MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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ABSTRACT MODELING CHAR OXIDATION AT ATMOSPHERIC AND ELEVATED PRESSURES USING AN INTRINSIC LANGMUIR RATE EQUATION AND AN EFFECTIVENESS FACTOR Jianhui Hong Chemical Engineering Department Doctor of Philosophy A global n-th order rate equation is often used to model char oxidation rates at atmospheric pressure. However, it was recently shown that this approach was inadequate for modeling char oxidation rates as a function of total pressure. It is generally thought that in order to model the effects of total pressure, an intrinsic modeling approach (i.e., pore diffusion effects are accounted for explicitly) is required, and a Langmuir- Hinshelwood type expression is needed. The objective of this project was to develop a model that can be used to explain and unify char oxidation rates over wide ranges of experimental conditions (including temperature, total pressure, oxygen mole fraction, particle size, etc.) without excessive computational efforts. In this project a new High Pressure Carbon Burnout Kinetics (HP-CBK) model was developed on the basis of the CBK model by Hurt and his co-workers. The HP-
CBK model uses: 1) an intrinsic Langmuir rate equation rather than global n-th order kinetics; 2) an analytical solution of the effectiveness factor for the Langmuir rate equation with a correction function (developed in this project) to improve its accuracy; 3) a pore structure model for calculation of the effective diffusivity, taking into account both Knudsen diffusion and molecular diffusion; and 4) general correlations for Nusselt and Sherwood numbers, which allow the HP-CBK model to be used for both entrained-flow, pulverized char oxidation and large-particle combustion in fixed beds. The HP-CBK model was evaluated by comparison with five sets of experimental measurements: 1) graphite flake oxidation data; 2) rough sphere combustion data; 3) large particle oxidation data; 4) pulverized char drop-tube data, and 5) TGA and FFB data from this study. Results showed that the HP-CBK model was able to quantitatively explain: 1) the effects of temperature, total gas pressure, oxygen mole fraction, particle size and gas velocity on reaction rates, and 2) the change of reaction order with temperature and oxygen partial pressure. Therefore, the Langmuir rate equation, when used with the appropriate effectiveness factor, seems to be satisfactory for modeling char oxidation over wide ranges of experimental conditions.
Page 1 and 2: MODELING CHAR OXIDATION AS A FUNCTI
Page 3: BRIGHAM YOUNG UNIVERSITY As chair o
Page 7 and 8: Table of Contents List of Figures..
Page 9: Appendices.........................
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
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
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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
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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
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where is the empirical burning mode
Page 96 and 97:
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
Page 104 and 105:
where r p1 is the macro-pore radius
Page 107 and 108:
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
Page 115 and 116:
= S int S ext D e r p a 2 2M C M O2
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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
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2.5x10 -4 2 /sec) 2.0 1.5 Rate (g/c
Page 125 and 126:
Table 7.5. The Experimental Conditi
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The burnout and particle velocity d
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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
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Currently the correlations between
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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
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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.
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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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