-ROTAMETER
1
GLASS FILl
BALANCE
I I
BURRELL T U B E 7 FURNACE SAMPLE,
He
co2---t--l
MANOMETER
Hg
MANOMETER
1
U
\ FiOTA M ETE R
1,
Y
I
HEATER
Reaction rate apparatus contains equipment for gas purification, metering, heating, and reaction measurement
I
P.
V. N.
RAMACHANDRA RAO and E. E. PETERSEN
Department of Chemical Engineering, University of Culifornia, Berkeley 4, Calif.
Effect of Carbon Dioxide Concentration on Gasification of Artificial Graphite The reaction of carbon dioxide and carbon to produce carbon monoxide has practical importance in combustion, water gas production, and gasification of solid fuels
THE
carbon-carbon dioxide reaction has been studied by many investigators ( 7 , 2, 4-8, 77, 73, 74, 77). Gulbransen and Andrew (7, 8) have shown that the internal surface area of graphite increases markedly during reaction with carbon dioxide and with oxygen. Walker, Foresti, and Wright (77) showed that internal surface area is important in characterizing carbon before and during the gasification reactions. Gasification of an artificial graphite rod undergoes three stages of progressive burnoff (74, 77): induction, constant rate, and decreasing rate. In any of
these stages, reaction rate is controlled by chemical reaction, by internal diffusion, by mass transfer from the main gas stream to the exterior carbon surface, or by a combination of these ( 9 ) . Reaction time, temperature, velocity and concentration of the main gas stream, pore shape and size distribution, reaction area, and intrinsic reactivity of the particular form of carbon reacting are the main variables governing these burnoff stages and determining reaction area. Intrinsic reactivity is defined (78) as the rate a t which a unit surface of carbon will react when the concentra-
tion of the reactant above this surface is unity. The kinetic order of the carboncarbon dioxide reaction to form carbon monoxide C [graphite]
+ COS [gas] = 2CO
[gas]
has been studied by Gadsby, Hinshelwood, and Sykes (4) using coal and nut charcoals. The over-all reaction was fractional order; however, later ( 5 ) they reported that the true reaction order is greater than the apparent order because the build-up of carbon monoxide concentration a t the carbon surface VOL. 50, NO. 3
MARCH 1958
331
Table 1. Impurity Aluminum
Boron Calcium Copper Iron
Lead Magnesium Manganese Potassium Silicon Silver Sodium Tin Titanium Vanadium
Spectroscopic Analysis of Graphite Electrodes" Sample 1 b Sample Z b Sample 3* Sample 4*
4
A V V 1
3
2
2 2
A
A
A
2
2
2
A A V A A A
A
A A A A A A A A
A V A A 1 A
A V A
2
A A A A
V A A A
A
A
A
A A A A A A
A V A
Lot 898; 0.5 X 12 inch ACKSP spectroscopic grade of graphite. Code. A = completely absent; J7 = barely vkible. Kumbers indicate relative intensity.
