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Isothermal compressibility of water-saturated rocks as a function of porosity and topology

Determine the isothermal compressibility of fully water-saturated rocks as a function of porosity and pore network topology to allow precise evaluation of the pressure derivative of the solid volume fraction and the characteristic relaxation frequency within differential effective medium models.

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Background

The calculation of the pressure derivative of the solid volume fraction in a two-phase rock-water system involves the isothermal compressibilities of the solid mineral, the water, and the fully saturated rock. While mineral and water compressibilities are known, the composite rock’s compressibility depends intricately on porosity and the topology of the pore network.

Because this dependence is not characterized, the authors provide only rough estimates using limited data for specific rocks, which constrains the accuracy of activation volume predictions. Establishing a general or measured relation for the rock’s compressibility would improve the fidelity of the pressure-dependent relaxation model.

References

The compressibility k of the water saturated rock is a complex function of the porosity and its topology, which prevents us from knowing the isothermal compressibility k of the water saturated rock.

— Pressure dependence of the interfacial polarization and negative activation volume for dielectric relaxation in heterogeneous systems (2505.16742 - Papathanassiou, 22 May 2025) in Section III, "The pressure dependence of the volumetric fraction of the solid phase" (after Eq. 8)