756
Energy & Fuels 1988,2,756-764
evaporation even a t temperatures as high as 1020 K or above. On the graphite sample, the migration and stabilization of potassium were not observed. Extraction with a HC1 solution is a useful techniaue to determine the amount of potassium existing at the carbon surface.
Acknowledgment. We wish to express our appreciation to Prof. T.-Osaka, the Castings &search Laboratory, Waseda University, for the use of the Auger spectrometer,
to M. Suzuki for his skillful assistance, and to J. Yasui, K. Saga, and M. Miyazawa, School of Science and Engineering, Waseda University, for their technical assistance with the EPMA work. This work was partially supported by Grant-in-Aidfor Scientific ResearchNo. 60640C-Gfrom the Ministry of Education, Science and Culture, Japan. Registry No. K2C03, 584-08-7; K20, 12136-45-7; graphite,
7782-42-5.
Intrinsic Reaction Kinetics of Microporous Carbons. 2. Catalyzed Chars J. K. Floess,* J. P. Longwell, and A. F. Sarofim Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received March 28, 1988. Revised Manuscript Received July 11, 1988
A study was conducted to determine the catalytic effect of calcium on the intrinsic reactivity of a high surface area microporous char to which calcium was added in various amounts and degrees of dispersion. Rate data were obtained by using a thermogravimetric analyzer for both the oxygen and carbon dioxide reactions over the complete conversion range and at rates up to 1.0 min-’. The results show that, over the range of calcium loadings studied, the addition of molecularly dispersed calcium results in a linear increase in reactivity. One atomic percent calcium increases the oxygen reaction rate by almost 2 orders of magnitude and the carbon dioxide reaction rate by almost 3 orders of magnitude. The increase in reactivity can be mostly accounted for by a lower activation energy for the reaction. For both reactions, the intrinsic activation energy was ca. 15% lower for the catalyzed char. This result and the observation that, over the initial range of conversion, the rate is a function of the calcium to remaining carbon ratio indicate that the catalyst probably changes the site energy distribution and thereby lowers an energy barrier for the rate-determining step. The catalyzed carbon-oxygen reaction was found to be first order in oxygen concentrationover the range investigated, and the preexponential factor was found to be of the same order as that calculated for mobile adsorption by using transition-state calculations. On the basis of these results, it is concluded that the rate-determining step for this reaction must involve oxygen chemisorption and that the most probable function of the catalyst is to lower the energy barrier for this step.
Introduction The reaction rate of carbon with oxidizing gases can be significantly increased upon the addition of small amounts of certain inorganic compounds to the carbon. This increase in rate, which in some cases has been reported to exceed 4 orders of magnitude, either because of the presence of inherent inorganic matter or because of the addition of specific compounds to the carbon, is broadly referred to as catalysis of the carbon gasification reactions. The considerable increase in carbon reactivity obtainable by catalyst addition has resulted in numerous investigations of this phenomenon. Generally these studies have been concerned with the effect of the addition of inorganic compounds to a char or graphite, and in recent years, the studies have focused principally on the addition of alkali-metal and alkaline-earth-metal elements. Most recent studies have been conducted with potassium since the catalyzed char is easy to prepare (usuallyjust by
wet impregnation) and probably because a commercial potassium-catalyzed gasification process has been proposed (Nahas’). Studies with calcium have been much less frequent even though calcium has been identified as the principal element responsible for the higher inherent reactivity of certain coals. In part, the reason for fewer studies with calcium has been due to conflicting results that have been reported on the effectiveness of calcium as a catalyst when only admixing calcium compounds with carbon. Studies by Radovic2 and Hippo and Walker3, however, have clearly demonstrated that ion-exchanged calcium is as effective a catalyst as potassium, indicating that the method of calcium addition is critical to the element’s catalytic effectiveness. In both studies, it was found that the initial reactivity of the carbon depended linearly (1) Nahas, N. C. Fuel 1982, 61, 621. (2) Radovic, L. R. Ph.D. Thesis, Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, 19R3
*Author to whom correspondence should be addressed. Present address: Department of Chemical Engineering, University of Illinois at Chicago, Chicago, IL 60680
(3) Hippo, E. J.; Walker, P. L., Jr. ‘Effect of Cation Exchange on the Subsequent Reactivity of Lignite Chars to Steam”;US.Department of Energy Report RE-2030-TR4; March, 1977.
