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Modern thermodynamic models, such as the PC-SAFT equation of state, are very accurate but also computationally intensive, which limits their applicability to process design optimization, for example. Surrogate models, which can be evaluated quickly, can be used to approximate the thermodynamic equilibria. However, this requires many data points from the flash calculation routine. In this paper, we investigate three approaches to reduce the number of samples and thus the effort needed to train the surrogate models. First, Sobolev training is used, where the surrogate model is trained not only on the output values, but also on derivative information. Second, data augmentation along the tie lines in LLE systems is proposed to generate samples without additional flash calculations. Third, adaptive sampling is revisited with a novel quality criterion. It is shown that the combination of these techniques can be used to significantly reduce the number of samples required. • An extensive neural network hyperparameter screening for pT-flash surrogate modeling is conducted. • Sobolev training and data augmentation are introduced to reduce the necessary number of samples. • Adaptive sampling is revisited and combined with Sobolev training and data augmentation for improved accuracy. [ABSTRACT FROM AUTHOR]

The rise in greenhouse gas emissions makes the research and development of renewable energy sources a crucial area, with a particular emphasis on biofuels derived from biomass. In this context, design, simulation, an optimization of such bio-based process will also pose many challenges for thermodynamic models. Classical equations of state usually fail to describe these systems and there is not enough experimental data to correlate binary parameters even for group contribution models like UNIFAC. In this case, COSMO-based models become an interesting alternative, since they do not depend directly on experimental data. Even for the well-know biodiesel production there are intermediaries and byproducts showing phase equilibria that are difficult to predict. The UNIFAC (Do) and COSMO-SAC-HB2 variant were used to predict phase equilibria for mixtures related to bio-compounds. For COSMO-SAC, the first step was the revision and extension of the sigma-LVPP public database for the related molecules. For the modified UNIFAC, literature parameters were considered. Vapor-liquid, infinite dilution activity coefficient, liquid-liquid and excess enthalpy data were collected, with a total of 135 systems were investigated. The COSMO-SAC-HB2 yielded satisfactory deviation results in equilibrium of mixtures involving biocompounds, water, and alcohols. UNIFAC (Do) demonstrated satisfactory results in mixtures involving biocompounds and esters, hydrocarbons and alcohols. • UNIFAC (Do) and COSMO-SAC-HB2 variant were used to predict phase equilibria for mixtures related to bio-compounds. • VLE, LLE, IDAC and excess enthalpy experimental data were used in this study. • COSMO-SAC-HB2 and UNIFAC (Do) alternate better results. • COSMO based models have the great advantage of being able to perform without any previous experimental information. [ABSTRACT FROM AUTHOR]

Highlights • The phase behavior of various amine phase change solvents was investigated. • DMCA-MCA-AMP system shows VLLE behavior at 60 and 90 °C. • The 3 M DMCA-MCA-AMP aqueous system results in higher CO 2 loading than the corresponding 5 M aqueous mixture. • The addition of Sulfolane did not result in higher CO 2 loading. Abstract Phase change solvents are receiving increased attention in the effort to significantly reduce regeneration energy requirements in post combustion CO 2 capture processes with chemical absorption. In this study, the phase behavior of various phase change, aqueous amine solutions, was experimentally investigated. A new experimental apparatus was developed and evaluated by determining the CO 2 solubility in aqueous monoethanolamine (MEA) solutions at 40, 60 and 80 °C. Subsequently, new experimental data were obtained for aqueous solutions containing N,N -dimethylcyclohexylamine (DMCA), methylcyclohexylamine (MCA) and 2-amino-2-methyl-1-propanol (AMP) at 40, 60 and 90 °C that exhibit phase change behavior. It was observed that the investigated solutions present vapor – liquid equilibrium (VLE) at 40 °C and vapor–liquid-liquid equilibrium (VLLE) at 60 and 90 °C for CO 2 partial pressures up to approximately 70 kPa. In addition, screening experiments were performed using sulfolane, which has been previously used for gas sweeting applications, instead of AMP in the DMCA-MCA mixture. However, such system presents relatively low CO 2 solubility, compared to the aforementioned (DMCA-MCA-AMP) system and aqueous MEA solutions. Finally, additional screening experiments were performed for two aqueous DMCA – 3-methylaminopropylamine (MAPA) amine solutions at different concentrations. [ABSTRACT FROM AUTHOR]

[Display omitted] • Mixed inhibitors MeOH/MgCl 2 are more potent and environmentally benign than MeOH. • New hydrate equilibrium data for high MgCl 2 content and temperatures down to 234 K. • MgCl 2 is more powerful THI than MeOH at concentrations > 5 mass% in solution. • The synergy MeOH/MgCl 2 is more pronounced as the concentration increases. • Complete map of the anti-hydrate activity in system CH 4 –MeOH–MgCl 2 –H 2 O was constructed. Gas hydrates formation is a primary complication in the oil and gas industry. The most universal gas hydrate prevention agents are thermodynamic inhibitors. The most prominent is methanol (MeOH), which has high toxicity and evaporation losses. We experimentally studied the methane hydrate phase equilibria to systematically explore the synergism of MeOH and MgCl 2. The new data extend the range of inhibitor concentrations and equilibrium temperatures studied for magnesium chloride systems. The higher the concentration of the components, the more potent the synergy. Parameters to quantify the synergism are proposed. The data were complemented by ice-freezing temperature measurements. The results indicate that the inhibitory properties of MeOH can be improved and consumption reduced by using its combinations with MgCl 2 due to the superior salt' anti-hydrate activity and the synergistic effect. Partial replacement of the toxic MeOH with the safer and non-volatile MgCl 2 could also reduce inhibitor losses and minimize environmental impact. [ABSTRACT FROM AUTHOR]