retards the reaction, even though the fraction of carbon dioxide reacting is small. Petersen and Wright (14) studied differential reaction rates (or point values of reaction rates) a t various depths within the sample. Using different temperatures with constant concentration of carbon dioxide in the bulk gas phase, they found a concentration gradient within the internal porous structure of the graphite sample at temperatures greater than about 900' C. In determining the effects of reaction temperature on surface area development within the carbon sample (73, 77), characteristic surface areas were produced at different reaction temperatures for the same weight of carbon reacted; the areas increased to a maximum a t a reaction temperature of about 1175' C. These observations suggested studies at a reaction temperature of about 1100" C. In this investigation the kinetics of the carbon-carbon dioxide reaction were determined a t 1100' C. by varying the partial pressure of carbon dioxide in the bulk gas stream and measuring changes in over-all reaction rate and differential reaction rates a t various depths within the pore system of graphite rods. Mass transfer between the bulk gas phase and the exterior of the graphite samples was not studied; therefore the flow rate of reactant was maintained well in the region where over-all reaction rate was independent of gas velocity. Experimental Reaction Rate Apparatus. The reaction rate apparatus consists of gas purification, metering, heating, and reaction measurement sections and is similar in many details to apparatus previously described (74, 77). The gas purification and metering sections consist of standard pieces of equipment and serve to purify, meter, and mix carbon dioxide, the reactant,
332
and helium, the inert a-cmosphere and diluent. Thus, carbon dioxide concentration is varied at constant total pressure of 1 atm. in the reaction chamber. Helium is metered through a rotameter and then enters the glass tube containing copper oxide, maintained at 400" C. by a cylindrical, resistance heating furnace. The hot copper oxide removes any traces of hydrogen contaminating the helium. Carbon dioxide is metered through a rotameter, mixed with the helium, and passed through a 96% silica tube containing reduced copper maintained at a temperature of about 600' C. to remove any oxygen present in the carbon dioxide. Traces of moisture are removed in a tower containing regenerated silica gel. The reaction chamber is similar to that used previously. The main reaction furnace is a Burrell (Model H-1-9) high temperature tube (Globar) furnace capable of maintaining temperaturesup toabout 1450' C. A platinumplatinum-1 3% rhodium thermocouple, located between the Globars in a porcelain protection tube, controls the furnace temperature to & l o C. The temperature inside the combustion tube is measured Mith another platinumplatinum-1 3% rhodium thermocouple enclosed in a porcelain sheath and located inside the main reaction chamber as indicated. The heating and reaction rate measuring section of the apparatus consists of a I1/g-inch inside diameter porcelain tube 34 inches long. Gases from the purification trains are introduced at the bottom of the combustion tube through a tapered joint a t the end as shown. .4 0.5 -inch porcelain tube 22 inches long is located in the larger combustion tube on a common axis and held in this position by packing the annular space with 6 X 8 mesh porcelain chips. Carbon samples, 2 inches long by 0.5 inch in diameter, are prepared for the run in the following manner. A hole
INDUSTRIAL AND ENGINEERING CHEMISTRY
I / g inch in diameter and 5/16 inch deep is drilled a t the center into each end of the sample, and a porcelain cone is inserted and cemented to the sample. At the other end, a top plate and a porcelain rod, I/g inch in diameter and 18 inches long, are similarly cemented in place to allow the sample to be weighed during gasification. The cone at the bottom and the plate at the top protect the ends of the sample from reaction. Carbon rods used in this study were special graphite spectroscopic electrodes obtained from National Carbon Co., whose spectroscopic analysis is given in Table I. Carbon dioxide was of 99.5% pure. Helium was 99.9% pure, the 0.1% impurity being mostly nitrogen. Operating Procedure. The furnace is brought u p to the operating temperature of 1107 'C., the preheater to 950' C., the reduced copper furnace to 600' C., and the copper oxide furnace to 400 ' C. Then the system is flushed with helium to remove all entrapped air and to maintain an inert atmosphere. Copper wool is reduced with hydrogen as described. Helium is then passed through the combustion tube, to obtain an inert atmosphere before the sample is introduced, at a flow rate of 200 cc. per minute for about half a n hour. The carbon sample is introduced into the combustion tube, and its initial weight is noted. The sample remains in the inert atmosphere for a minimum of one half hour before the reaction is allowed to proceed to ensure initial thermal equilibrium with the furnace. Before starting the reaction, the reaction chamber temperature is recorded, and the weight of the sample is again measured to be sure no weight change has occurred during preheating. The proper reactant mixture is then introduced. During all runs the carbon dioxide flow rate is held constant at 2000 cc. per minute. For the 75,50, and 25% carbon dioxide runs, the flow rate of helium is adjusted to 666,2000, and 6000 cc. per minute, respectively. As the reaction proceeds, the time is noted for each successive 0.1-gram weight loss. After the sample has reacted to a desired weight loss, carbon dioxide flow is turned off and helium flow turned on and maintained a t 800 cc. per minute for several minutes. The final weight is then recorded and the sample moved to the cooler portion of the combustion tube where it cools to about 200' to 300' C. in an inert helium atmosphere. The sample is then quickly transferred from the furnace tube into another tube and allowed to cool to room temperature in an argon atmosphere. Bulk Density Profile Determination. The apparatus required consists of a high-speed jeweler's lathe, an analytical balance, and a micrometer caliper. Although, in principle, the procedure involves measuring the weight and
G A S I F I C A T I O N O F ARTIFICIAL G R A P H I T E 50
I
0
1oo%co~
2.0 G R A M S LOSS
1 I
45 40 35 v)
r
- 30 25 0
-1
;2 0 0 W
3 15 I O
05
030 A
100% co, 7 5 % Cop
25%Hc
0
5 0 % CO2
5o%ne
0
A
100% 75 % COz
0
50%COp
0
25%COp
0
0
0
80
Figure 1.
