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