Comparison of activity coefficient models for electrolyte systems

Three activity coefficient models for electrolyte solutions were evaluated and compared. The activity coefficient models are: The electrolyte NRTL model (ElecNRTL) by Aspentech, the mixed solvent electrolyte model (MSE) by OLI Systems, and the Extended UNIQUAC model from the Technical University of Denmark (DTU). Test systems containing a single salt (NaCl), multiple salts, and mixed solvent aqueous electrolyte solutions were chosen. The performance of the activity coefficient models were compared regarding the accuracy of solid–liquid and vapor–liquid equilibrium calculations for the test systems. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Predicting NRTL binary interaction parameters from molecular simulations

A predictive approach for calculating the binary interaction parameters ( ) of the nonrandom two liquid (NRTL) local composition model is developed, combining molecular simulations with the two‐fluid theory. The binary interaction parameters are determined for the following three sets of model binary mixtures: water + methanol, methanol + methyl acrylate, and water + methyl acrylate. For each binary mixture, the interaction parameters are expressed in terms of molecular size and strength of interactions, which are in turn, calculated from molecular simulations. We show that the binary interaction parameters determined from simulations are in qualitative agreement with those estimated from regressing experimental data. The major factors that determine the binary interaction parameters are outlined based on simple thermodynamic arguments for each mixture. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2758–2769, 2018     

An electrolyte CPA equation of state for mixed solvent electrolytes

Despite great efforts over the past decades, thermodynamic modeling of electrolytes in mixed solvents is still a challenge today. The existing modeling frameworks based on activity coefficient models are data‐driven and require expert knowledge to be parameterized. It has been suggested that the predictive capabilities could be improved through the development of an electrolyte equation of state. In this work, the Cubic Plus Association (CPA) Equation of State is extended to handle mixtures containing electrolytes by including the electrostatic contributions from the Debye–Hückel and Born terms using a self‐consistent model for the static permittivity. A simple scheme for parameterization of salts with a limited number of parameters is proposed and model parameters for a range of salts are determined from experimental data of activity and osmotic coefficients as well as freezing point depression. Finally, the model is applied to predict VLE, LLE, and SLE in aqueous salt mixtures as well as in mixed solvents. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2933–2950, 2015     

Predicting phase behavior in aqueous systems without fitting binary parameters II: Gases and non‐aromatic hydrocarbons

This investigation continues a series of studies evaluating the capability of the recently proposed CP‐PC‐SAFT and sPC‐SAFT of Liang et al. to estimate the thermodynamic properties of aqueous systems in the entirely predictive manner. Similarly to the previously considered systems, CP‐PC‐SAFT remains a realistic estimator of the available data on critical loci, high pressure‐high temperature phase equilibria and volumetric properties also in the cases of non‐polar gases and non‐aromatic hydrocarbons from argon and nitrogen till n‐eicosane and squalene while keeping zero values of binary parameters. Nevertheless, such application of the model poses certain unavoidable compromises on its accuracy. Inter alia, CP‐PC‐SAFT is a particularly inaccurate estimator of the water‐rich liquid phases away from the critical points. sPC‐SAFT predicts these data in a more reliable manner. Moreover, its predictive capability goes beyond the liquid phases and it exhibits a remarkable accuracy in forecasting various phase equilibria below the critical point of water. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Predicting phase behavior in aqueous systems without fitting binary parameters I: CP‐PC‐SAFT EOS,aromatic compounds

This study examines an accuracy of CP‐PC‐SAFT attached by the 4C cross‐association scheme and zero values of binary parameters in predicting the high temperature‐high pressure phase behavior in aqueous systems of aromatic compounds containing one and two benzoic rings, CO₂ and cis‐decalin. In spite of the noteworthy complexity of these systems and the entirely predictive nature of the current approach, it correctly predicts the topology of phase behavior and typically yields the quantitatively accurate estimations of critical loci and the hydrocarbon–rich liquid phases in wide range of conditions. The available single phase volumetric data are also predicted accurately. Unfortunately, it is not a case of the water–rich phases exhibiting very small hydrocarbon concentrations. Nevertheless, the model is still capable of capturing the solubility minima characteristic for these phases around the room temperature. Predictions of the recent version of Simplified PC‐SAFT proposed by Liang et al. (2014) are also discussed. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4124–4135, 2017     

