Mixture Critical Point Research Articles

Controlling particle size of levan in powder form with different technologies

Levan is a fructose polysaccharide with multiple applications in different fields, but its obtaining in powdered form with a narrow particle size distribution is a complicated task. Two techniques, electrospraying and supercritical antisolvent (SAS) precipitation, were used to process levan that was first obtained enzymatically. The SAS process was able to micronize the polymer (at experimental conditions far above the mixture critical point of the solvent-antisolvent system) to obtain spherical particles between 0.30 and 0.50 μm with a proper particle size distribution. In this case, the Peng-Robinson equation of state was used to theoretically determine the mixture critical point. Bigger and elongated particles were obtained with electrospraying (0.60 μm). According to solution properties, mainly rheology, solubility and conductivity, the best solvent for levan electrospraying, in order to avoid problems of solvent evaporation and jet formation, was a mixture of water and ethanol with a polymer concentration of 50 mg·cm−3. Indeed, that solution has a viscous behavior (according to the oscillatory analysis), a low degree of pseudo-plasticity (based on the shear flow analysis), and the highest value of conductivity. Therefore, the particle size distribution of levan in powdered form can be tuned depending on the technique used.

A regularized-interface method as a unified formulation for simulations of high-pressure multiphase flows

The injection of multi-species fluids into high-pressure and high-temperature environments beyond the species' critical points is commonly found in engineering applications. At these conditions, for immiscible species, both subcritical interfacial dynamics and supercritical mixing can coexist due to variations in temperature around the mixture critical point. The modeling of these complex transcritical phenomena for large-scale configurations is so far not possible. To address this issue, we propose the Regularized-Interface Method (RIM) as a unified formulation that can describe both sub- and supercritical processes as well as the transition between them. The proposed method is derived via filtering of the nanoscale interface-resolving formulation based on van der Waals' linear gradient theory. Thus, this approach allows for the consistent modeling of interfacial dynamics that vanishes at supercritical conditions, while significantly reducing the temporal and spatial resolution constraints of the original nanoscale formulation. The resulting RIM formulation is examined in interface-capturing simulations of sub-, trans-, and supercritical fuel injection processes, involving droplets and jets. These results highlight the importance of resolving spatio-temporal transitions from subcritical interfacial dynamics to supercritical mixing in high-pressure multiphase simulations, in contrast to commonly employed diffused-interface methods, where interfacial dynamics are often neglected.

Deep-learning-based acceleration of critical point calculations

Computation of the critical point of complex fluid mixtures is an important part of understanding their thermodynamic phase behaviour. While algorithms for these calculations are well established, they are often slow when the number of constituting components is large. In this work, we propose a new procedure to significantly accelerate critical point calculations by leveraging deep neural network (DNN) models. A DNN model for critical point predictions of a given mixture is first trained based on the critical points of such a mixture with various compositions. The predictions of the DNN model are then used to initialize both of the commonly used algorithms for mixture critical point calculations: root finding and global minimization. We demonstrate that when using the DNN-based predictions to initialize the root-finding-based and optimization-based algorithms, we can achieve 50-90% and 80-90% reductions in the number of required iterations, respectively.

Fabrication of composite polymer microcapsules via the supercritical extraction of Pickering emulsion Method: Insights into emulsification and extraction

Polyphenylene oxide (PPO)/cellulose nanocrystal (CNC)/carbon black (CB) microcapsules were fabricated by the supercritical extraction of Pickering emulsion (SFEPE) method. The effects of Pickering emulsion formulations on the emulsion properties, emulsification kinetics, and CPM properties were investigated. The phase behaviors in the supercritical extraction process were studied, and the mass transfer between the emulsion droplet and supercritical carbon dioxide (SCCO2) was also interpreted. The results indicate that CNC concentration, CB concentration, and NaCl concentration can decrease the droplet size and creaming index of emulsions, while the water–oil ratio can decrease the droplet size but enhance the creaming index. The emulsion formulations of water–oil > 3, CNC concentration > 0.25 mg/mL, CB concentration < 2.5 mg/mL, and NaCl concentration > 2.5 mg/mL are conducive to the emulsion formation and emulsification kinetics. For the supercritical extraction on Pickering emulsions, the operation conditions slightly above the mixture critical point (9 MPa at 313 K, for example) are proved to be conducive to the extraction.

Application of thermodynamics at different scales to describe the behaviour of fast reacting binary mixtures in vapour-liquid equilibrium

The use of reactive working fluids in thermodynamic cycles is currently being considered as an alternative to inert working fluids, because of the preliminarily attested higher energy-efficiency potential. The current needs to simulate their use in thermodynamic cycles, which may operate in liquid, vapour or vapour-liquid state, are an accurate real-fluid equation of state and ideal gas thermochemical properties of each molecule constituting the mixture, to calculate the equilibrium constant. To this end, the appeal to a multi-scale theoretical methodology is paramount and its definition represents the objective of the present work. This methodology is applied and validated on the system N2O4 ⇌ 2NO2. Firstly, the equations solved for simultaneous two-phase and reaction equilibrium are presented. Secondly, ideal gas thermochemical properties of N2O4 and NO2 are computed at atomic scale by quantum mechanics simulations. Then, to apply the selected cubic equation of state, pure-component properties of the species forming the reactive mixture (critical point coordinates and acentric factor) are required as input. However, these properties are not measurable, since NO2 and N2O4 do not exist in nature as pure components. To get around this difficulty, the methodology relies on molecular Monte Carlo simulations of the pure N2O4 and NO2, as well as on the reactive N2O4 ⇌ 2NO2, enabling the determination of those missing pure-component properties and thus the calculation, on a macroscopic scale, of the reactive mixture properties. Finally, the comparison of calculated mixture properties with available experimental data leads to validate the accuracy of the proposed methodology.

Measurement and modelling of the interfacial tensions of CO2 + decane-iododecane mixtures at high pressures and temperatures

Experimentally determined interfacial tensions (IFTs) of CO2 and decane-iododecane mixtures are reported, with iododecane mass fractions of 0%, 50%, 70%, 90% and 100% over the temperature range of 298 K to 353 K and at pressures from 1 MPa up to the mixture critical point pressure. Measurements were carried out in a thermostatic high-pressure view cell by means of the pendant drop method. It was observed that the volume of a fresh drop of hydrocarbon initially increased, while the IFT decreased, before reaching equilibrium values. These observations correspond to two key mechanisms of CO2 flooding: oil swelling and IFT reduction. The equilibrium IFTs decrease with increasing pressure isothermally until the mixture critical point pressure is reached. The IFTs also increase with increasing mass fraction of iododecane. An empirical model was developed that is able to represent the experimental results with an overall average absolute deviation of 0.2 mN∙m−1.The IFT data were modeled with the square gradient theory coupled with the volume-translated Peng-Robinson equation of state. The temperature-independent influence parameters of decane and iododecane were regressed from their surface tensions, while the influence parameter of CO2 was taken from literature. The theoretical predictions are in good agreement with the experimental results with an average absolute deviation of 0.4 mN∙m−1. Finally, we extend a group-contribution approach for the binary interaction parameters in the Peng-Robinson equation of state to encompass the CH2I functional group, thereby facilitating application of the modelling approach to other systems comprising CO2 or N2 with iodoalkanes.

High-precision thermostat for light scattering experiments of critical samples

Abstract The characteristics of PID controllers lead to their widespread adoption and strong demand in temperature control systems since the experimental stability of temperature is required for many applied and research endeavours. The design and manufacture of both the thermal and electronic components of the milli-kelvin metallic thermostat, as well as the light scattering experimental set-up for the liquid mixture critical point research, are presented in this publication. The thermostat was tuned over a wide temperature range of 30–106°C, and short-term stability, long-term stability, and transient responses were studied in detail. The findings demonstrate that the thermostat provides accurate and steady temperature stability. The light scattering experimental setup was arranged and a LabVIEW software program was developed for data acquisition of the intensity of the incident beam, scattered beam, transmitted beam, and the temperature of the liquid mixture simultaneously.

Multicomponent Effects on the Supercritical CO2 Systems: Mixture Critical Point and Phase Separation

Multicomponent Effects on the Supercritical CO2 Systems: Mixture Critical Point and Phase Separation

High pressure viscosity measurements of ternary (methane + propane + heptane) mixtures

Prediction of thermophysical properties for natural gas mixtures close to the mixture's critical point and cricondenbar (the maximum pressure at which two fluid phases can co-exist) is challenging but important as often natural gas processes operate close to these conditions. Here we present a comprehensive study of the viscosity of (CH4 + C3H8 + C7H16) mixtures with heptane fractions up to 15 mol%. Accurate measurements of saturated-phase and compressed-fluid (single phase) viscosities, at temperatures from 200 K to 423 K and pressures up to 35 MPa, are presented. The collected data were compared with the prediction of the extended corresponding states (ECS) model, with relative deviations spanning between (−20 to 11) % from the model. Additionally, pure component parameters needed for the residual entropy scaling (RES) model were fit to literature data and then applied predictively to mixtures viscosity without any additional fit parameters. The relative deviation of the measured viscosities from values calculated with the RES model is generally within 15%. This work demonstrates that no current model satisfactorily predict mixtures viscosity, and that high quality experimental data are needed to anchor the methods used to design and optimize natural gas processing.

Direct numerical simulations of fluids mixing above mixture critical point

Direct numerical simulations are performed to quantify the mixing performance of reactors commonly used for crystallization assisted by supercritical fluid above the mixture critical point. Two different reactors are tested: the semi-continuous reactor of milliliter volume range and the continuous microfluidic chip of nanoliter volume range. The current work shows that high performance computing (HPC) is a modern tool useful to analyze various designs and to quantify performances in chemical engineering. In-depth discussions on the numerical methods chosen to strike a good balance between accuracy and CPU time are presented. Physical analysis is also conducted with an emphasis on the turbulent mixing performance of the reactors. The results show a good mixing for the supercritical technologies considered and underline the increased mixing performance of the microfluidic chip.

Molecular investigation of sub-to-supercritical transition of hydrocarbon mixtures: Multi-component effect

Molecular dynamics (MD) simulations were conducted to better understand the evaporation and mixing behavior of liquid hydrocarbon fuels in ambient gases of varying temperatures and pressures. The emphasis was to understand the multi-component effect of both the liquid fuel and the ambient on the transition from the classical two-phase evaporation regime to the diffusion-controlled mixing regime. Mixture critical point were calculated using the Heidemann and Khalil method to connect the MD observations to the critical locus criterion. Furthermore, vapour-liquid equilibrium (VLE) using the Peng-Robinson equation of state (PR-EOS) were also calculated to understand the phase equilibria. The results show for binary fuel at low ambient temperatures and pressure, evaporation is first dominated by the lighter species and then followed by the heavier species. However, under supercritical conditions, preferential evaporation does not occur and both the lighter and heavier species dominate the evaporation process concurrently. For binary ambient, the results show that the presence of helium has very minimal effect on the mixture critical temperature and pressure and does not change the transition behavior. However, the increasing presence of water in the ambient reduces the mixture critical pressure and promotes sub-to-supercritical transition. These observations support the critical locus criterion suggesting this criterion can be used to determine the exact state of a mixture at given temperatures and pressures.

Effects of supercritical fluid parameters and emulsion formulation on the production of quercetin nanocapsules by supercritical fluid extraction of emulsion

Quercetin nanoparticles encapsulated by Polysorbate 80 were produced by supercritical fluid extraction of emulsion. To analyze the effect of supercritical fluid parameters on organic solvent extraction by scCO2, Peng-Robinson equation of state was employed to obtain the pressure-composition diagram of the mixture system concerned. Also, Huang equation was adopted in combination with Peng-Robinson equation to calculate the density of the solvent/CO2 binary system. The effects of supercritical fluid parameters such as pressure and temperature on emulsion stability in the emulsion extraction stage and extraction efficiency in both emulsion and solution extraction stages were examined experimentally. The analytical and experimental results showed that phase separation could happen in the emulsion extraction stage because of the swelling and the rapid decrease in the density of ethyl acetate droplets in the emulsion to the minimum density point as the mole fraction of CO2 in ethyl acetate increased with the rise in pressure below the mixture critical point. To avoid the minimum density point, a lower pressure (<6 MPa) could be employed to guarantee the emulsion stability while the similar level of extraction efficiency in the emulsion extraction stage was retained. The supercritical fluid extraction was proven to be very efficient in reducing the content of residual organic solvent in the solution extraction stage with the minimum residual content as low as 5.3 ppm.

PVP microparticles precipitation from acetone-ethanol mixtures using SAS process: Effect of phase behavior

In the supercritical antisolvent (SAS) precipitation, the thermodynamic behavior of the system influences particles morphology. However, in the case of complex multicomponent systems, thermodynamic data are limited and there is the common tendency to neglect the solutes and consider the system as pseudo-binary (solvent−CO2). Polyvinylpyrrolidone (PVP) was precipitated using SAS from acetone-ethanol mixtures and different SAS morphologies were obtained at different operating conditions. To explain the obtained morphologies, VLEs of the ternary system acetone-ethanol−CO2 and of the quaternary system PVP-acetone-ethanol−CO2 were experimentally determined using a static synthetic method. It was evident that the presence of PVP, at different concentrations in the liquid solution, had an appreciable effect on the equilibria. Once the VLEs were determined, the morphologies of the powders precipitated by SAS were justified considering the position of the corresponding operating points with respect to the PVP-acetone-ethanol−CO2 mixture critical point.

