Ind. Eng. Chem. Fundam. 1986, 2 5 , 181-184
181
Optical Measurement of Slurry Concentration Profile in a Concurrent-Flow Ga s 4lurry Column Katsuyukl Kubota, Shlnya Hayashl, and Yasuhlko Bltoh Department of Chemical Engineering, Kobe University, Kobe, Japan
An optical technique is described which allows the measurement of steady-state slurry concentration profile in a slender concurrent-flow gas-sluny bubble column. The optically measured profile is compared with that predicted by a previously reported semiempirical dispersion model. Qualitative agreement is observed between them, and the reliability of the technique is supported by additional experimental data.
Introduction In the design of a bubble column operating under steady-state conditions it is important to be able to establish the variation in the slurry concentration in both the vertical and radial directions. It has been shown (Siemes and Weiss, 1957; Cova, 1966; Imafuku et al., 1968) that fine solid particles suspended in a bubble column tend to form a concentration profile when the densities of particles and medium differ. This profile has been shown to be a function of particle concentration, the slurry and gas flow rates, the feed location, and the bubble shape and size. In this work, a model has been used to predict the rate of change of slurry concentration with time and the vertical dimension. These predictions have been potentially supported by experimental data obtained under steady-state conditions. Previous workers withdrew slurry samples through sampling taps fitted in the column in order to monitor the experimental profiles. This method would detect the space-average values of the concentration rather than the local values with the result that any concentration gradient in the vertical direction will be lost. In this work, the slurry concentration profile was measured experimentally by using an optical technique which did not disturb the flow pattern. A beam of light was passed through the slurry, contained in a test cell, having a rectangular cross section and parallel sides (see Figure 1). The amount of light absorbed by the slurry was measured and used to determine the slurry concentration. The sampling taps were used to withdraw liquid for the determination of the tracer concentration, as described in the Appendix. The advantage of this technique is that an average is only taken over the space coordinate in the radial direction. As an example of the optical technique to measure a concentration profile along a slender bubble column, we can refer to an experimental work reported by Shah and Lemlich (1970). Along with the previous work (Cova, 1966; Imafuku et al., 1968), the equation of the continuity for the particles was derived under the assumption that the particle diffusivities were the same as those of the liquid. The predicted concentration profiles were compared with those obtained by the optical method. Experimental Section Finely crushed glass particles were employed as the suspended solid. The experimental apparatus is shown schematically in Figure 1. The bubble column, having inside dimensions 35.0 by 35.0 mm by 1500-mm height, 0196-4313/86/1025-0181$01.50/0
was set parallel to the optical assembly support shaft. The column was made from transparent acrylic resin. The table, carrying the optical assembly, was mounted such that it could move in the vertical direction by means of the screw shaft driven by the dc motor as shown in Figure 1. A laser beam, having a diameter of 0.8 mm, was generated from a laser beam source (He-Ne gas laser, GLG5340, X = 632.8 nm, NEC Inc.). The light was passed through the objective lens so as to increase the beam diameter to approximately 3 mm. The beam passed through a collimating lens and a polarizing plate before entering the cell. The intensity of the emerging beam was measured by a silicon diode (Type 529, Bell and Howell Inc.). The output voltage of the diode was recorded on a recorder chart. Nitrogen gas was fed to the bottom of the column through a sintered glass bubbler (Kinoshita ball glass filter, G-4). The gas flow rate was measured by using a glass orifice and a manometer. The slurry was fed from a constant-head reservoir through a capillary tube. The feed rate was adjusted to a constant value during each run by choosing a suitable capillary tube by trial and error. A suitable diameter for this purpose was found to be about 0.5 mm. A sufficient amount of the slurry was stored to establish a steady-state condition at the beginning of each experiment. The slurry feed connection was located at the base of the bubbler. The outlet connection was 970 mm above the feed connection; hence, the height of the operating column was 970 mm, as shown in Figure 1. Several dummy runs were carried out to obtain a relationship between the concentrations of the slurries and the absorbencies. In order to calibrate the cell, the absorbency of a slurry, having a known concentration of the glass particles in water, was determined. The data from the calibration are shown in Figure 2. It can be seen that the Lambert-Beer law holds within a slurry concentration from 0 to 2 kg/m3. The linear correlation is determined by cell dimensions, suspended particle size, and optical physical properties of the solid. Figure 3 shows frequency histograms for the magnitude of the vertical and horizontal dimensions of the glass particles. From the histograms, a rotational ellipsoidal volume having major and minor axes of 48 and 45 hm was calculated and a spherical equivalent diameter of 46 hm was estimated and used as a characteristic particle diameter. The terminal falling velocity in water was calculated as 1.79 mm/s by Stokes’ equation, and a Reynolds number based on the characteristic particle diameter was found to be 0.0823. This implies that the falling velocity is within the Stokes region. 0 1986 American Chemical Society
182
Chem. Fundam., Vol. 25, No. 2, 1986
Ind. Eng.
