Ind. Eng. Chem. Process Des. Dev. 1986, 25, 925-929
925
D. L. Ind. Eng. Chem. Process Des. Dev. I98lc,
can Chemical Soclety, Chlcago, 1977, ORQN 1. Yang, S. H.; Satterfield, C. N. Ind. Eng. Chem. Process D e s . D e v . 1984, 23,20.
Satterfield, C. N.; Yang, S. H. Ind. Eng. Chem. Process D e s . Dev. 1984, 23,11. Shih, S . S.; Katzer, J. R.; Kwart, H.; Stiles, A. B. Presented before the Dlvlslon of Petroleum Chemlstry at the 173rd National Meetlng of the Ameri-
Received for review May 30, 1985 Revised manuscript received January 21, 1986 Accepted April 15, 1986
Satterfield, C. N.; Qultekin, S. Ind. Eng. Chem. Process Des. D e v . 1981b,
20,62. Satterfleld. C. N.; Carte,
20,538.
Solvent Selection and Batch Crystallization Allan S. Myerson' Department of Chemical Engineering, Pdytechnic Universlty, Brooklyn, New York 1 120 1
Stefanle E. Decker and Fan Welplng School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
The kinetics of crystal growth and nucleation of hexamethylenetetramine in ethanol, methanol, and 76 wt 'YO 2-propanol-24 wt % water and adipic acid in methanol, 2-propanol, and water were measured. This kinetic data was employed along with a supersaturation balance to calculate the mean crystal size obtained during batch crystallization for two cooling policies (constant nucleation rate cooling and linear cooling). The calculated mean crystal sizes were compared to those obtained from batch crystallization experiments. Results indicate that the combination of the supersaturation balance and experimental kinetics does not accurately predict mean crystal size. The results Indicate, however, that In most cases the calculated results correctly predict trends such as the solvent or cooling policy which produces the largest (or smallest) mean crystal size.
A wide variety of specialty chemicals are manufactured and/or purified by employing batch crystallization. Because these batch crystallizers are often used for a variety of different substances, they do not incorporate any design features which would aid in producing the desired crystal size distribution, habit, and purity for a specific system. In general the only parameters that can be varied in these batch crystallizers are the cooling curve employed, the solvent used, and the agitation rate employed. Most manufacturing operations employ a trial and error procedure by varying these parameters until they produce product of the desired specifications. A technique for the prediction of the optimal solvent and cooling curve to employ in batch crystallizers to produce the desired crystal size distribution and purity would be of great practical use. The effect of controlled cooling on the crystal size distribution (CSD) in batch crystallizers was examined by Mullin and Nyvlt (1971) and Jones and Mullin (1974). They demonstrated that controlled cooling would keep the supersaturation level within the metastable limits, thus decreasing the rate of nuclei formation and improving the CSD. A supersaturation balance was employed to calculate cooling curves in a number of different situations. It has long been known that variations in solvent can affect crystal growth and habit (hence crystal size distribution). Solvents influence the crystal growth through changes in the physical properties of the solution (viscosity, density, and diffusivity) and through changes in the solid-liquid interfacial energy. Bourne and Davey (1976a-c) related the change in interfacial energy through a surface
* Author to whom correspondence should be addressed. 0196-4305/86/1125-0925$01.50/0
entropy (CY)factor to changes in crystal growth mechanism and kinetics, for the growth of hexamethylenetetramine from various solvents. Davey (1976) observed variations in crystal habit in succinic acid crystals grown from various solvents. It is the purpose of this work to determine whether mean crystal size can be predicted for a given substance, produced in a batch crystallizer under a given cooling policy, by employing experimental growth kinetics in conjunction with supersaturation balance techniques.
