An Investigation into the Nucleation Kinetics of Urea Crystallization in Water by Means of Crystal-Size Distribution Analysis Kulln D. Lodaya, Leslie E. Lahti,' and Millard L. Jones, Jr. Department of Chemical Engineering, The University of Toledo, Toledo, Ohio 43606
The nucleation kinetics of the crystallization of urea in water was investigatedusing a continuously stirred, mixed product removal crystallizer. Growth and nucleation rates were determined by using crystal size distribution analysis of the product and a steady-state population balance. Nucleation rate was then correlated in terms of suspension density, growth rate, and impeller velocity, using simple power function models. Crystal growth rate was found to obey McCabe's AL law. Secondary nucleation was observed only at 3 OC and higher supercooling. Perfect needle shaped crystals were formed at 3 to 4 OC supercooling, slightly veiled crystals were formed at 5 to 6 OC supercooling, and at 7 to 12 OC, dendritic crystal growth was observed.
Introduction Crystallization is characterized by the simultaneous occurrence of nucleation and crystal growth, which combine to produce a mixture of crystals of various sizes. The rate a t which nuclei are formed is of primary importance in determining crystal size distribution and crystal growth, and is intimately related to them. Crystal growth and size distribution are, in turn, of importance in the design and sizing of crystallizers, and in product finishing processes such as centrifugation, filtration, and drying. The study of nucleation kinetics is greatly hampered by the difficulty of observing nuclei and by the difficulty in measuring supersaturation. In the present work crystal size distribution (CSD) analysis and growth rate were used to bypass these difficulties to determine nucleation kinetics for urea in water solution. This in turn, was correlated with the important process variables. Theory and Previous Work Nucleation. Nucleation phenomena are broadly categorized into three different mechanisms: homogeneous, heterogeneous, and secondary. Homogeneous nucleation is defined as the random formation of primary crystals, as a result of thermal, density, or concentration fluctuations in the bulk phase. Homogeneous nucleation has been expressed by different models such as Meir's metastable model, the VolmerWeber model, and the kinetic theory model. Nucleation due to the presence of foreign particles is called heterogeneous nucleation. Secondary nucleation implies formation of nuclei because of the presence of the solute crystals. La1 et al. (1969) found that the secondary nuclei are formed due to direct phenomena such as initial breeding, collision breeding, and needle breeding. Evans et al. (1974) studied the mechanism of the secondary nucleation of ice in a vigorously agitated crystallizer. In a continuous stirred mixed product removal crystallizer, operated at 10%by weight of ice, crystal-crystallizer collisions were responsible for 55% and crystal-crystal collisions for 20% of the overall nucleation rate. The nature of the residual 25% was not understood but was speculatively attributed to fluid shear. Growth. As pointed out by Canning and Randolph (1967), it i s generally believed that crystal growth takes place in three steps: (1)the solute must diffuse from the bulk of the solution to the solid interface of the crystal; ( 2 ) at the interface a surface reaction occurs during which the solute becomes a part 294
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
of the crystal lattice and the heat of crystallization is liberated; and ( 3 ) the liberated heat must diffuse to the bulk of the solution. In most crystallization systems, the solute diffusion resistance is less than the resistance offered by the surface reaction. For these systems, a common simplifying assumption made is that McCabe's AL law holds (1929). This law states that geometrically similar crystals of a given material suspended in the same solution grow a t the same linear rate. Population Balance. Randolph and Larson (1962) developed a general steady-state population balance which describes the number of crystals as a function of size. The relationship is applicable to the MSMPR crystallizer used in this work, and is given in eq 1.
n = no exp(-L/rT)
(1)
Crystal Size Distribution. Larson and Randolph (1965) developed an experimental method of obtaining nucleation and growth kinetic data from the crystal size distribution (CSD) and the steady-state population balance equation. In their analysis, the growth rate was assumed to be independent of crystal size, first order with respect to supersaturation and that McCabe's AL law held. Many studies are reported in the literature using this technique but will not be mentioned here since the systems are different. However, Bennett and Van Buren (1969) studied the urea-water system using a CSMPR crystallizer. Nucleation kinetics were expressed by
J = KN(r)"
(2)
where a varied from -2.66 to -4.45 depending on different types of crystallizers.
