Mechanics of stratified anisotropic poroelastic media

AVERAGING RESULTS FOR ALL DRAINED OR ALL UNDRAINED BOUNDARY CONDITIONS

The two most common boundary conditions to consider in poroelastic media are the drained and undrained conditions. Drained conditions imply that the fluid pressure change is zero while the increment of fluid content in the individual layers may be considered arbitrary. Of course, the total amount of fluid present needs to be properly conserved in the analysis to be presented, but the usual idea for drained conditions is that the poroelastic systems is immersed in an infinite reservoir of fluid so that pore fluid is freely available to move in and out of the region of interest. For present studies, this situation implies that the layer increments $\zeta$ can take arbitrary (small) values, but the fluid pressure is constrained to be a constant value $p_f$ everywhere. So changes in $p_f$ always vanish for drained conditions.

Undrained boundary conditions place the hard constraint on the fluid increment $\zeta$ , requiring no flow at the boundaries, so $\zeta = 0$ at all boundaries. These conditions ensure that the fluid pressure $p_f$ does change, since as the boundaries move in or out the pressure on the confined fluid is increasing or decreasing.

Both of these conditions must be approximations to conditions in a generally realistic earth model. It is easy to imagine situations where some boundaries between layers (the vertical direction) are plugged, so undrained boundary conditions $\zeta_z \equiv 0$ might be correct while neighboring layers (horizontal direction) might be open to fluid flow (so $\zeta_x$ and/or $\zeta_y \ne 0$ ). I will consider these more general situations in later work, but for now limit the analysis to that for either all drained conditions or all undrained conditions. All undrained conditions are also appropriate, as mentioned previously, regardless of the physical boundary conditions if the probe changing the physical variables is a passing high frequency acoustic or seismic wave train or pulse.

Mechanics of stratified anisotropic poroelastic media