0887-0624/88/2502-0756$01.50/00 1988 American Chemical Society
Reaction Kinetics of Microporous Carbons
on the amount of ion-exchange calcium. Radovic et aL4 also attempted to measure calcium dispersion and to relate this quantity to a turnover frequency for the catalyst. The rationale for this approach was the assumption that the action of the catalyst is to increase the active site density, and therefore, a direct correspondence between reactivity and calcium dispersion should exist. Because of the analogous chemistry between the group I and IIA elements, it is generally assumed that the catalytic mechanism involving either calcium or potassium is similar. In recent studies, as mentioned above, the catalysis has usually been identified with an increase in the active site density. The kinetic mechanism itself presumably involves an oxygen transfer to the carbon at these sites (Mims and Pabd). An alternative mechanism, originally proposed by Long and Sykes,Bassumes that the catalyst alters the electron structure of the carbon as a consequence of the formation of a covalent bond between the carbon and the alkali metal and thereby increases the reactivity of the carbon. To date, however, no study has critically evaluated these proposed (qualitative) mechanisms, which are based largely on studies with potassium, against kinetic data obtained with calcium-added carbons. For example, one would expect in the case of the oxygentransfer mechanism that certain quantitative aspects of the reaction kinetics would be different for different catalysts. In this study, the reaction rate of a catalyzed char was determined with both oxygen and carbon dioxide, over the entire conversion range, under various heat treatment conditions, and to rates of -1.0 min-l. Insight into the role of catalysis by calcium was obtained by analysis of the kinetic data and by comparison to data obtained with the noncatalyzed char (presented in part 1 (Floess et al.')). This study was conducted with a high surface area microporous char that contained essentially no macropores. A model char was used so as to eliminate any effects of inorganic compounds and sulfur or nitrogen heteroatoms on the activity of the catalyst and to allow for various methods of calcium addition.
Experimental Section Experiments were conducted with a high surface area microporous char made from sucrose (reagent grade; less than 70 ppm residue after ignition). Three methods of calcium addition were used: calcium was added by dissolution of CaO in a sucrose solution, by incorporation of micrometer-size CaCOS particles during recrystallization of the sucrose from solution, and by ion-exchange onto the char. Although insoluble in water, calcium oxide is soluble in a sucrose solution, forming what is known as a saccharate (Honig). Apparently the behavior of the sucrose as a weak acid toward the calcium hydroxide results in the extensive solubility of the CaO. On the other hand, CaCOBis not significantJy soluble, and agitation of a SUCK)^^ solution containing fine calcium carbonate particles results in a dispersion of the particles in the liquid. The experimental procedure was as follows: for the saccharate, 0.3-2.0 g of calcium oxide (reagent powder, containing minimal carbonate) was added to 150 mL of a 40 wt % sucrose solution, which was stirred until the calcium oxide was completely dissolved. Dissolution of the CaO was slow. The mixture was then heated on a hot plate and continuously stirred until a viscous residue (4) Radovic, L. R.; Walker, P. L., Jr.; Jenkins, R. G. Fuel 1983,62,209. (5)Mims, C. A.; Pabst, J. K. Prepr. Pap.-Am. Chem. SOC.Diu. Fuel Chem. 1980, 25(3), 258. (6)Long, F . J.; Sykes, K. W. J. Chem. Phys. 1950, 47, 361. (7) Floees, J. K.; Longwell, J. P.; Sarofm, A. F. Energy Fuels 1988,2, 18. (8) Honig, P., Ed. Principles of Sugar Technology; Elsevier: Amsterdam, 1953.
Energy & Fuels, Vol. 2, No. 6, 1988 757 Table I. Calcium Content and Elemental Analysis of the Chars (1100 K Heat-Treatment Temperature) elem anal., w t % (ash-free basis) char designation C H Oa Cab sucrose char C-O 95.9 1.08 3.02 0.0 saccharate char c-1 0.97 saccharate char C-3.6 93.7 1.28 5.07 3.60 ion-exchange char C-ion 91.5 1.06 7.49 2.30 sucrose, CaC03 added C-CaCOS 6.80 OOrganic oxygen only (by difference). *Reported as w t of calcium/(wt of calcium-free char).
was obtained, which upon cooling hardened into a handleable solid. For the CaCOs-added char, a small quantity of CaCOs (primary standard powder; particle size approximately 1rm) was added to a 40 wt % sucrose solution. The mixture was continuously stirred while the mixture was heated to evaporate the excess water. As the sucrose recrystallized,the calcium carbonate particles were incorporated into the sugar crystallites. Calcium was ion-exchanged onto the char by stirring 180 mg of char for 6 h (at 298 K) in 230 mL of a 0.1 M calcium acetate solution to which a small amount of Ca(OH)zhad been added to raise the initial solution pH to 10. The reaction was conducted in a large excess of solution so that the exchange reaction could take place with the pH remaining as high as possible. At the end of the reaction, the mixture was filtered across a fritted glass filter, and the char was rinsed with distilled water. The sample was vacuum dried at 310 K. Preoxidation of the char at 675 K to 6 % conversion was necessary to obtain any significant amount of ion exchange. Chars were prepared from the precursor by pyrolysis in a small furnace at 925 K for 60 min. Swelling of the saccharate during pyrolysis was much less severe than for the sucrose. After pyrolysis, the char was crushed and sieved to various sized fractions; the nominal particle size used in these experiments was 90-106 Ccm. The calcium content and elemental analysis of the chars are given in Table I. The analyzed char samples were heat-treated to 1100 K, in the same manner as the char samples used in the oxygen-carbon runs. Since the samples were stored at room temperature prior to analysis, the analytical procedure included preliminary vacuum drying of the sample at 600 K with all subsequent sample transfers performed under nitrogen. The oxygen content (other than the carbonate oxygen) in all cases was determined by difference. The organic oxygen content of the calcium-added chars was obtained after correcting for any carbonate oxygen and for the inorganic oxygen-calcium stoichiometry, which was assumed to be 1:l. The surface areas of the sucrose ((2-0) and saccharate (C-3.6) chars were determined from nitrogen adsorption isotherms obtained at 77 K. Monolayer coverage was calculated from a new technique based on the desorption end point (described in part 1; Floess et al.') and also by application of the n-layer BET equation (Adamsong)to the adsorption data. Reaction rates were obtained by measwing the change in weight of the solid as a function of time with a Cahn Model 113 thermogravimetric analysis system (TGA). The equipment and experimental procedure are described in part 1.' The samples used for the carbon-oxygenexperiments were heat treated at 25 K/min to either 1100 or 1300 K prior to a run. After heat treatment, the samples were brought directly to the reaction temperature without any interim exposure to air. For the COz runs, the pretreatment and reaction temperatures were the same. As a result, for some of the COS runs with the catalyzed char the pretreatment temperature was less than 1100 K. A run was started by switching from nitrogen to the reactant gas. The rate constants for both reactions are defined as k=- r
ws
(1)
where r is the measured rate of weight loss, wi is the initial (9)Adamson, A. W. Physical Chemistry of Surfaces; Wiley: New York, 1976.
