Chain Statistical Associating Fluid Theory Research Articles

A study on thermophysical properties of binary mixtures of n-hexane with benzene and some alkyl-substituted benzenes within temperature range (293.15–323.15) K: Experimental and modeling approach

The current work reports densities and sound speeds, and related thermodynamic excess properties, namely excess molar volumes and excess isentropic compressibilities, measured at temperatures from (293.15 to 323.15) K and under atmospheric pressure conditions for binary mixtures of n-hexane with benzene, toluene, ethylbenzene, o-xylene, m-xylene, and p-xylene. Redlich-Kister polynomial correlated the thermodynamic excess properties to test the quality of experimental data. Excess properties contributed to understanding molecular interactions between involved molecules and the peculiarities of their packing in the mixture. The Jouyban-Acree model was used to correlate the mixtures' experimental densities, sound speeds, and their related derived properties, namely isobaric thermal expansivities and isentropic compressibilities. The average absolute percentage deviation of the correlated values from the experimental ones was better than 0.036 %, 0.058 %, 0.040 %, and 0.146 % for density, sound speed, isobaric thermal expansivity, and isentropic compressibility, respectively, attesting to the robustness of the Jouyban-Acree correlations. Additionally, the Perturbed Chain Statistical Associating Fluid Theory Equation of State modeled the densities of the current mixtures. Schaaff's Collision Factor Theory and Nomoto's relation were compared for their ability to model the sound speeds of the mixtures. The efficacy of these models was tested by computing the average absolute percentage deviations between experimental and computed values. The modeled densities are reasonably concordant with experimental data, with an overall deviation of 0.02 %. Notably, Nomoto's relation exhibited superior performance over Schaaff's theory in modeling sound speeds of current mixtures, with an overall deviation of 0.33 %. The current findings underline the efficacy and versatility of the used models for thermodynamic modeling in systems of varying complexity.

Density measurements of homogeneous phase fluid mixtures comprising CO2/methanol and CO2/ethanol binary systems and correlation with equations of state

Equations of state (EoS) are powerful tools for estimating a wide variety of physical properties. However, the applicability of parameter sets derived from specific physical properties for the correlation and estimation of various other physical properties has received limited attention. Additionally, the estimation of physical properties using EoS is anticipated to be affected by the association of molecules. The densities of homogeneous phase fluid mixtures comprising carbon dioxide (CO2)/methanol (MeOH) and CO2/ethanol (EtOH) binary systems were measured in the current study using a high-pressure vibration-type density meter equipped with a circulation pump and a variable-volume viewing cell. Homogeneity was ensured by observing the fluid through the viewing window of the variable volume cell. The measurements were carried out at a temperature range of 313–353 K, the CO2 mole-fraction range of 0–80 mol%, and at pressures up to 20 MPa. Subsequently, the as-obtained experimental data were correlated with two EoSs, viz. Sanchez-Lacombe (SL) EoS and Perturbed Chain statistical associating fluid theory (PC-SAFT) EoS. The density correlations between SL and PC-SAFT EoS were almost identical in accuracy. Additionally, the association between CO2 and alcohols in PC-SAFT EoS had no discernible effect on the reliability of the density correlations. The vapor liquid equilibria (VLE) of the CO2/MeOH and CO2/EtOH mixtures were further estimated using parameter sets determined from the density measurements. Both the EoSs demonstrated comparable estimation accuracy; however, the pressure was estimated primarily near the critical region of the mixture, which yielded a lower estimation accuracy. Additionally, the densities of the binary systems were determined using characteristic parameters derived from the VLE correlations. Of the EoSs, the PC-SAFT EoS yielded a good correlation of the VLE, including the region near the mixture's critical region, while taking the association between CO2 and alcohols into consideration. Although few of the correlations were observed to be inferior, the density of the homogeneous fluid mixture was accurately estimated using the two EoSs, with the parameters obtained from the VLE correlations. The findings of the study thus suggest that in order to estimate the density and VLE using EoS-shared parameters, the parameter sets must first be determined using a VLE that exhibits a wide range of conditions affected by the system's associations.

