for the reactor design, as are the polymerization kinetics and the gas flow model, have been studied. In the polymerization kinetics, the deactivation has been taken into account even through the initiation period. The cause of deactivation is the deposition of carbonaceous material coming from the degradation of growing polymer chains on the catalyst active sites (Olazar et al., 1996b). In order to represent the gas flow pattern, a disperse plug flow model has been proposed, in which plug flow deviation is quantified by a coefficient that is a function of the geometric factors of the reactor and of the operating conditions (Olazar et al., 1994a,b). © 1997 American Chemical Society
1638 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997
Figure 1. Reaction equipment (a) and reactor geometry (b).
2. Experimental Section The reaction equipment used is outlined in Figure 1a. The reactor is of Pyrex glass and has the following geometric factors (defined in Figure 1b): Dc ) 0.12 m; Di ) 0.02 m; Hc ) 0.20 m; γ ) 28°. At the gas inlet, cylindrical tubes of Pyrex glass of different diameter can be inserted, thus permitting selection of the value of the inlet diameter, Do ) 0.004, 0.006, 0.008, and 0.01 m. The height of the upper cylindrical section is 0.20 m. The reactor is installed in a convection oven. The circulating air is driven by blowers and heated by the resistance R2. From the tank T1 the benzyl alcohol is driven through a dispenser valve DV toward the reactor. Subsequently, it is mixed with a nitrogen stream whose flow rate is controlled by the mass flow meter-regulator FIR1 and it is vaporized and preheated by means of the preheater R1. The gaseous flow passes into the lower section of the reactor. The nonreacted alcohol, together with the nitrogen (diluent) and the steam produced, leaves the reactor through the upper section. The departing
gaseous mixture is cooled in a condenser so that the alcohol and the steam are condensed and collected in tank T2 (a graduated column is placed in this line, before the tank, for measurement of alcohol conversion). This tank is periodically emptied by means of the pneumatic valves NV7 and NV8. The nitrogen is recirculated. The lateral outlet for the catalyst coated with polymer is of 0.01-m diameter and is located at 0.07 m from the base of the reactor. A nitrogen connection to this outlet is controlled by a mass flow meter-regulator FIR2, avoiding the premature departure of the particles and controlling their diameter. The catalyst feed is measured by means of the vibratory hopper VH. The catalyst passes through the pneumatic valves NV1 and NV2 (which open and close in a coordinated way in order to avoid gas leakage) and falls into the reactor. If the gas inlet velocity is appropriate, the cyclic movement of the particles, which is characteristic of the dilute spouted bed regime, takes place in the reactor, at the same time as the polymer coats the catalyst particles. Consequently, and due to the residence time distribution, there is variance in size of the catalyst particles coated with polymer. These particles leave the reactor on reaching the lateral outlet and fall through valves NV3 and NV4 to an electronic weighing machine (charge cell CC) where the product is weighed. Valves NV5 and NV6 allow the departure of solids that fall through the central orifice (which does not take place above a certain gas inlet velocity). Valve V1, which is controlled by a vacuum meter, allows nitrogen to enter the circuit when pressure decreases (the system is maintained at atmospheric pressure) and valve V2, which is controlled by a pressure meter, releases gases to the outside if the pressure in the circuit increases. Total pressure in the circuit is around 1 atm. Partial pressure changes according to the alcohol-nitrogen mixture. The preheater must vaporize and raise the temperature of the mixture to the set value. Temperature in the reactor is between 250 and 310 °C. The movement of particles in the reactor favors thermal equilibrium and perfect mix conditions, which means that temperature uniformity is achieved. Gas inlet velocity must be suitable (to the order of 5-10 m s-1). A routine for data acquisition and real time control of the equipment components has been prepared. The catalyst used is a silica/alumina, with the following physical properties: particle size, between 0.32 and 0.50 mm; BET surface area, 286 m2 g-1; pore volume, 0.56 cm3 g-1; real density, 2.37 g cm-3; particle density, 1.02 g cm-3. The content of Al2O3 is 35 wt %. Acidity has been measured by titration with n-butylamine: pK+2.8 ) 23 mg of n-butylamine (g of catalyst)-1; pK+3.3 ) 26 mg of n-butylamine (g of catalyst)-1; pK+4.8 ) 35 mg of n-butylamine (g of catalyst)-1; pK+6.8 ) 48 mg of n-butylamine (g of catalyst)-1. 3. Reactor Simulation In Figure 2 an outline of the calculation procedures followed by the reactor simulation program is shown. The program consists of solving the mass conservation equation for benzyl alcohol (monomer). The input parameters are the reactor geometric factors (those mentioned in the experimental section), the kinetic equations for polymerization and catalyst deactivation (Olazar et al., 1996b), the reaction temperature (250, 270, 290, and 310 °C), the monomer concentration in the feed (0.1, 0.4, and 0.64 atm), the mean residence
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1639
Figure 3. Geometry of the gas flow model. Volume elements and streamtubes.
