Prediction of Porous Adsorption and Apparent Porosity Based on the Generalized van der Waals Model

This study proposes a novel methodology based on the generalized van der Waals model to systematically investigate the variation patterns of apparent porosity in porous materials. By introducing the concept of attractive regions and incorporating chemical potential equilibrium conditions, we derive expressions for number density within adsorption regions and subsequently calculate apparent porosity. Results indicate that apparent porosity is significantly influenced by pressure, temperature, and material type: in most cases, it decreases with increasing pressure, although it may increase under specific conditions; at the same pressure, materials with lower true porosity demonstrate higher pore utilization efficiency; and increased temperature typically reduces apparent porosity. Based on gas adsorption data obtained from molecular simulations, this paper systematically analyzes variations in apparent porosity under different porosity and temperature conditions, and constructs contour curves of true porosity-pressure-apparent porosity relationships. Research findings demonstrate that in most systems, fitting parameters obtained at the same porosity value can accurately predict adsorption behavior across different temperatures (with goodness-of-fit generally exceeding 0.8); while for systems such as CH4-MgO with complex temperature dependencies, despite certain limitations in cross-temperature predictions, temperature-specific fitting approaches effectively establish quantitative relationships between apparent porosity and key variables. This theoretical framework provides robust support for precise prediction of apparent porosity, with significant engineering application value.