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Optimization of Fine Solid Drying in Bubble Fluidized Bed

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Abstract

A commonly used method to dry fine solid particles is drying in a fluidized bed. This paper presents the optimization problem of fluidized drying of fine solids. A drying process proceeding in a three-stage cascade of fluidized cross-current dryers was considered. Solid flows from stage to stage, and fresh gas is introduced to each stage of the cascade. The hydrodynamics of bubble fluidized bed and kinetics of heat and mass transfer are taken into account. The bed hydrodynamics is described by a two-phase model. The drying process considered proceeds in the second period of drying. To optimize this problem a generalized version of a discrete algorithm with constant Hamiltonian was used. The optimization procedure is presented in the paper. In optimization calculations, gas parameters (temperature, humidity and flow rate) minimizing total process cost are sought. The results of calculation are presented as graphs. The results obtained and the conclusions drawn are discussed.

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Abbreviations

A,B :

Coefficients in performance index, kJ/(kg K2),kJ/kg

c g :

Gas specific heat , kJ/(kg K)

G :

Gas mass flow rate, kg/s

h :

Solid enthalpy, kJ/kg

h mf :

Bed height in minimum fluidization, m

i :

Gas enthalpy, kJ/kg

i vb :

Moisture enthalpy in bubble phase, kJ/kg

i vmf :

Moisture enthalpy in dense phase, kJ/kg

K :

Drying constant, 1/s

k b :

Mass transfer coefficient between dense and bubble phase, kg/m3

S :

Solid mass flow rate, kg/s

S v :

Volume solid flow rate, m3/s

T :

Temperature, °C, K

u g :

Gas superficial velocity, m/s

u mf :

Minimum fluidization velocity, m/s

u p :

Velocity of gas in bubble phase, m/s

W b :

Dimensionless resistance coefficients of mass transfer

X e :

Equilibrium moisture content in solid

X s :

Moisture content in solid

Y :

Moisture content in gas

Z b :

Dimensionless resistance coefficients of heat transfer between gas and solid

Z mf :

Dimensionless resistance coefficients of heat transfer between bubble and dense phases

Greek symbols :

 

αb :

Heat transfer coefficient between dense and bubble phase, kJ/m3K

αmf :

Heat transfer coefficient between solid and gas, kJ/m3K

κ:

Exergy coefficient of investment and gas pumping costs, kJ/kg

ρ:

Density, kg/m3

ζ:

Ratio of chemical exergy unit price to thermal exergy unit price

τ:

Average solid hold-up, s

σ:

Volume fraction of bubble phase in fluidized bed

θg :

Dimensionless gas flow rate (ratio of gas mass flow rate to solid one)

σg :

Mass fraction of gas flowing through bubble,

ɛmf :

Dense phase porosity

Subscripts :

 

b:

Outlet gas from bubble phase

g:

Inlet drying gas

k:

Outlet drying gas

mf:

Gas in dense phase

s:

Solid

Superscripts :

 

n:

Stage number

References

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Authors and Affiliations

  1. Department of Chemical and Process Engineering, Warsaw University of Technology, Warsaw, Poland

    Artur Poświata & Zbigniew Szwast

Authors
  1. Artur Poświata
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  2. Zbigniew Szwast
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Correspondence to Artur Poświata.

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Poświata, A., Szwast, Z. Optimization of Fine Solid Drying in Bubble Fluidized Bed. Transp Porous Med 66, 219–231 (2007). https://doi.org/10.1007/s11242-006-9016-0

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  • DOI: https://doi.org/10.1007/s11242-006-9016-0

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