Acoustic Measurements Aid Mechanical-Damage Characterization in Proppant Packs

Introduction

Mechanical damage that leads to compaction and crushing is studied for sands by measuring ultrasonic velocities. Elastic properties can be estimated from compressional- and shear-wave velocities calculated from acoustic ­measurements. The elastic properties of unconsolidated sands usually are ­studied by use of effective-medium models for granular media. Effective-­medium-theory approaches such as the Hertz-­Mindlin model are often used to derive the effective elastic moduli of packings of identical and spherical granular materials.