0
0.5
1.0 Z/L(-)
Figure 4. Effect of gas flow rate on slurry concentration profile in concurrent operation.
Figure 1. Schematic diagram of experimental apparatus.
0
0.5
1.0
-) Figure 5. Effect of inlet slurry concentration on slurry concentration profile in concurrent operation. Z/L(
0
0.5
1.5
1.0
2.0
2.5
C ( kg/rn3) Figure 2. Variation of absorbency against slurry concentration.
-
60
6G
c 10
40
20
20
0
0
Here V, and E, denote the particle terminal velocity and the particle diffusivity, respectively. Equation 2 is the general solution for eq 1, where A and B are constants. c = A + B exp(VL- VF)(z/Ep) (2)
I
v
0
2C
40
do
60
Prn
Experimental Results and Discussion For a differential element of the column the material balance for the particles can be written as eq 1 under steady-state conditions (VL - VF)(dc/dz) - E,(d2C/dz2) = 0 (1)
The boundary conditions for eq 2 are the following: VLCF= (VL - VF)C~ - E,(dc/dz),,o, z = 0 (3) VLC, 3
20
LO
60
db(,m)
Figure 3. Frequency histograms of crushed glass particles: left, histogram as to lateral dimensions; right, histogram as to vertical dimensions (no= total number of particles).
Figures 4 and 5 show the slurry profiles for the case where the gas and slurry streams flowed concurrently from the base of the column to the discharge point. Some 1.8 h had to elapse after start-up to establish steady-state conditions. All the experiments after start-up for the optical measurements were carried out in a darkroom. It was necessary to shut off both the gas and slurry streams during data collection as the bubbles disturbed the optical path. The concentration profile normally persisted for several minutes, slowly fading as the particles settled. The data were obtained by allowing a delay of about 1min after shutting off the gas and slurry streams. The column was scanned by moving the laserldetector assembly the full depth of the column. A scan required 30 s to complete.
= (VL - VF)CF- E,(dc/dz),,L,
z =L
(4)
As noted, it was assumed that the particle and liquid diffusivities are identical and that the particle falling velocity is equal to the terminal velocity in stagnant water. A particle density of 2.5 kg/dm3 was used for the calculation. By using eq 5 , one can predict the concentration profile semiempirically. Figure 4 shows the comparison between the measured and predicted profiles for the three concurrent operations. The slurry feed rates and concentration were held constant, while the gas flow rates were varied. Figure 5 shows the comparison between the measured and predicted profiles for the three concurrent operations. The slurry feed rates and the gas flow rates were held constant, while the slurry concentrations were varied. The concentration profile can be predicted semiempirically c = CF(VL/(VL- VF)) + (1 - (VL/(VL - VF)) exp(-(VL - VF)(L - z)/Ep)) ( 5 ) The solid and dotted curves denote the experimental and predicted results, respectively. From Figure 4,it can
Ind. Eng. Chem. Fundam., Vol. 25, No. 2, 1986
- 2.0
r
I
I
I
I
I
I
I
I
I
I
I
1
1
1
I
183 I
-3
[ V =3.833.10 m / s
\
"E
v ' I
0 .P
W
1.0
1,'
I
I
0
10.
