Low-Purity Beet House Sirups.
..
Crystallization Rates of Sucrose
M
OST quantitative studies of the crystallization rates of sucrose and other compounds have been confined t o solutions of the pure, or nearly pure, substances. Kucharenko (6),Silin (9),Smolenski and Zelazny (10),Breedweld and Waterman (I), and others have measured therates of crystallization of pure sucrose and studied the effects of relatively small amounts of anumber of organic and inorganic substances on the rate. There is little available information concerning rates of crystallization from sirups in the purity range encountered in raw side operations in a beet house. Since the efficient recovery of sugar from these sirups has an important bearing on the operation of the sugar end as a whole, information concerning the factors which influence crystallization is of considerable value. I n the study of the crystallization rates of pure substances the Noyes-Whitney equation ( 7 ) is generally assumed to be valid :
f
=
A . R . NEES AND E . H . HUNGERFORD The Great Western Sugar Company, Denver, Colo
.
A method is described for determining the rates of crystallization of sucrose from low-purity beet house sirups. The method is sufficiently accurate to show the trend and order of magnitude of the effects of purity, supersaturation, and temperature. At low purity ranges the quantity and character of the nonsugars have more effect on rates than temperature and supersaturation, so that laws governing the crystallization of pure substances are no longer applicable. The boiling of thinner massecuites at higher temperatures is indicated.
K S (C - C,)
where C = concentration at time t C, = concentration a t saturation S = total crystal area K = crystallization constant
Jenkins (5) applied the integrated form of the equation 0.4343 K S =
*,'
1t log ("(C -- C.)
and found the K values to be constant for the crystallization of napthalene, urea, ammonium nitrate, and acetanilide from various solvents, indicating that crystallization is a first order reaction. He found, however, that the addition of collodion to naphthalene solution in methanol gave K values which conformed to the r e q u i r e m e n t s of a second-order reaction. Jenkins also showed, in the case of pure substances, that the viscosity, 7 , had a constant effect, expressed by the relation
IC=---constant 9 0.59
and that this relation no longer held when collodion was added to the solutions. Calculations by the authors also indicate that there is no constant function of viscosity, which accounts for the change of rate of crystallization of sucrose with changes in purity of the solut i o n . T h e influence of impurities, e s p e c i a l l y a t their high concentrations, is such that the simple laws which appear to govern the behavior of pure s u b s t a n c e s can no longer b e a p p l i e d . I n the following discussion the results have been reported in a n em-
(Above) IRRIGATING SUGAR
BEETSIN COLORADO
893
INDUSTRIAL AUD EKGISEERING CHEMISTRY
894
J-OL. 28, ?-0. 8
\\ab then loRered to the saturation point. A t this time a sample nas carefully withdrawn without loss of water. This sample nas used for the determination of purity and impurity-water iatio. A veighed quantity of sugar, 25 to 35 per cent of the T? eight of sirup, M hich had been heated to the sirup temperature, nas then added, taking care to avoid loss of moisture. The temperature was maintained at the saturation point for one houi to allow time for thorough admixture of the sugar crlstals and sirup. At the end of this mixing period the temperature was lomered as quickly as possible to a predetermined value, such that the supersaturation coefficient mas about 108. This temperature nas maintained throughout the test. About 45 minutel. Rere usually required to reduce the temperature and establish uniform conditions. At this point a sample TTas quickly drann into a small centrifugal basket, previously heated to the temperature of the massecuite, and the mother liquor was spun off Subsequent samples were taken at sufficiently small time intervals to permit the construction of a satisfactory time-purity curve (Figure 2). Samples were usually taken a t 5-minute intervals during the first hour, at 15-minute intervals during the next 2 hours, and less frequently thereafter as the rate of purity change became slower. Individual tests were continued for from 24 to more than 100 hours.
