Equilibria In Multicomponent Systems Research Articles

Nonlinear liquid-liquid chromatography: Modeling a binary mixture separation

In liquid-liquid chromatography (LLC), mixture components are separated due to their different distribution between the phases of a biphasic liquid system composed of three or four solvents. LLC separations are typically modeled assuming that only the solutes distribute between the two liquid phases and their distribution can be described with a concentration-independent distribution constant. With increasing solute concentration, the physicochemical properties of the biphasic system change, and the distribution of the solutes becomes a function of their concentration. However, the experimental determination of liquid-liquid equilibria in multicomponent systems is time-intensive, and its prediction using thermodynamic models is often not sufficiently accurate for process design purposes. Thus, in this work, we propose a simple approach to model and simulate LLC separations in the nonlinear (concentration-dependent) range of the solutes’ distribution equilibria, namely cannabidiol (CBD) and cannabigerol (CBG). Using the inverse method, the distribution equilibrium equation parameters were estimated from pulse injection experiments of single solutes at concentrations ranging from 1 to 100 mg/mL and 1–50 mg/mL for CBD and CBG, respectively. The obtained parameters were then successfully used to predict the elution profiles of binary mixtures of different compositions at 40 mg/mL total cannabinoid concentration. The approach was demonstrated and validated for CBD and CBG as model compounds and n-hexane/methanol/water 10/7.5/2.5 (v/v/v) as the biphasic solvent system. It should be noted that the applicability of the proposed approach is system-dependent, and hence, it should be evaluated for each separation task individually.

Predicting Gas Hydrate Equilibria in Multicomponent Systems with a Machine Learning Approach

AbstractNatural gas production and transportation can be threatened by gas hydrate plugging, especially in offshore environments with low temperatures and high pressures. This can cause pipeline blockages, increased back pressure, production stoppage, and pipeline ruptures. Machine learning (ML) models were created to predict gas hydrate formation in multicomponent systems with and without inhibitors. The models utilized input parameters such as gas‐mixture specific gravity, pressure, and inhibitor concentrations, which were fed into five supervised ML algorithms. The accuracy of the models' predictions was compared, and three models had accuracy greater than 90%, while two had accuracies between 80 and 90%.

Topological transformations of phase diagrams of quaternary systems through the boundary tangential azeotrope stage

The specific features of quaternary system phase diagram transformations induced by formation ofboundary tangential azeotrope were investigated. The characteristics of bifurcation states corresponding to the transition from one structure of the diagram to another were determined. The principal possible transformations of diagrams with varying pressure were illustrated by the systems acetone-chloroform-ethanol-water and chloroform-ethanol-cyclohexane-water. The obtained results expand the understanding of thermodynamics of heterogeneous equilibria of multicomponent systems and make it possible to solve the practical problem of maintaining favorable phase equilibrium conditions for rectification in certain pressure ranges.

Interaction of Skutterudites with Contact Materials: A Metallurgical Analysis

More than hundred diffusion couples between p- and n-type skutterudites and various materials were prepared and interaction zones were investigated after heat treatment at 600 °C for 1100 h. The constitution of reaction/diffusion zones was discussed in terms of: (a) atom site preference in the skutterudite lattice, (b) phase equilibria in multicomponent systems and (c) particularities of the crystal structure of intermediate phases. It could be shown that phase composition and thermo-mechanical properties of bonding can be engineered by chemical substitution. The results obtained allowed the determination of several necessary criteria for the development of chemically and mechanically stable diffusion barriers/couples for skutterudite based thermoelectric (TE) modules.

