MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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can be used to bridge the effectiveness factor approach and the second effectiveness factor approach: 3 = S int S ext This relation is illustrative of how the value of changes from Zone I to Zone II. In Zone I, is unity, and =3S int/S ext. S int/S ext is usually a large number, which gives a 58 (5.31) large value, consistent with the values (10 4 ~10 5 ) reported by Essenhigh (1988). In Zone II, could be a very small value, which could possibly bring down to a value around 2 or 3 (Essenhigh, 1988). However, in order for to be a small value, has to be extremely small. The above relation should be considered qualitative rather than quantitative since careful examination showed that the derivation of the second effectiveness factor might be based on some problematic assumptions, which are detailed as follows: The mass change of a char particle can be written as: −1 S g dm dt = −1 d 2 d 1 6 ⎛ ⎝ dt d 3 ⎞ ⎠ =− d ⎛ ⎞ ⎛ − 6⎝ t ⎠ d 2 ⎝ Essenhigh went a step further to assume that the density change is solely due to the internal combustion, and the diameter change is solely due to the external combustion: Rint = − d ⎛ ⎞ 6 ⎝ t ⎛ Rext = − 2⎝ d t ⎠ d ⎞ ⎠ d t ⎞ ⎠ (5.32) (5.33) (5.34)
Both of these assumptions are arguable. Even if there were no reaction occurring on the external surface, the particle diameter would shrink under Zone II conditions. Due to the non-uniform distribution of oxygen concentration in the particle, the carbon consumption rate is higher near the pore mouth (but still inside a pore) than the rate deep into the pore. When pores overlap near the pore mouth, the particle diameter will shrink. Figure 5.2 illustrates how the internal combustion could decrease the particle diameter. Mitchell et al. (1992) recognized that the value of the burning mode parameter ( m) is not a quantitative estimate of the amount of internal reaction, as fragmentation and carbon densification (Hurt et al., 1988) also influence the evolution of diameter and density. The burning mode parameter m used by Mitchell et al. is defined as: c c ,o = m ⎛ c ⎝ ⎜ ⎞ ⎟ ⎠ m c,o m Note that the power index defined in Eq. 5.28 is closely related to the burning mode parameter m. In summary, the second effectiveness factor approach suffers the following problems as well as other problems mentioned in the literature review: 59 (5.35) 1. It is based on the arguable assumptions that the diameter decreases only due to external combustion and the density decreases only due to internal combustion. 2. The second effectiveness factor approach is adversely affected by other phenomena such as fragmentation and carbon densification.
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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
Page 28 and 29: coal-general kinetic rate constants
Page 30 and 31: Boundary Layer Diffusion The molar
Page 32 and 33: = q obs q max The factor can be use
Page 34 and 35: 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: where T p is in K, P is in atm. The
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 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
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The HP-CBK was used to predict the
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TGA and FFB Data-This Study The rea
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This equation can be derived as fol
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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
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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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