Fluid-mineral equilibrium under stress: insight from molecular dynamics

The interpretation of phase equilibria and reactions in geological materials is underpinned by standard thermodynamics that assumes that the stress in the systems is hydrostatic and homogeneous (i.e., the same for all the phases involved). However, stress gradients and non-hydrostatic stresses are common in rocks, and can be developed even in porous systems with coexisting solid minerals and fluids. In rocks with interconnected porosity, a fluid will always experience a hydrostatic stress gradient. On the contrary, the solid grains will experience different levels of stress due to the changes in the contact area between the grains. Therefore, rocks that are porous or have a granular structure will always experience stress gradients at the small scale, even if their macroscopic stress state is “lithostatic”.

The presence of a heterogeneous-stress distribution at the grain scale casts doubts on the predictive power and accuracy of existing multiphase thermodynamic models. However, currently there is still not an accepted theory which extends thermodynamics to include the effect of non-hydrostatic stress on reactions, and the use of several thermodynamic potentials in stressed geological system is still debated (e.g. [1-3]). Even experiments have not been conclusive, because the direct effect of the applied non-hydrostatic stress on the thermodynamics of the reactions cannot be separated from the indirect effect caused by local stress concentrations [4].

We have investigated the problem of the direct effect of a homogeneous non-hydrostatic stress on the solid-fluid equilibrium with molecular dynamics simulations. With such simulations the energy of the system, the pressure of the fluid and the stress of the solid can be monitored until the stressed system reaches the equilibrium conditions. Our results show that for simple systems at the stress range expected in the lithosphere, the shift of the pressure and temperature of the fluid-solid equilibrium is small for geological applications, consistent with theoretical predictions [5,6]. On the contrary, the mean stress of the solid is largely affected by the applied non-hydrostatic stress and can deviate substantially from the pressure of the fluid. These results suggest that hydro-mechanical-chemical models should not use the pressure of the fluid as a proxy of the mean stress of the solid, and therefore should not equate the thermodynamic pressure of the reaction to the mean stress of the solid. However, our analysis does not take into account the indirect effect of stress heterogeneities at the sample scale. Spatial variations of stress can reach GPa level and can therefore indirectly affect phase equilibria.

MLM is supported by an Alexander von Humboldt research fellowship.

References

[1] Wheeler, J. Geology 42, 647–650 (2014);

[2] Hobbs, B. et al. Geology 43, e372 (2015);

[3] Tajčmanová, L. et al. Lithos 216–217, 338–351 (2015)

[4] Cionoiu, S., et al. J. Geophys. Res. Solid Earth 127, e2022JB024814 (2022)

[5] Sekerka, R. et al. Acta Mater., 52(6), 1663–1668 (2004)

[6] Frolov, T. et al. Phys. Rev. B Condens. Matter Mater. Phys. 82, 1–14 (2010)