Equations of state for the calculation of fluid-phase equilibria

Hydrocarbon Extraction with Ionic Liquids

Separation and reaction processes are key components employed in the modern chemical industry, and the former accounts for the majority of the energy consumption therein. In particular, hydrocarbon separation and purification processes, such as aromatics extraction, desulfurization, and denitrification, are challenging in petroleum refinement, an industrial cornerstone that provides raw materials for products used in human activities. The major technical shortcomings in solvent extraction are volatile solvent loss, product entrainment leading to secondary pollution, low separation efficiency, and high regeneration energy consumption due to the use of traditional organic solvents with high boiling points as extraction agents. Ionic liquids (ILs), a class of designable functional solvents or materials, have been widely used in chemical separation processes to replace conventional organic solvents after nearly 30 years of rapid development. Herein, we provide a systematic and comprehensive review of the state-of-the-art progress in ILs in the field of extractive hydrocarbon separation (i.e., aromatics extraction, desulfurization, and denitrification) including (i) molecular thermodynamic models of IL systems that enable rapid large-scale screening of IL candidates and phase equilibrium prediction of extraction processes; (ii) structure-property relationships between anionic and cationic structures of ILs and their separation performance (i.e., selectivity and distribution coefficients); (iii) IL-related extractive separation mechanisms (e.g., the magnitude, strength, and sites of intermolecular interactions depending on the separation system and IL structure); and (iv) process simulation and design of IL-related extraction at the industrial scale based on validated thermodynamic models. In short, this Review provides an easy-to-read exhaustive reference on IL-related extractive separation of hydrocarbon mixtures from the multiscale perspective of molecules, thermodynamics, and processes. It also extends to progress in IL analogs, deep eutectic solvents (DESs) in this research area, and discusses the current challenges faced by ILs in related separation fields as well as future directions and opportunities.

An intermolecular potential for hydrogen: Classical molecular simulation of pressure-density-temperature behavior, vapor-liquid equilibria, and critical and triple point properties

An intermolecular potential is reported for molecular hydrogen that combines two-body interactions from ab initio data with three-body interactions. The accuracy of the two-body potential is validated by comparison with experimental second virial coefficient data. Experimental pressure-density-temperature data are used to validate the addition of three-body interactions, often yielding very accurate predictions. Classical Monte Carlo simulations that neglect quantum effects are reported for the vapor-liquid equilibria (VLE), critical properties, and the triple point. A comparison with experimental data indicates that the effect of quantum interactions is to narrow the VLE phase envelope and to lower the critical temperature. The three-body interactions have a considerable influence on the phase behavior, resulting in good agreement with the experimental density. The critical properties of the two-body + three-body potential for hydrogen provide an alternative set of input parameters to improve the accuracy of theoretical predictions at temperatures above 100 K. In the vicinity of the critical point, the coexistence densities do not obey the law of rectilinear diameters, which is a feature that has largely been overlooked in both experimental data and reference equations of state.

Development of thermodynamically consistent machine-learning equations of state: Application to the Mie fluid

A procedure for deriving thermodynamically consistent data-driven equations of state (EoS) for fluids is presented. The method is based on fitting the Helmholtz free energy using artificial neural networks to obtain a closed-form relationship between the thermophysical properties of fluids (FE-ANN EoS). As a proof-of-concept, an FE-ANN EoS is developed for the Mie fluids, starting from a database obtained by classical molecular dynamics simulations. The FE-ANN EoS is trained using first- (pressure and internal energy) and second-order (e.g., heat capacities, Joule-Thomson coefficients) derivative data. Additional constraints ensure that the data-driven model fulfills thermodynamically consistent limits and behavior. The results for the FE-ANN EoS are shown to be as accurate as the best available analytical model while being developed in a fraction of the time. The robustness of the "digital" equation of state is exemplified by computing physical behavior it has not been trained on, for example, fluid phase equilibria. Furthermore, the model's internal consistency is successfully assessed using Brown's characteristic curves.

