MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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1.0 m obs 0.5 0.0 -6.0 -3.0 38 0.0 3.0 ln(M T ) ln( 0.5) 1.20 1.15 1.10 1.05 correction function f c Figure 4.3. The correction function f c plotted as a function of both the general modulus (M T) and the observed reaction order in Zone I (m obs). Accuracy of the Corrected General Asymptotic Solution The accuracy of the corrected general asymptotic solution (Eq. 4.20) was determined by comparison with the numerical model. As shown in Tables 4.5 and 4.6, the corrected general asymptotic solution predicts the effectiveness factor with errors less than 2% for both the m-th order and Langmuir rate equations. Table 4.5. The Relative Error* (%) in the Corrected General Asymptotic Solution for m-th Order Rate Equations M T m 1.00 0.75 0.50 0.25 0.00 0.125 0.027 -0.041 -0.018 -0.069 0.162 0.25 0.046 -0.181 -0.066 0.268 0.549 0.5 0.097 -0.544 -0.269 0.326 -0.754 0.707 0.124 -0.884 -0.952 -1.083 -2.027 1 0.126 -1.197 -1.826 -1.910 -0.345 2 0.053 -0.916 -1.559 -1.901 -1.500 4 0.043 -0.480 -0.954 -1.337 -1.412 8 0.042 -0.243 -0.528 -0.742 -1.104 *Relative error = ( asymp - numerical)/ numerical ** asym = exact when m = 1.0
Table 4.6. The Relative Error* (%) in the Corrected General Asymptotic Solution for the Langmuir Rate Equation 1/(1+KC s) M T 1.00 0.75 0.50 0.25 0.00 0.125 0.019 -0.030 0.163 0.485 1.133 0.25 0.016 -0.158 0.375 1.354 0.001 0.5 -0.013 -0.729 -0.113 1.208 1.394 0.707 -0.076 -1.161 -0.849 0.128 -1.246 1 -0.215 -1.387 -1.197 0.076 1.374 2 -0.491 -1.178 -1.136 -0.324 0.545 4 -0.679 -1.068 -1.256 -1.243 -1.144 8 -0.933 -1.153 -1.337 -1.494 -1.743 *Relative error = ( asymp - numerical)/ numerical ** asym = exact when 1/(1+KC s) = 1.0 Simplified General Moduli for the Langmuir Rate Equation The standard general modulus in Eq. (4.3) is complex in form, and encounters division by zero at KC s = 0. However, the value of M T in Eq. (4.3) exists in the limit at KC s = 0: M T = L ok1 De . (4.23) which is the Thiele modulus for first order reactions (Thiele, 1939). Two moduli that have simpler forms were found to closely approximate the standard general modulus in Eq. (4.3). The first one was transformed from a modulus used by Levenspiel (1993): M T = L O k 0 K / D e 2KC s + 1 = L Ok1 / De . (4.24) 2KCs +1 The second modulus was constructed to better approximate the standard general modulus in Eq. (4.3) in this study: 39
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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
Page 7 and 8: Table of Contents List of Figures..
Page 9: Appendices.........................
Page 12 and 13: Figure A.2. Mass releases of the Ko
Page 14 and 15: Table 7.6. Parameters Used in Model
Page 16 and 17: Ed activation energy of desorption,
Page 18 and 19: vc the volume of combustible materi
Page 21 and 22: Background 1. Introduction The rate
Page 23: 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: correction. The values of functions
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
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and 2850 K). For consistency with t
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The value of the roughness factor w
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= S int S ext D e r p a 2 2M C M O2
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Reactor Head Flow Straightener Reac
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the large size of the particle, and
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taking into account convection, rad
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2.5x10 -4 2 /sec) 2.0 1.5 Rate (g/c
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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
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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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