Floess et al.
758 Energy & Fuels, Vol. 2, No. 6,1988
Table IT. Activation Energies and Pteexponential Factors for the Catalyzed Chars-Oxygen Reaction (1100 K Heat-Treatment TemneratureP --= - - - - -- -, ~
c-0
conversion
(Xd, %
E* 32.6 33.8 34.4 35.2
A0
20 40 60 90
1.67 X 3.44 X 3.76 X 2.08 X
c-1
10" 10" 10" 10"
C-3.6 E* 28.4 29.7 30.1 34.6
A0
1.3 X 5.8 X 7.4 X 4.7 X
10" 10" 10" 10l2
A0
1.2 X
lo'*
7.2 X 10" 8.8 X 1O'O 1.7 X 10"
C-ion
E* 29.6 28.7 26.2 29.4
C-CaCOS E* 31.9 31.1 30.7
A0
9.1 X 10l2 9.7 X 10l2 4.2 X 10l2
E* 33.3 33.0 31.0
A0
5.8 X 10" 5.3 X 10" 1.4 X 10"
" A oin cm3/(g mol s); E* in kcal/mol.
0.20
E- e
t-
A
0.0 wtl Ca
1.0 "tl ca
w\
"
1 t/ 0
.
0 0.10
0.00
Oxygen
0
1 0.20
Partial Pressure (atml
Results
(10)Ergun, S.; Mentaer. M. "Reactionsof Carbon with Carbon Dioxide and Steam". In Chemistry and Physics of Carbon; Walker, P. L.,Jr., Ed.; Dekker: New York, 1965; Vol. 1.
I
, , ,
,
,
0 C-CaCO3 I6 0 wtl Cal
Wi - WCO,
Kinetic data for the calcium-free and the calcium-added (saccharate) chars for the carbon-oxygen reaction at 40% conversion are presented in Arrhenius form in Figure 2. The data for t h e ion-exchange and C03-added chars are given in Figure 3. In all cases, the low-temperature section on the diagrams can be represented by a straight line over almost two decades of reactivity. In part 1 (Floess et al.'),
,
~~n 0 C-Inn I2 3 wtl cai
\\
W
where wi is the initial amount of (ash free) char, WCO,is the total weight of C02 (if any) added by the end of a run (due to recarbonation of CaO in some rum), and w is the sample weight at (mass) conversion zm. This definition assumes that any recarbonation of CaO that may have occurred during a run increased linearly with conversion. Neither the reaction rate nor the conversion was corrected for the oxygen content of the char. The amount of oxygen adsorbed on the char during the carbon-oxygen reaction was appreciable and as shown in part 1 (Floess et al.'), will significantly affect the rates calculated from gravimetric data at conversions less than approximately 20%. The reaction rate of the catalyzed charoxygen reaction shows a first-order dependence on oxygen partial pressure at least up to a partial pressure of 0.21 atm, as shown in Figure 1. By comparison, the reaction order of the noncatalyzed char tends to deviate from first order at partial pressures above -0.18 atm (Floess et al.'). The reaction order for the COz reaction was not determined. However, at low reaction temperatures, if the CO concentration is not negligible, the mechanism usually proposed for this reaction (Ergun and Mentser'O) predicts the rate to approach first order in C 0 2 (at constant CO concentration).
I
A 0 0 r t l Ca
(ash-free) sample weight, and P is the partial pressure of the reactant. Conversion was calculated as
xm=1--
, , , , , , ,
10'
Figure 1. Effect of oxygen partial pressure on the reaction rate of the C-3.6 char at 710 K.
$. .
-
-y 0 c)
10-l 100
10-2
'
1
"
'
1
1
'
'
1
1
'
'
'
1
Energy & Fuels, Vol. 2, No. 6, 1988 759
Reaction Kinetics of Microporous Carbons
A 760 K '
*
--
2.0-
m
N
1.5-
E
-
Y
c
1.0L
2
0.51
-E
-
/
i
/
0
6
2
10
8
i!
12
W t X C a l c i u m (gCa/g Ca f r e e c h a r )
Figure 4. Reaction rate (at 40% conversion) vs calcium content of the chars. Line through data points given by eq 8.