Predictive Modeling of Phase Behavior of Reservoir Fluids under Miscible Gas Injection Using the Peng-Robinson Equation of State and the Aromatic Ring Index

Improved correlations among critical temperature, critical pressure, and acentric factor are developed for an extensive database of hydrocarbons. The correlations rely on measurements of molecular weight and refractive index at ambient conditions and utilize the concept of the aromatic ring index (ARI) recently developed by Abutaqiya et al. as a distinctive characterization factor for nonpolar hydrocarbons [Abutaqiya M. I. L.Aromatic Ring Index (ARI): A Characterization Factor for Nonpolar Hydrocarbons from Molecular Weight and Refractive Index. Energy Fuels2021, 35( (2), ), 1113-1119.]. The new correlations are then implemented for modeling the phase behavior of a variety of oils under miscible gas injection in a fully predictive manner using the Peng-Robinson equation of state (PR EOS). The results indicate that the proposed modeling framework yield accurate predictions for bubble pressure of oil/gas blends with an average absolute deviation of 6.4% for a wide variety of oils and injection gases including lean, rich, H₂S, CO₂, and N₂. Additionally, an interesting crossover behavior in the phase envelope of live oils under CO₂ injection is observed using PR EOS. This behavior has been previously reported in the literature for modeling results using PC-SAFT EOS and seems to be characteristic of CO₂.

A Simple Equation for the Free Energy of Liquids

A simple, three-parameter equation is proposed for the free energy of classical fluids composed of molecules which are not hydrogen bonded. Agreement with experiment is much the same as has been obtained from more complicated three-parameter equations. For spherical and nearly spherical molecules, semiquantitative relations between intermolecular pair potential parameters and the parameters of the proposed equation were found. For alkanes, relations between the parameters and carbon number were noted. These relationships contribute to the understanding of fluid state properties in terms of the properties of the molecules of which they are composed.

Interatomic Interactions Responsible for the Solid-Liquid and Vapor-Liquid Phase Equilibria of Neon

The role of interatomic interactions on the solid-liquid and vapor-liquid equilibria of neon is investigated via molecular simulation using a combination of two-body ab initio, three-body, and quantum potentials. A new molecular simulation approach for determining phase equilibria is also reported and a comparison is made with the available experimental data. The combination of two-body plus quantum influences has the greatest overall impact on the accuracy of the prediction of solid-liquid equilibria. However, the combination of two-body + three-body + quantum interactions is required to approach an experimental accuracy for solid-liquid equilibria, which extends to pressures of tens of GPa. These interactions also combine to predict vapor-liquid equilibria to a very high degree of accuracy, including a very good estimate of the critical properties.

Generalized equation of state for fluids: From molecular liquids to colloidal dispersions

In this work, a new parameterization for the Statistical Association Fluid Theory for potentials of Variable Range (SAFT-VR) is coupled to the discrete potential theory to represent the thermodynamic properties of several fluids, ranging from molecular liquids to colloidal-like dispersions. In this way, this version of the SAFT-VR approach can be straightforwardly applied to any kind of either simple or complex fluid. In particular, two interaction potentials, namely, the Lennard-Jones and the hard-core attractive Yukawa potentials, are discretized to study the vapor-liquid equilibrium properties of both molecular and complex liquids, respectively. Our results are assessed with Monte Carlo computer simulations and available and accurate theoretical results based on the self-consistent Ornstein-Zernike approximation.

Effect of the range of particle cohesion on the phase behavior and thermodynamic properties of fluids

Molecular simulations are performed for the (m + 1, m) potential to systematically investigate the effect of changing the range of particle cohesion on both vapor-liquid equilibria and thermodynamic properties of fluids. The results are reported for m = 4-11, which represent a progressive narrowing of the potential energy well. The conventional Lennard-Jones potential is used as a reference point for normal fluid behavior. Small values of m result in a broadening of the phase envelope compared with the Lennard-Jones potential, whereas a contraction is observed in other cases. The critical properties are reported, and a relationship between the critical temperature and the Boyle temperature is determined. The low values of the critical compressibility factor when m < 6 reflect the behavior observed for real fluids such as n-alkanes. The results for supercritical thermodynamic properties are much more varied. Properties such as pressure, potential energy, isochoric thermal pressure coefficient, and thermal expansion coefficient vary consistently with m, whereas other properties such as the Joule-Thomson coefficient exhibit much more nuanced behavior. Maximum and minimum values are reported for both the isochoric heat capacity and isothermal compressibility. A minimum in the speed of sound is also observed.

