where ρf is the fluid density,
εp is the porosity, and
Qm is an external mass sink or source. The so-called Darcy velocity
vd is computed from Darcy’s law
where κ is the permeability of the porous matrix,
μ is the fluid viscosity, and
pf is the pore pressure. If gravity is included, Darcy’s velocity is augmented by
where g is the gravitational acceleration. Note that the Darcy velocity
vd is actually the relative velocity of the fluid with respect to the pore walls weighted by the porosity,
where the poroelastic storage term Sp is calculated from
Equation 8-4 for Biot poroelasticity and is equal to zero for biphasic poroelasticity. The second term is a mass source or sink
where ∂εvol/∂t is the rate of change in volumetric strain (of the porous matrix),
ρf is the fluid density, and
αB is the Biot–Willis coefficient. You can interpret the right-hand-side term as the rate of expansion of the pore space. As
εvol increases with time, the volume fraction available for the fluid increases and thereby gives rise to a fluid sink; as indicated by the negative sign in the source term
Qvol.