Tl2Se–TlInSe2–Tl4P2Se6 QUASITERNARY SYSTEM

Complex chalcogenide compound are widely used as working elements for semiconductor optical technology, thermal generation, solar power. Special attention is paid to compounds of the M2P2Se6 type (M – Ag, Cu) which due to its layer crystal structure possess promising ferroelectric, thermoelectric and electro-optical properties. Heterovalent substitutions of cations 2М2+ ® 4M1+ in the composition of M2P2Se6 type compounds must leads to deformation of the crystal structure, changing in the value of the dipole moment and, accordingly, to change the electro-physical properties.
 The Tl2Se–In2Se3–“P2Se4” system characterized by the formation of intermediate complex compounds which melts congruently TlInSe2 (1023 К), Tl4P2Se6 (758 К), TlInP2Se6 (875 К) and TlIn5Se8 (melts incongruently L+In2Se3«TlIn5Se8 at 1029 К), In4(P2Se6)3 (formed by syntactic reaction at 880 К). Triangulation of the Tl2Se–In2Se3–“P2Se4” system was shown that then divided on secondary quasiternary systems, one of them is Tl2Se–TlInSe2–Tl4P2Se6.
 Phase equilibria in the Tl2Se – TlInSe2 – Tl4P2Se6 quasiternary system were studied using classical methods of physicochemical analysis DTA (chromel-alumel thermocouple, with an accuracy of ±5 K), XRD (DRON-3-13 diffractometer, Cu Ka radiation, Ni filter, Guinier Huber G670 diffractometer, CuKα1 radiation), MSA (metallographic microscope Lomo Metam R1) in combination with the simplex method of mathematical modeling of phase equilibria in multi-component systems. Crystal structure calculation was carried out with program WinCSD.
 Investigation of physical-chemical interaction allowed to constructed perspective view of phase state diagram and liquidus surface projection of the Tl2Se–TlInSe2–Tl4P2Se6 ternary system. In the ternary system formed the boundary solid solution: a- on the basis of Tl2Se, b- on the basis of TlInSe2, g-, d-, e- on the basis of ltm-, mtm- and htm-Tl4P2Se6 (ltm, mtm, htm – low, middle and high temperature modification, respectively). The liquidus of the ternary system consists of primary crystallization areas: Tl2Se-е1-Е1-е2-Tl2Se (a phase), TlInSe2-е3-U2-U1-E1-TlInSe2 (b phase), m1-U1-E1-e2-m1 (g phase), m2-U2-U1-m1-m2 (d phase) and Tl4P2Se6-e5-U2-m2-Tl4P2Se6 (ε phase). The Tl2Se–TlInSe2–Tl4P2Se6 quasiternary system is characterized by the processes: monovariant eutectic L«htmTl4P2Se6+TlInSe2 (e5-U2, 776-693 К), monovariant eutectic L«Tl2Se+TlInSe2 (e1-Е1, 614-539 К), monovariant eutectic L«Tl2Sе+ltmTl4P2Se6 (e2-Е1, 610-539 К); monovariant peritectic L+mtmTl4P2Se6«ltmTl4P2Se6 (m1-U1, 640-620 К); monovariant peritectic L+htmTl4P2Se6« mtmTl4P2Se6 (m2-U2, 747-693 К); monovariant peritectic L+mtmTl4P2Se6«TlInSe2 (U2-U1, 693-620 К); monovariant peritectic L+ltmTl4P2Se6«TlInSe2 (U1-E1, 620-539 К). Lines of the monovariant equilibria are crossed in three point: U2 – invariant peritectic process L+htmTl4P2Se6«TlInSe2+mtmTl4P2Se6 (12 mol.% Tl2Se, 20 mol.% TlInSe2, 68 mol.% Tl4P2Se6, 693 К), U1 – invariant peritectic process L+mtmTl4P2Se6«TlInSe2+ltmTl4P2Se6 (38 mol.% Tl2Se, 9 mol.% TlInSe2, 53 mol.% Tl4P2Se6, 620 К), E1 – invariant eutectic process L « Tl2Se+TlInSe2+ltmTl4P2Se6 (47 mol.% Tl2Se, 7 mol.% TlInSe2, 46 mol.% Tl4P2Se6, 539 К). New complex compounds were not observed in the ternary system. Limited solid solutions on the basis of TlInSe2, Tl4P2Se6 initial compounds are not up to 5–8 mol%.
 Crystal-structure studies of Tl2Se, TlInSe2 and Tl4P2Se6 complex chalcogenides were carried out by a powder method, refinement of the structural parameters – by the Rietveld method. The lattice parameters are: Tl2Se – Р4/n, а=8,540; с=12,380 Å, TlInSe2 – I4/mcm, a=8.064, c=6.833 Å, Tl4P2Se6 – P121/c1, a=12.239, b=9.055, c=12.328 Å, b=98.83. Crystal-chemical analysis of the compounds showed that they are characterized by a mixed ion-covalent type of chemical bond. During the transition from the binary Tl2Se to TlInSe2 ternary compound the covalent component of the In–Se bond is enhanced, the opposite change is observed for Tl4P2Se6, an increase in the ion component of the Tl–Se bond. The study of the mechanisms of formation of solid solutions showed that with the reciprocal solubility of the TlInSe2, Tl4P2Se6 ternary compounds characterized by the formation of substitution structure, the dissolution of Tl2Se in ternary selenides follows the substitution and subtraction mechanism.

