Mixture Critical Pressure Research Articles

In situ adaptive tabulation of vapor-liquid equilibrium solutions for multi-component high-pressure transcritical flows with phase change

Vapor-liquid equilibrium (VLE) is a family of first-principled thermodynamic models for transcritical multiphase flows, which can accurately capture the phase transitions at high-pressure conditions that are difficult to deal with using other models. However, VLE-based computational fluid dynamics (CFD) simulation is computationally very expensive for multi-component systems, which severely limits its applications to real-world systems. In this work, we developed a new ISAT-VLE method based on the in situ adaptive tabulation (ISAT) method to improve the computational efficiency of VLE-based CFD simulation with reduced memory usage. We developed several ISAT-VLE solvers for both fully conservative (FC) and double flux (DF) schemes. New methods are proposed to delete redundant records in the ISAT-VLE table and the ISAT-VLE method performance is further improved. To improve the convergence of the VLE solvers, a modified initial guess for equilibrium constant is also introduced. Simulations of high-pressure transcritical two-phase temporal mixing layers and shock-droplet interaction were conducted using the ISAT-VLE CFD solvers. The simulation results show that the new method obtains a speed-up factor approximately from 10 to 60 and the ISAT errors can be controlled within 1%. The shock-droplet interaction results show that the DF scheme can achieve a higher speed-up factor than the FC scheme. The two sets of simulations exhibit the phase separation at high-pressure conditions. It was found that even at supercritical pressures with respect to each component, the droplet surface could still be in a subcritical two-phase state, because the mixture critical pressure is often significantly higher than each component and hence triggers phase separation. In addition, a shock wave could partially or completely convert the droplet surface from a subcritical two-phase state to a single-phase state by raising temperature and pressure.

Phase Behavior of Isobutane + CO2 and Isobutane + H2 at Temperatures Between 190 and 400 K and at Pressures Up to 20 MPa

Mixtures containing isobutane, carbon dioxide, and/or hydrogen are found in various industrial processes, green refrigerant systems, and the growing hydrogen industry. Understanding the thermophysical properties of these mixtures is essential for these processes, and depends on reliable experimental data. Making use of an automated static-analytical apparatus, measurements were made of the phase behavior of binary mixtures of isobutane with CO2 and with H2, extending the range of available data for both mixtures. Measurements of the system isobutane + CO2 were carried out along three isotherms at temperatures of (240, 280, and 310) K with pressures from the lower limit of the sampling system (~ 0.5 MPa) to the mixture critical pressure. The results exhibit good agreement with literature data. Measurements on isobutane + H2 were carried out along nine isotherms at temperatures of (190, 240, 280, 311, 339, 363, 375, 390, and 400) K with pressures up to 20 MPa, covering a much broader range of conditions than the one prior investigation. The results have been used to optimize temperature-dependent binary parameters in the Peng–Robinson equation of state with two different mixing rules. This approach was found to perform well in comparison to alternative models.

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.

Vapor–liquid equilibrium estimation of n-alkane/nitrogen mixtures using neural networks

Understanding fluid phase behavior, like VLE, in high P&T conditions is crucial for developing high-fidelity simulations of chemically reacting flows in liquid-fueled combustion systems and also forms an integral part of the design-modeling of the control processes in chemical industries. Two data-driven models have been proposed in this study, each of which was competent in estimating VLE for the Type III binary systems of C10/N2 and C12/N2, at pressures ranging up to 50–60 MPa. Both models showed better performance in predicting equilibrium pressure as compared to VLE modeled using PR-EOS. A modified model has also been proposed, capable of estimating the full phase envelope for the binary systems of C10/N2 and C12/N2 across a wide range of temperatures, and thus exhibit the mixture critical pressure at the concerned temperature. The diverse applicability of the proposed network architecture was further exhibited while estimating the VLE of a ternary system of C1/C10/N2.

