Improved granular medium model for unconsolidated sands using coordination number, porosity, and pressure relations

Abstract

We have developed a recipe for using closed-form expressions of effective-medium models to predict velocities in unconsolidated sandstones. The commonly used Hertz-Mindlin effective-medium model for granular media often predicts elastic wave velocities that are higher, and [Formula: see text] ratios that are lower, than those observed in laboratory and well log measurements in unconsolidated sediments. We use the extended Walton model, which introduces a parameter [Formula: see text] to represent the fraction of grain contacts that are perfectly adhered. Using the extended Walton model with [Formula: see text] ranging from 0.3 to 1, we obtain new empirical relations between the coordination number (C), porosity, and pressure for P- and S-wave velocities by inverting dynamic measurements on dry, unconsolidated sands. We propose using the extended Walton model [Formula: see text] along with these new C-porosity and C-pressure relations to study the mechanical compaction of unconsolidated sandstones. The model has been tested on two experimental data sets. It provides a reasonable fit to observed P- and S-wave velocities and specifically improves shear-wave predictions.