Page 98 - Reservoir Formation Damage
P. 98
Permeability Relationships 81
(5-1)
The pore volume can be expressed in terms of the total volume of
hydraulic tubes as:
(5-2)
The pore surface, E^, can be expressed in terms of the total cylindrical
surface of the hydraulic tubes as:
(5-3)
Dividing Eqs. 5-2 and 3 leads to:
(5-4)
The pore surface per unit bulk volume, Z fe , can be expressed in terms
of the pore surface per unit volume of the solid porous matrix, X , as:
(5-5)
Thus, invoking Eq. 5-5 into 4, the hydraulic tube diameter can be
expressed as:
D '
~
(5-6)
If the grains making up the porous media are assumed of the spherical
shape, then the specific grain surface is given by:
(5-7)
where D g is the grain diameter.
Next consider that the laminar flows through porous media and the
bundle of tortuous tubes can be described by the Darcy and the Hagen-
Poiseuille laws given, respectively, as:
