INDUSTRIAL AND ENGINEERING CHEMISTRY
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the calcium lactate to the free acid and then the coagulum and calcium sulfate filtered off together. The filtered lactic acid solution may then be evaporated to the desired concentration. Application to Other Fermentations
i The method of using alkali as a preservative for medium in storage is obviously particularly applicable to fermentations producing acid. The procedure of inoculating the medium in storage with the culture used in the fermentation, whereby the acidity of the partially fermented medium acts as its own preservative, is another possible means of accomplishing the same purpose. For many fermentations, however, it would be necessary to sterilize raw medium
Vol. 23, No. 5
either continuously or intermittently. The prevention of contamination of the fermenting medium with organisms producing undesirable substances may frequently be prevented by proper control of H-ion concentration. It must be remembered in this connection that the growth of acidproducing organisms is usually inhibited by the undissociated form of the acid produced, the concentration of which is a function of both the H-ion concentration and the total concentration of the acid (1). Literature Cited (1) Kolthoff, TLjdschr. uevgelijk. Geneeskunde, 11, 288 (1925). (2) Rogers and Whittier, J. Bazcl., 16, 211 (19281, and unpublished work. (3) Rogers and Whittier, I b i d . , 20, 127 (1930). (4) Whittier, J . Dairy Sci., 14, 26 (1931).
The Rate of Calcination of Limestone'" C. C. Furnas NORTH CENTRAL EXPERIMENT STATION, U. S. BUREAUOF MINES,MINNEAPOLIS, MI".
Calcination of limestone takes place in a very narrow s h o r t study of the rate of zone which is the phase boundary between calcium alone approximately 5 calcination of limestone, and carbonate and calcium oxide. This zone advances from million tons of limestone the data are reported in this the outside to the inside of the piece at a constant rate per year are burned for use paper. for each temperature, independently of particle size as lime; 20 million tons are Summary of Results or degree of calcination. Curves and data are given calcined in metallurgical furfor rates of calcination and temperature histories of T h e d a t a obtained may naces to be used as flux, and particles. Most of the resistance to heat transfer into b e s u m m a r i z e d in such a several times this much, of the piece appears to be in the narrow zone of calcinasimple manner that it seems the order of 75 to 100 million tion, and not in the body of the calcined material. best to present a statement tons, a r e calcined i n t h e The calcination data may be used to determine the of the results first and then manufacture of cement. Yet surface area of the particles. to offer the e x p e r i m e n t a l there is but little information available on the rate a t proof just as in- geometry a which calcination takes place. As far as the author knows, theorem is first stated and then proved. there are only three published investigations on the matter. Calcination proceeds only from the outside of the piece I n the first (2), the data were very meager and indefinite. inwards over a very narrow zone, practically a line. The The size of material used was not specified, and other attend- data reported in this paper are given as rates of advance of ing conditions of the system were not mentioned. this line of calcination from the outside to the inside of the I n the second (8) it was apparently assumed that heat trans- piece. As a first approximation, this line of calcination adfer and calcination were synonymous or, more correctIy, that vances a t a constant linear rate (measured in centimeters per they occurred together, which is not necessarily true. A par- hour), dependent only on the temperature of the surroundings ticle of limestone may acquire a calcining temperature and and independent of size or shape of particle, degree of calcinaremain that way for a long time before calcination actually tion, or amount of previous heating. The summarized data are given in Figure 1. The equation takes place. This second paper, then, is a clever correlation of the data of temperature acquisition in limestone, but its of the plotted curve is very simple, being applicability to lime burning is doubtful. loglo R = 0.003145t - 3,3085 (1) I n the third piece of work (7) nine different limestones were calcined a t various temperatures for varying lengths of time. where R = rate of advance of the line of calcination in centimeters per hour The data show the relative ease with which different limet = temperature, O C. stones may calcine, but the actual rates reported are hardly applicable to burning limestone in practice, for the material This equation is purely empirical and no theoretical imporused was mostly of small size ( - 4 mesh) and the calcining tance should be attached to it. was done in porcelain crucibles heated from the outside. The Obviously, since the rate of penetration of the line of calciresults obtained are really those for a confined bed of fine nation is constant throughout the entire period, the length material and do not give much information as to the specific of time required to calcine is directly proportional to the size rate of calcination within the limestone itself. It may be of the piece. I n Figure 2 are given computed curves for the said, however, that none of the data reported in Linzell's time required for complete calcination of pieces of different paper are qualitatively different from those of this present sizes a t different temperatures. The size is defined as the paper. greatest, thickness of the piece, where thickness is defined as Because of its importance in the heat-transfer phenomena the smallest of the three dimensions as contrasted with of the blast furnace, the Bureau of Mines has undertaken a breadth and length. 1 Received March 13, 1931. Presented before the Division of InThis makes the problem of t h e of calcination a very simple dustrial and Engineering Chemistry at the 81st Meeting of the American one. Undoubtedly, particle size and degree of calcination Chemical Society, Indianapolis, Ind., March 30 to April 3, 1931. do have an effect on the rate, but under the conditions of size Published by permission of the Director, U. S. Bureau of Mines. and temperature studies these effects, if they were there, were (Not subject to copyright.)
