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Ind. Eng. Chem. Process Des. Dev. 1980, 19, 352-358
Computer Model for Crystal Size Distribution Control in a Semi-Batch Evaporative Crystallizer Subhendra C. Mukhopadhyay and Mary Anne Farrell Epsteln' Department of Chemical Engineering and Applied Ctwmktty, Columbia University, New York, New York 10027
A semi-batch, perfectly mixed, evaporative crystaHizer was modeled to study changes in the moments of the crystal size distribution (CSD) with operating conditions. Although the specific model developed was based on an actual laboratory crystallizer, the approach used c a n be applied to both laboratory and industrial systems. Published correlations for growth dependent on supersaturation and for nucleation dependent on both supersaturation and magma density were used. The effect of operating variables on average crystal size, CSD coefficient of variation (C.V.), solis fraction, and supersaturation were examined and criteria for minimization of the coefficient of variation were derived. These criteria were used in computer simulations to determine the extent of C.V. control achieved and their effect on the average crystal size.
Introduction Crystal size distribution (CSD) is one of the most important aspects of an industrial crystallizer for separation of crystals from the mother liquor, the subsequent washing and drying of the crystals, and finally the end use of the product. Randolph and Larson (1962) were among the first to recognize the usefulness of the statistical population density function in the modeling of mixed suspension crystallizers. They used the population density function together with the concept of a mixed suspension mixed product removal crystallizer to derive a general population balance equation for continuous crystallizers. These equations have been successfully used to determine the growth and nucleation kinetics from experimental crystal size distributions. Numerous references are available in the literature in the field of continuous crystallizers (Moyers and Randolph, 1973; Randolph and Larson, 1971; Timm and Larson, 1968, Randolph, 1971; Desai et al., 1974; Hulburt and Stefango, 1969 Randolph, 1977). There are, however, many instances in practice where batch crystallization must be used, such as in the recovery of toxic compounds; in addition, the equipment required for batch crystallization is simpler than that for continuous operation and a wide range of operating variables may be studied within a short period of time (McNeil et al., 1978). The aforementioned studies on continuous systems are not directly applicable to batch crystallization. First of all, batch crystallization is essentially an unsteady-state operation. Hence, such assumptions as constant growth and nucleation rates and constant suspension density cannot be made. In spite of these inherent difficulties in analysis, batch crystallization remains important in industrial practice, especially for systems having apparent stability to highly supersaturated solutions with prolonged induction periods for crystallization (Misra and White, 1971). The present study is directed toward the application of population balance and process analysis techniques to investigate a semi-batch, isothermal, seeded evaporative crystallizer for an aqueous citric acid system. Semi-batch operation is a practical start-up mode for many continuous systems. It offers the additional advantages of another controllable variable, such as feed rate or evaporation rate in the case of an evaporative crystallizer, which can lead to product quality improvement and longer operating times than traditional batch operation. An aqueous citric acid system was selected for investigation for several reasons: citric acid is commercially recovered by evaporative batch crystallization, aqueous citric acid solutions have been 0196-4305/80/1119-0352$01 .OO/O
observed to sustain high supersaturations (Mullin and Leci, 1972), and experimental growth and kinetic data for this system have been reported recently (Sikdar and Randolph, 1976). Special emphasis was given to examining the interaction of growth and nucleation processes on the size dispersion of product crystals (coefficient of variation, C.V.) and to strategies of C.V. control based on changing the input variables.
