518
I n d . Eng. Chem. Res. 1989, 28, 518-523 Robinson, B. A.; Tester, J. W., submitted for publication in Int. J . Chem. Kinetics 1988. Robinson, B. A.; Tester, J. W.; Brown, L. F. SPE Reservoir Eng. 1988, 28(3), 227-234. Sohn, H. Y.; Kim, S.K. Ind. Eng. Chem. Process Des. Deu. 1980,19, 550-555. Solomons, T. W. G. Organic Chemistry, revised; Wiley and Sons: New York, 1978; p 649. Stock, L. M. Aromatic Substitution Reactions; Prentice Hall, Inc.: Englewood Cliffs, NJ, 1968; p 132.
Morrison, R. T.; Boyd, R. N. Organic Chemistry, 3rd ed.; Allyn and Bacon, Inc.: Boston, 1975; pp 826-841. Matsuda, H.; Goto, S. Can. J . Chem. Eng. 1984, 62, 103-111. Nebergall, W. H.; Holtzclaw, 3. F., Jr.; Robinson, W. R. College Chemistry With Quantitatiue Analysis, 6th ed.; D. C. Heath and Company: Lexington, MA, 1980; p 360. Ortiz Uribe, M. I.; Romero Salvador, A.; Irabien Gulias, A. Thermochim. Acta 19858, 94, 323-331. Ortiz Uribe, M. I.; Romero Salvador, A.; Irabien Gulias, A. Thermochim. Acta 198513, 94, 333-343. Radhakrishnamurti, P. S.; Sahu, T. Indian J . Chem. 1974, 12(4), 370-372. Ritchie, C. D.; Sawada, M. J . Am. Chem. Soc. 1977, 99(11), 3754-3761.
Received for review May 31, 1988 Reuised manuscript receiued December 19, 1988 Accepted January 4, 1989
Unification of Coal Gasification Data and Its Applications K. Raghunathant and Ray Y. K. Yang* Department of Chemical Engineering, West Virginia University, Morgantown, West Virginia 26506-6101
Various research groups have reported that their char conversion versus time data from different experiments can be unified into a single curve when conversion is plotted against normalized time, t / t l j z ,where t l j 2is the half-life of the reaction, or time taken for 50% conversion of char. On the basis of two-parameter rate models, the grain model and the random pore model, unification curves ( x versus t / t I j 2 with ) one adjustable parameter are derived for each model. For coal gasification, each model parameter lies within a range, and for this range, the plotted unification curves lie close to each other u p to about 70% conversion. With the aid of correlations reported in the literature for unification curves, a master curve is derived to approximate conversion-time data from most gasification systems. With an extension of the unification approach, it is shown that for steam and C 0 2 gasification, the product of half-life and average reactivity is nearly a constant with a value of 0.38. Since half-life is simply related to the average reactivity, it can be directly used as a reactivity index for characterizing the char-gas reaction. In the absence of structural or kinetic data, half-life data a t a few temperatures can be used to predict char conversion up to 70% over a reasonably wide range of temperatures. When char particles are gasified, the solid undergoes changes in pore structure and surface area with conversion or time, depending on the gasification conditions. There have been many attempts to unify these dynamic changes through various normalizing parameters such as half-life, reactivity, or surface area (Mahajan et al., 1978; Chin et al., 1983; Adschiri and Furusawa, 1987). According to the unification approach proposed by Mahajan et al. (1978), char gasification curves in the form of char conversion x versus gasification time t for different temperatures, pressures, gasifying agents, and chars approximately reduced to a single curve when x is plotted against the dimensionless time -7, where -7 = t/t,,,, t I j z being the half-life of the char-gas reaction. Kasaoka et al. (1985) and Peng et al. (1986) have also unified their data successfully by using this approach. The objective of this paper is to present a detailed analysis of this normalizing scheme and discuss useful applications. In the following discussions, a set of conversion-time data, when approximated by a single x--7 curve, is referred to as the “unified data” and the x--7 curve as the “unification curve”.
Experimental Section Kinetic studies of the charsteam reaction were carried out in a TGA apparatus a t atmospheric pressure. The
* To whom correspondence should be addressed. ‘Present address: Department of Chemical Engineering, The Ohio State University, Columbus, OH 43210.
