Ind. Eng. Chem. Res. 1987,26, 86-91
86 Registry
No. CMC, 9000-11-7.
L i t e r a t u r e Cited Godbole, S. P.; Schumpe, A.; Shah, Y. T.; Carr, N. L. AIChE J. 1984, 30, 213. Haque, M. W.; Nigam, K. D. P.; Joshi, J. B.Chem. Eng. J., in Press. Haque, M. W.; Nigam, K. D. P.; Viswanathan, K. Ind. Eng. Chem. Process Des. Deu. 1985b, in press. Kunii, D.; Levenspiel, 0. Fluidization Engineering; Wiley: New York, 1969.
Pandit, A. B.; Joshi, J. B. Chem. Eng. Sci. 1983, 38, 1189. Pandit, A. B.; Joshi, J. B. Rev. Chem. Eng. 1984, 2, 1. Ulbrecht, J. J.; Baykara, L. E. Chem. Eng. Commun. 1981, IOU-31, 165. Viswanathan, K. Ph.D. Thesis, Indian Institute of Technology, New Delhi, 1983. Viswanathan, K.; Rao, D. S. Chem. Eng. Sci. 1983, 38, 474. Viswanathan, K.; Rao, D. S. Chem. Eng. Commun. 1984, 25, 133.
Received for review August 8, 1985 Revised manuscript received April 24, 1986 Accepted May 30, 1986
Studies on Gas Holdup and Bubble Parameters in Bubble Columns with (Carboxymethy1)cellulose Solutions M. W.Haque and K. D. P. Nigam* Department of Chemical Engineering, Indian Institute of Technology, New Delhi 110016, India
K. V i s w a n a t h a n Particle Technology Consultants, Research Centre, B - I I 3 / 2 , East of Kailash, New Delhi 110065, India
J. B. J o s h i Department of Chemical Technology, University of Bombay,' L'DCT, Matunga Road, Bombay 400019, India
Experimental data are reported on the gas holdup in 0.20-, 0.38-, and 1.0-m-diameter bubble columns employing highly viscous pseudoplastic (carboxymethy1)cellulose (CMC) solutions. Although the liquid employed is viscous, it is shown that the inviscid circulation model explains the data extremely well. A new method is developed to obtain the isolated bubble rise velocity and the volume-to-surface mean bubble diameter from gas holdup data. T h e bubble size increases with HID until HID = 3, after which it becomes constant, and it increases with the CMC concentration. It is the characteristic feature of pseudoplastic systems t h a t the bubble size decreases with increasing gas velocity due to increasing shear. It is well-known that bubble columns are widely used in process industries as absorbers, strippers, gas-liquid reactors, etc. Biotechnology, food processing, and pharmaceutical processes constitute a wide spectrum of chemical industries where bubble columns are used and highly viscous media are processed. The rheological behavior of such viscous pseudoplastic non-Newtonian solutions can be fairly well simulated by the solutions of (carboxymethy1)cellulose (CMC) (Godbole et al., 1984). In bubble columns gas holdup is one of the most important parameters that characterizes the hydrodynamics. Gas holdup in gas-liquid systems gives the volume fraction of the gas phase and hence the gas residence time. Further, the gas holdup in conjunction with the knowledge of the mean bubble diameter allows the determination of interfacial area and mass-transfer rates between the gas and liquid phases. Thus, quantitative relationships among these factors are required, such relationships are available for Newtonian systems (Viswanathan and Rao, 1983,1984), but for CMC solutions available information is scarce for large-diameter columns. The gas holdup, the values of effective interfacial area, and the values of mixing are directly dependent etc. the bubble sizes. Bubble size and its distribution and bubble rise velocity have a direct bearing on the performance of bubble columns. Many methods are available to determine bubble sizes. Photographic techniques are widely used
* To whom correspondence should be addressed. 'Where experimental work was carried out.