Literature Review As background for this work, the literature for batch crystallizer operation was reviewed because there is little published work on semi-batch operation and the transient operating conditions for a semi-batch crystallizer are expected to be similar to those encountered in batch operation. A review of published batch crystallization studies indicated that cooling crystallizers were investigated most frequently. The objectives of these studies were determination of crystallization kinetic parameters as functions of such operating variables as stirring speed, cooling rate, seed CSD, and impurity levels (Nyvlt, 1976; Nyvlt et al., 1976; Kane et al., 1974; Janse, 1977). Only the study by Baliga (1970) reported the operation of a batch evaporative crystallizer. He derived a general population balance equation assuming the crystal growth to be a product of time and characteristic crystal length. He, however, neglected the volume fraction occupied by the solute phase with respect to the total suspension volume. In his experiments with an aqueous K,S04 system, the CSD's obtained appeared to have grown from the initial crystal size distribution formed during the high supersaturation existing at start-up. Nyvlt (1976) and co-workers (Nyvlt et al., 1976; Sohnel and Nyvlt, 1976) examined the effect of the quantity of seed, cooling rate, and the initial supersaturation on the CSD for batch systems. His theoretical studies predicted that there existed a range of seed concentration for which both growth and nucleation affected the product CSD; for seed concentrations exceeding this range, the product CSD resulted from the growth of the seed crystals and could be predicted completely from the seed CSD. Initial supersaturation did not appreciably change the product CSD compared to that obtained for saturated conditions a t start-up because the initial supersaturation was rapidly removed by the seed crystals. These predictions were verified by experimental studies. Kane et al. (1974) used the population balance approach to derive the dependence of the CSD and supersaturations 0 1980 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980 353
with time for seeded batch crystallizers assuming growth rate independent of size and secondary nucleation rate proportional to one of the moments of the CSD. They demonstrated that thLe CSD moment important for secondary nucleation could be inferred from the initial transient of the supersaturation vs. time curve. In his recent thesis, Janse (1977) investigated CSD's in batch systems in order to develop guidelines for design and operation of batch crystallizers. The development in time of the CSD for unseeded operations was simulated for assumed homogeneous and secondary nucleation mechanisms and two growth rate expressions: for the latter, he considered size independent growth rate as well as the case when growth dispersions occur due to increasing size. In his experimental work with aqueous solutions of potassium dichromate and potassium alum in unseeded batch cooling crystallizers, he established that the product CSD was actually a superpositon of two distributions due to homogeneous and secondary nucleation mechanisms and the relative distance between these two distributions depended on the growth rate expressions. The question of control of batch crystallization to attain specific CSD characteristics was first addressed completely by Jones and Mullin (1974) and Jones (1974) for cooling crystallizers. Their studies were motivated by earlier investigations of Ayerst and Phillips (1969) and Garside et al. (1972) on linear cooling modes and that of Mullin and Nyvlt (1971) on programmed cooling (i.e., the maintenance of supersaturation within the metastable limits as first suggested by Griffiths, 1925). In their programmed cooling model, Jones and Mullin predicted reduction of nucleation and consequent increase in mean crystal size and decrease in the C.V. compared with the CISD obtained with natural cooling. Similar findings were presented by Jones for batch studies with K2S04in a laboratory scale Crystallizer. Using empirical nucleation and crystal growth rate expressions, he predicted an increase in the terminal crystal size by controlled cooling as compared to natural or linear cooling a t