MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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Second Effectiveness Factor and ERE Essenhigh (1988) proposed a so-called “second effectiveness factor” to account for the internal combustion of char oxidation in conjunction with the Langmuir rate equation. This method has theoretical and practical difficulties (see Chapters 2 and 5). The effectiveness factor approach developed in this project can potentially overcome all these difficulties. Essenhigh (1988) also proposed a "Extended Resistance Equation" (ERE) to represent the char oxidation rates. The ERE takes into account boundary layer diffusion, adsorption, desorption and internal combustion (pore diffusion effects) while retaining a simple form. However, it was shown in Chapter 5 that the ERE is mathematically invalid except for some special cases (e.g., when the Langmuir kinetics reduces to first order, or when the film diffusion resistance can be neglected). The approach used in this project overcomes this difficulty with minimal computational efforts. Mechanisms Although the adsorption-desorption mechanism (Essenhigh, 1988) is commonly assumed when the Langmuir rate equation is used, many different mechanisms lead to expressions that can be simplified to the Langmuir rate equation. The approach of this project is general and independent of specific mechanisms. Therefore, k 1 and k 0 (two rate constants) are used in this project instead of k a (adsorption rate constant) and k d (desorption rate constant). It is commonly believed that the activation energy of adsorption is lower than that of desorption. Based on this belief and the adsorption-desorption interpretation of the 124
Langmuir rate equation, the reaction order should increase with temperature. However, some experiments showed that the reaction order of the char-oxygen reaction decreased with increased particle temperature at constant oxygen concentration (Ranish and Walker, 1993; Banin et al., 1997a). These observations indicated that either the adsorption- desorption interpretation of the Langmuir rate equation or the belief that E a is less than E d is not true. The understanding from this project is: 1) the mechanism of the Langmuir rate equation is not well understood, and the adsorption-desorption interpretation may not be true; 2) impurities can affect the activation energies of different processes to different extents. Keeping these two points in mind, it is no surprise that E 1 (E a is not used since the mechanism is not known) can be less than, equal to, or greater than E 0. Observed Activation Energy in Zone I An expression (Eq. 7.22) was developed to relate the observed activation energy to the activation energies of k 1p and K p under Zone I conditions, provided that the oxygen partial pressure at the external surface of the particle (P os) is constant. HP-CBK Model The High Pressure Carbon Burnout Kinetics model (HP-CBK) was developed in this project. This new model was based on the CBK model developed by Hurt et al. (1998b). The HP-CBK was shown to be satisfactory in modeling char oxidation at both atmospheric and elevated pressures. The HP-CBK model used: 1) intrinsic Langmuir kinetics rather than global n-th order kinetics; 2) the analytical solution of the 125
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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 * (%)
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The resulting observations regardin
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correction. The values of functions
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Table 4.6. The Relative Error* (%)
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Table 4.8. The Relative Error* (%)
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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
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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
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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
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: 0.5 due to the contribution from th
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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