MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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Single-Film Char Oxidation Submodel The single-film char oxidation model, developed by other investigators (Mitchell et al., 1992; Hurt et al. 1998) and summarized here to set a foundation for the HP-CBK model, consists of four aspects: 1) global n-th order kinetics; 2) film diffusion in the particle boundary layer; 3) heat generation and transfer; 4) mode of burning expressions. The kinetics of this submodel are simplistic. This submodel assumes that the particle is isothermal. Oxygen is assumed to be the sole oxidizer and the global n-th order rate equation is used to represent char oxidation rates: n qrxn = k sPs 70 (6.1) where k s is a temperature-dependent rate coefficient, n is the apparent reaction order, and P s is the partial pressure of oxygen at the particle surface. The global rate coefficient, k s, implicitly includes the combined effects of pore diffusion, internal surface area, and intrinsic surface reactivity. This rate coefficient is described by an Arrhenius equation: k s = A exp(-E/RT p) (6.2) Both CO and CO 2 are considered primary products of the heterogeneous char oxidation reactions. The CO/CO 2 product ratio (MR) is assumed to depend on particle temperature and is expressed as: moles of CO MR = = Ac exp(-Ec /RTp) (6.3) moles of CO2
The fraction of the carbon content of the particle converted to CO 2 is denoted as and determined from the CO/CO 2 product ratio (MR): = 1/(1 + MR). (6.4) The mass diffusion outside the particle is (Frank-Kamenetskii, 1969): qdiff = kDP ⎛ 1− Ps / P⎞ ln⎜ ⎟ when γ ≠ 0 (6.5a) ⎝ 1 − P / P g ⎠ q diff = k D(P og − P os ) when γ = 0 (6.5b) where the mass transfer coefficient is given by: k D = M cD ox Sh d p ′ R T m o 71 (6.6) o = 0.5(1+ ) (6.7) = − 1 + 1 This assumes, of course, that oxygen is the only oxidizer and that pyrolysis reactions have been completed. Slightly different and iterative forms can be used to account for (6.8) these effects, such as those in PCGC-3 (Smoot and Smith, 1985; Smith et al., 1994). The quasi-steady state assumption leads to q diff = q rxn (6.9) If the particle temperature is known or guessed, Eqs. (6.9), (6.1) and (6.5) can be used to determine the value of P s. Numerically, a value is guessed for P s, Eqs. (6.1) and (6.5) are used to compute q rxn and q diff, and then the difference q 1 = (q rxn - q diff) is driven to zero by changing the value of P s using the Newton-Raphson method. This procedure for computing P s is referred to in this study as the P s loop.
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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
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 and 86: Farrauto and Batholomew (1997) prop
Page 87: assumes a homogeneous, non-interact
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 +
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
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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
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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
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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MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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