longitudinal dispersion in nonuniform isotropic porous media

k ..
1J
aBT ..
1J
25
(2.7)
where B is the channel conductance (L2) and T .. (-) is the coordinate
1.J
transformation from a local coordinate system oriented along the pore
channels to a fixed Cartesian coordinate system. The overbar denotes a
volume average. As an example, Bear (1972) shows for an isotropic
medium consisting of straight cylindrical capillaries of radius a and
2
channel conductance B = a /8
2
oa
k = 24
(2.8)
which is the same result as found by Saffman (1959) (equation (2.5».
Although the model is difficult to evaluate in general, it does provide
a theoretical relation for anisotropic porous media.
2.1.5 Deterministic Network Model
A natural extension of the capillary tube model is a capillary
tube network which accounts for the exact nature of the
interconnections. This type of network model differs from the Saffman
(1959) model in that a deterministic network is used. The effects of
flow in one capillary tube on other capillaries in the network 1.S taken
into account. The network approach was investigated in detail by Fatt
(1956), who employed various two-dimensional regular networks to
represent porous media. Fatt's model also presents one of the earliest
investigations of the effect of nonuniform pore structure on