I
Tc' T H E U n i t e d S t a t e s
INDUSTRlAL AND ENGINEERING CHEXIXTRY
May, 1931
not of sufficient magnitude t o appear above the normal variation of the data. The particles varied from an equivalent spherical diameter of 2.5 to 8.5 cm.; the degree of calcination, from 39 to 100 per cent. Without further experimental work, confidence should not be placed in these data for particles less than 1 em. or greater than 15 or 20 em. in diameter. Details of Experiment
The study was divided into two parts: (1) calcination when hot gases flow through a bed of particles, and ( 2 ) calcination of single Dieces in a graDhite-walled induction furnace. The latter *experiments-were conducted at, a higher temperature than could be obtained with the ga,s-flow apparatus.
535
would be partially converted to carbon monoxide by the graphite walls and would burn a t the top of the furnace. All temperature records were kept on a Leeds and Northrup multiple-point recorder. The temperature history of the gas stream at the top of the column in the gas-flow experiments affords a means of determining the heat-transfer coefficients from the gas stream to the column of material (1). The amount of Calcination after a run was determined by loss of weight. The distance which the line of calcination had penetrated was determined by averaging a great many measurements of the width of the calcined band. The limestone used had the following analysis: %
I"
Ca 0
54.33 0.36
AlrOs
Si02 MgO
0.50
Loss
Fe
2 7
, /
LL--_---+--
?
;la---------'
.'
___-
1
1
2 _--_-AL
!
1 1 I,
I
,
'
I
I
I
!.
J I
O
!
.
cot
1.14
0.30 43.10 43.10
The complete operating and computed data are given in Table I. These data show wide variations of particle size and degree of calcination. In one of the runs the limestone was preheated before putting it into the furnace. A careful study of the complete set of data shows that none of these variables has a consistent, significant effect. It is very probable that continued, careful experimentation would give results which mere reproducible enough to show small variations with the other variables; particularly if a greater size range were studied. Mechanism of Reaction
Limestone decomposes according to the reaction CaCOa = CaO
+ COS
(2)
The reaction is endothermic, absorbing about 43,000 calories per formula weight. It can be shown by theoretical considerations that such a reaction cannot take place, except a t the boundary between these two phases (6). Since the two solid phases are fixed in position, it might be expected that the line of calcination would start a t the outside of the piece and advance inward. If there were chance calcium oxide molecules on the interior of the piece and the necessary heat
TIML, HOURS
Figure 2-Relation between T i m e Required for Complete Calcination, Temperature, and Thickness of Particle
were available a t that point, then centers of calcination might start a t various places on the interior of the piece. However, several hundred pieces were examined during the course of these experiments and in every one calcination had proceeded by the advance of a definite line or phase boundary from the outside toward the center.
536
I N D U S T R I A L A N D ENGINEERING CHEMISTRY Table I-Data
o n Heat Transfer a n d Calcination of Limestones
Av. EQUIV. MAX.
TEMP. O
RUN
c.
SPHERICAL DIAMETER OF PARTICLE TIME Cm. see.
CALCIXAWT. LOSS RUN
DURING
% A-GAS
835 840 875 875 900 910 910 9 10 940 945 950 965 1000
163C 162 166C 166D 163B 165C 166B 165E 164A l66A 165B 163A 165A
4.1 2.5 7.3 7.3 4.1 6.3 7.3 8.0 3.0 7.3 6.3 4.1
6,3
8100 5400 10190 10190 8400
7500 11100 7500 3900 12000 8100
9590 8700
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TION COMPLETED
%
Av. MEASURED DEPTHOF
PENETRATION C O X P U T E D RATEO F OF CALCINATION PENETRATION
Cm.
Cm./sec. X 10’ Cm./hr.
C O E F . HEAT R A T E OF TRANSFER GAS GAS FLOW TO S O L I D ” S l d . l./scc./cm.’
FLOWING THROUGH COLUMNS OF MATERIAL
30.7 25.0 30.5 30.5 30.7 32.6 30.5 18.6 26.2 30.5 32.6 30.7 32.6 B-SINGLE
72.2 58.0 70.8
70.8 71.3 75.6 70.9 43.2 60.8
70.9 75.6 71.2 75.6
0.29 0.45 0.64 0.66 0.82
0.52 0.84 0 80 0 71 1.05 0.79 1.55 1.32
0.36 0.62 0.65 0.98 0.69 0.76 1.07 1.83 0.88 0.98 1.62 1.52
0.13 0.30 0.22 0.23 0.35 0.25 0.27 0.38 0.66 0.32 0.35 0.58 0.55
2.50 2.87 2.19 3.63 3.61 3.61 3 89 3.89 3.61 4.55
0.90 1.03 0.79 1.31 1.30 1.30 1.40 1.40 1.30 1.64
0.84
0.08 0.13 0.08 0.08
0.08 0.08 0.08
0.08 0.13 0.08
0.08 0.08 0.08
0.0016 0.0047 0.00065 0.00065 0.0016 0.00078 0.00065 0.0032 0.00078 0.00065 0.0016 0.00078 0.00078
PIECES I N INDUCTION FURNACE
1035 170 7.3 5940 37.2 86.3 1.48 1035 176 4.0 3480 43.1 1.0 100.0 10406 5940 169 37.1 86.0 4.0 1.3 3300 1075 171 35.2 81.5 6.6 1.2 1075 172 1800 25,s 5.7 0.65 59.8 1085 173 1800 36.9 4.6 0.65 85.5 1085 900 3.6 0.35 174A 31.2 72.3 1085 174B 900 31.7 73.5 3.7 0.35 1.30 1125 3600 37.8 87.6 175 5.6 1140 3300 39.8 1.50 92.2 168 6.0 a Measured in calories per second per degree difference per cubic centimeter of bed. b Limestone was preheated to 500 C. before putting it into the furnace.
Distinction between Calcined and Uncalcined Material
Temperature Advances Faster than Calcination
The calcined portion is always soft and pure white. The uncalcined portion remains hard and is gray, probably owing to the presence of traces of unoxidized carbon from organic matter. Figures 4, 5 , and 6 show cross sections of typical pieces of partially calcined stone. The division line between the two phases is very sharp. Figure 6 is the photograph of a piece which was ground into the shape of a sphere. The dark, uncalcined portion has retained its spherical shape, showing that the phase boundary advances uniformly in all directions. The dark appearance of the central portion is not sufficient proof that there areas are uncalcined. However, several samples were taken a t various positions in the dark regions and calcined in platinum crucibles. All samples showed full loss of weight, indicating that no calcination had taken place inside of the white band.
It is particularly important to note (Table I) that the rate of advance of the line of calcination is quite slow, much slower than the rate of advance of a temperature wave. Temperature acquisition a t the center of a piece occurs long before calcination takes place. This means that the portion of the piece inside of the calcined zone is always in a metastable condition, but still unable to decompose until the phase boundary advances to it. The limiting factor in the rate of calcination a t low temperatures is the inherent rate of advance of this boundary line of the two solid phases, the center of the piece corning up to the temperature of the outside far ahead of calcination. However, as the temperature of the surroundings is raised, the specific rate of advance of the phase boundary is so increased that resistance to heat transfer begins to have an effect and the center temperature, although it is sufficiently high for calcination, lags behind the outside temperature until calcination is completed. This means that, after the temperature reaches a certain point, the 43,000 calories per formula weight being absorbed a t the phase boundary are being demanded so rapidly that no additional heat gets past the boundary to go into the center of the piece. Temperature of Interior of Pieces
Figure 3-Heat
Transfer Equipment
One investigator (4) has reported that there is a zone of partially calcined calcium carbonate inside of the completely calcined portion. If this is true, the zone is very narrow, for none of the samples of this investigation showed any such partial calcination close to the phase boundary.
These two effects are shown in Figure 7 . At the lower temperature (curve B ) ,the temperature of the center rose to that of the outside in the usual manner for the heating of a solid body. However, calcination lagged far behind this temperature, for it was only 72 per cent complete after 160 minutes of heating. At the more elevated temperature the center came up to a definite temperature and stayed there while calcination proceeded. At various Dlaces in the literature it will be found that “calcinationatemperatures” are reported as being from 900” to 950’ C . I n the run under consideration the temperature in the center remained constant a t about 940’ C. It is evident, then, that this so-called “calcination temperature,” which apparently is meaningless because calcination theoreti-
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May, 1931
537
tlie center acquires temperature much ahead of calciriation. If the external temperature is greater than 950" C., then the arrival of the center temperature to that of the outside is
evidence that calcination is complete to the center, but the temperature history has not been iri any way similar to the simple heating of a body. Carbon Dioxide Pressure Figure 4
Figure 5
The runs that were made at low temperatures werc for the system where gas flowed through a column of broken limestone. The total pressore \\'as approximately atmospheric and the carbon dioxide was 5 to 10 per cent. No significant variations could be found wit11 variations of the carlion dioxide percentage. In the liigli-temperature rum the pieces were iilaced in a graphite-lined induction furnace. Tho total gas pressure was 1 atmosphere. The gas cvolved in the furnace then was 100 per cent carbon dioxide, but it was in contact with hot grapliitc and was partially converted to carLon monoxide. The percentage of carbon dioxide in the gas ranged from 30 to.50 per cent. No significant variations wliich could be attributed to difference in gas compositions c i d d be found between the high- and low-temperature runs. Probable Driving Force of Reaction
Fieure 6
cally should proceed at any temperature if tlie carbon dioxide pressure is low enough, is actually a measure of the temperature which the center of a piece maintains while calcinatioii is proceeding a t more elevated temperatures. The difference in the temperature histories of the surface of the pieces in runs A and B is due to the fact that ruii A was a single piece in an induct.ion furnace, tho surface tcrnperature coming up almost at once. Run B was that of a piece at the top of R bed of material and tlie whole bed had to be heat,ed bcforc the t o p piece acquired temperature. From a consideration of Figure 7 it would seem that, if the outside of a piece is heated to some toinperatwe greater than IOW" C . , then the center should maintain a constant temperature between 900" and 950* C. until calcination oi tire piece is complete and then it sliould rise to the t,emperatiire of the outside. This is exactly what iiappens, as is shown in Figure 8. This curve is for the temperature history of a piece which was completely calcined before being taken from the furnace. Calcination Not Analogous to Heat Transfer From the preceding discussion i t can be seen that it is erroneous to consider that heat flow and calcination are analogous (3). If t,he external temperature is below 950' C., then
It seeins reasonable to suppose that tlie major driving force of the calcination is t.he equilibrium carbon dioxide pressure of tlie calcium carbonate. If this is true, tlre rate of calcination might be expected to be approximately proportional to tlie equilibrium carbon dioxide pressure. Measured equilibrium carbon dioxide pressures for calcium carbonate are shown in Figure 9 (5). It will be observed that the shape of the curve, when related to temperature, is the same as that for rate of calcination as shown in Figure 1. However, the sharp rise in the equilibrium carbon dioxide curve begins at a lower temperature than the corresponding rise in the rate curve. This w d d indicate that another factor besides the carbon dioxide pressure tends to limit the speed of reaction. As pointed out before, this limiting factor a t elevated temperatures is probably the resistance to heat transfer. So there are two tendencies in calcination, specific rate of advance of phase boundary and rate of lieat transfer, which are alternately controlling factors in the rate. Fortunately for simplicity of the problem, as a first approximation, the rate of advance of tlie calcination zone for a,U temperatures is constant arid independent of the size of the piece. This independence of particle size indicates that the resistance to lieat transfer is for the most part at the line of calcination and not tlimugt~outthe body of the calcined material. Rate of Carbon Dioxide Evolution I n mnie instances it is important to consider the rate of evolution of carbon dioxide during tlie course of the calcination. Obviously, if the line of calcination advances at a constant rate, this rate of gas evolution is proportional to the area of tlie calcining surface, which decreases as the reaotion proceeds toward tlie center. If the particles are considered