Nonrandom two-liquid activity coefficient model with association theory

Considered one of the most versatile and widely used classical thermodynamic models to correlate phase equilibria behavior of nonideal systems, the nonrandom two-liquid (NRTL) theory does not explicitly account for specific chemical associations such as hydrogen bonding. This deficiency has been recognized as the cause for unsatisfactory representation of association systems like methanol–alkanes binaries. This work presents a practical approach to integrate Wertheim's perturbation theory for association contribution with the classical NRTL model. Specifically, the association contribution is calculated from pre-determined molecule-specific association strengths while the physical interaction contribution is captured with NRTL binary interaction parameters. The resulting association NRTL model correlates fluid phase equilibria of association systems with few adjustable parameters and offers improved predictive capability for higher order systems.     

Calculations of complex phase equilibrium by equal‐area method

The equal‐area (EA) method is studied with respect to its applicability to a wide range of phase equilibrium scenarios for pure fluids and binary mixtures. The study covers vapor‐liquid equilibrium (VLE), liquid–liquid equilibrium (LLE), solid‐liquid equilibrium (SLE) and their crossover transitions. The thermodynamic models studied include equation of state, activity coefficient and solid solubility models and their combinations. The performance of the EA method for chain molecules, at very low temperature and nearby the critical point is also investigated. We conclude that the EA method is very reliable and efficient and has a number of advantages over the conventional method. Finally, we apply the EA method to the regression of the model parameters to demonstrate its attractive application. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Phase equilibria and structural properties of thiophene/[Bmim][BF4]: A molecular insight from monte carlo simulations

The phase equilibria of thiophene in 1‐butyl‐3‐methylimidazolium tetrafluoroborate ([Bmim][BF₄]) is calculated by Monte Carlo simulation in Gibbs ensemble using a united atom force field. The liquid density of studied ionic liquid and the vapor pressure of thiophene in [Bmim][BF₄] were compared with corresponding experimental data reported in the literature, and a good agreement was obtained. In order to describe the solubility of thiophene in this ionic liquid, we have calculated the radial distribution functions and spatial distribution functions of thiophene/IL mixtures to study the interaction of thiophene with cations and anions of [Bmim][BF₄] in the liquid phase. The local composition concept in fluid was also examined to give further insight into the liquid structure. The results show that thiophene is well organized around the terminal carbon atom of the butyl or methyl chain attached to the imidazolium ring of cations and tends to adopt a symmetrically distribution on the anions. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3916–3924, 2014     

A modified perturbed chain-statistical associating fluid theory equation of state for water which includes an association dependent hard sphere diameter

The concept of an association dependent hard sphere diameter is introduced as a means to obtain an accurate perturbed chain-statistical associating fluid theory (PC-SAFT) equation of state model for water. The new approach is demonstrated to be a step change in accuracy for the representation of pure water properties as compared with standard PC-SAFT applications. Extension of the approach to mixtures is discussed.     

Predictive molecular thermodynamic models for ionic liquids

Predictive molecular thermodynamic models can bridge the gap between the microscopic molecular level and macroscopic system scale. Over the past few decades, ionic liquids (ILs), as a class of green solvents and functional materials, have received widespread research interest in the field of chemical processing owing to their unique physicochemical merits. This review aims to provide an easy-to-read and exhaustive reference regarding state-of-the-art predictive thermodynamic models for ILs, with more focuses on UNIFAC- and COSMO-based models and various applications involving phase equilibrium prediction, guidance for IL screening and design, and building equilibrium stage models for separation processes. This review provides a theoretical perspective on the structure–property relationships between molecular structures and phase behaviors for the systems and the constituted components covering a multi-scale viewpoint from molecular level to industrial scale. Moreover, the predictive capacities of different thermodynamic models are comprehensively compared.     