0888-5885/89/2628-0518$01.50/0
reaction was studied in the range 800-1200 “C for a North Dakota lignite. The chars were generated in situ by devolatilization in a steam-nitrogen atmosphere and were gasified in the same environment without interruption. The weight loss of the sample was continuously recorded on a microcomputer and analyzed. The mean particle size of the coal sample was 178 km, and the steam concentration was 76 mol 9’0. Details of the experiments are described by Peng et al. (1986). Only the conversion-time data from our experiments will be presented in this paper, and a more detailed analysis of the results can be found in Raghunathan (1988).
Correlations for Unification Curves Mahajan et al. (1978) correlated their data for four gasifying agents separately and together up to x = 0.7 using the cubic form x = AT
+ Br2 + Cr3
(1)
Kasaoka et al. (1985) observed that data from 19 different chars can be reduced to a single curve for steam and COP gasification. For each gasifying agent, they fitted a modified volume reaction model of the form x = 1 - exp(-ATB)
(2)
and reported good approximations up to high conversions. Peng et al. (1986) normalized their data at different temperatures for each of the six chars and obtained good correlations for the cubic form above. C 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 5 , 1989 519 10
1
I
I
38 x
6
06
L v1
0
ti
3 4
i
?
L
ti
02
00 dimensionless time,
r
Figure 1. Unification of experimental data from different temperatures.
Conversion-time data were measured at different temperatures from our experiments and by Schmal et al. (1982) and Chin et al. (1983). Each of these three sets are unified when plotted as x versus -7, as shown in Figure 1. The empirical rate equation of the form dx/dT = A ( l - x ) ~
(3)
Figure 2. Plots of theoretical unification curves from eq 8 and 9.
By integrating eq 6 and setting x = 0.5 at t = t1/2,along with the definition of -7, it can be shown that
which is the unification curve based on the grain model, with one adjustable parameter, m. Similarly, the expression for the unification curve based on the random pore model (eq 7 ) can be shown to be
when solved for x gives
x = 1 - exp[-p(-7
x = 1 - [l - A ( l - B)T]~/(~-')
Unification Curves Based on Rate Models For each gasification run, with variables other than t being fixed, researchers usually fit rate expressions of the form (5)
where R, is the instantaneous char reactivity and Rd)the initial char reactivity. The grain model for gas-solid reactions is of the form dx/dt = Rd(1 - x)"
(6)
The parameter m is the grain shape factor; it can also be viewed as the order of the reaction with respect to the solid (Ishida and Wen, 1971). Equation 6 for m = 1 or 2/3 has been widely used to fit coal gasification data. The random pore model (Bhatia and Perlmutter, 1980; Gavalas, 1980) which is based on pore evolution, has become popular in recent years. For the reaction-controlling regime, this model gives dx/dt = RCo(l- x)[l where
+ In (1- x ) ] ' / ~
+ is a structural parameter.
+ p+?/4)]
(94
(4)
Each of the three sets of data shown in Figure 1 is correlated by the above expression using nonlinear regression, and the fitted curves are also shown. Figure 1 offers additional evidence that gasification kinetic data can be unified when t I j z is used as the correlating parameter. In gasification kinetics, the reactivity can either decrease monotonically with conversion or exhibit a maximum at an intermediate conversion. In the latter, the conversion-time curve is sigmoidal in shape. The unification plot shown by Kasaoka et al. (1985) includes curves of both types, yet the data seem to be well unified. However, plots of experimental x--7 data shown in Figure 1, as well as those presented by Kasaoka et al. (1985) and Peng et al. (1986), indicate that when x > 0.7 the scatter of data increases.