[Display omitted] • THI order of decreasing anti-hydrate activity in the mass% and mol% scale is inverse. • Vinyl lactam KHI loses its ability to inhibit CH 4 hydrate nucleation at ≥ 20 wt% MeOH. • CH 4 hydrate grows faster in case of MeOH/KHI blends compared to H 2 O and single KHI. • Addition of MEG or DEG to KHI significantly increases the hydrate onset subcooling. • KHI/MEG blends are optimal for a hybrid inhibition strategy. Gas hydrate inhibition is a relevant topic of flow assurance. Thermodynamic hydrate inhibitors (THIs) and kinetic hydrate inhibitors (KHIs) are applied to prevent gas hydrates formation in oil and gas production facilities. We have carried out extensive experimental studies to further develop the hybrid inhibition strategy involving KHI/THI formulations. We determined methane hydrate equilibrium conditions for an aqueous solution of methanol, MEG, and DEG (≤50 mass%). Subsequently, we studied the kinetics of methane hydrate nucleation and growth for an aqueous solution of commercial vinyl lactam KHI and its blends with alcohols. KHI loses its ability to inhibit hydrate nucleation at ≥ 20 mass% methanol. Adding MeOH to KHI solution also accelerated the growth of methane hydrate. The addition of glycols to KHI increases the hydrate onset subcooling. KHI/MEG blends are optimal for hybrid inhibition as they demonstrate the enhanced delay of gas uptake and reduced rate of methane hydrate growth. [ABSTRACT FROM AUTHOR]

• Expressions for activity coefficients at infinite dilution of mixtures of low molecular weight fluids. • Analytical expressions are obtained via perturbation of Non-Random Hydrogen Bonding EoS model. • The approach accounts for specific intermolecular and intramolecular interactions. Activity coefficients of solutes at infinite dilution play a central role in molecular thermodynamics of phase equilibria, solvation, solubility and related properties. Numerous equation-of-state models highly appropriate for concentrated systems have been developed in the open literature. Quite often, however, their equations for the chemical potential or the activity coefficient are not analytical and recursive numerical methods are needed for their use. This is the case for the versatile and widely used Non-Randomness with Hydrogen-Bonding equation of state model and, in the present work, a straightforward perturbation method is used for the derivation of analytical expressions for the chemical potential or the activity coefficient of solute at infinite dilution. The derivations are validated and compared with the full numerical calculations as well as with relevant experimental data. It is shown that calculations with the approximate analytical equations are essentially identical with the full numerical ones. These derivations are of a general character and may be used in a variety of other analogous thermodynamic models. [ABSTRACT FROM AUTHOR]

Accurate calculation of equilibrium formation conditions of hydrates is important for gas storage and separation based on hydrate technology. In this work, the hydrate formation conditions of a synthesized gas mixture in tetra-n-butyl ammonium bromide (TBAB) aqueous solution were measured at temperature ranging from 278.1 to 286.2 K. An inflection point in the P – T curve of hydrate phase equilibria was found. It is suggested that the hydrate structures transformed from semiclathrate hydrates to pure structure I hydrates with an increase in formation temperature. Then a thermodynamic model was proposed for calculating formation conditions of the semiclathrate hydrates formed from the gas mixtures+TBAB aqueous solution. The Patel–Teja equation of state was used to calculate the fugacity of gaseous hydrate former and several correlations were used to calculate the properties of TBAB. Ethylene molecules are supposed not to be able to occupy the dodecahedral small cages in the TBAB semiclathrate hydrates under the experimental P – T conditions. The presented model results show good agreement with the experimental data and the literature data. [ABSTRACT FROM AUTHOR]

The behavior of bulk Freon-12 hydrate samples containing inclusions of unreacted liquid water below the ice melting point at pressures below the hydrate–ice–gas equilibrium pressure has been studied using nuclear magnetic resonance (NMR) spectroscopy. The amount of liquid water in the samples was directly measured by transverse relaxation measurements of the hydrogen nucleus of the system studied. An evidence of the long-lived existence of gas hydrate as a metastable phase and hydrate dissociation into supercooled water and gas has been presented. It was shown that the dissociation of the bulk metastable hydrate into supercooled water and gas was reversible. An influence of the phase state of the unreacted water in the samples on the stability of the metastable hydrate and mechanism of hydrate dissociation was revealed: ice crystallization led to the decay of the hydrate metastability and the hydrate dissociation into ice and gas. [ABSTRACT FROM AUTHOR]

Optimization methods that use optimality conditions of first and/or second order are known to be efficient. Commonly, such iterative methods are developed and analyzed in the light of knowledge concerning the mathematical analysis in n -dimensional Euclidean spaces, whose nature is of local character. Consequently, these methods lead to iterative algorithms that perform only local searches. Thus, the application of such algorithms to the calculation of global minimizers of a non-linear function, especially non-convex and multimodal, depends strongly on the location of the starting points. The Topographical Global Optimization method is a clustering algorithm, which uses an ingenious approach based on elementary concepts of graph theory, in order to generate good starting points for local search methods, from points distributed uniformly in the interior of the feasible set. The purpose of this paper is two-fold. The first is a revisit to the Topographical Global Optimization method, where, for the first time, its foundations are formally described and its basic properties are mathematically proven. In this context, we propose a semi-empirical formula for computing the key parameter of this clustering algorithm, and, using a robust and efficient direction interior-point method, we extend the use of the Topographical Global Optimization method to problems with inequality constraints. The second objective is the application of this method to the phase stability analysis of mixtures, a difficult and important global optimization problem of the chemical engineering thermodynamics. Furthermore, in order to have an initial assessment of the power of this technique, first we solve 70 test problems, and then compare the performance of the method considered here with the MIDACO solver, a powerful software recently introduced in the field of global optimization. [ABSTRACT FROM AUTHOR]

A rigorous thermodynamic model in Aspen Plus® was developed to predict the thermodynamic properties of PZ-AMP-CO2-H2O over a wide range of conditions using the electrolyte non-random two liquid activity coefficient (e-NRTL) model. The sequential regression methodology was applied. This model is based on the piperazine (PZ) model developed by Frailie, in which PZ was treated as a Henry's component. Vapor-liquid equilibrium (VLE), heat capacity, and excess enthalpy data for the binary aqueous 2-amino-2-methyl-propanol (AMP) system were used to get the e-NRTL interaction parameters for AMP-H2O. Unavailable standard state properties of protonated amines were regressed from pKa data. VLE data for AMP-CO2-H2O were used to determine the e-NRTL interaction parameters for the molecule-electrolyte binaries. Finally, the thermodynamic model for PZ-AMP-CO2-H2O was obtained by regressing the VLE and heat capacity data for PZ-AMP-H2O and VLE data for PZ-AMP-CO2-H2O in two steps. The model succeeds in predicting CO2 solubility, NMR speciation, and heat of CO2 absorption for PZ-AMP blends with variable loading and temperature. The thermodynamic model can be used for the simulation and design of the CO2 capture process. [ABSTRACT FROM AUTHOR]

