Calculation of three-phase methane-ethane binary clathrate hydrate phase equilibrium from Monte Carlo molecular simulations

Methane and ethane are the simplest hydrocarbon molecules that can form clathrate hydrates. Previous studies have reported methods for calculating the three-phase equilibrium using Monte Carlo simulation methods in systems with a single component in the gas phase. Here we extend those methods to a binary gas mixture of methane and ethane. Methane-ethane system is an interesting one in that the pure components form sII clathrate hydrate whereas a binary mixture of the two can form the sII clathrate. The phase equilibria computed from Monte Carlo simulations show a good agreement with experimental data and are also able to predict the sI-sII structural transition in the clathrate hydrate. This is attributed to the quality of the TIP4P/Ice and TRaPPE models used in the simulations. (C) 2014 Elsevier B.V. All rights reserved.

High-pressure phase equilibrium in the {carbon dioxide (1) + 1-chloropropane (2)} binary system

Abstract The current study reports original vapour-liquid equilibrium (VLE) for the system {CO2 (1) + 1-chloropropane (2)}. The measurements have been performed over the entire pressure-composition range for the (303.15, 313.15 and 328.15) K isotherms. The values obtained have been used for comparison of four predictive approaches, namely the equation of state (EoS) of Peng and Robinson (PR), the Soave modification of Benedict–Webb–Rubin (SBWR) EoS, the Critical Point-based Revised Perturbed-Chain Association Fluid Theory (CP-PC-SAFT) EoS, and the Conductor-like Screening Model for Real Solvents (COSMO-RS). It has been demonstrated that the three EoS under consideration yield similar and qualitatively accurate predictions of VLE, which is not the case for the COSMO-RS model examined. Although CP-PC-SAFT EoS exhibits only minor superiority in comparison with PR and SBWR EoS in predicting VLE in the system under consideration, its relative complexity can be justified when taking into account the entire thermodynamic phase space and, in particular, considering the liquid densities and sound velocities over a wider pressure-volume-temperature range.

MODELLING OF HIGH-PRESSURE PHASE EQUILIBRIUM IN SYSTEMS OF INTEREST IN THE FOOD ENGINEERING FIELD USING THE PENG-ROBINSON EQUATION OF STATE WITH TWO DIFFERENT MIXING RULES

In this work, thermodynamic models for fitting the phase equilibrium of binary systems were applied, aiming to predict the high pressure phase equilibrium of multicomponent systems of interest in the food engineering field, comparing the results generated by the models with new experimental data and with those from the literature. Two mixing rules were used with the Peng-Robinson equation of state, one with the mixing rule of van der Waals and the other with the composition-dependent mixing rule of Mathias et al. The systems chosen are of fundamental importance in food industries, such as the binary systems CO(2)-limonene, CO(2)-citral and CO(2)-linalool, and the ternary systems CO(2)-Limonene-Citral and CO(2)-Limonene-Linalool, where high pressure phase equilibrium knowledge is important to extract and fractionate citrus fruit essential oils. For the CO(2)-limonene system, some experimental data were also measured in this work. The results showed the high capability of the model using the composition-dependent mixing rule to model the phase equilibrium behavior of these systems.

Fractionation of lemon essential oil by solvent extraction: Phase equilibrium for model systems at T=298.2 K

The fractioning of lemon essential oil can be performed by liquid-liquid extraction using hydrous ethanol as a solvent. A quaternary mixture composed of limonene, gamma-terpinene, beta-pinene, and citral was used to simulate lemon essential oil. In this paper, we present (liquid + liquid) equilibrium data that were experimentally determined for systems containing essential oil compounds, ethanol, and water at T = 298.2 K. The experimental data were correlated using the NRTL and UNIQUAC models, and the mean deviations between calculated and experimental data were less than 0.0053 in all systems, indicating the accuracy of these molecular models in describing our systems. The results show that as the water content in the solvent phase increased, the values of the distribution coefficients decreased, regardless of the type of compound studied. However, the oxygenated compound always showed the highest distribution coefficient among the components of the essential oil, thus making deterpenation of the lemon essential oil a feasible process. (C) 2012 Elsevier Ltd. All rights reserved.