0.0
I
'
I
20
0
I
40
'
I
60
I
I
,
60
\I
100
Conversion (XI
Figure 7. Normalized reaction rate w conversion (C-1char, 0.21 atm of 02). 1.0
2
Y
A 725 K 0 685 K 0 825 K
0.6
\ CK Y
tr" ,
,
,
,
,
,
l 0o
0
20
40
60
EO
0.4
100
Conversion ( X )
Figure 5. Normalized reaction rate VB conversion (C-0 char, 0.21 atm of 02).
20
40
60
80
100
Conversion (%I
Figure 8. Normalized reaction rate vs conversion (ion-exchange char - 0.21 atm of 02).
1.0
0.e
x
f
0
0.6
U
2 \ 0.4
0.2
0.0
0
20
40
60
SO
100
Conversion (XI
Figure 6. Normalized reaction rate vs conversion (C-3.6char, 0.21 atm of 02). calcium loading. The ion-exchange char is about a factor of 2 more reactive than the saccharate char. The CaC03 char is only slightly more reactive than the noncatalyzed char. Reaction rates (scaled with respect to the maximum rate) for the C-0 and calcium-added chars as a function of conversion are presented in Figures 5-8. As for the noncatalyzed char, the rate data obtained at different temperatures can be scaled to a single rate vs conversion curve over the complete conversion range. (Data obtained at different oxygen partial pressures for the C-3.6 char
could also be scaled to the same curve.) The saccharate chars exhibit no sudden catalyst deactivation; for both catalyst loadings (the curves for the C-1 and C-3.6 char are almost the same), the rate decreases monotonically to zero at 100% conversion. The ion-exchange char, however, reaches a deactivation point at about 80% conversion (compare Figures 6 and 8). The reason for this is uncertain, and it was not investigated in detail. Microscopic examination of the calcium residue from the saccharate and ion-exchange chars showed that in both cases the residual calcium formed a shell comparable in size to the original particle dimensions. A photomicrograph of this shell-like structure is shown in Figure 9. Because the ion-exchange char may have had a different initial calcium distribution, the development of this type of separation of the calcium from the carbon may be the cause of the earlier deactivation of the ion-exchange char. In comparison to the noncatalyzed char (Floess et al.'), the rates of both the saccharate and ion-exchange chars always show a greater variation between the initial and maximum rates. The maximum rate generally occurs at a later carbon conversion for the catalyzed char and is constant over a shorter conversion range. A number of experiments were also conducted in which up to 10% COPwas added to the reactant gas in runs with air to ensure CaC03 instead of CaO would be present if the catalyst was present as a separate solid phase. In some experiments the CO, was added only with the oxygen, and in other experiments, C02 was added both prior to and
760 Energy & Fuels, Vol. 2, No.6,1988
Floess et al.
7
\\
lo-'
10
100 Am
12
11
13
UT
14
15
16
17
xi04 ( ~ 1 - 1
Figure 11. Arrhenius diagram for the carbon-oxygen reaction at 40% conversion (heabtreatment temperature 1300 K 0.21 atm 9Cb106-pm particle). of 0,; I
I
I
I
1
100 :
\
8,
,
I
I
A 0.0 W t X CS 0 3.6 w t X Ca:
O'.?
1
I 10 yrn
Figure 9. Electron photomicrographs of the C-ion char at complete conversion. The lower photograph is an enlargement of the particle on the left in the upper photograph.
1
6.0
0 7.0
8.0
i/r
3 9.0
10.0
3 11.0
xi04 ( ~ 1 - 1
Figure 12. Arrheniw diagram for the carbon dioxide reaction at 40% conversion (1 atm of CO,; 90-106-pm particles).
t
0
l
l
10
l
l
20
l
l
l
30
l
40
l
l
50
Time (min)
Figure 10. EX& of heabtreatmenttime on the reactivity of the C-O and C-3.6 chars. The reaction rates are normalized to the rate for no isothermal heat treatment time. Table 111. Relative Reactivity under T w o Heat-Treatment Conditions Char ratio" Char ratio" C-O
c-1
0.50 0.17
C-3.6
Gion
0.21 0.081
"Theratio is equal to the rate at 1300 K heat treatment divided by the rate at 1100 K heat treatment.
