Ten Years with the CPA (Cubic-Plus-Association) Equation of State. Part 2. Cross-Associating and Multicomponent Systems

Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations

H2-CO2 mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H2-CO2 mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H2 due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO2, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO2 content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO2-H2-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO2 and H2 in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO2 in NaCl brine decreased in the ternary system compared to the binary CO2-NaCl brine system, the solubility of H2 in NaCl brine increased less in the ternary system compared to the binary H2-NaCl brine system. The cooperative effect of H2-CO2 enhances the H2 solubility while suppressing the CO2 solubility. The water content in the gas phase was found to be intermediate between H2-NaCl brine and CO2-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO2-H2 mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H2-CO2 mixtures.

Stability of nanoparticle laden aerosol liquid droplets

We develop a model for the thermodynamics and evaporation dynamics of aerosol droplets of a liquid, such as water, surrounded by gas. When the temperature and the chemical potential (or equivalently the humidity) are such that the vapor phase is in the thermodynamic equilibrium state, then, of course, droplets of the pure liquid evaporate over a relatively short time. However, if the droplets also contain nanoparticles or any other non-volatile solute, then the droplets can become thermodynamically stable. We show that the equilibrium droplet size depends strongly on the amount and solubility of the nanoparticles within, i.e., on the nature of the particle interactions with the liquid and, of course, also on the vapor temperature and chemical potential. We develop a simple thermodynamic model for such droplets and compare predictions with results from a lattice density functional theory that takes as input the same particle interaction properties, finding very good agreement. We also use dynamical density functional theory to study the evaporation/condensation dynamics of liquid from/to droplets as they equilibrate with the vapor, thereby demonstrating droplet stability.

Modeling Binary and Multicomponent Systems Containing Supercritical CO2 with Polyethylene Glycols and Compounds Relevant to the Biodiesel Production

The CPA equation of state is applied to model binary, ternary, and multicomponent mixtures that contain CO₂ with polyethylene glycols or compounds relevant to biodiesel production, such as glycerol and various triglycerides. Effort has been made to evaluate the model performance on correlating both the liquid and the vapor phase compositions, which is a demanding task, revealing the model’s and parameters’ limitations, due to the rather low concentrations of heavy compounds in the vapor phase. Initially the model’s binary parameters, which in all cases were temperature independent, were estimated using experimental data for binary systems. Those parameters were used to predict the phase behavior of supercritical CO₂ containing ternary and multicomponent mixtures. Since no parameter was adjusted to ternary or multicomponent systems’ data, the reported CPA results for such mixtures are considered as pure predictions. This is the final part of a series of studies [Tsivintzelis et al. Fluid Phase Equilibria 430 (2016) 75–92 and 504 (2020) 112337] that complete the parameterization of the CPA equation of state for systems relevant to the biodiesel production, which allows the application of the model to multicomponent mixtures of the relevant processes.

Measurements and Modelling of Vapour–Liquid Equilibrium for (H2O + N2) and (CO2 + H2O + N2) Systems at Temperatures between 323 and 473 K and Pressures up to 20 MPa

Understanding the phase behaviour of (CO2 + water + permanent gas) systems is critical for implementing carbon capture and storage (CCS) processes, a key technology in reducing CO2 emissions. In this paper, phase behaviour data for (H2O + N2) and (CO2 + H2O + N2) systems are reported at temperatures from 323 to 473 K and pressures up to 20 MPa. In the ternary system, the mole ratio between CO2 and N2 was 1. Experiments were conducted in a newly designed analytical apparatus that includes two syringe pumps for fluid injection, a high-pressure equilibrium vessel, heater aluminium jacket, Rolsi sampling valves and an online gas chromatograph (GC) for composition determination. A high-sensitivity pulsed discharge detector installed in the GC was used to measure the low levels of dissolved nitrogen in the aqueous phase and low water levels in the vapour phase. The experimental data were compared with the calculation based on the γ-φ and SAFT-γ Mie approaches. In the SAFT-γ Mie model, the like parameters for N2 had to be determined. We also obtained the unlike dispersion energy for the (H2O + N2) system and the unlike repulsive exponent and dispersion energy for the (CO2 + N2) system. This was done to improve the prediction of SAFT-γ Mie model. For the (H2O + N2) binary system, the results show that the solubility of nitrogen in the aqueous phase was calculated better by the γ-φ approach rather than the SAFT-γ Mie model, whereas SAFT-γ Mie performed better for the prediction of the vapour phase. For the (CO2 + H2O + N2) ternary systems, both models predicted the experimental data for each phase with good agreement.

