MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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Ed activation energy of desorption, kcal/mol Eobs observed activation energy Ep activation energy for Kp, kcal/mol Etrue true activation energy, kcal/mol fc correction function FFB flat-flame burner HP-CBK High Pressure Carbon Burnout Kinetics model, developed in this study HPCP high pressure controlled-profile reactor h heat transfer coefficient, cal/cm 2 /K hxm mass transfer coefficient, mol/cm 2 /sec K rate constant in the Langmuir rate equation, K= A exp(-E/RT), cm 3 /mol Kp equal to (K/RT), Kp = Ap exp(-Ep/RT), atm -1 K Kelvin k rate constant k0 defined as k1/K, equal to k1p/Kp, mol/cm 3 k1 /sec rate constant in the Langmuir rate equation, k1 = A1 exp(-E1/RT), sec -1 k1p equal to (k1/RT), k1p = A1p exp(-E1p/RT), mol C/cm 3 /sec/atm ka adsorption rate constant kc surface migration rate constant kd desorption rate constant kD composite parameter related to mass transfer, g/cm 2 /sec/atm km rate constant in the m-th order rate equation, (mol C/cm 3 ) 1-m sec -1 kmp equal to km/(RT) m kxm mass transfer coefficient, mol/cm 2 /sec L characteristic length, Vp/Sg , cm L reaction length between injection and collection points, cm M1 an intermediate modulus in the discretization equation m mass, g m intrinsic (true) reaction order MC molecular weight of carbon, 12 mobs observed reaction order in Zone I MR product CO/CO2 mole ratio MT general (Thiele) modulus N nitrogen N neighbor in the positive y direction, i.e., on the north side N molar flux, mol/cm 2 /sec N the number of layers into which the spherical particle is divided Np the number of pores in a char particle n the reaction order in the n-th order rate equation nobs observed reaction order in Zone II O oxygen P central grid point under consideration P, Ptot total gas pressure, atm PCFB pressurized circulating fluidized bed PCGC-3 Pulverized Coal Gasification and Combustion code (3 dimensional) P oxygen partial pressure in the bulk stream, atm xvi
Pos, Ps oxygen partial pressure at particle surface, atm Pr Prandtl number q carbon consumption rate in the form of mass flux, g/cm 2 /sec qdiff mass flux from boundary layer diffusion consideration, g/cm 2 /sec qheat mass flux from energy balance consideration, g/cm 2 /sec qmax maximum mass flux allowed by boundary layer diffusion, g/cm 2 /sec qobs observed mass flux, g/cm 2 /sec qps converged value of mass flux determined from the Ps loop; when the Ps loop is converged, qps = qdiff = qrxn qrxn mass flux from reaction kinetics consideration, g/cm 2 /sec R gas constant, 1.987 cal/mol/K Re Reynolds number r radial distance from the particle center rin''' intrinsic reaction rate per unit volume of particle, mol C/cm 3 /sec robs''' observed reaction rate per unit volume of particle, mol C/cm 3 /sec robs'' observed reaction rate per unit external surface area of particle, mol- C/cm 2 /sec rp1 average macropore radius rp2 average micropore radius rp,crit critical pore radius robs''' observed reaction rate per unit volume of particle, mol C/cm 3 /sec rs radius of the particle S sulfur S neighbor in the negative y direction, i.e., on the south side Sc Schmidt number Sext 2 external surface area of a particle, equal to 4πdp , cm 2 S g geometric external surface area of a particle, equal to 4πd p 2 , cm 2 Sh Sherwood number Sint internal surface area of a particle, cm 2 Sm surface area per unit mass, cm 2 /g SNDL simple, non-dissociative Langmuir rate equation (often referred to in this dissertation as the Langmuir rate equation for simplicity) Spore the surface area of a single pore, cm 2 Stot total surface area of a particle, Stot = (Sext + Sint) T temperature, K Tf same as Tm, film temperature, K Tg gas temperature, K TGA thermogravimetric analysis Tm film temperature, equal to (Tp + Tg)/2, K Tp particle temperature, K Tw wall temperature, K U unburned fraction of carbonaceous material, equal to (1 – B) Vp the total volume of a particle, cm 3 Vpore the volume of a single pore the volume of ash in a char particle v a xvii
Page 1 and 2: MODELING CHAR OXIDATION AS A FUNCTI
Page 3 and 4: BRIGHAM YOUNG UNIVERSITY As chair o
Page 5 and 6: 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 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 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 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
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
Page 163 and 164:
detaching the flame from the burner
Page 165 and 166:
To study the effects of steam, CO w
Page 167 and 168:
times at heights of 1, 2, 4, and 6
Page 169 and 170:
analysis. The char reactivities (in
Page 171 and 172:
Table A.5. Moisture, Ash and ICP Ma
Page 173 and 174:
Table A.9. Elemental Analyses of Fo
Page 175 and 176:
temperature profile of the post-fla
Page 177 and 178:
Apparent densities 1.00 0.75 0.50 0
Page 179 and 180:
This observation is somewhat surpri
Page 181 and 182:
It is interesting to compare Figure
Page 183 and 184:
The N 2 BET surfacea areas and H/C
Page 185 and 186:
collected in the #4 reactor conditi
Page 187 and 188:
Rate (gC /g C remaining /sec) 1.6x1
Page 189 and 190:
close to zero, the accumulated erro
Page 191:
Appendix B: Errors and Standard Dev
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MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

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