Theory The supersaturation balance (Mullin and Nyvlt, 1971; Jones and Mullin, 1974; Jones, 1974) for a batch crystallizer may be written as eq 1. The first term represents the -dAc/dt = dc*/dt
+ k,A(t)A@(t) + k,Ac"(t)
(1)
supersaturation created by cooling, the second term the desupersaturation due to crystal growth, and the third term the desupersaturation due to nucleation. The first term may be written as eq 2 where C ( t ) is the transient dc*/dt = (dO/dt)(dc*/dO) = C ( t ) dc*/dO
(2)
cooling rate and dc/dO is the temperature dependence on solubility. The solution of eq 1 depends on the crystallization kinetics, the solubility relationship, evaluation of the area term A ( t ) ,and the cooling mode employed. If linear or natural cooling is used, the transient supersaturation is found; if constant nucleation rate cooling is used, the transient temperature is found. When the procedure of Mullin and Nyvlt (1971) is used, nucleation is approximated as a burst of pulses during a @ 1986 American Chemical Society
926
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986
given time interval. The total number of crystals present a t any time is the sum of seed crystals added and nuclei formed, given by eq 3 and 4, and the total surface area, given by eq 5.
/ ISOPROPANOL +WATER
t
N ( t ) = NSO+ CRn(t)At/a&o i=O
0,08! OD7
(3) (4)
O.O6i
(5) The linear growth rate is related to the mass growth rate by eq 6. Combining eq 2-6 results in eq 7. The mathe-
G = Fzg(0,L)Acg/3cup
-
t
I
l
(6)
matical description of batch crystallization presented in eq 1-7 can be employed in the calculation of optimal
s 0.02 O'OI
x
METHANOL
-dAc/dt = C ( t ) dc*/dO + 3Wso/&(L,2G(t)) + 3CknAcn(t)/L~,(LE;(t)G,i(t))+ k,Ac"(t) (7) cooling curves, supersaturation vs. time relations (for a given cooling curve), crystal size distributions, and average crystal size if the kinetics of crystal growth on nucleation are known.
Experimental Apparatus and Procedure The experiments in this study were divided into three parts. First the solubility of the material to the crystallized in each of the solvents was determined. Second experiments were conducted to determine the kinetics of growth and nucleation (in each solvent) by employing an MSMPR crystallizer and through growing single crystals. Finally, batch crystallization experiments were conducted in a jacketed batch crystallizer employing several cooling policies. The solubilities of hexamethylenetetramine and adipic acid in each of the solvents of interest were obtained experimentally in the range 15-40 "C at 5-deg intervals. Details of the procedure employed can be found in Decker (1984). Experiments to determine the kinetics of crystal growth and nucleation were obtained by employing a mixed suspension, mixed product removal crystallizer (MSMPR) operating at steady state. The crystallizer employed is similar to those described in the literature (Randolph and Larson, 1971). Details of the operating procedure can be found in Decker (1984). Additional experiments to determine the kinetics of crystal growth were conducted by employing an apparatus similar to that of Herndon and Kirwan (1982). Well-formed seed crystals free of visual defects are attached to the tip of a needle and rotated at approximately 10 rpm in the supersaturated solution. Further details of the apparatus and procedure are given by Decker (1984). At the conclusion of the experiment, the crystal is removed, dried, and weighed. The growth rate is calculated from the weight gain. Batch crystallization experiments were performed in a 1-L jacketed vessel of 5 in. in diameter. The temperature in the jacket was controlled by using a Neslab RTE 9D circulator and an MTP-5 controller programmer. A Lightnin Series 20 variable-speed motor was used to agitate the solution. In each case the solution was cooled from 40 to 15 "C. The programmer was used to control the rate of cooling. Controlled cooling curves were approximated as a series of linear steps, up to 99 being allowed in the programmer. The solution to be crystallized was held at the temperature above 40 "C required by the initial con-
ETHANOL
0.00 I
I
am
10.00 15.00
500
I
20.00
!
I
so00
25.00
BOO
I
40.00
TEMPERANRE dag. C
Figure 1. Solubility of hexamethylenetetramine in various solvents. SOLUBILITY OF ADIPIC ACID IN DIFFERENT SOLVENT
y 0 H
J 3
0.10
1
2 aoo
I
L- ; 200
IN WATER : : : :
250
i .
