Ignition in Beds of Solid Fuel M. A. RIAYERS AND H. G. LdIVDAU Coal Research Laboratory, Carnegie Institute of Technology, Pittsburgh, Penna.
A nomograph has been designed for the calculation of the rate at which fuel can be ignited in pure underfeed burning when the characteristics of the fuel bed are known. By its use better values for the relation between the air flow rate and the rate of the combustion reaction, and between air flow rate and the rate of heat transfer between the gases and solids of the fuel bed than have heretofore been available have been calculated from the data on underfeed burning published by the United States Bureau of Mines. The significance of ignition temperature in such fuel beds is discussed, and its dependence on the characteristics of the bed is shown. A method is developed for calculating the effective ignition temperature under specified conditions when the reactivity characteristic, as determined by the Coal Research Laboratory test, is known. By the use of this method in conjunction with the nomograph, the rate of ignition of a given fuel under specified conditions can be calculated.
T
HE phenomena comprising the combustion of solid fuel may be divided into two parts-the preparation of the fuel for active combustion and the active burning with its accompanying release of energy. The groundwork for an understanding of the second of these has been laid by the experimental work of many investigators, and theoretical treatments that represent the experimental facts approximately are available (5, 11, I S , 15, 18). The preparation of the fuel entering fuel beds has until recently been studied relatively little; in fact, experimental investigation of this phase of the problem was first reported by Nicholls (11) in 1934. The preparation referred to comprises the processes of heating the fuel and causing i t to pass through any coking or decomposition reactions i t may undergo, and of bringing i t into contact with a stream of air while its temperature is high enough to allow rapid combustion. An analysis (8) of t h e process has been published in which the importance of certain physical properties of the bed appears. This analysis is based on the hypothesis that the fuel bed itself may be treated as if i t had a property equivalent to metallic thermal conductivity, which may be responsible for transferring heat to the incoming fresh fuel, even against the flow of cold air. It is recognized that real metallic conduction (7) does not exist in a fuel bed; bu't the radiation of heat among neighboring particles which goes on freely a t the high temperatures involved may be treated mathematically as equivalent to thermal conduction. I n fact, use of this mechanism of conduction permits the calculation of values of conductivity of the right order of magnitude for agreement with the experimental data (16).
PI = 0.21 hi = 6300 B. t. u./lb. of 0 2 cP = 0.28 B. t. u./(lb. (" F.) p = 0.34B. t. u./(lb.{ (" F.)
The analysis referred to introduces three quantities which are of extreme importance in determining the rates of ignition of solid fuel in underfeed firing: the ignition temperature Ti, the rate of the combustion reaction at high temperatures, p1, and the heat transfer coefficient between fuel and the air streaming through the bed, (2. These constants appear in the expression (Equation 1)
hl may vary from about 6000 B. t. u. per pound of oxygen for graphite to about 6500 for high-grade bituminous coal, but the other quantities vary little from case to case, and their
which determines the rate of ignition of the fuel as a function of the physical and chemical characteristics of the fuel bed considered as a unit. The present paper is devoted to further consideration of the significance and magnitudes of these quantities.
