Absolute Crystallization Rate of Sodium Sesquicarbonate P. T. DOLLEY Pacific Alkali Company, Lone Pine,Calif.
A method for determining the surface of a given batch of crystals has been developed and applied to the determination of the absolute crystallization rate of sodium sesquicarbonate at 35",43",and 49" C. from high- and low-chloride Owens Lake brines during the carbonation of such brines. During carbonation the crystallization rate decreases directly with the soda alkalinity of the brine in a regular manner and becomes zero at the transition point from sesquicarbonate to bicarbonate. The crystallization rate increases markedly with increase of chloride in the brine, probably because of
T
HE conditions of crystallization from water solution, such as temperature, concentration of solutes, and constituents of solution, may to a certain extent be varied a t will. By means of a feasible method for determining crystallization rates, the effects of these variables may be determined and compared. The work described in this article was carried out to develop a practical general method for determining absolute crystallization rates and to find the crystallization rate of sodium sesquicarbonate under various conditions. Such data are useful for determining the optimum conditions for a desired crystallization, for determining the capacity of a piece of equipment in which crystallization takes place, and for designing apparatus for a given crystallization. The absolute crystallization rate (for example, grams per hour per square meter per unit driving force or potential) varies for different faces of the same crystal. A knowledge of crystallization rates upon the different faces of a crystal would be valuable for controlling the crystal shape in addition to the purposes just mentioned. However the average crystallization rate on all the faces may be more readily determined and can be directly applied to the purposes mentioned. Few crystallization rate data are available which could be applied to the exact design of crystallization equipment. The capacity of such equipment especially is more or less of an uncertainty until the equipment has been actually used. The only crystallization rate data known to the author and directly useful for engineering purposes are those on sucrose (1, 3, 4, 6-9, 11-17, 21, 22). Other work has been done on crystallization rates to demonstrate the order of the reaction of crystallization and to compare the crystallization rate of a given substance under different conditions (5, 2s). In these cases the actual surface upon which crystallization took place was not determined. Either the same surface was used for different determinations or some quantity proportional to the surface (i. e., a given weight of a certain batch of seed crystals) was used in the calculations. The crystallization equation of Noyes and Whitney (18)
the accompanying increase of sodium ion. The crystallization rate increases directly with temperature but not in a regular manner. About 12" C. temperature rise doubles the crystallization rate. A general method for applying crystallization rate data to the calculation of the capacity of crystallization apparatus for producing a given size of crystal has been developed. An example of such application to the calculation of the capacity of a carbonation tower for producing 60-mesh crystals of sodium sesquicarbonate is given.
dc/dt = KX (C
- cg)
has been generally found to hold in previous work and was applied to the work here described. Efforts have been made, more or less successfully, to correlate crystallization rate and viscosity of solution and to derive a quantitative expression for the viscosity effect (2, 6, IO, 19). However, the viscosity of the solution and its effect are rather necessary concomitants of the conditions of the crystallization and need not be known specifically in order to make a practical engineering application of crystallization rate data, although a valid expression for the viscosity effect would make any given set of such data more generally applicable. Savinov has shown that, when the rate of stirring exceeds a given value (probably corresponding to a state of steady turbulent flow past the crystal surface), it no longer has any appreciable effect upon the crystallization rate (BO). This fact has been confirmed by the author when stirring was effected by gassing a solution and by experience of others when solution was pumped past a crystal face. I n carrying out a commercial crystallization, a stirring rate a t least equal to this critical rate is generally used; at any rate, good engineering practice predicates its use. Hence in this work the crystallization rate determinations were made when stirring (by gassing) rates faster than the critical were used. The most difficult part of a crystallization rate determination is the estimation of the actual crystal surface involved. In some cases the crystals are single and of sufficient regularity in their relative dimensions to make it possible to obtain a sufficiently accurate estimate by assuming a constant ratio between dimensions; i. e., Kukharenko (7) estimates the surface of a sucrose crystal to be : S = 0.000412 Mala
By counting the number of crystals per gram for a fraction of fairly uniform size the total crystal surface can be readily estimated with fair accuracy. I n the case of a mixture of
1101
1102
INDUSTKIAL AND ENGINEERING CHEMISTRY
aggregate and single crystals of varying ratio betxeen their dimensions, the estimation of the crystal surface, with any degree of accuracy, seems a t first glance to be so laborious as to be impractical. This is the case with sodium sesquicarbonate crystals from Owens Lake brine. However, as will be shown, it was possible to work out a practical method of estimation which gave, consistently, results of accuracy compatible with that of the other measurements required for a crystal-
PLLUTOF
THE
VOL. 29, NO. 10
the brine through a filter paper into a funnel made of a 100beaker with a stopcock in the stem and weighed directly from the funnel into a tared volumetric flask containing caustic solution. The samples were analyzed for total alkalinity by titrating with hydrochloric acid and for total chlorides by titrating with silver nitrate. From the chloride analyses (no chloride came out of solution during the carbonation) the alkalinities were corrected for change of weight of brine, due CC.