Experimental Equipment Figure 1 is a schematic flow diagram of the equipment used in this study. Feed flow rate from the constant head tank was adjusted using a needle valve and measured using a rotameter. This combination provided a reliably constant feed over the course of a run. Bath temperature was controlled within f O . l "C using continuous cooling and cyclic heating. The crystallizer was agitated with a 2-in. diameter, 3-blade marine propeller with a blade angle of 45" and a pitch twice its diameter (a phototachometer was used to measure stirrer speed). The crystallizer was cylindrical in shape, 3314 in. in diameter and 5 in. in height up to the overflow port. Crystallization temperature was measured using a carefully calibrated copper-constantan thermocouple.
Table I. Modes of Nucleation and Growth ~
~~
Nucleation Type of growth
Temperature ( A T , "C) 1 2
3 4 5
6 7
8
9 10 11
12
-
Absence of crystal solid contact
Presence of crystal solid contact
N o nucleation
No nucleation No nucleation Contact breeding Contact breeding Contact breeding Contact breeding Contact breeding and needle breeding Contact breeding and needle breeding Contact breeding and needle breeding Contact breeding and needle heeding Contact breeding and needle breeding Contact breeding and needle breeding
No nucleation No nucleation No nucleation
Good growth Good growth Veiled growth Veiled growth Dendritic, spikewise or brooming growth Dendritic, spikewise or brooming growth Dendritic, spikewise or brooming growth Dendritic, spikewise or brooming growth Dendritic, spikewise or brooming growth Dendrite, spikewise or brooming growth
No nucleation No nucleation 90nucleation No nucleation No nucleation No nucleation No nucleation
No nucleation
Experimental Procedure Feed was prepared in two polyethylene tanks and introduced into the constant head tank. Feed was introduced into the crystallizer, which was then operated at constant conditions-temperature, flow rate, and agitation speed-for 8 to 10 residence times to reach steady state while taking intermediate samples of the product. Then samples were taken, filtered immediately, and washed with isopropyl alcohol saturated with urea. This removed the water from the crystals without dissolving appreciable urea. The crystals were then dried a t 110-115 O F for 2 to 3 days to remove the last traces of alcohol while minimizing the decomposition of urea. The crystals were then weighed on the Mettler H-14balance and the crystal size distribution was determined by means of sieving screens. T o determine modes of growth and nucleation, urea solutions saturated at different temperature were prepared using a solubility correlation for urea-water systems obtained by Lee and Lahti (1972). Volumetric flasks of fifty 50-cm" capacity were filled with solution and were supercooled to different degrees. Then one crystal of urea was added to the flask and the flask was shaken. Once nuclei were formed they were allowed to grow for about 0.5 h. T h e dried crystals were observed under the microscope and photomicrographs of the crystals taken as shown in Figure 2 and summarized in Table
F
G
N Figure 1. Experimental equipment: A, constant head reservoir; B, needle valve; C, relay; D, microvolt ammeter; E, rotameter; F, reference junction (ice); G, constant temperature bath; H , heater; J , crystallizer; K, contact thermoregulator; L, pump; M, coolant reservoir; 0, cooler; N, filtration flask; P. drierite flask; S, vacuum pump.
r =
($1
(3b)
1.