160 240 320 400 480 R E A C T I O N T I M E (MINUTES)
560
640
I 5 G R A M S LOSS
Reaction isotherms a t 1 107' C.
Figure 2. Profiles of extent of gasification of graphite rods reacted to different weight losses at 1 107' C. A. B.
C. D.
Weight loss Weight loss Weight loss Weight lass
= 2 grams = 1.5 grams = 1 gram = 0.5 gram
cop
1.0 G R A M S L O S S
2 5 % He 50%He 75%He
0 25
I
t
0 20
0 15 0 10
0 05 0
REACTION TIME
(MINUTES)
Figure 3. Extent of gasification at outer sample surface with reaction time a t various concentrations of carbon dioxide
R (CMI
VOL. 50, NO. 3
MARCH 1958
333
Figure 4. Extent of gasification at outer sample surface per unit concentration with reaction time Figure 5. Differential reaction isotherms at various positions within samples at 1 107' C. A.
100% carbon dioxide
75% carbon dioxide-25% 50% carbon dioxide-50% D. 25% carbon dioxide-75%
B. C.
helium helium helium
0.2c
w
i-
a
I00 % c02
0.1 8
LL
7 5 % CO2 2 5 % H e 50 % C 0 2 5 0 % H e 2 5 % C02
cb2LL
75%He
0.16
0
-J
5
0.14
0.12
iZ W
0.10 iL iL
0 o.oe W 2 I-
a
0.06
J W
LL
0.02 0
R (CM)
Figure 6. Auxiliary plot used to calculate integral reaction rates from bulk density profiles 334
INDUSTRIAL AND ENGINEERING CHEMISTRY
0
60
120 180 240 300 360 R E A C T ON TiME ( N I N U T E S I
420
480
GASIFICATION OF ARTIFICIAL GRAPHITE diameter of the sample after successive cuts of 0.25 mm., particular care is needed to obtain the required degree of accuracy. The sample is first mounted in an ordinary machinist’s latheand a’/s-inCh holedrilled through it. A ‘/s-inch steel arbor is inserted into the hole, and the sample is clamped tightly by means of a nut on the threaded section of the arbor. The arbor is held in the chuck of the jeweler’s lathe, the other end being held by a “dead center” in the tailstock. The compound rest of the lathe is adjusted to generate a true cylinder with a taper of no more than 0.025 mm. per inch. A sharp, pointed tool is used to minimize “hogging” or digging into the material. At no time was chattering or sample slippage encountered. Considerable delicacy has to be exercised to measure the correct diameter of the samples with a micrometer, especially samples of large burnoff, as they are liable to be easily crushed. Results
The experimental investigation was carried out by gasifying graphite samples with different carbon dioxide concentrations to four different weight losses in each concentration and determining the rate of reaction as a function of concentration. The bulk densities of the unreacted and reacted samples were determined to get the gasification as a function of depth within the sample, Reaction Rate. The reaction isotherms for the four concentrations of 100, 75, 50, and 25% carbon dioxide are shown in Figure 1. Each run, except the 25% run, was continued until the carbon sample dropped into the furnace, which occurred after about 50% burnoff. For the 25% carbon dioxide run, the run was continued until 2.0 grams (about 23%) of the sample had reacted. Each curve in Figure 1 has an induction and a constant rate period. The decreasing rate period is shown only a t the higher carbon dioxide concentrations. For each