PACIFIC ALKALICOMPANY ON OWENSLAKE,CALIF.
lization rate determination. It was desired to compare the crystallization rates of sodium sesquicarbonate, from Omens Lake brine of various compositions and a t various temperatures, while carbonation of the brine was taking place and to compare the capacities of a given carbonation apparatus for sesquicarbonate production with the different brines operating a t the different temperatures.
Experimental Method The work resolved itself into three determinations for estimating each crystallization rate-namely, the grams of sodium sesquicarbonate being precipitated per hour, the supersaturation of the brine in per cent sodium sesquicarbonate by weight of the brine, and the total crystal surface in contact with the brine in square meters, under the conditions a t which the crystallization rate was desired. A weighed quantity of brine of known composition was carbonated witkl a mixture of carbon dioxide and air a t a regular rate. As noted above, a gassing rate was necessary which would give more than the critical amount of stirring. The absorption of carbon dioxide by the brine is a more rapid reaction than the crystallization of the sesquicarbonate. Hence the carbon dioxide concentration in the gas was adjusted to prevent such rapid absorption as to start new crystal nuclei during the course of the carbonation after the original nuclei had been started at the beginning of carbonation. Carbon dioxide concentrations of 4 to 14 per cent were used, depending upon the gassing rate. Rates from 195 to 307 cubic feet per hour per square foot of tower section a t atmospheric conditions (30" C. and 660 mm.) were used. The depth of brine in the tower was 6 feet. The brine was heated sufficiently to hold it a t the desired temperature.
Precipitation Rate To determine the precipitation rate of sesquicarbonate, beginning usually about 2 hours before the conditions for the desired crystallization rate were reached, samples of the clear brine were taken at approximately one-hour intervals. The last sample was withdrawn a t exactly the point where the crystallization rate was desired. The samples were taken by sucking
to absorption, evaporation, and precipitation, to make them comparable to the alkalinity of the brine a t its original weight. The drop in alkalinity was then plotted against time. Except for conditions where the crystallization rate was closely ampproaching zero, the conditions of carbonation could be and were so chosen that the resulting curve was nearly a straight line. The tangent to the last point of the curve was then determined graphically. Then, tangent (in milliliters of acid) times original weight of brine times factor equaled grams of sesquicarbonate precipitated per hour a t the time the last sample was taken.
Supersaturation The carbonation was stopped as the last sample was taken, and a portion of the unfiltered brine was stirred in a closed thermostat a t the temperature of carbonation until analysis of the brine for total alkalinity and carbon dioxide showed no further loss of either. Then the milliliters of acid drop in total alkalinity while stirring times factor equaled per cent by weight of brine of NazCO3.NaHCO3.2Hz0supersaturation. Likewise, per cent by weight of brine of carbon dioxide lost times factor equaled per cent sesquicarbonate supersaturation. The value from the carbon dioxide drop was used as a check upon that found from the total alkalinity drop, but the latter value was employed because of the greater accuracy in its determination.
