Extending van der Waals equation of state by molecular potential theory to study nano-confined gas properties

Understanding the properties of nano-confined gas is essential for the effective utilization of unconventional natural gas, but the classical equation of state (EOS) for bulk gas does not apply to nano-confined gas. In this work, based on the potential energy of nano-confined gas molecules, the gas density distribution function on a nano-pore cross section is derived and subsequently, a novel van der Waals (vdW) EOS is proposed that modifies the "internal pressure" term and extends the "external pressure" term. In this proposed EOS, the gas/solid and porous media properties, such as pore size, gas molecular size, solid molecular number density, and the gas-solid molecular interaction parameter, are applied to characterize the nano-confinement effect. Using the experimental results of nano-confined gas critical temperature, the applicability of this proposed vdW EOS model is verified and it has the largest relative deviation of 7% for nanopores with sizes greater than 2 nm. The gas molecular size and gas-solid molecular interaction are found to be important factors contributing to the nano-confinement effect, and they influence the critical point shift and density of nano-confined gas. Also, the solid molecular number density greatly affects the compressibility of nano-confined gas. Using this model, the U-shaped density distribution curve described in molecular dynamic simulations is obtained, and the equation to calculate the adsorption layer thickness is also obtained. The nano-confinement effect induces gas liquefaction and incompressibility because of the increased gas density and increased compressibility factor of nano-confined gas.