Gassmann Theory Applies to Nanoporous Media

TL;DR

This study demonstrates that Gassmann theory, traditionally used for macroporous media, can accurately predict wave propagation in nanoporous media like Vycor glass saturated with fluids, bridging a gap in understanding nanoscale porous materials.

Contribution

The paper validates the applicability of Gassmann theory to nanoporous media, providing a theoretical framework for ultrasonic analysis of fluid-saturated nanoscale materials.

Findings

Gassmann predictions match ultrasonic measurements in Vycor glass.

Bulk moduli of solid and fluid constituents can be estimated accurately.

Ultrasonic wave propagation in nanoporous media can be modeled using macroscopic theories.

Abstract

Recent progress in extraction of unconventional hydrocarbon resources has ignited the interest in the studies of nanoporous media. Since many thermodynamic and mechanical properties of nanoscale solids and fluids differ from the analogous bulk materials, it is not obvious whether wave propagation in nanoporous media can be described using the same framework as in macroporous media. Here we test the validity of Gassmann equation using two published sets of ultrasonic measurements for a model nanoporous medium, Vycor glass, saturated with two different fluids, argon and n-hexane. Predictions of the Gassmann theory depend on the bulk and shear moduli of the dry samples, which are known from ultrasonic measurements, and the bulk moduli of the solid and fluid constituents. The solid bulk modulus can be estimated from adsorption-induced deformation or from elastic effective medium theory. The fluid modulus can be calculated according to the Tait-Murnaghan equation at the solvation pressure in the pore. Substitution of these parameters into the Gassmann equation provides predictions consistent with measured data. Our findings set up a theoretical framework for investigation of fluid-saturated nanoporous media using ultrasonic elastic wave propagation.