MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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where is the empirical burning mode parameter (Mitchell et al., 1992; Hurt et al., 1998). The values of were calculated from high temperature char oxidation data (Mitchell et al., 1992) for ten U.S. coals and were found to vary only modestly from char to char, and a mean value of 0.2 can be taken as an estimate for an unknown char. After calculating a new c, Eq. (6.17) can be used to calculate the value of p, after which geometric considerations lead to: d p d p ,o = m ⎛ ⎝ mo ⎜ ⎞ ⎛ ⎠ ⎝ ⎜ ⎡ ⎢ ⎣ ⎟ p, o Statistical Kinetics and Properties p ⎞ ⎤ ⎟ ⎠ ⎥ ⎦ 1/3 74 (6.19) The CBK model accommodates statistical distribution of particle sizes (d p), single particle reactivites (represented by the global pre-exponential factor A) and apparent carbon densities ( c) in order to better describe the late stages of char oxidation (Hurt et al., 1996). The number fraction of particles in the incremental parameter space [d(d p)dAd c] is given by F(d p, A, c)d(d p)dAd c, where F(d p, A, c) is the joint distribution frequency function. Captive particle imaging results (Hurt et al., 1996) further suggested that the distribution functions of size, reactivity and carbon density were independent from each other, so that F(d p, A, c) can be expressed as the products of these functions: F(d p, A, c) = F d(d p) F A(A) F ( c) (6.20)
The size distribution function can be measured directly. The reactivity distribution function F A(A) is modeled as a gamma distribution function (Hurt et al., 1996): e − A −1 FA(A) = A Γ(A) where and are the distribution parameters and Γ(A) is the gamma function. The gamma distribution has the following properties: 75 (6.21) A mean = / (6.22) A = / (6.23) More recent work (Hurt et al., 1998) suggests that a correlation can be used generally: A / A mean = 0.325 (6.24) Eqs. (6.22) through (6.24) suggest that is a constant value 9.47. When A mean is specified, can be readily calculated from = /A mean = 9.47/A mean. The distribution of the initial carbon density determines the amount of carbon to be consumed in the complete burnout process. Recent measurements on a U.S. lignite using a unique electrodynamic balance technique (Hurt et al., 1996) yielded an approximate Gaussian distribution of carbon densities with a standard deviation given by: / c,o ,mean = 0.3 (6.25) The mean values ( c,o,mean) for ten U.S. coal chars are available (Mitchell et al., 1992). Statistical kinetics and properties seem to play an important role in certain cases. However, incorporating statistical kinetics and properties could dramatically increase the required computer time to predict the carbon burnout. For example, a typical full
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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
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 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
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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
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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
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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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MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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