Mixture Critical Points Research Articles

System-agnostic prediction of pharmaceutical excipient miscibility via computing-as-a-service and experimental validation

We applied computing-as-a-service to the unattended system-agnostic miscibility prediction of the pharmaceutical surfactants, Vitamin E TPGS and Tween 80, with Copovidone VA64 polymer at temperature relevant for the pharmaceutical hot melt extrusion process. The computations were performed in lieu of running exhaustive hot melt extrusion experiments to identify surfactant-polymer miscibility limits. The computing scheme involved a massively parallelized architecture for molecular dynamics and free energy perturbation from which binodal, spinodal, and mechanical mixture critical points were detected on molar Gibbs free energy profiles at 180 °C. We established tight agreement between the computed stability (miscibility) limits of 9.0 and 10.0 wt% vs. the experimental 7 and 9 wt% for the Vitamin E TPGS and Tween 80 systems, respectively, and identified different destabilizing mechanisms applicable to each system. This paradigm supports that computational stability prediction may serve as a physically meaningful, resource-efficient, and operationally sensible digital twin to experimental screening tests of pharmaceutical systems. This approach is also relevant to amorphous solid dispersion drug delivery systems, as it can identify critical stability points of active pharmaceutical ingredient/excipient mixtures.

A new high pressure phase equilibrium cell featuring the static-combined method: Equipment commissioning and data measurement

A new equilibrium cell featuring a floating piston with an internal variable volume and phase sampling mechanism was designed and commissioned for the measurement of phase equilibrium data. The experimental technique can be extended to the static-combined method. The apparatus was tested by measuring vapor-liquid equilibrium data for the binary system of carbon dioxide + n-hexane at 313.15 K. New experimental vapor-liquid equilibrium data were also measured for the binary systems of carbon dioxide + 1,1,2,2 tetrafluoroethyl 2,2,3,3 tetrafluoropropyl ether at four temperatures, viz. (303.15, 313.15, 323.15 and 333.15) K and modeled using the Peng-Robinson Equation of State. Data close to the mixture critical points were modeled using a scaling law. The average expanded uncertainty for T, P, x1 and y1 for all systems in this work were 0.08 K, 0.002 MPa, 0.004 and 0.0007, respectively.

Isothermal Vapor–Liquid Equilibrium Data for Binary Systems of CHF3 or C2F6 with Methylcyclohexane or Toluene

The isothermal vapor–liquid and vapor–liquid–liquid equilibria of four binary refrigerant–hydrocarbon systems were measured using a static-analytic apparatus at temperatures between 293.0 and 313.2 K and at pressures of up to 6.1 MPa. The two refrigerants that were investigated were trifluoromethane and hexafluoroethane, and the hydrocarbons were methylcyclohexane and toluene. At the temperatures that were investigated, the R-23 + toluene system alone did not exhibit any liquid–liquid immiscibility. The “bird’s-beak” phenomenon was observed for all of the systems. The experimental data were regressed with the PR MC EOS with the WS mixing rule. Either the NRTL or the UNIQUAC activity coefficient model was used within the WS mixing rule. A procedure for the calculation of the critical locus curves from thermodynamic models and an extrapolation technique for determining the mixture critical points from subcritical coexistence curves were employed. The van Konynenburg and Scott classifications of the four bin...

Surface tension and critical point measurements of methane + propane mixtures

Surface tension predictions of hydrocarbon mixtures at vapour-liquid equilibrium are crucially important and used in the design of many unit operations in the production of liquefied natural gas (LNG). Predictive models for surface tension are not well tested for hydrocarbon mixtures at high pressures due to the limited data available at relevant conditions. A differential capillary rise apparatus consisting of a high-pressure sapphire equilibrium cell was constructed and used to measure the surface tension of methane+propane mixtures along three isotherms T=(272.23, 285.51 and 303.34)K at pressures up to 9MPa. The capillary diameters were calibrated using pure saturated propane at 271K, and the technique was validated by measurements of pure ethane. The measured surface tensions were compared with the available data and the predictions of various models, including the Parachor method and Linear Gradient Theory: both were able to describe the data within their uncertainty. However, the default surface tension model for hydrocarbon mixtures implemented in the widely-used software package REFPROP 9.1 gave poor predictions; this was rectified through the implementation of the Parachor method in a beta-version of REFPROP 9.2. Critical points were also measured from observations of critical opalescence and the disappearance of the bulk interface. The measured mixture critical points were consistent with, and extended, literature values for this binary system. The measured critical points differed by between 0.5 and +27K from predictions made with the GERG-2008 equation of state (EOS) and between −5 and +10K for the Peng-Robinson EOS.