*
! ! ! ! *
t
30.0 34.0 400 TEMPERATURE, "C
I
450
Figure 2. Solubility of adipic acid in various solvents.
ditions. One liter was filtered and the temperature raised to dissolve any remaining particles and then transferred to the crystallizer. A t the end of a run the crystals were quickly filtered through a Buchner funnel, washed with acetone, and then dried. U S . Standard Sieves No. 18-170 were used to get the size distributions. Seed crystals were obtained from the unseeded runs. The arithmetic mean of a particular sieve cut was used.
Results and Discussion Solubility Studies. Hexamethylenetetramine is a fairly common organic compound. It is quite soluble in water (0.10 mol fraction at 25 "C); however, its solubility in water decreases with increasing temperature. Figure 1shows the measured solubility, in mole fraction, of HMT in three solvents: ethanol, methanol, and a mixture of 76 wt % 2-propanol-24 wt % water. The thermodynamic ideal solubility (Prausnitz, 1969) was calculated and is also shown. The solubility of adipic acid in ethanol, 2-propanol, and water along with the calculated thermodynamic ideal solubility is shown in Figure 2. Kinetic Studies. The growth rates of HMT in the solvents methanol and 2-propanol-water as a function of supersaturation were obtained from single-crystal studies. Only the overall growth rates were measured, and no at-
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986 927
Table I. Kinetics of Crystal Growth and Nucleation of Hexamethylenetetraminein Ethanol, Methanol, and 2-Propanol-Water crystal growth ethanol: G = 2.6 X 10-2Ac1.g6(m/s) (Bourne and Davey, 1976a methanol: G = (1.5 f 0.1) X 104Ac1.06'o.8 (m/s) 2-propanol-water: G = (1.3 f 0.1) X ~O"'AC'.~'~.' (m /SI nucleation ethanol: B = (5.0 k 2.0) X 10'0Ac2~6*0~8 methanol: B = (6.0 f 2.0) X 1013Ac4.0'2.0 2-propanol-water: B = (2.5 0.4) X ~ O ' A C ' . ~ ~ . ~
Table 11. Kinetics of Crystal Growth and Nucleation of Adipic Acid in Ethanol, 2-Propanol,and Water
wm seed cryst, wm solvent exptl theoret exptl theoret Constant Nucleation Rate Cooling ethanol 419 334 methanol 520 256 2-propanol-water 588 880 ethanol methanol 2-propanol-water
crystal growth ethanol: G = 4.7 X 104Ac1.03 2-propanol: G = 3.9 X 10-4Ac1.0 water: G = 4.01 X 10-5Ac'.02 nucleation ethanol: B = 7.2 X 1OsAc1.* 2-propanol: B = 2.8 X 108Ac'.6 water: B = 1.9 x I O ~ A C ~ . ~
Linear Cooling 404 257 455 138 415 657
Seeded Solutions-Constant ethanol methanol 2-propanol-water
tempt was made at determining the mechanism of growth. In these experiments the weight of the seed crystals employed ranged from 0.04 to 0.3 g (0.25-0.75cm in diameter) while grown crystals weighed from 0.045 to 0.40 g (0.26-0.76 cm in diameter). The change in crystal diameter was approximately 2-4% of the total diameter. The time elapsed during growth ranged from 20 to 60 min. The equilibrium temperature in all cases was 30 "C and undercooling ranged from 0.1 to 2.0 OC corresponding to supersaturations of 0.00024.0025 g of solute/g of solvent. The stirrer speed was identical for all runs. The data were fitted to a power law function of the form in eq 8 using linear regression. Results are given in Table I along with those of Bourne and Davey (1976a) for the growth of HMT in ethanol.
