Integrating adsorption and diffusion in nanopores using thermodynamics and Equations of State

In the orders of nanometres, diffusion and adsorption effects deviate significantly from current conventional models which result in limited estimation accuracy of hydrocarbons capacity and recovery potential. At such small pore sizes, limited pore space as well as wall superimposition effects affect both adsorption and diffusion behaviour. Classical laboratory experiments carried out on nanoporous material are unable to characterise adsorption behaviour accurately due to the presence of larger macropores within the network. At present, grand-canonical Monte Carlo (GCMC) molecular simulations are usually employed to model both diffusion and adsorption effects independently. However, this method is computationally expensive and does not provide a quantitative variation trend of adsorption isotherm with pore size. In this paper, a thermodynamics-based Two-Dimensional Equation of State (2-D EoS) model is introduced to characterise adsorption isotherms in small carbon and mineral capillaries. The effects of pore sizes on adsorption isotherm parameters are compared with that determined from a bulk scale predictive model. Regressed parameters from pure component isotherms are applied to a methane-carbon dioxide binary system. Results are consistent with that determined from molecular simulations. Therefore, it is concluded that by applying appropriate cubic equation of state, the 2-D EoS Adsorption Isotherm Model is able to produce an accurate quantitative representation of the adsorption behaviour in nanopores. Finally, thermodynamic factor (the correction factor for diffusivity for pure and binary component) is calculated directly from adsorption isotherms. The thermodynamic factor was also shown to have the ability to calculate diffusion coefficient without considering the type of transport mechanism.