Description Of Phase Equilibria Research Articles

Method for determining estimates of random variable models for describing phase equilibrium in rectification processes

The phase equilibrium modeling for multi-component systems is essential in process systems engineering. In particular, phase stability analysis, Gibbs free energy minimization and estimation of parameters in thermodynamic models are challenging global optimization problems involved in phase equilibrium calculations and modeling for both reactive and non-reactive systems. To date, many significant works have been performed in the area of global optimization, and several algorithms and computational contributions of global optimization have been used for solving these problems; global optimization methods used include both deterministic and stochastic algorithms. To the best of our knowledge, there is no review in the literature that focuses on the global optimization methods and their applications to phase equilibrium modeling and calculations. In this paper, we briefly describe the deterministic and stochastic optimization algorithms selected for our rectification process, and then consider their use for phase stability analysis, Gibbs free energy minimization, and parameter estimation in phase equilibrium models. In short, we present an overview of global optimization for modeling and computing the phase behavior of systems with and without chemical reactions, including the prediction of azeotropes and critical points.

Multiplicities in thermodynamic activity coefficients

AbstractThermodynamic activity coefficients play an essential role in the description of phase equilibria, which are fundamental to the simulation and optimization of all separation processes. Although it is known that multiplicities with respect to binary interaction parameters can occur, no systematic study of these multiplicities has been undertaken yet. In this contribution, their rigorous pointwise classification is presented, valid for the entire range of binary compositions. Furthermore, implications not only for the non‐random two‐lqiuid (NRTL)‐parameterization to capture temperature‐dependence are discussed, but also for extrapolation and regression tasks. The findings are illustrated for vapor‐liquid equilibria of different binary mixtures.

Interface Mass Transfer in Reactive Bubbly Flow: A Rigorous Phase Equilibrium-Based Approach

In this work, the driving force of interfacial mass transfer is modeled as deviation from the gas–liquid equilibrium, which by assumption is thought to exist at the interface separating the gas and liquid phases. The proposed mass transfer model provides a flexible framework where the phase equilibrium description in the driving force can be substituted without difficulties, allowing the mass transfer modeling of distillation, absorption/stripping, extraction, evaporation, and condensation to be based on a thermodynamically consistent phase equilibrium formulation. Phase equilibrium by the Soave–Redlich–Kwong equation of state (SRK-EoS) is in this work compared to the results of the classical Henry’s law approach. The new model formulation can predict mass transfer of the solvent, which Henry’s law cannot. The mass transfer models were evaluated by simulating a single-cell protein process operated in a bubble column bioreactor, and the solubilities computed from the SRK-EoS and Henry’s law were in qualitative agreement, albeit in quantitative disagreement. At the reactor inlet, the solubility of O2 and CH4 was 150% higher with the SRK-EoS than with Henry’s law. Furthermore, the SRK-EoS was computationally more expensive and spent 10% more time than Henry’s law.

Liquid-liquid equilibrium of systems containing acylglycerols from olive oil, glycerol and isopropanol

Oils enriched with diacylglycerol have received a great deal of attention due to their potential health benefits when used as a replacement for conventional edible oils. This work reports experimental results and thermodynamic modeling of liquid-liquid equilibrium of systems containing mono-, di- and triacylclycerols from olive oil, glycerol and isopropanol. The UNIQUAC model was used in the description of phase equilibria, which was well fitted to experimental data with root mean square deviations equal or lower then 1.4 wt% for the all studies systems. The results presented in this work show the feasibility of diacylglycerol separation from other acylglycerols through liquid-liquid extraction using glycerol and isopropanol as solvents.