Analysis of Sirups a n d Calculation of Rates FIGURE 1. MINIATURECRYSTALLIZER
pirical fashion, and no attempt has been made to formulate definite laws. The rate of crystallization of sucrose from high-purity solutions can be measured by determining the increase in size or weight of single large crystals suspended in solutions under definite conditions of concentration and temperature. This method was used by Kucharenko ( 6 ) ,who made a comprehensire study of the effect of temperature and supersaturation on the rates of crystallization from pure solutions and of the influence of the presence of relatively small amounts of certain nonsugars, such as caramel, calcium oxide, calcium chloride, and sodium carbonate, on the rate of crystal growth. The authors (4)have also used the method in studying the effect of raffinose and other substances on the rate of growth and crystal habit. The method, however, is not suitable for the study of lowpurity sirups. The rate of growth is so slow that the time required to obtain a significant increase in the weight of the crystal would almost surely permit the spontaneous formation of new crystals; the viscosity of the sirup is so high that circulation over the face of the test crystal becomes difficult; the high viscosity also makes it difficult to remove the sirup quantitatively from the crystal a t the end of the test. There is the further objection that the conditions imposed by the method are so different from those obtaining in actual practice that application of the results t o factory operation is questionable. A simple and direct method has not yet been de5, 8 vised by which the rate of deposition of sugar can be determined for the conditions existing in the raw pans $6 and crystallizers. The method described in the following paragraphs mas finally adopted for this work. It ua leaves much to be desired. Careful technic, both in mechanical manipulation and in analytical procedure, is required to obtain satisfactory results.
The sample of sirup taken immediately before the addition of "seed" was cooled to room temperature, weighed. and diluted to approximately 40 per cent dry substance and again weighed to determine the exact dilution. True sugar mas determined by the double enzyme method or by the double acid method of Osborn and Zirch (8) and dry substance by the method of Brown ( 2 ) . From these figures the true purity, dry substance, and impurity-water ratio of the original sirup nere calculated. Considerable care n a s taken in making this analysis, since it \vas used as the basis for calculating the results of the test. Apparent purity, based on direct polarization (on deleaded solutions) and oven-dry substance, was dctermiiied on the diluted mother-liquor samples taken during the run. The true purity of these samples was calculated by applying a correction to the apparent purity. This correction was based on the difference between direct polarization and true sugar as determined on the original sirup sample. The magnitude of the correction is proportional to the amount of impurities present. Thus, if R correction of 0.4 is required on 100 - 60 a 70-impurity sirup, a correction of 100 - 70 X 0.4 is required ~
on a 60-purity sirup. This correction is justifiable only where identical impurities are concerned and where polarizations are made a t approximately the same concentration. Both of these conditions were conformed to in these tests.
FIGCRE2. TIME-PURITY CURVESi~ 40" C.
2
Zb7
The Method -4 miniature crystallizer (see Figure 1) of 0.5-cubic foot (14 liters) capacity, water-jacketed for temperature control and equipped with a helical ribbon scroll for continuous mixing, was used. A thermostatically controlled mater bath and a circulating pump were provided for maintaining the desired temperatures. Sirups of known composition as to dry substance and true sucrose and of known solubility were made UP, and a Tvekhed quantity was transferred to the clean, dry crystallizer. The temperature was at C. for an hour or to dissolve crystals which may have formed during the transfer. The temperature
TIME IN t i R 5 .
Since loss of water m-as inevitable in the separatioll of the their true dry substance had to be armother liquor rived a t by calculation. The calculation is based on the impurity-water ratio of the original sirup, which remains constant throughout the test, and the true purity of the mother liquor as determined above. The relationship is indicated by the following equatioil :
AUGUST, 1936
ISDUSTRIAL .4XD ESGIXEERING CHElIISTRY
10,000 ~ _ :; dry .5utFtalice = -~ 100 - purity of mother liquor
'0°
+
-
(_1 )