The influence of temperature and pressure on macro- and micro-mixing in compressed fluid flows; mixing of carbon dioxide and ethanol above their mixture critical pressure

We report quantitative composition data on continuous jet-mixing of ethanol with ambient carbon-dioxide (CO2) at temperatures (T=[313 K–333 K]) and pressures (p=[9 MPa to 11 MPa]) in the vicinity of the mixture critical pressure of the binary system. Progress of mixing is quantified simultaneously on the macro- and on the micro-scale. The lag between mixing on both scales is quantified spatially resolved and in the jet-mixing region. We found that surprisingly mixing below the mixture critical pressure in the two-phase mixing regime can be more efficient than mixing above the mixture critical pressure in the single-phase mixing regime. Density was the key parameter influencing the mixing efficiency.

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.

Thermodynamic structure of supercritical LOX–GH2 diffusion flames

In this study, we evaluate the thermodynamic structure of laminar hydrogen/oxygen flames at supercritical pressures using 1D flame calculations and large-eddy simulation (LES) results. We find that the real fluid mixing behavior differs between inert (cold flow) and reactive (hot flow) conditions. Specifically, we show that combustion under transcritical conditions is not dominated by large-scale homogeneous real-fluid mixing: similar to subcritical atomization, the supercritical pure oxygen stream undergoes a distinct transition from liquid-like to gas-like conditions; significant mixing and combustion occurs primarily after this transition under ideal gas conditions. The joint study of 1D flame computations and LES demonstrates that real-fluid behavior is chiefly confined to the bulk LOX stream; real fluid mixing occurs but in a thin layer surrounding the LOX core, characterized by water mass fractions limited to 3%. A parameter study of 1D flame solutions shows that this structure holds for a wide range of relevant injection temperatures and chamber pressures. To analyze the mixing-induced shift of the local fluid critical point, we introduce a state-space representation of the flame trajectories in the reduced temperature and reduced pressure plane which allows for a direct assessment of the local thermodynamic state. In the flame, water increases the local mixture critical pressures, so that subcritical conditions are reached. This view of limited mixing under supercritical conditions may yield more efficient models and an improved understanding of the disintegration modes of supercritical flows.

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.

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.

New catalyst pushes lignin up on the value chain

Experimental measurements of the phase equilibria of (CO2 + butylbenzene) and (CO2 + butylcyclohexane) have been made with an analytical apparatus at temperatures of (323.15, 373.15 and 423.15) K at pressures from 2 MPa to the mixture critical pressure. These are the first results to be published for (CO2 + butylcyclohexane), while for (CO2 + butylbenzene) they are the first at pressures above 6 MPa. To model the data, we use the Peng–Robinson equation of state with Wong–Sandler mixing rules incorporating the NRTL equation. The model describes the measured bubble point curves very well at all temperatures, except close to the mixture critical points at high pressures. The dew point curves are described well only at the lowest temperature; otherwise, deviations increase in the approach to the mixture critical point.

Phase equilibria of (CO2 + butylbenzene) and (CO2 + butylcyclohexane) at temperatures between (323.15 and 423.15) K and at pressures up to 21 MPa

Experimental measurements of the phase equilibria of (CO2+butylbenzene) and (CO2+butylcyclohexane) have been made with an analytical apparatus at temperatures of (323.15, 373.15 and 423.15)K at pressures from 2MPa to the mixture critical pressure. These are the first results to be published for (CO2+butylcyclohexane), while for (CO2+butylbenzene) they are the first at pressures above 6MPa. To model the data, we use the Peng–Robinson equation of state with Wong–Sandler mixing rules incorporating the NRTL equation. The model describes the measured bubble point curves very well at all temperatures, except close to the mixture critical points at high pressures. The dew point curves are described well only at the lowest temperature; otherwise, deviations increase in the approach to the mixture critical point.

