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Modeling of vacuum desorption of multicomponent moisture in freeze drying

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Abstract

A mathematical model of multicomponent vacuum desorption, which occurs in the vacuum freeze drying process has been developed. Drying with conductive heating and constant contact surface temperature was considered. Pressure drop in the layer of the material to be dried was taken into account in the model formulation and process simulation. Equilibrium moisture content for pure water, toluene, and m-xylene and their two- and three-component mixtures on zeolite DAY 20F were described by means of the multitemperature extended Langmuir isotherm equation. Model equations were solved by the numerical method of lines. Moisture content and temperature distributions within the drying material were predicted from the model as a function of drying time.

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Abbreviations

a e :

Effective thermal diffusivity, m2/s.

a i :

Constant of multitemperature Langmuir isotherm of component i, K.

b i :

Constant of multitemperature Langmuir isotherm of component i, Pa−1.

c a i :

Specific heat of component i in adsorbed phase, J/(kg K).

c pg i :

Specific heat of component i in gas (vapor) phase, J/(mol K).

c i :

Constant of multitemperature Langmuir isotherm of component i, K.

c s :

Specific heat of adsorbent, J/(kg K).

C :

Molar gas density, mol/m3.

C i0 :

Initial molar concentration of component i in the gaseous phase, mol/m3.

C * i :

Dimensionless molar concentration of component i in the gas phase.

d p :

Particle diameter, m.

D eff i :

Effective diffusion coefficient of component i, m2/s.

D K i :

Knudsen diffusion coefficient of component i, m2/s.

D S i :

Surface diffusion coefficient of component i, m2/s.

ΔH i :

Heat of adsorption of component i, J/mol.

J z :

Mass flux density, mol/(m2 s).

k e :

Effective thermal conductivity of adsorbent bed, W/(mK).

k D :

Permeability of porous media (m2).

k E :

Parameter describing the inertial effect in Ergun’s equation (m).

K i :

Kinetic coefficient of component i, 1/s.

L :

Dried layer thickness, m.

M i :

Molecular weight of component i, kg/mol.

N :

Number of sections of drying material layer.

p i :

Partial pressure of component i, Pa.

ΔP :

Reference pressure variation for normalization, Pa.

P :

Total pressure, Pa.

X avg i :

Average moisture content of component i (dry basis), kg i/kg.

X i :

Moisture content of component i (dry basis), kg i/kg.

X * i :

Equilibrium moisture content of component i (dry basis), kg i/kg.

y i :

Mole fraction of component i in the gas phase, mol i/mol.

t :

Time, s.

ΔT :

Reference temperature variation for normalization, K.

T :

Temperature, K.

T i :

Initial temperature of drying layer, K.

T0 :

Contact surface temperature, K.

y i :

Mole fraction of component i, mol i/mol.

z :

Axial coordinate, m.

Z :

Dimensionless axial coordinate.

Greek symbols :

 

ε:

Bed void fraction.

ε p :

Particle porosity.

μ:

Viscosity of gas mixture, Pa s.

ω:

Normalized pressure.

θ:

Normalized temperature.

Ω i :

Dimensionless concentration of component i in solid phase.

ρ p :

Particle density of adsorbent, kg/m3.

ρ b :

Bulk density of adsorbent, kg/m3.

τ:

Dimensionless time.

Acronyms :

 

VC:

Vacuum chamber.

LDF:

Linear driving force.

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Authors and Affiliations

  1. Department of Chemical Engineering and Environmental Protection Processes, Szczecin University of Technology, Al. Piastów 42, 71-065, Szczecin, Poland

    J. F. Nastaj & B. Ambrożek

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  1. J. F. Nastaj
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  2. B. Ambrożek
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Correspondence to J. F. Nastaj.

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Nastaj, J.F., Ambrożek, B. Modeling of vacuum desorption of multicomponent moisture in freeze drying. Transp Porous Med 66, 201–218 (2007). https://doi.org/10.1007/s11242-006-9015-1

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