MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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approximated by the Knudsen diffusion within 5%. In summary, the diffusivity of oxygen in a pore with a radius r p is: D = D O2,N2, when r p ≥ 20r p,crit D = D K, when r p ≤ r p,crit/20 D = 1/(1/D O2,N2 + 1/D K), when r p,crit/20 ≤ r p ≤ 20r p,crit. The values of the critical pore radius were computed and shown in Table 5.2. Table 5.2. The Values of Critical Pore Radius (Å) at Different Temperatures and Gas Pressures. Tp (K) P (atm) 1 5 10 15 1000 2874 575 287 192 1250 3731 746 373 249 1500 4618 924 462 308 1750 5531 1106 553 369 For example, at 1500 K and 1 atm, the critical pore radius is 4618 Å, the Knudsen diffusion cannot be neglected unless the pore radius of the char is greater than 20 × 4618 = 92360 Å = 9.236 μm. Similarly, at 1500 K and 1 atm, the molecular diffusion should not be neglected unless the pore radius is less than 4618 / 20 = 231 Å (0.023 μm). Eq. 5.20 is generally applicable and is therefore recommended. Another way to tell whether Knudsen diffusion or molecular diffusion is important is to compare the pore radius to the mean free path of oxygen. Note that the critical pore radius is slightly different from the mean free path of oxygen molecules. According to classic kinetic theory (Bird et al., 1960), the mean free path of oxygen is: = 1 2 d 2 NC = 1 2 N RT p P 1 d 2 = 2.60 T p P 56 (Å) (5.25)
where T p is in K, P is in atm. The mean free path of oxygen is 3900 Å at temperature of 1500 K and pressure of 1 atm, slightly lower than the critical pore radius (4618 Å). Relationship between the Effectiveness Factor and the Second Effectiveness Factor The second effectiveness factor, according to Essenhigh (1988), is defined as = 1+ R int R ext 57 (5.26) where R int and R ext are internal and external reaction rates, respectively. Both R int and R ext are mass carbon consumption rates per unit geometric external surface area. The second effectiveness factor is calculated from the power index of the normalized density-diameter relationship: = 1+ /3 (5.27) o = d ⎛ ⎝ ⎜ d o ⎞ ⎟ (5.28) ⎠ Comparison between Eqs. (5.27) and (5.26) gives Rint Rext = 3 The ratio of the internal rate to the external rate, according to the definition of the effectiveness factor, can be expressed as: Rint Rext = S int S ext (5.29) (5.30) If both the effectiveness factor approach and the second effectiveness factor approach are correct, they should predict the same value for R int/R ext. Therefore, Eqs. (5.29) and (5.30)
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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
Page 26 and 27: 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: where D K is in cm 2 /sec, r p is t
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 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
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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
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
Page 189 and 190:
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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