Results Experimental Data. Six sets of experiments were conducted at stirrer rpm's 600,650,710, 800, 850, and 900. Each set consisted of five experiments a t different crystallizer temperatures between 3 and 16 "C. Feed solution was maintained approximately saturated a t room temperature. No attempts were made to operate a t other temperatures or concentrations, because a more elaborate control scheme would be required to prevent nucleation in the lines and/or freezing in the crystallizer. Data Treatment. Crystal size distribution data were fitted to eq 1, the population balance of Larson and Randolph (1965) by least squares, and extrapolated to zero to obtain the nucleation rate by the equations (3a)
where no is the nuclei population density, r is the growth rate, and (dN/dT)L,o and J are the nucleation rate. This is illustrated in Figure 3. The validity of this analysis depends upon the validity of McCabe's AL.law, which states that (dL/dt) is constant for all sizes of crystals. Plots of In ( n )vs. L are straight (within the percent standard deviation* of 7%), implying that McCabe's 1L law is fulfilled. (Percent standard deviation = standard deviation/mean X 100.) Correlation. The most significant variables in the correlation of nucleation rate were found to be growth rate, suspension density, and agitation. Linear multiple regression was used to fit these to a simple power function model, giving (4) Another correlation using power per unit volume was also made by Lodaya (1975),but is not shown here in the interest of brevity. Figure 4 shows a plot of the calculated rate from !nd.Eng. Chem., Process Des. Dev., Vol. 16. No. 3, 1977
295
A T = 50%
A T = &6"C
A T = 4.0"C
A T =5O"C
A T -70°C
AT
= B0"C
A T = 56°C
AT =6xpC
A T =ILS"c
AT :IZ.O"c
Figure 2. Photomicrographs of urea crystals at different degrees of supercooling
14
t
PLOT OF IN(") VS L,EXP 3, SAMPLE I
JEXP Figure 4. Plot of the nucleation rate calculated ( J C dusing eq 4 vs. experimental nucleation rate (Jexpj. this equation vs. the experimental rate with a correlation coefficient of 0.91. Modes of Nucleation and Growth. As can he seen from Table I, nucleation was not observed a t supercoolings up to 2 "C, with or without seeding, and no homogeneous nucleation occurred a t supercoolings up to 12 "C, when held for a t least 90 min. Secondary nucleation was observed a t supercoolings of 3 "C or higher after the samples were seeded. As seen in Figure 2, perfect needle-shaped crystals formed a t supercoolings of 3 and 4 "C, slightly veiled crystals formed a t supercoolings of 5 and 6 "C, whereas dindritic growth was observed a t supercoolings of 7 "C and greater. These needle like crystals could not grow during the vigorous agitation employed in the crystallizer studies. Discussion McCabe's AL Law. The growth rate of urea obeyed McCabe's AL law because of the straight line plot of In (n)vs. 296
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L. This indicated that the crystallization of urea in MSMPR crystallizer was surface reaction controlled, as discussed earlier. Nucleation Rate. The nucleation rate was found to correlate using eq 4 with a maximum error of f15%. This deviation was probably due to errors in the crystal size distribution caused by the crystal shape and secondarily to experimental errors such as variation in temperature within f O . l "C, rpm of stirrer within f 2 % , feed rate within f0.4 cm3/min, and to slight eccentricity and small inclination of the stirrer in the crystallizer. The correlation given by eq 4 indicates a dependence of nucleation rate on the negative power of the growth rate, which realistically is a measure of the supersaturation. This is in agreement with the earlier work on this system by Bennett and Van Buren (1969). A probable explanation is that the
nuclei wash out, during the low growth period, as was discussed by Randolph and Cise (19'72). In order to explore this further, experimental conditions should be varied so that more than 2% (by weight) of the total crystals formed are smaller than 47 p. Also the population density of the smaller particles would need to be measured. Suspension Density. As observed from the correlation, the nucleation rate varies almost linearly with the suspension density. This indicates the presence of secondary nucleation due to dislodging of the number of aggregates of solute molecules which are loosely held at a crystal surface. The importance of secondary nucleation was also confirmed by experiments on the mode of nucleation and growth where supercoolings of greater than 3 "C were required. Effect of Stirring Rate. The above correlation indicates a strong dependence of the nucleation rate on stirrer rpm. This provides strong evidence that secondary nuclei are generated by collisions of the seed crystals with the impeller blades. These observations are consistent mechanistically with the work of Strickland-Constable et al. (1969), Clontz and McCabe (19711, and Evans et al. (1974).The rpm or the power input of the stirrer are a measure of the energy input for crystal-crystal, crystal-impeller, and crystal-wall collisions. Thus, the results indicate that an increase in the energy input for crystal-crystal, crystal-impeller, and crystal-wall collisions increases the nucleation rate. This indicates the presence of collision breeding on contact nucleation.
