Ono-Kondo lattice model for propane multilayer adsorption in organic nanopores in relation to shale gas

Accurate characterization of shale gas adsorption capacity is of great importance to the gas-in-place estimation and prediction of well productivity. Propane is one of major constituents in shale gases which can have multilayer adsorption behavior on pore surfaces. While experiments can measure excess adsorption, the absolute adsorption, which describes adsorbed gas capacity, has to be converted from the excess adsorption. In previous works, absolute adsorption is usually calculated from excess adsorption with adsorbed phase volume or density based on the single-layer adsorption model. However, for heavier alkanes, such as ethane and propane, which can have multilayer adsorption behavior, single-layer adsorption model becomes invalid. While molecular simulation can characterize the multilayer adsorption behavior, it comes with expensive computational costs. Currently, there is no viable model to characterize the absolute adsorption of hydrocarbons which can have multilayer adsorption behavior. In this work, we conduct grand canonical Monte Carlo (GCMC) simulation to study propane adsorption in shale nanopores over a wide range of pressures at temperature higher than the critical temperature. We find that propane can form multiple adsorption layers, thus, using single-layer adsorption model to obtain the absolute adsorption becomes unjustifiable. Based on the propane density distribution characteristics, we propose a multilayer adsorption model and use Ono-Kondo (OK) lattice model with multilayer structures to regress propane excess adsorption and subsequently obtain the absolute adsorption in each layer. For propane, we take into account the correlation effect arising from strong adsorbate-adsorbate interactions beyond mean field theory (MFT) and the only predetermined parameters are number of layers and adsorption layer width. The proposed OK model shows an excellent agreement with GCMC simulations on the excess adsorption and absolute adsorption in each layer, with discrepancies less than 6% above 50 bar. The proposed OK model can readily take into account the propane multilayer adsorption behavior, while significantly reducing calculation time. Our method presents a reliable and highly-efficient approach for accurate characterization of adsorption of hydrocarbons with multilayer structures and provide important insights into the gas-in-place estimation in shale.