Quantification and Evaluation of Thermodynamic Miscibility in Nanoconfined Space

Abstract

In this paper, thermodynamic miscibility in nanoconfined spaces is quantified and evaluated. First, an analytical generalized equation of state (EOS) is developed by considering the effects of pore radius, molecule–molecule interaction, and molecule–wall interaction at nanometer scale, on the basis of which four extended cubic EOS are proposed. Second, the analytical formulations of the confined fluid free energy of mixing and solubility parameter at nanometer scale are developed thermodynamically. Third, the free energy of mixing and solubility parameter are calculated under different conditions, by means of which the conditions and characteristics of the fluid miscibility at nanometer scale are specifically studied. Finally, two important factors, the temperature and molecule–wall (m–w) interaction, are specifically studied to evaluate and compare their effects on miscibility. The fluid miscibility benefits from the reduction of the pore radius, while the m–w interaction is detrimental to the development of miscibility. Moreover, the molecular size of the single largest molecule in the mixture along with the wall-effect region radius is determined to be the bottom limit of the pore radius, above which fluid miscibility can be achieved and improved by reducing the pore radius. It is found that the solubility parameter is a better quantitative indicator of fluid miscibility; the calculated results from the extended van der Waals, Soave–Redlich–Kwong, and Peng–Robinson EOS are better than those from the extended Redlich–Kwong EOS. Furthermore, a more fluid miscible state is found to be achieved by reducing the temperature and wall-effect region radius. The extent of the effect of temperature on the fluid miscibility of different mixtures can be different. More specifically, the so-called lean gas (i.e., N2, CH4, and CO2)-induced miscibility through the vaporizing process is found to be affected by the temperature to a larger extent in comparison with the rich gas (i.e., C2H6, C3H8, and i- and n-C4H10)-induced miscibility through the condensing–vaporizing process.

Thermodynamic Parameters for Quantitative Miscibility Interpretations from the Bulk to Nanometer Scale

“…The detailed information with respect to the semianalytical correlation can be found in section 4 in the Supporting Information. The mathematical formulation of the interfacial energy (i.e., eq ) can be nanoscale-extended with the nanoscale surface energy, which is demonstrated as in the following In addition, the classic thermodynamic equation of the Gibbs free energy was modified in the previous study and is given here where Δ H is the enthalpy of mixing and Δ S is the entropy of mixing. The Gibbs free energy at the bulk and nanometer scale are obtained by substituting the conventional and nanoscale van der Waals equation of state (vdW EOS) as The specific derivations of the Gibbs free energy at the bulk and nanometer scale are stated in section 5 of the Supporting Information.…”

“…The interfacial energy (ε), which is a measurable parameter of the interfacial interactions, 42 and Gibbs free energy (Δε), which is a thermodynamic property representing the system work, 43 can be used as two quantitative indicators for describing the liquid−liquid and/or liquid−gas miscible state and development. In general, a smaller interfacial energy and Gibbs free energy usually stand for a better miscible state.…”

“…In addition, the classic thermodynamic equation of the Gibbs free energy was modified in the previous study 43 and is given here…”

Diffusion Behavior of Supercritical CO2 in Micro- to Nanoconfined Pores

“…The fluid phase behavior has been proven to be substantially different when the pore radius reduces to the nanometer scale. ,− Therein, the shifts of critical temperature and pressure are considered to be one of the most obvious phase changes, which is related with the ratio of the Lennard-Jones size diameter (σ LJ ) and the pore radius as follows where ; T cpk is the corrected critical temperature in nanopores, K; P cpk is the corrected critical pressure in nanopores, Pa; and r pk is the corrected pore radius, m. It is worthwhile to mention that the corrected average critical temperature and pressure as well as pore radius can be determined from the following equations where f k is the pore distribution frequency from the mercury intrusion test.…”

Main and Interactive Effects of Four Factors on CO2 Storage in Fractured Nanopores

“…For oxyfuel combustion power plants or depleted oil/gas reservoirs, the most common contaminants are nitrogen (N 2 ), oxygen (O 2 ), argon (Ar), and methane (C 1 ), or some alkane solvents. , The vapor–liquid equilibria (VLE) of pure CO 2 and its mixtures with some common impurities aforementioned are of critical importance to the design and operation of many CCS processes, especially for the storage processes. , Since the CO 2 storage process covers various operating conditions from normal atmosphere (surface transportations), to supercritical state (injections), and final high temperature and pressure (storage in deep reservoirs) conditions and involves multiple components, the experimental methods alone are unable to satisfy the complex requirements of the practical applications. Thus, equations of state (EOSs), which are thermodynamic equations relating the state variables that describe the state of matter under a series of physical conditions, − have been employed to predict the VLE of CO 2 and CO 2 mixtures in some previous studies. ,, Different EOSs and their reliabilities and applications for the CCS were conducted in some previous studies. ,, However, most existing studies have focused on the VLE of the CO 2 or CO 2 mixtures in bulk phase, while few studies have been found to study the phase behavior of the CO 2 storage processes in micro-/nanopores of the tight or shale formations. In addition, several important factors, such as the temperature and feed gas to liquid ratio, have long been considered to affect the fluid phase behavior to different extents. , Although some previous studies have been conducted to investigate the phase behavior of the pure CO 2 and its mixtures in bulk phase and nanopores, − most of them are limited to the main effect evaluations.…”