Abstract: Fluid phase equilibria involving nano-dispersed phases, where at least one of the coexisting phases is confined to a small volume, are investigated by molecular dynamics simulation. Complementing previous studies on nanoscopic droplets, simulation volumes containing a nanoscopic gas bubble surrounded by a subsaturated liquid phase under tension, i.e. at negative pressure, are conducted in the canonical ensemble. The boundary conditions are chosen such that the phase equilibrium at the curved interface is thermodynamically stable. Two distinct size-dependent effects of opposite sign are found for the density of the gas in the centre of the bubble. The curvature dependence of the surface tension is considered, employing an approach based directly on the average radial density profiles. [Copyright &y& Elsevier]

Usually, phase equilibrium measurements are performed with pure substances. On the other hand, in technical applications, technical grade substances are used. In this work, the differences in the phase behaviors of these two grades were investigated. The phase behavior of technical grade, nonionic surfactant Genapol X080+technical 1-dodecene+water was studied and compared to the phase behavior of the pure compound. First, binary subsystems (technical 1-dodecene+water; technical surfactant Genapol X080®+water; technical 1-dodecene+technical surfactant Genapol X080®) were studied. The solubility of water in technical 1-dodecene is slightly higher than the solubility of water in pure 1-dodecene. The cloud point curves of technical aqueous surfactant solutions and solutions made from pure surfactant show extreme differences in temperature and shape. The phase behavior of the ternary system was intensively studied visually by measuring Kahlweit's fish at a constant oil/water ratio ( =0.5). Tie lines were measured at temperatures between 30°C and 90°C at 10°C intervals. The results were compared to the measured tie lines in a system containing pure substances. The raw material's purity has an enormous influence on phase change temperatures. For the first time, a 4-phase liquid equilibrium was observed in a system containing technical grade substances. Furthermore, the solubility of the surfactant was compared at nearly constant feed concentrations in the aqueous and 1-dodecene-rich phases. [ABSTRACT FROM AUTHOR]

Abstract: The Perturbed Chain Polar Statistical Association Fluid Theory (PCP-SAFT) equation of state is applied to calculate phase equilibria data for several DMF/alkane systems. DMF/alkane systems exhibit a peculiar phase behavior, due to overlapping liquid–liquid and vapor–liquid coexistence regions. Hetero- and homoazeotropes appear and disappear depending on temperature/pressure conditions and the chain length of the alkane. The vapor–liquid, liquid–liquid and vapor–liquid–liquid equilibria of DMF/alkanes systems including alkanes from C5 to C10 were studied in detail over wide temperature and pressure ranges. A single, linear expression for the binary interaction parameter k ij as function of temperature and alkane chain length was used to model the experimental data. This expression was determined only by using experimental liquid–liquid equilibria (LLE) data of DMF/alkane systems. Using that, the PCP-SAFT equation of state provides very satisfying results for the description of the phase behavior in all considered systems. [Copyright &y& Elsevier]

Abstract: In this work a short-cut method for the conceptual process design is presented which enables an analysis of arbitrary flow sheets consisting of reactors, distillation columns, decanters, mixers, splitters, and component splitters. It is based on previous work (Ryll et al., 2012b, 2013), which is extended here to include reactors. Besides the flow sheet structure and the model for the physico-chemical properties only information on the feed streams and a set of desired product specifications is needed. The method is based on the consideration of thermodynamic limiting cases: for distillation columns is used (Ryll et al., 2012b, 2013). Decanters are described assuming equilibrium between the phases which are withdrawn from Ryll et al. (2013). The reactors are either described assuming that chemical equilibrium is reached or by specifying the conversion. The number of chemical reactions is not restricted. By applying a piecewise linearization to the separatrices of the vapor–liquid(–liquid) equilibrium diagram for distillation, to the liquid–liquid equilibria in decanters as well as to the chemical equilibrium surfaces of the reactions, the nonlinear process model is replaced by a piecewise linear model (Feng et al., 2003). An existing software tool in which these methods are implemented is extended to include reactors. The tool allows for a thermodynamic analysis of arbitrary reaction-distillation processes, e.g. for feasibility or multiplicity studies, without using simplifying assumptions on thermodynamic properties. Two examples for applications are discussed. [Copyright &y& Elsevier]

Abstract: Fluid phase equilibria involving nano-dispersed phases, where at least one of the coexisting phases is confined to a small volume, are investigated by molecular dynamics simulation. Complementing previous studies on nanoscopic droplets, simulation volumes containing a nanoscopic gas bubble surrounded by a subsaturated liquid phase under tension, i.e. at negative pressure, are conducted in the canonical ensemble. The boundary conditions are chosen such that the phase equilibrium at the curved interface is thermodynamically stable. Two distinct size-dependent effects of opposite sign are found for the density of the gas in the centre of the bubble. The curvature dependence of the surface tension is considered, employing an approach based directly on the average radial density profiles. [Copyright &y& Elsevier]

• Dimethyl sulfoxide decreases the thermodynamic stability of carbon dioxide hydrate. • Obtained CO 2 hydrate dissociation data are reliable and thermodynamically coherent. • Phases of sI hydrate, crystalline ice I h , and solid CO 2 were identified by PXRD. • DMSO avoids inclusion into the CO 2 hydrate framework. • DMSO is an effective thermodynamic inhibitor of CO 2 hydrate formation. The paper investigates dimethyl sulfoxide (DMSO) as a promising inhibitor of gas hydrates. The equilibrium conditions of the CO 2 hydrate were measured over a broad range of temperatures (from 243 K to 283 K) and DMSO concentrations (up to 50 mass%). DMSO decreases the thermodynamic stability of the CO 2 hydrate. Thermodynamic coherence of new hydrate equilibria data was demonstrated. The sI hydrate, crystalline ice I h , and solid CO 2 phases were identified using PXRD at 143 K. Measured unit cell parameter for sI hydrate (11.86 Å) coincided with the pure sI CO 2 hydrate literature value. The DMSO inhibition activity grows much faster in water solution in comparison to lower alcohols. We explain this behavior by the more pronounced non-ideality of DMSO water solutions. Thus, DMSO can be considered an effective thermodynamic inhibitor of the formation of CO 2 hydrate, superior in anti-hydrate activity to alcohol THIs within a specific range. [ABSTRACT FROM AUTHOR]

Abstract: A multi-stage counter-current crystallization is investigated theoretically and experimentally. The process allows separating mixtures, which form complete or partial solid-solutions. An equilibrium stage model is used to describe the progress of the purification with the specific solid–liquid equilibria as main input information. Results presented in this paper concern (a) the demonstration of the process principle for two selected generic systems characterized by complete miscibility in the solid state, namely K2SO4/(NH4)2SO4 and KCl/KBr, (b) the scale up from a laboratory unit to a pilot plant and (c) the evaluation of the potential of the process principle for the purification of systems characterized by partial miscibility in the solid state. [Copyright &y& Elsevier]

