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The effect of boric acid amino ester, which was obtained from triethanolamine, boric acid, and triethylene glycol, on the conditions of vapor–liquid equilibrium in the ethyl acetate–ethanol and ethyl acetate–isopropanol azeotropic binary mixtures and the ethyl acetate–ethanol–water ternary mixture was studied both by experimental methods of open evaporation with a Świętosławski ebulliometer, and by modeling using the UNIFAC method. Parameters of the interaction of the CCOO group (in ethyl acetate) with the boron group B were determined, which are absent in the literature. A process for separating the ethyl acetate–ethanol–water azeotropic mixture by extractive distillation was proposed. [ABSTRACT FROM AUTHOR]

The pressure effect on the relative volatility of binary mixtures of different natures and ternary mixtures containing potential separating agents such as dimethylsulfoxide (DMSO) and butyl propionate is studied. A wide range of information is obtained based on the data on the vapor–liquid equilibrium, and effects of the pressure on the relative volatility of various nature and cause for a fixed composition of the initial mixture are determined. In the presence of intersection points of the phase-equilibrium curves in the initial binary mixture and pseudobinary mixture (in the section with a constant concentration of the third high-boiling component), the concentration simplex is divided into regions in which the values of the relative volatility decrease (increase) upon varying pressure. This fact makes it possible to improve the procedure of separation process optimization at the stage of operating pressure selection in the columns. [ABSTRACT FROM AUTHOR]

The interaction of tungsten mineral raw materials with a mixture of NH4HF2 and (NH4)2SO4 upon heating was studied. It was determined that, first, at temperatures up to 200°C, the incoming components are fluorinated to form complex and simple fluorides. A further increase in temperature is accompanied by the decomposition of ammonium sulfate to form NH4HSO4, which leads to the conversion of fluorides into sulfates and of the tungsten ammonium fluoride complex into tungstic acid H2WO4. It was shown that water leaching of the product of the decomposition of tungsten-containing mineral raw materials with a mixture of NH4HF2 and (NH4)2SO4 makes it possible to extract tungsten from mineral raw materials in the form of the commercial product WO3. [ABSTRACT FROM AUTHOR]

The interaction of gold-containing rock and titanium-containing mineral raw materials with a mixture of ammonium hydrodifluoride NH4HF2 and ammonium sulfate (NH4)2SO4 at temperatures below 430°C has been studied. A comparative analysis showed that the use of a mixture of NH4HF2 and (NH4)2SO4 allows more complete winning of mineral raw materials compared to the use of ammonium hydrodifluoride alone. The mixture of NH4HF2 and (NH4)2SO4 is recommended as a new promising reagent for the decomposition of rocks and mineral raw materials for complete extraction of the product into solution during water leaching. [ABSTRACT FROM AUTHOR]

The synthesis of sharp separation sequences is one of the most researched challenges in the chemical process industry. Distillation may separate a multicomponent mixture in many distinct sequences, each of which produces the same products but at a different cost. In this article, we present a quantitative technique for determining the optimal column sequence by separation task based marginal vapour rate (MVR) of nonkey components present in a liquid mixture. The screening of design options is accomplished within a framework, which allows for the disintegration of the separation sequences into distinctive tasks. The application of the task approach decreases computing effort greatly. The MVR is computed for each separation task and then for the sequences; MVR is used to assign rankings to each sequence. The sequence with the lowest MVR is ranked first and is the best sequence. [ABSTRACT FROM AUTHOR]

In the large-scale production of phenol by the cumene method, an important constituent is the separation of multicomponent mixtures containing the target products and various impurities. The potential of distillation processes of a specific composition is determined by the structure of the vapor–liquid equilibrium diagram structure. The paper analyzes the phase diagram of a six-component system and its constituents of a smaller dimension. Thermodynamic restrictions on the distillation process associated with the presence of separatric manifolds are established, and ways to overcome them through the use of special techniques are shown. The structures of mixture separation flowsheets are proposed and the columns operation parameters are determined. The use of the re-extractive distillation process is a viable alternative for phenol purification, since it allows the second product of the cumene method, acetone, to be involved in the technological cycle. [ABSTRACT FROM AUTHOR]