Evaluation of the perturbed hard-sphere-chain equation of state for calculations of methane hydrate formation condition in the presence of ionic liquids

This work aims to evaluate the performance of the Perturbed Hard-Sphere-Chain (PHSC) equation of state (EoS) for the calculation of methane hydrate formation in the presence of ionic liquids (ILs). The van der Waals and Platteeuw model is utilized to calculate the hydrate dissociation pressure. The performance of the PHSC model is compared to cubic EoSs and the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) model. Two activity coefficient models are used to estimate the water activity in the presence of ILs. The results show that PHSC EoS with an activity coefficient model provides lower average error values (lower than 2%) and changing the activity coefficient models does not have a great effect on reducing the error. Also, the results of cubic-based EoSs are quite remarkable considering their simplicity. The PHSC model can be utilized as a robust and efficient thermodynamic model for hydrate dissociation pressure calculation in the presence of IL.

Interactions at the interfaces of the H2-brine-cement systems at elevated pressures for H2 storage

There is a global demand on assessment of potential subsurface gas storage sites in view of safely injecting hydrogen or carbon dioxide. One relevant aspect that has already been subject to thorough investigation is the mutual interaction of all participating compounds in terms of the wetting behaviour that on its turn is directly related to the predominating capture mechanisms. Given the diversity of the geophysical and geochemical circumstances, transferability of results from work conducted on one geological site to another location is limited. For instance, there is a large number of publications on wettability of many different rock types in hydrogen atmosphere that are partly controversal and strictly applicable only to the respective reported system. Hence, there is a gap in finding general model approaches that serve for a holistic understanding of predominating mechanisms and building the fundamentals for predicting the behaviour of systems that have not been studied so far. The presented work addresses this gap by quantifying mutual interactions of the participating phases in a solid-liquid-gas systems and determining the respective interfacial tensions, γSV (solid-vapor), γLV, (liquid-vapor) and γSL (solid-liquid).Neumann and Good demonstrated how to determine the solid-fluid interfacial tension based on the contact angle and the liquid-gas interfacial tension by calculating a so-called molecular interaction parameter. Up to date, this method has been applied, among others, for systems containing CO2 and solids such a teflon, glass, and steel. The methodology could be confirmed by testing systems comprising steel - H2O - CH4 /H2 and comparing the results to the aforementioned literature data.As one of the critical parts in H2 underground storage, the completion system containing a common well cement, H2 and brine was subject to this work. The interfacial tension between H2 and brine as well as the contact angle between the fluid phases and the cement were investigated experimentally up to 20 MPa, temperatures from 313.15 to 353.15 K and NaCl – concentrations of up to 10% wt. As a theoretical approach, the interfacial tension of the system H2O+H2 was investigated using the density gradient theory (DGT) in combination with the perturbed chain statistical associating fluid theory equation of state (PC-SAFT). Finally, the H2-cement interfacial tension is determined through the calculation of a so-called molecular interaction parameter. The interfacial tension data of H2O+H2 experimentally and theoretically determined in this work agree among each other as well as with previous literature data. Likewise, agreement was found between the brine+H2 interfacial tension and previous studies. The contact angle appears to be influenced mostly by pressure, producing a less H2O/brine-wet system as pressure increases. The H2-cement interfacial tension decreases from approximately 150 mN/m down to 100 mN/m, as the pressure increases from 0.1 to 20 MPa. The presented data suggest H2 to be slightly adsorbed on the one hand but the capillary entry pressure to decrease on the other, causing concerns regarding the integrity of the completion system.

