The scaled particle theory (SPT) is applied to describe thermodynamic properties of a hard sphere (HS) fluid in random porous media. To this purpose, we extended the SPT2 approach, which has been developed previously. The analytical expressions for the chemical potential of an HS fluid in HS and overlapping hard sphere (OPH) matrices, sponge matrix, and hard convex body (HCB) matrix are obtained and analyzed. A series of new approximations for SPT2 are proposed. The grand canonical Monte Carlo (GGMC) simulations are performed to verify an accuracy of the SPT2 approach combined with the new approximations. A possibility of mapping between thermodynamic properties of an HS fluid in random porous media of different types is discussed. It is shown that thermodynamic properties of a fluid in the different matrices tend to be equal if the probe particle porosities and the specific surface pore areas of considered matrices are identical. The obtained results for an HS fluid in random porous media as reference systems are used to extend the van der Waals equation of state to the case of a simple fluid in random porous media. It is observed that a decrease of matrix porosity leads to lowering of the critical temperature and the critical density of a confined fluid, while an increase of a size of matrix particles causes an increase of these critical parameters.

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Based on a new and consistent formulation of scaled particle theory for a fluid confined in random porous media, a series of new approximations are proposed and one of them gives equations of state with excellent accuracy for a hard sphere fluid adsorbed in a hard sphere or an overlapping hard sphere matrix. Although the initial motivation was to remedy a flaw in a previous formulation of the scaled particle theory for a confined fluid, the new formulation is not a trivial and straightforward correction of the previous one. A few conceptual and significant modifications have to be introduced for developing the present formulation.