Reliable mixture critical point computation using polynomial homotopy continuation

The numerical computation of multicomponent mixture critical points has been the subject of much study due to their theoretical and practical importance. Both deterministic and stochastic methods have been applied with varying degrees of reliability and robustness. In this work, we utilize numerical polynomial homotopy continuation (NPHC) to reliably identify all mixture critical points. This method is unique due to its robustness, initialization‐free nature and ease of parallelization. For a given system of equations, all complex solutions are found. Computational times are also found to be invariant to mixture composition. We validate this technique against previous work and extend the method to mixtures of up to eight components. NPHC is shown to be a modern and powerful technique which offers mathematical reliability at a moderate computational cost. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4497–4507, 2016

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.

General reflection on critical negative azeotropy and upgrade of the Bancroft's rule with application to the acetone + chloroform binary system

The possible shapes of continuous critical loci for binary systems exhibiting a negative azeotrope which persists up to the critical region are reviewed and extensively discussed. Such a review made it possible to prove that the existence of an intersection point – in a (P, T) projection – between the critical line and one of the vaporization curves was a sufficient condition for a binary system to exhibit a critical azeotrope. The Bancroft's rule which until now stated that the existence of an intersection point between the two vaporization curves in a (P, T) plane was a sufficient condition to observe an azeotropic behavior was thus upgraded to take into account the crossing of the critical line and one of the vaporization curves. Such a point was logically called a Bancroft point of the second kind.In a second part, mixture critical points of the acetone+chloroform binary system were measured in order to determine if such a system exhibited a Bancroft point of the second kind and consequently if the negative azeotrope persisted up to the critical region. Along the critical line, the acetone mole fraction was varied between 0.06 and 0.92.

Development of a Predictive Equation of State for CO2 + Ethyl Ester Mixtures Based on Critical Points Measurements

To design and optimize the noncatalytic supercritical process for biodiesel production based on ethanolysis and using carbon dioxide as a cosolvent, thermodynamic models are required to predict the fluid phase equilibria of the various mixtures involved within. This work is an attempt to extend the PPR78 predictive cubic equation of state to CO2 + ethyl ester systems. To do so, 105 mixture critical points of 11 CO2 + (saturated and unsaturated) ethyl ester mixtures were preliminary measured using a synthetic-dynamic apparatus. With the use of these data as well as vapor–liquid equilibrium data collected in the open literature, 2 new groups were added to the PPR78 model (the ester group −COO– and the ethyl acetate group) and 10 PPR78 group-interaction parameter values were determined. Although the PPR78 model offers a good predictive capacity, it is observed that the prediction may deteriorate with the ethyl ester chain length or the presence of double C═C bonds.

Isothermal vapor–liquid equilibrium data for the ethylene + 1,1,2,3,3,3-hexafluoro-1-propene binary system between 258 and 308 K at pressures up to 4.56 MPa

Isothermal vapor–liquid equilibrium data are reported for ethylene+1,1,2,3,3,3-hexafluoro-1-propene mixtures at six temperatures in the 258.35–307.38K range, and pressures up to 4.56MPa. The experimental data were measured using an apparatus based on the “static-analytic” method equipped with a movable ROLSI™ capillary sampler for repeatable and reliable equilibrium phase sampling and handling. The isothermal P–x–y data are well correlated with a model comprised of the Peng–Robinson equation of state containing the Mathias–Copeman alpha function, Wong–Sandler mixing rule, and NRTL local composition model. The combined model is termed “PR-MC-WS-NRTL”. The studied system does not exhibit azeotropic behavior nor liquid–liquid immiscibility over the range of investigated temperatures. Mixture critical points are calculated from the experimental vapor–liquid equilibrium data via the extended scaling laws and the PR-MC-WS-NRTL model, and are found to be in good agreement with the experimental isothermal phase envelopes.