Viscosity measurement and correlation for dense fluid mixture of carbon dioxide and ethanol at 313–343 K and 15–30 MPa

The viscosity ηm of dense fluid mixtures of carbon dioxide and ethanol was determined from the pressure drop between the inlet and outlet of a packed bed using the Ergun equation at temperatures from 313.2 K to 343.2 K and pressures from 15 MPa to 30 MPa over the entire range of ethanol composition. The ηm values for the fluid mixtures decreased with increasing temperature and increased with increasing pressure under isocratic conditions. In addition, the values measured ηm with Ergun eq. were correlated with the equation combining the Eyring theory and the perturbed chain statistical associating fluid theory equation of state (PC-SAFT EoS) and with that based on the rough hard-sphere (RHS) model proposed by Dymond and Assael. The accuracies of the Eyring + PC-SAFT EoS and the RHS model were 8.7% and 12%, respectively, in terms of average relative deviation for 80 conditions over the entire range of ethanol composition.

Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior.

The use of amorphous solid dispersions (ASDs) in commercial drug products has increased in recent years due to the large number of poorly soluble drugs in the pharmaceutical pipeline. However, the release behavior of ASDs is complex and remains not well understood. Often, the drug release from ASDs is rapid and complete at lower drug loadings (DLs) but becomes slow and incomplete at higher DLs. The DL where release becomes hindered is termed the limit of congruency (LoC). Currently, there are no approaches to predict the LoC. However, recent findings show that one potential cause leading to the LoC is a change in phase morphology after water-induced phase separation at the ASD/solution interface. In this study, the phase behavior of ASDs in contact with aqueous solutions was described thermodynamically by constructing experimental and computational ternary phase diagrams, and these were used to predict morphology changes and ultimately the LoC. Experimental ternary phase diagrams were obtained by equilibrating ASD/water mixtures over time. Computational ternary phase diagrams were obtained by Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). The morphology of the hydrophobic phase was studied with fluorescence confocal microscopy. It was demonstrated that critical point (plait point) composition approximately corresponded to the ASD DL, where the hydrophobic phase, formed during phase separation, became interconnected and hindered ASD release. This work provides mechanistic insights into the ASD release behavior and highlights the potential of in silico ASD design using phase diagrams.

Thermophysical properties of ethyl levulinate and n-alkanol systems

Some thermophysical properties such as densities, speeds of sound, refractive indices, and heat flows of the binary systems ethyl levulinate and n-alkanols (methanol, ethanol, 1-propanol, and 1-butanol) are reported in the temperature range T = (283.15–313.15) K and at p = 100 kPa. From these experimental data, the excess properties were calculated and correlated with the composition using a modified Redlich–Kister equation. The excess molar volumes were negative for short-chain alcohols and positive for 1-propanol and 1-butanol. The excess refractive indices exhibited the opposite behaviour. The excess isentropic compressibilities were negative and the excess molar enthalpies, were positive. The perturbed chain statistical associating fluid theory equation of state (PC-SAFT EoS) was successfully applied to correlate the densities of the mixtures, and good qualitative results in the computation of the excess molar enthalpy were obtained. Furthermore, Schaaff’s collision factor theory (SCFT) and the Laplace mixing rule were coupled with PC-SAFT to predict the speed of sound and the refractive index, respectively.

Application of PC‐SAFT EoS and SCFT for the modeling of thermophysical properties comprising deep eutectic solvent and alcohols

AbstractZinc (II) chloride based deep eutectic solvent (DES) were formed by mixing zinc (II) chloride with phosphoric acid. Fourier‐transform infrared spectroscopy was used to identify any possible shifts when the two compounds were assorted, and differential scanning calorimetry (SDT Q600 V20.9 Build 2D) was utilized to evaluate the formation of deep eutectic solvent. Densities, , and speed of sound, u, of [ZnCl2][phosphoric acid] 1:2.5 with methanol, ethanol, or propanol have been measured at T = (293.15, 303.15, 308.15, and 313.15) K and at atmospheric pressure. Excess molar volumes ( ), isentropic compressibilities ( ), deviation in isentropic compressibility ( ), and intermolecular free length ( ) were calculated from the densities, and speed of sound, respectively. To fit the excess molar volumes and deviation in isentropic compressibilities, the Redlich–Kister smoothing polynomial was used. Also, we have used perturbed chain statistical associating fluid theory equation of state (PC‐SAFT EoS) for modeling the densities of the binary mixtures, and Schaaff's collision factor theory (SCFT) and Nomoto's relation (NR) were used for modeling the speed of sounds for the binary mixtures.

