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In the extreme high-frequency limit, the fluid has no time to
significantly escape
from the porous grains (phase 2) and enter the main porespace
(phase 1). As such, the fluid pressure distribution
in each phase is reasonably modeled as

| |
(117) |

| (118) |

where *x* is again a local coordinate measuring distance
normal to the interface and where
*D*_{2} is the fluid-pressure diffusivity within the
porous grains that is given by .
In reality, the local confining
pressure throughout the grains has spatial fluctuations
about the average value and we have made the approximation
that = the average fluid
pressure throughout the grain space. It is easy to demonstrate that
under undrained and unrelaxed conditions,
| |
(119) |

| (120) |

Since these do not appear in the final result,
we do not bother substituting in the *a*_{ij} constants from
equations (90)-(95).
The continuity of fluid pressure *p*_{f2} = *p*_{f1} along
(*x*=0) requires that . The definition of
may now be used to write

| |
(121) |

| (122) |

| (123) |

where we have used, to leading order in the high-frequency limit, that
.
The desired limit is thus
.

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Stanford Exploration Project

10/14/2003