Modeling of the Mixture Critical Locus with a Modified Cubic Plus Association Equation of State: Water, Alkanols, Amines, and Alkanes

In a phase envelope, an adequate description of the critical point is of high importance. It identifies the conditions where the bubble and dew curves meet, and where the nature of the single phase region outside the phase envelope changes. The knowledge of the mixture critical point is relevant to preventing production and transport problems, as well as to optimizing near-critical and supercritical processes. A modified cubic plus association (CPA) model was recently shown to accurately describe the vapor–liquid equilibrium (VLE) critical temperatures and pressures of pure compounds. The model is usually fitted to pure component data between 0.45Tr and 0.85Tr, while forcing the correct description of both Tc and Pc. Here, the performance of the model is evaluated for mixtures. Interaction parameters are regressed from VLE/liquid–liquid equilibrium (LLE) data at lower temperatures. Accurate results, for binary and ternary mixtures, were obtained. These results concern mainly mixtures containing, water, al...

Vapor-liquid equilibrium data for the carbon dioxide and carbon monoxide (CO2 + CO) system at the temperatures 253, 273, 283 and 298 K and pressures up to 13 MPa

Vapor-liquid equilibrium measurements for the binary system CO2 + CO are reported at 253, 273, 283 and 298 K, with estimated standard uncertainties of maximum 9 mK in temperature, maximum 3 kPa in pressure, and maximum 0.001 in the mole fractions of the phases in the mixture critical regions, and 0.0003 in the mole fractions outside the critical regions. These measurements are compared with existing data. Although some data exist, there are little trustworthy literature data around critical conditions, and the measurements in the present work indicate a need to revise the parameters of existing models. The data in the present work have significantly less scatter than most of the literature data, and range from the vapor pressure of pure CO2 to close to the mixture critical point pressure at all four temperatures. With the measurements in the present work, the data situation for the CO2 + CO system is improved, enabling development of better equations of state for the system. A scaling law model is fitted to the critical region data of each isotherm, and high accuracy estimates for the critical composition and pressure are found. The Peng-Robinson EOS with the alpha correction by Mathias and Copeman, the mixing rules by Wong and Sandler, and the NRTL excess Gibbs energy model is fitted to the data in the present work.

Isothermal vapour-liquid equilibrium data for the binary systems of CHF3 with (n-nonane, n-decane, or n-undecane) and C2F6 with (n-nonane or n-decane)

The isothermal vapour-liquid and vapour-liquid-liquid equilibria of five binary refrigerant + n-alkane systems at near ambient temperatures were measured using a static-analytic apparatus and a static-synthetic apparatus. The phase equilibrium data for the systems of trifluoromethane (R-23) + n-nonane and hexafluoroethane (R-116) + n-decane were measured using the static-analytic apparatus, whereas bubble point data were measured with the static-synthetic apparatus for the systems of R-23 + n-decane, R-23 + n-undecane and R-116 + n-nonane. The temperatures that were investigated for these systems ranged between (272.9 and 323.1) K.The experimental phase equilibrium data were modelled with the PR EOS and the MC alpha function. The WS mixing rule, incorporating either the NRTL or the UNIQUAC activity coefficient model, was used to apply the model to the mixture data. The temperature independent forms of the thermodynamic model were found to provide a more accurate representation of the experimental data than the temperature dependent forms. A single mixture critical point was determined using the indirect extended scaling laws of Ungerer et al. (2005). The calculation procedure of Heidemann and Khalil (1980) was used to estimate segments of the critical locus curves for the binary systems for which data were measured close to the critical locus curve. The van Konynenburg and Scott classification for each system was defined, based upon the characteristics of the critical locus curves within the temperature ranges that were studied.