The vapor–liquid equilibrium of the tetrahydrofuran–acetonitrile system, the equimolar tetrahydrofuran–acetonitrile–chloroform mixture is experimentally studied. The effect of various amounts of dimethyl sulfoxide on the relative volatilities of the components at 101.32 kPa is investigated. The extractive distillation flowsheets of the tetrahydrofuran–acetonitrile–chloroform mixture with dimethyl sulfoxide are calculated. [ABSTRACT FROM AUTHOR]

Previously, a method for increasing the efficiency of extraction separation of liquid mixtures has been proposed, in which a solution of a mixture of components is introduced as a series of pulse injections in a cascade of mixing-settling extractors operating in the eluent chromatography mode. The present study is further development of this method as applied to separation in a cascade of mixing-settling extractors operating in a recirculation chromatography mode. A mathematical model was developed, and periodic and continuous processes of extraction separation were analyzed for conditions with a mixture of components loaded into a cascade of mixing-settling extractors in the form of a series of successive pulse injections separated by short time intervals. Experiments were performed on a cascade of mixing-settling extractors, which confirmed that the model is reliable. It was shown on some examples that the serial method of loading the solution into a closed circuit of extractors significantly increases the efficiency of separation. [ABSTRACT FROM AUTHOR]

SOLEX, a solid extractant for extracting metal chlorides from solutions, has been obtained by impregnating tributyl phosphate (TBP) and iodine into granulated macroporous polystyrene stitched by divinylbenzene. The sorption properties of the product are studied. The possibility of selectively extracting scandium from chloride solutions and its desorption by water are shown. This sorbent can be used for separation from REM. The value of separation coefficients of scandium/REM exceeds 1000. [ABSTRACT FROM AUTHOR]

Phase equilibria in the sections of the Ca(NO3)2–CO(NH2)2–H2O system and the deicing properties of calcium nitrate and carbamide mixtures with a ratio between the components ranging from 90 : 10 to 40 : 60 have been studied. Eutectic temperatures with ice, melting ability at a temperature of –5 and ‒10°C, and the character of interaction with water (the occurrence of an endothermic or exothermic effect) have been determined for these mixtures. Mixtures having the best anti-icing properties are revealed. [ABSTRACT FROM AUTHOR]

Lanthanum extraction from chloride-acetate solutions using mixtures of bis(2,4,4-trimethylpentyl)phosphinic acid (Cyanex 272) and caprylic acid in hexane has been studied depending on the composition of aqueous and organic phases. Based on the results, it is found that the lanthanum extraction from chloride-acetate solutions proceeds according to a cation-exchange mechanism occurring in the organic phase with the prevailing formation of Cyanex 272 complexes solvated with caprylic acid molecules. It is shown that, when the process is carried out fusing acetic acid–acetate solutions, it is quite possible to separate lanthanum and ytterbium while attaining high separation coefficients. [ABSTRACT FROM AUTHOR]

The change in the viscosity of a reaction mixture in the process of polystyrene synthesis and the possibility of controlling it in the course of polymerization have been studied. A laboratory reactor is used in this study, and the plots meeting our expectations are obtained for the change in the reactor stirrer rotation speed and output adjustable speed drive signal. An adequate fuzzy viscosity change model is created for use in the control system. [ABSTRACT FROM AUTHOR]

The mechanism and kinetics of the selective catalytic methylacetylene hydrogenation reaction in propane–propylene gas mixtures were studied until the complete consumption of methylacetylene in them on the Pd nanocatalyst (Pd/α-Al2O3) promoted by metals from Groups I, II, and VI of Mendeleev's Periodic Table at a Pd content of 0.05 wt %. The experiments were performed in an isothermic plug flow reactor of 100 cm3 in volume and a bench polytropic reactor of 8 dm3 in volume. The experiments were carried out by varying the feedstock hourly space velocity from 2000 to 3000 h–1, the reaction mixture temperature from 303 to 420 K, and the molar hydrogen/methylacetylene ratio from 1.5 to 3.0. Overall, 40 experiments in the isothermic flow-type reactor and 30 experiments in the bench polytropic reactor were carried out. Based on the results of laboratory experiments, a stagewise mechanism was proposed for this catalytic reaction, and the kinetic model corresponding to this mechanism was constructed. The model constants were estimated by the least-squares technique. For the studied reaction, the selective region where there was no methylacetylene, and the propylene concentration in the outlet flow was higher than in the initial flow of reagents, was determined. [ABSTRACT FROM AUTHOR]

On the basis of the classic concepts of the theory of solid-phase combustion, for the first time, a model with a detailed scheme of chemical reactions is numerically implemented, taking into account the dependence of properties on the composition and the ignition stage of the igniter. A theoretical substantiation of the non-thermal character of termination of the reaction after its initiation when the mass fraction of excess titanium in the reaction products reaches more than 50% is presented. It was found that, both in the simulation and in the experiment, the main SHS products in the studied concentration range are titanium silicide Ti5Si3 and titanium. The calculation showed that, in reaction mixtures with the target composition of SHS products Ti5Si3 + 20% Ti, combustion occurs in an oscillatory mode with an increasing amplitude of the combustion rate fluctuations during wave propagation through the reaction mixture, which can be the cause of the appearance of unstable silicides in SHS materials. The obtained theoretical results do not contradict the experimental data. [ABSTRACT FROM AUTHOR]

The boundaries of the regions of the synergistic extraction of lanthanum nitrate and cerium(III) nitrate from low-acid nitrate solutions containing the salting-out agent NH4NO3 with 1.0 M isomolar mixtures of tri-n-octylmethylammonium nitrate and tri-n-butyl phosphate (TBP) in toluene were determined by the method of isomolar series. For the first time, the chemistry of the extraction in the determined regions of the synergistic effect is defined as a continuous sequence of the mixed complexes being extracted with the composition (R4N)n[Ln(NO3)3 + n ⋅ mTBP], where n = 1–3, m = 3–1 for lanthanum and n = 1–3, m = 4–1 for cerium(III), depending on the molar ratio between the extractants. The opposite changes in n and m in the mixed complexes with increasing concentration of the quaternary salt in the mixture is explained by the replacement of phosphoryl ligands of tri-n-butyl phosphate by nitrate ligands of tri-n-octylmethylammonium nitrate until their complete replacement from the coordination sphere of the lanthanide. [ABSTRACT FROM AUTHOR]

The limit of the productivity of a binary distillation column is obtained depending on heat consumption. It is shown that the consumption of heat per mole of the mixture to be separated in a reversible process for multicomponent mixtures depends on the order of separation, and irreversible consumption is monotonically related to it. This allows reversible indicators to be used to select the order of separation. The problem of the expediency of using a separating agent to increase the efficiency of separating mixtures with close boiling points of the components is considered. [ABSTRACT FROM AUTHOR]

An equation of state based on the perturbed-chain statistical associating fluid theory (PC-SAFT) for estimates of sound speed in natural-gas mixtures is successfully applied in this work. Prediction results of the speed of sound for five binary and six multicomponent systems (dataset includes 1000 data points taken from literature) containing hydrocarbons, nitrogen, and carbon dioxide in a wide range of temperatures (250–415 K) and pressures (0.1–60 MPa) are presented. The fitting parameters of the binary interaction were not used in the calculations. The results of modeling for the speed of sound are shown to be in good agreement with the literature data. [ABSTRACT FROM AUTHOR]