Abstract: A short-cut method for the conceptual design of processes consisting of distillation columns and decanters is presented. It extends the previous work on homogeneous distillation columns and processes (Ryll et al., 2012b) to heterogeneous distillation processes. The approach is based on the consideration of thermodynamic limiting cases, e.g., for distillation columns is used. The decanters are modeled using the respective liquid multi-phase equilibria. By applying an appropriate piece-wise linearization to the separatrices of the vapor–liquid(-liquid) equilibria as well as to the liquid multi-phase equilibria, the original nonlinear process model is replaced by a piece-wise linear model (Feng et al., 2003). The algorithm for the simulation of the decanters is based on a recent publication (Ryll et al., 2012a). The new short-cut method enables the analysis of flow sheets consisting of an arbitrary number of distillation columns and decanters and yields to the stream table of feasible processes. The application range of the method is further enhanced by including the units mixer, component split and split. Two examples are discussed in detail to demonstrate the application of the new method. [Copyright &y& Elsevier]

Abstract: The solubility isotherms of gypsum and insoluble anhydrite in the ternary system CaSO4–H2SO4–H2O were determined at T=(298.1, 323.1, 348.1, and 363.1) K using the isothermal method. The kinetics of the transformation between gypsum and insoluble anhydrite in H2SO4 aqueous solutions at 298.1 and 363.1K were also studied. Our measured solubility isotherms for gypsum are generally in good agreement with the literature solubility data. However, the solubilities of anhydrite measured in this work are much lower than those reported by Zdanovskii and Vlasov (1968b) [Zdanovskii, A.B., Vlasov, G.A., 1968b. Russ. J. Inorg. Chem. 13, 1418–1420.]. Kinetic experiments showed that the complete transformation from gypsum to anhydrite at 363.1K takes at least 120h in 0.5molkg−1H2SO4 aqueous solution and over 6h for higher concentrations of H2SO4. Furthermore, much more time is needed for the Ca2+ concentration in the solutions to equilibrate with the end solid phase “insoluble anhydrite” than for the complete transformation of gypsum to insoluble anhydrite. These kinetic results were used to identify why the insoluble anhydrite solubilities in H2SO4 aqueous solution in the literature were higher than those in our results. A Pitzer thermodynamic model was chosen to simulate and predict the solubility isotherms of gypsum and insoluble anhydrite in this ternary system, and the good agreement between the experimental results and the model supports the reliability of the experimental solubility data obtained in this work. Finally, the stable fields for gypsum and insoluble anhydrite as a function of temperature and H2SO4 concentration were constructed by the thermodynamic model. [Copyright &y& Elsevier]

Abstract: The present work reports the measurement and mathematical correlation of phase equilibrium data for the binary system composed of carbon monoxide and water at temperatures up to 423.15K and pressures up to 50MPa. This data, although crucial when designing high pressure technologies, is not available in the literature. The experimental data were collected using a high pressure view cell. Mathematical correlation was performed using an online available programme tool Phase Equilibria (2000) with van der Waals cubic equation of state and a mixing rule proposed by Adachi and Sugie. The combination of EOS and mixing rule are found to be in good agreement with experimental data. [Copyright &y& Elsevier]

Abstract: The storage capacity, induction time and induction temperature of CO2 hydrates were investigated on pure water, SDS solutions, THF solutions and mixtures of THF and SDS. SDS did not present significant effect on increasing storage capacity, as it is usual to methane hydrates. However, mixtures of SDS and THF presented maximum % theoretical, 121(±12)% and reduction of temperature and time for induction, due to a synergistic effect. [Copyright &y& Elsevier]

Abstract: Based on the modified Othmer still, an instrument is developed for vapor–liquid equilibrium (VLE) measurements in a microwave field. The isobaric conventional binary VLE experimental data compare favorably with the literature data and the results predicted from the universal quasi-chemical (UNIQUAC) model, which also verifies the reliability of the new instrument. A systematic experimental study of the effects of a microwave field on the VLE for the binary mixtures is reported herein for the first time to the best of the author''s knowledge. Isobaric VLE data for two binary systems, benzene/ethanol and DOP/iso-octanol, at 101.33kPa are determined under conventional conditions and various microwave fields. The results clearly demonstrate that the VLE of benzene/ethanol in a microwave field is shifted compared to the conventional condition; no change is observed in the DOP/iso-octanol binary system. It is concluded that the ethanol can be vaporized selectively because the rate of microwave energy absorption of ethanol is higher than the rate of heat transfer from ethanol to benzene. Furthermore, various microwave irradiation powers and the dielectric constants of the binary mixture are chosen to investigate the influence of the microwave irradiation on the VLE. The results indicate that microwave field strengths from 25W to 200W have varying effects on the VLE. The results also show that the effect of the microwave field on VLE is more prominent in the binary system with a larger dielectric constant difference between the two substances. [Copyright &y& Elsevier]

Abstract: The characteristics and stability conditions of carbon dioxide (CO2) hydrate formation are crucial for hydrate-based CO2 capture and storage. The effects of a mixture of additives (THF/SDS) on CO2 hydrate formation and dissociation in porous media have been investigated experimentally using a graphic method. The Gibbs phase rule is used to analyze the experimental p–T curves. Hydrate formation processes can be divided into two cases, depending on the CO2 initial state. The experimental results showed that 1000mg/L SDS is the best additive and concentration for CO2 hydrate formation among those studied in this investigation due to its shorter induction time and resultantly higher hydrate saturation than those of other concentrations. The presence of 3mol% THF dramatically decreased the hydrate phase equilibrium pressure. The hydrate equilibrium temperature is 291.55K in the aqueous phase with 3mol% THF and 0mg/L SDS, which is the highest equilibrium temperature at 3.04MPa observed in this investigation. The experimental results also showed that “pseudo-retrograde” behavior exists at nearly 3.00MPa with all SDS concentrations. An improved model is used to predict the phase equilibrium conditions for CO2 hydrates in glass beads in the presence of THF, in which the mechanical equilibrium of force between the interfaces in a hydrate–liquid–vapor system is considered. [Copyright &y& Elsevier]