Crystal Surface As soon as the carbonation was stopped, part of the sesquicarbonate sludge was filtered and quickly washed, first with a solution of sodium carbonate and bicarbonate which would not dissolve sesquicarbonate, and then with 85 per cent methanol. The crystals were dried and weighed. The remainder of the sludge, including that from the thermostat mentioned above, was filtered, weighed, and analyzed for alkalinity and chlorides, From the chloride analysis the amount of mother liquor in the cake was found and from the corrected alkalinity the weight of solid sesquicarbonate in the cake was estimated and added to the weight of the washed dried crystals to ob-
OCTOBER, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
tain the total weight of sesquicarbonate crystals in contact with the brine a t the time carbonation was stopped. Screen analyses were made on the washed crystals until almost complete separation into the various fractions was obtained. The result was a series of fractions of uniformly sized crystals from +40 to +ZOO mesh. The -200-mesh fraction was not very uniform in size, but conditions were generally controlled to make it relatively small-5 to 15 per cent of the whole. The length, width, and thickness of the crystals of each fraction were then measured with a microscope fitted with a mechanical stage and a micrometer eyepiece. The shapes of the crystals obtained from the brine are shown in Figure 1. To measure the thickness of the crystals, they were placed on end by static electricity from a charged glass rod brought close to the slide. A light tap on the slide knocked the crystals flat while the operator watched them through the microscope; the length and width were then measured. The crystals of a given screen fraction were thinly sprinkled over the slide. Then starting a t one end of the slide, every crystal coming into the microscope field was measured until the other end of the slide was reached. The slide was cleaned, a fresh batch was sprinkled on, and the procedure was continued until fifty single crystals of the -200 fraction and twenty-five of each of the other fractions had been measured. All the single crystals in each of enough aggregates to give twenty-five or more sets of measurements for each fraction were measured. The aggregates varied from two crossed crystals to eight to ten crystals radiating endways from a common center. The carbonation was controlled to avoid very complex aggregates and to keep the proportion of aggregates as low as possible. Generally the aggregates constituted 20 to 30 per cent by weight of the crystals, and the average number of crystals per aggregate was two to four. Three shapes were presentsingle, aggregate, and broken crystals. Almost invariably the broken ones were half-crystals of the particular screen
1103
aggregates was estimated. The result wa3 divided by the sum of itself plus one-half the number per cent of broken crystals pluR the number per cent of singles, to obtain the per cent by weight of aggregates in each screen fraction. The screen analysis was recalculated to give the weight per cent of aggregates and of originally single crystals in each screen fraction. KO aggregates were found in the -200-mesh fraction. The average density of sodium sesquicarbonate was determined by displacement of amyl alcohol to be 2.150 grams per cc. in the temperature range ( 3 5 O to 49" C.) of the crystallization rate determinations. When the calculations of volume and surface, based on the actual shape of individual crystals, were compared with those based on the conventional shape shown in Figures 1B and C, the differences were found to be of the order of 0.5 per cent or less of the values found. Hence the conventional shapes were used as a basis for volume and area calculations. The ratio of'the axes of the elliptical ends is the average of a number of measurements of various sized crystals. Based on the conventional shapes of Figure 1, for aggregate and single crystals, Ve= (L
- 0.15 W ) TW
(1)
for aggregates, A = (2L
- 0.15 W ) W + ( 2 L + 0.645 W ) T
(2)
and for singles, A
=
(2L
- 0.3 W ) W 4- (2L
+ 1.29 W ) T
(3)
Various methods of obtaining an average volume and surface for the crystals of a given screen fraction were tried. Making the volume and surface calculations from the arithmetical averages of the dimensions, for the range of the dimensions encountered, gave values well within 5 per cent of the true averages of all fractions, except the -200 mesh, and in this case the error did not exceed 8 per cent. Hence the average volume and surface of a single crystal of each screen fraction was calculated from the arithmetical average of the dimensions of the measured crystals of that fraction. For any given screen fraction of crystals: 8 = MA/dV
A. ACTUAL SINGLE CRYSTAL .
(4)
where d = density of sesquicarbonate, grams per cc. (2.150). Combining Equations 4, 1, and 2, and Equations 4, 1, and 3 gives the following relations for the surface of the individual screen fractions. For aggregates,
(------~x ... ...............- .- - ..-...