G = k,Acg
Table 111. Comparison of Calculated and Experimental Weight Mean Sizes for the Batch Growth of Hexamethylenetetramine wt mean size, final size of
(8)
Growth and nucleation kinetics can be obtained from size distribution data obtained from the steady-state operation of an MSMPR crystallizer. The conditions necessary for this are steady-state operation, no particles in the feed, and no attrition of particles. A balance on a crystallizer operated in such a manner results in a population distribution of the form in eq 9. A plot of log n vs.
n = no exp(-L/GT) (9) L gives a straight line with intercept no and slope ~ / G T , The parameter no is related to the nucleation kinetics by eq 10 where BO is the nucleation rate. A power law function Bo = noG (10) of the form Bo = k,AC" was used to fit the nucleation kinetic data. These results are given in Table I. Growth and nucleation kinetics of adipic acid in three solvents were determined from MSMPR experiments. The resulting power law equations for each solvent are given in Table 11. Batch Crystallization Studies. In this study three different batch crystallization operating policies were examined: (1)unseeded solutions cooled at a constant rate of nucleation (constant supersaturation), (2) unseeded solutions cooled linearly, and (3) seeded solutions cooled a t a constant nucleation rate. Equation 7 was solved numerically for two cases: linear cooling in which the term C ( t ) is known and constant nucleation rate cooling where the supersaturation is constant. The second case results in a definite time period since a constant level of supersaturation is maintained
Nucleation Rate Cooling Seed Size, 550 wm 577 473 850 770 659 426 950 728 1000 1395 777 904
Table IV. Comparieon of Calculated and Experimental Weight Mean Sizes for the Batch Growth of Adipic Acid under Given Operating Policies wt mean size, gm solv theoret exDtl Constant Nucleation Rate Cooling ethanol 983 513 2-propanol 723 496 water 291 273 ethanol 2-propanol water
Linear Cooling 759 424 203
354 346 236
between a given initial and final temperature. The total batch time obtained for this policy is then used for comparison in the fixed time problem of linear cooling. The summation term in eq 7 is incremented by one for each time step. The nuclei generated during all the previous time increments are then increased in size by the expression for G at the current value of supersaturation, temperature, and crystal size. The time increment chosen was either 5 or 10 s. A mass balance was used as a check to see if the mass nucleation and growth during a step agreed with the supersaturation created by cooling for the same step. In most cases the difference was less than 3%. Additional details may be found in Decker (1984). The cooling curves calculated for unseeded solutions of HMT cooled at a constant rate of nucleation are shown in Figure 3 along with the linear cooling curves for the same time period. Batch crystallization experiments were conducted for HMT and adipic acid in each of the three solvents employing the calculated constant nucleation rate cooling curves. Experiments were also conducted using a linear cooling policy covering the same temperature range and time period employed in the constant nucleation rate cooling experiments. In addition, one set of experiments for the HMT system was conducted employing constant nucleation rate cooling in a seeded solution. Seeds (2.5 g) were added to 1 L of solution. A typical experimental distribution is shown in Figure 4. The frequency histograms are plotted as a percentage by weight of the fraction retained between two sieves. The figure shows the difference in distribution between linear and controlled cooling for HMT in ethanol. The weight mean sizes obtained experimentally and those calculated from the supersaturation balance are given in Tables 111 and IV.
928
Ind. Eng. Chem.
Process Des. Dev., Vol. 25, No. 4, 1986
20.0\
15.0
0.0 26.0 4.0 60.080.0IO00 120.0 i O . 0 160.0 180.0 TIME ( M I N I
Figure 3. Calculated cooling curves for constant nucleation rate cooling in the HMT system.
I
CONSTANT NUCLEATION RATE
I
I
s 12.0 _ i 3
I
;
480+ 0 W
z 3 36.0
WEIGHTMEAN SIZE
c
w LT
8
24.0
CRYSTAL SIZEpM
Figure 4. Experimentally determined batch size distribution for the growth of hexamethylenetetramine from ethanol.