YÜKSEK KROMLU BEYAZ DÖKME DEMİRLERDE FAZ DENGESİNİN BENZETİMİ

In this study, using the Materials Calculator software program, the pseudo binary phase diagrams (i.e. isoplethal maps) of high chromium white cast irons (~19% in weight) with different molybdenum contents were simulated. In order to test the accuracy of the calculated phase diagrams, the transformation temperatures read from the diagrams at certain compositions were compared with the phase transformation temperatures measured using Differential Scanning Calorimetry (DSC) analysis of the samples produced by casting in the same composition followed by slow cooling. With the same purpose, low temperature phases read from the phase diagrams were compared with the crystalline phases determined by X-Ray Diffraction (XRD) of the casted samples. Simulated diagrams predicted an increase in the amount of secondary M 23 C 6 carbides with increasing molybdenum content. The validity of this prediction was tested by determining the phase distribution and phase compositions in the casted samples by means of metallographic examinations and Scanning Electron Microscopy (SEM) - Energy Dispersive Spectroscopy (EDS) analyzes. When the hardness values of the samples were taken into consideration, it was seen that the hardness increased from 44.90 to 51.05 HRC with a 1% increase in Mo content and a corresponding increase in the amount of secondary carbides without any heat treatments. Results show that theoretical predictions and experimental measurements are in accord and estimating phase equilibria in multi-component systems is of practical importance.

КРИСТАЛЛИЗАЦИЯ КВАЗИБИНАРНОЙ ЭВТЕКТИКИ bnss-tss В СИСТЕМЕ Cu-Fe-Ni-S

Исследование посвящено изучению процессов зональной кристаллизации в четырехкомпонентной системе Cu-Fe-Ni-S, являющейся базовой при формировании медно-никелевых сульфидных руд. Образец исходного состава (мол. %): Cu = 17.19, Fe = 19.05, Ni = 19.66, S = 44.10 синтезирован с применением метода квазиравновесной направленной кристаллизации. Результаты микроскопического исследования показали, что полученный слиток образован из 6 зон с разным фазовым и химическим составом. Основная часть слитка представлена зоной IV. Образцы, вырезанные из этой зоны, исследовались методами дифференциального термического анализа (ДТА), растровой электронной микроскопии (СЭМ) и рентгено-спектрального микроанализа (РСМА). Микроскопические исследования позволили предположить, что слиток состоит из твердых растворов tss и bnss, но при дальнейшем охлаждении tss разложился на дочерние фазы. Однако эти данные можно трактовать и как кристаллизацию четверной эвтектики. Результаты ДТА исследования образцов позволили измерить температуры фазовых эффектов и однозначно установить образование бинарной эвтектики bnss-tss. Температура бинарной эвтектики (L → tss + bnss) составляет 578±1 °С (851±1 K). Температуры ликвидуса незначительно повышаются от 857±2 °С до 862±2 °С (1130±2 K - 1135±2 K). Указанное изменение объясняется небольшими изменениями состава исследуемых образцов. Полученные результаты подтвердили адекватность и согласованной предложенной методики, сочетающей методы направленной кристаллизации, дифференциального термического анализа, растровой электронной микроскопии и рентгеноспектрального микроанализа при исследовании фазовых равновесий в многокомпонентных системах.
 