Abstract: The chemical and phase equilibrium is important to be computed simultaneously in lipid transesterification which occurs in a two-phase system. Such analysis is highly desired to ease the reactor design and optimization problems. The objective of this study is to conduct a thorough investigation on lipid transesterification in a continuous stirred tank reactor (CSTR) with the consideration of chemical phase equilibrium (CPE) via modeling and simulation analysis. The transesterification of canola oil with methanol to fatty acid methyl ester was considered in this study. The UNIQUAC thermodynamic model was used to investigate the liquid–liquid equilibrium (LLE) behavior of the six-component system formed during the biodiesel production. By comparing the LLE behavior between ternary and six-component systems, the data shows that six-component system gave a better representation of the main phase variation in the transesterification process. In addition, the CPE model developed in this study was verified by comparing the simulated results with the results obtained from the transesterification reaction experiments in CSTR. The results obtained from the CPE model analysis show that the proposed CPE model is adequate to be used for the description of simultaneous chemical reaction and phase equilibrium during the transesterifcation process at an acceptable accuracy. The CPE investigation shows that if an efficient reaction needs to be achieved, the CPE needs to be controlled to obtain higher concentration gradients between the two reacting phases. [Copyright &y& Elsevier]

Abstract: The performance of 1-ethyl-3-methylimidazolium chloride (EMIM-Cl), one of novel ionic liquid inhibitors for gas hydrate, in inhibiting methane hydrate at low and high ionic liquid concentrations is investigated in a pressure range of 10–20MPa. Experiments on methane hydrate dissociation conditions in the presence of mixed ionic liquid and conventional inhibitors, such as sodium chloride (NaCl) and monoethylene glycol (MEG), as well as a mixture containing two ionic liquids, EMIM-Cl and 1-ethyl-3-methylimidazolium bromide (EMIM-Br), are also performed to investigate any possible synergistic effects. It is observed that single component solutions of EMIM-Cl demonstrate a progressive increase in inhibition effect with increasing concentration, which may surpass the effectiveness of MEG at high concentrations. Although the thermodynamic inhibition performance of the mixtures of EMIM-Cl and MEG does not show any synergistic effects at low pressures, it does at higher pressures. The mixture of EMIM-Cl and EMIM-Br also shows a synergistic effect at higher pressures. Unlike MEG or NaCl, inhibitors containing EMIM-Cl or EMIM-Br demonstrate an increase in inhibition effectiveness as pressure increases. [Copyright &y& Elsevier]

Abstract: A method for the analysis of flowsheets consisting of an arbitrary number of distillation columns and mixers in conceptual process design is presented in this work. The required information on the process is reduced to a minimum: besides the fluid property model, only information on the flow sheet structure, the overall feed streams and a suitable set of desired product specifications is needed. The method is based on the study of thermodynamic limiting cases by applying to distillation columns. Thus, the attainable distillate and bottom compositions are described by the invariant manifolds of the singular points of the respective vapor–liquid equilibria. The approach based on residue curve maps or distillation line diagrams is general and not limited to the number of components or azeotropes. Only homogeneous azeotropes are discussed in the present work. The nonlinearity in the resulting short-cut model is only introduced by the fluid properties. By applying a suitable linearization to the separatrices of the vapor–liquid equilibria the invariant manifolds of the singular points are represented by linear elements. This results in piece-wise linear sub-models for the attainable product compositions. Brute force enumeration of the combined linear sub-models allows finding of all solutions reliably and robustly. Hence, comprehensive feasibility and multiplicity analysis are possible. An overview of the method is given followed by some examples for its application to a number of azeotropic distillation processes. [Copyright &y& Elsevier]

Abstract: A new Newton homotopy based method is presented that is able to determine robustly all the stationary points for the tangent plane distance function (TPDF). The solving method is equipped with the features of homotopy parameter and variables bounding that together result in a continuous homotopy path. All the stationary points of TPDF can be approached on one path, assuming only that the temperature, pressure, and composition of the component system are known. The performance of the method is examined with various LLE cases gathered from literature. The liquid phase behavior is described with NRTL and UNIQUAC excess Gibbs energy models. The consistency of stationary points is verified with the topological criterion. Based on this consideration, the proposed modified Newton homotopy method is found to be a robust computational tool for solving phase stability problems. [Copyright &y& Elsevier]

Abstract: Clathrate hydrates have potential applications in various domains and particularly for CO2 capture where the search for additives able to speed up hydrate formation is of scientific, technological and economical interest. This study investigates the potentialities of two additives used in combination for enhancing CO2 enclathration rates: a surfactant (sodium dodecyl sulphate; SDS) and an organic compound (tetrahydrofuran; THF). Experiments performed in batch and in semi-continuous reactor configuration, reveal that this combination of additives efficiently promotes hydrate formation, allowing a full water-to-hydrate conversion despite the quiescent-forming conditions used. The possible action mechanisms of this combination of additives are analyzed and discussed on the basis of experimental data of hydrate phase equilibria (with and without additives), visual observations, and kinetics experiments. [Copyright &y& Elsevier]

Abstract: Melt crystallization is a technically proven and selective separation method for obtaining pure isomeric compounds. Nonetheless, a separation of isomeric long-chain aldehydes has not yet been realized by melt crystallization. Existing methods often use chemical reactions or require additives. In this work, we evaluated the feasibility of the purification of dodecanal from the isomeric long-chain mixture dodecanal/2-methylundecanal (C12H24O) with melt crystallization. For this purpose, the binary solid–liquid equilibrium of dodecanal/2-methylundecanal was measured with differential scanning calorimetry. The liquidus line of the binary system can be calculated using only the melting temperature and the enthalpy of fusion of dodecanal. On the basis of the solid–liquid equilibrium, layer melt crystallization experiments under an inert gas atmosphere were conceived. Depending on the process conditions (feed concentration and cooling rate), the growth rates of the crystalline layer were measured online, and crystal purities were determined as a function of the growth rate and melt concentration. Furthermore, the efficiency of sweating as a finishing treatment was investigated. To model the crystalline layer thickness, a site-specific heat flow balance at the crystal surface and a space- and the time-dependent enthalpy balance of the crystal volume were applied. The model is able to describe the crystallization process adequately, depending on the process parameters. [Copyright &y& Elsevier]