R, = dx/dt = R$(x)
(8)
x = 1 - [l - (1- (1/2)1-m)~]1/(1-m)
(7)
+
with as the parameter. The shape factor or the reaction order parameter, m, is intimately associated with the pore structure and hence the structural parameter, (Bhatia and Perlmutter, 1980), and = 0 corresponds to m = 1. For gas-solid reactions, m lies in the range 0-1 (Ramachandran and Doraiswamy, 1982; Ishida and Wen, 1971). Among the values of reported in the literature (determined through surface area measurements), the maximum we could find was 23.6 (Debelak et al., 1984). Equation 8 for 0 < m < 1 and eq 9 for 0 < < 25 are plotted in Figure 2 . The curves in Figure 2, which represent the entire range of gasification reactions based on these two models, lie fairly close to each other. The maximum variation between these curves is comparable to the scatter of data in experimental unification plots. It is no surprise that the experimental x versus -7 curves lie close enough that approximating them with a single curve is feasible. When we fitted the grain model to each of the four sets of x-t data from our experiments, the value of m varied between 0.57 and 0.75, although the data are unified when plotted as x versus -7. Schmal et al. (1982) reported that eq 6 for both m = 1 and 2 / 3 fitted their data well, and the two model curves shown in their plots were close to each other. These observations imply that, although the unification curve given by eq 8 depends on m, for the range of values assumed by m for coal gasification, i.e., 0 < m < 1, the dependence is weak. From the above discussion, it seems possible that a master curve can, with reasonable accuracy, approximate all x versus -7 data for coal gasification, up to about 70% conversion. For specific m = m and = $, eq 8 and eq 9 respectively are possible representations of the master curve. Correlations for unification curves reported in the literature and correlations derived in this work for the literature data and for our experimental data (Figure 1)are
+
+
+
+
+
520
Ind. Eng. Chem. Res., Vol. 28, No. 5 , 1989
medium
L J
02
temo,
“C
steow
510
steam CO,
900 1000-1400 1000-1400
stellm
rtaom ateam co2 otsom
Table I. R , Values for Unifications Reported by Various Sources normalizing no. of source medium Parameter runs R,, 5 0.374 this work steam tll2 25 0.379 Kasaoka et al., 1985 steam hi2 23 0.366 COB t1/2 25 0.378 Peng et al., 1986 steam tlj2 5 0.377 Schmal et a]., 1982 steam hi2 8 0.374 Chin et al., 1983 steam R‘S 15 0.387 Agarwal, 1978 C02-CO %*/2 4 0.393 C02 Rc.1i2 5 0.382 COP RC,l,Z
850 550
800-1200 801 -1003 500-1100
026
0 26
1
0 ‘8 0 18 133 100 0 ‘8 060
-3
Similarly, the average reactivity for a particular gasification run is
35-1 00
$ (dx/dt) dx 1
Figure 3. Plots of correlated unification curves (correlations are plotted as discrete points). Solid line: m = 0.5 in eq 8. Dashed line: $ = 2.7 in eq 9.
plotted as discrete points in Figure 3. As expected, these correlations lie within the band formed by the upper and lower limits of the theoretical curves in Figure 2. Each of the unification curves in Figure 3 (shown as discrete points) approximates a number of x versus t curves. These curves lie close to each other and hence can be reduced to a single master curve. To achieve this, the x versus -7 correlations are weighted with the number of x versus t runs comprised in each of them and fitted with eq 8 and 9 up to 70% conversion. The best fit gives m = m = 0.5 and $ = 4 = 2.7. These curves are nearly the same and are also shown in Figure 3. On the whole, the master curve approximates about 110 gasification curves involved in the unification curves.
