MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

More documents

Recommendations

Info

Table 4.10. Summary of the Uncorrected and Corrected General Asymptotic Solutions for Predicting the Effectiveness Factor for m-th Order Rate Equations and Langmuir Rate Equations Rate Equation r ′ = kmC m Differential Equation and Boundary Conditions General Asymptotic Solution (within 17%) m-th Order Rate Equation Langmuir rate Equation d 2 C 2 dC 2 + dr r dr − Ok C = Cs at r = rs m mC De = 0 dC/dr = 0 at r = 0 = 1 1 1 ( − ) MT tanh(3MT ) 3MT M T = r s 3 Thiele Modulus at First Order Extreme M T = r s 3 Thiele Modulus at Zeroth Order Extreme Corrected General Asymptotic Solution (within 2%) Correction Function f c m obs M T = r s 3 = f c 1 M T M T = r s 3 f c (M T ,m) = (1+ (m + 1) 2 Ok1 De O k 0 2D e C s 1 ( tanh(3MT ) (m + 1) 2 1 2M T m Ok m −1 mC De 44 r ′ = k1C 1 + KC d 2 C 2 dC 2 + dr r dr − Ok1C = 0 De (1 + KC) C = Cs at r = rs dC/dr = 0 at r = 0 = 1 1 1 ( − ) MT tanh(3MT ) 3MT M T = r s 3 Ok 1 2D e KC s 1+ KC s 1 − 2 [KC − ln(1+ KC )] s s Two approximate M T forms: M T = r s 3 or M T = r s 3 when m=1 M T = r s 3 when m=0 M T = r s 3 1/ 2 1 − ) 3MT Ok m −1 mC De 1 (1− m )2 2 2 + 2M 2 T ) = f c M T = r s 3 1 M T Ok1 / De 1 2KCs + 1+ KCs O k 1 / D e 2KC s +1 Ok1 De O k 0 2D e C s when KC s=0 1 ( tanh(3MT ) Ok 1 2D e KC s 1+ KC s 1 1/2 f (M , ) = (1+ c T 1 + KC 1 s 2MT when KC s=∞ 1 1 + KC s 1 − ) 3MT 1 − 2 [KC − ln(1+ KC )] s s 2 +2M 1 2 ) 2 T (1− 1 ) 1+ KCs 2
5. Theoretical Developments The intrinsic reaction order of char oxidation has been observed to vary within limits of zero and unity (Suuberg, 1988; Chan et al., 1987) although the intrinsic reaction order is often observed to be about 0.7 in TGA experiments at atmospheric pressure (Suuberg, 1988; Reade, 1995). No theory has been available to explain or predict how the reaction order changes with experimental conditions. The global n-th order rate equation has been under criticism (Essenhigh, 1996) and was shown to be inadequate in modeling high pressure char oxidation. It is generally accepted that the carbon-oxygen reaction involves adsorption of reactant(s), surface reactions, and desorption of products, although the exact reaction mechanism of the carbon-oxygen reaction is still unknown. There is little doubt that an appropriate Langmuir-Hinshelwood expression, with its sound theoretical basis and more adjustable parameters, holds more potential to model char oxidation rates over wide ranges of experimental conditions than the simplistic n-th order rate equation. However, a complex Langmuir-Hinshelwood expression with many parameters, which are difficult to determine both experimentally and theoretically, is not a desirable engineering option. Recently, Essenhigh showed that the simple Langmuir rate equation was satisfactory in modeling the carbon-oxygen reaction rate (Essenhigh, 1988; Essenhigh, 1991; Essenhigh, 1994; Essenhigh and Mescher, 1996), although there is still an unresolved question as to a suitable explanation of the empirical n-th order rate equation (Essenhigh and Mescher, 1996). It was also recognized (Essehigh and Mescher, 45
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 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: general asymptotic solution. An arc
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
show all

MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?