uij
∂PA ∂2PA 2D ∂PA FcRT(1 - ) -D + rP ) 0 ∂F F ∂F MP ∂F2
(1)
with the following boundary conditions: at the inlet of j streamtube (F ) Fo):
PA ) PAo D
∂PA ) u0j(PAo - PA) ∂F
(2) (3)
at the outlet of j streamtube (F ) FM):
∂PA )0 ∂F
Figure 2. Calculation steps for reactor simulation.
time of the catalyst in the reactor (1, 5, 10, 20, 30, and 40 min), and the bed voidage. High bed voidages have been set in advance (0.95 and 0.99) in order to assure that the steady state is the one corresponding to the dilute spouted bed regime (Olazar et al., 1992; San Jose´, 1993). The calculation procedure also ensures that the gas flow in the reactor feed is that needed for attaining the hydrodynamic regime corresponding to the dilute spouted bed (or a transition regime close to it). By means of the program the following are calculated: parameters describing the state of the catalyst in the reactor (catalyst amount, particle size distribution of the catalyst coated with polymer, activity distribution); hydrodynamic conditions of the bed (flow rate of benzyl alcohol and nitrogen in the feed, dispersion coefficient, radial and longitudinal profiles of gas velocity, and alcohol concentration profile); catalyst flow rate; polymer production. The gas flow rate along each one of the streamtubes, Figure 3, is assumed to be constant. In this way, the dispersion or any other gas mixing mechanism between streamtubes is neglected. The mass conservation equation in a differential volume element defined in Figure 3, in steady state and with the reaction term taken into account, is (expressed as a function of alcohol partial pressure):
(4)
For the N streamtubes a set of N equations is established, whose solution will give N functions that will describe the evolution of monomer concentration along each streamtube with time. The assumption that the one-dimensional disperse plug flow is fulfilled was discussed in a previous paper (Olazar et al., 1994b), in which it was proven that this assumption (which simplifies the modelling of the flow pattern as it does not require the experimental knowledge of velocity profile in the reactor) is correct for contactor angles γ < 33°, as far as the ratio between the inlet diameter and the contactor base diameter is not noticeably greater than 2/3. The value of the dispersion coefficient, D, is calculated by using the correlations corresponding to the dilute spouted bed (Olazar et al., 1994b), in which the reactor operates in most of the combinations of operating conditions. Nevertheless, when the particle population has a small diameter, the hydrodynamic regime of the bed corresponds to a transition between the spouted bed and the dilute spouted bed. Under these transition conditions, the dispersion coefficient is calculated by interpolation (Zabala, 1997), from the correlations proposed for dilute spouted bed (Olazar et al., 1994b) and spouted bed (San Jose´ et al., 1995). The polymerization rate (under conditions in which deactivation is not important, a ) 1) follows a Langmuir-Hinshelwood type expression (Bilbao et al., 1987b):
1640 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997
rPo ) P2A
K3M(k′d + k′m)PA + KMk′d (1 + KMPA)3
(5)
The polymerization rate is attenuated due to the rapid deactivation of the catalyst (which is important for contact times of more than a few minutes). The polymerization rate is related to the adsorbed monomer concentration, [M1], as follows (Olazar et al., 1996b):
rP )
dP ) k′d[M1]2 + k′c[M1]2b dt
(6)
where
d[M1] ) kMrPA[N]a - kMrPA[M1] - kMl[M1] dt
(7)
Catalyst activity, a, with time is expressed thus
-[N]
da ) k′c[M1]2b dt
Figure 4. Radial profile of alcohol partial pressure for different longitudinal positions in the reactor, at 270 °C, pAo ) 0.1 atm, tr ) 1 min, ) 0.95. Solid lines, calculated taking into account the dispersion. Dashed lines, calculated assuming plug flow. Curves 1, for F ) Fo (reactor inlet). Curves 2, for F ) Fo + (FM - Fo)/3. Curves 3, for F ) Fo + 2(FM - Fo)/3. Curves 4, for F ) FM (reactor outlet).