GE models and algorithms for condensed phase equilibrium data regression in ternary systems: limitations and proposals

Phase equilibrium data regression is an unavoidable task necessary to obtain the appropriate values for any model to be used in separation equipment design for chemical process simulation and optimization. The accuracy of this process depends on different factors such as the experimental data quality, the selected model and the calculation algorithm. The present paper summarizes the results and conclusions achieved in our research on the capabilities and limitations of the existing GE models and about strategies that can be included in the correlation algorithms to improve the convergence and avoid inconsistencies. The NRTL model has been selected as a representative local composition model. New capabilities of this model, but also several relevant limitations, have been identified and some examples of the application of a modified NRTL equation have been discussed. Furthermore, a regression algorithm has been developed that allows for the advisable simultaneous regression of all the condensed phase equilibrium regions that are present in ternary systems at constant T and P. It includes specific strategies designed to avoid some of the pitfalls frequently found in commercial regression tools for phase equilibrium calculations. Most of the proposed strategies are based on the geometrical interpretation of the lowest common tangent plane equilibrium criterion, which allows an unambiguous comprehension of the behavior of the mixtures. The paper aims to show all the work as a whole in order to reveal the necessary efforts that must be devoted to overcome the difficulties that still exist in the phase equilibrium data regression problem.

Some examples of modeling in chemical engineering: thermal treatment of polymers, phase equilibrium calculations and process design

Presentation submitted to PSE Seminar, Chemical Engineering Department, Center for Advanced Process Design-making (CAPD), Carnegie Mellon University, Pittsburgh (USA), October 2012.

Phase-equilibrium data and liquidus for the system "MnO"-CaO-Al2O3-SiO2 at Al2O3/SiO2 of 0.55 and 0.65

Phase-equilibrium data and liquidus isotherms for the system MnO-CaO-(Al2O3 + SiO2) at silicomanganese alloy saturation have been determined in the temperature range of 1373 to 1723 K. The results are presented in the form of the pseudoternary sections MnO-CaO-(Al2O3 + SiO2) with Al2O3/SiO2 weight ratios of 0.55 and 0.65. The primary-phase fields have been identified in this range of conditions.

Phase equilibrium studies at normal pressures

A total pressure apparatus has been developed to measure vapour-liquid equilibrium data on binary mixtures at atmospheric and sub-atmospheric pressures. The method gives isothermal data which can be obtained rapidly. Only measurements of total pressure are made as a direct function of composition of synthetic liquid phase composition, the vapour phase composition being deduced through the Gibbs-Duhem relationship. The need to analyse either of the phases is eliminated. As such the errors introduced by sampling and analysis are removed. The essential requirements are that the pure components be degassed completely since any deficiency in degassing would introduce errors into the measured pressures. A similarly essential requirement was that the central apparatus would have to be absolutely leak-tight as any leakage of air either in or out of the apparatus would introduce erroneous pressure readings. The apparatus was commissioned by measuring the saturated vapour pressures of both degassed water and ethanol as a function of temperature. The pressure-temperature data on degassed water measured were directly compared with data in the literature, with good agreement. Similarly the pressure-temperature data were measured for ethanol, methanol and cyclohexane and where possible a direct comparison made with the literature data. Good agreement between the pure component data of this work and those available in the literature demonstrates firstly that a satisfactory degassing procedure has been achieved and that secondly the measurements of pressure-temperature are consistent for any one component; since this is true for a number of components, the measurements of both temperature and pressure are both self-consistent and of sufficient accuracy, with an observed compatibility between the precision/accuracy of the separate means of measuring pressure and temperature. The liquid mixtures studied were of ethanol-water, methanol-water and ethanol-cyclohexane. The total pressure was measured as the composition inside the equilibrium cell was varied at a set temperature. This gave P-T-x data sets for each mixture at a range of temperatures. A standard fitting-package from the literature was used to reduce the raw data to yield y-values to complete the x-y-P-T data sets. A consistency test could not be applied to the P-T-x data set as no y-values were obtained during the experimental measurements. In general satisfactory agreement was found between the data of this work and those available in the literature. For some runs discrepancies were observed, and further work recommended to eliminate the problems identified.