values are fairly mell established. Of the other six quantities, L-, G, and T , are the independent variables and cover a considerable range of values; CY and pl are coefficients which change m-ith G, and both of these, as n-ell as k . vary somewhat with the properties of the fuel. For use in the nomograph Equation 1 can be rewritten in terms of four groups,
Nomograph
To facilitate calculations with Equation 1, a nomograph (Figure 1) was constriicted which can be used to determine the effect of changes in the values of the variables on the rate of ignition, or to obtain estimates of the values of the variables by comparison with experiment. Ten quantities occur in Equation 1. Four of these were given constant values as follows:
(2)
which contain all six variables that we desire to control. The nomograph is an alignment chart constructed according to well known methods ( 1 , 3 ) . The construction depends on writing the equation in the form of the following determinant: 563
~
W
0
1
0
T,
1
P1hl (1 +
- -v1 ( V T T S + ~ -~) cp 20
($2,
YZ)~(23, y,)-lie
e m) 1
( d r n+ e
-
%>
dn a straight line if, andbnly if,
I n the construction the x and y axes were made to intersect a t a n acute angle in order to reduce the size of the chart. The chart will usually be used to determine values of L? for given values of G. T o do this i t is necessary to know or assume the values of Ti, k , cyl and p1, when v and w can be computed from Equation 2. It is estimated that U can be obtained from the chart with an average error of 5 to 10 per cent. It would be pointless to strive for higher accuracy because of the uncertainties in the values of the coefficients and because greater accuracy is not needed in applications to actual fuel beds. The chart may also be used, however, to estimate values of the coefficients a and pl, in particular, from
=
0
(3)
such data a i those published by Sicholls (11) in which the dependence of the rate of ignition on the rate of primary air flow in pure underfeed burning was determined experimentally. This can be done by adjusting the values of the Coefficients and of their variation Rith G to permit the repro-
fi was concluded that this was due to neglect of the radiation component of the heat transfer coefficient, which was not determined in the experiments referred to but which might become important in the fuel bed. Inclusion of a n estimate of this component permitted the calculation of the results previously given (7, 8) and led to a heat transfer coefficient that was, t o a first approximation, independent of the air flow rate since the radiation intensity depends only on the temperature and gas composition. When, however, this coefficient was used in Figure 1, Sicholls' experimental results could be approximated only by assuming that p1 was a function of G which first increased and then decreased. Since such a dependence of reaction rate on air flow seems unlikely ( I S , 16,I S ) and since the convection contribution to a might not be negligible, other relations between a and G were investigated. It was found that Furnas' data for convection heat transfer could be used if they were supplemented by a radiation contribution that varies inversely as
FIGURE 1. NOMOGRAPH FOR CALCULATION OF EQUATIOX 1
APRIL, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
G, making a large contribution for small values of G and falling off to a negligible quantity as G increases. This results in the formulation of the heat transfer coefficient for - 1.5 1 inch fuel as follows:
+
y ,
= ~360
1 - 57iG
+ 16.9G0.’
Here the last term is the convection contribution calculated from Furnas’ formula for - 1.5 1 inch material, for a void \-olume of the bed of 40 per cent and using coefficient -4 found Iiy Furnas to be suitable for iron ore. This value of -4 is twice as great as that found for coke, but it is not clear why there should be any difference between them since the nature of the material would not be expected to play any part in convective heat transfer. I n any case, this choice of values gave agreement with the experimental data, but it should be noted that this agreement is not unique; other forms could be obtained by adjustment of the values of other quantities such as pl and k . Equation 6 was adopted as involving a minimum of adjustment of quantities for which there were independent experimental (lata. Additional measurements of these coefficients are required to permit extensiye use of this method of calculation.
+
FIGURE2. VARIATIOX OF HEAT TRANSFER COEFFICIENT CY WITH AIR FLOWRATE G (Fuel size, -1.5 1 inch)
+
0
The inverse relation between the radiation component, the first term in Equation 6, and G can be justified as follows: The total quantity of heat transferred by radiation per unit time depends only on the temperature and the gas composition (4)and hence may he considered constant with respect to changes of G. This total rate of heat transfer is equal to the product of the heat transfer coefficient by the temperature difference, so that where
2’1
T, a1
= =
=
al(T1- T,) = constant (7) constant temperature of the source temperature of the gas stream portion of the heat transfer coefficient due to radiation
If a stream of magnitude G is heated by a constant source, the temperature attained by the stream varies inversely as G; that is, T , = a/Gc,. Therefore the difference between the temperature of the source :and that of the stream becomes T1 - T , = TI - a/Gc,, where a represents the constant rate of heat input. Hence
where c1,
cz =
constants to be determined experimentally
This is the form of the first term of Equation 6 representing the radiation contribution to the heat transfer coefficient.
565
The values of the constants in this expression were determined by using Figure 1 to calculate a1from Sicholls’ data for the rate of ignition of high-temperature coke, 1 X 1.5 inches in size. This required the assumption of values of p1 and k; the former is discussed below and the latter is given by previous data ( 7 ) . From these values the convection component given by Furnas’ formula was subtracted and the remainders were correlated by the use of Equation 8 as a two-constant interpolation formula. It will be noted that QI becomes infinite for values of G less than 57; this occurs because below ~ the radiation intensity is more than sufficient this air f l o rate to raise the stream temperature at as high a rate as is required by the temperature gradient through which it flows, so that T , becomes equal to T . Equation 6 is shown graphically in Figure 2. The variation with particle size will be different for the convection and for the radiation contributions. The convection contribution may, in accordance with Furnas’ work, be expected to vary as the inverse 0.9 power of the average particle diameter. The radiation component may be expected to vary approximately as the 0.1 power of the particle diameter. This results from the same considerations as Twre outlined previously (7) where, for purposes of heat transfer, a fuel bed is considered to consist of a group of parallel tubes of diameter equal to the mean radiant distance calculated for conduction. The radiant heat transfer coefficient is proportional to the diameter of these hypothetical tubes and hence to the particle diameter; while the surface per unit volume of bed, from Furnas’ calculation of convective heat transfer varies inversely as the 0.9 power of the particle diameter. The product of these results in the dependence of the radiation component on the 0.1 power as mentioned above.
