- Email: [email protected]
Intrinsic rate constants for the oxidation of carbon char
Carbon Vol. 20, No. 2. pp. 117-i I& 1982 Printed in Great Britain.
CQO84223/82/MOI 17-02$03.00/0 @ 1982 Pergamon Press Ltd.
LETTERS TO THE EDITOR IntrinsicRate Constants for the Oxidation of Carbon Char (Received 20 April 1981) A recent article by Walker[l] has illuminated a general consistency between the carbon oxidation rates obtained by Laine et 0/.[2], based on Active Surface Area (ASA)t, and those determined by Lewis and Simons[3], based on Total Surface Area (TSA). The rates determined by Lewis and Simons are a factor of two lower than those of Laine ef al. Walker notes the consistency of this result in the light of the fact that TSA is greater than ASA. However, Lewis and Simons stated that their low temperature rates could be as much as factor of five too low. Hence, the deviations within the Lewis and Simons analysis are much greater than the deviation between the two results [2,3]. These large deviations[3] could reflect a fundamental error in the use of TSA based rates. Are-examination of the data base used by Lewis and Simons is necessary in order to isolate the source of the uncertainties in the rate constant. It is shown that the rates determined by Lewis and Simons are consistent for uncatalyzed reactions and the apparent uncertainty in the rates arose because Lewis and Simons did not properly account for the effects of catalysis in reducing the data of Mahajan ef al. [4]The implications and limitations of using kinetic rates based on TSA are briefly discussed. Analysis of the data of Mahajan et al. requires a fundamental model to describe the universal burnoff orofile141.For kinetically limited reactions, the carbon removal rate dgit (mass/time) is directly proportional to the intrinsic rate k (mass/area-time) and the internal surface area S,,
$+sp
Equation (4) was previously derived by Simons[6] but the explicit dependence of K4 on k and 1112was not obtained. Integration of df/dr accurately duplicated the universal burnoff profile[4] and K4 was determined from the constraint that f = l/2 at 7=1.
1f
(1 - 6$“2)(21’2+ ( 1+ tQ’*} K4 =In [ (I t eo1~2){21~2(1t eop2}
The current analysis has explicitly related the intrinsic rate constant k to the measured value of ftj2 via the constant K4. The intrinsic rate constant utilized by Lewis and Simons[3] is given by
hs
k=[I + MklPo2)1 where po2is the partial pressure of oxygen in atm, k, and k2 are the oxygen adsorption and desorption rates, respectively, k, = 900 exp (- 19,000/T(K))gC/cm2s atm 02 k2 = 90 exp (- 19,000/T(K))gC/cm2s
and e, has been introduced to represent an enhancement to the rate constants quoted above. The values of e, corresponding to the data of Mahajan et al. [4] may be calculated directly from the quoted values of 11,2.
A detailed analysis of pore combination[5] indicates that the internal surface area scales as
s = #‘*(I - 0) p
#9,“2(1 - 0,) %?
where 0 is the total porosity and the subscript zero denotes the variable at I = 0. The conversion f is defined such that f = 0 at f = 0 and f = 1 at burnout. The conversion is expressed as
ef =
&
(I+ k2/ktpoZ).
Results are illustrated in Fig. 1. The data suggest that the rate constants for Montana Lignite (PSOC-91) are a factor of four higher than the uncatalyzed rates correlated by Lewis and Simons[3]. This is consistent with the observation of Jenkins et a/.[71 that the effect of catalytic agents on the reactivity of this
and the conversion rate dfldf is obtained from eqn (l)-(3). Direct substitution yields
where DATA: MAHAJAN ET AL (1978)
J&b
’
PSOC-91 f?G- 0.4
spa
()
TSA - 400 m2/S
e,‘” MO ’
T-678K
and 11/zis defined as the time at which f = l/2. 0
tNote that ASA refers to the concentration of active sites and not to the available surface area which reflects the capacity of the porous structure to gaseous diffusion.