concentration, four samples were reacted to weight losses of 0.5, 1.0, 1.5, and 2.0 grams, respectively. The time corresponding to a given weight loss could be reproduced to within 2%. Bulk Density Profiles. The bulk density profiles of two unreacted samples indicated a uniform density of 1.53 grams per cc. throughout the sample. The average weight of unreacted samples was 9.437 i 0.072 grams. The volume of each sample was 6.12 cc. as determined from its dimensions. The computed average bulk density of the unreacted sample was 1.532 f 0.012 grams per cc., which checks well with the value obtained from bulk density
profile determinations. Bulk density profiles of the reacted samples are shown in Figure 2. The ordinate is Rap, where Ap is the difference between unreacted and reacted sample bulk densities, at a particular value of R, and R is the radial coordinate measured from the axis of the cylindrical sample. The product RAP, then, is proportional to extent of gasification of a radius R. Although the correlating lines represent the best fit of the experimental points, they are subject to additional restrictions: the bulk density of the sample should either be essentially constant or increase with decreasing R, and the area under the curve should correspond to the known weight loss of the sample. Values of RAP at the outer surface of the sample are plotted as a function of reaction time in Figure 3. The reaction time, e, is the number of minutes required to ‘react 0.5, 1.0, 1.5, or 2.0 grams, respectively, of the samples. Four points correspond to the reaction time 8 of the samples reacted to varying weight loss a t each concentration. At greater values of e, the slopes of the curves decrease. The gasification curve of the outer surface of the sample per unit concentration of carbon dioxide is shown in Figure 4. If the reaction is truly first order with respect to carbon dioxide, these points should be correlated by a single line. Differential a n d Integral Reaction Rates. Plots of RAp us e with R as a parameter (Figure 5) for 100, 75, 50, and 25% carbon dioxide runs, respectively, were obtained directly from Figure 2. In each case, the best line was drawn through the four points. All the lines do not pass through the origin-they are idealized representations of actual curves which bend and approach the abscissa asymptotically as RAP goes to zero. The slope of each line gives the differential reaction rate for any particular value of R ( R being the position variable within the sample). The differential reaction rate is eaual
The accuracy of the results can be tested by integrating the differential reaction rates with respect to R at a specified tima and comparing calculated values with observed values. For comparison, the time during which the reaction under each concentration was proceeding at a constant rate was chosen, and the integration was carried out graphically (Figure 6) and the results tabulated (Table 11). Close agreement between calculated and observed values of integral reaction rates indicates that differential reaction rates as calculated from bulk density profiles were not greatly in error.
Table
II.