 Исследование выполнено в рамках госзадания (проект 0330-2016-0001) и при частичной финансовой поддержке комплексной программы фундаментальных научных исследований СО РАН II.1. № 303.

A review on physicochemical measurements by headspace gas chromatography. Studies of vapour-liquid equilibria.

<p style="margin: 0cm 0cm 0pt; text-align: justify; line-height: normal;"><span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN-GB;" lang="EN-GB">Headspace gas chromatography (HS-GC) is a powerful technique for the analysis of volatile compounds. It has found broad applications for quantitative and qualitative analyses of various samples as well as for physicochemical measurements. This paper briefly reviews the basic physicochemical applications of HS-GC including vapour pressure measurements and studies of vapour-liquid equilibria in multicomponent systems. A special attention is paid to methodological aspects of these measurements. The advantages and limitations of HS-GC in this field as well as typical applications are also pointed out.</span></p>

Contemporary Methods for Modeling High-Temperature Systems1

FactSageTM software is used successfully in the Gruppa Magnezit engineering section making it possible to calculate thermodynamic equilibria in multicomponent systems, to construct phase diagrams, and to calculate viscosity in molten slags and glasses, etc. Use of specialized software makes it possible to both analyze premature wear of linings, and also the preliminary selection of refractory compositions, slag modifiers or directly for slag regimes optimum from the point of view of fulfilling metallurgical tasks and reducing refractory specific consumption. Modeling results are provided for processes occurring within ferrous and nonferrous metallurgy units.

Equilibrium Modeling of Ternary Adsorption of Phenols onto Modified Activated Carbon

The prediction of adsorption equilibria in multicomponent systems is of prime importance. Therefore, the equilibrium adsorption data for the following multicomponent systems have been studied. The present paper deals with the simultaneous removal phenol (P), 4-chlorophenol (CP), 4-nitrophenol (NP) and catechol (C), resorcinol (R), hydroquinone (HQ) onto modified activated carbon (MAC) from ternary mixtures. The BET surface area of SC was found to be 934 m2/g, whereas BJH adsorption/desorption surface area of pores is 53.03/58.15 m2/g. The equilibrium adsorption data were obtained at different initial concentrations (C0 = 50–1000 mg/L), 12 h contact time, 30°C temperature, MAC dosage of 10 mg/L at solution pH. Equilibrium isotherms for the ternary adsorption of P–CP–NP and C–R–HQ onto MAC have been analyzed by using non-modified Langmuir, modified Langmuir, extended Langmuir, extended Freundlich and Sheindorf–Rebuhn–Sheintuch (SRS) models. The competitive Sheindorf–Rebuhn–Sheintuch (SRS) model fits for both ternary adsorption equilibrium data satisfactorily and adequately.

A New Technique for Studying Vapour–liquid Equilibria of Multi-Component Systems

A Fourier transform infrared gas-phase method is described herein and capable of deriving the vapour pressure of each pure component of a poorly volatile mixture and determining the relative vapour phase composition for each system. The performance of the present method has been validated using two standards (naphthalene and ferrocene), and a Raoult’s plot surface of a ternary system is reported as proof-of-principle. This technique is ideal for studying solutions comprising two, three, or more organic compounds dissolved in ionic liquids as they have no measurable vapour pressures.

A Thermodynamic Model for the NH4+, K+ // H2PO4-, H2P2O72-, NO3-, Cl- - H2O System

We have developed a quantitative thermodynamic description of the NH4H2PO4-(NH4)2H2P2O7-KH2PO4-K2H2P2O7-NH4NO3-KNO3-NH4Cl-KCl-H2O system, which is of great importance for fertilizers applications. The liquid phase and all solid solutions were modeled using the Modified Quasichemical Model for short-range ordering. The liquid model includes the reaction of dimerization of AH2PO4 (where A = NH4+ or K+) according to: 2 AH2PO4(liquid) ↔ A2H2P2O7(liquid) + H2O(liquid or gas). The model parameters are mainly obtained by the critical evaluation and optimization of available thermodynamic and phase equilibrium data for the lower-order subsystems. The model is then used to estimate the properties of multicomponent salts from these assessed parameters for the lower-order subsystems, using interpolation methods along with Gibbs energy minimization software. When used in conjunction with thermodynamic databases for solids, solid solutions, and gases, these databases permit the calculation of complex multiphase equilibria in multicomponent systems, using the FactSage thermochemical software. In particular, calculations of interest for the production and storage of fertilizers may be performed.