.Ol
I
t
t1tt1tl
I
tt,t,
.l PARTtAL PRESSURE OF OXYGEN -ATMOSPHERES
Fig. 1. Rate enhancement factor for Montana lignite char. 117
Letters to the Editor
118
char is an enhancement of approximately a factor of four. Thus, the uncatalyzed rates used by Lewis and Simons are consistent with the data base and these rates, based on TSA, are a factor of two below the ASA based rates of Laine et al.[2]. It should be noted that the use of kinetic rates based on TSA inherently assumes that the ratio of TSA to ASA is a constant and that this ratio may be incorporated into the rate constant. The very existence of a universal burnoff protile[4] and the success of a TSA model[6] in describing that profile suggests that the ratio of TSA to ASA is generally invariant with burnoff. However, Walker[l] has reiterated that TSA is not fundamentally correct and that there are isolated cases where the ratio of ASA to TSA varies dramatically with burnoff or with carbonaceous material. Modeling efforts in heterogeneous chemistry must rely on fundamental laboratory studies[l, 21 to determine the limitations of such global approximations.
Carbon Vol. 20, No. 2. pp. 118420, Printed in Great Britain.
Physical Sciences Inc. Wobum MA 01801 U.S.A.
GIRARD
A.
SMONS
REFERENCES 1. P. L. Walker, Jr., Carbon 18,447 (1980). 2. N. R. Laine, F. J. Vastola and P. L. Walker, Jr., J. Phys. Chem. 67, 2030(1%3). 3. P. F. Lewis and G. A. Simons, Comb. Sci. Technol. 20, 117 (1979). 4. 0. P. Mahajan, R. Yarzab and P. L. Walker, Jr., Fuel 57,643 (1978). 5. G. A. Simons, Comb. Sci. Technol. 19,227 (1979). 6. G. A. Simons, Fuel 59, 143(1980). 7. R. G. Jenkins, S. P. Nandi and P. L. Walker, Jr., Fuel 52,288 (1973).
wo86223/82/0201 l843$03.00/0 Pcrgamon Press Ltd.
1982
Applicatfonof Potential Theory to Adsorptfonof Binary Mixtures on Activated Carbon (Receioed 30 April 1981) Potential theory has been successful in correlating the adsorption of a single adsorbate on activated carbon both at low temperatures and at temperatures near the critical temperature. The theory can be extended to binary or multicomponent mixtures. According to the suggestion of Dubinin and Radushkevich[l], the adsorption potentials [RT ln~‘/fa)] of homologous adsorbates are equal when the same volumes of the adsorbate are adsorbed. Thus, the equilibrium relation between component 1 and 2 is[l31:
(1) Here f” and f” are the fugacities of the adsorbate in the solid and gas phases, respectively, and V is the molar volume of the saturated liquid. The fugacity of the ith component in a liquid mixture can be written as
where yi is the activity coefficient, xi is the mole fraction in the adsorbed phase, and fi is the fugacity of the saturated adsorbate liquid. When the adsorbates have similar molecular properties or when their concentrations are low, Raoult’s law (fi”= .x&pcan be applied to calculate the fugacity of each component; in these cases, eqn (1) can be rewritten as
eqn (2) stipulates that a log-log plot of the dimensionless group (xPc/fg)l versus CxP,/f’)z is a straight line with a slope equal to VI/VZ,the ratio of the molecular volumes. The unknown fugacities of the liquids are factored into a constant term given by the intercept of the straight-line of eqn (4). Nikolayav and Dubinin[S] suggested a method for estimating the molar volume ratio VI/V*. We made a series of measurements on the adsorption capacities of acetylene and ethane mixtures to test eqn (1). The apparatus and the experimental procedures were described in previous articles[d 71. Different inlet concentrations were prepared by mixing two standard hydrocarbon-helium mixtures (each with a nominal concentration of 1%) in different proportions. The prepared mixture of acetylene and ethane flowed through an initially desorbed column packed with activated carbon. The quantity of acetylene and ethane adsorbed on the carbon can be calculated from a mass balance equation[‘l]: qiop(1 - e)L + c?eL = UC: /Om(l-$$)dl
(i=lor2)
(5)