S = lo-' M [0.9302/T
1. ~ ~ ,
+ 0.9302/W + 0.1605/(L- 0.15 W ) ] (5)
-+-
I
and for singles,
1
0. CONVENTIONAL SINGLE C R Y S T A L .
C.
CONVENTIONAL AGGREGATE CRYSTAL (5-COMPONENT CRYSTALS)
FIGURE1. SODIUM SESQUICARBONATE CRYSTALS
fraction in which they were found. A count was made of the aggregate, single, and broken crystals in each screen fraction, starting a t one end of the slide and counting every crystal coming into the field of the microscope as the slide was passed by, until two hundred to three hundred crystals had been counted. The numerical percentage of each species in each fraction was then calculated, and the average number of component crystals per aggregate for each screen fraction was determined. For each screen fraction, the average volume (estimated as noted below) per aggregate, divided by average volume per single crystal, times the number per cent of
S =
M [0.9302/T
+ 0.9302/W + 0.4605/(L- 0.15 W ) ]
(6) The sum of the surfaces of the various screen fractions, as calculated by Equations 5 and 6, was taken as the total crystal surface in contact with the brine a t the time carbonation was stopped. With a little practice the measurements of a batch of crystals can be made in 8 to 10 hours, and the calculation of the crystallization rate in about 3 additional hours. The crystallization rates are calculated as grams of NaZC03.NaHC03.2H20per hour per square meter per percentage of NazCOa.NaHCOa.2Hz0 supersaturation. The temperature was maintained within =t0.5" C . during the carbonation and within *0.1" during the last hour of carbonation and during the time of stirring in the thermostat to determine the supersaturation. The bottom of the carbonating tower was shaped and the gas inlet placed so that
INDUSTRIAL AND ENGINEERING CHEMISTRY
1104
there was no settling of crystals in the bottom of the tower during carbonation. It was found that, with the rate of stirring used, crystals greater than 30 mesh tended to sink to the bottom and pack more or less; hence the carbonation was made rapidly enough to prevent the growth of crystals larger than 30 mesh. The samples were taken within 0.5 minute. The time differences were thus measured well within an error of *1 per cent. The alkalinity differences, from which the alkalinity us. time curve was drawn and the supersaturation was determined, were generally 0.5 to 0.8 ml. of normal acid and were observed within an accuracy of 0.02 ml The supersaturation and rate of precipitation of sesquicarbonate were thus determined within an error of k 5 per cent. Generally the error was less than 5 per cent. The smallest dimension measured (crystal thickness) varied between ten and seventy divisions of the measuring scale and could be measured to plus or minus one division. By far the greater portion of the crystals was more than twenty divisions thick. The error of the crystal measurements was thus within ~5 per cent. The crystal measurements were made by five different individuals, and occasional checks showed an agreement within 5 per cent between individuals and between sets of measurements made by the same individaal. The gassing rate was varied from 200 (run 23) to 425 liters per hour (run 28) without changing the crystallization rate. Hence a gassing rate of 200 liters per hour gave the critical amount of stirring. For most runs a gassing rate of 425 liters was used. The gassing rate was increased from 425 (run 42) to 538 liters per hour (run 94) also without changing the rate. Barring accidental errors, the values of the crystallization rates were within *lo per cent error, with the exception of rates determined near the transition point (Figure 2) from sesquicarbonate to bicarbonate, where the amount of sesquicarbonate precipitated per hour was very small and could not be determined accurately. Also some determinations, near the start of crystallization when the crystals were very small and the crystal surface difficult to estimate, were obviously in greater error. This trouble could be eliminated by seeding with large crystals, but time was not available for checking the runs. Runs in which known experimental errors were involved were discarded.
VOL. 29, NO. 10
Results The crystallization rates of sodium sesquicarbonate from brine of two different compositions were determined for different concentrations of sodium carbonate, down to the transition point to sodium bicarbonate solid phase, a t three temperatures. The compositions of the two brines are shown in Table I and the rates in Table 11. TABLEI. COMPOSITION OF SODA BRINES Low-Chloride Brine 17.00 13.70 15.53 .70 2.88 10.74 3.76 2.62 .10 .25 L 18
High-Chloride Brine 15.07 14.78 14.09 .70 1.50 11.62 4.02 3.06
.ll
.39 .I6
a Total alkalinity exclusive of that required t o make all borate NazB401.