Equilibrium-kinetic model of water-rock interaction

A computer model was developed for chemical interaction in water-rock systems. The model is based on the concept of partial equilibrium [1] and combines the calculation of chemical equilibria in multicomponent systems with accounting for the kinetics of the congruent dissolution of minerals as a function of pH (zeroth order kinetic reactions). The development of the process in time is simulated as a series of sequential partial equilibria, and the bulk chemical composition of the system is calculated at each time step from the chemical composition of aqueous solution at the beginning of the step and masses of minerals dissolved during time Δt. The dissolution rates of individual minerals are calculated at each time step for the given temperature, current pH value, and the degree of solution saturation with respect to minerals. Variations in the surface area of minerals due to precipitation and dissolution are accounted for. Model application is exemplified by the calculation of chemical equilibria in the water-granite system. The model may be useful for understanding the character of low-temperature interactions in water-rock systems under stagnant conditions, in particular, the multistage development of groundwater chemistry, interaction of liquid radioactive waste injected into underground repositories, etc.

Experimental Methods and Prediction with COSMO-RS to Determine Partition Coefficients in Complex Surfactant Systems

Surfactant-based separation processes are a promising alternative to conventional organic solvent processes. A crucial parameter to describe the efficiency of such processes is the partition coefficient between the surfactant aggregates (micelles) and the aqueous bulk phase. In this work, several experimental methods to determine these partition coefficients (micellar liquid chromatography, micellar enhanced ultrafiltration, and cloud point extraction) are evaluated and compared. In addition, these results are compared to predictions with the thermodynamic model COSMO-RS. In particular, systems with the nonionic surfactant TritonX-100 are studied. The partition equilibria of various solutes (pyrene, naphthalene, phenanthrene, phenol, 3-methoxyphenol, and vanillin) and the influence of different additives (alcohols) are investigated. All experimental methods show very good reproducibility. Moreover, the results from different methods are in good agreement, supplementing one another concerning the temperature ranges. Notably, the COSMO-RS model is capable of predicting partition coefficients between micelles and water in the investigated temperature range and at different alcohol concentrations. The results demonstrate the potential of the model COSMO-RS to facilitate the selection of optimized process parameters for a given separation problem. By predicting partition equilibria in multicomponent systems, the selection of surfactant, temperature, and appropriate additives can be facilitated.

Diagrams of phase equilibria: a basis for implementing technologies of technogenic waste product conversion

Diagrams of the phase equilibria of multicomponent systems simulating the composition of technogenic waste products of thermal power stations’ burning of vanadium-containing fuel were obtained. The possibility of controlling the degree of vanadium extraction during oxidative calcinations was shown by varying the proportions of the mixture of two types of waste: thermal power station energy silts and wastewater treatment silts.

A review of the isobaric (vapor+liquid+liquid) equilibria of multicomponent systems and the experimental methods used in their investigation

Abstract An overview of the multicomponent systems for which isobaric (vapor + liquid + liquid) equilibrium (VLLE) data has been published, is presented. This overview comprises 36 ternary and three quaternary systems. For each one of these systems is specified a reference, pressure range, experimental method and the amount of equilibrium data determined. This is followed by a brief description for each experimental method of the specific procedure carried out to determine the (vapor + liquid) equilibrium in the case where the liquid is heterogeneous. Lastly, a final assessment is presented of the experimental procedures used to determine the (vapor + liquid + liquid) equilibria (VLLE).