2.0 E.IO I
I
I
( m2/s )
I
1
0.5
I I 1.0
Figure 7. Effect of gas flow rate on tracer concentration profile.
be seen that as the gas flow rate increases all the profiles tend toward more uniform distributions due to the increase in the liquid diffusivity. From Figure 5, it can be seen that as the feed concentrations increase the outlet concentrations are increased accordingly. The general features of Figures 4 and 5 show that eq 1 and the subsequent assumptions are generally satisfactory, although eq 5 does not predict the experimental data correctly. Some additional phenomena appear to be present. One postulate is of a diffusivity for air bubbles in water rather than air bubbles in a slurry. It is foreseeable that the motion of the particles may not be solely governed by the scale of the eddy structure within the slurry. To adapt the present dispersion model to the experimental profiles, we propose a parameter a in E, = aEl as shown in Figure 6. By use of eq 5 and trial and error, the particle diffusivities, E,, which can fit the experimental curves were estimated and are shown in Figure 6. In spite of the particle distribution shown in Figure 3, the falling velocity, VF, predicted from the characteristic diameter, was used in the model. This effect would be included in the experimental constant, a. Further, a may include any wall effect on the slurry concentration profile. Two supplemental runs were carried out to confirm the reliability of the optical method. After the concentration profiles had been measured, the slurry was withdrawn from the column and centrifuged for several minutes. Then the particles were collected, dried, and weighed. The weight of the particles corresponding to the area under the curve of the absorbency vs. length plot agreed with that measured above with an error of about 6%.
Appendix Observation of the Vertical Mixing Profile. This profile was observed by injecting a NaCl solution of known concentration into the bubble column at the injection point (see Figure 1)in the vertical direction. For each injection, samples of the solution in the column were withdrawn at 100-mm intervals upstream of the injection site and the Na ion concentrations were determined at a wavelength of 589 nm by an atomic absorption spectrophotometer. A material balance a t a stationary volume element of unit cross section and length a t a distance z from the base of the column gives (A-1)
By integrating and introducing p = dcNa+/dZ,one can transform eq A-1 to In ( p / p l ) = ( V d E J ( z - 21)
I
z(m)
Figure 6. Experimental correlation between E, and E,.
El(d2CNa+/dzz)= VL(dcNa+/dz)
1
0
(A-2)
A semilog plot of p vs. z yields a straight line of slope VL/El. Hence, El may be obtained for any VL.
-
0.001 0.3
0.9
0.6
z(m) Figure 8. Experimental correlation for eq A-2.
h
Ln N '
E
v
0
._
0 W
0
0.5
1.0
1.5
G . I O ~( m3, Figure 9. Variation of liquid diffusivity against gas flow rate.
The tracer concentration profiles and the plots of p vs. z for the three assigned values of the gas flow rates are
shown in Figures 7 and 8, respectively. From Figure 7 it can be seen that the gradients of the curves become more pronounced as the gas flow rates decrease. From Figure 8 it can be seen that linear correlations using semilogarithmic coordinates are obtained. This approach avoids the complex experimental technique needed in other methods (Himmelblau and Bishoff, 1968). The results of the conversion to the diffusivities are shown in Figure 9. A linear correlation was available and applied to eq 5 to obtain the predicted curves. Figure 9 is a plot of gas flow rate, G, vs. the liquid diffusivities determined from Figure 8. These points fall on straight lines with correlation coefficients determined from the least-squares method.
Nomenclature c = concentration of slurry, kg/m3 CF = concentration of slurry in feed stream, kg/m3 co = concentration of slurry at bottom of column, kg/m3 cNa+= concentration of tracer ion, kg/m3
Ind. Eng. Chem. Fundam. 1986, 25, 184-189
184
d, = lateral particle dimension, m
db = vertical particle dimension, m E, = liquid diffusivity, mz/s E,, = particle diffusivity, m2/s G = gas flow rate, m3/s I = intensity of beam emerging from cell filled with slurry Io = intensity of beam emerging from cell filled with pure water L = pool depth of operating column, m V, = terminal falliig velocity of characteristic particle through stagnant water, m/s V , = superficial liquid velocity, m/s
pool height measured from bottom, m Literature Cited
z =
Cova, D. R. Ind. Eng. Chem. Process Des. Dev. 1966, 5 , 21. Hlmmelblau, D. M.; Blshoff, K. 9. “Process Analysis and Simulation”; Wiley: New York, 1968; Chapter 4. Imafuku, K.: Wang, T.: Koide, K.; Kubota, H. J . Chem. Eng. Jpn. 1968, 7 , 153. Shah, G.; Lemlich, R. Ind. Eng. Chem. Fundam. 1970, 9 , 350. Siemes, W.: Welss, W. Chem.-Ing.-Tech. 1957, 2 9 , 7 2 7 .