In the HMT system the predicted sizes were smaller than the observed sizes in the solvent ethanol and methanol (for all cooling policies) and were larger than the observed sizes in the solvent 2-propanol-water. In the adipic acid system the predicted sizes were larger than the observed sizes in all but one case (water-linear cooling). The crystal growth kinetics in the HMT system were obtained from single crystal growth experiments where care was taken to ensure that surface kinetics (not volume diffusion) was the limiting factor. In a batch suspension crystallizer, mass transfer (hence volume diffusion) often limits crystal growth rate. If this waa the case, the crystal growth rates used in the calculations would be too high, resulting in a prediction of a crystal size larger than the observed size. This was observed in HMT-2-propanolwater. Secondary nucleation is often significant in the crystallization of organics. When this is the case the nucleation rate constant, k,, is a function of suspension density and impeller speed. If the value of k , employed
in the calculation is too low, the average crystal size calculated would be larger than the observed size. This could explain the results observed in the adipic acid system. The results show that the supersaturation balance technique failed in general to predict the mean crystal size. The actual prediction of the mean size, however, is not the only indication of the value of this technique. The prediction of the cooling policy and/or solvent system which produces the largest (or smallest) mean size from a group of possibilities would itself be of value. On this basis results are much better. The predicted results for all cases in the adipic acid system follow the experimental trends. The model correctly predicted that for all solvents, constant nucleation rate cooling would produce a larger mean size than linear cooling and that ethanol would produce crystals of the largest mean size (qsing either cooling policy), 2-propanol the second largest, and water the smallest. The results in the HMT system also correctly predicted that in all cases, constant nucleation rate cooling produces a larger average crystal size than linear cooling. In addition, the model also correctly predicted that 2propanol-water would produce crystals of the largest mean size. The model did not, however, predict the correct trend in average crystal sizes for the other two solvents. It is probable that more accurate kinetic growth and nucleation data, taking into account agitation, and masstransfer conditions would result in better predictions.
Acknowledgment The financial support of the Research Laboratories, Eastman Chemical Division, Eastman Kodak Co. for a portion of this work is gratefully acknowledged. Nomenclature A = surface area of crystals, m2 Bo = nucleation rate, no./(s L of solvent) c, c, = concentration, g of solute/g of solvent c* = equilibrium concentration, g of solute/g of solvent Ac = supersaturation, g of solute/g of solvent C ( t ) = cooling curve, d/dt, OC/min CSn = crystal size distribution g = crystal growth rate order G = growth rate, m/s k, = area shape factors k, = growth rate constant, m/s/[(g of solute/g of solvent)g] k , = nucleation rate constant, [(gof solute/g of solvent)/s]/(g of solute/g of solvent)"] L = size of crystal, m L,, = length weight mean of size distribution, m L,-L, = shortest, middle, and longest crystal dimensions, m MT = slurry density, g/L n = nucleation rate order n, no = population density function, no./m N = number of crystals, no./g of solvent t = time, s T = temperature, "C W = weight of seed crystals, g/g of solute x 2 = solubility in mole fractions Subscripts and Superscripts 0 = initial f = final ij = summation subscripts s = seeds n = nuclei Greek Symbols = volume shape factor 0 = temperature, K p = density of crystal T = residence time (Y
Ind. fng. Chem. Process Des. Dev. 1986, 25, 929-938
Literature Cited Bourne, J. R.; Davey, R. J. J . Cryst. (;row1976t1, 34, 230. Bourne, J. R.; Davey, R. J. J . Cryst. Qowih 1976b, 36,278. Bourne, J. R.; Davey, R. J. J . Crysf. &wih 197(lC, 36, 287. Davey, R. J. J . Ctyst. Qowih 1976, 34, 109. Decker, S. M.S. Thesis, Georgla Institute of Technology, Atlanta, 1984. Hemden, R. C.; Kirwan, D. J. AICMSymp. Ser. 1982, 79(215), 19. Jones, A. G. Chem. Eng. Sci. 1979. 29, 1075. Jones, A. G.; Mullin, J. W. Chem. Eng. Sci. 1974, 2 9 , 105.
929
Mullln, J. W.; Nyvtt, J. Chem. Eng. Sci. 1971, 2 6 , 369. Prauenitz, J. W. Mleculer ThemmYynamics of Fluhi phese Equlllbrium; Pren tlce Hall: Englewood Cliffs, NJ, 1969; p 391. Randolph, A. D.; Larson, M. A. Theory of Partlcukte Processes; Academic: New York, 1971.