Extension of Unification Approach According to the unification approach, when char conversion x is plotted with dimensionless time -7, the x versus -7 data from widely different conditions can be approximated by a single curve. This may be represented symbolically as x = f(T) (10) where f is the functional form of the unification curve. For coal gasification, since x increases monotonically as r increases, there is always an one-to-one correspondence between x and -7. Thus, alternately, eq 10 may be written as -7
= g(x)
(11)
The above two equations are mathematical statements of the unification concept. From both equations, dx/dr = f’(r)= f’[g(x)] = C(x) (12) Thus, d x l d r is a function of conversion alone, and averaging this reactivity over the entire conversion range, we remove the dependence of the normalized curve on conversion as well. Hence, if we define a quantity R, as
-_ R, = d x / d r =
L1(dx/d-7) dx = L1(dx/d-7) dx
R , = dx/dt =
0
(14)
which, as shown above, is a constant quantity for each run. Thus, from eq 13 and 14 and from the definition of r ,
t!/PRc = R,
(15)
Therefore, we have obtained a simple relation that states that (1)when x versus t data from different experiments are unified, the average reactivity R , for each run is inversely proportional to the half-life tllzof that experiment with R, as the proportionality constant and (2) R, is unique for a unification curve. We have seen that unification curves from different sources lie close enough to be approximated by a single curve. Hence, the corresponding R, values should almost be the same, which will be elaborated further. In the above discussions, t l j 2was the unifying parameter. In several studies, coal gasification data have been unified using reactivity parameters as well. Chin et al. (1983) identified initial reactivity as a normalizing parameter and obtained a single curve by plotting normalized .reactivity, R,/RcO,against conversion. Agarwal (1978), for C 0 2 gasification, unified his data and data from Dutta et d. (1977) with reactivity a t x = 0.5 as the normalizing parameter. For each unifying parameter, we have calculated the value of R, from the reported correlations using eq 13 and the results are shown in Table I. R, values are not evaluated for the data of Mahajan et al. (19781, because eq 1, for the values of A , B, and C reported by them, results in a decrease in conversion with increasing t when extrapolated beyond x = 0.7; their correlation does not approach x = 1 asymptotically and thus may lead to incorrect values when used in eq 13. From this table, it is clear that, for coal gasification, R, varies over a small enough a range to be assumed a constant with a value of 0.38. This value of R, corresponds to m = 0.61 for the grain model and $ = 2.3 for the random pore model. These are in good agreement with m = 0.5 and ;C. = 2.7 obtained before by correlating the unification curves up to x = 0.7. Here, the upper limit for calculations is x = 1, and this may explain the slight difference in the parameter values. These differences have little effect on the plotted curves as seen from Figure 2.
(13)
Lldx then R, is a constant for the unified data or the unification curve. The upper limit for the above integral is x = 1.0, although the x--7 unification curve approximation is good only up to x = 0.7. However, since the curve flattens out a t higher conversions, contribution to the above integral above x = 0.7 and hence the error involved are small.
Reactivity Index for Characterization of Coal Gasification Reaction The ability of coal to react in a gas medium is the most important property of coal. An index of reactivity may be chosen as an indicator of this property. Some researchers choose initial reactivity, RcO,or reactivity a t an intermediate conversion as the index. Rd)is evaluated by fitting a model to the conversion-time data or from the
Ind. Eng. Chem. Res., Vol. 28, No. 5 , 1989 521 initial slope of the x versus t curve. If evaluated from a model, the value of Rd depends on the model chosen, especially for sigmoidal-shaped gasification curves; in estimating the slope, there is the usual error associated with numerical differentiation. Similar problems exist in the case of the reactivity at an intermediate conversion. Some studies choose an averaged “specific gasification rate” (e.g., Kasaoka et al. (1985)) for this index, and to estimate its value, a model needs to be chosen and fitted to the x - t data. Most of the above difficulties can be eliminated if average reactivity, R,, defined by eq 14, is chosen as the reactivity index. Since R , is an average property calculated through an integral approach, it truly reflects the experimental data; different rate models should result in almost the same values for R, for a particular gasification curve. Moreover, R , can be conveniently calculated from the half-life of the reaction: since R, = 0.38 is a good approximation for coal gasification data, eq 15 gives
R , = 0.38/t,,,
(16)
Therefore, half-life can be used directly for the characterization of the coal-gas reaction. Indeed, half-life is a function of reaction temperature, pressure, coal type, gasifying agent, etc. Few studies utilize half-life as an indicator of reactivity, but only on a qualitative basis (Maloney and Jenkins, 1984).
Activation Energy Estimation Previously, we had seen that conversion-time data for a wide range of experimental variables can be approximated by a single unification curve. Consider x versus t curves from experiments where only the temperature is varied with all other variables held constant. As explained before, the unification curve representing these data has a unique value of R, associated with it. Each of the three data sets shown in Figure 1 is an example of such unification. When temperature is the only variable, the reaction rate or reactivity can be expressed as
R, = k o exp(-E/RT)f(x)
(17)
where k o is the preexponential factor, E is the activation energy, and f ( x ) is some function of conversion. From eq 14 and 17,
R, = ko exp(-E/RT)&lf(x) dx
(18)
For the unified data, since a single curve approximates conversion-time data at different temperatures, the function f ( x ) is independent of temperature. Hence, the above integral is a constant for the unified data. Therefore,
R , = A exp(-E/RT)
(19)
where A is a constant. This, when combined with eq 15, gives tlj2 = (R,/A) exp(E/RT)
(20)
Since R, is a constant for the unified data, a plot of In t , versus 1/ T should yield a straight line with a slope of E l k . If S is the intercept of this semi-ln plot, i.e., S = R,/A, and since R , = 0.38, the reactivity index, R,, at any temperature can be readily found from
R , = (0.38/S) exp(-E/RT)
(21)
For more details on this method of activation energy estimation, refer to Raghunathan and Yang (1987).