Supercritical CO2 utilization for solubility measurement of Tramadol hydrochloride drug: Assessment of cubic and non-cubic EoSs

In this study, the solubility of the tramadol hydrochloride (T-HCl) drug in supercritical carbon dioxide (SC-CO2) was determined for the first time. The experiments were conducted at various operating pressures (100–270 bar) and temperatures (308–338 K). The solubility of T-HCl ranged from 0.309 × 10−4 to 1.384 × 10−4 in terms of mole fraction. Two different models, namely the Soave-Redlich-Kwong (SRK) and the simplified perturbed chain statistical associating fluid theory (sPC-SAFT) EoSs, along with seven semi-empirical correlations (including the Kumar-Johnston, Sung-Shim, Garlapati and Madras, Chrastil, Bian et al., Bartle et al., and Sodeifian et al., models), were employed to predict the solubility of T-HCl in SC-CO2. The findings indicated that the sPC-SAFT EoS (with an average absolute relative deviation of 10.18%) and the Sung-Shim correlation (with an average absolute relative deviation of 7.29%) outperformed the other models, respectively. The total, solvation, and vaporization enthalpies of the T-HCl/SC-CO2 binary system were estimated by applying these semi-empirical correlations.

Improving the estimation accuracy of confined vapor-liquid equilibria by fine-tuning the pure component parameter in the PC-SAFT equation of state.

We propose a thermodynamic model that combines the Young-Laplace equation and perturbed chain-statistical associating fluid theory (PC-SAFT) equation of state to estimate capillary condensation pressure in microporous and mesoporous sorbents. We adjust the PC-SAFT dispersion-energy parameter when the pore size becomes comparable to the molecular dimension. This modelling framework is applied to diverse systems containing associating and non-associating gases, various sorbents, and a wide range of temperatures. Our simulation results show that under extreme confinement, a higher value of the dispersion-energy parameter (ε) is required. Furthermore, using the experimental saturation pressure data for 18 different associating and non-associating confined fluids, we find that the shift in the PC-SAFT dispersion energy correlates with the ratio of the sorbent mean pore size to the PC-SAFT segment size (rp/σ). By fitting to the capillary condensation data, the relative deviation between the confined and bulk PC-SAFT dispersion energy parameter is only 0.1% at rp/σ = 15; however, this deviation starts to increase exponentially as rp/σ decreases. For a sorbent with large pores, when rp/σ > 15, the capillary condensation pressure results from our model are similar to the predictions from the Kelvin equation. Using a dataset containing 235 saturation pressure data points composed of 18 pure gases and 4 binary mixtures, the overall AARD% from our model is 12.26%, which verifies the good accuracy of our model. Because the mean sorbent pore radius (rp), the PC-SAFT energy parameter (ε), and segment size (σ) are known a priori, our model estimates the corrected energy parameter for small pores and, thus, extends its applicability.

Comprehensive study on deep eutectic solvent density based on various EoSs: SRK, PT, VTSRK, sPC-SAFT

In this communication, the capability of a two-parameter cubic equation of state (EoS) i.e. Soave-Redlich-Kwong (SRK) EoS to predict the density behavior of deep eutectic solvents (DESs) in the wide range of temperature conditions and at atmospheric pressure, was improved using the volume-translated concept. At first, the c-parameter of 139 DESs (1793 experimental data points) was obtained referring to volume-translated SRK (VTSRK) EoS. The obtained results were compared with the original SRK and Patel-Teja (PT) EoSs and sPC-SAFT (simplified perturbed chain statistical associating fluid theory) EoS. Afterward, three c-parameter correlations were recommended based on molecular weight and acentric factor (Case 1), acentric factor (Case 2), and critical compressibility factor (Case 3). The capability of recommended c-parameter correlations was investigated by density modeling of 67 new DESs systems (419 experimental data). The AARD% (average absolute relative deviation) of Case 1, Case 2, Case 3 and sPC-SAFT EoS was 4.24%, 3.24%,4.19% and 0.5677%, respectively.