The electroflotation extraction of sparingly soluble rare-earth compounds from aqueous solutions containing chloride ions was studied. At pH in the range 5–9, the recovery did not exceed 15%. The influence of various organic additives on the efficiency of electroflotation was also investigated. When the SUPERFLOC C-494 cationic flocculant was introduced in the system at pH 9, the recovery was 74%. The maximum recovery of sparingly soluble compounds of all elements of the multicomponent system was observed at pH 7 after addition of SeptaPAV (c) (α = 97–98%) and PEO-1500 (n) (α = 86–98%). The efficiency of the process remained high at a high NaCl concentration (100 g/L) in the presence of surfactants and flocculants. It was shown that electroflotation makes it possible to effectively extract sparingly soluble compounds of a mixture of rare-earth metals both from wash waters when washing rare-earth precipitates to remove chloride ions and from the (NaCl) salt solutions of filtrates. [ABSTRACT FROM AUTHOR]

The extractive distillation of an isobutanol–isobutyl acetate mixture using dimethylformamide has been considered. Schemes that use vapor recompression heat pumps and partially thermally coupled distillation systems both without and with a heat pump are considered in comparison with the conventional schemes. It is shown that the use of heat pumps in the process under investigation allows for a considerable reduction in the energy consumption and total annual costs. [ABSTRACT FROM AUTHOR]

The use of dividing-wall columns for separating the C4+ pyrolysis fraction is considered. The influence of the phase state of the feed flow on the energy consumption in column reboilers is investigated. It is shown for the first time that the use of dividing-wall columns is more efficient when using the feed stream with a high vapor fraction of 80–100%. The largest energy-saving effect of the dividing-wall column is provided by using the feed in the vapor phase. In this case, the energy savings can reach 30%. In addition, it is shown that the use of dividing-wall columns reduces capital costs by 18–21%. [ABSTRACT FROM AUTHOR]

On the basis of a thermodynamic–topological analysis of phase equilibrium diagrams of reaction mixtures formed during the liquid phase epoxidation of allyl chloride with an aqueous solution of hydrogen peroxide in an organic solvent in the presence of a heterogeneous catalyst, two principal technological separation schemes are proposed. Two lower alcohols are considered as solvents: methanol and propanol-2. Both schemes are aimed at the isolation of all components in pure form and are based on the use of special separation methods: extractive rectification with dimethyl sulfoxide (separation of allyl chloride–methanol and propanol-2–water component pairs) and a combination of rectification and delamination (separation of binary allyl chloride–water and water mixtures–epichlorohydrin). The material balances of separation schemes for mixtures of a specific composition are calculated (one composition for both mixtures is considered). To determine the operation parameters of rectification columns (the number of separation stages, feed plate, and reflux ratio), a computational experiment is conducted using the Aspen Plus® software. Preference is given to parameters ensuring the production of all substances with a purity that meets GOST (State Standard) with minimum energy consumption. The separation scheme of the mixture with propanol-2 containing one column less is characterized by a lower total number of separation stages (by 32 theoretical plates) and lower (by 11%) energy consumption compared to the separation scheme of the mixture with methanol. In addition, the epoxidation reaction with an excess of propanol-2 (the alcohol concentration should be at least 68 wt %) can significantly simplify the allocation of the target product of epichlorohydrin, which is impossible for a system with methanol. [ABSTRACT FROM AUTHOR]

Under the conditions of preliminary treatment during the preparation to annealing of a mixture of Tuva clays with the dearsenation cake of the Khovu-Aksy dump sludge, the material was found to undergo a chemical process that forms nepheline. Based on the calculated Gibbs energies of the reactions, it was concluded that the reaction occurs at the minimum number of components in the system: silicate Na4Mg2Si3O10–kaolinite (kaolinite + orthoclase). [ABSTRACT FROM AUTHOR]