a constant nucleation rate. However, the experimental results did not quite agree with theoretical prediction for either the change in crystal length or improvement in C.V. The discrepancies between the theoretical predictions and experimental results reported by Jones underscore the need to investigate other control strategies for batch crystallizer operations. Theory In the present study, a realistic semi-batch crystallization system was conceived and modeled mathematically. The system equations, a set of five coupled ordinary differential equations obtained from population balance and mass balance, were solved numerically on a computer by fourth-order Runge-Kutta integration. Established growth and nucleation models jfor aqueous citric acid systems were used with realistic initial conditions suitable for seeded operations. The resulting moments and concentration profile described the entire system for the time period considered. These moments can also be used to recover the distributions as described by Hulburt and Katz (1964). Mathematical Modeling of a Semi-Batch Evaporative Crystallizer. (a) Population Balance Equation and Its Solution by the Moment Transformation Method. For a Continuous Mixed Suspension Mixed Product Removal (CMSMPR) crystallizer, the population balance equation is
of the crystallizer suspension is maintained constant by adding feed solution with no seed crystals (Le., ni = 0), Q, may be considered as evaporation rate Q, with no entrainment (Le., n = 01, and considering size-independent growth rate (McCabe, 1929), the above reduces to an an -+G-=O at aL Using moment transformation method as developed by Hulburt and Katz (1964), we obtain the following moment equations (Mukhopadhyay, 1979) (3)
dm,/dt = Gmo
(4)
dm,/dt = 2Gm,
(5)
dm3/dt = 3Gm2
(6)
where mot ml, m2, and m3 describe the number, length, area, and volume related moments about the origin for the crystal size distribution, respectively. The equation describing the concentration of the system would be developed from the overall mass balance
From the physical property data for aqueous citric acid solutions, it has been found that density of citric acid solution depends strongly on concentration (approximately a linear function) but is relatively insensitive to temperature. Thus from the plot of density vs. concentration p = 985 + 465C (8) For an isothermal, semi-batch, evaporative crystallizer the depletion of total crystallizer volume by evaporation is to be made up by addition of fresh feed solution, so that the total crystallizer volume (of suspension) remains constant and Qi = Q,. For this case, eq 7 reduces to
By definition t(t) = 1 - Jmk,L3n(t,L)dL = 1 - k,m3
(10)
Substituion of the above expressions for c (eq lo), d t l d t (eq 111, and p (eq 8) into eq 9 yields Qi
Hence, the complete set of system equations is given by eq 3, 4, 5 , 6, and 12. (b) Expression for Coefficient of Variation (C.V.). The average particle size as well as the size dispersion, given by C.V., are two important parameters of any distribution as obtained from a crystallization operation. The C.V. is given in terms of the moments of the distribution about the origin as
an - 8, Q, _ ---n--n--
d(Gn) (1) at ~7 v aL For a semi-batch evaporative system, where the volume
dmo/dt = noG = Bo
so that
354
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980
.
100
a 90.
dt n
.
80
which on simplification after substitution of the moment eq 3, 4, and 5 reduces to d(C.V.) --
/e@---:.-.-.-.-
-
e ,"
,fl ,g,
I
I
*& . .. . ' .
A ,*
, , , I
. . . TO=BOO
'
---
___ ___ where Bo = k , M ~ ~and s ~ G. = ~ ~ (Sikdar and Randolph, 1976). Substituting numerical values for mo, ml, m2, m3, and also corresponding to any chosen kinetic order for nucleation, eq 15 reduces to d(C.V.) -- f(s) (16) dt Carrying out the analysis further, it can be easily established that d(C.V.1/dt monotonically increases for higher values of supersaturation, s, which is expressed as s=---C
C, 1-C,
1-C
0
465(s + 2.436) (s + 3.436) - Pc
+ 3k,Gm2
) ]1,,/
-
p,)
,032 'OS
f
,016
.a12