Calculated and Observed Integral Reaction Rates Integral Reaction Rates, coz Gram/Hour Concn., % Calcd. Obsd. 100 75 50 25
0.996
0.987
0.562 0.414
0.569 0.423 0.295
0.291
Discussion
Thiele (76) has developed a mathematical treatment for simultaneous chemical reaction and diffusion within porous catalysts; his work has been extended by Wheeler (78). Thiele’s analysis of a cylindrical pore model may be used to interpret results from the study of the artificial graphite-carbon dioxide reaction. The equation for a reaction of first order is: DhCo
Rate per halfpore = mz-- L tanh ( h ) (1) wher6 I is the radius of a cylindrical pore of length L, D is the diffusivity, C’o is the concentration of the reactant at the pore mouth, and h is a dimensionless number given by Equation 2, h = L d a2k and k is the intrinsic reactivity of the surface. The fraction area available, f,is given by:
f
=
tanh ( h )
(3)
The intrinsic reactivity, k , and the diffusivity, D, are functions of temperature and are essentially independent of concentration. The dimensions L and r are characteristic of the solid phase. Therefore, under isothermal conditions, h is a constant. Hence, from Equations 1, 2, and 3, first order heterogeneous reactions have the following characteristics for all values of h : over-all reaction rate is proportional to initial (pore mouth) reactant concentration and the fraction of area available for reaction is independent of initial concentration. Similar analyses for zero and second order reactions have been carried out by Wheeler (78) and Thiele (76), respectively, in which equations of the same form are developed and modulus, h, is modified as: (41
where n is the kinetic order of the over-all reaction. From Equation 4, it can be readily shown that the apparent order is not identical with the true order of the reaction, and the fraction of the surface available for reaction is a function of the initial concentration. VOL. 50, NO. 3
MARCH 1958
335
Table 111.
Comparison of Over-all Reaction Rate and External Surface Reaction Rate A B
Over-all reaction COa,
%
100
75 50
25
hr,-1
Rate per gram external surface, hr.-1
B,f A
0.1327 0.0765 0.0569 0.0397
0.4493 0.2696 0.2046 0.1384
3.386 3.542 3.596 3.486
rate per gram,
Results of the present work appear to be satisfactorily interpreted by Equations l , 2, and 3 which apply to an over-all first-order reaction. Curves of RAp us. R show that gasification rate is not uniform throughout the interior of the sample but decreases as R decreases because of either a temperature effect or a concentration gradient within the sample. The reaction between carbon and carbon dioxide is endothermic. Hence, a temperature gradient may be set u p with the temperature decreasing radially inwards. This could explain the shape of the bulk density profile curves. The profile for a sample reacted at 100% carbon dioxide concentration is the same as one reacted at 25% concentration, but the time for heat transfer and hence the time for temperature equilibration varies approximately fourfold between samples. If the shape of these curves were due solely to a radical temperature gradient, the shape of the bulk density profile for a sample reacted at the lower concentration should be more constant than that for the sample reacted a t the higher concentration. The shape of the bulk density curves is therefore attributed to a concentration gradient within the pore structure rather than a temperature gradient. Figure 2 shows that at 1107' C. the amount of sample reacted decreases as R decreases. The value of logarithm of the equilibrium constant, K, for the reaction as written in the introduction is f 1 . 9 3 at 1107" C. Consequently, this reduced reaction cannot be explained on the basis of approach to equilibrium because the equilibrium concentration of carbon dioxide is low. Accordingly, the carbon dioxide concentration must be decreasing with decreasing R . Again, such a concentration gradient will result only when the rate of mass transfer within the internal porous structure of the sample is rate-controlling. Three facts indicate that the carboncarbon dioxide reaction is an over-all first-order reaction : Over-all reaction rate is approximately proportional to initial carbon dioxide concentration only when the reaction is first order, as shown in Equation 1. The differential gasification rate at the external surface of the sample is directly proportional to carbon dioxide
336
Ratio