INDUSTRIAL AND ENGINEERING CHEMISTRY
538
Table 11-Data
Vol. 23, S o . 5 on Calcination of Limestones SAMPLE A SAMPLE B
%
Analysis: CaO MgO SiOa AliOq Ignition loss Diameter of svhere. cm. Specific gravify ' Temperature of calcination C. Rate of calcination, cm. pe; hour TIME, SECONDS
%
49.60 4.38 0.52 0.05 44.60
43.40 9.25 0.26 0.11 45.00
5.2 2.66 1075 1.55
2.55 1050 1,77
5.1
By referring to Figure 1 it can be seen that these rates are distinctly greater than that of the average curve given there. In all probability this increased rate is due to the presence of the greater percentage of magnesia (4.38 and 9.25 per cent, as compared with 1.14 per cent in the first limestone). The dissociation pressure of magnesium carbonate is many timesfhat of calcium carbonate at the temperatures considered, and hence might be expected to increase the rate of reaction quite appreciably. It is evident that, for limestones which are quite different from the one studied, tests should be conducted to determine their specific decomposition rates. This could easily be done by placing one or more spheres of limestone in a muffle furnace, a t 1000° C., and the rate of calcination determined by loss of weight after a certain time (about 1 hour). It would be necessary to keep the temperature of the furnace controlled quite accurately, as the temperature has the major effect upon rates of calcination.
Figure 7-History of Surface a n d Center Temperatures of Typical Pieces of Limestone during t h e Calcining Period a t Different Temperatures
TIME, SECONDS
Figure -8-Temperature History for Complete Calcination a t Elevated Temperatures
spheres, then the rate of gas evolution for pure calcium carbonate will be given by the equation dG - = de
4rRd 22.4 ( r 100
- Re)2
(3)
E de
= rate of gas evolution from one piece in liters per hour
8 I
= time in hours since beginning of calcination = rate of calcination as determined by Equation 1 = outside diameter of particle
d
= specific gravity of limestone
R
This equation may be written de = 2.82Rd(r
- RB)a
(4)
Surface Area
This study furnishes a means of making an approximate determination of the surface area of irregular pieces of limestone. If a piece of limestone is calcined for a short distance inward, the volume of calcined material is approximately the surface area times the thickness of the calcined layer. The amount of calcination-that is, the volume calcined-is determined by loss of weight. The boundary of the calcined zone is very sharp and uniform around the piece. After breaking the piece, the thickness of this zone may be determined by the average of several measurements. Dividing this average thickness into the volume calcined gives the surface area. A number of such determinations were made. It was found that for irregular pieces of limestone the surface area was 20 to 50 per cent greater than for a sphere of the same volume. Rates of Calcination of Different Limestones
I n order to determine the effect of composition of limestone upon the rate of calcination, two samples of two other limestones used in commercial blast-furnace work were calcined. The samples were ground into the form of spheres, 5 cm. in diameter, and the rate of calcination was determined in the, induction furnace. The data on the two samples are given in Table 11.
Figure 9-Johnson's Data of Equilibr i u m Carbon Dioxide Pressures in t h e Decomposition of Calcium Carbonate
After the rate was determined for one temperature, the rates for other temperatures can be estimated from Figure 1, as the other curves should run approximately parallel to this curve. The determination of the rate of calcination is quite simple and can easily be done in almost any laboratory. Acknowledgment
The author wishes to acknowledge the aid and suggestions of T. L. Joseph, H. F. Holbrook, and E. P. Barrett, of the S. Bureau of Mines, during the course of this work. Literature Cited Furnas, C. C., IND. END.CHEM.,22, 721 (1930);Trans. Ins!. A m . Chem. Eng., 24, 142-93 (1930). Gilkey, W. A,, IND. END. CAEM.,18 727 (1926). Haslam, R. T.,and Smith, V. C., I b i d . , 20, 170 (1928). Hiittig. G. F., and Lewinter, M., 2. angew. Chem., 41, 1034 (1928). Johnson, J., J . A m . Chem. Soc., 80, 1357 (1908). Langmuir, Irving. I b i d . , 38, 2263 (1916). Linzell, H.K., Holmes, M. E., and Withrow. J. B., Trans. A m . Inst. Chcm. Eng., 81, 249-81 (1926).