Receiued for review September 27, 1982 Revised manuscript received March 25, 1985 Accepted May 28, 1985
Transient Analysis of Deactivation in a Single Pellet with Changing Diffusivity and Voidage K. B. S. Prasad and R. Valdyeswaran Regional Research Laboratory, Hyderabad, India
M. S. Ananth’ Department of Chemical Engineering, Indian Institute of Technology, Madras, Indla
The transient deactivation process is modeled taking into account for the first time pore size reduction due to coke deposition and consequent changes in voidage and Knudsen dffwhrity. A coupled set of partial differential equations is set up to describe systems in which the deactivating reaction is too rapid for the pseudo-steady-state analysis to be useful. The model contains three parameters: 4 , the Thiele modulus, 7,the ratio of molal density of coke to the bulk concentration of the fluid reactant, and p, the reciprocal of the minimum fractional coke loading at which the reaction ceases. The governing equations are solved numerically, and the results are presented in terms of 7 a s a function of time with 7,p, and 4 a s parameters. It is shown that q passes through a minimum value at a time that is characteristicof the system and the operating conditions. This is the time for which it is most beneficial to operate the reactor in question.
Introduction Catalyst deactivation, in its most general form, manifests itself in a complex chemical reaction network as a physicochemical process that leads to a progressive reduction in the catalytic activity. The process may involve a reactant, a product, or an impurity present in the feed stream or a combination of these besides the catalyst itself. Except possibly when the deactivation is due to the poisoning effect of an impurity, the active surface area of the catalyst is progressively covered by a layer of a coking complex which needs to be burnt off periodically to restore the catalytic activity. Though it is generally recognized that all forms of deactivation are intrinsically transient, the pseudo-steady-state simplification has almost come to be accepted because the deactivating process is slower than the main process by several orders of magnitude. The extremely short life of cracking catalysts is but one example that defies this simplification. Further, where the deactivation is due to deposition of a coking complex, the transient phenomenon is complicated by the presence of diffusional resistance which may itself be influenced by continuing deactivation (Stoll and Brown, 1974). Analysis of deactivation with all these complications is undoubtedly a formidable task. Masamune and Smith (1966) and recently Do and Weiland (1981) have studied this difficult problem and theoretically computed catalyst effectiveness 0 1 96-43 13/86/ 1025-0 184$01.50/0
factors a t constant diffusivity to a reasonable approximation. A sharp fall in both the diffusivity, especially in the Knudsen regime, and the voidage has, however, been reported during deactivation (Stoll and Brown, 1974; Richardson, 1972). Further, the observed maxima in the rate as a function of process time in the oxidation of hydrogen sulfide over activated carbon (Menon, Murthy, and Murthy, 1972) (an example of rapid deactivation) have not yet been satisfactorily explained. The present work deals with deactivation caused by a coking complex which is itself a product of thermal degradation of the reactant and the product. The unsteadystate phenomenon influenced by the changing catalyst diffusivity and voidage is investigated theoretically. A three-parameter unified representation of the reactiondiffusion-deactivation system has been attempted. The pseudo-steady-state simplification is one of the natural asymptotes of the present analysis. On the basis of this analysis it is possible to quantify the effect of deactivation on catalyst diffusivity and finally to recommend steps to increase the productive life of the catalyst even in the face of rapid deactivation. Development of Theory The following triangular reaction network is assumed to take place in an isothermal catalyst slab having uniform 0 1986
American Chemical Society