Vapor–Liquid Equilibrium Measurements and Modeling for the Ethane (R-170) + 1,1,2,3,3,3-Hexafluoro-1-propene (R-1216) Binary System

Novel isothermal (p–x–y) vapor–liquid equilibrium data are reported for ethane (R-170) + 1,1,2,3,3,3-hexafluoro-1-propene (R-1216) mixtures at five temperatures in the (282.93 to 322.89) K range, at pressures up to about 4.6 MPa. The experimental data were measured using an apparatus based on the “static-analytic” method taking advantage of two electromagnetic capillary samplers for repeatable and reliable equilibrium phase sampling and handling. The experimental data are well-correlated with the “PR-MC-NRTL-WS” model constituted by the Mathias–Copeman α function, nonrandom two-liquid (NRTL) local composition model, and Wong–Sandler mixing rule introduced in the Peng–Robinson equation of state. The studied system did not exhibit azeotropic behavior nor liquid–liquid immiscibility over the range of investigated temperatures. Mixture critical points have been estimated from the experimental vapor–liquid equilibrium data via the extended scaling laws and the “PR-MC-NRTL-WS” model and are found to be in good agreement with the experimental isothermal phase envelopes.

Vapor−Liquid Equilibrium Data and Predictive Correlations for the Carbon Dioxide−Dimethyl Carbonate Binary Mixture

Mixture critical points and liquid-phase density, component concentration, and volume expansion were measured for the carbon dioxide−dimethyl carbonate binary mixture at temperatures between (310 and 423) K [(37 to 150) °C] and pressures between (1.1 and 14.4) MPa. Data were correlated well by the Redlich−Kwong−Aspen equation of state as well as several empirical engineering correlations. Importantly, the experimental and modeling procedures outlined in this work may be adapted to other carbon dioxide−liquid binary mixtures and used to facilitate the design of CO2-based reaction and separation processes.

Efficient and reliable mixture critical points calculation by global optimization

Multicomponent systems may exhibit several critical points or no critical point at all. Local methods can find only one critical point for a given initial guess. Recently, several global methods have been proposed for finding all the solutions of the problem. In the present work, we propose a gradient-based calculation method using global optimization, with temperature and molar volume as primary variables, and with analytical partial derivatives calculated from a two-parameter cubic equation of state. The Tunneling global optimization method is used for finding all the global minima. The implementation is based on a unique feature of the Tunneling method, which is able to find efficiently and reliably multiple minima at the same level. Several mixtures from binaries to petroleum reservoir fluids are used to test the proposed method. Numerical experiments proved the efficiency and reliability of the Tunneling method for finding all mixture critical points.

High-pressure phase equilibrium for the hydroformylation of 1-octene to nonanal in compressed CO 2

The hydroformylation reaction in supercritical carbon dioxide or CO 2-expanded liquids (CXLs) has many advantageous properties. However, accurate phase behavior and equilibrium must be known to properly understand and engineer these systems. In this investigation, the vapor–liquid equilibrium and mixture critical points of CO 2 systems with 1-octene, nonanal, 1-octene and nonanal mixtures, and mixtures of 1-octene, nonanal and syngas (CO/H 2) were measured at 60 °C up to 120 bar of pressure. The Peng–Robinson equation of state with van der Waals two-parameter mixing rule was employed successfully to correlate the binary mixture data and predict the ternary mixture data. The presence of CO/H 2 pressure increased the mixture critical points and decreased the volume expansion at any given pressure. In an actual reaction, the mixture critical point would increase throughout the reaction, while the volume of the liquid phase would decrease. These data will aid the understanding and reaction engineering for the hydroformylation reaction in CO 2-expanded liquids and supercritical fluids.

High-pressure phase equilibria for the synthesis of ionic liquids in compressed CO 2 for 1-hexyl-3-methylimidazolium bromide with 1-bromohexane and 1-methylimidazole

The use of carbon dioxide in the synthesis of ionic liquids (ILs) has many advantages over conventional solvents. Here, the high-pressure phase equilibria (including CO 2 solubility, volume expansion, and mixture critical points) are measured and modeled for the system involved in the synthesis of a model imidazolium ionic liquid 1-hexyl-3-methylimidazolium bromide ([HMIm][Br]) from 1-bromohexane and 1-methylimidazole. The global phase behavior of 1-methylimidazole was investigated and found to be a Type V system (or potentially IV) from the classification of Scott and van Konynenburg with regions of vapor–liquid equilibrium, vapor–liquid–liquid equilibrium, liquid–liquid equilibrium, an upper and lower critical endpoint and mixture critical points. The solubility and volume expansion of CO 2 in 1-methylimidazole, 1-bromohexane, a 1:1 mixture of 1-methylimidazole and 1-bromohexane and [HMIm][Br] was determined at 313.15 K and 333.15 K for pressures ranging from 10 to 160 bar. The solubility of CO 2 and the volume expansion increases in the order of [HMIm][Br] ≪ 1-methylimidazole < 1:1 mixture of reactants < 1-bromohexane. The Peng–Robinson equation of state with van der Waals 2-parameter mixing rules was used with estimated critical properties to well correlate the vapor–liquid equilibrium. The results have important ramifications on the kinetics and process constraints of an actual IL synthesis with CO 2.

