Four nanoscale-extended equations of state: Phase behaviour of confined fluids in shale reservoirs

Abstract

In this paper, the thermodynamic phase behaviour of pure and mixing nanoconfined fluids in shale reservoirs are studied. First, an analytical generalized equation of state (EOS) is developed by including the effects of pore radius and intermolecular interactions. Based on the generalized EOS, four extended cubic EOS are proposed and used to calculate the thermodynamic phase behaviour. The four extended cubic EOSs, the extended van der Waals (vdW), Redlich−Kwong (RK), Soave−Redlich−Kwong (SRK), and Peng−Robinson (PR) EOSs, are found to accurately predict the pressure–volume (P–V) diagrams of different systems in nanopores. More specifically, the extended RK (E-RK) EOS may fail to accurately calculate the phase behaviour at high temperatures and the extended PR (E-PR) EOS is more accurate for liquid phase pressure calculations. The overall calculated P–V diagrams for the pure components in nanopores from the extended EOS shift up and right relative to those of the bulk-phase case and the EOS only including the intermolecular interactions. Furthermore, as a physical meaningless phenomenon, the negative pressure state is completely avoided in the calculated P-V diagrams from the extended EOSs. Compared to the measured bubble-point pressure (Pb) for the four different confined mixing fluids, the E-vdW, E-RK, and E-SRK EOS provide accurate estimates of Pb with overall percentage average absolute deviations (AAD%) of 10.95%, 12.07%, and 9.37%, respectively. The proposed extended EOSs are capable to accurately predict the critical properties and their shifts in nanopores. A bottom limit for the continuous reduction of the critical properties by decreasing the pore radius is obtained from the proposed extended EOSs, which is, for example, 5 nm for C8H18.