Automated Pressurized Liquid Extraction of Microbial Lipids from Oleaginous Yeasts

The lipids produced by oleaginous microbes are considered sustainable resources for biofuels. To facilitate controlled lipid production and lipid analysis, more efficient lipid extraction methods are required. This study describes the automated pressurized liquid extraction (APLE) method for lipid extraction from dried cells of the oleaginous yeast species Rhodosporidium toruloides and Cryptococcus curvatus. Cells were mixed with diatomite in a mortar, added to the sample chamber, and treated with a mixture of chloroform and methanol at 105 °C. More than 95% lipids were extracted. Analysis by using high-performance thin-layer chromatography showed that the neutral lipid contents in the obtained samples by APLE method were similar to those by the ball milling-assisted extraction method. The lipids had an essentially identical fatty acid composition compared with lipids extracted with the acid-heating extraction (AHE) method. This demonstrated that lipids can be efficiently extracted from oleaginous yeasts in less time and without harsh pretreatment procedures.

Thermodynamic properties and anomalous behavior of double-Gaussian core model potential fluids

The structural, thermodynamic, and vapor-liquid equilibria properties of the double-Gaussian core model (DGM) potential are studied via molecular simulation. Results are presented for the pressure (p), potential energy (U), isochoric and isobaric heat capacities (C_{V,p}), isothermal compressibility (β_{T}), isochoric thermal pressure coefficient (γ_{V}), thermal expansion coefficient (α_{p}), speed of sound (ω_{0}), and the Joule-Thomson coefficient (μ_{JT}), which are compared with simulations for the Gaussian core model (GCM) potential. A feature of the simulations is that both the GCM and DGM potentials reproduce many of the anomalous properties of water, such as a maximum density, γ_{V}<0, maximum values for both α_{p} and β_{T}, and minimum values in both C_{p} and ω_{0}. The presence of attractive interaction enhances the anomalies and also yields some additional features such as a more structured vapor phase and Joule-Thomson inversion.

Application of the group contribution volume translated Peng-Robinson equation of state to new commercial refrigerant mixtures

This work evaluates the performance of the group contribution volume translated Peng-Robinson model when predicting the vapor-liquid equilibrium and single phase densities of 28 commercial refrigerant mixtures with low global warming potential and zero ozone depletion potential. Cubic equations of state, and particularly the Peng-Robinson equation of state, are widely used in the refrigeration industry due to their easy applicability for new substances, and their low computational time, although generally lower prediction accuracies must be expected compared to multiparameter equations of state. The group contribution volume translated Peng-Robinson equation of state combines the Peng-Robinson equation of state with a new attraction term, improved mixing rules using a group contribution approach, and volume translation. The results are compared with the estimates obtained using the non translated Peng-Robinson equation of state, and a multiparameter equation of state.

Nematic-isotropic transition in a density-functional theory for hard spheroidal colloids

We introduce a density-functional formalism based on the Parsons-Lee and the generalized van der Waals theories in order to describe the thermodynamics of anisotropic particle systems with steric interactions. For ellipsoids of revolution, the orientational distribution function is obtained by minimizing the free energy functional and the equations of state are determined. The system exhibits a nematic-isotropic discontinuous transition, characterized by a phase separation between nematic and isotropic phases at finite as well low packing fractions. The model presents a phase behavior which is in good agreement with Monte Carlo simulations for finite aspect ratios.

Simulation of High Pressure Separator Used in Crude Oil Processing

The aim of this research was to simulate a high-pressure (HP) separator in order to investigate the effect of changing separator operating conditions on product properties. In this study, the results obtained using the CHEMCAD simulation software package were compared with those obtained using the UniSim software package. The simulation results were comparable with industrial data. A sensitivity study was conducted by changing the gas stream properties, such as temperature, pressure, and flow rate, in order to investigate and optimize the process. The results showed that increasing the separator inlet pressure from 30 to 80 bar decreased the outlet gas flow rate from 1202 to 871.15 kmol/h. Also, the methane mole fraction increased from 0.69 to 0.74; however, the preheater heating duty was increased from 8.71 to 11.48 GJ/h. The simulation results showed that increasing the temperature of the separator feed stream from 43 to 83 °C increased the flow rate of the outlet gas stream from 871.15 to 1142.98 kmol/h. However, this temperature change reduced the methane concentration in the gas product and decreased the heating duty of the heat exchanger. Finally, the study demonstrated that there is no effect of increasing the inlet feed flow rate on the produced methane gas concentration.