The step-wise dissolution method: An efficient DSC-based protocol for verification of predicted API–polymer compatibility

The development of an amorphous solid dispersion (ASD) is a promising strategy for improving the low bioavailability of many poorly water-soluble active pharmaceutical ingredients (APIs). The construction of a temperature–composition (T–C) phase diagram for an API–polymer combination is imperative as it can provide critical information that is essential for formulating stable ASDs. However, the currently followed differential scanning calorimetry (DSC)-based strategies for API solubility determination in a polymer at elevated temperatures are inefficient and, on occasions, unreliable, which may lead to an inaccurate prediction at lower temperatures of interest (i.e., T = 25 °C). Recently, we proposed a novel DSC-based protocol called the “step-wise dissolution” (S-WD) method, which is both cost- and time-effective. The objective of this study was to test the applicability of the S-WD method regarding expeditious verification of the purely-predicted API–polymer compatibility via the perturbed chain-statistical associating fluid theory (PC-SAFT) equation of state (EOS). Fifteen API–polymer T–C phase diagrams were reliably constructed, with three distinct API–polymer case types being identified regarding the approach used for the S-WD method. Overall, the PC-SAFT EOS provided satisfactory qualitative descriptions of the API–polymer compatibility, but not necessarily accurate quantitative predictions of the API solubility in the polymer at T = 25 °C. The S-WD method was subsequently modified and an optimal protocol was proposed, which can significantly reduce the required experimental effort.

Isochoric bubble point data for binary systems of 1 (ethane) in 2 (decane, undecane, dodecane and tridecane)

In this communication, a new set of vapour liquid equilibrium (bubble point) data were obtained for ethane-decane, ethane-undecane, ethane-dodecane and ethane-tridecane binary systems. The datasets were obtained using constant-volume (isochoric) method. The datasets cover temperatures from 260 to 373 K and pressures from 0.6 to 10 MPa for all binary systems. A total of five compositions were studied for each of the binary systems ranging from ethane rich compositions to compositions rich in decane, undecane, dodecane and tridecane respectively. Datasets obtained were used to adjust the binary interaction parameters (BIP) for Peng-Robinson (PR), Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) and the Multi-Fluid Helmholtz Energy Approximation (MFHEA) equations of state (EoS). Quadratic temperature dependent BIP functions were obtained for PR-EoS using a combination of datasets from this work and those published in the literature for the ethane-decane and ethane-dodecane binary systems. Correlation of the datapoints from this work with the PR-EoS, PC-SAFT-EoS and MFHEA EoS yielded very low average absolute deviations (AADs) of less than 5 % for all the datasets. Expanded uncertainties associated with each of the bubble point temperatures and pressures obtained are also reported at 95 % confidence interval. Expanded uncertainties in all the compositions studied were found to be less than 0.002 at 95 % confidence interval.

Some experimental and theoretical studies of diethylene glycol diethyl ether and 2-alkanol mixtures

Experimental density and dynamic viscosity data for the diethylene glycol diethyl ether +2-alkanol (C3 to C6) mixtures have been published at 293.15 K, 303.15 K, 313.15 K, and 323.15 K and at pressure of 0.1 MPa. Excess molar volume and deviation in dynamic viscosity were obtained from experimental data and correlated with Redlich–Kister equation, from the values obtained, the interaction forces were studied. Perturbed chain-statistical associating fluid theory equation of state was used for modeling the density for pure fluids and mixtures. Free volume theory coupled to Perturbed chain-statistical associating fluid theory equation of state was used to modeling the viscosity of pure fluids and mixtures; in the case of binary mixtures, we proposed a simple mixing rule and used the Pourabadeh et al. mixing rule. Good results in the prediction and correlation of experimental liquid density and dynamic viscosity for binary mixtures were obtained, 0.12% and 2.28%, respectively.

