Ind. Eng. Chem. Res. 2002, 41, 3139-3144
3139
Process Intensification in a Model Trickle-Bed Reactor G. Sivalingam, M. Radhika, D. P. Rao,* and M. S. Rao Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India
The industrial trickle-bed reactors are bulky because the liquid flow is controlled by the gravity. To explore the possible process intensification in trickle-bed reactors, we have measured the rates on a rotating string of particles on which the liquid flows under the influence of a centrifugal field. To quantify the intensification, we have determined rates on the same string of particles with flow due to gravity. A model for the reaction rate was proposed. The enhancement in the rate was in the range of 6-10 times as the centrifugal acceleration was varied from 350 to 700g. Moreover, it is possible to use particles of smaller size and achieve a higher interfacial area. Preliminary estimates showed that a reduction in the volume of the reactors by a factor of 50 appears feasible with rotating packed beds. Introduction Trickle-bed reactors used for hydroprocessing of petroleum fractions are very bulky1 because the liquid flows under the influence of gravity. It appears that it is feasible to achieve process intensification by the application of a centrifugal force and to reduce the volume of the reactors using rotating packed beds. Ramshaw and Mallinson,2 Munjal et al.,3 Basˇic´ and Dudukovic´,4 and Liu et al.5 have shown that enhancement in mass-transfer rates by 1 order of magnitude can be achieved in rotating packed beds. Further, the use of rotating beds permits the use of smaller catalyst particles. The increased interfacial area also contributes to the process intensification. We have explored the possible enhancement in the reaction rates in rotating packed beds. The objective of the present study is to quantify the process intensification in “trickle-bed” reactors using rotating packed beds. To achieve this end, we have selected a simple flow geometry, namely, a string of spheres, to carry out the studies. To quantify the enhancement in the reaction rates, we have carried out studies with liquid flow under the influence of gravitational and centrifugal fields. We have proposed a model for the reaction rate, which can be extended to rotating beds. Experimental Setup Satterfield et al.6 and Funk et al.7 have studied the hydrogenation of R-methylstyrene to cumene on Pd/γalumina. We have chosen this reaction system to facilitate the comparison of data. The experimental setup consisted of a reactor, a preheater, a feed tank, and a peristaltic pump. Figure 1 shows the reactor. It was a cylindrical vessel made of 6 mm thick borosil glass with 20 cm diameter and 28 cm height. Its side glass wall was sandwiched between two metal plates. A motor was mounted on the top plate, and a bowl was attached to the shaft of the motor. The string of spheres was fixed to the bowl through a hole in its side wall. An ac motor, the speed of which was set using an inverter drive, drove the string. A digital stroboscope (Cole-Parmer, Vernon * To whom correspondence should be addressed. E-mail:
[email protected].
Figure 1. Rotating string reactor assembly: (1) manometer tap, (2) gas outlet, (3) liquid inlet, (4) thermowell, (5) gas inlet, (6) rotating bowl, (7) glass wall, (8) cotton wick coil, (9) cotton wick, (10) catalyst string, (11) stand, (12) product removal. Table 1. Properties of γ-Alumina Particles diameter total surface area (N2, BET method) apparent porosity total pore volume packing density
5.1 mm 200-240 m2/g 0.65-0.75 0.57-0.67 cm3/g 0.61-0.72 g/cm3
Hills, IL, Series 87002) was used to measure the speed and to examine wetting of the particles. The string was assembled by passing a thin wire through the hole drilled through the center of the particles. The string was made up of 14 γ-alumina particles of 5.1 mm diameter (supplied by Norton Co., Philadelphia, PA). The first particle was located at a radial distance of 4 cm. The γ-alumina particles were impregnated with 2.5 mass % of Pd as per the procedure suggested by Herskowitz et al.8 Visual observation indicated that the palladium was distributed uniformly throughout the particles. The physical properties of the particles are given in Table 1. A peristaltic pump (Cole-Parmer, Vernon Hills, IL, VC-280) was used to deliver liquid to the reactor from a 2.5 L feed tank. The feed tank was kept in a water bath to maintain the liquid at a constant temperature. In the preliminary runs, rivulet flow was observed. To overcome this, a piece of cotton wool was wound around
10.1021/ie0107237 CCC: $22.00 © 2002 American Chemical Society Published on Web 05/23/2002
3140
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002
