Previous oil/water counter-current imbibition experiments on shale and tight rock samples showed that oil can be spontaneously recovered by water. The pore size distribution analysis showed the samples are composed of 2nm to 10nm organic nanopores. The oil recoveries range from 10% to 25%, which cannot be explained by the classical imbibition models. We hypothesize that the recoverable oil are the part of the adsorbed oil in small organic nanopores, the density of which is higher than the bulk oil density. We test this hypothesis by analytical modeling the number density profiles and estimating the free energy of oil and water molelcules in the organic nanopores of the target samples, ranging from 2nm to 10nm. We apply the proposed model on octane and water molecules in carbon nanotubes to investigate the driving force of the oil/water counter-current imbibitions in the organic nanopores of the samples. Results show that the number densities of the octane molecules in the adsorbed region of 2nm to 10nm nanopores are higher than the bulk octane value. As a result, the estimated surface tensions of the adsorbed octane molecules in 2nm to 6nm carbon nanotubes are higher than the surface tension of the bulk water. This reveals the driving force of the adsorbed oil in the small organic nanopores is positive during the oil/water counter-current imbibition experiments on shales. In addition, we compare the surface tension of the octane and water molecules in the carbon nanotubes. This result presents the driving force of the adsorbed octane is higher than that of the adsorbed water. These results indicate the part of the adsorbed oil in small organic nanopores can be spontaneously displaced by the water. Particularly, the estimated oil recoveries in the carbon nanotubes increase as the pore size increasese to 3nm, and then decrease as the pore size increase to 6nm. Based on the pore size distribution of the samples, the calculated oil recoveries of 3 samples show a good agreement with the previous oil/water counter-current imbibition experimental results. These results suggest that most of the recoverable oil of shales and tight rocks during the imbibieion experiments are produced from small organic nanopores.

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