Comparison of PR-EOS with Capillary Pressure Model with Engineering Density Functional Theory on Describing the Phase Behavior of Confined Hydrocarbons

Abstract

Abstract Peng-Robinson equation of state (PR-EOS) with capillary effect has been extensively used to describe the phase behavior of hydrocarbons under nano-confinement in shale reservoirs. In nanopores, surface adsorption may be significant and molecular distribution is heterogeneous. While PR-EOS cannot take into account these effects, statistical thermodynamic approaches such as density functional theory (DFT) can explicitly consider the intermolecular and fluid-surface interactions. In this work, we compare the phase behavior of pure hydrocarbons and mixtures in nanopores from PR-EOS with capillary effect and engineering DFT. We apply the Young-Laplace (YL) equation assuming zero contact angle to calculate the capillary pressure in PR-EOS with capillary effect. On the other hand, we extend the PR-EOS to inhomogeneous conditions by using weighted density approximation (WDA) in engineering DFT. For pure components, both approaches predict that the dew-point temperature increases in hydrocarbon-wet nanopores. While engineering DFT predicts that the confined dew-point temperature approaches bulk saturation point when pore size approaches 20 nm, the saturation point obtained from PR-EOS with capillary effect approaches bulk only when the pore size is as large as 1 μm. With engineering DFT, the critical points in nanopores deviate from that in bulk, but no change is observed from PR-EOS with capillary effect model. The difference between PR-EOS with capillary effect and engineering DFT on the dew-point temperature decreases as the system pressure approaches the critical pressure. At low pressure conditions, PR-EOS with capillary effect model becomes unreliable. For binary mixtures, both approaches predict that the lower dew-point decreases and the upper dew-point increases. More interestingly, phase transition can still occur when the system temperature is higher than the bulk cricondentherm point. Engineering DFT predict that the confined lower dew-point approaches bulk when pore size approaches 20 nm, whereas the dew-point obtained from PR-EOS with capillary effect approaches bulk only when the pore size is as large as 100 nm. This work illustrates that assuming homogeneous distributions in nanopores may not be applicable to predict the phase behavior of hydrocarbons under nano-confinement.