the wire between the liquid inlet and the first particle in the string. This ensured complete wetting of the catalyst particles over the range of liquid flow rate covered in this work. However, at the top of the string, an inactive γ-alumina particle (without the catalyst) was kept to eliminate possible entrance effects. Using a cathetometer, each particle in the string was scanned to observe the liquid film over the particles. It appeared that the liquid flowed uniformly over the particles as a thin film. The maximum linear velocity of the outermost sphere was about 30 m/s. The excess pressure at the stagnation point on this sphere was 30 Pa. This excess pressure was likely to thin the liquid film, but we ignored it. Two sets of experiments were carried out. In the first set, the bowl was removed and the string was attached to the liquid feed inlet. It was vertically hung downward. In the second set, the string was attached to the bowl through a side hole. Before the experiment was started, hydrogen was passed over the catalyst particles for about 1-2 h to avoid possible catalyst deactivation and to obtain reproducible results. Before R-methylstyrene was charged, it was freed from the polymerization inhibitor, p-tert-butylcatechol. The string of catalyst particles was soaked in R-methylstyrene to ensure complete prewetting. A small amount liquid was drawn for analysis from the reactor outlet. A gas chromatograph (Nucon model 5765) was used for the analysis. It was operated with a bentone-34 column of 2 m length with a dual flame ionization detector. It was found that the cumene concentration increased with time and attained a steady value after 1 h from the start of the run. Therefore, for each run a period of 1 h was allowed before the samples were drawn for analysis. The rate, Rv, based on the volume of catalyst particles, was calculated based on the conversion of R-methylstyrene to cumene. All of the experiments were carried out at room temperature and 1 atm of hydrogen pressure. In all of these runs, R-methylstyrene was presaturated with hydrogen.
Figure 2. Flow geometry.
ks )
φDeff 1 1 R tanh φ φ
[
]
(2)
and
φ ) RxkI/Deff
(3)
in which φ is the Thiele modulus, Deff is the effective diffusivity of hydrogen, and kI is the intrinsic reaction rate constant. For this reaction system, the Thiele modulus has been found to be large (40.2) and the effectiveness factor, η, to be 0.025. ks can be written as
ks ) ηkIR/3
(4)
An outline of the method of finding the reaction rate averaged over all of the particles is given below. (a) Film Region. Considering the liquid flow to be laminar, the film thickness, δ, can be obtained from the equations of motion as
δ ) δ0 sin-2/3 θ
(5)
δ0 ) (3µQ/2πRFg)1/3
(6)
and Model Rates with Gravity Flow. To analyze the reaction rates with the flow under the influence of gravity, we adopted the treatment proposed by Satterfield et al.6 and Ravindra et al.9 They considered that the liquid is held as pendular rings around the points of contact of adjacent particles and that it flows as a thin film between the pendular rings, as depicted in Figure 2. On the basis of the visual observation, they found the filling angle, β, for the pendular rings to be 30°. Therefore, the region of film flow was taken to be the one between 30° and π - 30°. As far as the liquid flow is concerned, we considered the particles to be nonporous. The reaction is known to be irreversible, first order with respect to dissolved hydrogen, and zero order with respect to R-methylstyrene. As the hydrogen diffuses through the liquid film, a part of it reaches the surface of the particle and the rest is carried into the pendular ring. The reaction rate based on the surface of the particle is
-rs ) kscs
(1)
where cs is the surface concentration of hydrogen and ks is the apparent rate constant. It is given by
where δ0 is the film thickness at the equator, Q is the volumetric flow rate of the liquid, F is the liquid density, and g is the gravitational acceleration. The liquid velocity, Vθ, in the θ direction can be found to be
Vθ ) Vθ,m[1 - (x/δ)2]
(7)
and
Vθ,m )
Fgδ2 sin θ 2µ
Vθ,m ) Vθ,m° sin-1/3 θ
(8) (9)
where x is the inward radial distance from the outer surface of the film. The concentration profile within the film can be found as follows. Let
Vθ,mδ02 x c C ) /, X ) , P ) δ RD c
(10)
where c/ is the concentration of dissolved hydrogen at
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3141
x ) 0 (in equilibrium with the gas phase), D is the diffusivity of hydrogen in the liquid, and δ0 and V0,m° are the film thickness and the maximum liquid velocity at the equator, respectively. The differential mass balance in terms of the dimensionless variables is