From eq 19 it can be observed that a decrease in the value of Qi or pi will result in a decrease in supersaturation-time gradient and hence minimize C.V. by maintaining a low supersaturation. Solution Method Before we solve the five coupled, nonlinear ordinary differential equations (eq 3, 4, 5, 6, and 12) numerically using an IBM-360 digital computer, it is necessary to identify the kinetic expressions for growth and nucleation rates to be used for the semi-batch, initially seeded, evaporative crystallizer for an aqueous citric acid system. Also the intital conditions for the numerical solution need to be determined. (a) Kinetic Expressions. Experimental studies on growth and nucleation mechanisms for an aqueous citric acid system by Sikdar and Randolph (1976), as adapted in the present investigation, lead to the following
G = k,s0.65
[ k g = exp(14.28) exp(-3584/T)X 10-9 (20)
BO = k,MTiS0.54 [k, = exp(-8.735) exp(4781/T)
X lo6] (21)
The rate constants kg and k, were evaluated at 50 O C (323 K) and MT = kvpcm3. In the secondary nucleation rate expression, MT is the most dominant parameter since it
IW
IZS 1M 175 2W 225 250 27$ I RINUTES
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I
/
. . . TO=800
---
TO-400, T.20 T 0 = 4 0 0 UNSAT.T=ZO TO=400 SRTIUNSRT *T=IO
___ ___
' 8
.con
0
[465(1 - k,mJl (19)
75
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.Wd
ds dt = ((s + 3.436)2[ %pi V
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T0=400.T=20 TO=dOO UNSflT.T=ZO TO=4OO SATIUNSRT r T = l O
TlflE
(17)
For isothermal operation at 50 "C, C, = 0.709 and hence s + 2.436 C= (18) s + 3.436 Equating dC/dt to eq 12 yields
25
;:--
'
'
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Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980
355
Table I. Summary of Simulation Conditions Studied" ~~~~~~
run
conditions
A-1
Figure
i = 0.5, saturated feed, constant volumetric flow rate i = 0.5, feed rate halved at time t = 50 rnin i = 0.5, feed rate halved at time t = 20 min = 1,similar to A-1,2, and 3, respectively
A- 2 A-3 A-4,5,6 A-7,8,9
= 1.5, similar t o A-1, 2, and 3, respectively
A-10
= 0.5, feed rate doubled a t time t = 20 min = 1,same as A-10
A-11 A-1 2 A-13
run considered as a base case; C.V., average crystal size, and crystal volume fraction plotted against time C.V. improved; av crystal size and crystal volume fraction grew a t a slower rate C.V. improved better than A-2; av crystal size and crystal volume fraction grew even slower than A-2 similar observations for C.V. and crystal volume fraction; av crystal size grows to a max. of 350 r m after t = 170 min similar observations for C.V. and crystal volume fraction except that improvement in C.V. is more pronounced; av crystal size grows to a max. and then drops gradually C.V. increased very rapidly, av crystal size and crystal volume fraction grew a t a faster rate similar observations for C.V. and crystal volume fraction, av crystal size attains a max. at t = 60 min, then drops to a constant value at t = 170 rnin same as cases A-7, 8, and 9 there was not much deviation from the base case A-4
i = 1.15, same as A-10 i = 1, feed rate constant at base cond, feed conc changed between satd. and unsatd. every 50 min i = 0.5, 1, 1.5, respectively, feed rate constant a t base cond, feed concn changed to unsat. ( 6 5 wt %) a t time t = :20min i = 0.5, 1, 1.5, respectively, change between satd. and unsatd. ( 6 5 wt %) feed every 1 0 min a t base case flow rate i = 0.5, saturated feed a t constant volumetric flow rate i = 0.5, feed rate doubled at time t = 20 min i = 1,similar t o B-1 and B-2, respectively
A-14,15,16
A-17,18,19
B-1 B- 2 B-3, 4 B-5, 6
results/comments
observations indicate n o appreciable change due to change in concentration only
same as above
run considered as a base case; C.V., av crystal size and crystal volume fraction plotted against time C.V. was higher, also av crystal size and crystal volume fraction grew at a faster rate similar observations for C.V. and crystal volume fraction, but av crystal size approaches a constant value of 334 p m similar observations for C.V. and crystal volume fraction except that change in C.V. is more pronounced; av crystal size grows t o a max. and then drops
i = 1.5, similar to B-1 and B-2, respectively
a Bo = knMTiso.YI,i = 0.5, 1.0, 1.5; C(0) = initial condition a t time zero (i.e., t h e instant of seeding) = 71.72 wt % corresponding to supersaturation s = 0.1. Runs: A, basis turn-over period 400 min; B, basis turn-over period 800 min.
i
/
1
0
25
50
75
100
125
TIflE
.