impurity-n-ater ratio
At this point the following data are ayailable: the iiiipuritj-water rat,io, which remains constant, the composition a i d weight of original sirup, the solubility of sugar (previously determined) in the sirup, the weight' of sugar crystals used as seed, the purity and percentage dry subst,aiice in tlie inother liquor a t various t,ime inkrvals during the period of the test. The rate of deposition of sugar, in graiiis per square meter per hour a t any given supersaturation, is calculated froin these data. The calculation involves three steps: ( I ) the calculation of the gross rate of crystallization of sugar a t various purities-i. e.. the grams crystallized per unit time; (2) the calculation of crystal surface exposed a t the time t'hese purities were reachetl: ant1 (3) the calculation of supersatnratioii coefficients. GROSSR a n : O F CIZYST.ILLIZ.ITIOS.The first - t q ~is to ])lot a time-purity curre for each test with the true purity of inot,her liquor as ordinate and time in hours as abscissa (Figure 2 ) . The dope of the curve a t any point represents the rate of change of the purity a t that point. The follon-ing calculation shows how the value of the tangent (slope) is applied to the rate determination. Since the water reiliains coiistaiit throughout, it is conrenient to uye that as a reference suhstance and t o express the other components of tlie systeni in terins of grams per 100 gra11:s of water. Thus dry ~uh-raiic.c, (D. 8.)per 100 \rater = 100 ( c C dry zubstancc-, (2: 100 - ' 2 dry suh-tance Conibiiiirig Equation- 1 aiitl 2 and simplifying:
\vliei~ca =
895
impui,ity-\wter ratio
P = t r u r purity
1)ifierentiatiiip Equation 3 with respect to t h e , 1: d(D. S.) - 10,000 a , dP (100 - P)' dt dt ~
(4)
The loss of dry substance per 100 water repre3ents the deposition of a corresponding quantity of wgar iC. S.)on the seed crystals; therefore, \vli(ir(, IZg = gruss rate of crystallization
The teriii dP, dt is the tangent to the tiiiie-purity curre a t point P , and its numerical value can he obtained hy laying a straight edge tangent to the curve at the desired point and reading off tlie intercept 011 the cciordinates. Substituting this value in Equation I ,the grois rate of crystallization, in grains of sugar per 100 grams water per kLour,is obtained. The sugar used for seeding CRYSTAL AREA CALCULATIOS. the crystallizer was carefully screened, and that portion was retained which was finer than 50 and coarser than 70 mesh. The number of crystals per grain was determined by an actual count of ~ e i g h e dportions. Therefore the average weight of each crystal was known, and the total number of crystals used in a given test could be calculated. This number remained constant throughout the test. The size of t,he crystals, and consequently their area, increasetl as time proceeded and a correction for this increase had to be made before the rate of crystallization per unit area could be tleterniiiied for any given t iiiie , Kucharenko (6)deterniinetl the relation between the surface in square meters (S) and the weight in grams (W) of a single crystal to be:
S
0.000412T1~''3
(6)
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896
Considering N crystals with a total weight of Rr grams, S (total) = 0.000412 N or S (total) = 0.000412
(,)*' ,
N"3W2'3
(7)
The initial weight (W,) of seed sugar per 100 grams of water is given by the equation; 100 (% seed on sirup)
wo= 100 - % dry substance of sirup
(8)
If b is the number of crystals per gram, then N = bWo (9) The weight, W , in grams of solid sugar per 100 grams of water a t any time, may be calculated from the impuritywater ratio, a, the initial purity of the sirup, Po, and the purity of the mother liquor Pt at the given time: 10 000 a 10,000 a
-
w = wo+ o*
.
Equations 9 and 10 give the necessary data for calculating S (total) in Equation 7. The rate of crystallization, R, in grams per square meter per hour, is R = Rg/S
COEFFICIENT OF SUPERSATURATION. It is common practice to express the supersaturation as the ratio of the percentage dry substance or sucrose in the solution to the percentage in a saturated solution a t the same temperature. Thus Coefficient of supersatn.
=
% D. S. in sirup yo D. S. in satd. sirup
(11)
This method of expression is entirely arbitrary, but since it is convenient and yields comparative relations quite as good as any other, it is used in this paper. The solubility of sucrose in the sirups was determined by the method of Brown (3). The data are given in Table I. OF SUCROSE I N SIRUPS TESTED TABLEI. SOLUBILITY
Per Cent Dry Substance
Purity
Temp.
60 62 64 66
40
c.