concentration (Figures 3 and 4). Therefore, the reaction is also first order when not influenced by diffusion. Gasification curves of carbon samples reacted to the same weight loss but under different initial concentrations of carbon dioxide (Figure 2) are identical which indicates that the fraction of area available, f, is independent of concentration. Equations 2 and 3 show that f is independent of concentration only for a first order reaction. The carbon-carbon dioxide reaction has been observed to be first order with respect to carbon dioxide by Gadsby and coworkers (4, 5 ) who studied the reaction using charcoal instead of artificial graphite. Their reaction mechanism differs from the mechanism suggested above in that below some critical velocity the reaction rate is a function of linear velocity of the reacting gas. They studied the reaction above the critical velocity-when reaction rate is independent of linear velocity-and observed that the apparent activation energy for the reaction is "high." From its magnitude they concluded that the reaction is under chemical reaction control and is not influenced by the rate of diffusion within the porous structure of the carbon. However, a heterogeneous reaction can have a high apparent activation energy and still be influenced by internal diffusion, The magnitude of the apparent activation energy when diffusion influenced is approximately one half the true activation energy, as can be verified by inspection of Equations 1 and 2. The reaction rate a t the external surface of the sample is much greater than the over-all reaction rate, both rates being based on 1 gram of the sample. Table I11 shows the over-all rate per gram and the differential rate per gram at the external surface for samples reacted to exactly 2.0 grams of weight loss at various concentrations. The ratio of the rate at the external surface to the over-all rate (Table 111) is approximately constant with an average value of 3.50. This value should be constant for an over-all firstorder reaction. Rate Expression. From the time of Langmuir (77), considerable attention has been given to a rate expression for the carbon-carbon dioxide reaction based on a model in which carbon
INDUSTRIAL AND ENGINEERING CHEMISTRY
dioxide and carbon monoxide compete for active sites. The expression is:
+
+
k1pcol/(l k3pCOn kzpco) (5) where p,,, and pco are partial pressures of carbon dioxide and carbon monoxide, respectively, and k l , kt, and ka are reaction constants. This expression has subsequently been derived by several workers (3, 75). Gadsby and his coworkers (4, 5, 72) have used this expression to correlate their results. The present work does not purport to verify this expression. O n the other hand, the fact that bulk density profiles of samples reacted to the same weight loss are independent of carbon dioxide concentration shows that carbon monoxide is either not poisoning the reaction or that its concentration within the pore system of the graphite is too low to affect the results at 1107' C. The reaction time for the 25% carbon dioxide runs was four times longer than for 100% carbon dioxide runs. If poisoning effects had been appreciable, bulk density profiles at the two reactant concentrations would not have been the same. No conclusion can be drawn from the present investigation regarding the applicability of the Langmuir type rate expression to this reaction. Rate
=
Literature Cited (1) Bonner, F., Turkevich, J., J . Am. Chem. Soc. 73. 561 (1951). (2) Bowring, J., Crone,". G., J . Chem. Phys. 47, 322 (1950). (3) Frank-Kamenetzky, D. .4.,Compt. rend. acad. sci. U.R.S.S. 23, 663 (1938). ( 4 ) Gadsby,' J., Hinshelwood, C. N., Svkes, K. W., Proc. Roy. Sac. (London) 187A, 129 (1946). (5) Gadsby, J., Long, F. J., Sleightholm, P., Sykes, K. W., Ibzd., 193A, 357 (1948). (6) Goring, G. E., Curran, G. P., Tarbox,
R. P., Gorin, Everett, IND.END. CHEW44, 1057 (1952). ( 7 ) Gulbransen, E. A., Andrew, K. F., Zbzd., p. 1034. (8) Ibid., p. 1048. (9) Hougen, 0. A., Watson, K. M., Ibtd., 35, 529 (1943) (10) Johnstone, H. F., Chen, C. Y . , Scott, D. S., Zbrd., 44, 1564 (1952). (11) Langmuir, J., J . A m . Chem. Sac. 37, 1154 (1915). (12) Long, F. J., Sykes, K. W., Proc. Roy. SOC. (London) 193A, 377 f 1948). Petersen, E. E., Walker, P. L., Jr., Wright, C. C., IND.ENG.CHEM. 47, 1629 (1955). Petersen, E. E., Wright, C. C., Ibid., p. 1624. Semeshkova, A. F., Frank-Kamenetsky, D. A., Acta Physicochim. U.R. S.S. 12, 829 (1940). Thiele, E. W., IND.ENG.CHEM,31, 916 (1939). Walker, P. L., Jr., Foresti, R. J.,
Jr., Wright, c. c . , CHEM. 45.1703 (1953).
hD.
ENG.
249-327 (i951).
RECEIVED for review December 26, 1956 ACCEPTEDJuly 12, 1957
