INDUSTRIAL A N D ENGINEERING CHEMISTRY
498
drop was noted with the earlier apparatus. The improved design of the apparatus or the chromium-plated surface eliminated conditions tending to cause this effect. A further study is to be made of the surface resistance effect of different surfaces.
Acknowledgment This investigation was carried on at the Massachusetts the author was a member Of InstituteOf the department of physics. He wishes to express his appreciation to John C. Slater and Gordon B. Wilkes of that department. Acknowledgment is also made to Carl G . Selig, Walter Gllenbach, and Kenneth Robes for their suggestions and cooperation in constructing the apparatus.
VOL. 28, NO. 4
Literature Cited (1) Bates, cIIEM,, 25, 431 (1933). . , 141 (1923). (2) Bridgman, Proc. Am. Acad. Arts S C ~ 59, (3) Davis, Phil. Mag., 47, 972 (1924). (4) International Critical Tables, Vol. V, pp. 227-8, New York, McGraw-Hill Book Co., 1929. (6) Jakob, Ann. Physik, 63, 637 (1920). (6) Kaye and Higgins, Prod. Roy. SOC.(London), A117, 459 (1928). (7) Landolt-Bornstein, Physikalisch-chemische Tabellen, 5th ed. Berlin, J. Springer, 1923. (8) Schmidt, E., Mitt. Forschungsheim Warmesh No. 5, Munich, 1924, reported in Schaok’s “Industrial Heat Transfer” (tr. by Goldsohmidt and Partridge), p. 352, New York, John Wiley & Sons, 1933. (9) Wilkes, G*Be, J. Am. Ceram. S0C.v 16, NO. 3 (March, 1933). RECEIVED September 21, 1936.
SOLID CARBON REACTIVITY A New Method of
Interpreting
Reactivity Data C. C. FURNAS Yale University, New Haven, Conn.
@T
H E term “reactivity of carbon” has been used a great deal but apparently it has never been exactly defined. In many cases a qualitative description is attached to it; in others there is some arbitrary basis of quantitative estimation but such systems are of very limited utility, for the significance of the constants obtained is confined to the particular apparatus being used. The author proposes to give an exact definition to reactivity; namely, the reactivity of a bed of solid carbon is measured by the reaction rate constants of the two consecutive carbon-oxygen reactions :
c+ c 0 2
0 2
=
coz
+ c = 2co
It is not possible to define reactivity in terms of a single constant, for two independent reactions are involved. Much of the previous confusion in dealing with reactivity has been due to the attempt to define it by a single constant. The author defines the reaction rate constants by the following two approximate differential equations which apply to a fuel bed of solid carbon being supplied with oxygen:
error, for it states only that the rate of reaction in the carbonoxygen system is directly proportional to the gas concentration. Experimental work has shown that this is substantially true (1,9). For Equations 1 and 2 to be exact, the variable on the left side should be the mass of gas (oxygen or carbon dioxide) present instead of concentration. If there is no change of volume as the system reacts, the two quantities are proportional; but that is not true in this case, for reaction B involves a volume change. However, the present development does not follow the reactions through to the end. For the first portion of the reaction the volume change is so small that it may be neglected, hence the use of concentrations instead of amounts is justsed. It makes the integration of the equations much simpler. To be exact, Equation 1 should have another term on the right with another constant, to express the reverse reaction in A . The same should hold for reaction B. However, both reactions A and B go so nearly to completion at the temperature of a fuel bed that the rate of the reverse reaction is negligible; hence the simplified equation is justified. Equation 2 requires a further explanation for there is the term - on the right. This term is to take care of the fact dt
The brackets refer to Concentration of gas; 2 = time Equation 1 refers to reaction A, Equation 2 to reaction B. These equations are those of reaction rates in homogeneous, one-phase pystems which obviously do not apply here for these gas-solid reactions are in a heterogeneous system. However, if the concentration (more properly, the activity) of the carbon is constant, the rates cf reactions A and B are approximately fixed by concentration in the gas phase; thus the use of the homogeneous reaction equation introduces but little
that A and B are consecutive reactions. Expressed in words, the carbon dioxide concentration is decreasing because of its reaction with carbon (first term) but is increasing because of the reaction of oxygen with carbon (second term). These two opposing tendencies should make the concentration of carbon dioxide in a thick fuel bed go through a maximum as the gas progresses from the bottom to the top, which, of course, it does. The concentration of oxygen, on the other hand, should progressively decrease. The concentration of carbon monoxide should progressively increase. These tendencies are illustrated qualitatively in Figure 1. The general character of these curves of concentration of oxygen, carbon dioxide, and carbon monoxide is familiar to all who have worked with fuel beds.