Dependence of SAS particle morphologies on the ternary phase equilibria

In this work, the precipitation of a model compound (cefonicid) from DMSO by Supercritical Antisolvent (SAS) was performed. Various morphologies; i.e., expanded microparticles, microparticles, and nanoparticles were obtained, varying operating conditions. In order to explain these results, high-pressure vapor–liquid phase equilibria (VLEs) of the binary system DMSO-CO2 and of the ternary system DMSO-CO2-cefonicid were investigated, using a static analytic method.At 313K and low concentrations, the presence of the solute had a negligible effect on VLEs with respect to the binary system solvent-CO2. At concentrations up to 90mg/mL (at 313K) or increasing temperature at 333K (at 30mg/mL), a large modification of the VLEs was observed.The changes in phase behavior were successfully correlated to the powder morphologies, considering the position of the SAS operating point with respect to the ternary mixture critical point. The given explanations can be readily extended to other compounds.

Heat capacities of supercritical fluid mixtures: Comparing experimental measurements with Monte Carlo molecular simulations for carbon dioxide-methanol mixtures

Accurate thermophysical properties of supercritical fluid mixtures are important to today’s practicing scientists and engineers as they endeavor to correctly capture the unique attributes of these high pressure fluids in chemical processes and energy systems. Isobaric heat capacity, pertinent to many heat exchange calculations and thermodynamic variable manipulations, was measured for carbon dioxide-methanol mixtures using a flow calorimeter over a wide range of compositions (5–30mol% methanol), temperatures (60–150°C), and pressures (90–300bar). Heat capacity predictions from Monte Carlo molecular simulations were compared to experimental measurements at each state point. The average absolute difference between simulation predictions and measurements was slightly larger than +4%. Maximum deviations occurred in the near critical region for each mixture composition. In additions to providing new experimental data, this study validates the utility of molecular simulations as a predictive tool for this mixture in this experimentally challenging region of phase space, though more work is required to accurately calculate fluid properties in regions proximate the mixture critical point.

Modification of solid-state property of sulfasalazine by using the supercritical antisolvent process

In this study, the supercritical antisolvent (SAS) process was used to recrystallize an active pharmaceutical ingredient, sulfasalazine, to modify the solid-state properties including particle size, crystal habit and polymorphic form. Supercritical CO2 and tetrahydrofuran were used as the antisolvent and solvent, respectively. SAS results obtained from different operating temperatures (35, 45, 55 and 65°C) were compared and discussed. The results indicate that at 55°C, spherical sulfasalazine crystals were produced and that their mean particle size was micronized to approximately 1µm. In addition, according to the analytical results of powder X-ray diffractometry (PXRD), a novel polymorphic form of sulfasalazine was obtained after SAS. Furthermore, the spectroscopic and thermal behavior of produced sulfasalazine crystals were also studied by Fourier transform infrared spectrometry (FTIR), differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Finally, SAS results obtained from different operating temperature was discussed on the basis of the mixture critical point (MCP) of CO2 and tetrahydrofuran. Operation at slightly higher than the MCP is favorable for recrystallization of sulfasalazine through SAS. These results demonstrate that the SAS process is an efficient tool for controlling and modifying the solid-state property of sulfasalazine.

Vapor-liquid equilibrium data for the carbon dioxide and oxygen (CO2 + O2) system at the temperatures 218, 233, 253, 273, 288 and 298 K and pressures up to 14 MPa

Accurate thermophysical data for the CO2-rich mixtures relevant for carbon capture, transport and storage (CCS) are essential for the development of the accurate equations of state (EOS) and models needed for the design and operation of the processes within CCS. Vapor-liquid equilibrium measurements for the binary system CO2 + O2 are reported at 218, 233, 253, 273, 288 and 298 K, with estimated standard uncertainties of maximum 8 mK in temperature, maximum 3 kPa in pressure, and maximum 0.0031 in the mole fractions of the phases in the mixture critical regions, and 0.0005 in the mole fractions outside the critical regions. These measurements are compared with existing data. Although some data exists, there are little trustworthy literature data around critical conditions, and the measurements in the present work indicate a need to revise the parameters of existing models. The data in the present work has significantly less scatter than most of the literature data, and range from the vapor pressure of pure CO2 to close to the mixture critical point pressure at all six temperatures. With the measurements in the present work, the data situation for the CO2 + O2 system is significantly improved, forming the basis to develop better equations of state for the system. A scaling law model is fitted to the critical region data of each isotherm, and high accuracy estimates for the critical composition and pressure are found. The Peng-Robinson EOS with the alpha correction by Mathias and Copeman, the mixing rules by Wong and Sandler, and the NRTL excess Gibbs energy model is fitted to the data in the present work, with a maximum absolute average deviation of 0.01 in mole fraction.