because of their simplicity. Though the original bubble size distributions obtained from various measurement techniques differ markedly, the volume-to-surface mean bubble diameters evaluated consequently differ only slightly (Shah et al., 1982). However, it may be pointed out that photographic, electrical, and optical techniques give reliable results only in the bubbly flow regime, whereas the churn-turbulent regime is the most commonly encountered regime in the industrial bubble columns (Bach and Pilhofer, 1978). All the techniques stated above are direct measurement techniques. They have the disadvantage that special arrangements are necessary and that, further, the results may not be reliable. Liquid circulation induced by bubble movement has been experimentally measured by many investigators, and these results have etc. critically discussed (Viswanathan and Rao, 1984). Some investigators (Rietema and Ottengraf, 1970; Crabtree and Bridgewater, 1969) have analyzed circulation created by gas bubbling in viscous liquids. However, most of the literature data is for air-water-like systems. For such systems, viscous effects are negligible under normal operating conditions, and hence, inviscid theory is a reasonable approximation. Viswanathan and Rao (1983, 1984) proposed a model to calculate inviscid liquid circulation in cylindrical columns, and the resultant equations were analytical in nature. They also proposed a theoretical equation for gas holdup. The experimental information available on circulation in bubble columns with pseudoplastic solutions (CMC) are those of Franz et. al. (1980), Schugerl(1981),and Schumpe 1987 American Chemical Society
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 87 WATER A
-
AGITATOR
B
-
BY.PASS
B C - BUBBLE C Y - CHECK
D P R
S
TANK COLUMN JALVE
. DRAIN . GEAR PUMP . ROTAMETER . SPARGER FOR
GAS
V . VALVE
Figure 1. Schematic diagram of the experimental setup.
and
and Deckwer (1982). These data were obtained mainly in small-diameter bubble columns (D5 0.15 m). The flow regime in large-diameter columns is widely different from that in small columns. No data are available on bubble columns of the order of 1.0-m diameter when CMC solutions are employed. An attempt is made in the present paper to show that the inviscid liquid circulation model is applicable to highly viscous pseudoplastic non-Newtonian solutions as well in large-diameter bubble columns. A new technique is presented to estimate the average bubble diameters from the isolated bubble rise velocities (ubrvalues) obtained experimentally. Experimental resulta are presented for bubble columns of different diameters using (carboxymethy1)cellulose solutions.
Equation 6 is valid for the ranges M C Eo < 40, and Rebr> 0.1. The following equations can be obtained from eq 6-13.
or Advs = BdvSzm - 0.857
Theoretical Section For inviscid liquid circulation, the vorticity divided by the radial distance from the axis of symmetry is a function of stream function only (Lamb, 1932). Whalley and Davidson (1974) have analyzed such a situation where they assumed w / r to be proportional to +. This led to eq 1. Viswanathan and Rao (1983,1984) gave an analytical solution of eq 1 and used this effectively to
(15)
where
The following method is recommended: (1)Plot UG2vs. and obtain the slope. (2) Obtain experimental Ubr from the slope by using eq 5 as obtain a simple, nonnumerical, and completely predictive model to calculate the flow strength and velocity profiles in the liquid. The final theoretical expression for the gas holdup was derived by them as
or t
= 0.5U~0'8Ubr4'4(gR)4'2
(3)
or Ubr
= U ~ ~ 2 ~ . ~ / ( 2 t ) ~ . ~ ( 2 g R ) ~(4) '~
Rearranging eq 4 gives eq 5 . From eq 5 , it follows that Ubr can be obtained from the slope of the plot of UG2vs. c2.5
u~~= 4Ubr(gD)0'5t2'5
(5)
The terminal rise velocity of single bubbles (Ubr) can be predicted by the method of Clift et al. (1978), which has also been recommended by Shah et al. (1982). The expression is Ubr
=
" M4.149(J- 0.857) PLdvs
where
Ubr,exptl
= slo~e/4(gD)~,~
(18)
(3) Obtain A from eq 16 by using the estimated Ubr in step 2 above and calculate B by using eq 10-13 and 17. (4) Solve eq 15 for d, by the Newton-Raphson technique. (5) To obtain B, a: and m are required, for which eq 11 is applicable in most cases.