I
I
7
6
8 1/T
I
I
10
9
X 10’ (K-’)
Figure 4. Arrhenius plots of half-life for determining E and S. Table 11. Comparison of Activation Energy Values activation energy (kJ/mol) from this work Schmal et al., 1982 Lee et al., 1984 Chin et al., 1983
64.5 165.3 249.5 148.1
62.8 158.8 225.1 150.7
Prediction Curves from Half-Life Data For the grain model, eq 8, when combined with eq 20, leads to (1- (1/2)1-7t
A similar treatment for the random pore model also gives x=l-exp
I
-
X
pexp(:’RT)
where p depends only on $as i shown in eq 9b. Thus, from only the half-life data at a few temperatures, E and S can be calculated. Then, the conversion at any temperature can be predicted from eq 22 or 23, once the parameter m or # is known. Previously, we had obtained values of 0.5 and 0.61 for m and 2.3 and 2.7 for $. It was also shown that x versus r curves for various values of these parameters lie fairly close to each other. Hence, = 0.55 and $ = 2.5 are average values for these parameters. Equation 22 or 23 therefore provides us with an explicit analytical expression for conversion of coal char in a gasifier at any instant during gasification. These relations are useful for design calculations and suitable for incorporation into a design software. This method can be applied to any gasification system where some half-life data are available. To demonstrate this, the conversion-time behavior predicted by these equations is compared with experimental data from four sources that represent different gasification conditions: (1)this work, steam gasification of North Dakota lignite char; (2) Schmal et al. (1982), steam gasification of Brazilian high-ash, subbituminous char; (3) Lee et al. (1984), C 0 2 gasification of Montana Rosebud char; (4)Chin et al. (1983), steam gasification of activated carbon from brown coal char.
522 Ind. Eng. Chem. Res., Vol. 28, No. 5 , 1989
0.9 x
c‘ .-3 0.6 7
0
c 0
0.4
3.2
0 . 0 , “ ~ ~ I 20 40 I
,
,
,
,
69
I
,
’00
80
j 120
0.0
time, : (set)
time, : ( s e c )
Figure 5. Prediction curves for data from this work. Solid lines: eq 22, m = 0.55. Dashed lines: eq 23, $ = 2.5.
Figure 7. Prediction curves for the data from Lee et al. (1984). Solid lines: eq 22, m = 0.55. Dashed lines: eq 23, $ = 2.5.
/.
c‘
.-0 c 5 L7 t 0
c.4
P 801
c.2
OC
32
851 “C 900 T 950
I003 30-
40
2c
1; ~
I
6C
time, t [ T i r l
n ^ d J
25
I
iC
4: t Te,
f
8G
”
‘GO
I
‘23
:VIP)
Figure 6. Prediction curves for data from Schmai et al. (1982). Solid lines: eq 22, m = 0.55. Dashed lines: eq 23, $ = 2.5.
Figure 8. Prediction curves for data from Chin et al. (1983). Solid lines: eq 22, m = 0.55. Dashed lines: eq 23, $ = 2.5.