∂C ∂2C + (X2 - 1)P sin-5/3 θ 2 ∂θ ∂X
(11a)
The boundary conditions are
C)1
at X ) 0 for all θ
(11b)
C)1
at θ ) β for the first particle
(11c)
at θ ) -β for all of the rest of the C ) Ce(X,β) particles, where the subscript e denotes the liquid entering the pendular ring (11d) ∂C ksδ° ) sin-2/3 θC(1,θ) ∂X D
(11e)
Equation 11a can be solved along with the boundary conditions to obtain the reaction rate and concentration in the film. The rate of reaction in the film region, rf, is found from
rf )
β kscs(θ) 2πR2 sin θ dθ ∫π-β
(12)
(b) Pendular-Ring Region. The flow field within the pendular region is unknown. Therefore, we have considered the liquid flow to be well mixed. In the case of well-mixed flow, the concentration of hydrogen is uniform and its mass balance is
Qcji ) Qc0 + VP(-rP)
(13)
where VP is the volume of the pendular ring, cji is the average concentration in the pendular region, c0 is the concentration of the outgoing liquid from the pendular ring, and rP is the rate based on the volume and is related to rs as
-rP ) AP(-rs)/VP
(14)
where AP is the surface area of the sphere encompassed by the pendular ring. The average reaction rate for the string of particles based on the volume is N
rv )
(rfi + rPi) ∑ i)1 NVP
(15)
where i is the sphere number and N is the total number of spheres in the string. Rates with Flow under a Centrifugal Field. For the case of a rotating string, visual observation indicated the volume of the pendular ring to be negligible. Therefore, the film flow spanned from one end of the particle to the other. Hence, to determine the rate, we employed the film flow model, replacing g with ac ()ω2Li), in eqs 6 and 7. Note that ac varies from one particle to another, unlike in the case of gravity flow. However, for the sake of calculation, we have set the filling angle to be 1°.
Figure 3. Comparison of the reaction rates.
Method of Solution. To obtain the concentration profile in the liquid film over the region, -β e θ e β, over a sphere. Equation 11 was solved numerically using a finite difference scheme. The average concentration of the liquid entering the pendular ring was found from the concentration profile at β. The concentration of liquid emerging from the ring was found from eq 13. The overall rate was found from eq 15. For the rotating string, the g appearing in eq 8 was replaced with the centrifugal acceleration for the sphere under consideration. The rate was found for the region 1° e θ e 179° and by ignoring the contribution of the pendular ring. The details are given elsewhere.10 Results and Discussion The effect of the liquid flow rate on the hydrogenation rate of R-methylstyrene was studied. The measurements were performed at a gas flow rate of 1.67 cm3/s and at liquid flow rates in the range of 0.005-0.2 cm3/s, which corresponds to the flow in the trickling regime in a bed of particles of the size used in this study. The centrifugal acceleration for the last sphere was varied from 350 to 675g. Rates with Flow under Gravity. Figure 3 shows the reaction rate with the flow rate. For the sake of comparison, the data reported by Satterfield et al.,6 Funk et al.,7 and Subramanyam11 are also presented. The latter conducted studies employing a setup similar to the one used by Satterfield et al.,6 with the same particles that are used in the present study. The experimental details are available elsewhere.11 The data obtained in the present study and that by Subramanyam11 are in close agreement as expected. It can be seen that, at low flow rates, the reaction rate decreased rather sharply with an increase in the liquid flow rate. However, there is a marginal increase in the reaction rate at high flow rates. The trend is similar to the one reported in trickle-bed reactors for hydrogenation of R-methylstyrene8 and for the oxidation of sulfur dioxide over activated carbon.12 They attributed the trend to partial wetting. The present study indicates that the minimum in the reaction rate may not be due to the partial wetting of the catalyst particles. Satterfield et al.6 observed no significant effect on the reaction rate with the liquid flow rate for the hydrogenation of R-methylstyrene in a string of spherical particles. Funk et al.,7 by design, carried out their runs under partial wetting conditions. Unfortunately, there are only two data under complete wetting condition.
3142
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002
Figure 4. Variation of the intrinsic rate constant with catalyst loading.
Figure 6. Effect of f on the estimated reaction rates.
Figure 5. Estimated and experimental rates in rationalized units.
Figure 7. Relative contribution of the film and pendular regions at f ) 0.835.