Experimental measurements and correlation of vapor–liquid equilibrium and critical data for the CO2 + R1234yf and CO2 + R1234ze(E) binary mixtures

Isothermal (P-x-y) vapor–liquid equilibrium data for the CO2 + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) binary system are reported at seven temperatures ranging from 283.15 K to 353.15 K. The experimental values were measured using a static–analytic type apparatus coupled with two electromagnetic capillary samplers (Rolsi™, Armines' patent) for repeatable and reliable equilibrium phase sampling and handling. Moreover, for the four temperatures above the critical temperature of pure CO2 (304.3 K), the mixture critical compositions (xc) and pressures (Pc) were calculated at each temperature using extended scaling laws.In a second step, the critical loci of the CO2 + R1234yf and CO2 + trans-1,3,3,3-tetrafluoroprop-1-ene [R1234ze(E)] were measured over the whole composition range using a synthetic-dynamic type apparatus. The subcritical and critical experimental data determined in this study were compared to those available in the open literature and were correlated using the Peng–Robinson equation of state with temperature-dependent binary interaction parameters.

Quantification of the mass transport in a two phase binary system at elevated pressures applying Raman spectroscopy: Pendant liquid solvent drop in a supercritical carbon dioxide environment

Mass transport between organic solvents (S) and carbon dioxide (CO2) has been investigated at pressures below the mixture critical pressure (MCP). Acetone and dimethyl sulfoxide (DMSO) have been used as organic solvents. Profiles of the mixture composition have been measured through liquid solvent drops pendant at steady conditions in a pressurized CO2 environment. The drop has been kept steady by feeding exactly that amount of liquid through a feed glass capillary into the pendant drop that evaporated at the same time from the drop into the CO2 environment. The liquid fed into the pendant drop has been either pure organic solvent or organic solvent with some CO2 dissolved. Profiles of the mixture composition have been quantified applying an optical Raman line imaging technique and the respective involved mass transport mechanisms are discussed comprehensively. Evaporative cooling was shown to dominate the temperature change at the inner margin of the drop, while mixing enthalpies were shown to be of minor importance. By fitting a mass transport model to DMSO concentration profiles, calculated from the mass fraction composition profiles, the mass transport properties diffusivity D, Biot-number Bi and mass transfer coefficient β could be derived. When acetone has been used as solvent, no steady drops could be formed not allowing a model based quantification of the mass transport.

Interactions of phase equilibria, jet fluid dynamics and mass transfer during supercritical antisolvent micronization: The influence of solvents

This work reports the mixing behavior of some organic solvents, used for the supercritical antisolvent technology (SAS), when they are injected into supercritical carbon dioxide. Different mixing characteristics can condition the morphology of the particles produced during the precipitation process. The results, obtained using an elastic light scattering technique, show, that for chloroform and acetone, there is sharp transition from two-phase mixing to single phase jet mixing at pressures larger than the mixture critical pressure of the binary system solvent–carbon dioxide. N-methyl-2-pyrrolidone, ethanol and dimethylsulfoxide show a large transition range between the two-phase mixing regime below the mixture critical pressure and the completely developed one-phase mixing regime above the mixture critical pressure. The transition may cover a pressure range of up to 6MPa. Mixtures of acetone and dimethylsulfoxide show a mixing behavior that is intermediate between the one of the two pure solvents. The influence of an increase of temperature on the mixing behavior was analyzed for dimethylsulfoxide only; the transition range moved to higher pressures according to the corresponding shift of the mixture critical pressure of the binary system with temperature. A practical indication is, that it is very difficult or even impossible to produce spherical microparticles by SAS, if solvents with a sharp transition between the two-phase and the one-phase mixing regime are used.

