MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...
MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ... MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...
Zone III rate ∝ C og E obs → 0 ρ = const. boundary layer diffusion Zone II n = (m+1)/2 E obs = Ε true /2 ρ and d p vary pore diffusion and kinetics 6 1/T Zone I n = m Eobs = Εtrue dp = const. reaction kinetics control Figure 2.1. Rate-controlling zones for heterogeneous char oxidation. It should be noted that the three-zone theory idealizes and simplifies the actual variation of reaction rate with temperature. First, the “three-zone” theory assumes that boundary layer diffusion (BLD) resistance dominates in Zone III, is present during the transition from Zone II to Zone III, and is totally absent from Zone I to Zone II. In reality, BLD resistance is often present in Zone II. In other words, char oxidation rate is typically influenced by all three processes: BLD, pore diffusion, and chemical kinetics. Second, the three-zone theory applies only to m-th order kinetics and fails to predict the variation of reaction rate with temperature for Langmuir-Hinshelwood kinetics. For example, Essenhigh (1991) suggested that the true activation energy of the char-oxygen reaction changed from 32.95 kcal/mol to 10.04 kcal/mol (corresponding to desorption control and
adsorption control, respectively) as temperature increased. Third, the three-zone theory assumes that the combustion rate contributed from the external surface area is negligible compared to the rate contributed from the internal surface area. This assumption is true for most cases, since the internal surface area is typically much larger than the external surface. However, the external surface area can become important under some conditions, these being favored by low internal surface area (typically in highly ordered carbons) or severe pore diffusion limitations, which lead to an extremely low effectiveness factor (Hurt, 1998). When the external combustion rate cannot be neglected compared to the internal combustion rate, the so-called “rough sphere combustion” occurs (Banin et al., 1997a, b). Char Oxidation Model Classifications Char oxidation models can be classified into two main categories: global models and intrinsic models (Smith et al., 1994). Global models consider char particles impervious to pore diffusion effects or else lump intraparticle diffusion effects into the chemical reaction rate constants. These models are highly empirical, basing the reaction rate on the particle’s external surface area and on the oxidizer concentration at the external surface. In contrast, intrinsic models relate char oxidation rate to the active surface area involved in the reaction and consider the non-uniform oxidizer concentration profile within the particle. Intrinsic models rely on pore structure models to describe gaseous diffusion through complex pore structures and to model the local oxidizer concentration at the active surface area. Thus the intrinsic model approach has the potential of providing 7
- 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 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 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
Zone III<br />
rate ∝ C og<br />
E obs → 0<br />
ρ = const.<br />
boundary<br />
layer<br />
diffusion<br />
Zone II<br />
n = (m+1)/2<br />
E obs = Ε true /2<br />
ρ and d p vary<br />
pore<br />
diffusion<br />
and<br />
kinetics<br />
6<br />
1/T<br />
Zone I<br />
n = m<br />
Eobs = Εtrue dp = const.<br />
reaction<br />
kinetics<br />
control<br />
Figure 2.1. Rate-controlling zones for heterogeneous char oxidation.<br />
It should be noted that the three-zone theory idealizes and simplifies the actual variation<br />
of reaction rate with temperature. First, the “three-zone” theory assumes that boundary<br />
layer diffusion (BLD) resistance dominates in Zone III, is present during the transition<br />
from Zone II to Zone III, and is totally absent from Zone I to Zone II. In reality, BLD<br />
resistance is often present in Zone II. In other words, char oxidation rate is typically<br />
influenced by all three processes: BLD, pore diffusion, and chemical kinetics. Second, the<br />
three-zone theory applies only to m-th order kinetics and fails to predict the variation of<br />
reaction rate with temperature for Langmuir-Hinshelwood kinetics. For example,<br />
Essenhigh (1991) suggested that the true activation energy of the char-oxygen reaction<br />
changed from 32.95 kcal/mol to 10.04 kcal/mol (corresponding to desorption control and
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