Phase equilibrium modeling for interfacial tension of confined fluids in nanopores using an association equation of state

https://doi.org/10.1016/j.supflu.2021.105322Get rights and content

Highlights

  • Two novel interfacial tension models.

  • Application of CPA EoS for interfacial tensions in nanopores.

  • Comparison of three association schemes of H2S.

  • Mutual solubility and interfacial tensions of mixtures in bulk and nanopores.

  • Effects of temperature, pressure and pore radius for interfacial tensions in nanopores.

Abstract

Two novel interfacial tension (IFT) models are presented, and four thermodynamic models—CPA-G, PCPA-G, CPA-P, and PCPA-P—based on the cubic-plus-association (CPA) equation of state and four IFT models are presented to predict the IFTs of fluids in bulk and nanopores. Among three association schemes of H2S that were studied, the 0d-1a association scheme is suitable for predicting mutual solubility of H2S-H2O system. The CPA-G and PCPA-G models can accurately describe the IFTs of H2S-H2O, CO2-H2O, CO2-n-C10H22, and CH4-n-C10H22 systems, whereas the CPA-P and PCPA-P models are inappropriate for IFTs of systems containing H2O. The IFTs of confined fluids in nanopores are lower than those in bulk. Under the same condition, IFTs of confined fluids decrease with an increase in pressure, but increase with the pore radius. Further, the effects of nanoconfinement for IFTs of confined fluids mainly occur at a pore radius below 100 nm.

Introduction

Hydrogen sulfide (H2S)-water (H2O) and carbon dioxide (CO2)-H2O systems play paramount roles in the petroleum industry [1], [2], [3], [4], [5]. Accurate calculations of both the phase equilibria and the interfacial tensions (IFTs) of binary H2S-H2O and CO2-H2O systems are critically important. Therefore, it is necessary to construct a thermodynamic model to investigate the phase behavior of both mutual solubility and IFTs of H2S-H2O and CO2-H2O systems.

Density functional theory (DFT) was presented by Kohn and Sham [6] and used to compute the IFTs of both pure compounds and mixing fluids [7], [8], [9], [10]. Fu et al. [11], [12] proposed a model based on DFT to examine the IFTs of both non-polar and polar substances. Moreover, they established an equation of state (EoS) based on perturbation theory [13] and statistical associating fluid theory (SAFT). Fu et al. [14], [15], [16], [17] modified the DFT model to formulate excess Helmholtz energy functional and predicted the density profiles and IFTs of Lennard-Jones (LJ) fluids in confined spaces. Yu [18] proposed a novel weighted DFT model for the inhomogeneous 12-6 LJ fluids to investigate fluid-solid IFTs. Li et al. [19], [20], [21], [22] constructed a DFT model combined with Peng–Robinson (PR) EoS to examine the IFTs of pure compounds and mixing fluids. Siderius and Gelb [23] introduced a lattice DFT to predict gas adsorption in complex mesopore materials. Sauer and Gross [24] presented a perturbed-chain polar SAFT EoS based on dispersion functional to study both the vapor-liquid equilibria (VLE) and liquid-liquid equilibria (LLE) of confined systems. However, DFT models for modeling complex fluids have high a lot of the computational demand and is not convenient for practical use.

Grand canonical Monte Carlo simulations were used to investigate the IFTs of LJ fluids confined in nanopores [25]. Jin and Firoozabadi [26], [27], [28] investigated the phase equilibria in shale nanopores using various molecular simulations and computed the amount of dissolved molecules. Hoang et al. [29] examined the phase equilibria and the IFTs of non-associating fluids using molecular simulations based on the homonuclear Mie chain model. Brumby et al. [30] studied the IFTs of fluids in planar confinement using Monte Carlo simulation. Feng et al. [31] examined IFT in nanopores using an analytical model based on 12-6 LJ potential function. Although various molecular simulations have been used to calculate the phase equilibria of confined fluids, they have a high computational cost similar to DFTs.

