Phase equilibrium modeling for interfacial tension of confined fluids in nanopores using an association equation of state
Graphical Abstract
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 2DSAFTVR 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 SAFTVR 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: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
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2022, Petroleum ScienceCitation Excerpt :Xiong et al. (2021a) proposed an extended cubic-plus-association EOS to determine the interfacial tensions (IFT) of CH4–CO2–H2O mixtures in shale nanopores. Zhao et al. (2021) calculated the IFT of H2O–CO2 and n-C10H22–CO2 systems in nanopores based on an association EOS. However, these models do not consider the effect of water-oil-gas adsorption on the fluid phase behavior.