where qP is the solid-phase concentration, co is the gas-phase concentration, p is the density of the carbon granule, L is the length of the column, u is the superficial flow velocity, and e is the void fraction. In eqn (9, the first term on the 1.h.s. is the amount of adsorbate on the solid phase, and the second term is that in the gas phase. Note that eqn (3) shows that the solidIn xtfio _ VI x2.Q phase concentration qf of component i depends explicitly on the ft’ v2 h” time dependence of the concentration ci(t) of component i in the gas phase; however, the influence of the second component is Equation (3) offers a method for testing the interaction between the adsorbed species; for an ideal solution, a plot of ln(xJ?/f18) demonstrated in the change of the shape of the transmission of vs ln(xf20/f28)will be a straight line with a slope equal to YL/VZ, acetylene alone. Figure 1 shows a typical transmission curve for the ratio of molar volumes. At a temperature equal to or higher acetylene-ethane mixtures. Acetylene elutes earlier than ethane and the transmission exceeds unity; this overshoot phenomena than the critical temperature, the fugacity of a liquid is not appropriate for calculating the adsorption potential. To calculate remains steady until ethane elutes. Also, we observed that the the adsorption potential, Grant and Manes[2] extrapolated low overshoot increases when the concentration of acetylene temperature fugacity to supercritical temperatures, and decreases and the concentration of ethane increases. In Table 1 are listed values of q”, f(=c’/RT), and x for both acetylene and Dubinin[4] estimated the fugacity f” by the Pc(T/T,)*. We propose an alternative method which still permits a straight-line test ethane in each run. Figure 2 is a plot of the dimensionless of the data for adsorption of mixtures. By introducing the critical quantity xPc/f for ethane versus the same dimensionless group pressure P, and rearranging variables, we can rewrite Eqn. (3): for acetylene. The data points give a straight line with slope 1.18. Since the temperature in this study is very close to the critical ln(4),=$ln(4)2+ln(+),+$ln($)~ (4) temperatures of acetylene and ethane, the volume ratio is calculated using critical volumes. The experimental value of this Note that each term in eqn (4) is dimensionless. Equation (4) like ratio is very close to the critical volume ratio of 1.1s. The sum of In
CQO84223/82/MOI 17-02$03.00/0 @ 1982 Pergamon Press Ltd.
LETTERS TO THE EDITOR IntrinsicRate Constants for the Oxidation of Carbon Char (Received 20 April 1981) A recent article by Walker[l] has illuminated a general consistency between the carbon oxidation rates obtained by Laine et 0/.[2], based on Active Surface Area (ASA)t, and those determined by Lewis and Simons[3], based on Total Surface Area (TSA). The rates determined by Lewis and Simons are a factor of two lower than those of Laine ef al. Walker notes the consistency of this result in the light of the fact that TSA is greater than ASA. However, Lewis and Simons stated that their low temperature rates could be as much as factor of five too low. Hence, the deviations within the Lewis and Simons analysis are much greater than the deviation between the two results [2,3]. These large deviations[3] could reflect a fundamental error in the use of TSA based rates. Are-examination of the data base used by Lewis and Simons is necessary in order to isolate the source of the uncertainties in the rate constant. It is shown that the rates determined by Lewis and Simons are consistent for uncatalyzed reactions and the apparent uncertainty in the rates arose because Lewis and Simons did not properly account for the effects of catalysis in reducing the data of Mahajan ef al. [4]The implications and limitations of using kinetic rates based on TSA are briefly discussed. Analysis of the data of Mahajan et al. requires a fundamental model to describe the universal burnoff orofile141.For kinetically limited reactions, the carbon removal rate dgit (mass/time) is directly proportional to the intrinsic rate k (mass/area-time) and the internal surface area S,,
$+sp
Equation (4) was previously derived by Simons[6] but the explicit dependence of K4 on k and 1112was not obtained. Integration of df/dr accurately duplicated the universal burnoff profile[4] and K4 was determined from the constraint that f = l/2 at 7=1.