Rate of the Combustion Reaction, pi I n the present work ,ul is given by pi
=
183G”‘
(9)
The value of the coefficient is somewhat smaller than that given previously ( 7 ) but does not lie outside the scatter of the experimental data there considered. The exponent of G (I(’>) is not to be considered in disagreement with the value 0.37 observed (18, 16, 18) in measurements on single particles. 1T7efeel that the extension of these measurements to continuous fuel beds is too distant and the precision of the data calculated from fuel bed experiments is too low to justify a t present the additional calculation entailed in the use of the precise exponent, 0.37, rather than the simpler square root. The variation of pClwith particle size, which previously (7) mas given as being inyersely proportional to the 0.9 power of the average particle diameter, should be calculated according to the formula given by Thiele (17) for case I1 of his recent article. This calculation is similar to that referred to in a contribution (6) from this laboratory, where it was shown that in reactions with carbon dioxide, not only the external surface but also a portion of the internal surface of a fuel particle contributes to the reaction. The same thing will be true of the reaction with oxygen, but since the specific reaction rate is greater, the volume contribution will become important only at smaller particle diameters. I n the present case i t results that for comparing large sizes (of the order of an inch), p I is inversely proportional to the average particle diameter, as is usually assumed. However, i t will be necessary below to calculate the rate of reaction of the 1-1.5 inch size from that of 40-mesh to 60-mesh particles. This can be done by assuming that the rate of reaction of the 40-60 mesh particles is the same as that of infinitely small particles, when the ratio of the rates of reaction of large and small size particles becomes three times the inverse ratio of the average diameters.
566
INDUSTRIAL AND ENGINEERING CHEMISTRY
Ignition Temperature The ignition temperature, Ti, as used above is defined as the point below which the combustion reactions do not occur, whereas above Ti the reactions proceed a t a rate independent of temperature. The reaction rate does not behave in this discontinuous fashion; this behavior was assumed in order to reduce the mathematical difficulties of solving the system set up previously (8). It has been shown elsewhere (14) that the rates of reaction of solid fuels with oxygen a t low temperatures vary with temperature as predicted by the Arrhenius equation-that is, p = p,e-EfRT
(10)
Thus, the reaction rate is finite a t all finite temperatures, although the transition from very small to large values is rather sharp. This equation no longer holds above about 1650" F. (900" C.) where the slower rate of transport of oxygen t o the reacting surface by diffu'A sion and convection -05 0 05 TANCE FROM PLANE OF IGNITION, F limits the reaction rate and the temFIGURE3. VARIATION OF RATE perature coefficient OF COMBUSTION REACTION WITH becomes small ( I S , POSITION IN THE BED NEAR THE 1 5 , 18). U n d e r PLANEOF IGNITION these conditions the A. Discontinuous reaction assumed previously c o m p l e t e expresB. Continuous reaction sion given by Parker and Hottel ( I S ) in their Equation 8 is required but may be approximated, as above in the discussion of pl,as a function of G and particle size only. The use of ignition temperature as defined above is an approximation to reality represented by the use of curve A in Figure 3 instead of the correct function given by curve B. If the rising portion of curve B is relatively steep, curve A becomes a good approximation to it. This occurs in fuel beds, and the closeness of the approximation is enhanced by the fact that ignition occurs in a region where the temperature gradient is very high. Although the concept of ignition temperature as a discontinuity in the reaction rate of the fuel must be discarded, the term may be retained as indicating the temperature a t which the rate of heat release by reaction reaches some value fixed by the criterion of ignition, as in the Coal Research Laboratory test for reactivity (14). It will be recognized that in this sense the ignition temperature will depend not only on the characteristics of the fuel but also on the apparatus in which the fuel is used or tested. However, it is possible to relate the ignition temperature so defined to the reactivity characteristics of the fuel as measured in the Coal Research Laboratory test when the conditions in the fuel bed considered are known. For example, the ignition temperature of a fuel of known characteristics may be determined for a pure underfeed fuel bed. I n such a fuel bed, with the assumption of discontinuity previously used (8), ignition occurs a t the point a t which the second derivative of temperature with respect to position in the bed changes discontinuously from positive to negative values (IO). I n a real bed, in which the reaction rate varies