Gradient theory (GT) combined with conventional EoS has been used to calculate the IFTs of fluids. Mejía et al. [32] predict IFTs of mixing fluids using GT and PR EoS. Subsequently, Mejía et al. [33], [34] proposed a model that combined square GT and SAFT-VR Mie EoS to calculate the IFTs of pure fluids. Khosharay et al. [35] proposed a model based on GT combined with simplified PC-SAFT EoS to examine the IFTs of pure CO2, H2S, H2O, and binary mixtures. Oliveira et al. [36] combined GT with cubic-plus-association (CPA) EoS to examine the IFT of non-associating and associating components. Pereira et al. [37] calculated CO2/H2O IFT using GT combined with CPA EoS. However, GT approaches are also complex for calculating IFT in the petroleum industry.

Parachor is a surface-related property [38], [39], [40], and the parachor equation combined with EoS is frequently used to calculate IFTs [41]. Zhang et al. [42], [43], [44] proposed a generalized van der Waals (vdW) EoS combined with parachor equation to investigate the IFTs and adsorption thicknesses of confined fluids in nanopores. Zuo et al. [45] employed a parachor model to determine IFTs between the vapor and liquid phases and proposed a framework to calculate the phase envelopes of shale gas and oil in confined spaces. Liu et al. [46] used a the parachor model to calculate the capillary pressure under nanoconfinement and illustrated that assuming homogeneous distributions in confined space were inappropriate to describe the phase behavior. For inert compounds, IFTs can be calculated by combining EoS with parachor equation [47], [48], [49], whereas this approach is inappropriate for polar mixtures.

A lot of modified EoS have been presented to investigate the phase behavior of confined fluids. Travalloni et al. [50], [51], [52], [53], [54], [55] extended vdW (or PR) EoS to calculate the phase equilibria of pure compounds and mixtures in confined space and predict adsorption isotherms. Martinez et al. [56], [57], [58] presented a 2Dsingle bondSAFTsingle bondVR model based on statistical associating fluid theory for potentials of variable range [59] to describe the adsorption of fluids on solid surfaces and used a new approach to describe the adsorption isotherms for nitrogen and methane on dry activated carbon. Furthermore, Franco et al. [60], [61] extended the SAFTsingle bondVR Mie EoS [62] to calculate the adsorption isotherms of pure substances and mixtures by considering explicitly the residual energy due to the confinement effect.

CPA [63], [64], [65] is an appropriate model to investigate associating fluids. Tsivintzelis et al. [66], [67], [68], [69] examined the phase behavior of acid gas mixtures, including H2S-H2O, CO2-H2O, H2S-CO2, and H2S-alkane systems, using CPA EoS. Xiong et al. [70], [71], [72] examined the VLE of binary H2O-CO2, H2O-methane (CH4), and ternary H2O-CH4-CO2 systems in confined spaces using a generalized CPA EoS. Mohagheghian et al. [73] evaluated the phase behavior of shale gas under nanoconfinement using the equations of critical property shift. Zirrahi et al. [74], [75], [76], [77], [78], [79] investigated H2O and carbon dioxide solubility in reservoir fluids, including n-alkanes, petroleum fractions, bitumen, and heavy crudes, using conventional CPA EoS.

It is difficult to accurately predict the IFTs of associating fluids in bulk and nanopores using a thermodynamic model because the empirical parachor model is ineffective. In this study, four thermodynamic models based on generalized CPA EoS are presented to predict the IFTs of mixtures in bulk and nanopores. First, the IFTs of pure substances in bulk and nanopores are calculated using the CPA EoS combined with parachor model. Second, the mutual solubility for CO2-H2S, H2S-H2O, and CO2-H2O systems is examined using CPA-vdW model, and three association schemes of H2S for H2S-H2O system are investigated. Third, four models are used to calculate the IFTs of mixing fluids. Finally, the effects of temperature, pressure, and pore radius on the IFTs of confined fluids in nanopores are investigated using these models.