Half-life data at a few temperatures are obtained from the respective conversion-time plots. An Arrhenius plot of t I j zfor each work is shown in Figure 4, and for each of these plots, E and S are determined. Table I1 compares the activation energies estimated with this method with those estimated from conventional methods, Le., from the Arrhenius plot of initial reactivity. Clearly they are in excellent agreement. With E and S known from Figure 4 and with m = m = 0.55 and = $ = 2.5, prediction curves can be generated from eq 22 and 23. The experimental data along with the predicted results are shown in Figures 5-8, and the curves from eq 22 and 23 are almost the same. For x < 0.7, the agreement with experimental data, in view of the fact that only the half-life data at several temperatures are used for prediction, is satisfactory. It should be emphasized that, in the above analysis, the parameters m and IC. are merely empirical, and from their correlated values, one should not arrive at conclusions about the physical nature of the char-gas reaction. Also, unification curves for different values of these parameters lie close to each other. Therefore, to verify a rate model or to interpret experimental data based on a model, it is necessary, but not sufficient, that the experimental data fit the model expression. Further evidence through analysis of surface area, pore structure, etc., is essential to achieve a proper understanding of the char-gas reaction.
to higher conversions, a more accurate analytical expression can be used to represent the data. A number of studies choose the grain model expression (eq 6), and to determine the best fit for this model, a value is chosen for m. With m known, Rd)can be determined by integrating eq 6 and applying linear regression. This procedure is repeated for various values of m to determine the best fit parameters. Instead, a simple iterative procedure to estimate parameters m and R,, is outlined below. If x-t data are available up to higher conversions, the data can be normalized into x-7 form since t l I zis known. Then, eq 8, which is the grain model for the normalized data, can be used to fit the data. This equation has the functional form
+
Estimation of Grain Model Parameters The above analysis applies when the only data available are tI,2. On the other hand, if x-t data are available up
x = d-7,m)
(24)
Previously it was shown that the dependence of the x-r curves on parameter m is weak (Figure 2) and also m lies between 0 and 1. Hence, in a Taylor’s series expansion of the above equation around m = mo,the second-order and higher order terms can be neglected. Therefore, x = Cb(7,mO)+ ( m - mo)$’(.r,m,J
(25)
It can be shown that minimizing the sum of errors between the experimental (xexp) and model values ( x ) gives the following expression for m: m = [moX(@)2(-7,mo) + Xxexp~’(7,mo) -
C $ ( ~ , m o ) ~ ’ ( - 7 , m o ) l / ~ ~ ( ~ ’ ) 2 ( -(26) 7,mo)l Since the master curve is a good approximation for the x--7
Ind. Eng. Chem. Res., Vol. 28, No. 5 , 1989 523 data, for the first iteration, we can choose mo = 0.55. Then, from the normalized experimental data and from the above equation, a better estimate is obtained for m. This m becomes mo for the next iteration. For all the x-t data shown in Figures 5-8, to determine m to within an accuracy of four decimal places, only two or three iterations are required. With this m, since tllz is known, R,, can be calculated from
m, m = grain model parameters p = constant dependent only on $ as defined in eq 9b
The above expression is obtained by integrating eq 6 and setting x = 0.5 at t = tl,z. For the experimental data from this work, the grain model parameters thus calculated are compared with those determined through rigorous nonlinear regression, and the maximum error is 5% in m and 4% in Rs. It is clear that the iterative method is reliable and converges rapidly.
Greek Symbols T = dimensionless time, t/t,,z $, $ = random pore model parameters 4 = defined in eq 24 4' = first derivative of 4
Conclusions Most of the conversion data for coal gasification reported in the literature, when plotted against dimensionless time 7,can be unified into a single curve with reasonable accuracy. A master curve, which is an approximation for all the conversion-time data for coal gasification, has been correlated based on the grain model and the random pore model for gas-solid reactions. With an extension of the unification approach, it is shown that the the product of half-life t l l z and average reactivity R, has a constant value of 0.38 for most coal gasification reactions. For characterization of the coal-gas reaction, R , can be used as an index of reactivity, as it is a consistent and reliable measure of reactivity. Furthermore, it can be conveniently determined from the half-life data directly. On the basis of the grain model and the random pore model, analytical expressions suitable for design calculations are developed. From the half-life data at a few temperatures, activation energy of the reaction and the prediction curves for char conversion can be generated. These expressions are tested with the experimental data from this work and with three other sets of data from the literature. The conversion-time behavior predicted by these equations is in agreement with the experimental data up to about 70% conversion. When conversion-time data are available up to higher conversions, to fit the grain model, the model expression can be approximated to a linear form and the parameters estimated through a simple iterative scheme. Acknowledgment This work was supported in part by the Department of Energy under Contract AC21-83MC20320. We thank I. C. Lee for help with the experiments. A version of this paper was presented at the 4th Annual Pittsburgh Coal Conference, 1987.
