Numerical modelling of the micromechanics of sandstone compaction: Developing a Finite Element Model to asses stress-distributions in flat grain-to-grain contacts versus Hertzian point contacts

Abstract

Reservoir sandstones are highly porous and contain varied amounts of pressurized hydrocarbons and water. The depletion of these reservoirs, i.e. reducing the fluid pressure, increases the effective stresses at the microscale which results in compressive and tensile stresses near grain-to-grain contacts. The response of the individual grains is initially elastic but, if grain-scale stresses become too large, may eventually lead to failure and the grains will show inelastic behaviour causing irrecoverable deformation. This grain-scale deformation translates to compaction of the sandstone reservoir. Thus, these microscale compaction mechanisms initiate deformation at a reservoir scale leading to surface subsidence and microseismicity. The ability to predict the occurrence and the extent of inelastic deformation in such reservoirs is therefore essential to predict future reservoir behaviour. However, the grain-scale behaviour of sand is still poorly understood, especially in terms of stress-distributon across grain-contacts and within grain bodies, which drives grain-scale deformation. Since grain-scale stresses cannot be measured in laboratory experiments, it is needed to model them using numerical codes like Finite Elements. Within this research such a first Finite Element Model is developed for a configuration of simple spherical grains in contact. As a benchmark for the model, a comprehensive description of the Hertzian contact problem is represented addressing all corresponding facets of grain contact modelling at a microscale. The finite element model ELEFANT is tested for elastic behaviour within a single grain using analytical solutions based on the original solution for stresses by Hertz in 1896. The benchmarking of the Finite Element Model ELEFANT produced some satisfactory results as the computed stress- and displacement values by ELEFANT were in good agreement with the analytical solutions.