(8)
In eq 8, activity has been defined as the fraction of active sites that are not occupied by the irreversibly deposited coke:
a)
[N] - [Cn] [N]
(9)
The kinetic constants are (Olazar et al., 1996b)
b ) 1.5 k′c ) 3.6 × 1032 exp[(-37 600 ( 400)/T]
(10)
k′d ) 8.2 × 1019 exp[(-21 600 ( 300)/T]
(11)
k′m ) 2.4 × 1014 exp[(-15 300 ( 200)/T]
(12)
kM1 ) 0.51 exp[(100 ( 20)/T]
(13)
kMr ) 3.46 × 10-13 exp[(16 100 ( 300)/T] (14) 4. Results Equation 1, with its initial and boundary conditions (for the experimental conditions of monomer in the feed) has been numerically solved. In this way, the monomer concentration values are calculated along the bed, for any radial position. In Figure 4 the results of PA vs the radial position in the reactor are shown for different longitudinal position in the reactor and for given conditions (270 °C, pAo ) 0.1 atm, tr ) 1 min, ) 0.95). The solid lines have been determined by solving eq 1 with the corresponding dispersion coefficient, D. The dashed lines correspond to the solution of eq 1 with plug flow assumption (D ) 0). These results and those corresponding to the subsequent figures correspond to the value of inlet diameter Do ) 0.008 m. In Figure 4 it is observed that the nearer the flow is to the reactor outlet, the more pronounced the radial profile of monomer concentration. The results differ wildly when the flow dispersion is not taken into account, especially when catalyst residence time is small (small particles made up of catalyst slightly coated with polymer). The simulation program allows for calculation of particle size distribution of the catalyst (coated with
Figure 5. Function of particle size distribution in the reactor for different values of mean residence time, at 270 °C, PAo ) 0.65, ) 0.95.
polymer) in the reactor. For that purpose the corresponding population balance (Himmelblau and Bischoff, 1968) is solved by assuming the solid to be in perfect mix regime, which has been proven to be a reasonable assumption when trials have been carried out by using solid tracers (Zabala, 1997). In Figure 5 the function of particle size distribution, fdp, is shown as an example for 270 °C, PAo ) 0.65, ) 0.95 and for three values of mean residence time, tr ) 1, 5, and 20 min. An important effect of mean residence time on particle size distribution is observed. Thus, for tr ) 1 min, the average diameter of the particle population is close to the inlet mean diameter (origin of abscissas), which is a consequence of the polymerization being in the initiation step. As the residence time increases, the distribution function becomes unimodal, progressively narrower, and with a maximum gradually displacing toward higher values of particle diameter. For the reaction system in Figure 5, the values of mean particle diameter are, for tr ) 1 min, XTO(dp) ) 0.83 mm; for tr ) 5 min, XTO(dp) ) 1.29 mm; and for tr ) 20 min, XTO(dp) ) 1.68 mm. In Figure 6 the function of catalyst activity distribution in the reactor, fa, has been plotted for the same conditions as in Figure 5. The shape of the curves and the effect of the mean residence time of the catalyst are similar to those mentioned above referring to the function of particle size distribution. The gas flow pattern (Olazar et al., 1994b) has a special incidence on the simulation program. The
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1641
Figure 6. Function of catalyst activity distribution in the reactor for different values of mean residence time, at 270 °C, PAo ) 0.65, ) 0.95.
Figure 8. Comparison of the calculated values (lines) and the experimental ones (points) of polymer production, for different values of the mean residence time of the catalyst, and of the alcohol partial pressure in the feed, at 270 °C: a, ) 0.95; b, ) 099.
Figure 7. Effect on the dispersion coefficient of the mean residence time of the catalyst and of partial pressure of alcohol in the feed, at 270 °C: a, ) 0.95; b, ) 0.99.
characteristic parameter in solving the gas flow model is the dispersion coefficient, D, whose value is sensitive to the operating conditions. In Figure 7 the values of D corresponding to 270 °C have been plotted for ) 0.95 (Figure 7a) y for ) 0.99 (Figure 7b) against the mean residence time of the catalyst and for several values of partial pressure of alcohol in the feed. The dispersion coefficient is smaller (regime closer to plug flow) as the monomer concentration at the inlet, and consequently the monomer concentration in the reactor, is greater. It is also evident in Figure 7 that the dispersion coefficient decreases in a less pronounced way as the mean residence time is longer. These results are a direct consequence of the effect of particle diameter on the dispersion coefficient. The difference between the values of the dispersion coefficient in parts a and b of Figure 7 is noteworthy. For ) 0.95 (Figure 7a) the gas-solid regime corresponds to a transition state between the regimes of spouted bed and dilute spouted bed (Olazar et al., 1992).
