MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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oxygen partial pressure. This contradicts the theoretical prediction of reaction order, which says the reaction order should decrease with increasing oxygen partial pressure (see Eq. 5.4). There are several possibilities for this difference: First, the reaction order is often obtained by plotting ln(reaction rate at a certain temperature) vs. ln(oxygen partial pressure) and then finding the average slope of the curve. Due to the logarithm operation and the averaging process, the subtle change of reaction order is often hard to observe. This will be further illustrated by the graphite oxidation data (Ranish and Walker, 1993) in Chapter 7. Second, both of the above studies used TGA to measure the reaction order. In TGA experiments, the gas temperature is measured and controlled. The particle temperature is assumed to be the same as the gas temperature. However, local heating of the particles is possible due to the highly exothermic nature of the char oxidation reaction. Here local heating means the particle temperature is higher than the gas temperature by a margin that makes a considerable difference in kinetics. As oxygen partial pressure increases, the reaction rate increases, thus making the local heating more severe and causing the particle temperature to increase, which causes the reaction rate to increase further. The result of local heating is over-estimation of the reaction order at higher oxygen partial pressure. According to Eq. 5.4, the true reaction order decreases with oxygen partial pressure. Thus local heating disguises the true reaction orders and serves to “stabilize” the observed reaction orders. The third possibility is that the Langmuir rate equation is insufficient to model the carbon-oxygen reaction. Firstly, the wide variation of <strong>AS</strong>A poses a great challenge to the applicability of the Langmuir rate equation. Secondly, the Langmuir rate equation 66
assumes a homogeneous, non-interacting surface, thus implying constant values of E a and E d. However, for a non-homogenous surface, the most active sites are filled first. For an interacting surface, filling of nearby sites creates repulsion forces, thus inhibiting adsorption and promoting desorption. The Temkin isotherm (Laurendeau, 1978) might be required to describe the adsorption-desorption processes of char oxidation. In summary, the constant fractional order observed in TGA experiments at atmospheric pressure does not prove or disprove the Langmuir rate equation. The Langmuir rate equation is assumed to sufficiently describe the carbon-oxygen reaction in this study and is evaluated by comparison with experimental data. 67
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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
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
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: Farrauto and Batholomew (1997) prop
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 +
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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
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Langmuir rate equation, the reactio
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II, in agreement with many observat
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9. Recommendations The predictive c
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References Ahmed, S., M. H. Back an
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Essenhigh, R. H., D. Fortsch and H.
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Mehta, B. N. and R. Aris , “Commu
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Szekely, J. and M. Propster, "A Str
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Appendices 139
Page 161 and 162:
Introduction Appendix A: Experiment
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detaching the flame from the burner
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To study the effects of steam, CO w
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times at heights of 1, 2, 4, and 6
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analysis. The char reactivities (in
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Table A.5. Moisture, Ash and ICP Ma
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Table A.9. Elemental Analyses of Fo
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temperature profile of the post-fla
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Apparent densities 1.00 0.75 0.50 0
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This observation is somewhat surpri
Page 181 and 182:
It is interesting to compare Figure
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The N 2 BET surfacea areas and H/C
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collected in the #4 reactor conditi
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Rate (gC /g C remaining /sec) 1.6x1
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close to zero, the accumulated erro
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Appendix B: Errors and Standard Dev
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