I n addition to the constituents given in Table I, the brine contains small amounts of sodium salts of fatty acids and resinous material, tungsten, vanadium, rubidium, cesium, copper, zinc, antimony, arsenic, aluminum, palladium, rare earth, and alkaline earth elements. The crystallization rates together with the data from which they were calculated are plotted in Figure 2. It is possible to determine the degree of supersaturation compatible with the most rapid growth of crystals without starting new nuclei, by observing the crystallization under different rates of carbonation. However it was most feasible to operate the carbonating apparatus in question a t a constant gassing rate. The fastest rate that would yield the desired size of crystal without aggregates and small crystals was found, and the resultant amount of supersaturation throughout the carbonation was determined. The use for these data will appear in the application to equipment capacity calculations, The data are given in Figure 3.
RATESOF SODIUM SESQUICARBONATE FROM OWENS LAKEBRINES TABLE 11. CRYSTALLIZATION Run No.
43 69 73 67 40 18 19 32 39 46 70 45 72 44 71 41 48 13 14 15 12 5 6 34 74 66 38 35 42 94
NazCOa Temp. .4lkallnity OC.
%
35
14.29 14,06 14.06 12.41 12.40 10.76 9.34 8.19 7.69 14.57 14.31 13.38 13.35 12.06 11.96 11.09 10.25 9.46 9.33 9.17 8.86 8.42 8.14 13.92 13.50 13.33 12.65 11.94 11.91 11.43
43
49
Pptn. Rate
Superaatn. yosesquiG./hr. carbonate Low-Chloride Brine 0.534 65.4 24.2 0.226 59.9 0.490 0.482 58.8 55.1 0.534 0.565 47.6 32.7 0.633 0,399 26.8 0.512 1.88 81.5 0.550 0.392 58.3 106,3 0.641 38.3 0.350 57.0 0.401 44.5 0.392 53.3 0.489 0.633 94.9 0.421 40.6 0.452 81.9 0.339 33.1 0.415 53.1 0.542 59.7 0.437 34.1 0.542 79.2 72.6 0.407 0.362 66.5 94.0 0.505 0.413 74.5 72.3 0.286 0.378 67.4
Surface Sq. m.
31.06 39,89 39,35 71.81 105.9 103.2 100,9 174.7 170.0 29.12 28.07 46.80 46,84 92.65 74.31 75.47 124.4 101.0 126.5 123.5 107.0 152.6 120.8 23.90 34,09 33.3s 64.00 56.61 87.69 64.57
Crystallization Rate G./hr./ sq. m./%
4.08 2.69 3.11 1.70 0.97 0.82 0.51 0.39 0.02 5.10 5.30 3.55 2.33 1.53 1.53 1.45 1.21 0.96 1.43 0.79 1.20 0.72 0.65 .~ 6.11 5.24 5.50 3.45 3.19 2.88 2.76 ~
Run No.
NazCOa Temp. Alkalinity OC.
27 65 36 33
49
37
28 23 26 31 20 62 59 5s 81 63 57 55 51 56 90 50 54 64 78 80 79 86
35
49
Pptn. Rate
Supersatn. Surface % seapui% G./hr. carbonate Sg. m. Low-Chloride Brine (Continued) 10.92 47.8 0.339 83.49 10.89 42.3 0.489 45.36 10.14 62.9 0.331 95.96 9.80 69.6 0.263 130.2 9.fi4 87.0 0.466 88.00 0.647 85.30 8 50 54.4 0.347 62.34 8.39 23.3 8.21 0 407 57 83 14.2 8 10 20 5 0 292 120 0 0.565 75 19 8 03 30 8 High-Chloride Brine 0.441 29.99 12.87 44.0 0.381 49.94 43.0 12.03 0.648 41.68 57.3 11.19 0.579 36.46 11.04 39.8 0.475 54.90 10.87 43.8 0.467 99.53 49.6 9.91 92.14 58.4 0.489 9.74 0.557 94.09 8.65 44.4 0.520 92.57 7.66 38.7 0,332 118.2 7.31 28.2 0.468 128.5 6.78 12.0 13.55 100.3 0.556 16.67 12.08 87.0 0.444 32.20 11.24 51.2 0.415 36.20 71.17 9.75 50.8 0.407 7.5s 27.3 0.331 73.14 6.33 10.0 0.332 84.50
Crystallization Rate S
x
y
%
1.69 1.91 1.98 2.03 2.12 0.99 1.08 0.60 0.59 0.73 3.33 2.26 1.94 1.89 1.68 1.07 1.30 0.85 0.80
0.72 0.20 10.83 6.08
3.41 1.75 1.13 0.36
OCTOBER, 1937
INDUSTRIAL AND E W G I N E E R I N G CHEMISTRY
1105
2-
LOW-CHLORIDE BRINE D
-
HIGH-CH LORIDE: BRINE
IO -
AT43'C.
