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We describe the thermodynamic state of a single-phase fluid confined to aporous medium with Hill's thermodynamics of small systems, also known asnanothermodynamics. This way of defining small system thermodynamics, with aseparate set of control variables, may be useful for the study of transport innon-deformable porous media, where presently no consensus exists on pressurecomputations. For a confined fluid, we observe that there are two pressures,the integral and the differential pressures. We use molecular simulations toinvestigate and confirm the nanothermodynamic relations for a representativeelementary volume (REV). For a model system of a single-phase fluid in aface-centered cubic lattice of solid spheres of varying porosity, we calculatethe fluid density, fluid-solid surface tension, replica energy, integralpressure, entropy, and internal energy.

Defining the pressures of a fluid in a nanoporous, heterogeneous medium