MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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pore structure models require extensive computational efforts, it is desirable to use a macroscopic pore structure model and an effectiveness factor to model the char oxidation rates. Further, since the pore growth did not play a significant role in determining the reaction rate as a function of burnout (or time), the potential benefit of using microscopic pore structure models was not realized. Therefore, the values of porosity, reactivity and pore size are assumed to be spatially uniform (a necessary assumption in order to use the effectiveness factor approach) and temporally constant (not a necessary assumption to use the effectiveness factor approach, but used for simplicity). Results and Discussion The following Langmuir rate equation was used in the HP-CBK model: r in ′ = 2.26 × 1011e −46,500/ RT PO 2 1+ 1.67 ×10 4 e − 18,800/ RT PO 2 This means that E 1p = 46.5 kcal/mol, and E 0 = (46.5 - 18.8) = 27.7 kcal/mol. The observed reaction rate is: Vp qrxn = r obs ′ ′ Sg MC = + S ⎛ ext ⎝ ⎜ ⎞ ⎟ ⎠ S d int pMC r in′ ′ 6 S int A mono-disperse pore structure model was used to calculate the effective diffusivity D e and to estimate the value of S ext/S int (as discussed in Chapter 6). The parameters related to the pore structure model are in Table 7.1. S tot Table 7.1. Pore Structure Parameters in Modeling the Data by Banin et al. Roughness factor = 5 (Pre-set) Porosity = 0.5 (Pre-set) Pore diameter = 10.8 Å (Adjusted) 92 (7.2) (7.3)
The value of the roughness factor was pre-set to be 5, which seemed high compared to the value of 2.5 used by Banin et al. (1997). Following the argument of Banin et al. (1997), the roughness factor accounts not only for the increased surface area due to surface roughness, but also for penetration of oxygen molecules within a pore before the first collision with the pore wall. The latter mechanism means internal diffusion does not play any role up to a distance equal to about the pore diameter. Figure 7.2 illustrates how this latter mechanism makes one unit of void surface area equivalent to 4 units of solid surface area. Figure 7.2. Schematic of a pore connected to the surface of a char particle. One unit of void area is equivalent to 4 units of solid area since internal diffusion does not play any role up to a distance equal to about the pore diameter. The void area of a pore mouth is πr p 2 , while the internal pore wall that is not affected by internal diffusion and must be counted as external surface area is 2πr p •2r p = 4πr p 2 . Assuming that the surface roughness increases the surface area by a factor of 2, the overall roughness factor can be calculated from the porosity of the particle: 2[(1- ) + 4 ] 93 2r p r p O 2 O 2 O 2 O2
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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* (%)
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 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 2850 K). For consistency with t
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
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
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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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