Phase-Behavior Modeling of Hydrocarbon Fluids in Nanopores Using PR-EOS Coupled with a Modified Young–Laplace Equation

Abstract

The effect of capillary pressure on the vapor–liquid two-phase equilibrium calculation has been extensively studied for the past two decades. However, the calculation accuracy is often weakened by the false assumptions and inherent flaws present in the modeling process. In this work, a modified Young–Laplace equation proposed by Tan and Piri [Tan, S.; Piri, M. Equation-of-State Modeling of Confined-Fluid Phase Equilibria in Nanopores. Fluid Phase Equilibr. 2015, 393, 48–63.] is coupled with volume-translated Peng–Robinson equation of state to study the effect of capillary pressure on the two-phase equilibrium calculation in confined nanopores. In order to successfully apply the modified Young–Laplace equation during the vapor–liquid equilibrium calculation process, this study models the tuning parameter λ in the modified Young–Laplace equation (as proposed by Tan and Piri for perturbed-chain statistical associating fluid theory equation of state) for several pure hydrocarbons and their mixtures by matching experimental data collected from the literature. The tuning parameter λ can be expressed as a unique function for each pure substance or mixture. It is found that the tuning parameter λ shows a quadratic polynomial relationship with temperature, and the value of λ is always less than one. The λ can become negative under certain circumstances, which adjusts the capillary pressure to a lower value. It increases with an increasing pore radius; this is different from the results obtained by Tan and Piri which showed that the tuning parameter λ decreases with an increasing pore radius. The above rules apply to the tuning parameter λ obtained for both pure substances and mixtures. Using the two-phase equilibrium calculation coupled with the modified Young–Laplace equation, the calculated vapor pressures for pure substances and two-phase boundaries for mixtures match very well with the experimental data. Implementation of the modified Young–Laplace equation greatly improves the accuracy of the two-phase equilibrium calculation considering the capillarity effect. Such a modeling strategy could be integrated into a reservoir simulator to conduct more accurate flow simulations for tight/shale reservoirs.

Phase Transition and Criticality of Methane Confined in Nanopores

“…On the modeling side, approaches in the literature include various modified equations of state, which rely on an auxiliary equation, such as the Young–Laplace equation, to account for the nanoconfinement effects. − In some modeling works in petroleum engineering , to describe confined fluids, PCP has been used to replace the bulk critical point in deriving the parameters of cubic EOS. This latter approach has been shown to be incorrect and unable to account for the effects of confinement .…”

Experiments of Vapor–Liquid Phase Transition of Fluids Confined in Nanopores: Implications on Modeling

“…In eq 60, x i and λ i are the mole fraction and λ parameter of the individual component i of the mixture, respectively. The same approach has also been adopted and applied with PR cubic EOS 129 and Cubic Plus Association (CPA) EOS. 130 The obvious drawback of this implicit EOS group is the inability to describe the adsorption prior to capillary condensation, the hysteresis, the liquid-like phase after capillary condensation, and the CPF beyond PCP, even though they may involve some sort of equilibrium with the bulk outside the pores.…”

“…In eq , x i and λ i are the mole fraction and λ parameter of the individual component i of the mixture, respectively. The same approach has also been adopted and applied with PR cubic EOS and Cubic Plus Association (CPA) EOS …”

Study on the Phase Behavior Simulation Method of High-Salinity Reservoirs

“…Under formation conditions, Neshat et al, Achour et al, Wang et al, and Sandoval et al carried outgas–liquid flash calculations through considering the influence of the capillary force. The modified method greatly improves the accuracy of the calculation considering the capillarity effect . In addition, the calculation of phase equilibrium is also well applied under high-pressure conditions such as frozen soil and seabed …”

“…With the deepening of research, some scholars 18−21 have proposed four-phase and multiphase flash calculation methods. Under formation conditions, Neshat et al, 22 Achour et al, 23 Wang et al, 24 and Sandoval et al 25 carried outgas−liquid flash calculations through considering the influence of the capillary force. The modified method greatly improves the accuracy of the calculation considering the capillarity effect.…”