Hybridized method of pseudopotential lattice Boltzmann and cubic-plus-association equation of state assesses thermodynamic characteristics of associating fluids

It is crucial to properly describe the associating fluids in terms of phase equilibrium behaviors, which are needed for design, operation, and optimization of various chemical and energy processes. Pseudopotential lattice Boltzmann method (LBM) appears to be a reliable and efficient approach to study thermodynamic behaviors and phase transition of complex fluid systems. However, when cubic equations of state (EOSs) are incorporated into single-component multiphase LBM, simulation results are not well matched with experimental data. This study presents the utilization of cubic-plus-association (CPA) EOS in the LBM structure to obtain more accurate modeling results for associating fluids. An approach based on the global search optimization algorithm is introduced to find the optimal association parameters of CPA EOS for water and primary alcohols in the lattice units. The thermodynamic consistency is verified by the Maxwell construction and is also improved by the forcing scheme of [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)10.1103/PhysRevE.86.016709]. The spurious velocity is reduced with increasing isotropy in the gradient operator. Furthermore, an extended version of CPA EOS is introduced, which increases the system stability at low reduced temperatures. There is a very good match between the LBM results and experimental data, confirming the reliability of the model developed in the present study. The introduced approach has potential to be employed for simulating transport phenomena and interfacial characteristics of associating fluids in porous systems.

Effect of Ion Valency on the Properties of the Carbon Dioxide-Methane-Brine System

Molecular dynamics simulations and theoretical analysis were carried out to study the bulk and interfacial properties of carbon dioxide-methane-water and carbon dioxide-methane-brine systems under geological conditions. The density gradient theory with the bulk phase properties estimated using the cubic-plus-association (CPA) equation of state (EoS) can well describe the increase in the interfacial tension (IFT) of the CO₂-water system in the presence of methane. The theoretical estimates of species mole fractions in the carbon dioxide-methane-water system are in good quantitative agreement with the experimental results. Furthermore, simulations of carbon dioxide-methane-brine system show that the IFT of the CaCl₂ case is generally higher than that of the NaCl case. This is probably due to the stronger hydration of Ca²⁺ ions and their stronger repulsion from the interface compared to Na⁺. While the overall shape of the ionic profiles is not much affected by the ion type, the water profiles show a local enrichment at the interface in the system with CaCl₂. In contrast to the case of NaCl, the slopes of the plots of IFT vs CaCl₂ concentration are dependent on temperature. Species mole fractions in the carbon dioxide-methane-brine system predicted by combining the CPA EoS with the Debye-Hückel electrostatic term are in good agreement with simulation results.

Review and selection criteria of classical thermodynamic models for acid gas absorption in aqueous alkanolamines

The knowledge of vapour-liquid equilibrium (VLE) and thermodynamic properties plays a pivotal role in the process development of absorption systems for acid gas capture in precombustion and postcombustion streams. A large number of thermodynamic modelling approaches for acid gas absorption in aqueous alkanolamine solutions are published in the literature. However, the reviews of these modelling techniques are limited and scattered. Moreover, poor guidelines exist for the selection of an appropriate modelling approach for the VLE prediction of the aforementioned system. Therefore, the current study presents a concise classification and review of classical thermodynamic models for acid gas absorption in aqueous alkanolamine solutions since their inception. The article systematically details the chronological development and highlights the major capabilities and limitations of classical thermodynamic approaches, namely, semiempirical models, activity coefficient models, and equation of state (and equation of state/excess Gibbs energy) models. A graphical comparison of VLE prediction by each classical approach is presented to form a general guideline in the selection of a suitable approach for process development studies. The review precisely discusses the issues, challenges, and future prospects of each classical thermodynamic approach in the context of application, complexity, and development.