68
70 72 60 62 64 66 68 70 72 60 62 64 66 68 70 72
50
60
Sirup 6,'" Brighton,b 1928 82.08 80.91 79.91 79.01 78.20 77.40 76.69 85.00 83.15 81,95 81.00 80.10 79.30 78,60
Sirup 3," Brighton, 1933
Sirup 1.0 Lyman, 1933
84.30 8 4 . SO 82.17 82.52 80.57 80.57 79.35 79.40 78.34 78.34 77.43 77.44 76.69 76.69 a Figure 5. 6 Brown e t al. (3)
Sirups 2, 4 , 5, 7, 8.a Brush, 1934 84.80 82.52 80.57 79.40 78.37 77.49 76.72
86:ZO 84.40 83.23 82.30 81.55 80.83
Discussion of Results As previously stated, the tests were made on sirup in the purity range encountered in raw side operation. The purities ranged from 60 to 72 per cent, the temperatures from 40" to 60" C., and the supersaturations from 1.02 to 1.08. It is recognized that the method does not yield highly accurate results, such as are needed to formulate an exact mathematical
VOL. 28, NO. 8
relationship between the factors temperature, supersaturation, viscosity, and purity, all of which influence crystallization rates. The results are, however, sufficiently accurate to indicate the trend and order of magnitude of their effect. These effects are shown g r a p h i cally in Figures 3 to 6. Figure 3 shows the effect of temperature on the rates of crystallization from 60 to 69 per cent purity. Above 65 per cent purity the rate increases rapidly with temperature and is practically doubled for each 10" C. rise. At lower purities the temperature effect diminishes markedly, giving f u r t h e r confirmation to the operating man's contention that about 60 per cent purity for final molasses is the limit which can be reached economically in factory pracTEMF: 'C tice. Figure 4 shows the variaFIGURE 3. EFFECTOF TEMPERATCRE AND PURITYON tion in rates of crystallizaRATESOF CRYSTALLIZATIOXtion from a given sirup with varving smersaturation a t 40" C. and a t puritiesrangingfrom 60 to 7'2 pe; cent. Above 65 per cent purity the rates increase continuously as the supersaturation increases. Below this purity there is an ill-defined tendency for the rate to reach a maximum a t 1.06to 1.08 supersaturation. At higher temperatures this tendency disappears. It is evident that the rate increases rapidly with increasing purity-for example, the rate a t 72 purity is approximately twice that a t 70 purity, and one-fifteenth that found by Kucharenko for pure sucrose under the same conditions of supersaturation and temperature. 14 These curves 12 also indicate that a t 1ow supersaturations the rate of lo crystallization approaches a c o n 6 stant value. The time-purity curves in Figure 2 illus4 t r a t e this point 2 more clearly. After a few hours the t i m e - p u r i t y IO2. c OE :;i"Ochi ;%sh%RsA%t7keoN ID8 becomes a FIGURE4. EFFECT OF SUPERSATUs t r a i g h t 1i n e , RATION AND PURITY ON RATESOF CRYSwhich means that T 4LLIZATION the rate of crystallization remains practically unchanged, although the coefficient of supersaturation is constantly decreasing. The rate in this range is so slow that zero supersaturation would be reached only after a period of months. It has been observed that the point a t which the rate approaches a constant value is not fixed by the purity-supersaturation relations, as we might expect, but that time becomes an important factor. It was found that the rate a t any given purity and supersaturation is influenced by the time elapsing between the beginning of the test and the point a t which the given purity-supersaturation condition is reached. The longer the time, the slower is the rate a t this point. This means that elapsed time becomes a dependent variable and
AUGUST, 1936
INDUSTRIAL A4SDENGINEERING CHEMISTRY
should be taken into account as such in making a comparison of rates. There is probably some connection between this time effect and the rhythmic variations in the rate of purity drop shown in Curves 1 and 2 in Figure 2 . This effect, while not always .so marked, was indicated in nearly every case. There is a possible explanation from the standpoint of the adsorption of nonsugars a t the crystal face and their incorporation in the crystal as it increases in size. The net result of such adsorption is a diminution of the effective crystal area At relatively high supersaturations and purities existing in the early stages of the test, this adsorption layer may be periodically overgrown by sugar molecules in such a way that a fresh surface is exposed and the rate of deposition increased for a time. As time proceeds and purity and supersaturation drop, the resistance to the deposition of sugar offered by the adsorption layer becomes the limiting factor and the effectof supersaturation, viscosity, etc., are no longer apparent. Recent tendencies in sugar boiling practice are to carry a during the “looser”-i. e., a less concentrated-massecuite major portion of the boiling period. The immediate and visible effect is an improvement in circulation, acconipanied by a decrease in the boiling time of the pan because of a