MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...
MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ... MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...
temperatures are so limited. However, it is thought that the approach used in the HP- CBK model is unique and promising, and may eventually yield coal-general correlations. Graphite Flake Data Ranish and Walker (1993) measured the oxidation rates of some highly crystalline graphite flakes in pure oxygen at pressures between 1 and 64 atm and temperatures between 733 and 842 K. They observed that the reaction order decreased from 0.83 to 0.69 as the reaction temperature increased from 733 to 813 K. This observation contradicts the prediction of Essenhigh (1988), which suggested that the reaction order should increase with increased temperature at constant oxygen pressure. The graphite flakes used in these experiments had a very low reactivity. Under the conditions of these experiments, boundary layer diffusion resistance can be safely neglected. Since these graphite flakes were non-porous, pore diffusion did not occur. The reaction temperatures were controlled, and therefore heat transfer between gas and the graphite flakes does not need to be considered. For all the above reasons, these data are free from the complications of mass and heat transfer, and are ideal for testing kinetic expressions. The Langmuir rate equation was applied to these rate data and seemed to agree well with these rate data at three temperatures over the entire range of oxygen pressure (see Figure 7.1). The Langmuir rate equation also captures the change of observed reaction order with temperature. Note that the reaction orders (the m’s in Figure 7.1) are the averaged slopes of the lines in Figure 7.1. Since the graphite flakes used in these 88
experiments are non-porous, the rate equation can be expressed in a slightly different form. The best-fit kinetic parameters from this study are in the following equation: r in ′ = k 1′ pPO 2 1+ K p P O 2 = 6.29 × 10 8 e −51,100/ RT P O2 1 +13.4e −10,100/ RT P O 2 89 (7.1) where r in ′ is in mol C/(gC remaining)/sec, R is the gas constant (1.987 cal/mol/K), and T is the reaction temperature in K, P O2 is the oxygen partial pressure in atm. log 10 Rate (mol C/sec/g C rem.) -3.2 -3.6 -4.0 -4.4 -4.8 -5.2 -5.6 -6.0 -6.4 0.0 813 K 773 K 733 K 0.5 1.0 1.5 log10 O2 Pressure (atm) m=0.69 m=0.75 m=0.83 Figure 7.1. Comparison of predictions of carbon reactivity with graphite flake data (Ranish and Walker, 1993) obtained as a function of P O2 and T p. Symbols represent measured data. Curves represent predictions from a single Langmuir rate expression (Eq. 7.1). One important observation in these experiments was that the reaction order decreased with temperature over the same range of oxygen pressure. In order to allow the reaction order to decrease with temperature, the activation energy of K p must be positive 2.0
- Page 57 and 58: correction. The values of functions
- Page 59 and 60: Table 4.6. The Relative Error* (%)
- Page 61 and 62: Table 4.8. The Relative Error* (%)
- Page 63 and 64: general asymptotic solution. An arc
- Page 65 and 66: 5. Theoretical Developments The int
- Page 67 and 68: order of a reaction is usually dete
- Page 69 and 70: nobs = 1 (KCs ) 2 2 1 [KCs − ln(1
- Page 71 and 72: The observed reaction order in Zone
- Page 73 and 74: Bulk Diffusion vs. Knudsen Diffusio
- Page 75 and 76: where D K is in cm 2 /sec, r p is t
- Page 77 and 78: where T p is in K, P is in atm. The
- Page 79 and 80: Both of these assumptions are argua
- Page 81 and 82: 2 r obs ′ − [kD Pog + k d + kD
- Page 83 and 84: oxygen partial pressure (Suuberg et
- Page 85 and 86: Farrauto and Batholomew (1997) prop
- Page 87: assumes a homogeneous, non-interact
- Page 90 and 91: Single-Film Char Oxidation Submodel
- Page 92 and 93: where and An energy balance is used
- Page 94 and 95: where is the empirical burning mode
- Page 96 and 97: calculation uses a 7 × 7 × 7 matr
- Page 98 and 99: HP-CBK Model Development The HP-CBK
- Page 100 and 101: Effective Diffusivity The major obs
- Page 102 and 103: where r p1 and r p2 are the average
- Page 104 and 105: where r p1 is the macro-pore radius
- Page 107: 7. Model Evaluation and Discussion
- Page 111 and 112: and 2850 K). For consistency with t
- Page 113 and 114: The value of the roughness factor w
- Page 115 and 116: = S int S ext D e r p a 2 2M C M O2
- Page 117 and 118: Reactor Head Flow Straightener Reac
- Page 119 and 120: the large size of the particle, and
- Page 121 and 122: taking into account convection, rad
- Page 123 and 124: 2.5x10 -4 2 /sec) 2.0 1.5 Rate (g/c
- Page 125 and 126: Table 7.5. The Experimental Conditi
- Page 127 and 128: The burnout and particle velocity d
- Page 129 and 130: The HP-CBK was used to predict the
- Page 131 and 132: TGA and FFB Data-This Study The rea
- Page 133 and 134: This equation can be derived as fol
- Page 135 and 136: q = A 1p e − E 1 p / RT P os 1 +
- Page 137 and 138: m obs = 0 at high temperatures) and
- Page 139 and 140: Currently the correlations between
- Page 141 and 142: 8. Summary and Conclusions The obje
- Page 143 and 144: 0.5 due to the contribution from th
- Page 145 and 146: Langmuir rate equation, the reactio
- Page 147 and 148: II, in agreement with many observat
- Page 149 and 150: 9. Recommendations The predictive c
- Page 151 and 152: References Ahmed, S., M. H. Back an
- Page 153 and 154: Essenhigh, R. H., D. Fortsch and H.
- Page 155 and 156: Mehta, B. N. and R. Aris , “Commu
- Page 157 and 158: Szekely, J. and M. Propster, "A Str
experiments are non-porous, the rate equation can be expressed in a slightly different<br />
form. The best-fit kinetic parameters from this study are in the following equation:<br />
r in ′ =<br />
k 1′ pPO 2<br />
1+ K p P O 2<br />
= 6.29 × 10 8 e −51,100/ RT P O2<br />
1 +13.4e −10,100/ RT P O 2<br />
89<br />
(7.1)<br />
where r in ′ is in mol C/(gC remaining)/sec, R is the gas constant (1.987 cal/mol/K), and T is<br />
the reaction temperature in K, P O2 is the oxygen partial pressure in atm.<br />
log 10 Rate (mol C/sec/g C rem.)<br />
-3.2<br />
-3.6<br />
-4.0<br />
-4.4<br />
-4.8<br />
-5.2<br />
-5.6<br />
-6.0<br />
-6.4<br />
0.0<br />
813 K<br />
773 K<br />
733 K<br />
0.5 1.0 1.5<br />
log10 O2 Pressure (atm)<br />
m=0.69<br />
m=0.75<br />
m=0.83<br />
Figure 7.1. Comparison of predictions of carbon reactivity with graphite flake data<br />
(Ranish and Walker, 1993) obtained as a function of P O2 and T p. Symbols<br />
represent measured data. Curves represent predictions from a single<br />
Langmuir rate expression (Eq. 7.1).<br />
One important observation in these experiments was that the reaction order<br />
decreased with temperature over the same range of oxygen pressure. In order to allow the<br />
reaction order to decrease with temperature, the activation energy of K p must be positive<br />
2.0
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