Phase equilibrium studies at moderate pressures

The theory of vapour-liquid equilibria is reviewed, as is the present status or prediction methods in this field. After discussion of the experimental methods available, development of a recirculating equilibrium still based on a previously successful design (the modified Raal, Code and Best still of O'Donnell and Jenkins) is described. This novel still is designed to work at pressures up to 35 bar and for the measurement of both isothermal and isobaric vapour-liquid equilibrium data. The equilibrium still was first commissioned by measuring the saturated vapour pressures of pure ethanol and cyclohexane in the temperature range 77-124°C and 80-142°C respectively. The data obtained were compared with available literature experimental values and with values derived from an extended form of the Antoine equation for which parameters were given in the literature. Commissioning continued with the study of the phase behaviour of mixtures of the two pure components as such mixtures are strongly non-ideal, showing azeotopic behaviour. Existing data did not exist above one atmosphere pressure. Isothermal measurements were made at 83.29°C and 106.54°C, whilst isobaric measurements were made at pressures of 1 bar, 3 bar and 5 bar respectively. The experimental vapour-liquid equilibrium data obtained are assessed by a standard literature method incorporating a themodynamic consistency test that minimises the errors in all the measured variables. This assessment showed that reasonable x-P-T data-sets had been measured, from which y-values could be deduced, but that the experimental y-values indicated the need for improvements in the design of the still. The final discussion sets out the improvements required and outlines how they might be attained.

Phase diagram and dielectric studies of binary organic materials

The phase equilibrium studies of organic system, involving resorcinol (R) and p-dimethylaminobenzaldehyde (DMAB), reveal the formation of a 1:1 molecular complex with two eutectics. The heat of mixing, entropy of fusion, roughness parameter, interfacial energy, and the excess thermodynamic functions were calculated based on enthalpy of fusion data determined via differential scanning calorimetric (DSC) method. X-ray powder diffraction studies confirm that the eutectics are not simple mechanical mixture of the components under investigation. The spectroscopic investigations (IR and NMR) suggest the occurrence of hydrogen bonding between the components forming the molecular complex. The dielectric measurements, carried out on hot-pressed addition compound (molecular complex), show higher dielectric constant at 320 K than that of individual components. The microstructural investigations of eutectic and addition compound indicate dendritic and faceted morphological features. (C) 2000 Elsevier Science B.V. All rights reserved.

Experimental and Computational Characterization of Alloy--Spinel--Corundum Equilibrium in the System Fe--Co--Al--O at 1873K

The three-phase equilibrium between alloy, spinel solid solution and alpha -Al sub 2 O sub 3 in the Fe--Co--Al--O system at 1873k was fully characterized as a function of alloy composition using both experimental and computational methods. The equilibrium oxygen content of the liquid alloy was measured by suction sampling and inert gas fusion analysis. The O potential corresponding to the three-phase equilibrium was determined by emf measurements on a solid state galvanic cell incorporating (Y sub 2 O sub 3 )ThO sub 2 as the solid electrolyte and Cr + Cr sub 2 O sub 3 as the reference electrode. The equilibrium composition of the spinel phase formed at the interface between the alloy and alumina crucible was measured by electron probe microanalysis (EPMA). The experimental results were compared with the values computed using a thermodynamic model. The model used values for standard Gibbs energies of formation of pure end-member spinels and Gibbs energies of solution of gaseous O in liquid Fe and cobalt available in the literature. The activity--composition relationship in the spinel solid solution was computed using a cation distribution model. The variation of the activity coefficient of O with alloy composition in the Fe--Co--O system was estimated using both the quasichemical model of Jacob and Alcock and Wagner's model along with the correlations of Chiang and Chang and Kuo and Chang. The computed results of spinel composition and O potential are in excellent agreement with the experimental data. Graphs. 29 ref.--AA