水盐体系汽液平衡的热力学模型研究

水盐体系的相平衡性质是化工单元操作的基础,在化学化工、海洋、地质等领域有着重要的研究价值。国内外许多学者对水盐体系汽液平衡进行了实验和理论的研究,构筑了各具特色的经验和半经验的模型。针对水盐体系,在NRTL理论的基础上,基于水化作用和混合盐假设建立了能够预测混合体系汽液平衡的活度系数扩展模型。通过对21组二元水盐体系和14组混合体系的关联计算,验证了该模型的可行性;同时,该模型可以采用二元体系参数直接预测计算混合水盐体系汽液平衡。     

Predicting the thermodynamic properties and dielectric behavior of electrolyte solutions using the SAFT‐VR+DE equation of state

We extend the SAFT‐VR+DE equation of state to describe 19 aqueous electrolyte solutions with both a fully dissociated and a partially dissociated model. The approach is found to predict thermodynamic properties such as the osmotic coefficient, water activity coefficient, and solution density, across different salt concentrations at room temperature and pressure in good agreement with experiment using only one or two fitted parameters. At higher temperatures and pressures, without any additional fitting, the theory is found to be in qualitative agreement with experimental mean ionic activities and osmotic coefficients. The behavior of the dielectric constant as a function of salt concentration is also reported for the first time using a statistical associating fluid theory (SAFT)‐based equation of state. At high salt concentrations, the stronger electrostatic interactions between the ionic species due to the dielectric decrement, is captured through the inclusion of ion association. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3053–3072, 2015     

Future directions in physiochemical modeling of the thermodynamics of polyelectrolyte coacervates

We review theories of polyelectrolyte (PE) coacervation, which is the spontaneous association of oppositely charged units of PEs and phase separation into a polymer-dense phase in aqueous solution. The simplest theories can be divided into “physics-based” and “chemistry-based” approaches. In the former, PEs are treated as charged, long-chain, molecules, defined by charge level, chain length, and chain flexibility, but otherwise lacking chemical identity, with electrostatic interactions driving coacervation. The “chemistry-based” approaches focus on the local interactions between the species for which chemical identity is critical, and describe coacervation as the result of competitive local binding interactions of monomers and salts. In this article, we show how these approaches complement each other by presenting recent approaches that take both physical and chemical effects into account. Finally, we suggest future directions toward producing theories that are made quantitatively predictive by accounting for both long range electrostatic and local chemically specific interactions.     

Thermodynamics of protein aqueous solutions: From the structure factor to the osmotic pressure

An analytical expression for the structure factor for globular proteins in aqueous solution is presented. This expression was obtained considering a potential given by the sum of a hard core, a van der Waals attractive, and a screened Coulomb contribution. Experimental data of small angle x‐ray scattering for bovine serum albumin (BSA) in aqueous solutions containing sodium salts at different protein concentrations and pH values are also presented. The developed expression for the structure factor describes accurately these experimental data provided a dependence of the attractive parameter on protein concentration is established. An expression for the osmotic pressure was derived from the structure factor. With attractive parameters adjusted from x‐ray scattering data, the osmotic pressure of BSA aqueous solutions could be predicted with very good agreement with experimental data. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2871–2880, 2015     

Understanding cubic equations of state: A search for the hidden clues of their success

This work investigates the hidden details that are responsible for the practical success of cubic equations of state (EOS) in phase equilibrium calculations. A detailed consideration of the van der Waals method for evaluating the pure compound EOS parameters sheds new light on the reasons why the elimination of the actual critical volume as parameter was also adopted in the Redlich–Kwong and the Peng–Robinson (PR) frameworks. It is shown that an interesting relationship for the critical compressibility factor arising from the Martin–Hou method opens a new door for future exploration of different frameworks. A consideration of the key steps of Soave's reasoning for determining the temperature dependence of the attractive parameter explains the larger success of the Stryjek–Vera modification of PR EOS over the PR EOSs. A reference to the extension of cubic EOS to calculate liquid densities and enthalpies and a ready to use algorithm for the evaluation of the roots of a cubic equation are included for instructional purposes. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2824–2831, 2015     