Thermodynamic models and databases for slags, fluxes and salts

The evolution of thermodynamic models of molten salts and slags, starting with Temkin in 1948, has culminated in today's sub-lattice models. These modern models have permitted the development of large thermodynamic databases of model parameters, which can be used to calculate and predict accurately the properties of multicomponent solutions. The model parameters are mainly obtained by the critical evaluation and optimisation of available thermodynamic and phase equilibrium data for binary and ternary subsystems. The models are then used to estimate the properties of multicomponent slags and salts from these assessed binary and ternary parameters. When used in conjunction with thermodynamic databases for solids and solid solutions (salts, oxides, sulphides, metals, etc.), other liquid solutions (such as liquid metals), and gases, these databases permit the calculation of complex multiphase equilibria in multicomponent systems, with applications in a wide variety of industries. These calculations can be performed with general commercial software for Gibbs energy minimisation, which can also be incorporated into process simulation software packages.

Thermodynamic equilibrium in systems with multiple adsorbed and bulk phases

A new procedure is proposed for the calculation of adsorption equilibria in multicomponent systems. This methodology is capable of predicting equilibrium of one or more fluid phases with one or more adsorbed phases. The specifications are the total volume available for the bulk phases, the total area available for adsorption or total mass of adsorbent, the number of moles of each species, and the temperature. The problem is formulated and solved as a minimization of the total Helmholtz free energy, using the Peng–Robinson equation of state as a model for the bulk phases and a lattice-gas model for the adsorbed phases. As a result we obtain the number of moles of each species in each phase of the system, the volume occupied by each bulk phase and the area occupied by each adsorbed phase. There is excellent agreement between the results of our methodology and experimental data for a pure component and Monte Carlo simulation data for a binary mixture. In multicomponent systems, very interesting predictions of phase multiplicity of bulk and/or adsorbed phases are obtained. However, experimental data would be necessary to confirm the phase behavior predicted by the calculations presented here.

Modeling of the Sorption Dynamics in Multicomponent Ion-Exchange Systems with Consideration of Complexation Reactions on the Basis of the Surface Complexation Theory

The sorption dynamics in multicomponent ion-exchange systems with consideration of complexation reactions in solution is theoretically described by solving (on a computer) nonlinear material balance equations and kinetic equations of internal diffusion. Equilibria in multicomponent ion-exchange systems are characterized using the surface complexation theory. According to this theory, fixed groups of an ion exchanger and counterions form complexes located in different layers (Stern layers) at different distances from the surface. These layers constitute a circuit of series-connected capacitors. The fundamental advantage of such an approach is the fact that equilibria in multicomponent systems can be described in terms of a set of parameters obtained for binary systems. Additional account is taken of complexation reactions in the solution in the space between sorbent grains in an ion-exchange column. The H+–A–B three-component metal-ion exchange in various systems (A, B = Zn2+, Co2+, Ni2+, Cd2+, Ca2+, and Na+) is studied. Comparison is made between the results of numerical calculations of the characteristics of the H+–An+–Bn+ ion exchange in multicomponent systems containing metal ions with and without consideration of chemical reactions.

Remarks about data reliability in experimental and computational alloy thermochemistry

The determination of phase equilibria in multi-component systems, which is fundamental to the synthesis, thermal treatments and application of several materials, may be efficiently approached through a combination of experimental measurements and computational methods. To this end, however, reliable experimental data should be available, even if obtained for a reduced set of crucial composition and temperature conditions. Among these experiments a relevant and pre-eminent role is played by thermal and thermodynamic measurements. The estimation of uncertainties in thermochemical measurements, however, is especially difficult due to the presence of errors from different sources (such as sample impurities, side reactions, deviations from equilibrium, etc.) which, mainly in alloy science, are generally larger than the instrumental errors and not easy to evaluate. On the basis also of the research carried out in the Author's laboratory, various sources of errors related to a few experimental techniques in alloy thermochemistry are examined. Some comments on the reliability and consistency of results from thermochemical optimisation, which are heavily affected by the experimental data uncertainty, (especially when large temperature and/or composition extrapolations are needed) are also given. A few comments about the overall coherence of the data concerning a certain alloy system are presented and the need for enhancing and developing experimental alloy thermodynamics underlined.