with the oxygen. No effectof C02on the reactivity of the catalyzed char was noted in either case. This result is in agreement with a mechanism whereby the catalytic-active species is not a separate solid phase. Reactivity data were obtained at various heatitreatment conditions although no comprehensive set of measurements were made covering a broad range of conditions. The results are summarized in Table 111and Figure 10. In all cases, a higher heat-treatment temperature results in a
lower reactivity. An increase of 200 K in the heat-treatment temperature results in a factor of 5 decrease in the reactivity of the catalytic char and a factor of 2 decrease in the reactivity of the noncatalyzed char. Below -1050 K, isothermal heat treatment of the catalyzed char did not significantly change its reactivity, whereas above this temperature, heat treatment results in a marked decrease in activity with time. The time-dependent behavior of the reactivity is suggestive of a fmtiorder catalyst deactivation model; however, the rate constants so determined do not have an Arrhenius temperature dependence. The reactivity of the noncatalyzed char does not change with isothermal heat treatment, indicating that changes occurring in the structure of the char, which are responsible for the lower reactivity of the noncatalyzed char, must take place on a time scale that is faster than the heating rates used in these experiments. A comparison of kinetic data, presented in Arrhenius form, for the C-0 and C-3.6 chars at 1300 K heat-treatment temperature is given in Figure 11. The higher heat-treatment temperature reduces the relative effectiveness of the catalyst by the amount given in Table 111. Arrhenius diagrams for the C-O and C-3.6 chars reacted in 1atm carbon dioxide at 40% conversion are given in Figure 12. The rate data for the C-3.6 char are represented by two separate lines. The departure of the C-3.6 data from the low-temperature straight line coincides closely with the temperature at which isothermal heat treatment of the catalyzed char begins to significantly decrease the reactivity of the char. On the basis of the response of the catalyzed char to heat treatment, it is inferred that the falloff in reactivity at temperatures above
Energy & Fuels, Vol. 2, No. 6,1988 761
Reaction Kinetics of Microporous Carbons
larger than 200 A in diameter. Partially reacted samples were obtained by reaction in air at 615 K; samples were not outgassed after reaction.
0 1025 K
0 995
K
0.21
1
t 0.01
0
I
I
20
a
40
I
1
'
1
BO
60
J
100
Conversion I%)
Figure 13. Normalized reaction rate v8 conversion for the C-3.6
char-carbon dioxide reaction.
Table IV. Surface Area, Pore Volume, and Average Pore Radius of the C-3.6 Char (Samples Reacted in Air at 615 K) conversion (XJ.
0 7 22 38 58
-
%
surface area: m2/gof carbon
cm3/gof carbon
remaining
remaining
A
114 374 553 558 475
0.049 0.192 0.278 0.309 0.270
8.6 7.9 8.5 9.0
pore volume,
pore radius,
From desorption end point measurement.
1050 K is most likely caused by thermal deactivation of the catalyst. (In the C02runs, the pretreatment and run temperatures were the same.) The change in slope on the Arrhenius diagram does not coincide with the calcium carbonate decomposition temperature (1170 K) at 1 atm of COP Furthermore, since no change in slope is observed at this rate in the oxygen runs, this break in the Arrhenius line is presumably not due to intraparticle diffusion. The activation energy is 70.6 f 3.1 kcal for the C-0 char and 58.1 f 3.9 kcal for the C-3.6 char. The normalized rate w. conversion data for the catalyzed char are given in Figure 13. In comparison to the oxygen data, the rate is constant over a larger conversion range and the difference between the initial and maximum rates is less. The surface area, pore volume, and average pore radius of the C-3.6 char are given in Table IV. Surface areas were calculated from the end point of the nitrogen desorption isotherm at 77 K. (Comparable values for the surface area were obtained from the n-layer BET equation). Nitrogen adsorption was rapid except for the unreacted char. In this case, equilibrium was not reached in the time interval between adsorption points (-20 min). However, as discussed in part 1, restricted diffusion at reaction temperatures is apparently not important since C02adsorption at 298 K was rapid at all conversions. The surface areas of the C-3.6 char are on average about 15% lower than those for the C-0 char. Pore volumes were determined by aplication of the Dubinin-Polanyi equation to the nitrogen adsorption isotherm, and the pore radii were calculated from the surface area and pore volume data by using the random pore model (Gavalasl'). Mercury porosimetry measurements showed that the catalyzed char, similar to the noncatalyzed sucrose char, had negligible volume in pores (11) Gavalas, G . R. AZChE J. 1980,26, 677.
Discussion The results of this study confirm that small amounts of atomically dispersed calcium can significantly increase carbon reactivity. A substantial increase in char reactivity only occurs when the calcium is atomically dispersed on the carbon either by ion exchange or by the formation of a char from the saccharate precursor. The atomically dispersed calcium presumably forms a surface complex with the carbon, which is the catalytically active form of the calcium. The presence of such carbon-alkali-metal complexes and their role in the catalytic reaction have been demonstrated by Mims and Pabst12for potassium, and the analogies between the chemistry of group IA and group IIA elements make the formation of such complexes with calcium probable. Calcium as a separate solid phase is catalytically inactive, and unlike potassium, calcium oxide because of its higher melting point does not self-disperse on the carbon surface. The increase in reactivity of the CaC03-added char, if based on the ratio of carbon to calcium atoms on the surface of the calcium crystallite (0.0015 mole fraction surface atoms for a 1 pm CaO crystallite), is in agreement with the approximately linear relationship between calcium loading and reactivity shown in Figure 4. This implies that surface complexes can form at the carbon-calcium phase boundary but that no further dispersion of calcium in the carbon takes place. The factor of two difference in reactivity between the saccharate and ion-exchange chars is possibly due to the formation of polyatomic calcium groups during the sucrose-CaO reaction or during subsequent pyrolysis of the saccharate. Honig? for instance, states that the calcium in the saccharate may be polyatomic. The fact that the rate vs conversion curves of the saccharate and ion-exchange chars are almost identical, however, indicates that all of the catalytic sites present in the saccharate char participate in that reaction and that few, if any, initially inaccessible sites are present even though it is probable that not all of the calcium necessarily ends up on the surface of a pore during manufacture of the saccharate. Attempta to measure calcium dispersion directly by using COz chemisorption were not successful. The amount adsorbed was found to depend on reaction conditions, and it was not possible to obtain a correlation between reactivity and the amount of C02 chemisorbed. Both the carbon dioxide and oxygen reactions show significant variations in rate with respect to conversion, and as will be shown later, the initial variation in rate can be correlated with the change in the ratio of calcium to carbon remaining. The dependence of the rate on the calcium to carbon ratio is evidence that the role of the catalyst cannot be to only increase the number of energetically equal active sites. In this case, the rate would be expected to remain constant or to decrease with conversion, if deactivation of the catalytic sites occurred in parallel with carbon conversion, but not to show an increase with the calcium to carbon ratio. Instead, it is more probable that the primary role of the calcium is to change the energy distribution of the active sites, resulting in a lowering of the energy barrier of the rate-controlling step. Such an interpretation of the catalyst's action is further supported by the observation that the activation energies rather than the preexponential factors show the more (12) Mims, C. A.; Pabst, J. K., Fuel 1983, 62, 176.