APRIL, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
Equations 1 and 2 represent, with reasonable accuracy, what happens in the fuel bed. The author defines reactivity of carbon as the values of K1 and K z which are determined by experiment when a fuel bed is being burned with air. These constants are true, though approximate, measures of the rates of reactions A and B. I n order to determine these constants conveniently, it is necessary to FIQURE 1. GASCOMPOSITIONS IN THE integrate Equations 1 and 2. TYPICAL AIR-BLOWN FUELBED It is assumed that the initial concentration of oxygen at the bottom of the bed is 0.20, expressed as volume fraction. This is too low a value for dry air, but most tests are run with moist air and 0.20 will represent average conditions. The details of the integration of Equations 1 and 2 are given later in the paper. The results are:
*
If any initial concentration of oxygen other than 0.20 is used, the equations are changed only by changing the coefficient 0.20 to the proper figure. Symbol t for time may be used interchangeably with distance, for time is proportional to distance up the bed. Equation 10 represents a curve that goes through a maximum. Three such computed curves are plotted in Figure 2. In each of the three curves the value of Kl is arbitrarily set a t 1.0 and the curves are plotted for K f = 0.1, 0.5, and 2.0. The ordinate is the volume fraction of carbon dioxide in the bed. The abscissa is time or distance from the bottom of the bed. For the smaller values of Kz the maximum point in the curve rises to higher values of carbon dioxide, and this maximum occurs at a greater distance up the bed. This is in keeping with the chemical picture of the reaction. If K z is small, the second reaction (conversion of carbon dioxide to carbon monoxide) is small so the carbon dioxide does not disappear rapidly from the gas stream. A curve has also been plotted in Figure 2 which shows one of the set of results of carbon dioxide content vs. distance from Sherman and Bliaard’s experiments (8). The experimental curve does not coincide even approximately with any of the computed curves, but this is because the curve is plotted on
The term “reactivity” of carbon has long been used, and several arbitrary and qualitative means of measurement have been proposed but apparently the term has never been quantitatively defined or measured. The author proposes to measure reactivity in terms of the reaction rate constants for the equations: (A) C O2 = CO,; and (B) COz C = 2CO. In other words, reactivity consists of two distinct entities and cannot possibly be defined by a single constant, for the rate of reaction A has no direct connection with the rate of reaction B. By starting with the differential equa-
+
+
499
18 14
0“ v 12 5 ew W OL
“a a W Q 5
6
3 u
4
2
Oo
1
2
3 4 5 6 TIME, SECONDS
7
a
9
FIGURS, 2. THEORETICAL RELATION BETWEEN TI- AND PERCENTAQE OF CARBON DIOXI D E ~IN A FUEL BED OF SOLIDCARBON
a different scale-that is, inches instead of seconds. The abscissa values are pulled out to the right but the general shape of the curve is the same as the computed ones. However, the left-hand segment has a smaller slope than the computed ones. This is undoubtedly due to the fact that fuel bed temperatures are not constant, so that reaction rate is slower in the lower, cooler part of the bed. The equations were developed on the supposition that Kl and Kz were constant, and hence that temperature was constant. This is no serious shortcoming of the theory, for, when observed data are used to determine K , and K z , the result will be an average for the average temperature involved. Using the relations developed in the above equations, it is simple to determine the values of the reaction rate constants, K1 and Kt; it is necesssary only to have data on the variation of carbon dioxide in the bed, or, even less, it is necessary only to know the maximum value of carbon dioxide in the bed and the point at which it occurs. Differentiating Equation 10 and setting equal to 0 gives the value of time t a t which the maximum occurs; Thus:
Substituting this value of tm-. in Equation 24 gives the value which [Con]will have a t its maximum point; thus:
tions of the rates of the above reactions and making a few simple but noninjurious assumptions, the author develops a simple method for obtaining approximate rate constants for reactions A and B. To obtain these constants it is necessary only to know the maximum percentage of carbon dioxide and its position in the bed for a solid fuel being burned with air. The reaction rate constants are computed from fuel bed data already in the literature. The tabulation of the data brings out many interesting comparisons between various fuels.