150 175
200
225
250
275
300
tlINUTES
Figure 2. Effect of different feed flow rates on solute volume fraction for Bo = k,M+"".&', where i = 0.5, 1.0, 1.5; base turn-over period = 400 min.
crystals (based on previous data on batch experiments), total seed charge per unit suspension volume will be 1.33
X lo3 x 0.709 X 0.05/100 = 0.47 kg/m3, where 1.33 is the specific gravity of the saturated solution. For spherical crystals with diameter L = characteristic length, volume shape factor lz, = 7r/6 = 0.52. Total number of crystals NT per unit volume is given by NT X hv(LaJ3 X pc = 0.47, where La, = 40 pm = 40 X m. NT = 9.2 x IO9 crystals/m3. Consider the instant of seeding as the beginning of crystallizer operation, so that at zero time: number of seed crystals/volume = mo(0)= 9.2 X lo9 crystals/m3; length of seed crystals/volume = ml(0)= 36.8 X lo4m/m3; area of seed crystals/volume = k,mz(0) = 46.24 m2/m3; and volume of seed crystals/volume = k,m,(O) = 0.3083 X m3/m3; corresponding to the intital supersaturation s = 0.1, C(0) = 0.7172. (c) Numerical Solution. The system equations were solved numerically by using the fourth-order Runge-Kutta method. An important aspect of the study was to establish a suitable time interval for the integration step. Several time steps were considered ranging from 2.4 s to 16 min, and it was found that a time step of 1 min was adequate for the particular system studied. Several simulation runs were carried out on a computer and the program calculated among other parameters the coefficient of variation of the distribution, average particle
356
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980 1W r
a loo90
I
a
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,*e-
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lo
0
"
0
25
50
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75
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.
I
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,032
"
150 175 x4
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225
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t
. . . TO400
. ..
TO=4OO TO=800. T-50 T0=800.T=20
---
___
___
'ooal
,012
t
~0=200.1=20
---
___ ___
1
,004
0 1 ' 0
25
'
50
0
25
50
75
IW
I25
TIflE
'
'
75
100
'
125
TIflE
'
150
.
'
"
175 200 225
'
250
'
'
275 )w
flINUTES
Figure 3. Effect of different feed flow rates on coefficient of variation (a) and average crystal size (b) for the nucleation mechanism Bo = knMT0,5~0,M; base turn-over period = 400 min.
size, and fraction of the total batch volume occupied by solute. It was found necessary to keep track of volume fraction of solids in order to determine the time at which the batch operation should be discontinued before the suspension becomes too heavy. Average size of the crystals is an indication of growth pattern. Size dispersion occurs due to the competing effects between growth and nucleation, and coefficient of variation is a measure of this phenomenon. (a) Computer Simulations. In the present study of an isothermal, semi-batch, evaporative crystallization system, temperature was kept constant at 50 "C and the evaporation rate (and thus the input rate of feed solution) was varied within realistic limits for the model under consideration. The ratio of crystallizer suspension volume (V)to the input volumetric flow rate (Qi) is the turn-over period for a batch crystallizer which is similar to a nominal residence time for continuous crystallizers. The value of the turn-over period selected for the base case was around 400 min which compared favorably with actual commercial crystallizers. It was apparent from the simulation runs that batch operations should be discontinued earlier than one turn-over period based on the volume fraction of solute, the value of which should not be allowed to exceed 0.5-0.6
TO=800.T=50 T0=800,T=20 To=200,T=20
150 175 200
225 250 275 3W
MINUTES
Figure 4. Effect of different feed flow rates on coefficient of variation (a) and average crystal size (b) for the nucleation mechanism Bo = k,M+O."; base turn-over period = 400 min.
for adequate mixing of the solution. Table I summarizes the various simulation conditions studied.