1f
(1 - 6$“2)(21’2+ ( 1+ tQ’*} K4 =In [ (I t eo1~2){21~2(1t eop2}
The current analysis has explicitly related the intrinsic rate constant k to the measured value of ftj2 via the constant K4. The intrinsic rate constant utilized by Lewis and Simons[3] is given by
hs
k=[I + MklPo2)1 where po2is the partial pressure of oxygen in atm, k, and k2 are the oxygen adsorption and desorption rates, respectively, k, = 900 exp (- 19,000/T(K))gC/cm2s atm 02 k2 = 90 exp (- 19,000/T(K))gC/cm2s
and e, has been introduced to represent an enhancement to the rate constants quoted above. The values of e, corresponding to the data of Mahajan et al. [4] may be calculated directly from the quoted values of 11,2.
A detailed analysis of pore combination[5] indicates that the internal surface area scales as
s = #‘*(I - 0) p
#9,“2(1 - 0,) %?
where 0 is the total porosity and the subscript zero denotes the variable at I = 0. The conversion f is defined such that f = 0 at f = 0 and f = 1 at burnout. The conversion is expressed as
ef =
&
(I+ k2/ktpoZ).
Results are illustrated in Fig. 1. The data suggest that the rate constants for Montana Lignite (PSOC-91) are a factor of four higher than the uncatalyzed rates correlated by Lewis and Simons[3]. This is consistent with the observation of Jenkins et a/.[71 that the effect of catalytic agents on the reactivity of this
and the conversion rate dfldf is obtained from eqn (l)-(3). Direct substitution yields
where DATA: MAHAJAN ET AL (1978)
J&b
’
PSOC-91 f?G- 0.4
spa
()
TSA - 400 m2/S
e,‘” MO ’
T-678K
and 11/zis defined as the time at which f = l/2. 0
tNote that ASA refers to the concentration of active sites and not to the available surface area which reflects the capacity of the porous structure to gaseous diffusion.
.Ol
I
t
t1tt1tl
I
tt,t,
.l PARTtAL PRESSURE OF OXYGEN -ATMOSPHERES
Fig. 1. Rate enhancement factor for Montana lignite char. 117
Letters to the Editor
118
char is an enhancement of approximately a factor of four. Thus, the uncatalyzed rates used by Lewis and Simons are consistent with the data base and these rates, based on TSA, are a factor of two below the ASA based rates of Laine et al.[2]. It should be noted that the use of kinetic rates based on TSA inherently assumes that the ratio of TSA to ASA is a constant and that this ratio may be incorporated into the rate constant. The very existence of a universal burnoff protile[4] and the success of a TSA model[6] in describing that profile suggests that the ratio of TSA to ASA is generally invariant with burnoff. However, Walker[l] has reiterated that TSA is not fundamentally correct and that there are isolated cases where the ratio of ASA to TSA varies dramatically with burnoff or with carbonaceous material. Modeling efforts in heterogeneous chemistry must rely on fundamental laboratory studies[l, 21 to determine the limitations of such global approximations.
Carbon Vol. 20, No. 2. pp. 118420, Printed in Great Britain.
Physical Sciences Inc. Wobum MA 01801 U.S.A.
GIRARD
A.
SMONS
REFERENCES 1. P. L. Walker, Jr., Carbon 18,447 (1980). 2. N. R. Laine, F. J. Vastola and P. L. Walker, Jr., J. Phys. Chem. 67, 2030(1%3). 3. P. F. Lewis and G. A. Simons, Comb. Sci. Technol. 20, 117 (1979). 4. 0. P. Mahajan, R. Yarzab and P. L. Walker, Jr., Fuel 57,643 (1978). 5. G. A. Simons, Comb. Sci. Technol. 19,227 (1979). 6. G. A. Simons, Fuel 59, 143(1980). 7. R. G. Jenkins, S. P. Nandi and P. L. Walker, Jr., Fuel 52,288 (1973).
wo86223/82/0201 l843$03.00/0 Pcrgamon Press Ltd.
