MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...
MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ... MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...
general asymptotic solutions predict the effectiveness factors within 2% for both rate forms. In addition, two simplified moduli were found for the Langmuir rate equation. These empirical moduli are more computationally robust than the theoretically-derived modulus. Theoretical Developments The Observed Reaction Order in Zone I and Zone II The reaction order was observed to vary with experimental conditions (temperature and oxygen partial pressure) with limits of zero and unity. The Langmuir rate equation was used to quantitatively predict how the observed reaction order would change in Zone I and Zone II assuming the Langmuir rate equation was adequate for describing the char oxidation rates (see Eqs. 5.4 and 5.13). The Langmuir rate equation allows the observed reaction order to change between zero and unity in Zone I, and to change between 0.5 and unity in Zone II if external combustion is negligible compared to internal combustion (see Table 5.1). Rough Sphere Combustion Under some conditions, the reaction rate of char oxidation is influenced by both pore diffusion and kinetics (Zone II combustion), while the reaction order is observed to be less than 0.5, which contradicts the conventional three-zone theory. This phenomenon is called rough sphere combustion. Rough sphere combustion occurs when the reaction rate contributed from the external surface area cannot be neglected compared to the rate contributed from the internal surface area. The apparent reaction order can be less than 122
0.5 due to the contribution from the external surface area. Rough sphere combustion is favored by factors that reduce the product of the internal surface area and the effectiveness factor. These factors include: 1) Small specific surface area (typically in highly ordered carbon). 2) Factors that reduce the effective diffusivity (D e) and hence reduce the effectiveness factor ( ), such as pore constriction, blind pores and low porosity. Small pore size can reduce the effective diffusivity but is often associated with larger internal surface area, and therefore is excluded from this category. 3) Very fast kinetics, which increases the value of the general Thiele modulus and hence reduces the effectiveness factor. Knudsen Diffusion and Molecular Diffusion In modeling pore diffusion, Knudsen diffusion and molecular diffusion are used to calculate the effective diffusivity. It is well known that molecular diffusion can be neglected for very small pores and Knudsen diffusion can be neglected in very large pores. It is desirable to quantitatively define the threshold pore sizes for these simplifications. The concept of a “critical pore size” was proposed in this project and the mathematical expression was given for this critical pore size. At the critical pore size, the Knudsen diffusivity is equal to the molecular diffusivity. When the pore size is at least 20 times larger than the critical pore size, Knudsen diffusion can be neglected. When the pore size is at least 20 times smaller than the critical pore size, molecular diffusion can be neglected. In most char oxidation cases, both diffusion mechanisms have to be considered. 123
- 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 and 108: 7. Model Evaluation and Discussion
- Page 109 and 110: experiments are non-porous, the rat
- 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: 8. Summary and Conclusions The obje
- 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
- Page 159 and 160: Appendices 139
- Page 161 and 162: Introduction Appendix A: Experiment
- Page 163 and 164: detaching the flame from the burner
- Page 165 and 166: To study the effects of steam, CO w
- Page 167 and 168: times at heights of 1, 2, 4, and 6
- Page 169 and 170: analysis. The char reactivities (in
- Page 171 and 172: Table A.5. Moisture, Ash and ICP Ma
- Page 173 and 174: Table A.9. Elemental Analyses of Fo
- Page 175 and 176: temperature profile of the post-fla
- Page 177 and 178: Apparent densities 1.00 0.75 0.50 0
- Page 179 and 180: This observation is somewhat surpri
- Page 181 and 182: It is interesting to compare Figure
- Page 183 and 184: The N 2 BET surfacea areas and H/C
- Page 185 and 186: collected in the #4 reactor conditi
- Page 187 and 188: Rate (gC /g C remaining /sec) 1.6x1
- Page 189 and 190: close to zero, the accumulated erro
- Page 191: Appendix B: Errors and Standard Dev
general asymptotic solutions predict the effectiveness factors within 2% for both rate<br />
forms. In addition, two simplified moduli were found for the Langmuir rate equation.<br />
These empirical moduli are more computationally robust than the theoretically-derived<br />
modulus.<br />
Theoretical Developments<br />
The Observed Reaction Order in Zone I and Zone II<br />
The reaction order was observed to vary with experimental conditions<br />
(temperature and oxygen partial pressure) with limits of zero and unity. The Langmuir<br />
rate equation was used to quantitatively predict how the observed reaction order would<br />
change in Zone I and Zone II assuming the Langmuir rate equation was adequate for<br />
describing the char oxidation rates (see Eqs. 5.4 and 5.13). The Langmuir rate equation<br />
allows the observed reaction order to change between zero and unity in Zone I, and to<br />
change between 0.5 and unity in Zone II if external combustion is negligible compared to<br />
internal combustion (see Table 5.1).<br />
Rough Sphere Combustion<br />
Under some conditions, the reaction rate of char oxidation is influenced by both<br />
pore diffusion and kinetics (Zone II combustion), while the reaction order is observed to<br />
be less than 0.5, which contradicts the conventional three-zone theory. This phenomenon<br />
is called rough sphere combustion. Rough sphere combustion occurs when the reaction<br />
rate contributed from the external surface area cannot be neglected compared to the rate<br />
contributed from the internal surface area. The apparent reaction order can be less than<br />
122
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