Application of a Crossover Equation of State to Describe Phase Equilibrium and Critical Properties of Propane

An equation of state that predicts the thermodynamic behavior of propane is formulated. This equation takes into account the global behavior that includes the singular thermodynamic behavior asymptotically close to the critical point and the crossover to the regular thermodynamic behavior far away from the critical point. The formulated equation based on the transformation of a truncated classical Landau expansion. This equation of state (EOS) can represent the thermodynamic properties of propane in a wide range of temperatures and densities around the critical point. Comparisons of the pressure P–ρ–T data measured by Mark Mclinden of NIST group calculated with crossover EOS and those computed by the EOS of Eric Lemmon and selected results of other experimentalists are presented, as well as the isochoric-specific heat data measured by Abdulagatov et al. of the Russian groups are presented. We also give the comparison with a set of isobaric-specific heat data of Yesavage et al. The description of the rectilinear diameter singularity near the critical point is also discussed.

Physicochemical Properties and Solubility of Hydrochloride Mucolytic Agents

Two widely used active pharmaceutical ingredients (API), ambroxol hydrochloride (AMB·HCl) and bromhexine hydrochloride (BMH·HCl), belong to the expectorant and mucokinetic group of drugs. Their applications are found in the treatment of the upper respiratory tract and bronchopulmonary diseases. The compounds have similar chemical structures, but are different enough to distinguish their physicochemical properties. To understand better the bioavailability of the drugs a series of experiments was performed to establish significant parameters. With differential scanning calorimetry (DSC) the temperature and the enthalpy of fusion were determined with no observed polymorphic transformations. The phase diagrams for binary systems {active agent (1) + solvent (2)} were determined with three solvents: 1-octanol, water and ethanol, to describe phase equilibria by correlation with the local composition models: Wilson, UNIQUAC and NRTL. Finally, the Bates–Schwarzenbach method was used to establish the ionization constants of AMB·HCl and BMH·HCl at two temperatures: room temperature 298.2 K and human body temperature 310.2 K. Our study can give an insight into further drug delivery system design and help to create more effective drug application forms.

Tert-Butanol–water mixture separation by extractive distillation: Application of experimental data in process simulations

Effect of two solvents on the tert-butanol–water azeotropic mixture separation efficiency and economy has been studied. As solvents, two imidazolium ionic liquids (ILs), namely 1-ethyl-3-methylimidazolium bromide [EMim]Br and 1-butyl-3-methylimidazolium bromide [BMim]Br, were selected. For the original diluted tert-butanol (TBA) mixture separation, a separation unit composed of pre-concentration and extractive distillation columns was proposed. Simulations of separation equipment were carried out based on the equilibrium stage model of a distillation column implemented in ASPEN+. Regarding phase equilibrium description, the original NRTL excess Gibbs energy equation was used for the components’ activity coefficients calculation. Phase equilibrium data of IL-containing binaries were measured experimentally in a broad range of ILs’ concentrations and original binary parameters of the NRTL equation were evaluated from these data. To avoid ILs decomposition, regeneration of extraction solvents, ILs, in a vacuum film evaporator was considered. The effect of temperature and pressure in the vacuum film evaporator on the purity of the recovered ILs was tested experimentally in laboratory equipment and the results were applied in separation unit design simulations. For the proposed separation unit, operation costs were evaluated using the ASPEN+ software. Influence of the state of feed entering the extractive distillation column on operation costs was also investigated. By replacing the total condenser at the pre-concentration column head for a partial one, overall operation costs of the separation unit were reduced by about 20%.

Description of phase equilibrium and volumetric properties for CO2+water and CO2+ethanol using the CPA equation of state

Properties of fluids under high pressure is of interest for processes design. A literature survey was conducted on experimental vapor-liquid equilibrium (VLE) and density for CO2+water and CO2+ethanol. Phase equilibrium and density of pure water, ethanol and CO2 were evaluated considering 1868 data points. VLE and saturated liquid density data were collected: 544 data points for CO2+water and 859 data points for CO2+ethanol. Soave Redlich-Kwong (SRK) equation of state (EoS) with Cubic Plus Association (CPA) was applied for calculation of these properties. Peng-Robinson EoS was evaluated to demonstrate CPA improvement in properties description. The binary interaction parameters were estimated from VLE. For pure compounds, the results indicated suitable description for both phase behavior and density. For CO2+water, density calculations were accurate (Δρ = 0.5%) and VLE was adequately described (ΔxH2O = 0.49% and ΔyCO2 = 4.63%). CO2+ethanol volumetric behavior and VLE were also satisfactorily described in CO2 concentrations up to 30% (Δρ = 2.92%, ΔxEtOH = 1.37% and ΔyCO2 = 5.86%, respectively).

