A Nonlinear Compaction Model for Sandstone

Abstract

Constitutive relations for the compaction behavior of porous sandstone have been formulated to describe the results of uniaxial and triaxial tests under reservoir pressure and temperature conditions. An expression for loading behavior in uniaxial compression is derived by treating the loading modulus as an independent variable. Similar relations are derived for uniaxial and triaxial compaction tests. Elastic unloading takes a quadratic form when described by incremental stresses and strains. The constitutive equations relate the values of the incremental stress and strain on loading and unloading using parameters that are a function of the state of prestress in the material. Published data on samples cored from three different wells at various depths exhibited a similar dependence of rock properties on mechanical and pore pressure loads.