----jkr
VOL. 32, NO. 4
as shown in curve B, Figure 3, the analogous point would be that a t which the second derivative, now varying continuously, changes sign and hence vanishes. This point is similar to the condition observed in the Coal Research Laboratory reactivity test because, since k(d2T/dx2)represents the flow of heat into an element of volume by conduction, the condition that d2T/dx2= 0 is equivalent to the statement that the element of volume neither receives nor loses heat by conduction from other parts of the bed. This point is also critical because, since d2T/dx2vanishes, dT/dx has a maximum; hence a t this point pU(dT/dz), the heat required per unit time by the incoming fuel is also a maximum. At this point the reaction rate must have reached a value given by PipA = PU
dT
+ a(T - To)
(11)
where p i = reaction rate a t plane of ignition This expression is obtained by setting the second derivative in Equation 5 of the previous paper (9) equal to zero. To evaluate the right-hand side of this expression, it is necessary to evaluate the temperature without making use of the discontinuous second derivative. This can be accomplished by use of the first integral of the previous Equation 5 (9) :
(12)
T h i s expression deserves attention because i't shows that the sensible heat in the gas and fuel streams a t any point is equal, not to the heat released by reaction up to that point, but to the heat released, diminished by the heat loss from the bottom of the bed and increased by the heat conducted down through the bed to t h a t point. The appearance of FIGURE4. CALCULATED RATES OF IGNITIOX OF COKEWHOSE REACTIVITY these a d d i t i o n a l CHARACTERISTIC Is GIVENBY T16 = terms explains 885" F., T75 = 975' F. Nicholls' failure (12) to secure a heat balance in calculations based on his tests of underfeed burning. The analysis will not be given here in detail since it is similar to that given previously. The evaluation of the righthand side of Equation 11 results in the expression for the reaction rate a t the plane of ignition, PL(iPlh1 =
k(c
+ 6)2T$
C - b
(13)
where pi is given by Equation 10 for the absolute temperature T,. The last fraction on the right is a correction for the extent t o which reaction proceeds below the plane of ignition and is usually equal to 1. It may become different from unity, however, for unusually low values of E / R T , which may occur with exceptionally reactive fuels burned a t medium rates.
APRIL, 1940
INDUSTRIAL AND ENGINEERING CHEhlISTRY
flow rate and a rate of ignition and from them to calculate a n ignition temperature according to Equation 13. Using this value of Ti, the rate of ignition is calculated by the use of Figure 1. If this differs from the assumed value, the assumption is corrected and the procedure repeated.
TABLEI. IGSITION TEMPERATURES -------Ignition Air R a t e Lb./(sq. f f . ) ( h r . )
Rate of Ignition Lb./(sp. f t . ) f h r . j
100
20 25 30 35
300
500
High-temp. coke
' F.
567
Temp.l'ittsburgh seam coal
F.
20
25 30 35
1710 1720 1730 1730
20 25 30
35
Reactivities According t o Coal Research Laboratory Test 7 -
-TIS--F.
High-temp. coke Pittsburgh seam coal
885 445
C. 475 230
-T;aF. 975 545
C. 525 285
B . t . u./ Ib. mole 69,100 29,300
E
Cal./gtam mole
38,400 16,300
Table I gives the ignition temperatures that would be observed in pure underfeed burning of a typical high-temperature coke and of a Pittsburgh seam coal at various primary air rates and rates of ignition, both being burned in the - 1.5 1inch size. These ignition temperatures are much higher than the values of T I Sand T7&observed in the Coal Research Laboratory reactivity test. The reason is that the heat requirement for ignition in the fuel bed is much greater than in the test: hence the reaction rate of the fuel must be proportionately greater and the temperature a t which the reaction becomes self-supporting is raised accordingly. The concordance of the calculated ignition temperatures in the fuel bed with those observed in experiments with similar beds (11) supports the interpretation of the Coal Research Laboratory reactivity test as a measurement of reaction rate. The calculated ignition temperatures increase with air flow rate and with rate of ignition. Those calcuFIGURE5. RATE OF ADVANCEOF IGNITIOX ZONE IN HIGH-TEMPERAlated for coal are TURE COKE(11) hypothetical, because the coal obTiously would have been carbonized before reaching these temperatures and would thus have changed the reactivity characteristic from t h a t measured a t low temperatures t o one more like that of the coke considered.