Highlighting Thermodynamic Coupling Effects in the Immersion Precipitation Process for Formation of Polymeric Membranes.

In the immersion precipitation process for membrane formation, a polymer casting film is placed in contact with a nonsolvent in a coagulation bath; an essential feature of the membrane formation process is the foray into the metastable region of the ternary phase diagram for the nonsolvent/solvent/polymer system. The primary objective of this article is to trace the origins of such forays. The Maxwell–Stefan diffusion formulation is combined with the Flory–Huggins description of phase equilibrium thermodynamics to set up a model for describing the transient equilibration trajectory that is followed in the polymer casting film. Four different systems are analyzed: water/acetone/CA, water/DMF/PVDF, water/NMP/PSF, and water/NMP/PEI (CA = cellulose acetate; PVDF = poly(vinylidene fluoride); PSF = polysulfone; PEI = polyetherimide, DMF = dimethyl formamide; NMP = N-methyl-2-pyrrolidone). The analysis shows that diffusional forays are mainly engendered due to thermodynamic coupling effects; such effects are quantified by the set of thermodynamic factors , where ai, the activity of species i, is dependent on the volume fractions, ϕi and ϕj, of both nonsolvent (i) and solvent (j). In regions close to phase transitions, the off-diagonal elements Γij(i ≠ j) are often negative and may attain large magnitudes in relation to the diagonal elements Γii. Strong thermodynamic coupling effects cause the transient equilibration trajectories to be strongly curvilinear, causing ingress into the metastable region. If thermodynamic coupling effects are ignored, no such ingress occurs. It is also shown that analogous diffusional forays may lead to emulsion formation in partially miscible liquid mixtures.

Separation of phenol from aqueous solution by 2-octanone: Phase equilibrium measurements and thermodynamic studies

The applicability of 2-octanone as solvent for the liquid phase extraction of phenol from aqueous solution was investigated in this work. The liquid liquid equilibrium (LLE) for the ternary systems {2-octanone + phenol + water} was experimentally determined at 298.15 K, 318.15 K and 338.15 K under atmospheric pressure. Distribution coefficients and separate factors calculated from the experimental LLE data were used to judge if 2-octanone can be used as potential solvent to extract phenol from aqueous solution. Distribution coefficients and separation factors of 2-octanone were also compared with other extractants and results show that 2-octanone has excellent extraction performance. Binary interaction parameters were regressed by the NRTL and UNIQUAC methods, and related physical meaning is explained by interaction forces. The root mean squared deviations (RMSDs) show that both models can well describe phase equilibrium behavior of ternary system {2-octanone + phenol + water}. In order to predict ternary LLE data at other temperatures, the NRTL model was used to simultaneously regress ternary experimental data at all temperatures and the largest RMSD is 0.49%.

Comparison of alternative methods for methyl acetate + methanol + acetic acid + acetic anhydride mixture separation

Objectives. The paper is a comparative analysis of methyl acetate + methanol + acetic acid + acetic anhydride industrial mixture separation flowsheets based on the use of special distillation methods (extractive distillation and pressure-swing distillation). The results obtained illustrate the variability of the structure of the technological separation flowsheet.Methods. Mathematical modeling using the software package Aspen Plus V. 10.0 was chosen as the research method. The simulation was based on the local composition equation NRTL and the Hayden–O’Connell equation of state. The relative uncertainties of phase equilibrium description do not exceed 3%.Results. The vapor–liquid diagram of the quaternary mixture of methyl acetate + methanol + acetic acid + acetic anhydride was studied using thermodynamic topological analysis. It was shown that the system contains one binary azeotrope and is characterized by one distillation region. Although the structure is not complex, there is a possibility of using several methods for mixture separation: pressure-swing distillation, and extractive distillation with different entrainers. Twelve flowsheets with different structure were proposed, and 29 variants of separation were compared.Conclusions. It was shown that the most perspective structure for the separation of a methyl acetate + methanol + acetic acid + acetic anhydride mixture is a combination of distributed sequence separation and extractive distillation.