AT49OC. AT35'C.
o
-
8-
-
6-
4-
-
c-
8
9
12 SODA ALKALINITY IO
FIGURE 2.
II
%
I3
15
14 Nd,C05
CRYSTSLLIZATION
High chloride
Length X Width
2.563 2.743 3.100 1.997 2.837
Area,
Wz 5.645 6.211 7.037 4.231 6.180
I
I
I
I
I
I
8
9
IO
II
12
I3
14
SODIUM SESQUICARBONATE DURINQ CARBONATION O F
TABLE 111. RELATIVEDIMENSIONS OF SODIUM SESQUICARBONATE CRYSTALS Temp., Thickness O C . X Width 35 0.1286 43 0.1490 49 0,1518 35 0,1005 49 0.1148
7
SODA ALKALINITY
RATEO F
The various crystal measurements were averaged and indicated definite trends, in the relative dimensions of the crystals, with brine composition and temperature. The dimensions and volume surface relations are given in Table 111.
Brine Low chloride
I
Vol., Wa 0.3100 0.3860 0.4480 0.1856 0.3085
Inspection of the curves of Figure 2 indicates that the crystallization rate roughly doubles for about a 12' C. increase in temperature. However, the temperature effect of the crystallization rate is the result of temperature effects on more than one variable. Likewise the effect of varying the constituents of the brine upon the crystallization rate seems to be complex. The crystallization rate changes in a fairly regular way in direct proportion to the amount of alkali present. It becomes zero a t the transition point from sesquicarbonate to bicarbonate and would no doubt become increasingly negative-i. e., a solution rate-below the transition point. An investigation of the crystallization rate of bicarbonate a t and below the transition point should be of interest. Viscosity data were taken along with the crystallization rate data, but no valid expression for the viscosity effect has been evolved. Because of the averaging effect, points on the curves of Figure 2 are probably not more than * 5 per cent in error except a t the extreme ends of the curves.
% Na,CO, BRINES
Substituting in Equation 9: A = b-2'3 a M2/31.667-1 = 7.22 M 2 / 3
sq. m.
(10)
It is desired to carbonate the brine until the alkalinity drops to 8.5 per cent sodium carbonate. Under these conditions the weight of sodium sesquicarbonate precipitated when any percentage of sodium carbonate residual alkalinity, 2, is reached can be expressed by: MI= B [0.2415;+ (1.053%+10.3446%')/(0.1222% - 0.9896)] (11)
Equation 11 is an empirical equation developed in the laborabory of the Pacific Alkali Company. Taking a value for B (2.021 x 10-4 gram) corresponding to a final value for M of gram, Equation 11 beone 60-mesh crystal, or 2.783 X comes
lo-'
+ (21.27 f 6.96%)lo-'
%/(1.222%- 0.9896) (12) From Equations 12 and 10, values of M and A may be calculated for various values of per cent sodium carbonate alkalinity during carbonation. Then values of the crystallization rate and the per cent supersaturation, corresponding to the same values of per cept alkalinity, may be taken from Figures 2 and 3. The product of the crystallization rate times the corresponding values of area and per cent supersaturation equals the grams per hour of sesquicarbonate precipitated for each corresponding value of per cent sodium carbonate alkalinity and grams of sesquicarbonate precipitated, M . The
M = 4.88 X
HIGH-CHLORIDE BRINE
Application of Data Given the problem: How many hours will be required to carbonate a given brine a t a certain t e m p e r a t u r e f o r example, low-chloride Owens Lake brine a t 49" C.-to produce 60-mesh crystals (0.3068 mm. wide)? From Table 111, A = aW2 V = bW3 Combining Equations 7 and 8: A = VZ/3 b - 2 / 3 a (9) The volume of the sesquicarbonate may be expressed: V = M/2.15
LOW-CHLORIDE BRINE.
