MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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kcal/mol for char #2 and 7.0 kcal/mol for char #4) compared well with the value (10.1 kcal/mol) observed for graphite flakes (Ranish and Walker, 1993). The values of E 0 (28.1 kcal/mol for char #2 and 32.1 kcal/mol for char #4) compared well with the value (27.7 kcal/mol) observed for the rough sphere combustion data (Banin et al., 1997). For both char #2 and char #4, the Langmuir rate equations reduced to zero-th order rate equation at high temperatures (e.g., at a gas temperature of 1900 K), consistent with the observations in modeling the data by Monson (1992) and those by Mathias (1996). At a gas temperature of 1743 K (corresponding to a particle temperature of 1672 K for char #2 and 1676 K for char #4), the observed reaction order (n obs) was about 0.6, implying an intrinsic order (m obs) of about 0.2 (see Chapter 5). Table 7.8. Parameters Used in Modeling the TGA and FFB Data (This Study) For Condition #2 (methane fuel-lean, with 8% post-flame oxygen) A1p = 2.34 × 10 6 mol/cm 3 /sec/atm E1p = 36.6 kcal/mol Ap = 9.11 × 10 2 atm -1 Ep = 8.50 kcal/mol (A0 = A1p/Ap = 2.57 × 10 3 mol/cm 3 /sec E0 = E1p – Ep = 28.1 kcal/mol) Macro-porosity M = 0.3 (Assumed) Macro-pore radius rp1 = 22 Å (Calculated from Eq. 7.15) For Condition #4 (CO fuel-lean, with 9.6% post-flame oxygen) A1p = 2.44 × 10 6 mol/cm 3 /sec/atm E1p = 39.1 kcal/mol Ap = 3.64 × 10 2 atm -1 Ep = 7.0 kcal/mol (A0 = A1p/Ap = 6.70 × 10 3 mol/cm 3 /sec E0 = E1p – Ep = 32.1 kcal/mol) Macro-porosity M = 0.3 (Assumed) Macro-pore radius rp1 = 33 Å (Calculated from Eq. 7.15) The HP-CBK model unified the TGA reactivity and the high temperature reactivity, and quantitatively explained the reaction orders (m obs = 0.7 at 823 K and 116
m obs = 0 at high temperatures) and activation energy, although the values of reaction order and activation energy were assumed rather than measured. In the future, the measured values of reaction order and activation energy of these chars may become available, and more extensive comparisons will become possible. A global n-th order rate equation is inadequate to unify reaction rates in both Zone I (TGA data) and Zone II (FFB data). Although an intrinsic m-th order rate equation has the possibility to unify the rates in both Zone I and Zone II, it cannot explain the change of reaction order with temperature, such as those observed by Ranish and Walker (1993). Assuming a constant reaction order of 0.7 would yield an apparent reaction order of 0.85 in Zone II, which is not commonly observed at high temperatures. Summary The HP-CBK model theoretically could use up to 7 adjustable parameters (E 1p, A 1p, E p, A p, r p1, r p2 and M). Compared to the n-th order rate equation, which has three parameters (A, E obs, and n), the HP-CBK model has more adjustable parameters. However, in many cases the number of adjustable parameters were reduced. For example, for non-porous graphite flakes, no pore structure parameters (r p1, r p2 and M) were needed. In some cases, the Langmuir rate equation reduced to a zero-th order rate equation, and E 0 (which is equal to E 1p-E p) and A 0 (which is equal to A 1p/A p) were required as input parameters instead of E 1p, A 1p, E p, and A p. The curve-fitted parameters and assumptions used for each set of data are listed in Table 7.9. The global n-th order rate equation has obvious difficulties: it cannot be extrapolated between Zone I and Zone II; it insufficiently describes the effects of total 117
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MODELING CHAR OXIDATION AS A FUNCTI
Page 3 and 4:
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..
Page 9:
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
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: q = A 1p e − E 1 p / RT P os 1 +
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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