Nomenclature A = preexponential constant in eq 19 A, E , C = unification curve parameters E = activation energy F ( x ) , G ( x ) = arbitrary functions of char conversion KO = preexponential factor in Arrhenius expression
R, = char reactivity, dx/dt RcO= initial reactivity Rcv112 = reactivity at x = 0.5 R, = average char reactivity R, = defined in eq 13 S = R , / A , intercept of the plot of In t I j zversus l / T t = gasification time t I j z= half-life of a reaction T = reaction temperature x = char conversion
Literature Cited Agarwal, A. K. Kinetics of Char Reaction with C02-C0 Gas Mixtures. Ph.D. Dissertation, West Virginia University, Morgantown, 1978. Adschiri, T.; Furusawa, T. Estimation of Dynamic Change in Gasification Rate of Chars-I. A Common Formulation of Dynamic Change in Experimentally Observed Surface Area during Steam Gasification of Char. AIChE J . 1987, 42, 1313-1317. Bhatia, S. K.; Perlmutter, D. D. A Random Pore Model for FluidSolid Reactions: I. Isothermal, Kinetic Control. AIChE J . 1980, 26, 379-386. Chin, G.; Kimura, S.; Tone, S.; Otake, T. Gasification of coal char with steam (part 2). Pore structure and reactivity. Intl. Chem. Eng. 1983, 23, 113-120. Debelak, K. A.; Malito, J. T.; Patrick, R. M. Influence of Particle Structure on the Rate of Gas-Solid Gasification Reactions. Prepr.-Am. Chem. soc., Diu. Fuel Chem. 1984, 29(1), 82-89. Dutta, S.; Wen, C. Y.; Belt, R. J. Reactivity of Coal and Char. 1. In Carbon Dioxide Atmosphere. Ind. Eng. Chem. Process Des. Deu. 1977, 16, 20-30. Gavalas, G. R. A Random Capillary Model with Application to Char Gasification a t Chemically Controlled Rates. AIChE J. 1980,26, 577-585. Ishida, M.; Wen, C. Y. Comparison of Zone-Reaction Model and Unreacted-Core-Shrinking Model in Solid-Gas Reactions. Chem. Eng. Sci. 1971,26, 1031-1041. Kasaoka, S.; Sakata, Y.; Tong, C. Kinetic evaluation of the reactivity of various coal chars for gasification with carbon dioxide in comparison with steam. Intl. Chem. Eng. 1985,25, 160-175. Lee, S.; Edwards, R. V.; Gardner, N. C. Noncatalytic Coal Char Gasification. AIChE J. 1984, 30, 583-593. Mahajan, 0. P.; Walker, P. L., Jr.; Yarzab, R. Unification of coalchar gasification reaction mechanisms. Fuel 1978, 57, 643-646. Maloney, D. J.; Jenkins, R. G. Effects of Coal Peroxidation and Heat Treatment on Resulting Char Structure of Caking Coal. h?pr.Am. Chem. SOC., Diu. Fuel Chem. 1984, 29(1), 55-65. Peng, F. F.; Lee, I. C.; Yang, R. Y. K. Reactivities of In-situ and Non-in-situ Coal Chars during Gasification in Steam a t 1000 to 1400 "c. proc. 3rd Pittsburgh Coal Conj. 1986, 730-744. Raghunathan, K. Kinetics, Structural Effects, Modeling and Unification of Char Gasification Reactions. Ph.D. Dissertation, West Virginia University, Morgantown, 1988. Raghunathan, K.; Yang, R. Y. K. A New Method for Estimation of Activation Energies Associated with Coal Gasification Reactions. Prepr.-Am. Chem. soc., Diu. Fuel Chem. 1987,32(1), 478-785. Ramachandran, P. A.; Doraiswamy, L. K. Modeling of Noncatalytic Gas-Solid Reactions. AIChE J . 1982, 28, 881-900. Schmal, M.; Monteiro, J. L. F.; Castellan, J. L. Kinetics of Coal Gasification. Ind. Eng. Chem. Process Des. Deu. 1982, 21, 256-266. Received for review May 9, 1988 Revised manuscript receiued December 19, 1988 Accepted January 4, 1989