Abstract: Reliable estimation of vapor pressure is of great significance for chemical industry. In this communication, the capability of the Quantitative Structure–Property Relationship (QSPR) technique is studied to represent/predict the vapor pressure of pure chemical compounds from about 55 to around 3040K. Around 45,000 vapor pressure values belonging to about 1500 chemical compounds (mostly organic ones) at different temperatures are treated in order to present a comprehensive, reliable, and predictive model. The sequential search mathematical method has been observed to be the only variable search method capable of selection of appropriate model parameters (molecular descriptors) regarding this extremely large data set. To develop the final model, a three-layer artificial neural network is optimized using the Levenberg–Marquardt (LM) optimization strategy. Through the developed QSPR model, the absolute average relative deviation of the represented/predicted properties from the applied data is about 7% and squared correlation coefficient is 0.990. In addition, the outliers of the model are identified using the Leverage Value Statistics method. [Copyright &y& Elsevier]

Abstract: This work focuses on the extension of group parameters and application of the group-contribution lattice-fluid equation of state (GCLF EOS) for the systems with ionic liquids (ILs). The new group parameters e kk and R kk for ILs in GCLF EOS were obtained by means of correlating the liquid density of pure ILs at different temperatures, while the group binary interaction parameters α mn were obtained by means of correlating the activity coefficients of solutes at infinite dilution in ILs at different temperatures, which were exhaustively collected from references. New IL groups were added into the current parameter matrix. It was verified that GCLF EOS for ILs can be used for predicting liquid densities of pure ILs or the mixture of IL and solute, vapor–liquid equilibria (VLE) and liquid–liquid equilibria (LLE) at finite concentration, as well as identifying the structure–property relation in separation science. This is the first work for us to extend the predictive GCLF EOS to the systems with ILs. [Copyright &y& Elsevier]

Abstract: The 1H NMR chemical shifts of alcohol+hydrocarbon systems over the whole concentration range at 298.15K were measured. Based on the concept of local composition (LC), the concentration-dependent 1H NMR chemical shift data of the OH and CH groups for 13 alcohol+hydrocarbon systems were correlated with only one energy parameter, respectively. Using the parameters obtained from the spectra alone, the isothermal and isobaric vapor–liquid equilibria (VLE) data of the above-mentioned alcohol+hydrocarbon systems were predicted with satisfactory results. By this way, the spectroscopic information can be used to predict VLE data of alcohol+hydrocarbon systems directly. [Copyright &y& Elsevier]

Abstract: Mixed solvents based on tertiary amine and sterically hindered amine were tested for CO2 capture performance with 2-methylpiperidine (2MPD) as an additive to improve the mass transfer rate of those absorbents, which have slow reaction rate with CO2. The absorbents are triethanolamime (TEA), N-methyldiethanolamine (MDEA), and 2-amino-2-methylpropan-1-ol (AMP). A wetted wall column (WWC) was used to measure the mass transfer rate of the mixed solvents and the CO2 loading was evaluated by vapor–liquid equilibrium (VLE) measurement. The mass transfer rate of both tertiary amines (TEA, MDEA) and sterically hindered amine (AMP) increased greatly as 2MPD was added. The AMP/2MPD containing 10wt% of 2MPD showed the highest mass transfer rate of 3.92×10−10 mol/cm2 sPa, even higher than that of 30wt% MEA (3.30×10−10 mol/cm2 sPa). The CO2 loading capacities of the mixed solvents were excellent compared to MEA. The absorption capacities of the AMP/2MPD and MDEA/2MPD were about 0.8 to 0.9, 1.7 times better than that of MEA (about 0.5). [Copyright &y& Elsevier]

Abstract: The solubility of CO2 in aqueous potassium salt of l-proline solutions has been measured in the temperature range of 285 and 323K, for amino acid salt concentrations of 0.5, 1, 2 and 3moldm−3 and CO2 partial pressures relevant to flue gas conditions, and up to 70kPa. Precipitation was encountered in the system when absorbing CO2 in 3moldm−3 potassium l-prolinate solution at 285K. A beneficial effect of the solid formation on the overall CO2 solubility was observed. The vapor–liquid equilibrium data from the present work (for the non-precipitating regime) were interpreted by a concentration-based chemical equilibrium model. In spite of numerical simplicity of the model, a reasonable good description of the CO2–AAS–H2O systems could be observed. In the absence of literature data on equilibrium constant of the carbamate hydrolysis for l-prolinate, this parameter was calculated from the equilibrium CO2 solubility data. In addition, the enthalpy of absorption of CO2 in l-prolinate solutions was estimated using the solubility data, compared to that of monoethanolamine (MEA) and other common CO2 absorbents. Potassium salt of l-proline was found to be a promising candidate for CO2 capture. [Copyright &y& Elsevier]

Abstract: Preliminary results are presented on the use of nuclear magnetic resonance (NMR) relaxation spectroscopy for analysis of water phase transformations during dissociation of gas hydrate dispersions below 273K. Freon-12 hydrates formed a cubic structure II were used for model studies without need for high pressure. Freon hydrates were formed from micron-sized water droplets with an average radius of about 5μm dispersed in polyethylsiloxane fluid (PES-5). This research demonstrates the possibility of using NMR relaxation spectroscopy to study phase transformations of water in gas hydrate systems at temperatures below 273K, including the region of their metastable states on the P–T phase diagram below the ice–hydrate–gas equilibrium pressure. [Copyright &y& Elsevier]

Abstract: We have described the behavior of a subgroup of regular solutions not very far from ideality () that is analogous to the behavior of ideal solutions. For this subgroup the composition of each phase in equilibrium may be related logarithmically. We have found that some cases of isothermal, isobaric and ternary liquid–vapor systems in equilibrium follow this scheme. In each case the resulting calculations of phase compositions are in good agreement with the experimental data reported in the literature. This approach is consistent with correlations frequently used in liquid–liquid case (known as the equations), as well as adsorption of liquid on solid (known as Langmuir–Freundlich isotherm ()). For fluids mixtures presenting this behavior we use the term of semi-regular mixtures. For this kind of fluid mixtures it can be found a simplified procedure to relate the equilibrium compositions that may be used as “shortcut” for chemical engineering designs. [Copyright &y& Elsevier]

Abstract: Liquid densities, osmotic coefficients, and mean ionic activity coefficients (MIAC) at 25°C of single-salt alcohol (methanol and ethanol) solutions containing univalent ions were measured and modeled with the ePC-SAFT equation of state. In accordance with our previous work [Held, C., Cameretti, L.F., Sadowski, G., Fluid Phase Equlilib. 270 (2008) 87–96], only two solvent-specific ion parameters were adjusted to experimental solution densities and osmotic coefficients: the solvated ion diameter and the dispersion-energy parameter. ePC-SAFT was able to reproduce experimental data of the respective alcohol/salt systems with reasonable accuracy. Based on the solvent-specific ion-parameter sets, it is possible to predict densities and MIACs in ternary and quaternary water/alcohol(s)/salt solutions by introducing appropriate mixing rules that do not contain any additional fitting parameters. [Copyright &y& Elsevier]