An algorithm and an application software package have been developed for calculating the vapor–liquid equilibrium of multicomponent mixtures using the optimal parameters of equilibrium models (namely, the Wilson, NRTL, and UNIQUAC models) for binary pairs of the pure components of a mixture. The parameters of the models have been optimized by extremum localization, simple iteration, and certain other methods at the minimum of the optimization criterion, i.e., the sum of the squared deviations between experimental and calculated values for the equilibrium compositions of the vapor phases (at checkpoints) for each of the binary pairs of pure components. [ABSTRACT FROM AUTHOR]

Technical re-equipment in construction industry tends toward the wide use of cellular concrete. The formulation and advantages of these materials were analyzed. The technological difficulties in their manufacture were mentioned. The most difficult problem is to ensure uniformity by quickly mixing the aerated concrete mixtures of components that differ in composition and mass fraction before the start of active gas formation, gas retention, and especially solidification. These difficulties can be eliminated by using the new technique of vibrojet mixing of both Bingham and Newtonian media. Forced high-frequency vibration actually increases the thixotropy of the mixture regardless of the number of components and their mass and physicomechanical properties. At the same time, monitoring the vibration parameters increases the circulation and interaction of the generated submerged jet flows. Rheological models were developed to determine the technical characteristics of the mixer vibrodrive and the process parameters. Supercomputer modeling of various scenarios of vibrojet mixing in the FlowVision program allowed visualization and optimization of modes to completely exclude stagnant zones in the mixer. In a full-scale experiment, test samples were prepared from the aerated concrete mixtures obtained by centrifuging and vibromixing. Their growth and strength characteristics were compared in accordance with GOST (State Standard) 10180-2012. The results showed that the new method for the preparation of mixtures and products from aerated concrete is highly effective. [ABSTRACT FROM AUTHOR]

An analytical review on methods for extracting arsenic from acidic solutions using various classes of industrial and advanced organophosphorus extractants and their mixtures is given. The states of arsenic(IV) and arsenic(V) in solutions of acids are described. Comparative data on the extraction of different forms of arsenic from acidic process solutions, including cutoff electrolytes of the copper industry, are given. [ABSTRACT FROM AUTHOR]

Numeric simulation of the pervaporation process is carried out using molecular dynamics. Various conditions of the separation of an ideal binary Lennard-Jones mixture using a crystalline membrane are considered. Components of separated mixtures differ in regards to the energy of interaction with molecules of the membrane. As a result of simulation, fields of concentrations and densities along the cell, as well as flux values of components, are obtained. In addition, coefficients of the diffusion of components in the membrane are computed. It is shown that the correspondence of numeric simulation data to macroscopic mass transfer equations are observed in all cases. It can be concluded that the behavior of molecules in a nonequilibrium system with a scale of several dozens of molecule diameters corresponds to transfer equations of linear nonequilibrium thermodynamics. Results of numeric simulation show the selectivity of a membrane in regard to the component with a larger interaction energy. It is shown that molecular simulation is able to predict the main characteristics of membrane separation (fluxes, selectivity, adsorption, and diffusion coefficients). [ABSTRACT FROM AUTHOR]

An alternative solvent for the production of epichlorohydrin via the epoxidation of allyl chloride with an aqueous hydrogen peroxide solution over a heterogeneous catalyst based on a granulated titanium-containing zeolite has been selected. The problem of replacing toxic methanol with other solvents, which provide, in particular, a simplification of the separation flowsheet, has been solved. Five water–allyl chloride–epichlorohydrin–solvent–heavily boiling fraction five-component systems have been studied (methanol, ethanol, propanol-1, propanol-2, and butanol-1). A thermodynamic topological analysis of phase equilibrium diagrams and an assessment of the possibility and feasibility of separating the mixtures via a method based on a combination of distillation and splitting have been conducted. The most promising solvent for the allyl chloride epoxidation reaction is propanol-2. [ABSTRACT FROM AUTHOR]

