Rock physics modeling of unconsolidated sands: Accounting for nonuniform contacts and heterogeneous stress fields in the effective media approximation with applications to hydrocarbon exploration

By treating contact stiffness as a variable, one can extend the effective medium approximation used to obtain elastic stiffness of a random pack of spherical grains. More specifically, we suggest calibrating effective media approximation based on contact mechanics by incorporating nonuniform contact models. The simple extension of the theory provides a better fit for many laboratory and field experiments and can provide insight into the micromechanical bonds associated with unconsolidated sediments. This approach is motivated by repeated observations of shear-wave measurements in unconsolidated sands where observed shear-wave velocities are lower than predicted by the Hertz-Mindlin contact theory. We present the calibration process for well-log data from a North Sea well penetrating a shallow-gas discovery and a deepwater well in the Gulf of Mexico. Finally, we demonstrate the benefit of using this model for amplitude variation with angle (AVA) analysis of shallow sand targets in exploration and reservoir studies.