more rapid crystallization rate, in spite of a lower supersaturation. The advantage is due largely to the maintenance of a higher average purity in rthe solution phase. el-----__Higher purity and better c i r c u l a t i o n . I more than counterCOWF S U P E W S A T N I 06 balance the effect of $ 4 P U R I T Y 7; r0 T E M P 40-c -t reduced supersatu2 ration. SIRUP NQ The temperatureFIGURE5 v.4RIATIOK IN RATES OF r a t e r e l a t i o n deCRYSTALLIZATION DUE TO CHARACTERscribed clearly inOF NONSCGARS IN THE SIRCP dicates the advantage of boiling raw pans a t as high a temperature as is possible without causing excessive decomposition and consequent darkening of the sirups. S o arbitrary upper limit of temperature can be set, bince this will vary with the character and condition of the beets and with operating practices employed during the earlier stages of the process. Rate measurements made on sirup obtained from different agricultural districts and on sirups from the same district but produced during different years, show widely varying results (Figure 5 ) . The effect of soil, climatic conditions, and agricultural practices on the quality of beets is, therefore, clearly reflected in the working qualities of the juices and sirups. Mills operating in the districts producing slowly crystallizing sirups are often unable to obtain the standard molasses purity of 60 per cent, but a mill handling the sirups with :t high crystallization rate has no difficulty in obtaining molasses purities below the standard. It has also been found that rates of crystallization vary at different periods of the same campaign. At one factory five average samples of sirup were taken, representing successive periods of the campaign, and rates of crystallization for each were determined (Figure 6 ) These results clearly indicate that the quality of the beets as measured by crystallization rates increased rapidly as the season progressed, finally reaching a maximum and then dropping off during the time when stored and frozen beets were being worked. This is in accord n i t h operating experience, since juice from immature or decomposed beets generally slows up the sugar end. Kucharenko (6) showed that sodium carbonate and lime reduce the crystallization rate by about 50 per cent when present to the extent of 2 per cent in sucrose solutions,~andthat the
&R*Fz8
*
897
decrease in rate is proportional to the salt concentration. Since 72 purity beet sirups a t 1.05 supersaturation contain about 12 Der cent of ash constituents, it is evident that these alone are Lore than sufficient to account for the observed diminution in rate, even without the added influence of colloidal a n d o t h e r organic substances which are present. Although the rates of crystallization from different sirups are not uniquely fixed by their purities, the general similarity of the pattern of the rate curves suggests the possibility that, if we construct a family of such curves FIGURE6. VARIATIOX IN OF CRYSTALLIZAfor a representative sirup and RATES TION WITH CONDITION OF then determine the rate for an- THE BEETS AS INFLUEXCED BY TIME OF HARother sirup a t a given purity, a VEST AND STORAGE new family of curves for the latter may be fairly accurately determined by transposition. The feasibility of such a procedure is suggested by the observed fact that, if two different sirups have the same rate of crystallization a t 70 and 72 purity, respectively, under given conditions, they will likewise have the same respective rates a t 66 and 68 purity, so that we need only to change the purity values of one set of curves by 2 points in order to produce the other. This sort of transposition can hardly be defended except on grounds of expediency. It is apparent that the quantity and character of the nonsugars present in the sirups are, in the last analysis, the predominating factors in determining the rate a t which sucrose will crystallize from them. The rates cannot be completely defined as a simple mathematical relation between temperature, supersaturation, and viscosity. I n addition, account must be taken of an indeterminate factor-nonsugar concentration and composition-which as yet cannot be given a definite numerical value.
Literature Cited Breedweld, G. J. F., and Waterman, H . I., Rev. t m v . chim., 51, 2 3 9 4 7 (1932).
Brown, R. J., et al., 1x0. ESG. CHEX, 20, 945-8 (1928). Ibid., 20, 1230 (1928). Hungerford, E. H., and Nees, A. R., I bid., 26, 462 ( 1 9 3 4 ) . Jenkins, J. D., J . Am. Chem. Soc., 47, 903-22 (1925). Kucharenko. J. h.,Planter Sugar M f r . , 75, 130 (192.5). Noyes, A. .1., and W-hitney, W. R., 2. p h y s i k . Ciiem., 23, 689 (1897).
Osborn, S. J., and Zisch, J. H., IND.EXQ.CHEM.,Anal Ed., 6, 193 ( 1 9 3 4 ) .
Silin, Bull. assoc. chim. sucr. dist., 52, 265-75 ( 1 9 3 5 ) . Smolenski, K., and Zelazny, h.,Gal. Cukrowniczu, 74, 303-17 (1934).
RECEIVED April 27, 1936
L
Courtesy, Bromborough Port EYtatc