Abstract: New experimental data for vapor–liquid equilibrium of CO2 in aqueous monoethanolamine solutions are presented for 15, 30, 45 and 60 mass% MEA and from 40 to 120°C. CO2 partial pressures over loaded MEA solutions were measured using a low temperature equilibrium apparatus while total pressures were measured with a high temperature equilibrium apparatus. Experimental data are given as CO2 partial pressure as function of loading in solution for temperatures from 40 to 80°C and as total pressures for temperatures from 60 to 120°C for the different MEA concentrations. The extended UNIQUAC model framework was applied and model parameters were fitted to the new experimental VLE data and physical CO2 solubility data from the literature. The model gives a good representation of the experimental VLE data for CO2 partial pressures and total pressures for all MEA concentrations with an average absolute relative deviation (AARD) of 24.3% and 11.7%, respectively, while the physical solubility data were represented with an AARD of 2.7%. Further, the model predicts well literature data on freezing point depression, excess enthalpy and liquid phase speciation determined by NMR. [Copyright &y& Elsevier]

Abstract: In this work, experimental data and a simplified vapor–liquid equilibrium (VLE) model for the absorption of CO2 into aqueous solutions of piperazine (PZ) activated 2-amino-2-methyl-1-propanol (AMP) are reported. The purpose of the work was to find the AMP/PZ system with the highest concentration and cyclic capacity, which could be used in the industry without forming solid precipitations at operational temperatures. The effect of the AMP/PZ ratio and the total concentration level of amine was studied. The highest possible ratio of AMP/PZ, which does not form solid precipitates during the absorption of CO2 at 40°C (40wt% amine), was identified. Considering the maximum loading found in the screening tests for AMP/PZ (3+1.5M) and for 30wt% MEA systems, the AMP/PZ system has about 128% higher specific cyclic capacity if operating between 40 and 80°C, and almost twice the CO2 partial pressure at 120°C compared to MEA. [Copyright &y& Elsevier]

Abstract: This work uses vapour–liquid equilibrium (VLE) to explain the observed two-alpha product distribution in Fischer–Tropsch (FT) reactors. We discuss three possible scenarios or cases of Anderson–Schulz–Flory (ASF) product distribution and VLE. The three cases assume the following: (1) the reaction sets up a single alpha ASF distribution in the total (vapour+liquid) products, (2) the vapour phase follows a single alpha distribution and (3) a single alpha distribution is set up in the liquid phase. We then look at the consequences of these assumptions in conjunction with a simple Raoult''s law VLE model on the exit product distributions. We find that only gives rise to a two-alpha model in accordance with experimental results that is frequently observed in FT reactors. This model further predicts a relationship between the two values of alpha that are consistent with the measured experimental results. [Copyright &y& Elsevier]

Abstract: This work introduces the Least Dot Products (LDP) method, a new algorithm for phase stability analysis of thermodynamic mixtures. Starting with the fact that tangent plane distance function (the objective function used in global stability tests) is, essentially, the dot product between the vector of compositions of a trial phase and the vector that describes the differences among the chemical potential of the components in the phases, our approach tries to obtain the least values of an auxiliary function that represents an appropriate dot product on a unitary sphere of the n-dimensional space, which is a good approximation for the stability test function. In agreement with the foundations of the Gibbs plane tangent criterion, the new algorithm simply tries to find points where the objective function is negative, which are not (necessarily) stationary points or global minima. Thus, our main contribution is not a new method for general nonlinear problems, or a rule-based termination criteria for a classical optimization method. Consequently, if such points do not exist, then LDP method is not capable to recognize the stability condition. To overcome this problem, we develop also a powerful safeguard algorithm, denominated Projected Simulated Annealing (PJSA) algorithm, which is obtained by projecting the Simulated Annealing algorithm onto the unitary sphere. In the present article, firstly we consider liquid–liquid equilibria at low or moderate pressures, where the excess Gibbs energy is described by NRTL or UNIQUAC models. Secondly, we address vapor–liquid equilibria at high pressures with cubic equations of state. To illustrate the performance of the new methodology, we use here 20 systems studied by other authors. Such problems possess 2–12 variables and constitute severe tests for many optimization methods. For some mixtures, we show that LDP method is capable of determining the instability condition using just two iterations. [Copyright &y& Elsevier]

Abstract: A systematic procedure for synthesizing the multi-stage crystallization process was developed for resolution of enantiomeric mixtures involving solid solutions in the crystalline phase. The model compound investigated was citalopram oxalate, which revealed a complete solid solution in the solid phase. The counter-current multi-stage batch crystallization was suggested to isolate the target enantiomer from enantiomerically enriched mixtures. The solid–liquid equilibria in the presence of a solvent and the distribution diagrams were quantified and used in designing the crystallization process and defining adequate processing conditions. Different flowsheet schemes were considered and compared with respect to the process performance. The design procedure was verified by the experimental separation of enantiomeric mixtures of citalopram. [Copyright &y& Elsevier]

Abstract: Hyperbranched polymers get more and more interesting for several applications due to their tailor-made properties influenced by the architecture and the functional groups of the polymer. The liquid–liquid phase behavior of hyperbranched polymer solutions is an important issue for various applications. Until now, the calculations of these phase equilibria are limited to solutions of hyperbranched polymers in a single solvent using Lattice Cluster theory (LCT). The LCT permits the incorporation of the architecture of the polymer directly in thermodynamic properties, as the Helmholtz energy, without any additional adjustable parameter. This papers aims at the extension of the LCT to ternary systems made from hyperbranched polymer (Boltorn H20), water and propanol. The derived expression for the Helmholtz energy allows for the first time the prediction of miscibility gaps in the ternary system based on experimental data of the binary subsystems. Additionally to the architecture of hyperbranched polymers also the functional groups of hyperbranched polymers play an important role in phase equilibrium. In order to include the association phenomena in the theoretical framework, a modified version of the Wertheim association theory is used. However, during the application of this approach the model lost its predictive power, because ternary data must be used for the parameter estimation procedure. Nevertheless, the combined theory is able to model the experimental phase behavior within the experimental accuracy. [Copyright &y& Elsevier]