Interfacial tensions of industrial fluids from a molecular‐based square gradient theory

This work reports a procedure for predicting the interfacial tension (IFT) of pure fluids. It is based on scaling arguments applied to the influence parameter of the van der Waals theory of inhomogeneous fluids. The molecular model stems from the application of the square gradient theory to the SAFT‐VR Mie equation of state. The theory is validated against computer simulation results for homonuclear pearl‐necklace linear chains made up to six Mie (λ ? 6) beads with repulsive exponents spanning from λ = 8 to 44 by combining the theory with a corresponding states correlation to determine the intermolecular potential parameters. We provide a predictive tool to determine IFTs for a wide range of molecules including hydrocarbons, fluorocarbons, polar molecules, among others. The proposed methodology is tested against comparable existing correlations in the literature, proving to be vastly superior, exhibiting an average absolute deviation of 2.2%. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1781–1794, 2016     

Multiphase isenthalpic flash: General approach and its adaptation to thermal recovery of heavy oil

Isenthalpic flash is a basic equilibrium calculation in process simulation. The recent interest in isenthalpic multiphase flash is mainly caused by the need for simulating thermal recovery of heavy oil. We present here systematic solutions to multiphase isenthalpic flash with full thermodynamics (such as EoS models) or with correlations for K-factors, and discuss how to tailor the general methods to systems encountered in thermal recovery of heavy oil. First, for the general situation with full thermodynamics we recommend a solution strategy which uses Newton's method for rapid convergence in the majority of cases and Q-function maximization to safeguard convergence when Newton's method fails. The solution procedure is a generalization of Michelsen's state function based two-phase flash to multiple phases. The general solution does not need special considerations for the components in the system and is not limited to the selected thermodynamic models and the number of phases. For thermal recovery processes where gas, oil, and aqueous phases are typically involved, the stability analysis and initialization steps are tailored to improve the efficiency. Second, as it is quite common in thermal reservoir simulators to describe phase equilibrium and heat properties with temperature-dependent K-factors and separate correlations for heat capacities, we propose a formulation as an extension of the ideal solution isothermal flash formulation to solve such problems. It uses a Newton–Raphson procedure to converge in the majority of cases and a nested loop procedure with the outer loop for a temperature search as a fallback approach for convergence. If the correlations for K-factors and for heat capacities are thermodynamically consistent, the outer loop can be treated as a maximization. Finally, we present systematic tests of the proposed algorithms using examples with full thermodynamics or K-factor based thermodynamics. The algorithms prove robust and efficient even in challenging cases including a narrow-boiling system, a degenerate system, and a four-phase system. The additional computational cost relative to the corresponding isothermal flash is modest and would be suitable for the purpose of thermal reservoir simulation. © 2018 American Institute of Chemical Engineers AIChE J, 65: 281–293, 2019     

A molecular design method based on the COSMO‐SAC model for solvent selection in ionic liquid extractive distillation

In this study, a molecular design method was used to select solvents for extractive distillation. A COSMO‐SAC model was used to screen for prospective solvents from a wide variety of ionic liquids for extractive distillation. Based on the COSMO‐SAC model, the σ‐profile database of ILs was established. Selectivity and solubility were used as the indexes for solvent screening. According to the molecular design method, three suitable extractive distillation solvents were determined for acetonitrile‐water and ethanol‐cyclohexane systems. Vapor ‐ liquid equilibrium experiment were used to test chosen ILs. This study showed that the experimental and design results were consistent with each other. Therefore, this method is effective and applicable to pick ILs solvents for extractive distillation, and the results could provide a theoretical foundation for industrial production. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2853–2869, 2016