+
Application The methods and data developed above have been applied to the calculation of the rates of ignition of several fuels in pure underfeed burning. The procedure is to assume a n air
A I R FLOW,
LBS. P E R HR. P C R
SQ.FT.
FIGURE 6. CALCULATED RATES OF IGNITION OF COKE WITH IGNITION TEMPERATURE OF 1000" F. (8)
Figure 4 shows the results of the calculations for several sizes of high-temperature coke. This is to be compared with Figure 5, reproduced from Nicholls' work. The values of a for the 1 X 1.5 inch size were calculated from the experimental points for that size shown in Figure 5 . The values of all the coefficients for the other sizes were calculated according to the methods outlined above. The agreement of calculated with experimental curves is about as good for the other sizes as i t is for the 1 X 1.5 inch size. Figures 4 and 5 may also be compared with Figure 6, reproduced from the first paper on this subject ( 8 ) , where a: was considered to depend on size only and where Ti was considered constant, the temperature a t which the combustion reaction suddenly started. The comparison shows a greatly improved fit in the present work and emphasizes the agreement of the calculated trend with change of size with that determined experimentally.
Nomenclature cp = specific heat of air and combustion gases, B. t . u./
(lb.)(" F.)
hl = heat of reaction C hz = heat of reaction C
+ +
0 2 4 COX, B. t. u./lb. 0 2 COZ-+ 2C0, B. t. u.,/lb. COa thermal conductivity of fuel bed, B. t. u./(ft.)(hr.) (" F.) pl = concentration of O2 pa = concentration of CO z = distance from grate, ft. E = activation energy of reaction C OZ + COZ, B. t. u./ lb. mole G = rate of gas flow through fuel bed, lb./(sq. ft.)(hr.) PI = concentration of oxygen in entering air
k
=
+
INDUSTRIAL AND ENGINEERIXG CHEMISTRY
568
R = gas constant, B. t. u./(lb. mole)(" F.) T = temperature elevation of fuel bed above surroundings, O F. T , = temperature elevation of air and combustion gases, F. Ti = ignition temperature of fuel, F. T o = temperature of fuel at 5ottom of bed, F. T = absolute temperature, Rankine Tl5,T7j = temperatures at which rate of increase of fuel temperature in Coal Research Laboratory reactivity test reaches 27" F. (l!' C.) and 135" F. (75" C.) per min., respectively, F. U = rate of ignition, lb./(sq. ft.)(hr.) a = coefficient of heat transfer between solids of fuel bed and combustion gases, B. t. u./(cu. ft.)(hr.)(' F.) 8 = coefficient of heat transfer from bottom of fuel bed to surroundings,B. t. u./(sq. ft.)(hr.)(' F.) O
O
pi pi
= =
p
=
++
-
rate of reaction C 0 2 C O , lb. OZ/(CU.ft.)(hr.) rate of reaction C 0 2 + CO2, a t the plane of ignition, lb. 02/(cu. ft.)(hr.) specific heat of fuel, B. t. u./(lb.)(" F.)
This nomenclature is the same as that used previously (7, 8) except that P here is equivalent to Vi in the earlier papers.
VOL. 32, NO. 4
Literature Cited (1) Allcock, H. J., and Jones, J. R., "The Somogram", London, Sir Isaac Pitman & Sons, 1936. ( 2 ) Furnas, C. C., Trans. Am. Inst. Chem. Engrs., 24, 142-66 (1930). (3) Hewes, L. I., and Seward, H. L., "Design of Diagrams for
Engineering Formulas", New York, McGraw-Hill Book Co., 1923.
(4) Hottel, H. C., and Smith, 1 '. C., Trans. Am. SOC.Mech. Engrs., 57. 463-70 (1935).