Experimental Section The schematic diagram of the experimental setup is shown in Figure 1. The columns were made up of transparent Perspex material to enable visual observation of the column. Air and aqueous (carboxymethy1)cellulose solutions were used as the gas and liquid phases, respectively. Different concentrations of CMC solutions were used to study the effect of viscosity as well as non-Newtonian liquid behavior on gas holdup. The clear liquid heights were varied in 0.20- and 1.0-m-diameter bubble columns to study the effect of HID on fractional gas holdup. Table I lists the details of the range of operating variables covered in this investigation. Three different sized columns were used in the present study, 0.20-, 0.30-, and 1.0-m inside diameters. Experiments were carried out in a semibatch manner. The column was filled with the desired liquid up to a predetermined level. The air flow rate was measured with a precalibrated rotameter. The values of gas holdups were determined from the clear liquid height and the height of
88 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 Table I. Details of t h e Gas SDarners a n d Bubble Columns column diameter column (id.) D , no. ni length, m gas sparger details 1 0.20 2.0 sieve plate, 109 holes; hole diam = 2.0 mm 2 0.38 2.0 sieve plate, 109 holes; hole diam = 2.0 mm 3 100 2.4 ring sparger; ring diam = 580 mm; tube diam (inside) = 26 mm; 148 holes, hole diam = 2.0 mm ~
~
Table 11. Phvsical Prunerties of Aaueous CMC Solutions consistency surface CMC concn, flow behavior index k , density, tension u, 9c wt index n Pa# ke/m3 Nim 0.10 0.80 0.012 1000 0.073 0.50 0.70 0.061 1003 0.072 1.00 0.67 0.102 1006 0.070 1.50 0.61 0.350 1008 0.069 2.00 0.50 1.320 1009 0.069 ~~
HID ratio 1-3, 5 3 1, 2
~
053
c
the dispersion. In CMC solutions, mainly churn-turbulent flow was observed visually. This agrees with the observations of Godbole et al. (1984). The CMC solutions were prepared by dissolving CMC powder (CEPOL, M/s Cellulose product of India Ltd.) in the water. The flow behavior of the pseudoplastic CMC solutions was characterized by the power law model of Ostwald-de Waele as r = ky"
(19)
c25
Figure 2. UG2vs. solutions.
for 0.20-m-diameter column and 0.5% CMC
and
I
Peff
=
b"-'
1
(20)
In order to calculate the effective viscosity prevailing in the bubble columns, the effective shear rate should be known. Nakanoh and Yoshida (1980), Schumpe and Deckwer (1982), and Godbole et al. (1984) applied a relation for shear rate, y, proposed by Nishikawa et al. (1977), and this is used in the present study as well (eq 21 where y = 5000UG (21) y and UGare in s-l and m/s, respectively). The rheological properties were measured with a Couette viscometer (Haake) at shear rates from 10 to 1200 s-'. This closely corresponds to the range of shear rates encountered in bubble columns. Table I- summarizes the fluid consistency index k and the flow behavior index n of the various solutions.
Results and Discussion It has been theoretically obtained by Viswanathan (1985) that inviscid theory can be used for predicting circulation in bubble columns if eq 22 is satisfied where the symbols N = R e c ~ e D b , 2 ' 3 / F r 2 ( r ~ / R )> 1 013 / 3 744 (22) are explained in the Nomenclature section. Though the theory predicts the transition from viscous to inviscid conditions to occur ai an N value of 13 744, it is obvious that practically the transition may occur over a range of N values. However, if the N value for any system is an order of magnitude higher than the critical value, say about lo5, then it can be said with certainty that the inviscid theory can be safely applied. The estimated N values for the present system using the mean effective viscosities are of the order of 103-106,104-107,and 105-10s for 0.20-, 0.38-, and 1.0-m-diameter bubble columns. This clearly indicates that one is reasonable in using the inviscid model for a highly viscous system especially in large columns. This is confirmed further below. The data of UG2vs. tZ.' are plotted in Figures 2-4 for a 0.20-m-diameter column. It can be seen that the data fall
331
L
!
c
'4
,
0 01
0 02
c c3
1
[25
Figure 3. UG2vs. solutions.
for 0.20-m-diameter column and 1.0% CMC
on good straight lines for all cases except at low HID values and high CMC concentrations. The 'following conclusions are possible from these figures: (1)The good linear correlation in most cases confirms the validity of the inviscid circulation model. (2) The slope and therefore Ubr increase with HID until about HID = 3, after which ubr becomes constant. As H I D increases, the bubbles have a greater chance for coalescence and increasing their size. For HID > 3, bubble splitting also becomes important, and an equilibrium bubble size
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 89 Table 111. Experimental CMC % by wt
0.1 0.5 1.0 1.5 2.0
Values for Different Column Diameters and H I D Ratios D = 1.0 m D = 0.20 m D = 0.38 m, HID = 1 HID = 2 HID = 3 HID = 1 HID = 2
Ubr . . (m/s)
0.061 0.104 0.133
0.069 0.117 0.148
0.171
0.134 0.198 0.272 0.421 0.604
0.123 0.143 0.137
H I D = 3.5 0.105 0.201 0.273 0.357
0.164 0.195 0.201
Table IV. Predicted Range of d,, (mm) Values for Different Column Diameters and H I D Ratios D = 1.00 m D = 0.38 m D = 0.20 m 0.012-0.06,” 0.032-0.167,” CMC 7% by 0.012-0.06,” 0.033-0.170,’ 0.033-0.170,’ 0.033-0.170,“ HID = 2 HID = 3 wt HID = 1 HID = 1 HID = 2 HID = 3 , 5 0.1 1.06-0.95 1.15-1.03 1.90-1.70 0.5 2.32-1.96 2.60-2.23 4.62-3.96 2.46-2.22 3.49-2.98 4.72-4.35 1.0 3.42-2.90 3.73-3.32 8.89-5.42 3.28-2.70 5.02-3.20 8.86-7.50 1.5 26.35-21.80 4.23-3.40 7.05-5.75 19.0-16.0 2.0 8.30-6.58 “Range of U , in m/s.