Characterization of Alloy-Spinel-Corundum Equilibrium in the System Fe-Ni-Al-O

The three phase equilibrium between alloy, spinel solid solution and α-alumina in the Fe-Ni-Al-O system has been fully characterized at 1823K as a function of alloy composition using both experimental and computational methods. The oxygen potential was measured using a solid state cell incorporating yttria-doped thoria as the electrolyte and Cr+ Cr2O3 as the reference electrode. Oxygen concentration of the alloy was determined by an inert gas fusion technique. The composition of the spinel solid solution, formed at the interface between the alloy and an alumina crucible, was determined by EPMA. The variation of the oxygen concentration and potential and composition of the spinel solid solution with mole fraction of nickel in the alloy have been computed using activities in binary Fe-Ni system, free energies of formation of end member spinels FeO•(1+x)Al2O3 and NiO•(1+x)Al2O3 and free energies of solution of oxygen in liquid iron and nickel, available in the literature. Activities in the spinel solid solution were computed using a cation distribution model. The variation of the activity coefficient of oxygen with alloy composition in Fe-Ni-O system was calculated using both the quasichemical model of Jacob and Alcock and the Wagner's model, with the correlation of Chiang and Chang. The computed results for the oxygen potential and the composition of the spinel solid solution are in good agreement with the measurements. The measured oxygen concentration lies between the values computed using models of Wagner and Jacob and Alcock. The results of the study indicate that the deoxidation hyper-surface in multicomponent systems can be computed with useful accuracy using data for end member systems and thermodynamic models.

Phase relations and gibbs energies in the system Mn-Rh-O

Phase relations in the system Mn-Rh-O are established at 1273 K by equilibrating different compositions either in evacuated quartz ampules or in pure oxygen at a pressure of 1.01 x 10(5) Pa. The quenched samples are examined by optical microscopy, X-ray diffraction, and energy-dispersive X-ray analysis (EDAX). The alloys and intermetallics in the binary Mn-Rh system are found to be in equilibrium with MnO. There is only one ternary compound, MnRh2O4, with normal spinel structure in the system. The compound Mn3O4 has a tetragonal structure at 1273 K. A solid solution is formed between MnRh2O4 and Mn3O4. The solid solution has the cubic structure over a large range of composition and coexists with metallic rhodium. The partial pressure of oxygen corresponding to this two-phase equilibrium is measured as a function of the composition of the spinel solid solution and temperature. A new solid-state cell, with three separate electrode compartments, is designed to measure accurately the chemical potential of oxygen in the two-phase mixture, Rh + Mn3-2xRh2xO4, which has 1 degree of freedom at constant temperature. From the electromotive force (emf), thermodynamic mixing properties of the Mn3O4-MnRh2O4 solid solution and Gibbs energy of formation of MnRh2O4 are deduced. The activities exhibit negative deviations from Raoult's law for most of the composition range, except near Mn3O4, where a two-phase region exists. In the cubic phase, the entropy of mixing of the two Rh3+ and Mn3+ ions on the octahedral site of the spinel is ideal, and the enthalpy of mixing is positive and symmetric with respect to composition. For the formation of the spinel (sp) from component oxides with rock salt (rs) and orthorhombic (orth) structures according to the reaction, MnO (rs) + Rh2O3 (orth) --> MnRh2O4 (sp), DELTAG-degrees = -49,680 + 1.56T (+/-500) J mol-1. The oxygen potentials corresponding to MnO + Mn3O4 and Rh + Rh2O3 equilibria are also obtained from potentiometric measurements on galvanic cells incorporating yttria-stabilized zirconia as the solid electrolyte. From these results, an oxygen potential diagram for the ternary system is developed.