( 5 ) Mayers, M. A , , Chem. Rev., 11, 31-53 (1934). (6) Mayers, M. A . , J . A m . Chern. SOC.,6 1 , 2053 (1939). (7) Mayers, M.A,, Trans. Am. Inst. M i n i n g Met. Engrs., 130, 40823 (1938). (8) Mayers, M. -4.,Trans. Am. SOC.Mech. Engrs., 59, 279-88 (1937). (9) Ibid., 59, 260, Equation 6 (1937). (IO) I b i d . , 59, 282, Equation 21 (1937). (11) Nicholls, P.. U. S. Bur. Mines, Bull. 378 (1934). (12) Ibid., Bull. 378, 9-11 (1934). (13) Parker, A. S.,and Hottel, H. C., IXD. ENG.CHEM.,28, 1334-41 (1936). (14) Sebastian, J. J. S., and Mayers, M. A., Ibid., 29, 1118-24 (1937). (15) Smith, D. F., and Gudmundsen, A,, Ibid., 23, 277 (1931). (16) Terres, E. et al., Angew. Chem., 48, 17-21 (1935). (17) Thiele, E. W., IND.ESG. CHEM.,31, 916-20 (1939). (18) Tu, C. M., Davis, H., and Hottel, H. C., Ibid., 26, 749-57 (1934). PRESENTED in the Symposium on t h e Combustion of Solid Fuels before the Division of Gas and Fuel Chemistry a t the 98th Meeting of t h e Amerioan Chemical Society, Boston, Mass.
Barium Chloride from Barite
and Calcium Chloride Factors Affecting Production R. NORRIS SHREVE AND R. K. TONER1 Purdue University, Lafayette, Ind.
HIS investigation was a continuation of experiments in
T
these laboratories concerning the utilization of organic solvents as a n aid in inorganic reactions; it was an extension of the published work of Shreve and Pritchard (6, 7 ) and was carried out simultaneously with that of Shreve and Watkins (8). The reaction Bas04
+ CaCI2e BaCL + Cas04
may be carried out in aqueous solution or in the fused state. This is in contrast to the reaction as it norm all^ occurs, since the reverse reaction is ordinarily assumed to be quantit'ative in the presence of water. Under the former condition i t was thought desirable to study the effects of reaction time, molar ratio of reactants, and quantity of water present, changing one variable a t a time. The effect of ternperature is not reported here since it mas adequately discussed in a previous publication ( 6 ) . The effect of varying time, temperature,and concentration of calcium &loride concurTenth' was next studied. Finally the effects of time, temperature, and molar ratio of reactants under conditions of fusion were investigated. These factors plus a study of the reaction from the opposite side (is e,, the formation of barium sulfate 1
Present address, Lehiph University, Bethlehem, Penna.
from barium chloride and calcium sulfate) gave the answer to the questions: How far can the reaction proceed under given conditions? How far does i t actually go? How fast is it? It has already been shown (6) that ethylene glycol-methano1 (1 to 3) is a good solvent for both barium and calcium chlorides, and that these salts can be removed quantitatively from the corresponding sulfates by its use. Attempts were made to substitute aqueous methanol for this more expensive solvent, the purpose being to increase the solvent power of methanol without incurring the reversion of the reaction which was caused by water alone.
Procedure All reactions in aqueous solution involving but one variable were carried out in a de Khotinsky constant-temperature Oven at 1750 * 10 C. (Other temperatures are given by Shreve and Pritchard, 6.) The reactants, consisting of carefully dehydrated c . P. chemicals, were weighed out into heavy-walled Pyrex glass \
~
;
f
$lltg ,t$a$i:dwt?
~,',",~~a~~ifi,",: ~ b ~ ~ ~
means of microvolumetric apparatus, and then the tube was sealed. A t the conclusion of the reaction time, during which the tubes constantly revolved, the tubes were cooled and broken open, and their contents quantitatively transferred to 125-ml. tincture bottles by the desired organic solvent. The reaction mass was agitated Tvith the organic solvent for 3 hours on a shaker. It was then filtered and the extract analyzed for barium chloride. Aqueous reactions involving variation of more than one factor were carried out on a pilot-plant scale in an electrically heated ball mill. A suspension of barium sulfate in a calcium chloride solution was charged to the mill, and heat xyas applied. As the