cc3-
0 357 m /s
004/
.
D z 038r HID z 3 3
:Symbol 7. CMC Slope 1
0
00 01
21
ubr m i ’
I
38182 10384
3 2500 46660
0 421 0 604
I 002
3 03
004
(25
Figure 5. UG2vs. P for 0.38-m-diameter column.
0 01
002
0 03
€25
1
Figure 4. UG2vs. t2,5for 0.20-m-diameter column and 1.5% CMC solutions. C : lm
distribution is established which results in constant Ubr. (3) For the case where HID = 1, low UG,and high CMC concentrations, the data do not fall on a straight line because bubbles do not stay in the column for a sufficient time to get coalesced. This is substantiated by the data a t high HID where even the data points corresponding to low UG fall on the same straight lines (because of the availability of sufficient residence time for coalescence). In Figure 5, the data of UG2vs. c2.5 for a 0.38-m-diameter column are shown for different CMC concentrations. The Ubr values can be Seen to increase with CMC concentration. This is because of higher bubble sizes during the formation in solutions with higher CMC concentrations, which more than counterbalances the effect of higher viscosity. The data obtained in the larger 1.0-m-diameter column are shown in Figures 6 and 7. It can be seen that all the data corresponding to such a large column obey the predictions of the inviscid circulation model. The effects of
1
P 20
30
4
40
25
10 x c
Figure 6. UG2vs. c2.5 for 1.0-m-diameter column and H I D ratio = 1.
UG and CMC concentration are similar to those obtained in the smaller columns discussed above. For small columns, the data points at low U G do not fall on the straight line, whereas for the 1.0-m-diameter column all the data points fall on the line, thereby indicating validity of the inviscid model at low UG as well. The estimated Ubr values for the different cases are summarized in Table 111. These are used to calculate the
90 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 Table V. Predicted Range of U,(m/r) Values for Different Column Diameters, H I D Ratios, and CMC Concentrations D = 0.20 m D = 1.00 m D = 0.38 m, CMC 0.0124.06,n 0.012-0.06, 0.032-0.167, 0.033-0.17, 0.033-0.17, 0.033-0.17, %wt HID = 1 HID = 2 HID = 3 HID = 1 HID = 2 HID = 3 0.1 0.563-1.07 0.55-1.05 0.484-0.928 0.5 0.51-0.964 0.495-0.941 0.447-0.866 0.385-0.742 0.364-0.701 0.349-0.673 1.0 0.482-0.917 0.472-0.898 0.420-0.813 0.374-0.72 0.351-0.677 0.328-0.633 1.5 0.385-0.745 0.377-0.727 0.349-0.673 0.311-0.60 2.0 0.458-0.872 0.358-0.693 Range of UG in m/s.
r-/=30-
d’
Symbol %CMC
’
’ t
I
P 5yrrboi
,i‘ /
-
shows
i
1
5 104x
25
range c f b v i
IO la?d,,
15
20
[ml
for 1.0-m-diameter column and HID ratio =
Figure 8. Terminal bubble rise velocity (ubr)vs. mean bubble diameter (dJ.
volume-to-surface mean bubble diameters, d, as explained in the Theoretical Section. These are summarized in Table IV. The estimated Ubr and d,, values are similar to those reported in the literature (for example, see: Viswanathan, 1983;Viswanathan and Rao, 1984). It is interesting to note from Table IV that d,, decreases with increasing U G . Visual observations of bubble sizes in the 1.0-m-diameter column also were in conformity with the above trend. This is a feature unique to pseudoplastic systems and is explainable as follows. As UG increases, the shear rate increases, which leads to a decrease in the effective viscosity of the liquid phase (because n < 1in eq 20). The reduction in the effective viscosity is responsible for the smaller bubble sizes, because the bubble splitting effect is greater and, further, the bubble size during formation is smaller. This is perhaps the only feature which clearly differentiates Newtonian from pseudoplastic systems. A plot of Ubr vs. d,, obtained in the present study is shown in Figure 8; the horizontal lines represent the range of d, obtained for different UGvalues for which Ubr is fixed. A t small d,,, Ubr increases with d,,, but the increase becomes more gradual and almost zero later. The well-known constancy of Ubr for 3-8-mm-diameter bubbles for Newtonian systems seems to occur for a somewhat larger bubble size range in viscous pseudoplastic solutions of CMC. This is expected because viscous systems can maintain the “rigidity” of larger bubbles as compared to nonviscous systems, and Ubr increases with d,, only where this “rigidity” is maintained. The average circulating liquid velocity is a key parameter that determines the extent of turbulence (i.e,, inviscid conditions) in the bubble column. Therefore, it has been calculated according to the Viswanathan and Rao (1984) equation (23) and is included in Table V for the conditions u,= U b r ( g R u ~ / U b r 3 ) o ’ 4 (23)
studied here. It can be seen that the more critical parameters are gas velocity and column diameter, and HID and CMC weight percent are relatively insignificant variables.
Figure 7. UG2vs. ”L.
e2.5
Conclusions The inviscid liquid circulation model is applicable for bubble columns employing highly viscous pseudoplastic non-Newtonian solutions as well, especially for industrial-scale bubble columns. The isolated bubble rise velocities were obtained from the plots of UG2vs. t 2 5 , as suggested by Viswanathan and Rao’s (1983, 1984) inviscid circulation model. A new method was developed to obtain the volume-to-surfacemean bubble diameters using the estimated isolated bubble rise velocities; such estimated bubble sizes were found to be reasonable visd-vis the values reported in the literature for Newtonian systems. Although a direct check of the proposed method is possible only by measuring the bubble sizes directly, until such data and a comprehensive correlation become available, the method proposed here may be used with reasonable confidence. It was obtained that the mean bubble sizes increase with increasing liquid depths up to about HID = 3, after which an equilibrium bubble size distribution is established. The bubble sizes were found to increase with increasing CMC concentration, but significantly they decreased with increasing gas velocity for a given CMC concentration. This reduction of bubble sizes with increasing gas velocity was noted to be a characteristic feature of pseudoplastic systems, the reason for which was explained to be the result of increasing shear tending to split the bubbles. The whole procedure would be complete if a relationship is developed to predict the mean bubble sizes in nonNewtonian systems. The work in this direction is in progress.
Ind. Eng. Chem. Res. 1987,26,91-95
Nomenclature A = defined in eq 16 B = defined in eq 17 D = column diameter, m d,, = volume-to-surface mean diameter, m Eo = Eotvos number, defined in eq 9 Fr = ubr/(gD)0.5,Froude number, dimensionless g = gravitational acceleration, m/s2 H = clear liquid height, m Ho = defined in eq 13 J = defined in eq 10 K: = proportionality between w / r and \k in the cylindrical bubble column, m-4 k = fluid consistency index, Pad' M = Morton number defiied in eq 7 m = defined in eq 10-12 N = defined in eq 22, dimensionless R = column radius, m r = radial coordinate, m ro = sparger radius, m ReG = D U G p L / p L , Reynolds number Rebr = bubble Reynolds number, defined in eq 8 ReDbr = ( D U b r p L ) / p L , dimensionless U,= average liquid circulation velocity, m/s U, = superficial gas velocity, m/s Ubr = single bubble rise velocity, m/s Ubr,exptl = defined in eq 18, m/s w = vorticity, l / s y = vertical coordinate in three dimensions, m Greek Letters = defined in eq 10 y = shear rate, s-l pG = gas-phase density, kg/m3 p L = liquid-phase density, kg/m3 g = interfacial tension, N/m t = gas-phase holdup p L = liquid-phase viscosity, Pes CY
p,ff
91
= effective viscosity, Pa.s
pw =
viscosity of water, Pas
\k = stream function, m3/s T
= shear stress, Pa Registry No. CMC, 9000-11-7.