Floess et al.
762 Energy & Fuels, Vol. 2, No. 6, 1988 Table V. Comparison of Measured Reaction Rates to Theoretical Calculations adsorDtion mobile" immobile exptl C-0 Char-Oxygen Reaction temp, K 873 873 873 34 OOO activation energy, cal/mol preexponential factor, cm/s 1.87 X lo' 7.36 X rate: molecules/(cmZ s) 9.9 x lola 3.9 x lo8 3.4 x 1013~ ~~
~~~
C-3.6 Char-Oxygen Reaction temp, K 700 700 activation energy, cal/mol preexponential factor, cm/s 1.7 X lo' 9.9 X rate: molecules/(cm2 s) 4.4 X 1Ola 2.6 X lo8 adsorption (mobile) desorptiond temp, K activation energy, cal/mol preexponential factor rate, molecules/ (cmz s)
700 28 600 3.4 x 1013
C-O Char-COz Reaction 1360 1360
exptl 1360 70 700
2.0 x io4 5.7 x 10%molecule/(cmz s) cm/s 4.7 X lolle 2.5 X 10'' 2.0 x 1013
C-3.6 C h d 0 2 Reaction temp, K activation energy, cal/mol preexponential factor rate, molecule/ (cmz 8)
1075
1075
1.8 X 10' cm/s 2.0 X 10"
4.5 X lp molecule/(cm2 8) 7.2
X
1075 58 OOO
10le
2.0 x 1013
a Quivalent to the Hertz-Knudsen equation. *Calculated for an oxygen partial preasure of 0.21 atm. cSurface are=: C-O char, 640 X lo4 cmz/g; C-3.6 char, 550 X lo' cm2/g. Stoichiometry: 0.75 mol of 02/mol of C. "Calculations assume a site density of 2 X site/cm2 (Blyholder and Eyring, 1959);reaction assumed to be zero order in COz. 'At 1 atm COP.
significant differences between the catalyzed and noncatalyzed chars. The average difference in activation energy between the C-0 and C-3.6 chars for the oxygen reaction is over 5 kcal, whereas the error bands at a 90% confidence level for the C-0 and C-3.6 data at 20-80% conversion are on average 0.85 and 1.6 kcal, respectively. This is less than half the difference in the activation energy of the two chars. Also, only a small difference in activation energy is in fact required to obtain the difference in rate between the catalyzed and noncatalyzed chars. This result is more clearly demonstrated in transition-state calculations presented in Table V. Transition-state calculations were made at equivalent reaction rates (and therefore at different temperatures) for the C-O and C-3.6 chars for cases of mobile adsorption and immobile adsorption (Laidler13). The calculations assume a surface site density of 2 X 10l6sites/cm2 (Blyholder and Eyring"9 and values of unity for the vibrational partition functions. The results of the calculations show that the experimental preexponential factors are a factor of 3 lower than for the case of mobile adsorption, and that a difference of 15% in the activation energy can account for the higher reactivity of the catalyzed char. (Data are compared at 40% conversion since the rate at this conversion is most representative of a region of constant reactivity. In addition, the Arrhenius parameters at this conversion are approximately equal to the average of the (13) Laidler, K. J. Chemical Kinetics; McGraw-Hill: New York, 1965. (14) Blyholder, G.; Eyring, H. J. Phys. Chem. 1969, 63, 1004.