The extraction of scandium from solutions of the waste of sulfuric-acid leaching from the magnetic separation of titanomagnetites via toluene solutions of equinormal mixtures of D2EHPA and MTAA sulfate has been studied. The conditions for scandium quantitative extraction from solutions containing 2.0-3.0 mol/L of HSO and 5-10 mg/L of Sc have been determined with the saturation of the organic phase up to 300-450 mg/L with respect to Sc. It has been shown that the two-stage reextraction of scandium from the saturated organic phase by alkaline-carbonate solutions containing 12 wt % of NaCO + 1 wt % of NaOH allows scandium and accompanying impurities of nonferrous and rare metals to be completely converted into a solid that forms a rough scandium concentrate containing 4-8 wt % of Sc, which can be used to prepare high-purity scandium oxide. [ABSTRACT FROM AUTHOR]

The extraction of medium-heavy rare-earth elements, such as gadolinium (Gd), terbium (Tb), and dysprosium (Dy), with extractant mixtures that comprise technical di-2-ethylhexyl phosphoric acid (D2EHPA) and tri- n-butyl phosphate (TBP) has been investigated individually and in their simultaneous presence. Synergistic coefficients and separation factors of the Tb/Gd, Dy/Gd, and Dy/Tb pairs of elements have been calculated. The mathematical simulation of the extraction isotherm has been performed based on the example of Gd and some assumptions about the chemical composition of the extracted complexes have been made. [ABSTRACT FROM AUTHOR]

The simulation of phase equilibrium in a multicomponent reaction system of ethanol dehydrogenation process has been performed. The structure of the distillation diagram of this system has been found and its evolution during changes in pressure has been studied. An analysis of the diagram properties has made it possible to define the range of values of the operating parameters that allow for the separation of the reaction mixture in order to propose a structure of technological separation system and to carry out its parametric optimization. [ABSTRACT FROM AUTHOR]

This work deals the computational performance improvement of vapor-liquid equilibria solver for fluids mixtures. The code here developed is based on the chemical potential equality (expressed in terms of fugacity) and implements Soave-Redlich-Kwong and Peng-Robinson equations of state with classical van der Waals mixing rules. To reduce the bulk of the computational effort required by the solver we propose the following approaches: (i) exploit high-order methods for the solution of Rachford-Rice equation; (ii) develop an efficient programming methodology for the sub-routines devoted to the fugacity coefficients computation in order to reduce their overall impact on the CPU-time exploiting the parallelism at CPU level, i.e. CPU pipelining, and cache blocking. In this paper we have carefully evaluated the effectiveness of the aforementioned approaches performing a suite of computations of the equilibrium properties of several literature mixtures. The pros and cons of the strategies here suggested are outlined and discussed. [ABSTRACT FROM AUTHOR]

Heat consumption in various two-column arrangements for separating ideal and real ternary mixtures by distillation have been compared. It has been shown that the first specified separation of ternary mixtures is not always the least energy-consuming process. The minimum heat consumption in different separation arrangements has been explained. [ABSTRACT FROM AUTHOR]

The results of studying the process of distillation in a column with 21 vortex contact stages have been reported. The partial condensation of an ascending ethanol-water mixture vapor at the contact stages has been shown to intensify the mixture distillation process by threefold compared to adiabatic distillation. The process parameters that intensify heat and mass transfer in thermal distillation have been established. Some relationships for estimating the efficiency of a vortex contact stage have been derived. [ABSTRACT FROM AUTHOR]

The results of studies of the hydrodifluoride leaching of the perovskite concentrate have been presented. It has been shown that processing the perovskite concentrate using fluoride technology enables one to transform niobium and tantalum into a solution, along with fluoroammonium salts of titanium, iron, and silicon, and to isolate rare-earth elements in the form of complex fluoroammonium salts mixed with CaF within a few stages. [ABSTRACT FROM AUTHOR]

