Abstract
A mathematical model of heat-transfer regimes is proposed for reactor-regenerator systems with powdered catalysts. The model takes into account feedbacks between the thermal and chemical processes. Thermal closeness and a temperature feedback parameter are the two parameters introduced in the model. Catalytic cracking is considered, and the existence of one, two, or three steady-state solutions is demonstrated, which, depending on process parameters, define eight types of topological structure. Process stability and control are discussed.
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Abbreviations
- A :
-
heat removal parameter
- C :
-
degree of coking of the regenerated catalyst,g/g
- C 0 :
-
degree of coking of the spent catalyst, g/g
- c :
-
specific heat, kJ/(kg K)
- D :
-
parameter accounting for heat loss through the apparatus surface, kJ/kg
- d :
-
coking capacity of the feedstock
- E :
-
activation energy, kJ/(mol K)
- F :
-
mass flux, kg/h
- f :
-
dimensionless mass flux
- G cat :
-
weight of catalyst in the fluidized bed, kg
- gcat :
-
dimensionless catalyst weight
- ΔH :
-
enthalpy of the main reaction
- Q :
-
nominal heat abstraction, kJ/h
- q :
-
heat of combustion, kJ/kg
- R :
-
universal gas constant, J/(mol K)
- T :
-
reactivation temperature, K
- T 0 :
-
reaction temperature, K
- t :
-
time, h
- t* :
-
catalyst residence time in the reactivator, h
- u 1 :
-
dimensionless heat-balance parameter of the reactor
- U 2 :
-
heat-balance parameter of the reactor; K
- u 2 :
-
dimensionless heat-balance parameter of the reactor
- W(C, T) :
-
rate of coke combustion, h-1
- w(ε, θ):
-
normalized rate of coke combustion
- Z(C, T) :
-
specific coke yield in the main reaction, kg/kg
- z(ε, θ):
-
normalized specific coke yield
- α1, α2 :
-
mass-balance parameters of the system
- β1,β2 :
-
heat-balance parameters of the system
- γ1, γ2 :
-
characteristic parameters of the system
- δ:
-
catalyst adsorption capacity, kg/kg
- ε:
-
dimensionless degree of coking of the catalyst
- θ:
-
dimensionless reactivation temperature
- θ0 :
-
dimensionless reaction temperature
- θcr :
-
dimensionless maximum reactivation temperature
- ρ:
-
density, kg/m3
- τ:
-
dimensionless time
- ψ:
-
degree of conversion of the feedstock
- ω :
-
thermal stability region of the system
- ads:
-
adsorbed hydrocarbons
- air:
-
air
- feed:
-
feedstock
- env:
-
environment
- cat:
-
catalyst
- *:
-
nominal valu
References
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Nagiev, A.G. Multiplicity of steady states of reaction-regeneration systems with a highly coking catalyst. Theor Found Chem Eng 34, 274–280 (2000). https://doi.org/10.1007/BF02755975
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DOI: https://doi.org/10.1007/BF02755975