Abstract
A mathematical model was proposed to describe the mass-transport phenomena in packed column with spherical composites which are consisted of the outer shells and the inner spheres. Any contact resistance between the former and the latter was assumed to be negligible. The first and the second moments were derived by means of the moment generating properties of Laplace transform.
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Abbreviations
- C(z, t):
-
concentration in void space of column
- C(z, p):
-
Laplace transform of C(z, t)
- D1 :
-
diffusion coefficient in inner sphere of spherical composite
- D2 :
-
diffusion coefficient in outer shell of spherical composite
- D ax :
-
axial dispersion coefficient in void space of column
- k f :
-
mass transfer coefficient, defined by Eq. (8)
- p:
-
Laplace domain variable
- q1 :
-
concentration in inner sphere of spherical composite
- q2 :
-
concentration in outer shell of spherical composite
- r:
-
radial variable in spherical composite
- r 0 :
-
radius of outer shell of spherical composite
- r s :
-
radius of inner sphere of spherical composite
- t:
-
time variable
- v:
-
interstitial fluid velocity in void space of column
- z:
-
axial variable in column
- ε:
-
fractional volume of void space of column
- ε1 :
-
fractional volume of inner sphere of spherical composite
- ε2 :
-
fractional volume of outer shell of spherical composite
- μ1 :
-
the first absolute moment of C(z, t)
- μ ’2 :
-
the second central moment of C(z, t)
References
Schneider, P. and Smith, J.M.:AIChE J.,14, 886(1968).
Haynes, H. W. and Sarma, P. N.:AIChE J.,19, 1043 (1973).
Kawazoe, K., Suzuki, M. and Chihara,K.:Seisan Kenkyu (Tokyo Univ.),25, 38(1973).
Crank, J.: “The Mathematics of Diffusion” 2nd Ed., Oxford Univ., Press(1975).
Carslaw, H. S. and Jaeger, J. C: “Conduction of Heat in Solids” 2nd Ed., Oxford Univ. Press(1959).
Romdhane, I. H. and Danner, R. P.:AIChE J.,39, 625 (1993).
Wakao, N. and Kaguei, S.: “Heat and Mass Transfer in Packed Beds” Gordon and Breach(1982).
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Park, IS., Ahn, DY. Moment equation for the packed column with spherical composites. Korean J. Chem. Eng. 10, 240–243 (1993). https://doi.org/10.1007/BF02705274
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DOI: https://doi.org/10.1007/BF02705274