where S, is specific storage [L-1], and t is time [T]. Specific storage is a measure of the
volume of formation fluid per unit volume of media per unit head of a saturated
formation that is stored or expelled from storage due to compressibility of the matrix and
change in fluid pressure. Specific storage is defined as Ss=pfg(a+nl) where a is matrix
compressibility [M-1 L T2], and fl is the compressibility of the formation fluid [M-1 L T2].
Matrix compressibility (a) is defined by a = [1/(V)](dV /doe) where V is the bulk
volume [L3] and oe is the effective stress [ML-1T-2]. The second term on the right hand
side is a source term representing changes to fluid volume or pressure, such as due to
loading, per time per unit volume of media [T-1].
During loading, the stress added from the sediment load is partitioned between the
pore fluid and the matrix. The loading efficiency, y, denotes the fraction of the stress
added to the pore fluid pressure and, assuming the sediment grains are incompressible
relative to the matrix, is defined as follows (after Neuzil, 1986)
y= a/(a+nf ) (6)
For highly compressible sediments, the loading efficiency is near 1.
The increase in pore pressure caused by loading drives fluid flow. When initial
conditions, boundary conditions and the controlling hydrogeologic parameters k and a
are known, Equation 5 can be solved for hydraulic head at any point at any time, and
thus, pore fluid velocity relative to the sediment framework can be calculated using
Equation 4a.
The pore pressure is related to effective stress (Ge) by
o O P