Literature Cited Bach, H. F.; Pilhofer, T. Ger. Chem. Eng. 1978, 1 , 270. Clift, R.; Grace, J. R.; Weber, M. E. Bubbles, Drops and Particles; Academic: New York, 1978; Chapter 7. Crabtree, J. R.; Bridgewater, J. ,Chem. Eng. Sci. 1969,24, 1955. Franz, K.; Buchholz, R.; Schugerl, K. Chem. Eng. Commun. 1980, 5 , 165. Godbole, S. P.; Schumpe, A.; Shah, Y. T.; Carr, N. L. AIChE J . 1984, 30, 213. Lamb, H.Hydrodynamics; Cambridge University Press: New York, 1932; p 236. Nakanoh, M.; Yoshida, F. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 190. Nishikawa, M.;Kato, H.; Hashimoto, K. Ind. Eng. Chem. Process Des. Dev. 1977,16, 133. Rietema, K.; Ottengraf, S.P. Trans Inst. Chem. Eng. 1970,48T,54. Schugerl, K. Ado. Bio. Chem. Eng. 1981,19,71. Schumpe, A.; Deckwer, W. D. Ind. Eng. Chem. Process Des. Dev. 1982,21, 706. Shah, Y. T.; Kelkar, B. G.; Godbole, S. P.; Deckwer, W. D. AIChE. J . 1982,28, 353. Viswanathan, K. Ph.D. Thesis, Indian Institute of Technology, New Delhi, 1983. Viswanathan, K. Encyclopedia of Fluid Mechanics, Cheremisinoff, N. P., Ed.; Gulf Publishing: Washington, DC, 1986. Viswanathan, K.; Rao, D. S.Chem. Eng. Sci. 1983,38, 474. Viswanathan, K.; Rao, D. S.Chem. Eng. Commun. 1984,25,133. Whalley, P. B.; Davidson, J. P. Inst. Chem. Eng. Symp. Ser. 1974, 38, 55.
Received for review August 9, 1985 Revised manuscript received April 24, 1986 Accepted May 30, 1986
Study of Char Gasification by Carbon Dioxide. 1. Kinetic Study by Thermogravimetric Analysis I s a o M a t s u i , Daizo Kunii, and T a k e h i k o F u r u s a w a * Department of Chemical Engineering, The University of Tokyo, Bunkyo-ku, Hongo, Tokyo, Japan
Coal char gasification with carbon dioxide was performed in a thermogravimetric apparatus. In the derivation of the kinetic rate equation by use of the thermogravimetric apparatus, the temperature investigated ranged from 1158 to 1253 K and the carbon dioxide partial pressure from 30.3 to 70.9 kPa. The reaction rate was independent of the particle size from 44 to 710 pm under these conditions. T h e volume reaction model and the grain model were examined to interpret the experimentally obtained conversion-time curves. The experimental results could be well expressed by the volume reaction model. T h e Langmuir-Hinshelwood-type rate equation was derived from the slope of the conversion-time curve. The rate constants in the Langmuir-Hinshelwood-type rate equation were obtained from the various levels of the carbon conversion. The effects of the level of the carbon conversion on the rate constants in the Langmuir-Hinshelwood-type rate equation were observed. The best understanding of reaction kinetics as well as the hydrodynamic model is necessary for the rational design of a coal gasifier. The hydrodynamic model which describes physical processes of gas-olid contact within the reactor is required to predict the conversions of gas as well as outgoing solids. The purpose of the present work reported in this paper is part of a larger program utilizing a small laboratory-scale fluidized bed gasifier to examine the possibility of using thermogravimetrically obtained kinetics of gasification for the prediction of the behavior of the fluidized bed gasifier.
* Author to whom correspondence should be addressed. 0888-5885/ 87 / 2626-009 1$01.50/ 0
This program proposes to demonstrate how the empirical kinetic equation obtained by thermogravimetric analysis .can be incorporated into a modified Kunii-Levenspiel model to simulate the fluidized bed gasifier for the design purpose. For the initial study along these lines, the gasification of the partly pyrolyzed char by carbon dioxide is chosen, since this is one of the simplest heterogeneous gasification reactions of carbon. The gasification of coal consists of two major reactions: pyrolysis and gasification of in situ formed char. Since the rate of the latter reaction is much slower than that of the former reaction, the volume of the gasifier is dependent on the gasification rate of char. The present reports consist 0 1987 American Chemical Society
