Theory of earth tide and barometric effects in porous formations with compressible grains

TLDR

The analysis generalizes earlier derivations of pore‑pressure response to earth tides and barometric loading in porous media. Using three‑dimensional equations for pore pressure, stress, and strain in a homogeneous porous medium with compressible grains, the authors derive fluid‑pressure response expressions while assuming a laterally extensive formation that neglects horizontal flow. Vertical flow induced by pore‑pressure changes is governed by a diffusion equation, yielding a specific‑storage coefficient that incorporates solid‑grain compressibility; earth‑tide and barometric measurements thus provide in‑situ tests of bulk formation hydraulic and elastic properties.

Abstract

The general three‐dimensional equations for pore pressure, stress, and strain in a homogeneous porous medium with compressible grains are used to derive expressions for the response of fluid pressure to the stress changes due to earth tides and barometric loading effects. The analysis constitutes a generalization of earlier derivations. The formation is assumed to be of large extent laterally so that horizontal flow may be neglected. It is shown that vertical flow induced by the pore pressure changes can be analyzed by means of a diffusion equation. An expression for the specific storage coefficient is derived which is valid if horizontal deformations are negligible and which includes the effect of the compressibility of the solid grains. Measurements of earth tide and barometric effects constitute two in situ tests of bulk formation properties. Such measurements can therefore make an important contribution to the characterization of the hydraulic and elastic properties of a particular formation.