Results and Discussion The computer simulations as detailed in Table I essentially featured two basic modes of operation-effect of changing feed flow rate and feed concentration. The importance of these two controllable variables for minimization of the coefficient of variation was identified in eq 16 and 19. Since the crystallizer volume was kept constant, changes in the flow rate were directly reflected by the turn-over period. The cases studied simulated changes in flow rate of about 300% equivalent to turn-over periods ranging from 200 to 800 min. Consequently, the effect of changing flow rate was more pronounced than the effect of changing feed concentration since density variation between saturated (70.9 w t 70)and unsaturated solution (65 wt % ) was only about 2% (Figure l). As stipulated in the semi-batch model, the rate of generation of solid phase depends only on the feed flow rate-this is evidenced also from the linear plots for volume fraction of crystals vs. time, irrespective of the secondary kinetic parameter i for MT in the nucleation rate expression (Figure 2). Depending on this kinetic parameter i, Bo would have a higher or lower value leading to a more or less pronounced effect on coefficient of variation. It may
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980 357 '@I
I
N
;
s e/ Y
10
'OM
1 6' I
b
...
---
___ ___
TO-400 TO-BOO. T.50 TO=BOO.T=20 T0=200. T=20
decreases. Effects of step changes in feed concentration (unsaturated at t = 20 min) as well as a periodic change (saturated/unsaturated every 10 or 50 min) were also negligible compared to the effect of flow changes due to reasons mentioned earlier (Figure 1). Conclusion In this study, guidelines for control of semi-batch, evaporative crystallizer were studied. It was established that feed flow rate is the most important variable for control of coefficient of variation of the crystal size distribution. It was also observed that the magma density MT is closely related to C.V. through the nucleation rate expression. The average crystal size follows a definite trend depending on the kinetic order for MT. The volume fraction of the crystals in the batch helps in determining the time interval at which the batch operation should be discontinued, and accordingly, one can decide about the type as well as the time of control action to achieve the optimal end results with respect to C.V., average crystal size, and the overall yield of the process. Nomenclature Bo = nucleation rate, number of nuclei/(m3 min) C = concentration, wt % (kg/100 kg of solution) C* = concentration, kg of solute/kg of water C, = equilibrium concentration, wt % CSD = crystal size distribution C.V. = coefficient of variation G = linear growth rate, m/min i = kinetic order in nucleation expression k , = area shape factor, dimensionless k , = growth rate constant in eq 20 k , = nucleation rate constant in eq 21 k , = volume shape factor, dimensionless L = length, m La, = average length of seed crystals, pm II = lower limit of seed crystal size, pm l2 = upper limit of seed crystal size, pm mj = jth moment of the distribution = u n ( t , L )dL m4O) = initial condition for the jth moment hdT = weight of crystals/volume of crystallizer, kg/m3 n = population density function, number/(length x volume) ni = crystal population density in feed n, = seed crystal population density N T = total number of crystals, number of crystals/m3 no = nuclei population density Qi = input feed flow rate, m3/min Q, = output flow rate, m3/min Q, = volumetric flow rate of condensed vapor, m3/min s = supersaturation, kg of solute/kg of water t = time, min T = temperature, K TO = turn-over period, (V/Qi), min V = volume of the crystallizer (volume of the cryst. suspension), m3 Greek Symbols t = fraction of total suspension volume that is liquid, dimensionless p = density of solution, kg/m3 p c = density of crystals (1540 kg/m3) pi = density of feed solution, kg/m3 pv = density of condensed vapor (i.e., water), kg/m3 Literature Cited
so"
0
25
so
7s
100
.
12s 154
TIRE
115
m
225
2M
m
3Cc
MINUTES
Figure 5. Effect of different feed flow rates on coefficient of variation (a) and average crystal size (b) for the nucleation mechanism R ' = ~ J ~ T base ~ tuirn-over ~ ~ s ~ period ~ ~= 400 ; min.