SODA ALKALINITY % Na,co, FIGURE 3. SUPERSATURATION OF BRINEDURING CARBONATION TO PRODUCE 60-MEsH CRYSTALS
reciprocal of grams per hour gives values for hours per gram or hours to precipitate one gram of sesquicarbonate, corresponding to the M values or grams of sesquicarbonate precipitated. Then,
INDUSTRIAL AND ENGINEERING CHEMISTRY
1106
VOL. 29, NO. 10
d
(hr./g.) M
=
and
hr. required for carbonation
where M O= 0.037 X 10-6 M I = 2.15 V ,or weight of final 60-mesh crystal Plotting hours per gram against M ( F i g u r e 4), the i n t e g r a l can be evaluated graphically. The data upon which the c a l c u l a t j o n s are based begin t o apply a t the time crystaIIization beeo m e s apparent, and from this time on, the supers a t u r a t i o n is such that no new c r y s t a l nuclei form. This point corresponds to an I z alkalinity drop of GRAMS PRECIPITATEDXIO-5 FIGTJRE 4. HOURSFOR CARBONATION about 0.1 per cent sodium carbonate OF LOW-CHLORIDE BRINE TO MAKE or an M value of ~O-MESHCRYSTALS 0.037 X 1 0 - 5 ~ r a m in this case. The significance of an infinite value for precipitation time is that, under the Conditions to which the data apply, crystallization will not start. However, during the time necessary for crystallization to become apparent other conditions apply, such as higher supersaturation, so that crystallization does start. This situation does not invalidate the method, since the time for crystallization to become apparent is taken into account in completing the calculations for capacity. (Table IV.) The value of the integral is -i
%
0
17.0 16.9 16.5 16.0 15.5 16.0 14.5 14 0 13.0 12.0 11.0 10.5 10.0 9.6 9.0 8.. . 6 Values
Superzation satn. Raten ' yo sesqui- U./hr./ C. X 105 carbonate aq.m./% 0 (15.9) 0.037 i,X3 15.6 0,184 14.3 1.33 0 3365 12.6 1.33 0.550 10.9 1.25 8.2 0.728 1.13 7.80 0.902 0.94 1.073 6.53 0.74 1.408 4.47 0.46 1.732 2.93 0.46 2.044 2.07 0.40 1.98 2,200 0.35 2.05 2.348 0.32 2.02 2,492 0.34 1.70 2.640 0.37 1.13 2.783 0.40 above 14.0 per cent NsnCOa were
A
M
Sg.rn. X 108
Pptn. Rate G./hr.
X 108
Pptn. Time Hr./g. X IO-'
V S
-
a
M2la
1.667-1
Acknowledgment The author wishes to commend J. B. Fair, Jr., Elmer Thompson, C. D. Bobbit, J. W. Sprauer, and F. K. Thompson for their faithful assistance in this work.
Nomenclature = = c = Cn = d- = n = t = z = A = B = a
b
K = L =
M
=
factor for expressing area of crystal in terms of width factor for expressing volume of crystal in terms of width molal concentration of crystallizing substance at time t molal concentration at saturation density number of crystals making up M,final weight considered time, hours NaaCOa alkaIinity of brine during carbonation X 0.01, % area of a single crystal, sq. em. or sq. m. weight of a raw brine, g. a constant length of a crystal, cm. weight of crystals or crystal, g. surface of crystals, sq. m. thickness of a crystal, em. volume of a crystal, cc. width of a crystal, om.