In this situation, the dispersion coefficient is noticeably higher than that corresponding to the dilute spouted bed (Figure 7b corresponding to ) 0.99). The validity of the simulation model is shown in Figure 8, where the calculated values (solid lines) and the experimental ones (points) of polymer production, Qp, vs mean residence time of the catalyst are compared for different values of alcohol partial pressure in the feed, at 270 °C and ) 0.95 (Figure 8a) and ) 099 (Figure 8b). The existence of a maximum at relatively low residence times is due to the fact that the steps of initiation, of polymerization, and of catalyst deactivation are opposed. In a catalytic reaction such as this one it is interesting to study the relative production with respect to catalyst requirements. In Figure 9 the results of the ratio between polymer and catalyst mass flow rates, QP/Qc, have been plotted against catalyst residence time in the reactor at 270 °C, for ) 0.95 (Figure 9a) and ) 0.99 (Figure 9b), and for different values of alcohol partial pressure in the feed. It is observed that the values of QP/Qc are similar for both values of bed voidage, although, as is observed in Figure 8, polymer production is much higher for ) 0.95. The results in Figure 9 are a consequence of the important effect of the reactant concentration on polymerization and on catalyst deactivation during its stay in the reactor. For low values of reactant concentration (PAo ) 0.1 atm) deactivation is reduced and the results in Figure 9 fit a straight line. This result is explained on the basis of the linear relationship between 1/Qc and tr under these conditions. Nevertheless, when deactivation is appreciable, as happens for PAo ) 0.4 and 0.65 atm, the results corresponding to Figure 9 deviate from
1642 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997
rigorous consideration of a kinetic model for polymerization that takes into account catalyst deactivation. The ranges of the operating conditions within which the gas flow model can be simplified, that is, where plug flow assumption is valid, have been delimited. The simulation program gives information not only on the operation output parameters (polymer yield, alcohol conversion, catalyst flow rate needed) but also on the state of the catalyst inventory in the reactor (by means of the calculation of the particle size distribution and catalyst activity). This is valuable information in reactions of this nature in order to progress in the optimization of the product quality and in order to design product separation systems. In particular, the function of catalyst activity distribution at the reactor outlet is required for the design of the equipment for regeneration (by combustion of the coke deposited within the catalyst with air or with air diluted with N2). Acknowledgment This work was carried out with financial backing of the Department of Education, University and Research of the Basque Country (Project PI94/33) and of the DGICYT (Project MEC 069.310-1359/94). Notation
Figure 9. Ratio between polymer and catalyst mass flow rates against catalyst residence time in the reactor for different values of alcohol partial pressure in the feed, at 270 °C: a, ) 0.95; b, ) 0.99.
linearity, as in this situation the catalyst mass in the reactor is a function of both PAo and tr. It must be taken into account that, as has has been previously pointed out, reactor operation requires a suitable value of bed voidage or, which is the same, a constant value of total mass in the reactor (catalyst plus polymer). It must be pointed out that the optimum operating conditions in a process, like the one studied here, correspond to a compromise between production requirements and yield of catalyst, so the results of QP and QP/Qc must be seen in light of the economics of the process. 5. Conclusions The conical spouted bed is of great versatility for its use as a reactor in catalytic polymerizations. In a dilute spouted bed, as well as in a transition state close to it, a vigorous gas-solid contact is attained, which allows for circulation of catalyst coated with polymer. The pilot plant designed allows for operating continuously in a wide range of operating conditions (mean residence time of the catalyst in the reactor and monomer concentration at the inlet). On the other hand, as has been studied in previous papers (Olazar et al., 1993), the scaling up is simple, so the use of a similar reactor at larger scale than the one studied in this paper seems encouraging. The simulation program shown in this paper can be of general application in other catalytic polymerizations with catalyst circulation, or even in other applications of conical spouted beds. The main academic contributions in the development of the program are centered on solving the gas flow model proposed and on the
a ) catalyst activity defined as the fraction of active sites that are not blocked by coke, eq 9 b ) number of polymer chains irreversibly adsorbed that end up by occupying a catalyst active site Cn ) irreversibly adsorbed polymer molecules (coke) D ) dispersion coefficient, m2 s-1 Dc, Di, Do ) top diameter of the column, of the bed bottom, and of the inlet, respectively, m dp ) particle diameter, m Hc ) height of conical section of the bed, m k′c, k′d, k′m ) apparent rate constants of deactivation, spontaneous desorption, and desorption by monomer, respectively kM1, kMr ) kinetic constants of adsorption and desorption of the monomer on an active site, s-1 KM ) equilibrium constant of the adsorption of the monomer on an active site M1 ) adsorbed monomer molecules Mp ) molecular weight of the structural unit of the polymer N ) total number of active sites n ) number of monomer molecules in the polymer P ) polymer weight, g PA, PAo ) partial pressure of benzyl alcohol at a position in the reactor and at the reactor inlet, atm Qc, QP ) catalyst flow rate and polymer production, kg s-1 QG ) volumetric flow rate of the gas at the inlet of the reactor, m3 s-1 R ) gas constant, kcal mol-1 K-1 rP, rPo ) polymerization rate and zero time polymerization rate, g of polymer (g of catalyst)-1 min-1 T ) temperature, K t ) time on stream, min tr ) mean residence time of the catalyst in the reactor, min uij ) gas velocity at the ij volume element in the j streamtube, m s-1 uoj ) gas velocity at the contactor inlet at the j streamtube, m s-1 Greek Letters R ) angle defined in the geometric model for gas flow, deg ) bed voidage γ ) cone angle, degrees F, θ ) spherical coordinates
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1643 Fc ) catalyst density, kg m-3 Fo, FM ) lower and upper longitudinal positions of the developed bed, m
Olazar, M.; San Jose´, M. J.; Zabala, G.; Bilbao, J. A New Reactor in Jet Spouted Bed Regime for Catalytic Polymerizations. Chem. Eng. Sci. 1994a, 49, 4579-4588.
