Analysis of porous media heterogeneities using the diffusion of pressure waves

Abstract

We present an experimental study and a model of the diffusion of sinusoidal pressure waves through porous media. We show that measurements of the hydraulic admittance A (ω) in the sine wave mode allow us to probe the structure of porous samples with an adjustable investigation depth depending on the frequency ω. The variations of A (ω) in heterogeneous media with a percolationlike geometry are modeled numerically on two‐dimensional percolation networks. One obtains a transition from normal diffusion at low frequencies (| A (ω)| ∝ ω ½ ) to anomalous diffusion at higher frequencies (| A (ω)| ∝ ω 0.7 ). At the transition, the penetration depth of the wave is of the order of the percolation correlation length. The hydraulic admittance and transmittance of 20% porosity pressed calcite have been investigated experimentally with sine wave excitations at pulsations ω between 2 × 10 −4 and 0.42 rad/s. Both the modulus and the phase of the complex admittance A (ω) display normal diffusive variations as ω increases. Increasing the viscosity reduces the frequency above which the diffusive behavior is observed. The measured diffusion coefficient is 25% higher than that computed from permeability and compressibility values measured independently; this difference may be associated with nonconnected porosity.