Numerical analysis of the characteristic times controlling supercritical antisolvent micronization

In this work jet break-up time and of dynamic surface tension vanishing are considered as mechanisms in competition during supercritical antisolvent precipitation and a mathematical model, based on these two characteristic phenomena, is presented.Jet break-up time has been evaluated solving continuity and conservation of momentum equations; on the other hand, dynamic surface tension vanishing time has been evaluated according to the time-evolution model proposed by Cahn and Hilliard. Phase equilibria have also been taken into account, considering the Peng and Robinson equation of state and the related mixing rules.Calculations have been applied to yttrium acetate (YAc) as model solute, dimethylsulphoxide (DMSO) as liquid solvent and carbon dioxide (CO2) as antisolvent.The cross-over times, between jet break-up dominated and dynamic surface tension vanishing dominated regions, have been calculated at different pressures for pure DMSO and at different YAc concentrations in the liquid solution; a good agreement with previous experimental results has been obtained. The numerical results also correctly describe the influence of solute concentration on the pressure at which cross-over between the two regions is obtained.The characteristic times for acetone (AC) have also been evaluated, to perform a comparison with DMSO; in this case, cross-over has been observed in proximity of the mixture critical point pressure of the binary system.

Observation of liquid solution volume expansion during particle precipitation in the supercritical CO2 antisolvent process

An optical measurement technique, which is based on the Foerster resonant energy transfer (FRET) between two different dye molecules, has been applied successfully to observe volume expansion of a liquid solution, when it is pressurized with CO2. Rhodamine-B and Rhodamine-700 were dissolved in ethanol to form the FRET active dye solution. In a first “prove of principle” experiment, the sensitivity of the FRET efficiency towards volume expansion was demonstrated by pressurizing the liquid dye solution in a cuvette with CO2. From the rise of the meniscus of the solution inside the cuvette as a function of CO2 pressure, the simultaneously acquired FRET spectra could be correlated with the volume expansion of the dye solution. In a second experiment, the dye solution was injected into CO2 at different supercritical antisolvent operation pressures. FRET spectra were recorded 3mm downstream of the injector nozzle, always upstream of the breakup of the injected liquid solution. At pressures below the thermodynamic mixture critical pressure (7.9MPa @ 313K) of the system ethanol/CO2 no liquid phase volume expansion was observed. At pressures between the thermodynamic and the dynamic mixture critical pressure (8.5MPa @ 313K) of the same system, volume expansion could be evidenced before the breakup of the injected liquid solution.

Mixing effects on particle formation in supercritical fluids

The process termed solution enhanced dispersion by supercritical fluids (SEDS™) is investigated. In the process particles are created in the rapid antisolvent process using a twin-fluid nozzle to co-introduce the SCF antisolvent and solution. Results of experimental and numerical studies are presented for two regions of pressure: above the mixture critical pressure where a single-phase exists for all solvent–antisolvent compositions, and below the mixture critical pressure where the two-phase region is observed. In experimental studies paracetamol (in the single-phase system) and nicotinic acid (in the two-phase system) were precipitated from ethanol solution using supercritical CO 2 as an antisolvent. To interpret the phenomena affecting creation of the supersaturation and to predict suprsaturation distribution, balances of momentum (flow), species (mixing), energy (heating and cooling) and population (droplet and crystal size distributions) are applied. The Favre averaged k– ɛ model of the CFD code FLUENT is applied together with specific models for precipitation subprocesses and Peng–Robinson equation of state. This includes application of the PDF closure procedure for precipitation and the drop breakage kernel that is based on multifractal theory of turbulence for modelling drop dispersion. Thermodynamic effects of mixing and decompression are included as well. Predicted values not always agree with experimental data but anyhow simulations predict all trends observed in experiments.