INDUSTRIAL AND ENGINEERING CHEMISTRY
500
VOL. 28, NO. 4
0 MAXIMUM PER CENT COa IN FUEL BED
FIGURE3. RELATIONBETWEEN MAXIMUM PERCENTAGE OF CARBON DIOXIDE IN FUEL BED AND RATIOOF REACTION RATE CONSTANTS
where
a =
DISTANCE FROM BOTTOM OF BED T O POINT OF MAXIMUM Co1 IN FEET
FIGURP~ 4. COMPUTED VALUEOF K I RELATEDTO MAXIMUM PERCENTAGE OF CARBON DIOXIDE AND THE POSITION OF TRATMAXIMUM IN THE BED
K Z Ki
Equation 15 shows that the maximum value of [COZ]in the bed depends only on the ratio of Kz to K1, not upon the actual magnitude of either. This equation is plotted in Figure 3. In order to determine the actual value of K z and K 1 it is necessary to use Equation 13 which may be rewritten as:
If the maximum value of carbon dioxide’in the bed is known, then a can be determined. With a known, Equations 16 and 17 can be used to determine K1 and K2, provided t is known. Since t is obviously proportional to distance up the bed, the distance itself may be used, provided the constants are defined in such terms. The author has made the indicated computations and plotted the results in Figures 4 and 5. The curves are plotted on log-log coordinates in order to have them all on one plot. The ordinate of Figure 4 is the computed value of Kl, the abscissais the distance from the bottom of the bed to the point of maximum carbon dioxide, in feet. Each curve is for a given percentage of carbon dioxide a t the maximum point. Figure 5 is the same for K P . Determining the reactivity constants, then, involves only the simple task of reading a point from each of two curves, provided the maximum value of [COJ and its position in the bed are known. It should be emphasized that the values of K1 and K2 are in no way dependent upon each other. That is, the rate of reaction A (oxygen with carbon) may be very rapid and that of reaction B (carbon dioxide with carbon) may be very slow, or the reverse may be true. A fuel that reacts rapidly with oxygen will not necessarily react rapidly with carbon dioxide, though, of course, it often does. The value of K z should be of more importance in the consideration of blast furnace fuels, for this is the constant which determines the extent of ‘(solution loss” with which furnace operators are always dealing. The substitution of distance for time calls for a certain amount of interpretation. Since distance is in feet and time
FIQURE 5. COMPUTED VALUES OF K z RELATED TO MAXIMUM PERCENTAQE OF CARBON DIOXIDE AND THE POSITION OF THAT MAXIMUM IN THE BED
is in seconds, the substitution implies that the gas has a linear velocity of 1 foot per second. However, it has been experimentally shown that in a fuel bed the position of maximum carbon dioxide does not change a significant amount with increasing gas velocity, over a wide range of gas velocities. Hence the position of the maximum a t any gas velocity may be used. In terms of physical chemistry this fact merely means that reaction rate is directly proportional to the gas ’ velocity. Hence the values of K1 and Kz obtained from these plots may be inferpreted as being the values of K1 and K z which the system would have if the linear velocity through the bed were 1 foot per second. This simple device puts all data on the same basis and so may be used to compare various fuels, sizes, and temperatures. A few of the data available in the literature have been compiled in Table I to illustrate the use of this method of interpreting reactivity experiments. Items 1 to 10 are for gas samples taken from the tuyhres of iron blast furnaces, in