1982
Applicatfonof Potential Theory to Adsorptfonof Binary Mixtures on Activated Carbon (Receioed 30 April 1981) Potential theory has been successful in correlating the adsorption of a single adsorbate on activated carbon both at low temperatures and at temperatures near the critical temperature. The theory can be extended to binary or multicomponent mixtures. According to the suggestion of Dubinin and Radushkevich[l], the adsorption potentials [RT ln~‘/fa)] of homologous adsorbates are equal when the same volumes of the adsorbate are adsorbed. Thus, the equilibrium relation between component 1 and 2 is[l31:
(1) Here f” and f” are the fugacities of the adsorbate in the solid and gas phases, respectively, and V is the molar volume of the saturated liquid. The fugacity of the ith component in a liquid mixture can be written as
where yi is the activity coefficient, xi is the mole fraction in the adsorbed phase, and fi is the fugacity of the saturated adsorbate liquid. When the adsorbates have similar molecular properties or when their concentrations are low, Raoult’s law (fi”= .x&pcan be applied to calculate the fugacity of each component; in these cases, eqn (1) can be rewritten as
eqn (2) stipulates that a log-log plot of the dimensionless group (xPc/fg)l versus CxP,/f’)z is a straight line with a slope equal to VI/VZ,the ratio of the molecular volumes. The unknown fugacities of the liquids are factored into a constant term given by the intercept of the straight-line of eqn (4). Nikolayav and Dubinin[S] suggested a method for estimating the molar volume ratio VI/V*. We made a series of measurements on the adsorption capacities of acetylene and ethane mixtures to test eqn (1). The apparatus and the experimental procedures were described in previous articles[d 71. Different inlet concentrations were prepared by mixing two standard hydrocarbon-helium mixtures (each with a nominal concentration of 1%) in different proportions. The prepared mixture of acetylene and ethane flowed through an initially desorbed column packed with activated carbon. The quantity of acetylene and ethane adsorbed on the carbon can be calculated from a mass balance equation[‘l]: qiop(1 - e)L + c?eL = UC: /Om(l-$$)dl
(i=lor2)
(5)
where qP is the solid-phase concentration, co is the gas-phase concentration, p is the density of the carbon granule, L is the length of the column, u is the superficial flow velocity, and e is the void fraction. In eqn (9, the first term on the 1.h.s. is the amount of adsorbate on the solid phase, and the second term is that in the gas phase. Note that eqn (3) shows that the solidIn xtfio _ VI x2.Q phase concentration qf of component i depends explicitly on the ft’ v2 h” time dependence of the concentration ci(t) of component i in the gas phase; however, the influence of the second component is Equation (3) offers a method for testing the interaction between the adsorbed species; for an ideal solution, a plot of ln(xJ?/f18) demonstrated in the change of the shape of the transmission of vs ln(xf20/f28)will be a straight line with a slope equal to YL/VZ, acetylene alone. Figure 1 shows a typical transmission curve for the ratio of molar volumes. At a temperature equal to or higher acetylene-ethane mixtures. Acetylene elutes earlier than ethane and the transmission exceeds unity; this overshoot phenomena than the critical temperature, the fugacity of a liquid is not appropriate for calculating the adsorption potential. To calculate remains steady until ethane elutes. Also, we observed that the the adsorption potential, Grant and Manes[2] extrapolated low overshoot increases when the concentration of acetylene temperature fugacity to supercritical temperatures, and decreases and the concentration of ethane increases. In Table 1 are listed values of q”, f(=c’/RT), and x for both acetylene and Dubinin[4] estimated the fugacity f” by the Pc(T/T,)*. We propose an alternative method which still permits a straight-line test ethane in each run. Figure 2 is a plot of the dimensionless of the data for adsorption of mixtures. By introducing the critical quantity xPc/f for ethane versus the same dimensionless group pressure P, and rearranging variables, we can rewrite Eqn. (3): for acetylene. The data points give a straight line with slope 1.18. Since the temperature in this study is very close to the critical ln(4),=$ln(4)2+ln(+),+$ln($)~ (4) temperatures of acetylene and ethane, the volume ratio is calculated using critical volumes. The experimental value of this Note that each term in eqn (4) is dimensionless. Equation (4) like ratio is very close to the critical volume ratio of 1.1s. The sum of In