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Bilbao, J.; Olazar, M.; Romero, A.; Arandes, J. M. Design and Operation of a Jet Spouted Bed Reactor with Continuous Catalyst Feed in the Benzyl Alcohol Polymerization. Ind. Eng. Chem. Res. 1987a, 26, 1297-1304. Bilbao, J.; Olazar, M.; Arandes, J. M.; Romero, A. Polymerization of Gaseous Benzyl Alcohol. 2. Kinetic Study of the Polymerization and of the Deactivation for a SiO2/Al2O3 Catalyst. Ind. Eng. Chem. Res. 1987b, 26, 1960-1965. Bilbao, J.; Olazar, M.; Romero, A.; Arandes, J. M. Optimization of the Operation in a Reactor with Continuous Catalyst Circulation in the Gaseous Benzyl Alcohol Polymerization. Chem. Eng. Commun. 1989, 75, 121-134. Epstein, N. Introduction and Overview. Can. J. Chem. Eng. 1992, 70, 833-834. Himemmblau, D. M.; Bischoff, K. B. Process Analysis and Simulation; John Wiley & Sons, Inc.: New York, 1968; Chapter 4. Kalwar, M. I.; Raghavan, G. S. V.; Mujumdar, A. S. Bibliography on Spouted Bed Technology. In Drying of Solids; Mujumdar, A. S., Ed.; Sharita Prakastan: Meerut-New Delhi, 1990; Chapter 16, pp 343-355. Markowski, A.; Kaminski, W. Hydrodynamic Characteristics of Jet Spouted Beds. Can. J. Chem. Eng. 1983, 61, 377-381. Mathur, K. B.; Epstein, N. Spouted Beds; Academic Press: New York, 1974. Olazar, M.; San Jose´, M. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Stable Operation Conditions for Gas-Solid Contact Regimes in Conical Spouted Beds. Ind. Eng. Chem. Res. 1992, 31, 17841792. Olazar, M.; San Jose´, M. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Design Factors of Conical Spouted Beds and Jet Spouted Beds. Ind. Eng. Chem. Res. 1993, 32, 1245-1250.
Olazar, M.; San Jose´, M. J.; Cepeda, E.; Ortiz de Latierro, R.; Bilbao, J. Hydrodynamics of Fine Solids in Conical Spouted Beds. Fluidization VIII 1996a, 197-206. Olazar, M.; Zabala, G.; Arandes, J. M.; Gayubo, A. G.; Bilbao, J. Deactivation Kinetic Model in Catalytic PolymerizationssTaking into Account the Initiation Step. Ind. Eng. Chem. Res. 1996b, 35, 62-69. San Jose´, M. J.; Olazar, M.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Expansion of Spouted Beds in Conical Contactors. Chem. Eng. J. 1993, 51, 45-52. San Jose´, M. J.; Olazar, M.; Pen˜as, F. J.; Arandes, J. M.; Bilbao, J. Correlation for Calculation of the Gas Dispersion Coefficient in Conical Spouted Beds. Chem. Eng. Sci. 1995, 50, 2161-2172. Zabala, G. Catalytic Polymerization in Conical Spouted Bed. Ph.D. Dissertation, University of the Basque Country, Bilbao, 1997.
Received for review October 4, 1996 Revised manuscript received January 30, 1997 Accepted January 30, 1997X IE960616Q
X Abstract published in Advance ACS Abstracts, March 15, 1997.
