18
2. Hydrodynamic Dispersion in Porous Media
tortuosity of a porous medium is also abasie parameter to the depietion of
the porous medium.
Pressure and Water Head
Let the volume of a liquid phase in a REV of porous media be [UO,y], and p
be the mieroseopie statie pressure distribution, then by spatial averaging we
ean obtain
p(x,t) = U. 1( ) r p(x',t)dUo,y,
O,y x JIUo.,(x)]
(2.1.34)
whieh is ealled the mean pore pressure of the porous medium. We ean also
define water head at point x as
h =z + P
pg'
(2.1.35)
where z is the height ofx above a given datum and p is the maeroseopie mean
fluid density at x. The water head h is dependent on p and p, and is also a
maeroseopie property. It gives the mean potential energy ofunit mass offluid
at that point. Since groundwater movement is relatively slow, its kinetie
energy ean virtually be ignored, and so h ean also be treated as the total
meehanieal energy per unit mass of water. The bars above p and p will be
omitted later in the text. Sinee we are diseussing flow phenomena in porous
media, no eonfusion will be eaused by this omission.
Coeffieient of Permeability
Darcy's Law is abasie law in seepage theory. For an anisotropie porous
medium, Darey's Law is expressed as
(2.1.36)
where (Ql,Q2,Q3) are the eomponents of Darey velocity q. The seeond rank
symmetrie tensor
[
Ku K12 K13]
K = K 21 K 22 K 23
K 31 K 32 K 33
(2.1.37)
is ealled the hydraulic conductivity of porous media. Using Einstein's summa-