MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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5. Theoretical Developments.........................................................................................45 The Observed Reaction Orders in Zone I and Zone II...................................................46 Rough Sphere Combustion.............................................................................................50 Bulk Diffusion vs. Knudsen Diffusion..........................................................................53 Relationship between the Effectiveness Factor and the Second Effectiveness Factor...57 Extended Resistance Equation (ERE).............................................................................60 Various Mechanisms for the Carbon-Oxygen Reaction.................................................62 Constant Fractional Reaction Order Issue.....................................................................65 6. High Pressure Char Oxidation Model........................................................................69 CBK Model....................................................................................................................69 Single-Film Char Oxidation Submodel.....................................................70 Statistical Kinetics and Properties...........................................................74 Thermal Annealing Submodel...............................................................76 The Ash Encapsulation Submodel..........................................................77 HP-CBK Model Development......................................................................................78 Kinetics ........................................................................................78 Effective Diffusivity..........................................................................80 Estimating S ext /S int Using Pore Structure Model...........................................82 Thermodynamic and Transport Properties.................................................84 Range of Reynolds Number.................................................................85 7. Model Evaluation and Discussion..............................................................................87 Graphite Flake Data.......................................................................................................88 Rough Sphere Combustion Data....................................................................................90 Results and Discussion.......................................................................92 Large Particle Oxidation Data.........................................................................................95 Pulverized Char Drop-Tube Data................................................................................103 Approach......................................................................................104 Results ........................................................................................109 TGA and FFB Data-This Study..................................................................................111 Results ........................................................................................115 Summary......................................................................................................................117 8. Summary and Conclusions.......................................................................................121 Analytical Solutions of the Effectiveness Factors.......................................................121 Theoretical Developments...........................................................................................122 The Observed Reaction Order in Zone I and Zone II....................................122 Rough Sphere Combustion.................................................................122 Knudsen Diffusion and Molecular Diffusion.............................................123 Second Effectiveness Factor and ERE ....................................................124 Mechanisms ..................................................................................124 HP-CBK Model...........................................................................................................125 Principal Conclusions...................................................................................................127 9. Recommendations....................................................................................................129 References........................................................................................................................131 viii
Appendices......................................................................................................................139 Appendix A: Experiments................................................................................................141 Introduction..................................................................................................................141 Experimental Technique...............................................................................................142 Flat-Flame Burner Considerations.........................................................142 Reactor Conditions ..........................................................................143 Procedures and Apparatus...........................................................................................146 Char Preparation.............................................................................146 Proximate and Ultimate Analysis ..........................................................147 Internal Surface Area........................................................................147 TGA Reactivity...............................................................................147 Bulk Density and True Density.............................................................148 High Temperature Reactivity...............................................................148 Results..........................................................................................................................149 Discussion....................................................................................................................154 Mass Release.................................................................................155 Tap Densities and True Densities ..........................................................156 N 2 BET Surface Area and CO 2 Surface Area.............................................157 TGA Reactivities: Effects of Reactor Conditions ........................................159 TGA Reactivities: Effects of Coal Types..................................................162 High Temperature Reactivity...............................................................163 Elemental Analysis...........................................................................167 Conclusions..................................................................................................................169 Appendix B: Errors and Standard Deviation....................................................................171 ix
Page 1 and 2: MODELING CHAR OXIDATION AS A FUNCTI
Page 3 and 4: BRIGHAM YOUNG UNIVERSITY As chair o
Page 5 and 6: CBK model uses: 1) an intrinsic Lan
Page 7: Table of Contents List of Figures..
Page 12 and 13: Figure A.2. Mass releases of the Ko
Page 14 and 15: Table 7.6. Parameters Used in Model
Page 16 and 17: Ed activation energy of desorption,
Page 18 and 19: vc the volume of combustible materi
Page 21 and 22: Background 1. Introduction The rate
Page 23: the CBK model developed at Brown Un
Page 26 and 27: Zone III rate ∝ C og E obs → 0
Page 28 and 29: coal-general kinetic rate constants
Page 30 and 31: Boundary Layer Diffusion The molar
Page 32 and 33: = q obs q max The factor can be use
Page 34 and 35: where k 1 and K are two kinetic par
Page 36 and 37: particle can therefore be convenien
Page 38 and 39: This is the first time that the gen
Page 40 and 41: Data of Mathias Mathias (1996) perf
Page 42 and 43: urn with shrinking diameters, and t
Page 45 and 46: 3. Objectives and Approach The obje
Page 47 and 48: Introduction 4. Analytical Solution
Page 49 and 50: Task and Methodology Task One of th
Page 51 and 52: 2 [ (i +1) − (i − 1)] i b = −
Page 53 and 54: 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* (%)
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
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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
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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
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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
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Farrauto and Batholomew (1997) prop
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assumes a homogeneous, non-interact
Page 90 and 91:
Single-Film Char Oxidation Submodel
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where and An energy balance is used
Page 94 and 95:
where is the empirical burning mode
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calculation uses a 7 × 7 × 7 matr
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HP-CBK Model Development The HP-CBK
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Effective Diffusivity The major obs
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where r p1 and r p2 are the average
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where r p1 is the macro-pore radius
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7. Model Evaluation and Discussion
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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
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= S int S ext D e r p a 2 2M C M O2
Page 117 and 118:
Reactor Head Flow Straightener Reac
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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
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Table 7.5. The Experimental Conditi
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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
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q = A 1p e − E 1 p / RT P os 1 +
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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
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0.5 due to the contribution from th
Page 145 and 146:
Langmuir rate equation, the reactio
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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
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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
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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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MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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