be indicated here that MT is a more dominant parameter in the nucleation rate expression than supersaturation, which does not vary much during the effective period of batch operation. Hence for a constant feed flow rate (i.e., fixed solute resource) as i increases more nuclei surfaces are available for crystal growth and consequently the coefficient of variation of the distribution becomes larger. Thus a more dramatic improvement in C.V. is expected by decreasing feed flow rate when the system has a higher kinetic order. This is a.pparent upon comparison of Figures 3,4, and 5. In addition, better control of C.V. is achieved by reducing the flow rate at an earlier time, Le., a t t = 20 min instead of at t = 50 min. The trend of average particle size is different: for i = 0.5, it grows larger with time; for i = 1.0, it approaches a constant value of approximately 350 pm (it may be recalled here that the average size of seed crystals was 40 pm); for i = 1.5, it reaches a maximum value and then drops (Figures 3, 4, and 5). This phenomenon can also be explained by considering the dependence of Bo on MT. For lower values of i, the number of new nuclei generated is not large enough to offset the linear growth of the crystals, but for higher values of i, after an operating period sufficient for attaining a large value of MT,the number of new nuclei generated is so large that average linear crystal size
Ayerst, R. P., Phillips, M. I.,"Industrial Crystallization", p 58, Institution of Chemical Engineers, Symposium, London, 1969. Baiiga, J. E., Ph.D. Dissertation, Iowa State University, 1970. Desai, R. M., Rachow, J. M., Timm. D. C., AIChE J., 20, 43 (1974). Garside, J., Gaska, C., Mullin, J. W., J. Cryst. Growth. 13/14, 510 (1972). Garside, J., Shah, M. B., Paper 689 presented at 72nd AIChE Annual Meeting, San Francisco, Calif., 1979. Griffiths, H., J. SOC. Chem. Ind., 44, T.7 (1925). Hulburt, H. M., Katz S., Chem. Eng. Sci., 19, 555 (1964). Hulburt. H. M.. Stefango, D. G., Chem. Eng. Prog. Symp. Ser., No. 95, 65, 50 (1969).
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Janse, A. H., Delft University of Technology, WTHD, 102 (1977). Jones, A. G., Chem. Eng. Sci., 29, 1075 (1974). Jones, A. G., Mullin, J. W., Chem. Eng. Sci., 29, 105 (1974). Kane, S.G., Evans, T. W., Brlan, P. L. T., Sarofirn, A. F., AIChE J., 20, 855 (1974). McCabe, W. L., Ind. Eng. Chem., 21, 30 (1929). McNeil, T. J., Weed, D. R., Estrin, J., AIChE J., 24, 728 (1978). Misra, C., White, E. T., Chem. Eng. Prog. Symp. Ser., No. 710, 67, 53 (1971). Moyers, C. G.,Randolph, A. D., AIChE J., 19, 1089 (1973). Mukhopadhyay, S. C., M.S. Thesis, Columbia University, 1979. Muiiin, J. W., Leci, C. L., AIChE Symp. Ser., No. 727, 68, 8 (1972). Mullin, J. W., Nyvlt, J., Chem. Eng. Sci., 28, 369 (1971). Nyvlt, J., Wurzelova, J., Cipova, H.,Collect. Czech. Chem. Commun., 41, 29 (1976). Nyvlt, J., Collect. Czech. Chem. Commun., 41, 342 (1976).
Randolph, A. D., Larson, M. A,, AIChE J., 8, 639 (1962). Randolph, A. D., Larson, M. A., "Theory of Particulate Processes", Academic Press, New York, 1971. Randolph, A. D., Chem. Eng. Prog. Symp. Ser., No. 170, 67, 1 (1971). Randolph, A. D., Paper 53a presented at AIChE Meeting, New York, 1977. Slkdar, S.K., Randolph, A. D., AIChE J., 22, 110 (1976). Sohnel, O., Nyvlt, J., Krlst. Tech., 11, 239 (1976). Tlrnrn, D. C., Larson, M. A,, AIChE J., 14, 452 (1968).
Received for review April 16, 1979 Accepted March 12, 1980
Presented in part at the 72nd Annual Meeting of the American Institute of Chemical Engineers, San Francisco, Calif., Nov 1979.