Literature Cited
nM/2.16
(1) Breedveld and Waterman, Rec. trav. chim., 51,239(1932). (2) Cossel and Landt, 2. Ver. deut. Zucker-Ind., 77,483(1927). (3) Dedek, Chirnie et industrie, Special No. 563 (May, 1927). (4) Honig and Alewijn, Java Proefstat. Med. I d e r n . Sugar J . , 33, 595 (1931). (6) Jenkins, J . A m . Chem. Soc., 47,903 (1925). (6) Kukharenko,Facts About Sugar,30,34(1935). 75,130 (1925). (7) Kukharenko, Planter Sugar Mfr., (8) Kukharenko, Sucr. belge, 45'3 (1925). (9) Kukharenko and Benine, Ibid.,46,131 (1926). (10) Kukharenko and Kartashev, Nauchnuie Zapiski,5,177 (1927). (11) Kukharenko and Krassilchikov, Sucr. belgs, 46,107 (1926). (12) Kukharenko and Nakhmanovich, Centr. Zuckerind., 33, 1609 (1925). (13) Kukharenko and Nakhmanovich, Zapiski,2,53 (1925). (14) Kukharenko and Savinoff, Planter Sugar Mfr., 76, 129, 289 (1926). (15) Kuznetzov, 2. Ver. deut. Zuclcer-Ind., 1926,19. (16) Nakhmanovich and Zelikman, Nauchnuie Zapiski, 6, 32, 109 (1928). (17) Nees and Hungerford,IND.ENQ.CHEM.,28,893(1936). (18) Noyes and Whitney, 2.physik. Chem., 23,689 (1897). (19) Sandera,2. Zuclcerind. cechoslovak. Rep., 51,410(1927). (20) Savinov, Nauch. Zapiski Xakhurnoi Prom., 7,416 (1929). (21) Silin, Bull. assoc. chim. sucr. dist., 52,265(1935). (22) Smolinski and Zelazny,Gar. Cukrownicza, 74,303 (1934). 23,670(1931). (23) Whittier and Gould, IND. ENG.CHB~M.,
nA
RECEIVED February 20,
OD 0 0 0.0372 0.772 12.96 2.07 4.83 0.1084 2.87 3.48 0.1712 3.27 3.06 0,2246 3.88 2.58 0.2780 4.36 2.30 0.3130 1.70 5.88 0.3512 0.866 11.55 0.4213 0.650 15.40 0.4825 22.40 0.446 0.5392 0.393 25.45 0.5665 25.78 0.388 0.5916 0.423 23.65 0.6155 0.402 24.86 0.6397 0.299 33.43 0.6625 obtained by extrapolation.
36.3 hours, The capacity of an apparatus holding a given charge of brine for making 60-mesh crystals of sodium sesquicarbonate can thus be accurately estimated, allowing for the proper nonproductive time for filling, supersaturating, etc. In case it is desired to make several calculations a t once, various sets of values of hours per gram may be calculated for one set of values of M by making Equation 10 general-i. e., taking then
b - 2 1 3 nl/3
(10A) Values of n may be calculated from the relative values of V given in Table 111. Then for brines of different composition or for different ranges of carbonation, different values of B have to be substituted in Equation 11 to derive Equation 12. The data on time for crystallization, calculated on a oomparative basis, may be used to estimate comparative capacities for different compositions of brine and different conditions of crystallization for a given apparatus, even though the crystals produced are of some other size than 60 mesh or are a mixture of sizes. If the capacity of an apparatus is known for one of the brines under one of the sets of conditions to produce a given size or mixture of sizes of crystals, the capacity may be calculated exactly for another brine or set of crystallization conditions to produce the same size of crystals, from the relative times of crystalIization. The precipitation rate (Table IV) falls off to about 10 per cent sodium carbonate alkalinity and then increases again. This phenomenon actually takes place in the sesquicarbonate carbonation towers and, previous to this work, was unexplained.
S = TABLEIV. DATAFOR ESTIMATION OF TIMEREQUTRED FOR CARBONATION OF LOW-CHLORIDE BRINEAT 49' C . TO PRODUCE T = V = 60-MESH CRYSTALS O F SODIUM SEBQUICARBONATE W -CrystalliAlkalinity NaZCOa
=
1937.