Section snippets

CPA EoS

Generalized CPA EoS [70] is used for calculating the VLE and LLE in both bulk and nanopores as follows:P=RTvba(T)v(v+b)12RTv(1+1vlng(1/v))i=1nxiAi(1XAi)where P is the pressure (MPa); T is the temperature (K); R is the universal gas constant; v is the molar volume (cm3 mol-1); g is the radial distribution function; b is the co-volume of CPA EoS; subscript “A” stands for the bonding site; xi is the molar fraction of ith component; XAi is the molar fraction of molecules i not bonded at site

IFTs of pure substances

The IFTs of pure substances are directly related to molar densities in Eq. (3), especially the molar density of the liquid phase. Therefore, the CPA EoS combined with parachor model (PCPA-P) is employed to accurately compute the IFTs of pure substances in bulk and nanopores, and the parameters of this model are listed in Table S4 [91]. The IFTs of several pure substances—CH4, ethane (C2H6), propane (C3H8), n-butane (n-C4H10), n-pentane (n-C5H12), n-hexane (n-C6H14), n-heptane (n-C7H16), n

Conclusions

An interface tension model is derived from Gibbs free energy, and two novel IFT models are presented. Four thermodynamic models, i.e., CPA-G, PCPA-G, CPA-P, and PCPA-P, based on a generalized CPA EoS and four IFT models are presented to predict the interfacial tensions of mixtures in bulk and nanopores.

The three association schemes of H2S for H2S-H2O system were investigated. The 0d-1a association scheme of H2S is suitable for predicting both the VLE and LLE of H2S-H2O system at the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by National Science and Technology Major Project of China during the 13th Five-Year Plan Period (2016ZX05062), National Natural Science Foundation of China (Key Program) (Grant No. 51534006), National Natural Science Foundation of China (Grant No. 51874251 and 51704247), International S&T Cooperation Program of Sichuan Province (Grant No. 2019YFH0169), the Deep Marine Shale Gas Efficient Development Overseas Expertise Introduction Center for Discipline Innovation (111

References (124)

  • S.P. Tan et al.

    Equation-of-state modeling of confined-fluid phase equilibria in nanopores

    Fluid Phase Equilib.

    (2015)
  • S.P. Tan et al.

    Equation-of-state modeling of associating-fluids phase equilibria in nanopores

    Fluid Phase Equilib.

    (2015)
  • M. Tjahjono et al.

    A new modified parachor model for predicting surface compositions of binary liquid mixtures. On the importance of surface volume representation

    J. Colloid Interface Sci.

    (2010)
  • S.P. Tan et al.

    Application of material balance for the phase transition of fluid mixtures confined in nanopores

    Fluid Phase Equilib.

    (2019)
  • K. Zhang et al.

    Confined fluid interfacial tension calculations and evaluations in nanopores

    Fuel

    (2019)
  • Y. Wang et al.

    Validity of the Kelvin equation and the equation-of-state-with-capillary-pressure model for the phase behavior of a pure component under nanoconfinement

    Chem. Eng. Sci.

    (2020)
  • S. Wu et al.

    Influence of confinement effect on recovery mechanisms of CO2-enhanced tight-oil recovery process considering critical properties shift, capillarity and adsorption

    Fuel

    (2020)
  • D.V. Nichita

    Density-based phase envelope construction including capillary pressure

    Fluid Phase Equilib.

    (2019)
  • L. Travalloni et al.

    Thermodynamic modeling of confined fluids using an extension of the generalized van der Waals theory

    Chem. Eng. Sci.

    (2010)
  • L. Travalloni et al.

    Critical behavior of pure confined fluids from an extension of the van der Waals equation of state

    J. Supercrit. Fluids

    (2010)
  • L. Travalloni et al.

    Phase equilibrium of fluids confined in porous media from an extended Peng–Robinson equation of state

    Fluid Phase Equilib.

    (2014)
  • E. Barsotti et al.

    A review on capillary condensation in nanoporous media: implications for hydrocarbon recovery from tight reservoirs

    Fuel

    (2016)
  • G.D. Barbosa et al.

    Cubic equations of state extended to confined fluids: new mixing rules and extension to spherical pores

    Chem. Eng. Sci.

    (2018)
  • S. Luo et al.

    A novel pore-size-dependent equation of state for modeling fluid phase behavior in nanopores

    Fluid Phase Equilib.

    (2019)
  • A. Martínez et al.

    Predicting adsorption isotherms for methanol and water onto different surfaces using the SAFT-VR-2D approach and molecular simulation

    Fluid Phase Equilib.

    (2017)
  • I.S. Araújo et al.

    A model to predict adsorption of mixtures coupled with SAFT-VR Mie Equation of state

    Fluid Phase Equilib.

    (2019)
  • M.B. Oliveira et al.

