MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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particle can therefore be conveniently expressed by its rate based on surface reactant concentrations multiplied by the effectiveness factor: r obs(C ′ s) = − dnC V dt p = S int V p ( + S ext S int = 1 V p ( Sint + Sext ) r in ′ (Cs) ) r in ′ ′ (Cs) = ( + Sext ) Sint Sint Stot 16 S tot V p r in ′ ′ (Cs ) = ( + Sext ) Sint Sint r in ′ ′ (Cs) (2.21) Stot It is commonly observed that the external surface area is negligible compared to the internal surface area. Therefore the above equation becomes: r obs ′ (Cs ) = r ′ ′ in (C s ) (2.22) The intrinsic char oxidation rate can be represented by an intrinsic m-th order rate equation in the form of r in ′ = kmC m where k m is the kinetic coefficient in (mol C/m 3 ) 1-m sec -1 , and m is the intrinsic reaction order. Correspondingly, the observed reaction rate becomes m r obs ′ = kmCs Alternatively the intrinsic char oxidation rate can be represented by the Langmuir rate equation (Eq. 2.17), and the observed reaction rate becomes: r obs ′ = k 1 C s 1 + KC s (2.23) (2.24) (2.25) It has been established that the effectiveness factor can be approximately (except that it is exact for first order reactions) predicted by (Bischoff, 1965; Thiele, 1939):
= tanh(M T ) M T = 1 M T MT = L O ′ ′ r 2 ⎛ 1 ⎝ tanh(3MT ) ⎜ ( ) in C s in Cartesian coordinates (2.26) 1 ⎞ − ⎟ in spherical coordinates (2.27) 3MT ⎠ C s [ ∫ De ( C) O r in′ ′ ( C)dC 0 ] 17 − 1 2 (2.28) where L is the characteristic length of the particle (Aris, 1957), which is equal to V p/S g, C is the local concentration of oxidizer in the particle, r in ′ is the intrinsic molar reaction rate in any form, o is the stoichiometric coefficient of oxygen for each mole of carbon consumed, which converts the carbon consumption rate into oxygen consumption rate, and D e is the effective diffusivity, which can be a function of oxygen concentration, but is assumed to be spatially uniform (but still allowed to vary temporally) in this study for simplicity. In particular, the general modulus for the m-th order rate equation (Eq. 2.23) becomes (Bischoff, 1965): M T = L (m + 1) 2 okmC m −1 s De (2.29) This general modulus has been widely used in the chemical engineering literature (Laurendeau, 1978; Hill, 1977; Bischoff, 1965; Aris, 1975; Carberry, 1976; Fogler, 1992; Froment and Bischoff, 1979; Levenspiel, 1993; Levenspiel, 1999; Mehta and Aris, 1971). For the Langmuir rate equation, a general modulus was obtained in this study by substituting Eq. 2.17 into Eq. 2.28: M T = L o k 1 KC s 2De 1 + KCs 1 − 2 [KCs − ln(1 + KCs )] . (2.30)
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 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 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
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 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 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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MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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