operation. Items 11 to 21 are for blast furnace cokes that were tested in small, air-blown producers. The computed values of K1 and Kz are naturally quite variable since fuels and apparatus vary widely. However the values of K1 (which measures the rate of reaction with oxygen) for the blast furnaces (items 1 to 10) are consistently much smaller than the values obtained for coke in experimental apparatus (items 11 to 21). This is undoubtedly due to differences in size of the solid particles. The size of coke a t the blast furnace tuyhres is not known but it is probably about 4 to 5 inches, while most of the fuel bed experiments were on 1-1.5 inch material. The values of K2 (rate of reaction of carbon dioxide with carbon) show a similar trend. The ratio of K z to K I (ratio of rate of reaction with carbon dioxide to that with oxygen) is consistently larger for the blast furnace data than for the experimental apparatus. This might be due to more rapid increase of reaction B than reaction A with decreased particle size, but it is probably due to temperature effects. The blast furnace temperatures are much higher than those of fuel beds because of the hot blast. If increased temperature speeds up reaction B much more than reaction A, then the ratio of K Z to K1 might be expected to be greater for the blast furnaces. This is in agree-
APRIL, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
ment with the findings of the effect of temperature upon reaction B where only a single piece of fuel is involved (9). In only two cases in the data given is the value of K z as large as K1-for wood charcoal and for lignite char. The physical structure in these cases is probably different from that of other fuels. To obtain consistent and satisfactory values for these reaction rate constants, it will be necessary to do more careful experimentation than has yet been done. Gas samples in fuel beds should not be snap samples but should be taken slowly and continuourjly over a considerable period. They should be taken a t several points a t a given level so that the sample will represent a composite of the entire cross section of the bed. If exact experimental data are available, the method outlined should be of considerable aid in building up a picture of the actual mechanism of the reaction in the burning of solid fuel. The use of these equations is not confined to mere determination of the reactivity constants, K 1 and K2. They can be used to predict the approximate performance in a fuel bed, provided values of K1 and K 2 are known. The simplest way to do this is to compute the curve for the given values by means of Equation 10. For instance, for a blast furnace coke with K1 = 1.0 and Kz = 0.5, the proper curve of Figure 2 can be used. As an illustrative problem: If the carbon dioxide composition a t some point in the bed is 8 per cent and is past the maximum, what will be the concentration 2 feet farther up the bed? From Figure 2 the composition 2 feet farther up the bed will be 3.7 per cent, provided feet are substituted for seconds. This is in keeping with convention of the method used in evaluating the constants, as already given. This solution is only approximate, for the derivation does not take into account the change in volume due to the formation of carbon monoxide. The greater the proportion of carbon monoxide, the greater the error. Before the method of prediction can have extensive use, it will be necessary to have exact information on the effect of temperature on the constants.