Water Vapor Adsorption on Desiccant Materials for Rotary Desiccant Air Conditioning Systems

In order to determine the water vapor adsorption performance of a rotary desiccant-based air conditioning system, the behavior of water adsorption on cylindrical pores of different sizes was studied by using classical density functional theory (CDFT) based on perturbated chain statistical associating fluid theory (PC-SAFT). Firstly, the structural parameters of the desiccant material were characterized by scanning electron microscopy (SEM), X-ray Energy Dispersive Spectrum (EDS), and N2 adsorption/desorption isotherms, as well as adsorption equilibrium measurements of water vapor at temperature range 293–308 K. Secondly, the potential energy equation of water molecules in cylindrical pores was determined, and contribution of various terms of PC-SAFT for simulating fluid in cylindrical pores were established. Finally, the pore size distribution (PSD) of the desiccant materials is determined by the PC-SAFT kernel. Moreover, water vapor condensation was investigated with the PC-SAFT model in micropores. The results indicate that the rotary desiccant materials have a large number of micropores with a volume of 0.3669 cm3/g and the amount of water adsorption is about 0.285 g/g. The condensation pressure and the pore width corresponding to the saturated pressure P0 grow with an increase in the temperature, signifying that adjusting the PSD of the material has a significant effect on improving the dehumidification performance. The research concludes that the PSD range of the oxide cylindrical pore between 1.09 and 1.53 nm is particularly beneficial for dehumidification. This study provides valuable theoretical guidance for optimizing dehumidification materials.

Study of Nonideality Behavior of p-Methylacetophenone and 1-Alkanol Mixtures from Measurement and Modeling of Density and Viscosity

The aim of this work is to investigate experimentally and theoretically thermophysical properties (density and viscosity) and derived properties (excess molar volume and viscosity deviation) of p-methylacetophenone + alkanols (C5 to C9) in the range of 293.15 to 323.15 K and a pressure of 0.1 MPa. The properties studied were density, viscosity, excess molar volume, and deviation in viscosity. To model the density of the liquid mixtures, we used the perturbed chain-statistical associating fluid theory equation of state (PC-SAFT EoS) and the volume translated Peng-Robinson-Stryjek-Vera equation of state (VTPRSV EoS). Using a correlation approach an overall deviation of 0.34% and 0.28% was obtained, respectively, while good predictive results were obtained (0.44% using PC-SAFT EoS and 0.46% using VTPRSV EoS). Also, we use two correlations without fitted parameters (Kendall-Munroe correlation and Nguyenhuynh correlation) to model the experimental viscosity and obtained an overall deviation of 5.07% and 3.07%. In addition, the Redlich–Kister correlation (with three fitted parameters) was able to correctly correlate the excess molar volume and the deviation in viscosity for all mixtures. Finally, the results obtained from the work have been discussed in terms of the nature of molecular interactions between the components of the p-methylacetophenone + alkanol mixture.

Computer-aided molecular design of CO2-based mixture working fluid harvesting engine waste heat

