Elastic stiffening of reservoir rocks with rising pore pressure under constant biaxial far-field stress: application to the Porthos geological carbon-dioxide sequestration project

This study systematically quantifies elastic stiffening in fluid-saturated porous media, distinguishing the critical influence of biaxial far-field stress from simplified uniaxial conditions. The Linear Superposition Method (LSM) of elastic displacements is used to quantify solutions of the detailed stress state within a pressure-saturated poro-elastic framework, consisting of regularly arranged cylindrical pores under uniaxial and bi-axial loads. The model examines the impact on the effective bulk modulus of changes in internal pressure, while varying the relative magnitude of the horizontal and vertical stresses ($$\sigma_{yy}$$ = $$\lambda \sigma_{xx}$$). A sensitivity analysis reveals that lateral confinement under biaxial loading significantly accelerates the stiffening process. Specifically, the effective bulk modulus reaches a porosity-independent state when the internal pore pressure balances the far-field confining stress, a condition reached at a significantly lower pressure-to-stress ratio than observed under uniaxial loading. To demonstrate practical implications, the model is applied to the Porthos Geological Carbon Sequestration (GCS) project in a depleted offshore gas field (Netherlands). The results indicate that injection-induced pore pressure increases lead to a non-linear increase in the reservoir's bulk modulus, which in turn increases hydraulic diffusivity. This suggests that depleted gas reservoirs may accommodate slightly higher injection rates than predicted if the faster pressure dissipation associated with elastic stiffening is neglected.