MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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Effective Diffusivity The major obstacle to rigorous description of the transition between Zone I and Zone II is the treatment of pore diffusion through the complex pore structures of char. According to Smith (1981), the optimum model would include a realistic representation of the geometry of the voids (with tractable mathematics) that can be described in terms of easily measurable physical properties of the char. These properties include the surface area, porosity, density (true density or apparent density), and the distribution of void volume according to size. In general, both molecular and Knudsen diffusion may contribute to the mass transport rate within the porous structure of the char. The combined effects of these two diffusion mechanisms can be described by the combined diffusivity D (Smith, 1981): 1 D = 1/ DAB + 1/ DK The Knudsen diffusivity can be calculated from classical kinetic theory (Smith, 1981): DK = 9.70 ×10 3 ⎛ rp ⎝ ⎜ T p M A 1/2 ⎟ ⎞ ⎠ where D K is in cm 2 /sec, r p is the pore radius in cm, T p is in K, and M A is the molecular 80 (6.37) (6.38) weight of oxygen. The bulk diffusivity can be calculated using a correlation by Mitchell (1980): DO2 / N2 = 1.523 ×10 − 5 1.67 Tp / P (6.39) Pore structure models are used to convert the diffusivity to the effective diffusivity. By using the effective diffusivity, the measurable diffusion flux can be based on the geometric external surface area rather than the total cross-sectional area of holes on
the external surface (Smith, 1981). In addition, the effective diffusivity takes into account the deviation of the actual diffusion path from ideal cylindrical pore, such as “zigzag”, constrictions, overlaps, and other effects. Two pore structure models are often used in converting diffusivity into effective diffusivity: the parallel pore model and the random pore model. The parallel pore model (Wheeler, 1951) uses the porosity and a “tortuosity factor” to correlate the effective diffusivity to the diffusivity: D e = D (6.40) where is the porosity, and is the tortuosity factor. The random pore model was originally developed for catalytic pellets containing a bi-disperse pore system. The details of the development of this model are given elsewhere (Wakao and Smith, 1962). The resultant expressions for the effective diffusivity may be written: 2 De = MDM + 1 DM = 1/ DAB + 1/(DK ) M D = 1 1/ D AB + 1/(D K ) ( − M) 2 (1 + 3 M ) D (6.41) 1− M (DK ) M = 9.70 × 10 3 ⎛ T r ⎞ p,1⎝ 32⎠ (DK ) = 9.70 ×10 3 ⎛ T r ⎞ p,2⎝ 32⎠ 1/2 1/2 81 (6.42) (6.43) (6.44) (6.45)
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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
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 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 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
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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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