Abstract: Vapor–liquid equilibrium (VLE) measurements were conducted for both unloaded and CO2 loaded aqueous amine amino acid salt (AAAS) solutions; 3-(methylamino)propylamine/sarcosine (SARMAPA). Vapor–liquid equilibrium for unloaded solutions for 1.0–5.0M SARMAPA were measured using a Swietoslawski ebulliometer for temperatures 40–100°C and for total pressures 4.08–99.1kPa. CO2 equilibrium was determined for loaded 5M SARMAPA using low and high temperature VLE apparatuses from 40 to 120°C. A thermodynamic model representing equilibrium in the H2O–AAAS–CO2 system was developed using the extended UNIQUAC thermodynamic framework. The developed model predicts simplified speciations in H2O–SARMAPA–CO2 system and adequately correlates the experimental total and partial pressure data with an average absolute deviation of 8.9%. [Copyright &y& Elsevier]

Abstract: In this work new experimental data on the rate of absorption of CO2 into piperazine (PZ) activated concentrated aqueous solutions of 2-amino-2-methyl-1-propanol (AMP) over the temperature range 303–323K are presented. The absorption experiments have been carried out in a wetted wall contactor over CO2 partial pressure range of 5–15kPa. PZ is used as a rate activator with a concentration ranging from 2 to 8wt% keeping the total amine concentration in the solution at 40wt%. The physical properties such as density and viscosity of concentrated aqueous AMP+PZ, as well as physical solubility of CO2 in concentrated aqueous AMP+PZ, are also measured. New experimental data on vapor liquid equilibrium (VLE) of CO2 in these concentrated aqueous solutions of AMP+PZ in the temperature range of 303–323K have also been presented. The VLE measurements are carried out in an equilibrium cell in CO2 pressure range of 0.1–140kPa. A thermodynamic model based on electrolyte non-random two-liquid (eNRTL) theory is used to represent the VLE of CO2 in aqueous AMP+PZ. Liquid phase speciations are estimated considering the nonideality of concentrated solutions of the amines and the calculated activity coefficients by eNRTL model. The CO2 absorption in the aqueous amine solutions is described by a combined mass transfer-reaction kinetics model developed according to Higbie''s penetration theory. The model predictions have been found to be in good agreement with the experimental results of the rates of absorptions of CO2 into aqueous AMP+PZ. [Copyright &y& Elsevier]

Abstract: Methane+ethane+1,1-dimethylcyclohexane+water system was investigated by using Raman spectroscopy and isothermal phase equilibrium measurements under four-phase (gas+aqueous+large guest species+hydrate phases) equilibrium conditions at 288.15K. The results suggest that three kinds of hydrate structures emerge at 288.15K in the methane+ethane+1,1-dimethylcyclohexane+water system. The hydrate structure for this system changed from structure-H to structure-I via structure-II with increase in the mole ratio of ethane to methane. [Copyright &y& Elsevier]

Abstract: An accurate and tractable model of solubility is a pre-requisite for any careful study of precipitation. Reviewing the abundant literature on the sodium aluminate solutions and Bayer Liquor, the authors point out the need for a new model for the apparent solubility of aluminium in actual Bayer Liquors and propose such a model, based on the well established Wesolowski''s expression for the infinite dilution solubility and extended Debye–Hückel expression including a large empirical b I term for the “activity coefficient effect”. They suggest a chemical interpretation for this feature. [Copyright &y& Elsevier]

Abstract: Vapor–liquid equilibrium (VLE) measurements were carried out for both unloaded and CO2 loaded aqueous amino acid salt (AAS) solutions of the potassium salt of sarcosine (KSAR). Vapor–liquid equilibrium for unloaded solutions; 1.0–5.0M KSAR was measured using a Swietoslawski ebulliometer for temperatures 40, 60, 80 and 100°C and for total pressures 4.08–97.8kPa while vapor–liquid equilibrium for CO2 loaded solutions of 3.5M KSAR was measured using both low and high temperature VLE apparatuses for 40, 60, 80, 100 and 120°C and for CO2 partial pressures ranging from 0.03 to 971kPa. A thermodynamic model representing the AAS solvent system was developed using the extended UNIQUAC framework. The developed model accurately predicts the equilibrium speciation in loaded solutions from 13C NMR data and gives a very good representation of the solubility of CO2 in the amino acid salt solution as well as the total pressure of the unloaded system at all measured temperatures, loadings and pressures. [Copyright &y& Elsevier]

Abstract: Detailed knowledge of refrigerant absorption in refrigerant–oil mixtures is essential for understanding the behavior of hermetic compressors under transient conditions. In some types of refrigeration systems, important operation parameters, such as the equalizing pressure and the energy consumption, are directly influenced by the rates of refrigerant absorption in the compressor oil. In this work, we study the absorption of isobutane (R-600a) through the free surface of a stagnant layer of alkylbenzene lubricant oil in a closed system (PVT cell). Experiments were conducted in a transparent test section that enabled the absorption process to be visually monitored. The mass of isobutane that entered the test section was measured for each experimental test. The instantaneous system pressure and temperatures in the vapor, liquid and interface regions were recorded at temperatures of 25, 40, 55 and 70°C (nominal). The experimental data were then used to validate a transient mass diffusion model that takes into account the departure from the ideal solution behavior. [Copyright &y& Elsevier]

Abstract: In this study, the dissociation of isolated carbon dioxide hydrate particles of sizes in the range 0.25–2.5mm was investigated. It was found that below the ice melting point, the hydrates dissociated into supercooled water (metastable liquid) and gas. The formation of the liquid phase during CO2 hydrate dissociation was visually observed, and the pressures of the hydrate dissociation into supercooled water and gas were measured in the temperature range 249–273K. These pressures agreed well with the calculated data for the supercooled water–hydrate–gas metastable equilibrium (). In the P–T area on the phase diagram bounded by the ice–hydrate–gas equilibrium curve and the supercooled water–hydrate–gas metastable equilibrium curve, hydrates could exist for a long time because the metastable phase and their stability are not connected to the self-preservation effect. The growth of the metastable CO2 hydrate film on the surface of supercooled water droplets formed during the hydrate dissociation was observed at pressure above the three-phase supercooled water–hydrate–gas metastable equilibrium pressure but still below the three-phase ice–hydrate–gas equilibrium pressure. It was found that the growth rate of the metastable CO2 hydrate film was higher by a factor of 25 and 50 than that for methane hydrate and propane hydrate, respectively. [Copyright &y& Elsevier]