Crystallisation pressure in porous media with compliant crystals

The Correns equation for crystallisation pressure is revisited through the lens of poromechanics. First, it is recognised that crystal formation in subsurface systems occurs in the presence of kinematic constraints governed by the geomaterial deformability. Then, a theoretical framework is established by incorporating principles of physical chemistry, thermodynamics, and generalised poroelasticity, through which the stiffness of both crystals and surrounding matrix are accounted for. The proposed framework explicitly accounts for the eigenstrain terms associated with crystal growth. The upshot is an estimation of a generalised crystallisation pressure which deviates from the standard expression. Parametric analyses reveal that less stiff crystals generate higher pressure, while more compliant porous skeletons accommodate greater crystal growth. Notably, the strain within the crystal phase can readily become substantial, especially in the case of highly compliant secondary solids. This finding emphasises the necessity of examining these processes with suitable non-linear constitutive laws for all the involved solid phases. In addition, the risk of overestimation of the crystallisation pressure identified in this work under isotropic conditions suggests that the mechanical anisotropy of both crystal and matrix shall be explicitly introduced, as they may influence the components of the in-pore crystallisation stress and, consequently, the direction of crystal growth.