MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...
MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ... MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...
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.
- 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
Both of these assumptions are arguable. Even if there were no reaction occurring on the<br />
external surface, the particle diameter would shrink under Zone II conditions. Due to the<br />
non-uniform distribution of oxygen concentration in the particle, the carbon consumption<br />
rate is higher near the pore mouth (but still inside a pore) than the rate deep into the pore.<br />
When pores overlap near the pore mouth, the particle diameter will shrink. Figure 5.2<br />
illustrates how the internal combustion could decrease the particle diameter.<br />
Mitchell et al. (1992) recognized that the value of the burning mode parameter<br />
( m) is not a quantitative estimate of the amount of internal reaction, as fragmentation and<br />
carbon densification (Hurt et al., 1988) also influence the evolution of diameter and<br />
density. The burning mode parameter m used by Mitchell et al. is defined as:<br />
c<br />
c ,o<br />
= m ⎛<br />
c<br />
⎝<br />
⎜<br />
⎞<br />
⎟<br />
⎠<br />
m c,o<br />
m<br />
Note that the power index defined in Eq. 5.28 is closely related to the burning mode<br />
parameter m.<br />
In summary, the second effectiveness factor approach suffers the following<br />
problems as well as other problems mentioned in the literature review:<br />
59<br />
(5.35)<br />
1. It is based on the arguable assumptions that the diameter decreases only due to external<br />
combustion and the density decreases only due to internal combustion.<br />
2. The second effectiveness factor approach is adversely affected by other phenomena<br />
such as fragmentation and carbon densification.
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