Silicon-Rich Corner of the Yb–Pt–Si Ternary System at 850°C

We have studied phase equilibria in the silicon-rich part of the Yb–Pt–Si system. To this end, 22 alloys were prepared by a standard arc-melting process in an argon atmosphere and annealed at a temperature of 850°C. Physicochemical characterization of the samples included electron microscopy, X-ray microanalysis, X-ray diffraction, and differential thermal analysis. We have confirmed the existence of four previously known intermetallic compounds: YbPtSi, YbPt2Si2, Yb3Pt4Si6, and Yb2Pt3Si5. In addition, three new phases have been identified: YbPtSi2, Yb33Pt17Si50, and Yb11Pt33Si56. The structure type of the YbPtSi2 compound has been determined. We present statistical crystallographic data for the ternary phases and describe phase equilibria in the region studied in the 850°C isothermal section of the Yb–Pt–Si phase diagram.

Development of Reaction-Rectification Process of Obtaining Mesityl Oxide. II. Analysis of Statics and Modeling of the Process

Using the results of an earlier study of the physicochemical properties of the reaction system of the process of producing mesityl oxide, an analysis of the statics of the combined variant of the organization of this process was carried out. It is shown that of practical interest are the modes of the process corresponding to the first specified separation. In this case, the limiting stationary states, characterized by the maximum acetone conversion, selectivity, and the yield of the target product — mesityl oxide, are distinguished. The possibility of practical implementation of the limiting stationary state of the reactive distillation process for producing mesityl oxide, which provides almost complete conversion of acetone with a yield of mesityl oxide approaching 100%, has been proved. The limit stationary state corresponds to the reaction-distillation process with the selection of a single product stream. For the mode of carrying out the combined process that corresponds to the selected limiting stationary state, a schematic flow chart for the production of the target product has been proposed. By means of computational research, it has been established that the most rational option for organizing a reaction hub is to use a single apparatus in it — the reaction-distillation column. In the Aspen Plus® software package, a process model was constructed that corresponded to the proposed technological scheme and through a computational experiment, its structural and parametric optimization was carried out. As a result, the static parameters of the technological system were established, as well as the characteristics of the apparatuses, allowing to obtain the required quality product in the reactiondistillation column. output, approaching 100%. It has been shown that when modeling a chemicaltechnological system, it is necessary to use different sets of parameters of the basic equation used to describe phase equilibrium. Thus, for calculating reactive distillation and distillation columns, the liquid – vapor phase equilibrium parameters for the mesityl oxide–water system should be used, and when calculating the Florentine vessel for this mixture, it is necessary to use the parameters corresponding to the liquid – liquid equilibrium. The use of a single set of parameters of the basic equation leads to significant errors and inadequate description of the process of producing mesityl oxide by condensation of acetone.

Liquid–Liquid Equilibrium in an Extraction System Based on Polyvinylpyrrolidone-3500 and Sodium Nitrate

Liquid–liquid phase equilibrium for a new extraction system based on polyvinylpyrrolidone-3500 and sodium nitrate at 298.15, 313.15, and 333.15 K has been studied. Binodal data and phase diagrams with liquid–liquid tie lines have been presented. Mathematical modeling of phase equilibrium in the given system has been performed. New parameters for the UNIQUAC equation have been selected. The UNIQUAC model can be successfully used to describe phase equilibrium in the system. The results of this study can be used in the development of new extraction processes for the recovery of organic compounds.

