On Poro-Elasticity in Finite-Element Geomechanical Simulations: Theory and Implementation

Abstract

The volume changes of grains (solids) are usually neglected in numerical geomechanical simulations of production from - or injection into - reservoir rocks, assuming that all rock volume changes translate into porosity changes. When grain compressibility is taken into account, it is usually done by modifying the pore pressure changes with the so-called Biot factor (α). Rock failure criteria, like fracturing or pore collapse, are fully dependent on (Terzaghi's) effective stress and not on total stress or Biot-modified effective stress. This pore pressure modification provides a wrong estimation of plasticity and fracturing and, hence, is not suitable for these types of analyses. In this paper we propose a different method for incorporating grain compressibility in Finite Element modelling. The effect of stress, pressure and temperature changes on the volume of the grains can be calculated separately and translated into a total volume change and a pore volume change. These effects can be incorporated into the constitutive model of plasticity, which uses standard effective stresses for plastic behaviour. The mismatch of elastic volume changes between total stress and pore pressure changes is corrected for by a volume strain loading that is equal to pore pressure change (Δp) divided by the Grain Bulk Modulus (K g ). For linear elasticity, the equations reduce to poro-elasticity. This volumetric strain can be directly calculated when the fluid pressure change is known or for undrained materials. The pore volume changes are also computed since they are relevant for undrained behaviour and for the amount of expelled fluids in the drained situation, which is an input for Reservoir Engineering (fluid flow) computations. This method has been incorporated in Shell's propriety FEM application GEOMEC, based on TNO-Diana FEM. In this paper, we explain the method above fully, starting from poro-elasticity theory.