Particle formation in supercritical fluids—Scale-up problem

The process of antisolvent precipitation of particles, termed solution enhanced dispersion by supercritical fluids (SEDS™), is applied to precipitate the model drug, paracetamol, from ethanol solutions. In the SEDS process the substrate solution is quickly mixed in a mixing chamber of the coaxial two-component nozzle with an antisolvent, represented in this case by the supercritical CO 2. Resulting partially mixed, highly supersaturated solution is introduced into the precipitation vessel as a jet, which generates intensive circulation of residual fluids that dilute the fresh supersaturated solution. Nucleation starts in the nozzle chamber, whereas particle growth completes the process in the precipitation vessel. The process is carried out above the mixture critical pressure; the antisolvent is thus completely miscible with the solvent. Under such conditions the macro-, meso-, and micro-mixing processes can affect the particle size distribution (PSD) and should be considered when the process is scaled up. Scaling up considerations of the precipitation process are based on scale-up rules, CFD simulations and experimental data for paracetamol precipitation. In simulations the model presented earlier ( Bałdyga et al., 2004) that is based on the population balance equation and CFD modelling of compressible flow processes is applied. Results of experimental investigations and numerical simulations are applied to verify scale-up strategies for the SEDS processes.

Interactions of phase equilibria, jet fluid dynamics and mass transfer during supercritical antisolvent micronization

Supercritical antisolvent (SAS) precipitation has been successfully used in the micronization of several compounds. Nevertheless, the role of high-pressure vapor–liquid equilibria, jet fluid dynamics and mass transfer in determining particle size and morphology is still debated. In this work, CO 2 has been adopted as supercritical antisolvent and elastic light has been used to acquire information on jet fluid dynamics using thin wall injectors for the investigation of the liquid solvents acetone and DMSO at operating conditions of 40 °C in the pressure range between 6 and 16 MPa. The results show that two-phase mixing after jet break-up is the phenomenon that characterizes the jet fluid dynamics at subcritical conditions. When SAS is performed at supercritical conditions a transition between multi-phase and single-phase mixing is observed by increasing the operating pressure. Single-phase mixing is due to the very fast disappearance of the interfacial tension between the liquid solvent and the fluid phase in the precipitator. The transition between these two phenomena depends on the operating pressure, but also on the viscosity and the surface tension of the solvent. Indeed, single-phase mixing has been observed for acetone very near the mixture critical point, whereas DMSO showed a progressive transition for pressures of about 12 MPa. In the second part of the work, a solute was added to DMSO to study the morphology of the microparticles formed during SAS precipitation at the different process conditions, to find a correlation between particle morphology and the observed jet. Expanded microparticles were obtained working at subcritical conditions; whereas spherical microparticles were obtained operating at supercritical conditions up to the pressure where the transition between multi- and single-phase mixing was observed. Nanoparticles were obtained operating far above the mixture critical pressure. The observed particle morphologies have been explained considering the interplay among high-pressure phase equilibria, fluid dynamics and mass transfer during the precipitation process.

Global phase behavior of imidazolium ionic liquids and compressed 1,1,1,2‐tetrafluoroethane (R‐134a)

AbstractNovel processes involving ionic liquids with refrigerant gases have recently been developed. Here, the complete global phase behavior has been measured for the refrigerant gas, 1,1,1,2‐tetrafluoroethane (R‐134a) and 1‐n‐alkyl‐3‐methyl‐imidazolium ionic liquids with the anions hexafluorophosphate [PF6], tetrafluoroborate [BF4] and bis(trifluoromethylsulfonyl)imide [Tf2N] from ∼0°C to 105°C and to 33 MPa. All of the systems studied were Type V from the classification scheme of Scott‐van Konynenburg with regions of vapor‐liquid equilibrium, miscible/critical regions, vapor‐liquid‐liquid equilibrium, and upper and lower critical endpoints (UCEP and LCEP). The effect of the alkyl chain length has been investigated, for ethyl‐([EMIm]), n‐butyl‐([BMIm]), and n‐hexyl‐([HMIm]). With increasing chain length, the temperature of the lower critical end points increases and pressure at the mixture critical points decrease. With a common cation, the temperature of the LCEP increased and the mixture critical point pressures decreased in the order of [BF4], [PF6], and [Tf2N]. © 2008 American Institute of Chemical Engineers AIChE J, 2009