Reactivity Correlation for the Coal Char-CO, Reaction J. T. Sears," H. S. Muralidhara, and C. Y. Wen Department of Chemical Engineering, West Virginia University, Morgantown, West Virginia 26506
The kinetics of the coal char-C0, reaction have been studied in the absence of effects of particle size, bed size, and gas film diffusion. The reaction rate is shown by multiple regression to fit an expression involving intrinsic carbon activity and dominant terms involving the weight percent calcium oxide (from ash) and residual oxygen in the char. There is a cross-product interaction term between the weight percent CaO and oxygen which indicates an apparent catalytic mechanism. A correlation coefficient of 0.978 was obtained for the proposed expression. Good agreement was obtained with previous published results on reactivity. If the activation energy for the intrinsic carbon reactivity is taken at 70 kcal/mol, a value of 55 kcal/mol for the "catalytic" reactivity is found.
Introduction The kinetics of the coal char gasification reactions has been extensively studied due to its importance in coal gasification schemes. Both fundamental and applied studies have been performed in order to predict the reactivity with all types of coal chars and to examine methods of enhancing the reactivity with an added catalyst. It has been established that calcium compounds, alkali oxides, and organic oxygen have some effect. Unfortunately, in most investigations, parameters which influence the reaction were not all isolated or controlled, so the rate information is not clearly delineated in the literature. The reaction of coal char and carbon dioxide is nominally a solid-gas noncatalytic reaction. However, it has been shown that mineral matter catalytically enhances the reaction (Muralidhara and Sears, 1978; Hippo and Walker, 1975; Chauhan et al., 1977). Muralidhara and Sears (1978) observed that the rate of reaction with C02 increases in direct proportion to the calcium content, whether the calcium is inherent in coal or added to coal externally by doping. Walker et al. (1968) and Muralidhara and Sears (1978) showed the dependence of rate on initial oxygen content (coal rank) of the coals. This paper examines how the C-C02 kinetics are affected by oxidized mineral matter and the presence of oxygen in the char. It discusses a mechanism for the effects due to calcium oxide and organic oxygen content. Experimental Section A Fisher TGA (thermogravimetric analyzer) Model 120 P (Figure 1) with Cahn electrobalance was used in this investigation to conduct experiments a t atmospheric pressure and temperatures in the range of 850-1100 "C. The hangdown tube and concentric flow tube (2) of the
TGA are constructed of quartz. The Cahn RG electrobalance (6) converts the sample weight into electrical potential. A Cahn time derivative Mark I1 computer automatically gives the time derivation of this potential, A potential recorder has two channels and records the sample weight and time derivative of weight change simultaneously. The linear temperature programmer Model 260 P sets the oven a t a desired temperature f 5 "C. Preparation of the Chars. All the chars used for determining the kinetic reaction rate with carbon dioxide were prepared as follows. The coal particles (37-49 pm, i.e., -325 +400 mesh) were placed in a specially fabricated nichrome wire basket. The TGA was flushed with carbon dioxide for at least 1.5 h to ensure a nonoxidizing atmosphere for devolatilization. Lack of oxygen was verified by gas chromatography. Then the preheated furnace was raised outside the quartz tube. The temperature of the sample rapidly reached temperature inside the tube and was thereafter maintained at reaction temperature. The samples were devolatilized in the atmosphere of C02 for a period of 2 min. (During this time the particles are heating up and pyrolyzing but minimal reaction with COz occurs.) For noncaking coals, the reaction rate was determined in the same apparatus immediately following the devolatilization by adjusting the temperature at this time. For caking coals the furnace was lowered after devolatilization at 900 "C. The devolatilized chars were crushed and classified according to the requirement of particle size. The particles were then placed in the basket again, and the procedure was repeated for reaction at the appropriate reaction temperature. The chars obtained for determining the oxygen content and calcium content were prepared as follows. Four grams of coal sample were spread evenly on a rectangular plate and enclosed in a chamber which had provision for a gas
0196-4305/80/1119-0358$01.00/00 1980 American Chemical Society
