An empirical model for predicting saturation pressure of pure hydrocarbons in nanopores

Due to the confinement and strong adsorption to the pore wall in meso‑ and nano pores, fluid phase behavior in the confined media, such as the tight and shale reservoirs, can be significantly different from that in the bulk phase. A large amount of work has been done on the theoretical modeling of the phase behavior of hydrocarbons in the confined media. However, there are still inconsistencies in the theoretical models developed and validations of those models against experimental data are inadequate.

In this study, we conducted a comprehensive review of experimental work on the phase behavior of hydrocarbons under confinement and analyzed various theoretical phase-behavior models. Emphasis was given to the modifications to the Peng-Robinson equation of state (PR EoS). Through the comparative analysis, we developed a modified alpha-function in PR EoS for accurate prediction of the saturation pressures of hydrocarbons in porous media. This modified alpha-function accounts for the pore size and was derived based on the regression results through minimizing the deviation between the experimentally measured and numerically calculated saturation pressure data. Meanwhile, the thermodynamic properties of propane were calculated in the bulk phase and in the nanopores. Finally, we validated the newly developed model using the experimental data in synthesized mesoporous materials and real reservoir rocks.

By applying the modified PR EoS, a more accurate representation of the experimentally measured saturation pressure data in confined nanopores was achieved. This newly developed model not only enhanced the accuracy of the predictions but also provided valuable insights into the confinement effects on the phase behavior of hydrocarbons in nanopores. Notably, we observed significant changes in the properties of propane within confined nanopores, including suppressed saturation pressure and fugacity, indicating a greater tendency for the gas to remain in the liquid phase. Enthalpy of vaporization was found to increase highlighting increased difficulty in transitioning from liquid to gas phase under confinement. Additionally, the new model predicts an increased gas compressibility factor in the nanopores suggesting a close resemblance of ideal gas due to the counterbalance between the attractive and repulsive forces. To validate the model, new datasets containing saturation pressures of propane and ethane under a wide range of temperatures and pore sizes were employed. The newly developed model was further applied to the experimental data obtained in real rock samples (sandstones, limestones, and shales). Interestingly, it was observed that the phase change in these samples predominantly occurred in the smallest pores. This finding highlights the importance of considering the pore size distribution when studying the phase behavior of hydrocarbons in a capillary medium even if the rock has high permeability.

This study provided a simple and easy-to-implement modification to the PR EoS for accurate prediction of the phase behavior of petroleum fluids under confinement. The newly developed model for calculating saturation pressures of hydrocarbons demonstrates improved accuracy in representing experimental data compared to the previous models, while offering a more straightforward and simplified approach.