Reconsideration of the alpha coefficient in NRTL model on the vapor liquid phase equilibrium description of refrigerant mixtures

The NRTL equation provides a good representation of vapor-liquid equilibrium of mixed-refrigerants, but it needs three parameters for each pair of components, including a non-randomness parameter alpha. In order to reduce the number of adjustable parameters from three to two, this work aims to establish an adequate expression for alpha in terms of readily available molecular parameters. The regressed alpha coefficients vary from -1 to 10, while 74% of them are between 0 and 1. Alpha has a great effect on the AARDp, although there is a region with a small AARDp difference. The relationship between alpha and molecular weight, dipole moment is established. As expected, positive correlation between alpha and molecular weight, while negative correlation between alpha and dipole is found. Better AARDp (0.59%) is achieved by a proposed equation, comparing to alpha = (0.2, 0.3, 0.4 and 0.47), although it is slightly worse than the regressed alpha.

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

Supercritical CO2 extraction of solids using aqueous ethanol as static modifier is a two-step mass transfer process

This study re-analyzes literature data on S. platensis’ chlorophyll (CHL) extraction using 5-25 cm3 of 20–80% v/v ethanol in water (static modifier) and 82.5–62.5 cm3 of CO2 at 50 °C and 40 MPa. Under these conditions, a CO2-expanded aqueous ethanol (liquid) phase coexists with an aqueous-ethanol-modified CO2 (SCF) phase in the extraction vessel. Authors hypothesize the resulting extraction is a two-step process consisting of slow transfer of CHL from the substrate to the liquid phase, followed by fast (equilibrium) transfer of CHL to the SCF phase. For analysis, we described the ternary (CO2 + ethanol + water) system at 50 °C and 40 MPa using Peng-Robinson Equation of State and Wong-Sandler mixing rules with binary interaction parameters describing phase equilibrium of binaries (CO2 + ethanol), (ethanol + water), and (CO2 + water). Authors propose a simple mathematical model of the extraction process, and identify research needs to validate/refine it.

Phase Equilibrium and Surface Properties of a Binary System Containing Nanoparticles

A consistent description of phase equilibrium and surface phenomena in binary systems containing monodisperse spherical nanoparticles of arbitrary (including nanoscale) size is presented in the context of the classical method with separating surfaces. Using the obtained relations, we have calculated the composition of coexisting phases and interface layer, and interfacial tension on the boundary between nanoparticles and the matrix at different temperatures in Ti-Mo system. The results of the calculations are consistent with the available experimental data.

Фазовое равновесие и поверхностные характеристики в бинарной системе, содержащей наноразмерные частицы

AbstractA consistent description of phase equilibrium and surface phenomena in binary systems containing monodisperse spherical nanoparticles of arbitrary (including nanoscale) size is presented in the context of the classical method with separating surfaces. Using the obtained relations, we have calculated the composition of coexisting phases and interface layer, and interfacial tension on the boundary between nanoparticles and the matrix at different temperatures in Ti-Mo system. The results of the calculations are consistent with the available experimental data.

Application of a Crossover Equation of State to Describe Phase Equilibrium and Critical Properties of n-Alkanes and Methane/n-Alkane Mixtures

Crossover equations of state (EOSs) are models that incorporate density fluctuations into mean-field thermodynamic models, changing their behavior close to the critical point. In this way, they are capable of describing the analytical behavior of fluids far from the critical region and the asymptotic one near the critical point. Although several crossover EOSs have been developed in the last decades their use in modeling industrial processes is rather limited. In this work, we use the crossover Soave–Redlich–Kwong (CSRK) to describe phase equilibrium and critical properties of pure n-alkanes and methane/n-alkane binary mixtures and compare the results to two other modeling approaches of the SRK EOS. In the case of the pure fluids, CSRK gives an accurate overall description of the phase equilibrium and critical properties; nevertheless, a minor increase in the deviation of the saturation pressure and other properties is observed when compared to that of the mean-field model. For the binary mixtures, an imp...