Mathematical Modeling of Carbon Nanotubes Formation in Fluidized Bed Chemical Vapor Deposition
-
Firoozeh Danafar
,
Said S. Elnashaie
Abstract
This study investigates mathematical modeling of carbon nanotubes (CNTs) formation on catalyst particulate in a fluidized bed chemical vapor deposition (FBCVD) reactor. The mass of CNTs formed corresponds to the catalyst activity directly. The catalyst deactivation occurs as active sites are occupied by CNTs and thus causes unsteady state behavior of the process. The effects of catalyst loading (as bed height) as well as reaction temperature on the reaction progressing were investigated. The model, validated with our experimental data, indicates a good accuracy to predict the yield of CNTs formation for a given operating conditions. The model presented also can predict the optimized time as well as the suitable amount of catalyst loading to produce CNTs for a given reactor conditions.
Acknowledgements
The authors gratefully acknowledge the Shahid Bahonar University of Kerman and Universiti Putra Malaysia for their support.
Nomenclature
- A
cross section area of reactor
- Ar
dimensionless number
- CETH
concentration of ethanol (mol/m3)
- db
bubble diameter (m)
- DEA
diffusivity of ethanol vapor in argon (m2/s)
- DEM
diffusivity of ethanol vapor in gas mixture (m2/s)
- E
activation energy (kJ/mol)
- g
gravitational acceleration (m/s2)
- H
height of active part in the reactor or bed height of fluidized bed (m)
- Hmf
height of fluidized bed at minimum fluidization velocity (m)
- k0
pre-exponential kinetic constant (1/s)
- Kbd
overall mass transfer coefficient between dense phase and bubble phase (1/s).
- MAr
molecular weight of argon (g/mol)
- METH
molecular weight of ethanol (g/mol)
- NAvo
Avogadro number
- nC
moles of carbon formed by the reaction (mol)
- NC-CNT
number of carbon atoms involved in formation of one CNT (dimensionless)
- nETH
molar rate of ethanol conversion (mol/s)
rate of carbon atoms formation (1/s)
- P
pressure (Pa)
- qB
volumetric flow rate of stream in bubble phase (m3/s)
- qD
volumetric flow rate of stream in dense phase (m3/s)
- qmf
volumetric flow rate of stream corresponding to minimum fluidization velocity (m3/s)
- R
perfect gas constant (J/mol. K)
- rETH
rate of cracking reaction of Ethanol converted to CNT (mol./m3s)
- T
temperature (K)
- Ub
rising velocity of bubble (m/s)
- UF
feed superficial gas velocity (m/s)
- Umf
minimum fluidization velocity (m/s)
- xETH
mole fraction of ethanol (dimensionless)
- xAr
mole fraction of argon (dimensionless)
- α0
initial numbers of active sites (dimensionless)
- γ
numbers of active sites covered by CNTs (dimensionless).
- δ
fractional volume of bubbles (dimensionless)
- εd
dense-phase voidage (dimensionless)
- εmf
dense-phase voidage at minimum fluidization velocity (dimensionless)
- ρf
density of fluids (kg/m3)
- ρP
density of particulates (kg/m3)
- ψ
parameter of dimensionless catalyst activity (dimensionless)
- vAr
specific molar volume of argon (m3/mol)
- vETH
specific molar volume of ethanol (m3/mol)
- Subscripts
- B
Bubble phase
- D
Dense phase
- F
Feed
- ETH
Ethanol
- Ar
Argon
References
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