Phase equilibria of imidazolium ionic liquids and the refrigerant gas, 1,1,1,2-tetrafluoroethane (R-134a)

A number of applications with ionic liquids (ILs) and hydrofluorocarbon gases have recently been proposed. Detailed phase equilibria and modeling are needed for their further development. In this work, vapor–liquid equilibrium, vapor–liquid–liquid equilibrium, and mixture critical points of imidazolium ionic liquids with the hydrofluorocarbon refrigerant gas, 1,1,1,2-tetrafluoroethane (R-134a) was measured at temperatures of 25 °C, 50 °C, 75 °C and pressure up to 143 bar. The ionic liquids include 1-hexyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)amide ([HMIm][Tf 2N]), 1-hexyl-3-methyl-imidazolium hexafluorophosphate ([HMIm][PF 6]), and 1-hexyl-3-methyl-imidazolium tetrafluoroborate ([HMIm][BF 4]). The effects of the anion and cation on the solubility were investigated with the anion having greatest impact. [HMIm][Tf 2N] demonstrated the highest solubility of R-134a. The volume expansion and molar volume were also measured for the ILs and R-134a. The Peng–Robinson Equation of State with van der Waals 2-parameter mixing rule with estimated IL critical points were employed to model and correlate the experimental data. The models predict the vapor–liquid equilibrium and vapor–liquid–liquid equilibrium pressure very well. However, the mixture critical points predictions are consistently lower than experimental values.

Understanding Biphasic Ionic Liquid/CO2 Systems for Homogeneous Catalysis: Hydroformylation

A biphasic ionic liquid (IL) and compressed carbon dioxide system has a number of advantages for efficient homogeneous catalysis. The hydroformylation of 1-octene to nonanal catalyzed by a rhodium−triphenylphosphine complex was used as a model reaction to illustrate the effects of carbon dioxide in a biphasic ionic liquid/CO2 system using the model ionic liquid, 1-hexyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)amide ([HMIm][Tf2N]). Detailed phase equilibrium studies were conducted to determine volume expansion of the IL phase and the multiphase equilibria and mixture critical points between the reactant, product, and IL with CO2 and syngas (CO/H2). These data ultimately affect the concentration of the reactant and, thus, the apparent reaction rate. The viscosity of the IL with CO2 pressure was measured and demonstrates the dramatic decrease with increasing CO2 pressure. The self-diffusion coefficient of the ionic liquid and 1-octene were measured and indicate a large increase with CO2 pressure (so...

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

Phase Behavior of Poly(propylene glycol) Monobutyl Ethers in Dense CO2

An oxygenated hydrocarbon-based polymer, poly(propylene glycol) monobutyl ether (PPGMBE), is very CO2-soluble. Therefore PPGMBE may serve as the CO2-philic portion of CO2-soluble surfactants, dispersants, thickeners, and chelating agents. CO2−PPGMBE isothermal pressure−composition phase diagrams were determined at 298 K for PPGMBE average molecular weights of 340, 1000, and 1200. All the diagrams share the same features of one vapor−liquid−liquid three-phase equilibrium line and three two-phase equilibrium regions. The mixture critical points for the pseudobinary solutions were determined to be (7.2, 31.0, and 41.7) MPa for molecular weights of 340, 1000, and 1200, respectively.

High-pressure phase equilibria with compressed gases

An apparatus is described that is capable of determining high-pressure vapor-liquid equilibrium, liquid-liquid equilibrium, solid-liquid-vapor equilibrium, vapor-liquid-liquid equilibrium, and mixture critical points and transitions. The device is capable of temperatures to 150 degrees C and pressures to 300 bars (higher with slight modifications). The construction and operation are described in detail and do not require the use of mercury. This method requires very low sample volumes and no analytical equipment nor system-specific calibration. The apparatus was verified by comparison with literature data for the decane-CO(2) mixture and CO(2)-ionic liquid [1-hexyl-3-methyl-imidazolium bis(trifyl)imide)] systems. The experimental data have excellent agreement with the literature data that used different experimental methods. A rigorous error analysis of the system is also presented.