This paper deals with a new method of dynamic countercurrent cyclic extraction. Each cycle consists of two lightand heavy-phase motion stages. The time of each phase is variable and must be specified for each process cycle. A mixture of components to be separated is injected with one of the phases during a certain time period, which does not exceed the time of this phase motion stage in the initial process cycle. A mathematical model of dynamic countercurrent cyclic extraction is developed. Some analytical relationships for calculating the separation of liquid mixtures by this method are derived. The proposed dynamic regime of extraction has been established to considerably (by several times) increase the operational efficiency of extraction units. A comparison of the experiment and theory demonstrates satisfactory agreement between them. [ABSTRACT FROM AUTHOR]

Possible process flow sheets for the separation of a quaternary mixture formed in the production of methyl tert-butyl ether were synthesized using different special methods, and the most energy-efficient flow sheet was selected. [ABSTRACT FROM AUTHOR]

The pre-reforming of diesel fuel combined with subsequent steam reforming of pre-reforming products integrated with membrane separation of hydrogen is the most promising way of obtaining pure hydrogen for fuel cells. Here, we consider the first part of this problem-diesel fuel pre-reforming. The following commercial nickel-containing catalysts have been tested in the pre-reforming reaction: NIAP-18 (Ni, 15 wt %; CaO, 8 wt %; AlO, 74.4 wt %), NIAP-12-05 (Ni, 48 wt %; CrO, 27 wt %), NIAP-07-01 (NiO, 36 wt %), NIAP-07-05 (NiO, 38 wt %; CrO, 12 wt %). A number of new pre-reforming catalysts based on manganese and cobalt compounds have also been examined. The tests have been carried out at pressures of 1, 6, and 15 atm, temperatures of 470-560°C, and gas hourly space velocities of 6000-12000 h. The experiments have demonstrated that the nickel-containing catalysts afford a near-equilibrium product composition, while the reaction over the catalysts based on manganese and cobalt compounds yields a nonequilibrium product composition. A mathematical model has been developed for diesel fuel pre-reforming in an adiabatic reactor with a fixed catalytic bed. Model parameters ranging from process kinetics to heat and mass transfer coefficients have been estimated. The results of modeling have been compared to experimental data available from the literature. The potential of the mathematical model has been illustrated by performing calculations for adiabatic reactors with various output capacities. [ABSTRACT FROM AUTHOR]

A general approach to the synthesis of the complete set of distillation flowsheets for multicomponent zeotropic mixtures is considered, which includes construction of generalized separation graphs and an analysis of all intermediate fractions. The approach is applied to the distillation of particular zeotropic four-component mixtures of different compositions. An optimal distillation flowsheet is obtained for each of the 60 cases examined. The dynamic programming conception is inapplicable to mixtures consisting of a few components, because some of the columns of the optimal flowsheet may function in a nonoptimal way, which is in agreement with the optimization theory for large systems. [ABSTRACT FROM AUTHOR]

Various aspects of the mathematical modeling for distillation of multicomponent mixtures, the general properties of dynamic systems for distillation, and the features of the simplest mathematical model based on the boundary layers and the main mass transfer resistance in each phase are under consideration. The linear gradient of concentrations in the layers is used in the model. The decisive role of the driving force, i.e., the difference between the equilibrium and working nodes represented as corresponding vectors, is also discussed. [ABSTRACT FROM AUTHOR]

A comparative analysis of the direct and indirect splits and class-1 fractionation of ternary zeotropic mixtures has been carried out in terms of total vapor flow rate by means of a mathematical experiment. Composition regions in which a certain separation flowsheet minimizes the total vapor flow rate have been found. [ABSTRACT FROM AUTHOR]

