A statistical thermodynamics-based equation of state and phase equilibrium calculation for confined hydrocarbons in shale reservoirs

Abstract

The phase behavior of confined fluid in nanopores of shale reservoirs deviates significantly from that of bulk fluid. Confined fluid refers to fluid whose thermal motion is affected by nanopores, since nanopores have a comparative size to the mean free path of fluid molecules. To describe deviated phase behavior in nanopores, Travalloni et al. proposed PR-C EOS by introducing empirical modifications to the canonical partition function. The modifications consider the two main mechanisms that cause nanopore phase behavior to deviate: the finite volume effect and the fluid-pore wall interaction effect. However, in addition to its weakness on a theoretical basis, PR-C EOS possesses imperfections when applied to predict nanopore phase behaviors. In this work, we propose a new EOS derived from statistical thermodynamics for slit-like nanopores, named PR-X EOS. The PR-X EOS has an extra term to represent the fluid-pore wall interaction effect and a modification to the cubic EOS parameter to represent the finite volume effect. PR-C EOS and PR-X EOS are non-cubic, and each has some new parameters. The new parameters can be determined by fitting adsorption isotherms. When pore size approaches infinity, PR-C EOS and PR-X EOS both degenerate into classic PR EOS. To apply these two non-cubic EOS in reservoir simulators, we improve gas-oil phase equilibrium calculation methods. The improved simulator can model chemical potential equilibrium between the nanopore grid and the bulk grid, with chemical potentials of the two grids calculated using the modified EOS and conventional EOS, respectively, so that bulk grid pressure can be obtained. As a consequence, we can plot the adsorption isotherm or phase diagram under bulk pressure, which is practically measurable pressure. Therefore, we can validate the modified EOS with experimental or molecular simulation data. Validations demonstrate that PR-X EOS can match type I and type IV adsorption isotherms; whereas, PR-C EOS fails to match the type IV adsorption isotherm. Moreover, the phase diagrams calculated using PR-X EOS consistently shrink as pore size decreases, while PR-C EOS cannot guarantee this consistency. These two facts show that PR-X EOS is superior to PR-C EOS in modeling phase behavior of confined hydrocarbons. Furthermore, shale oil reservoir simulation shows that considering the confinement effect would lead to lower GOR.