For 02: d- [COz = I dt
For GOz:
= - Kldt [Oz] = c1 e-Rlt When t = 0, [OZ] = 0.20, c1 = 0.20 [OZ]= 0.20 e - K l t
(4)
(5)
- K z [ C O z ]- dI0.20dle-xlt]
d&= l dt
- Kz[COz]+ K1 0.20 e - K l t
d‘Co21 -= dt
(6)
Equation 6 is a linear differential equation usually written in the form,
+
Y’ PY = Q where P and Q are functions of x alone. In this case: [Coal = y t = x
An equation of the above type may be solved by multiplying by an integrating factor, ef In this case P = K ZSO that the integrating factor is e K z x . Multiplying Equation 6 by the integrating factor:
d[COzleKzt dt
+ Kz[COz]eRzt= 0.20Kle(K2-K1V
(7)
Integrating, {CO,]
=
0.20 ___ Ki Kz - Ki
0, [COZ]
=
0; therefore,
eKd
When t
=
e(Kz--Kl)t
+c
(8)
e = - - 0.20K1 K2 - Ki
The particular solution then is
TABLEI. COMPUTED REACTION RATECONSTANTS FOR AIR-BLOWN BEDS OF VARIOUS FUELS
Distance Fuel Max. from Size COz Grate KI K2 Inches % Feel Coke i n Blast Furnaces 0.63 0.3 10.5 2.17 1. Ala. No. 1 1.45 0.38 12.2 1.25 2. Ala. No. 2 1.13 0.275 12.5 1.67 3. Ala. No. 4 0.87 0.40 10.2 1.67 4. Ala. No.5 1.45 0.58 10.8 1.08 5. Pa. No. 1 0.64 0.24 10.9 2.5 6. Pa. No. 2 0.71 0.34 10.1 2.0 7. Pa. No. 3 1.05 0.41 10.8 1.5 8. Pa. No.4 0.67 0.37 9. Ill. 9.5 2.0 1.67 0.30 1.5-2 13.5 1.25 10. Provo Blast Furnace Coke i n Fuel Bed 14.2 0.376 6.0 0.9 1-1.5 11. St. Louis 1.25 4.8 1-1.5 12.2 0.375 12. Clairton underheated 14.2 0.417 0.8 5.4 1-1.5 13. Clairton overheated 0.61 8.0 1-1.6 16.0 0.375 14. Benham 0.60 9.4 16.5 0.333 15. S. York 13 B 18.8 0.250 17.0 0.30 16. 27 B 1.2 5.0 12.5 0.375 1-1.5 17. Clairton underheated 0.27 4.3 16.5 0.71 1-1.5 18. Leisenring beehive 0.48 7.4 16.4 0.417 1-1.5 19. Wilkerson 0.41 1-1.5 7.7 16.9 0.417 20. J. and L. 0.52 5.5 21. Continental No. 1 1-1.5 15.5 0.500 0.45 8.9 17.0 0,375 22. Domestic cokea 1-1.5 13.0 0.25 1.7 1-1.5 7.6 23. Snthracitea 24. Bituminous coda . . 1-1.5 14.0 0.375 6.2 0.93 Charcoal 1.3 16.0 0.166 18.0 25. Wood (5) 5.5 3.9 6.2 0.21 26. Wood (8) 27. Lignite chara (4) 0.5-2 2.0 0.125 3.0 15.0 a Value for 12-inch fuel bed and a rate of burning of approximately 40 pounds per foot per hour. Reference
- Kz[COzI - d [OzI
Evaluating [O,], d ln,[O,]
Integration of Equations 1 and 2 The development of the equations is given herewith. The physical interpretation is given in the text.
501
Simplifying,
Kz/K,
0.477 0.262 0.244 0.460 0.400 0.375 0.480 0.392 0.55 0.16 0.15 0.26 0.148 0.077 0.064 0.018 0.24 0,063 0.065 0.053 0.095 0.051 0.22 0.15 0.072 1.42 5.0 square
Values of K , and Kz can be obtained from an experimental curve by obtaining the position of the maximum. At the maximum the slope = 0. Differentiating the particular solution (Equation 10) and setting equal to 0, a t maximum: Kle-Kit
t(K2
- K,e--Rzl
- K1)
3
0
(11)
K2 Ki
= In,-
Therefore a t maximum:
From Equation 10, 0.20K1 [ e - K Kz ? Ine&K ,&sa.
=
- K,
Kt
-e
K --Kx K-IK I ’ne&]
(14)
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VOL. 28. NO. 4
For other oxygen concentrations the appropriate value of the constant may be substituted.
2 =a Let K K1 Rearranging,
Literature Cited
Substituting a for K z / K , in Equation 13 and rearranging,
and preceding equations The ‘Onstant o‘20 in refers to the proportion of oxygen in the original gas stream.