Prima facie, there appears to be a wide discrepancy in the reaction rates. The reaction takes place essentially at the outer shell of the pellet. Therefore, it is appropriate to base the rate on the surface area rather than the volume of the particles because their shapes and sizes are different. Moreover, the mass percent of Pd used in these studies is different. The intrinsic rate constant reported in the literature6,8 shows the linear trend with mass percent of Pd (see Figure 4). Therefore, the reaction rates were recomputed based on the surface area and unit mass percent of Pd. These rates are shown in Figure 5. It is seen that the rates of different groups are in reasonable agreement. We have estimated the average reaction rate based on the model presented earlier. It was found that the estimated rates are higher than the experimental data. It is likely that the liquid in the pendular rings may not be well mixed. A portion of the film may bypass the pendular ring. This effectively reduces the hydrogen concentration in the pendular ring, which in turn leads to lower rates. Therefore, we have considered that the liquid film near the entrance of the pendular ring can be divided into two layers. The lower layer of fractional thickness f flows into the pendular ring, whereas the upper one of 1 - f thickness bypasses the pendular ring. The factor f may be considered as a model-fitting parameter. The estimated rates for different values of f are shown in Figure 6. It was found that the estimated rates are in good agreement with the data for f ) 0.835 (see Figure 5).
The relative contributions of the film and pendular regions for f ) 0.835 are shown in Figure 7. At low liquid flow rate, the film thickness is less and the amount of hydrogen reaching the catalyst is high. Because the flow into the pendular ring is small, the reaction rate in this region is small, as can be seen in Figure 7. As the flow rate increased, the film region contribution decreased sharply and then increased marginally. The increase is due to an increase in the flow of hydrogen through the feed that is saturated with hydrogen. We found that the rate decreased with an increase in the feed rate for the feed without saturation. On the other hand, the pendular-ring contribution increased and attained a constant value. Note that the reaction in the pendular region is smaller than that in the film region. Thus, the minimum in the total rate results from the relative contribution of the film and pendular regions. Thus, it appears possible to explain the observed trends without invoking the partial wetting of the particles. In a trickle bed, the number of contact points that a particle will have with its nearest neighbors will be more than that in a string. Hence, the region covered by the pendular rings will be large. Therefore, the role of pendular rings in understanding the performance of the trickle-bed reactors appears to be even more imperative. Rates with Flow under a Centrifugal Field. Figure 8 shows the average reaction rates with flow under centrifugal acceleration. For the sake of compari-
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3143
the rotating bed of spheres. The trickle (film) flow with the centrifugal field can be achieved with 1 mm particles.2 Thus, the combined enhancement in the reaction rate by centrifugal force and interfacial area can lead to a 40-50 times higher reaction rate. Hence, a reduction in the reactor size by 40-50 times appears feasible. Conclusions
Figure 8. Experimental and estimated rates at 497g.
Reaction rates were measured on a string of spheres in the trickling regime under complete wetting of the particles. It was observed that the reaction rates decreased steeply at low flow rates and marginally increased at high flow rates. The role of the pendular rings has to be taken into account in the evaluation of the reactor performance. The process intensification in trickle-bed reactors can be achieved by use of a centrifugal field. It appears possible to reduce the reactor size by a factor of 50 with rotating packed beds. Acknowledgment The authors acknowledge the financial support received from Department of Science and Technology, Government of India, for carrying out the present study. Nomenclature
Figure 9. Effect of the centrifugal acceleration on the reaction rate.