CAS = equilibrium concentration J = nucleation rate, number/L min Jcal = calculated nucleation rate using eq 4 J e x p = experimental nucleation rate K N = constant MT = suspension density, g/100 cm3 of slurry N = number of crystals per unit volume n = population density, number11 L no = population density of nuclei ( L = 0) L = characteristic crystal length, p r = growth rate, k/min rpm = stirrer speed, revolutions per minute T = turnover time, min N = supersaturation ratio, C.A./CAS
Literature Cited Bennett, R. C., Van Buren, M., Chem. Eng. Prog. Symp. Ser., 65 (95), 44-49 (1969). Canning, T. F., Randolph, A. D., AlChEJ., 13, 5 (1967). Clontz, N. A., McCabe, W. L., Chem. Eng. frog. Symp. Ser., 67 (110), 6 (1971). Evans, T. W., Margolis, G., Sarofim, A. F., AlChEJ., 20 (5), 950 (1974). Lal, D. P., Mason, R. E. A,, Strickland-Constable,R . F., J. Cryst. Growth, 5, 1-8 ( 1969). Larson, M. A., Randolph, A. D., Chem. Eng. Prog. Symp. Ser., 61 (55). 1-13 (1965). Lee, Fu-Ming, Lahti, L. E., J. Chem. Eng. Data, 17, 304-306 (1972). Lodaya, K. D., Ph.D. Dissertation, University of Toledo, 1975. McCabe, W. L., lnd. fng. Chem., 21, 30-33 (1929). Randolph, A . D., Cise, M. D., AlChEJ., 16, 806 (1972). Randolph, A . D., Larson, M. A,, AlChEJ., 8, 639 (1962).
Nomenclature CA = bulk concentration
Received for reuieu: April 21, 1976 Accepted February 24, 1977
Development of an Electrolytic Dissolver for Plutonium Metal Earl J. Wheelwright* Chemical Technology Department, Battelle Memorial hstitute. Pacific Northwest Laboratories, Richland, Washington 99352
Richard D. Fox Research Department, Atlantic Richfield Hanford Company, Richland, Washington 99352
A critically safe dissolver was fabricated and demonstrated during the dissolution of ten plutonium buttons and two plutonium ingots totaling 23.9 kg of metal. Maximum dissolution rates exceeding 400 g/h and an average rate exceeding 300 g/h were demonstrated with a dissolver current of 150 A or 12 A/in.2 of anode surface. The production of a solids-free dissolver solution was demonstrated by maintaining a dissolver solution composition of 10 M HN03-0.05 M HF. High dissolver efficiency was achieved by the unique design of a "traveling" cathode which maintained a minimum, constant separation from the plutonium metal surface as that surface dissolved.
Introduction The conversion of plutonium metal to an aqueous solution suitable for reprocessing by conventional methods has been a continuing problem. Small, thin pieces of metal can be satisfactorily dissolved in 15 M "03 containing up to 0.1 M H F at boiling temperatures, but the passivity of plutonium metal in such systems greatly restricts the dissolution rate. Rapid dissolution of plutonium metal in 3-4 M "03-0.13 M HF was reported by Miner et al. (1969) at the Rocky Flats Plant, Golden, Colo.. but they reported that the reaction is difficult
to control. In the process currently used in metal reclamation facilities at the Hanford Atomic Plant, Richland, Wash., plutonium metal buttons (hemioblate spheroids with diameters up to 4 in.) are mechanically sectioned into smaller pieces and burned to oxide. The oxide is then screened, pulverized when necessary, and dissolved in 15 M HNO, containing H F at boiling temperatures. The oxide is difficult to dissolve, often requires several hours per batch, and frequently an insoluble residue remains when the dissolution is terminated. Electrolytic dissolution of normally passive metals in "03 was first demonstrated by Pitzer (1951). He anodically dislnd. Eng. Chem., Process Des. Dev., Vol. 16, No. 3 , 1977
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