Clement, J. K., Adams, L. H., and Haskins, C. N., Univ. Ill. Expt. Sta., Bull. 30 (1909). Kinney, 5. P.,Bur. Mines, Tech. Paper 454, 66 (1930). Kreisinger, H.,Augustine, C. E., and Harpster, W. C.,Ibid., 207 (1919). Kreisinger, H.,Ovitz, F. K., and Augustine, C. E., Ibid.. 137 (1916). Mott, R. A., and Wheeler, R. V., “Coke for Blast Furnaces,” p. 130 and Table XLV, Colliery Guardian Co. Ltd., 1930. (6) Perrott, G. St. J., and Kinney, 9. P., Trans. Am. I n s t . Mining Met. Engrs., 49,543-84 (1923). Sherman, R.A., Iron Age, 115,1043-5 (1925). Sherman, R. A., and Blizard, J., Trans. Am. I n s t . iManing Met. Engrs., 49,526-42 (1923). Tu, C . M., Davis, H., and Hottel, H. C., IND. ENG.CHBM.,26, 749-57 (1934). RECEIVED September 28, 1935. Presented before the Division of Gas and Fuel Chemistry at the 90th Meeting of the American Chemical Society, Ban Frmoisco, Calif., .4ugust 19 to 23, 1936.
Granule Disintegration of Cornstarch T. C. TAYLOR AND JOHN C. KERESZTESY Columbia University, New York, N. Y.
HEN the viscosity of pastes made from air-dried cornstarch that had been ground for various periods of time in a ball mill under specified conditions (7‘) falls to substantially that of the soluble corn p-amylose of the same concentration, the ratio of the insoluble fatty-acid-bearing a-amylose to the &amylose as determined by an electrophoretic separation is approximately 15 to 85. With the precision for this type of measurement the ratio corresponds to the one obtained by Taylor and Iddles (9) in pastes where the granule disintegration was effected by the use of concentrated solutions of ammonium thiocyanate followed by separation in an electrophoretic cell or on an ultrafilter. For cornstarch the stopping point in the grinding of the dry starch occurs after 168 hours have elapsed at the particular ball load, size of mill, speed of revolution, etc., that had been selected. If we grind beyond that point, no great changes in viscosity of the subsequently made pastes occur as they do in the early part of the operation. It is necessary, therefore, to look to other variable and determinable factors in order to search for significant effects in this region; that exploration has been made and the results are reported here. To follow the changes, use was made of the alkali-labile determination ( l a ) , estimation of yield of a-amylose, and determination of combined fatty-acid content of a-amylose as a function of period of grinding. For reference, some samples were analyzed in the same way after treatment with cold acid according to the method of Lintner (4). Th’is was done because cold acid so affects the starch that the granules disintegrate more readily in water and give lumped dispersions which are similar in many respects to those from ground starch.
The a-amylose was recovered in each case after migration and washing the solid deposited on the positive membrane of the electrophoretic cell. The combined fatty acids were determined after acid hydrolysis of the residue, and the alkalilabile determinations were made on the samples by the recently revised method (8).
Alkali-Labile Value The latter apparently gives a sensitive measure of the change in available reducing groups during the treatment, for it is here that the attack by alkali on an amylose chain begins. It serves, therefore, as a guide to the progress of certain types of transformation that take place during soluble starch formation. The simple reducing value of samples without the alkaline treatment does not change sufficiently to be significant. Briefly, the method depends on the ready attack of hot aqueous alkali on certain fractions of the amylose or the starch in contrast to the slowness of attack on other parts
I
I n making soluble starch, certain changes take place that can be followed by determination of the ’alkali-labile” value. Dry-grinding cornstarch produces changes similar to those produced by the Lintner acid treatment when alkali-labile value is taken as a criterion. Corn alpha amylose loses combined fatty acids and amyloid material becomes soluble, but the insoluble residue has a higher fatty acid content than the material from which it came. A working hypothesis is discussed briefly in connection with interpretation of the results.