data between 20 and 60% conversion.) If the rate-controlling step of the reaction is assumed to be adsorption, based on the observation that the reaction is first order, a sticking coefficient,sa, for the adsorption step, which is defined as the ratio of the net rate of adsorption of a molecule to the collision rate of the molecule with the surface, can be calculated. The sticking coefficient can be expressed as sa = P exp(-E/RT) (3) where P is known as a probability factor and E is the activation energy for the chemisorption step. The subscript 9 indicates that the sticking coefficient is a function of the extent of surface coverage on active sites. P is the ratio of the measured preexponential factor to the collision frequency; usually, it is expected to be smaller than unity since some entropy is lost in the formation of the transition state (i.e., the transition state is not expected to be completely mobile) and the surface is presumably not bare. Values of P at or greater than unity imply that adsorption involves more than a single elementary step (Boudart and Dj6ga-Mariadassou16). Boudart and DjBga-Mariadassou propose the following sequence of steps for adsorption of a molecule on a surface: trapping of the adsorbate into a precursor state; transition of the trapped molecule to a chemisorbed state, which may include dissociation of the trapped molecule, or desorption of the trapped molecule. With the assumption that the concentration of the intermediate species is at steady state, the sticking coefficient in terms of the rate constants of the elementary steps given above is (4)
where CY is a trapping coefficient and k, and kd are the rate constants for the chemisorption and desorption steps, respectively. The trapping coefficient is related to the accommodation coefficient, which for moleculea in 10-%lpores must be approximately unity. The sticking coefficient, therefore, depends primarily on the ratio of k, to kd. In order to be consistent with the experimental data for the noncatalyzed char, the ratio of the preexponential factors of k, and kd must be near unity, provided that 9 is not too large. Since the preexponential factor for kd is expected to be on the order of a molecular vibration, the frequency factor should be near an upper bound. It follows, therefore, that the ratio of the preexponential factors of k, to kd cannot be greatly higher for the catalyzed char. As a result, the principal action of the catalyst must be to lower the activation energy for the chemisorption step (k,), which is in agreement with the experimental data. At low temperatures, the carbon-oxygen reaction is frequently assumed to be desorption controlled (Laurendeau16); however, this assumption is inconsistent with the reaction order and the magnitude of the activation energy determined in this study. For the carbon dioxide reaction, the results of the calculations agree with the mechanism usually proposed for this reaction (at the reaction conditions of this study: moderate temperatures and negligible CO), which assumes the rate-controllingstep to be product desorption, and the oxygen-exchange reaction to be in approximate equilibrium (Ergun and Mentser'O). Agreement between the experimental and theoretical values requires an active site density of lo4. On the basis of the analysis of the oxygen
-
(15) Boudart, M.; Djbga-Mariadassou,G. Kinetics of Heterogeneous Catalytic Reactiom; Princeton University Press: Princeton, NJ, 1984. (16) Laurendeau, N. M. B o g . Energy Combust. Sci. 1978,4,221-270.
Energy & Fuels, Vol. 2, No. 6, 1988 763
Reaction Kinetics of Microporous Carbons
t
0.00
0.02
0.06
0.04
0.08
0.10
Calcium to carbon r a t i o lwt/ntl
t
01
0
I
I
20
I
I
1
40
60
I
I so
Conversion (XI
Figure 16. Oxygen content of the C-3.6 char as a function of conversion at 615 K.
0.00
0 02
0.04
0.06
0.08
0.10
Calcium t o carbon r a t i o lwt/wtl
Figure 14. Correlation of activation energy with catalyst loading. Curve through points given by eq (5): (A) oxygen reaction (al = 1100, a2 = 2000); (B)carbon dioxide reaction (al = 2000, a2 = 9100). al and a2 are defined in the text.
reaction and the experimentally measured Arrhenius parameters, the role of the catalyst in this case must also be to provide a lower energy pathway for the desorption step of the reaction. The results for the COBkinetics reported here differ from results reported by Freund,,' who concluded that the catalyst acts solely to increase the number of energetically equivalent active sites. Freund observed the activation energy for various catalyzed chars and some noncatalyzed chars to be almost the same. However, it should be pointed out that for one noncatalyzed char, a glassy carbon, the reported activation energy was ca. 15% higher that the average value of 58.3 kcal found for the catalyzed carbons. Unfortunately, this particular char was not used as a carbon substrate in any of the catalytic runs. Clearly, additional studies with various types of carbons are necessary to fully reconcile these differences. The observed variation in activation energy with catalyst loading can be related to the approximately linear dependence of the rate on calcium content. The change in activation energy with increasing calcium content can be correlated by the empirical equation AE = al In (1 + a2m) (5) where AI3 is the change in activation energy as a function of the catalyst content, m is the catalyst loading (weight fraction of calcium), and al and a2 are constants. Substitution of this equation into a first-order rate equation yields after rearrangement
r = S(x) A. (1
+ ~ ~ m ) " l / ~ ~ ( e x p [ - E / R T ] )(6) Co
where r is the reaction rate per unit mass (initial)of carbon, S(x) is a function describing the variation in rate with conversion, A. is the preexponential actor, E is the acti(17)Freund, H.Fuel 1985,64, 667.