son, the rates with gravity flow are also presented. The rate sharply decreased with an increase in the liquid flow rate and attained a constant value. It can be seen that enhancement in the rate at 497g was about 9 times at low flow rates. It decreased to about 6 times at higher flow rates. Considering that the pendular region is negligible, the average reaction rate was estimated from the film model. The estimated rate is lower than the experimental values. The alumina particles are not exactly spherical; they are dimpled. This could have led to the radial mixing within the film, and such mixing will result in higher rates. It is likely that there could be flow through the macropores in the outer shell of the particles due to the centrifugal acceleration, which might have contributed to higher rates. Figure 9 shows the variation of rates with centrifugal acceleration. The rate increased with the acceleration. The enhancement in the rate in excess of a factor of 10 was achieved at higher accelerations. In the trickle-bed reactors, particles of size 4-8 mm are employed to achieve trickle flow under gravity. If the centrifugal acceleration is 750-1000g, the volume of the pendular rings would be negligible. The film region extends to most of the surface of the particles. However, a particle will have more than two contact points unlike in a string. If the surface covered by the pendular rings around the contact points is accounted for, the model for the film region can be extended for
ac ) centrifugal acceleration, cm/s2 c ) concentration of hydrogen, mol/cm3 cc ) concentration of cumene, mol/cm3 ce ) concentration of hydrogen entering the film region, mol/cm3 ci ) concentration of hydrogen entering the pendular region, mol/cm3 c0 ) concentration of hydrogen leaving the pendular region, mol/cm3 cs ) surface concentration of hydrogen, mol/cm2 C ) dimensionless concentration of hydrogen D ) diffusivity of hydrogen in the liquid, cm2/s Deff ) effective diffusivity of hydrogen, cm2/s f ) fractional thickness of the liquid layer flowing into the pendular ring g ) acceleration due to gravity, cm/s2 kI ) intrinsic rate constant, 1/s ks ) apparent rate constant based on the surface area, cm/s Li ) distance of the sphere from the center of the shaft, cm N ) number of spheres Q ) volumetric flow of liquid, cm3/s Rv ) reaction rate based on the volume of the particle, mol/ s‚cm3 of catalyst rf ) reaction rate in the film region, mol/s‚cm2 rs ) reaction rate based on the surface area, mol/s‚cm2 rP ) reaction rate in the pendular region, mol/s‚cm2 rv ) average reaction rate, mol/s‚cm3 R ) radius of the particle, cm VP ) volume of the pendular ring, cm3 Vθ ) θ component of velocity in the film, cm/s Vθ,m ) θ component of velocity in the film at the gas-liquid interface, cm/s Vθ,m° ) θ component of velocity in the film at the gasliquid interface at the equator, cm/s x ) perpendicular distance from the gas-liquid interface into the liquid film, cm X ) dimensionless distance Greek Letters β ) filling angle δ ) film thickness, cm
3144
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002
δ0 ) film thickness at the equator of the particle, cm φ ) Thiele modulus η ) effectiveness factor µ ) viscosity, g/cm‚s θ ) angle measured from the vertical axis of the sphere F ) density, g/cm3 ω ) rotational speed, rad/s
Literature Cited (1) Gianetto, A.; Specchia, V. Trickle-bed reactors: state of art and perspectives. Chem. Eng. Sci. 1992, 47, 3197. (2) Ramshaw, C.; Mallinson, R. H. Mass transfer process. U.S. Patent 4383255, 1981. (3) Munjal, S.; Dudukovic´, M. P.; Ramchandran, P. Mass transfer in rotating packed bedsI. Development of gas-liquid and liquid-solid mass-transfer correlations. Chem. Eng. Sci. 1989, 44, 2245. (4) Basˇic´, A.; Dudukovic´, M. P. Liquid Holdup in Rotating packed beds: Examination of film flow assumption. AIChE J. 1995, 41, 301. (5) Liu, H. S.; Lin, C. C.; Wu, S. C.; Hsu, H. W. Characteristics of a rotating packed bed. Ind. Eng. Chem. Res. 1996, 35, 3590. (6) Satterfield, C. N.; Pelossof, A. A.; Sherwood, T. K. Mass transfer limitation in a trickle bed reactor. AIChE J. 1969, 15, 226.
(7) Funk, G. A.; Harold, M. P.; Ng, K. M. Experimental Study of Reaction in a Partially Wetted Catalytic Pellet. AIChE J. 1991, 37, 202. (8) Herskowitz, M.; Carbonell, R. G.; Smith, J. M. Effectiveness Factors and Mass Transfer in Trickle-Bed Reactors. AIChE J. 1979, 25, 272. (9) Ravindra, P. V.; Rao, D. P.; Rao, M. S. A Model for Sulphur dioxide oxidation in Trickle-bed reactors. Ind. Eng. Chem. Res. 1997, 36, 5125. (10) Radhika, M. Process Intensification Studies on a Rotating Trickle-bed reactor. M.T. Thesis, Indian Institute of Technology, Kanpur, India, 1999. (11) Subramanyam, S. Reaction rate studies in a model Rotating Trickle-Bed Reactor, M.T. Thesis, Indian Institute of Technology, Kanpur, India, 1995. (12) Mata, A. R.; Smith, J. M. Oxidation of Sulfur Dioxide in a Trickle-Bed Reactor. Chem. Eng. J. 1981, 22, 229.
Received for review August 31, 2001 Revised manuscript received February 19, 2002 Accepted February 22, 2002 IE0107237
