MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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pressure on reaction rates; and it insufficiently reflects the change of reaction order (which means it insufficiently models reaction rates as a function of oxygen partial pressure). The use of the intrinsic Langmuir rate equation eliminates these difficulties. The increase of adjustable parameters is a cost for all these advantages. In addition, as understanding of the pore structures of chars grows, the uncertainties with pore structure parameters will reduce over time. Table 7.9. Parameters and Assumptions (If Any) Used in the HP-CBK Model Data Set Parameters A1p Ranish and Walker (1993) 6.29 × 10 8 mol C/(gC remaining)/sec/ atm Banin et al. (1997) 2.26 × 10 11 mol/cm 3 /sec/ atm 118 Mathias (1996) Monson (1992) This study (Conditions #2) N/I N/I 2.34 × 10 6 mol/cm 3 /sec/ atm E1p (kcal/mol) 51.1 46.5 N/I N/I 36.6 Ap (atm -1 ) 13.4 1.67 × 10 4 N/I N/I 9.11 × 10 4 Ep (kcal/mol) 10.1 18.8 N/I N/I 8.5 A0 =A1p/Ap N/I N/I 0.75 mol/cm 3 2.42 × 10 /sec 3 mol/cm 3 /sec E0 = E1p - Ep (kcal/mol) N/I N/I 18.2 21.7 rp1 N/A (non- N/A (mono- Large enough 200 nm (Pre- Calculated porous)disperse) so that Knuden diffusion can be neglected. set) rp2 N/A (non- 1.08 nm * * Effects assumed porous) negligible. M N/A (non- N/A (mono- 0.28 0.25 0.3 (assumed) porous)disperse) Total number of adjustables 4 5 3 3 4 CO/CO2 ratio N/A** CO is the only product† ‡ ‡ ‡ Note: N/A stands for “Not applicable”; N/I stands for “Not independent”. * Effects of micropores are negligible. ** No CO/CO2 ratio is needed since particle temperatures are known. † Particle temperatures are between 1480 and 2850 K. CO can be assumed as the only product with little error at such high temperatures. ‡ 4.0 × 10 4 exp(-30000/1.987/Tp)
Currently the correlations between the kinetic parameters and measurable char properties have not been established. In order to use the HP-CBK model to predict char oxidation rates at high temperatures and high pressures for a new char, the following experimental data is required: 1) high pressure TGA reactivities at different total pressures (e.g., 1, 3 and 10 atm) at different (at least 2) temperatures. These data can be used to determine the kinetic parameters (A 1p, E 1p, A p and E p) for the Langmuir rate equation. 2) porosity, N 2 BET surface area and CO 2 surface area of the char. These data can be used to estimate pore structure parameters. However, additional high temperature reactivity data as a function of coal type are needed for complete verification of the model. 119
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MODELING CHAR OXIDATION AS A FUNCTI
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BRIGHAM YOUNG UNIVERSITY As chair o
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CBK model uses: 1) an intrinsic Lan
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Table of Contents List of Figures..
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Appendices.........................
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Figure A.2. Mass releases of the Ko
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Table 7.6. Parameters Used in Model
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Ed activation energy of desorption,
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vc the volume of combustible materi
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Background 1. Introduction The rate
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the CBK model developed at Brown Un
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Zone III rate ∝ C og E obs → 0
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coal-general kinetic rate constants
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Boundary Layer Diffusion The molar
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= q obs q max The factor can be use
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where k 1 and K are two kinetic par
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particle can therefore be convenien
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This is the first time that the gen
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Data of Mathias Mathias (1996) perf
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urn with shrinking diameters, and t
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3. Objectives and Approach The obje
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Introduction 4. Analytical Solution
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Task and Methodology Task One of th
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2 [ (i +1) − (i − 1)] i b = −
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Table 4.1. The Relative Error * (%)
Page 55 and 56:
The resulting observations regardin
Page 57 and 58:
correction. The values of functions
Page 59 and 60:
Table 4.6. The Relative Error* (%)
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Table 4.8. The Relative Error* (%)
Page 63 and 64:
general asymptotic solution. An arc
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5. Theoretical Developments The int
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order of a reaction is usually dete
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nobs = 1 (KCs ) 2 2 1 [KCs − ln(1
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The observed reaction order in Zone
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Bulk Diffusion vs. Knudsen Diffusio
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where D K is in cm 2 /sec, r p is t
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where T p is in K, P is in atm. The
Page 79 and 80:
Both of these assumptions are argua
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2 r obs ′ − [kD Pog + k d + kD
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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 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: m obs = 0 at high temperatures) and
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
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
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