vation energy, and Co is the gas concentration. The rate will be approximately linear in catalyst loading if a , is about equal to RT. The constants al and a2 were determined by fitting the activation energy for the sucrose and saccharate chars to eq 5. For the C-1 char an activation energy of 29.7 kcal was used. At a 90% confidence interval, the error bands on the activation energies for the C-1 char at 20, 40, and 60% conversion are 3.2, 2.9, and 2.3 kcal, respectively. (The activation energy for the ion-exchange char was not included in the calculation, since the 90% confidence interval for these data were f6.5kcal, making the location of the datum point for this char uncertain.) The data fitted to (6) are shown in Figure 14. For the catalyst loading used in these experiments, a2m >> 1, and therefore (6) can be written as
r = ro.4(a2m)01/RT
(7)
or at 715 K r = r0.4(20"I)~*'~ (8) where ro.4 is the reaction rate of the noncatalyzed char at 40% conversion. This equation can quite accurately describe the variations in rate with respect to catalyst loading (see Figure 4), although the magnitude of the predicted rate relative to the rate of the noncatalyzed char is lower by a factor of 2. (The curve shown in Figure 4 is offset by this amount in order to more clearly show the rate dependence on catalyst loading.) The factor of 2 arises from the difference in the preexponential factors at 40% conversion between the catalyzed and noncatalyzed chars. Results similar to those presented above were obtained for the C02 data. However, since only one datum point is available, the constant a , was determined by assuming that a, = RT at 1000 K. The predicted variation in activation energy is shown in Figure 14. The model predicts a rather sharp decrease in activation energy with small amounts of calcium loading. Additional experiments in this regime would provide data for further testing of this correlation. For the oxygen reaction, substantial amounts of oxygen were found to adsorb on the catalyzed char during the reaction, as shown by the data presented in Figure 15. The oxygen content was determined from elemental analysis and was corrected for inorganic oxygen associated with the calcium. (No measurable amounts of oxygen are present on the char in the COP runs.) The amount of adsorbed oxygen is comparable to the quantity present on the noncatalyzed sucrose char (see part 1) during the oxygen reaction. In order to obtain the true carbon reaction
Floess et al.
764 Energy & Fuels, Vol. 2, No. 6, 1988
L m
1 X
0.6-
v
m
0.4-
o.2
t
‘i
the rate decrease almost linearly with conversion. For the catalyzed char the falloff in rate occurs near 50% carbon conversion, whereas for the noncatalyzed char the rate decreases at 25% carbon conversion. The falloff in rate beyond the maximum rate, however, cannot be accounted for by this model. The conversion at which the maximum rate occurs for the C-1 char is only slightly higher than for the C-3.6 char. Thus the falloff in reactivity for the 1% calcium char begins at a lower calcium to carbon ratio than for the C-3.6 char, which indicates that carbon conversion as well as a saturation in calcium to carbon ratio may be important in catalyst deactivation. Nevertheless, these results show that the important factor in catalysis is the total dispersed calcium to carbon ratio and that, at least over the initial half of the conversion range, the calcium remains with the carbon and does not deactivate.
1
0 00
20
40
60
BO
100
Carbon Conversion 1x1
Figure 16. Normalized rate vs carbon conversion curve of the C-3.6 char-oxygen reaction corrected for the variation in calcium to carbon ratio at conversions less than TM.
rate and extent of conversion, particularly at conversions of less than 2070,it is necessary to correct the TGA data for the weight of the adsorbed oxygen. The calculations to make these corrections are described by Floess et al. in part 1. The oxygen-corrected rate w conversion curves still exhibit a substantial difference between the initial and the maximum rates; however, this difference can be explained and the rate vs conversion curves for both the catalyzed and noncatalyzed chars brought into close agreement by taking into account the change in the calcium to carbon ratio with burnout. Quation 7 becomes, after substitution of mo/(l - x ) for m,where mois the initial calcium loading and x is conversion
Normalization of the rate with respect to the maximum rate gives
where xM refers to the value of the conversion at the maximum rate and &)ISM is the rate vs conversion curve normalized with respect to the maximum rate. Calculated for the oxvalues of S(x)/SM at conversions less than ygen-corrected catalyzed char data are presented in Figure 16. The line through the points at carbon conversions less than x:M is a trend line; at conversions greater than xM, the line represents the oxygen-corrected data versus carbon conversion. The general shape of the curve is the same as that obtained for the noncatalyzed sucrose char (presented in part 1). In both cases, the initial rate is the maximum rate, and only after some carbon conversion does
Conclusions 1. The increase in char reactivity on addition of molecularly dispersed calcium is approximately linear over the range studied. Particles of calcium admixed with carbon do not have a significant catalytic effect, but an increase in reactivity consistent with the ratio of the surface calcium atoms to carbon is observed. 2. The C-3.6 char, containing 1 mol 7O dispersed calcium, increases carbon reactivity by almost 2 orders of magnitude for the oxygen reaction and 3 orders of magnitude for the carbon dioxide reaction. The effectiveness of dispersed calcium as a catalyst is comparable to results reported in the literature for potassium. 3. The increase in reactivity can mostly be accounted for by a lower activation energy. This result and the dependence of the initial part of the rate vs conversion curves on the calcium to carbon ratio indicate that the probable action of the catalyst is to change the site energy distribution of the carbon and thereby lower the energy barrier of the rate-determining step. No evidence was obtained that the catalyst acts by increasing the number of energetically equivalent active sites. 4. Transition-state calculations show that the preexyonential factor for the oxygen reaction is of the same order as the collision frequency. If the rate-controlling step for this reaction is assumed to be dissociative adsorption, based on the observed first-order dependence of the rate on oxygen concentration, the higher reactivity of the catalyzed chars must be principally due to a lower activation energy for this step. 5. The activity of the calcium catalyst decreases at heat-treatment temperatures above 1050 K. Acknowledgment. Support for this study by the Exxon Research and Engineering Co. is gratefully acknowledged. Redstry No. Ca, 1440-10-2;02,1182-44-1;COz,124-38-9;C, 7440-44-0.
