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 I or Zone II at different oxygen concentrations, the kinetics parameter K in the Langmuir rate equation may be estimated. n obs 1.0 0.9 0.8 0.7 0.6 0.5 0.01 0.1 1 10 KCs 100 1000 Figure 5.1. The relationship between KC s and the observed reaction order (n obs) as predicted by Eq. (5.13). Rough Sphere Combustion It is commonly assumed that the external surface area is negligible compared to the internal surface area. This assumption is usually valid since the internal surface area of a char particle is usually much larger than the external surface area. However, the external surface can play a role under some conditions and the rough sphere combustion phenomenon occurs. In rough sphere combustion, the reaction rate contributed from the external surface area can no longer be neglected. The observed rate corresponding to the Langmuir rate equation is (see Eq. 2.21) r obs ′ = ( + Sext ) Sint Sint Stot k1Cs . (5.16) 1 + KCs 50
The observed reaction order in Zone II can be less than 0.5 for rough sphere combustion due to combustion on the external surface. The effects of the external surface on the observed reaction order can be seen by substituting Eq.5.16 into Eq. 5.5. Although Eq. 5.16 was developed to explain the rough sphere combustion phenomenon, it can be used in general for porous solid combustion. However, in most cases (which are not rough sphere cases), the S ext/S int term in Eq. 5.16 is negligible compared to the effectiveness factor η, and the S int/S tot term can be well approximated by unity. In other words, Eq. 5.16 reduces to Eq. 2.25 in most cases. Similarly, the observed rate corresponding to the m-th order rate equation is r obs ′ = ( + Sext ) Sint Sint m kmCs . (5.17) Stot The conditions favoring the rough sphere combustion are explored here. In order for rough sphere combustion to occur, S ext/S int must be of the order of the effectiveness factor (see Eqs. 5.16 and 5.17). In other words, the ratio of external rate to the internal rate (S ext/S int ) must not be negligibly small. Note that the external surface area is proportional to d p 2 , the internal surface area is proportional to dp 3 (since Sint = m pS m = V p pS m), while the effectiveness factor in Zone II is inversely proportional to d p (see Chapter 4). Consequently, the ratio of the external rate to the internal rate (S ext/S int ) is independent of size. Therefore particle size is not a factor that favors rough sphere combustion. However, small particle size helps to avoid Zone III combustion and hence allows the observation of the rough sphere combustion phenomenon. Strictly speaking, Zone III 51
- 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
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- 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: nobs = 1 (KCs ) 2 2 1 [KCs − ln(1
- 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
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- 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
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- 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
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Zone I or Zone II at different oxygen concentrations, the kinetics parameter K in the<br />
Langmuir rate equation may be estimated.<br />
n obs<br />
1.0<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.01 0.1 1 10<br />
KCs 100 1000<br />
Figure 5.1. The relationship between KC s and the observed reaction order (n obs) as<br />
predicted by Eq. (5.13).<br />
Rough Sphere Combustion<br />
It is commonly assumed that the external surface area is negligible compared to the<br />
internal surface area. This assumption is usually valid since the internal surface area of a<br />
char particle is usually much larger than the external surface area. However, the external<br />
surface can play a role under some conditions and the rough sphere combustion<br />
phenomenon occurs. In rough sphere combustion, the reaction rate contributed from the<br />
external surface area can no longer be neglected. The observed rate corresponding to the<br />
Langmuir rate equation is (see Eq. 2.21)<br />
r obs ′ = ( + Sext )<br />
Sint Sint Stot k1Cs . (5.16)<br />
1 + KCs 50
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