Received for review July 1, 1985 Revised manuscript received March 25, 1986 Accepted April 15,1986
Fast Rate Coal Conversion in a Hypervelocity, High-Temperature Gas Jet Woo K. Park' and Rkhard L. Mayer Mound-Monsanto Research Corpmtlon, Miamisburg, Ohio 45342
An experimental study on fast rate coal conversion in a hyperveiocity, high-temperature gas jet showed that the yield of hydrocarbon products could be significantly increased by using a faster rate process incorporating jet-mixing induced fast heating under controlled temperatwe-timsreactkm medium conditions. Experimentation was carried
out in which powdered coal was used as the primary feed, and conditions were varled to achieve reaction temperatures from 900 to 1250 OC, reaction times from 3 to 60 ms, reaction media from neutral to reducing conditions, and coal-togas mass ratios from 0.2 to 0.5. The results of the experimentation indicated that up to 86% of the coal can be converted to gaseous products within 5-ms reaction time and that the product slate for hydrocarbons and/or synthesis gas may be controlled to provide up to 50 % hydrocarbons (by volume) in the product gas.
Background Coal gasification reactors have typically involved heating the feed coal to some desired temperature, while subjecting it to steam and/or oxygen to provide a product gas (typically a mixture of CO and H,)which could be used as a fuel or further processed to provide chemical feedstock. This approach, although successful for reliable production of easily transportable energy, fails to take advantage of the hydrocarbon makeup of coal, as virtually all hydrocarbon bonds are destroyed. Conversely, liquefaction reactors, which do exploit the hydrocarbon nature of coal, typically rely on the use of complicated operating conditions, such as dissolving the coal in hydrogen-donor solvents in the presence of catalysts under high pressure, which result in expensive processes for which the reliability is questionable. An advanced coal processing technique, which takes advantage of the reliability of gasifier operating characteristics while also utilizing the hydrocarbon nature of coal, is to rapidly subject the coal to a high reaction temperature for only a short period of time, thus causing partial breakdown of the coal structure, and then quenching the reaction to preserve these intermediate reaction products which contain significant amounts of valuable hydrocarbons. The results published on these short residence time, flash pyrolytic process studies reveal that the optimum residence time for such processes usually lies between 0.1 and 10 s depending on the reactor type and its operating mode for the selected product slate (Talwaker, 1983; Fufari, 1982; McCarthy et al., 1981). Operation using reaction times significantly less than 0.1 s (e.g., 20-100 ms) was impractical in most cases because less desirable products, such as heavy tars and oils, were produced and/or the total yield was low, thus indicating the intrinsic limitations of these reactors. A review of the literature (Woodburn et. al., 1974; Nettleton and Stirling, 1974; Kansa and Perlee, 1980) on 0 196-43051861 1 125-0929$0 1.5010
the shock heating of coal and also theoretical calculations indicated, however, that reaction times much less than 100 ms and resulting high hydrocarbon yield were feasible, since the rates of occurrence of physical phenomena, such as particle heating and devolatilization, were still the limiting factors rather than rates of major chemical reactions. This led to the development of jet reactors in both batch and continuous-flow modes that are capable of achieving coal processing at a faster rate with optimum reaction times of 5 ms or less. A study was, therefore, carried out by using the batch jet reactor, which verified that much faster rate reactions than those previously reported could be achieved with up to 90% conversion of coal to gaseous and liquid products (Park and Mayer, 1981). Based on the resulta of this study, experimentation with the continuous-flow jet reactor was conducted with the purpose of developing a fast rate coal conversion scheme for optimum control of the rate of coal devolatilization and stabilization of primary reaction products for the production of fuels and/or chemicals and for identifying and examining potential reaction pathways leading to these products. Process Description An overview of the coal conversion mechanism for the jet reactor is shown in Figure 1. The figure shows that thermal energy generated in a high-temperaturegas jet by combustion of an H2-02 mixture is used to heat the coal rapidly. As the coal undergoes fragmentation and recombination upon heating, the coal and its intermediate products continuously interact with the reactive combustion gas. The sign in the figure denotes the preferred pathways, and the "-n sign denotes the nonpreferred pathways for the production of a high yield of more desirable products, consisting of light hydrocarbons. It is believed that the fast rate reactions induced by the jet reactor force the preferred pathways to become the pre-
"+"
0 1988 American Chemical Society