The CO2 transcritical power cycle is an important method for recovering waste heat. The cycle performance can be further improved by using CO2-based mixtures instead of pure CO2. To avoid the empirical screening of CO2 mixtures, a computer-aided molecular design method, which is based on the group contribution method and perturbed chain-statistical associating fluid theory equations of state, is used for the first time in this study to design CO2-based mixtures for power cycles. The calculation method for group to system thermodynamic performance is established and verified. A molecular identification model is used to obtain all compounds based on the group library, calculate their thermodynamic properties for ranking, and find the best CO2-based mixture in the global range. The performance and cost of the expander are also briefly discussed. Taking the simple transcritical power cycle as an example, the results show that when the mole fraction of CO2 is greater than 0.70, the optimal CO2-based mixture, CH3-C≡CH, can increase the system efficiency and net output work by 16.58% (9.07%) and 17.88% (17.87 kW), respectively, compared to those of pure CO2. The peak system efficiency is 9.83% at an evaporation pressure of 24 MPa. Shorter-chain additives can improve thermodynamic performance, which is demonstrated by extracting the contribution of each group to the performance of the system using statistical methods. This method enables the ranking of CO2 mixtures on a global scale and provides some rules. It is also suggested that further economic analysis is necessary.

CO2 solubility and diffusivity in poly(vinyl acetate) studied using the PC-SAFT and free volume theory

Poly (vinyl acetate) (PVAc) is a polymer used in various industrial applications, and the quantitative determination of CO2 solubility and diffusion coefficient is important for designing foaming processes involving supercritical CO2. In this study, these two physical properties were obtained experimentally and theoretically using the perturbed chain–statistical associating fluid theory (PC–SAFT) and free volume theory at temperatures between 353 K and 473 K and pressures up to 20 MPa. CO2 solubility increased almost linearly with pressure and could be correlated with the PC–SAFT equation of state and binary interaction parameter kij within the average relative deviation of 2.1%. Furthermore, the fitted plot of kij versus temperature can be used to predict CO2 solubility at lower temperatures. The diffusion coefficient of CO2 in PVAc was experimentally determined from CO2 sorption curves. Its value increased with increasing CO2 solubility and temperature, which was consistent with the free volume theory.

VLE property measurements and PC-SAFT/ CP- PC-SAFT/ E-PPR78 modeling of the CO2 + n-tetradecane mixture

This paper presents a new experimental VLE property data in the binary system of carbon dioxide – n -tetradecane at three selected isotherms of 313.15 K, 333.15 K, and 353.15 K in the pressure range from (3.8 to 19.0) MPa. The measurements were made using a high-temperature and high-pressure optical cell. The standard absolute u and relative u r uncertainties of temperature, pressure, concentration measurements are: u ( T ) =7.5 mK; u r ( P ) =0.00025; u r ( x ) =0.015; and u r ( y ) =0.015. The measured VLE data were used to determine the critical P C - T C curve data. Based on the derived values of the critical parameters of CO 2 + n -tetradecane mixture the value (-67.58 MPa) of the Krichevskii parameter has been determined. The predictive capabilities of the perturbed chain-statistical associating fluid theory (PC-SAFT), the critical point-based modification of PC-SAFT (CP-PC-SAFT), and the Enhanced -Predictive-Peng-Robinson-78 ( E -PPR78) models were examined.

Investigation of the Antisolvent Effect on the Phase Behavior of Amino Acid Solid Solutions

This work focuses on the experimental measurement and modeling of solid–liquid equilibria containing continuous binary solid solutions crystallized from solvent mixtures for the usage in antisolvent crystallization. The newly constructed quaternary phase diagrams of l-valine/l-leucine in water/2-propanol and water/acetone systems are analyzed and compared to those of water/ethanol mixtures. Experimental data sets are determined via high-performance liquid chromatography, while the formation of solid solutions is confirmed with powder X-ray diffraction. Our validated modeling approach for the ternary l-valine/l-leucine/water mixture is extended to the aforementioned quaternary systems. The modeling combines the Perturbed Chain-Statistical Associating Fluid Theory and the Non-Random Two-Liquid model to describe the liquid and solid phases, respectively. Additionally, two modeling approaches (predictive and semi-predictive) are proposed. Both models show good agreement with the experimental solubility data sets of the binary solutions. However, larger deviations were observed in three- and four-component systems, especially toward the solubility maxima. Therefore, the modeling approach should be used for qualitative initial antisolvent screenings for the separation of solid solutions using counter-current crystallization.