Quasi-Chemical PC-SAFT: An Extended Perturbed Chain-Statistical Associating Fluid Theory for Lattice-Fluid Mixtures

In this study, a new modification of the perturbed chain-statistical associating fluid theory (PC-SAFT) has been proposed by incorporating the lattice fluid theory of Guggenheim as an additional term to the original PC-SAFT terms. As the proposed model has one more term than the PC-SAFT, a new mixing rule has been developed especially for the new additional term, while for the conventional terms of the PC-SAFT, the one-fluid mixing rule is used. In order to evaluate the proposed model, the vapor-liquid equilibria were estimated for binary CO₂ mixtures with 16 different ionic liquids (ILs) of the 1-alkyl-3-methylimidazolium family with various anions consisting of bis(trifluoromethylsulfonyl) imide, hexafluorophosphate, tetrafluoroborate, and trifluoromethanesulfonate. For a comprehensive comparison, three different modes (different adjustable parameters) of the proposed model were compared with the conventional PC-SAFT. Results indicate that the proposed modification of the PC-SAFT EoS is generally more reliable with respect to the conventional PC-SAFT in all the three proposed modes of vapor-liquid equilibria, giving good agreement with literature data.

Similarity law for Widom lines and coexistence lines

The coexistence line of a fluid separates liquid and gaseous states at subcritical pressures, ending at the critical point. Only recently, it became clear that the supercritical state space can likewise be divided into regions with liquidlike and gaslike properties, separated by an extension to the coexistence line. This crossover line is commonly referred to as the Widom line, and is characterized by large changes in density or enthalpy, manifesting as maxima in the thermodynamic response functions. Thus, a reliable representation of the coexistence line and the Widom line is important for sub- and supercritical applications that depend on an accurate prediction of fluid properties. While it is known for subcritical pressures that nondimensionalization with the respective species critical pressures p_{cr} and temperatures T_{cr} only collapses coexistence line data for simple fluids, this approach is used for Widom lines of all fluids. However, we show here that the Widom line does not adhere to the corresponding states principle, but instead to the extended corresponding states principle. We resolve this problem in two steps. First, we propose a Widom line functional based on the Clapeyron equation and derive an analytical, species specific expression for the only parameter from the Soave-Redlich-Kwong equation of state. This parameter is a function of the acentric factor ω and compares well with experimental data. Second, we introduce the scaled reduced pressure p_{r}^{*} to replace the previously used reduced pressure p_{r}=p/p_{cr}. We show that p_{r}^{*} is a function of the acentric factor only and can thus be readily determined from fluid property tables. It collapses both subcritical coexistence line and supercritical Widom line data over a wide range of species with acentric factors ranging from -0.38 (helium) to 0.34 (water), including alkanes up to n-hexane. By using p_{r}^{*}, the extended corresponding states principle can be applied within corresponding states principle formalism. Furthermore, p_{r}^{*} provides a theoretical foundation to compare Widom lines of different fluids.

Helmholtz Energy Transformations of Common Cubic Equations of State for Use with Pure Fluids and Mixtures

Comprehensive sets of derivatives of Helmholtz energy transformations of several common cubic equations of state are presented. These derivatives can be used for implementing cubic equations of state into complex multi-fluid mixture models when no multiparameter equation of state is available for a mixture component. Thus, pure fluids (or mixtures) for which no accurate model exists in literature can be modeled with a relatively small set of fluid property data. Composition derivatives have been calculated for the cases where the last mole fraction is either an independent or dependent variable. Analytic derivatives are presented up to fourth order in the independent variables combined with composition derivatives up to third order; this set covers the common requirements for derivatives needed in the state-of-the-art thermophysical property libraries. A C++ implementation of the presented analyses, data for computer code validation, and information about the computer algebra tools used to calculate the intermediate derivatives are provided as supplementary information.