    Evaluation of the CO2 behavior in binary mixtures with alkanes, alcohols, acids and esters using the Cubic-Plus-Association equation of state

    J. Supercrit. Fluids

    (2011)
  • I. Tsivintzelis et al.

    Modeling phase equilibria for acid gas mixtures using the CPA equation of state. Part II: binary mixtures with CO2

    Fluid Phase Equilib.

    (2011)
  • M.G. Bjørner et al.

    Modeling derivative properties and binary mixtures with CO2 using the CPA and the quadrupolar CPA equations of state

    Fluid Phase Equilib.

    (2016)
  • W. Xiong et al.

    A generalized equation of state for associating fluids in nanopores: application to CO2-H2O, CH4-H2O, CO2-CH4, and CO2-CH4-H2O systems and implication for extracting dissolved CH4 by CO2 injection

    Chem. Eng. Sci.

    (2021)
  • W. Xiong et al.

    Phase equilibrium modeling for methane solubility in aqueous sodium chloride solutions using an association equation of state

    Fluid Phase Equilib.

    (2020)
  • M. Zirrahi et al.

    Prediction of water solubility in petroleum fractions and heavy crudes using cubic-plus-association equation of state (CPA-EoS)

    Fuel

    (2015)
  • M. Zirrahi et al.

    Prediction of CO2 solubility in bitumen using the cubic-plus-association equation of state (CPA-EoS)

    J. Supercrit. Fluids

    (2015)
  • H. Baled et al.

    Prediction of hydrocarbon densities at extreme conditions using volume-translated SRK and PR equations of state fit to high temperature, high pressure PVT data

    Fluid Phase Equilib.

    (2012)
  • A. Péneloux et al.

    A consistent correction for Redlich-Kwong-Soave volumes

    Fluid Phase Equilib.

    (1982)
  • L. Chunxi et al.

    A surface tension model for liquid mixtures based on the Wilson equation

    Fluid Phase Equilib.

    (2000)
  • H. Zhao et al.

    Phase behavior of the CO2–H2O system at temperatures of 273–623 K and pressures of 0.1–200 MPa using Peng-Robinson-Stryjek-Vera equation of state with a modified Wong-Sandler mixing rule: an extension to the CO2–CH4–H2O system

    Fluid Phase Equilib.

    (2016)
  • J.N. Jaubert et al.

    VLE predictions with the Peng–Robinson equation of state and temperature dependent kij calculated through a group contribution method

    Fluid Phase Equilib.

    (2004)
  • W. Xiong et al.

    Phase equilibrium modeling for confined fluids in nanopores using an association equation of state

    J. Supercrit. Fluids

    (2021)
  • P. Théveneau et al.

    Vapor–liquid equilibria of the CH4+CO2+H2S ternary system with two different global compositions: experiments and modeling

    J. Chem. Eng. Data

    (2020)
  • J.N. Jaubert et al.

    Benchmark database containing binary-system-high-quality-certified data for cross-comparing thermodynamic models and assessing their accuracy

    Ind. Eng. Chem. Res.

    (2020)
  • W. Kohn et al.

    Self-consistent equations including exchange and correlation effects

    Phys. Rev.

    (1965)
  • D.W. Oxtoby

    Density functional methods in the statistical mechanics of materials

    Ann. Rev. Mater. Res.

    (2002)
  • J. Wu

    Density functional theory for chemical engineering: from capillarity to soft materials

    AIChE J.

    (2006)
  • C. Ebner et al.

    Density-functional theory of simple classical fluids. I. Surfaces

    Phys. Rev. A

    (1976)
  • R. Evans

    The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids

    Adv. Phys.

    (1979)
  • J.A. Barker et al.

    Perturbation theory and equation of state for fluids. II. A successful theory of liquids

    J. Chem. Phys.

    (1967)
  • D. Fu

    Investigation of excess adsorption, solvation force, and plate-fluid interfacial tension for Lennard-Jones fluid confined in slit pores

    J. Chem. Phys.

    (2006)
  • D. Fu et al.

    Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

    J. Chem. Phys.

    (2006)
  • Y.X. Yu et al.

    Density functional theory for inhomogeneous mixtures of polymeric fluids

    J. Chem. Phys.

    (2002)
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