Based on an analysis of the results of a series of numerical experiments, the principles of isotope-selective mass transfer have been analyzed in ordinary square cascade from gas centrifuges to separate multi-component mixtures depending on the relationship between external flows. It has been shown that the ratio of product and feed flows considerably affects the mass transfer of the components of separated mixture along the square cascade primarily on the components with intermediate mass number (in a series of mass numbers of all components of separated mixture). With change in the given ratio, the transfer of intermediate components may undergo qualitative changes and shift the direction of enrichment, e.g., from the light end of the cascade to the heavy end. The determined principles rationalize the opportunities to control mass transfer of intermediate components due to the change in the ratios between external flows of cascade. [ABSTRACT FROM AUTHOR]

The vapor-liquid equilibrium for a benzene-heptane- N-methylpyrrolidone mixture is experimentally studied. The mathematical modeling of phase equilibrium is performed using the NRTL equation. The existence of a binary pseudoazeotrope in the system under study is experimentally found. [ABSTRACT FROM AUTHOR]

Extractive agents for separating benzene-perfluorobenzene biazeotropic mixture have been suggested according to the results of excess Gibbs energy analysis for systems containing benzene, perfluorobenzene and selective substances. [ABSTRACT FROM AUTHOR]

Mathematical model of flotation in dispersed mixture of liquid, solid, and gas phases has been designed within the considerations of the mechanics of multiphase media with the assumption of the degree of mineralization of the bubble surface. The application of the designed model has been demonstrated based on the example of one-dimensional stationary flotation and it has been shown that the equations that describe the emergence of bubbles are singularly disturbed ('rigid'). The effect of size and concentration of bubbles, as well as volume content of dispersed particles, on flotation has been analyzed. [ABSTRACT FROM AUTHOR]

The hydrodynamic conditions in a centrifugal thickener that consists of a cylindrical tube divided by longitudinal baffles into a certain number of sectors were studied. The separation of a two-phase mixture was described using the equations of the mechanics of heterogeneous media in the cylindrical coordinate system with consideration for flow pattern peculiarities. The problem was solved semi-analytically. The constructed mathematical model of the separation process was used to perform some numerical calculations. [ABSTRACT FROM AUTHOR]

The influence of grinding the initial quartz sand on the degree of activation of the sand-grain surface during processing using a fluorinating reagent has been studied. Using the method of the synchronous thermal analysis, the technological parameters of producing ammonium hexafluorosilicate using mixtures of different fractions of sand at temperatures in the range of 25-400°C were examined. The investigation of intermediate phases, formed during the thermogravimetric experiment was carried out with the X-ray analysis. It was established that formation of ammonium hexafluorosilicate with crushed quartz sand occurs at temperatures of 30-40°C lower than the source conditions. [ABSTRACT FROM AUTHOR]

A mathematical description of the process of the removal of water-soluble admixtures from finely dispersed precipitates formed on a filter baffle in the regime of the cyclic supply of a washing liquid was developed based on the mechanism of the molecular diffusion of a water-soluble admixture in a paste and through pores to enable the calculation of the concentration of water-soluble admixtures in a paste and a washing liquid at any time moment. [ABSTRACT FROM AUTHOR]

The problem of optimal superstructure-based synthesis of a system of distillation columns is formulated as a mixed integer nonlinear programming problem, and a branch-and-bound method is suggested for solving this problem. A two-stage approach to the problem is described, and the corresponding computational algorithm is presented. [ABSTRACT FROM AUTHOR]

The article provides a rationale for nonlocal laws governing dynamic systems, using vapor-liquid equilibrium diagrams as an example. [ABSTRACT FROM AUTHOR]

The chemical and thermal components of exergy of solid-phase reaction systems have been analyzed. Chemical exergy is the measure of energy maintenance of chemical reaction; therefore, chemical exergy is intrinsic, not for a particular substance, but rather for a reaction mixture with a particular composition. The temperature dependence of the chemical exergy of the exothermic reaction mixture has a maximum and the temperature dependence of the chemical exergy of endothermic reaction mixture has a minimum. Equations for calculating the exergy components have been suggested, which assume the possibility of the presence of structural polymorphism for the crystal components of reaction mixture. [ABSTRACT FROM AUTHOR]