Phase Equilibrium Measurements Research Articles

Determination and molecular simulation of ternary solid–liquid phase equilibrium of succinic acid + maleic acid + water from 283.15 K to 333.15 K

This study used the isothermal saturation gravimetric method to examine the solid–liquid phase equilibrium relationships composed of succinic acid + maleic acid + water spanning from 283.15 K to 333.15 K. The experimental data were utilized for the purpose of plotting the equilibrium phase diagrams of ternary systems in the studied temperature range. There were three crystalline regions in each isothermal ternary phase diagram, two saturation boundary curves, and a co-saturation point. To broaden the use of data from binary and ternary phase equilibrium measurements, Wilson and NRTL models were utilized for correlation and expectation, while relative average deviation (RAD) and root mean square deviation (RMSD) were utilized to evaluate the computational exactness. The results show that the theoretically calculated values were found to be in near agreement with the experimental values, and both models were able to obtain more precise theoretical data under different experimental conditions. In addition, molecular simulation was employed to elucidate the interaction between succinic acid, maleic acid, and water. This study provides accurate and reliable data for the separation of succinic acid and maleic acid mixture in water. These findings can be utilized to make sense of the dissolvability conduct of succinic acid and maleic acid in aqueous solution.

Tuning effect of DIOX on the thermodynamics and cage occupancy of CH4/CO2 + DIOX mixed hydrates

Hydrate technology could provide a novel approach to deliver convenient CO2-rich natural gas. The identification of a suitable and environmental-friendly promoter for enhancing CO2/CH4 hydrate kinetics is critical. In this study, we evaluated the thermodynamics, kinetics, and morphology of CH4/CO2 + DIOX mixed hydrates in the presence of a thermodynamic promoter 1,3-dioxolane (DIOX) at and below its stoichiometric concentration (SC, CDIOX = 5.56 mol%). Due to the thermodynamic preference of DIOX enclathration in mixed hydrates formation, a decrease in CDIOX in the unconverted solution was observed post nucleation below SC and the hydrates formed exhibit significant heterogeneity in cage occupancy. As CDIOX in the unconverted solution decreases, the DIOX concentration in hydrate (RDIOX) and the thermodynamic stability of the newly formed hydrates decreases. Based on the step-wise heating design, the thermodynamic stability of the hydrates formed below SC with high-RDIOX is close to that of hydrates formed at SC, while hydrates with low-RDIOX undergo dissociation at their P-T trajectories above the measured phase equilibria. Raman measurement indicates that the lower-RDIOX hydrates possess a higher CO2 composition. This study provides new insights into the tuning effect of DIOX on mixed hydrates formation and the basis for using low thermodynamic promoter concentration in hydrate-based technologies.

Measurement of Phase Equilibrium for R-1233zd(E) with Three Pure Esters between 298.15 and 343.15 K

Measurement of Phase Equilibrium for R-1233zd(E) with Three Pure Esters between 298.15 and 343.15 K

Thermodynamic Assessment of the Fe–Mn–Ni System and Diffusion Mobility of Its Face-Centered Cubic Phase

Through extrapolation of updated binary descriptions, the Fe–Mn–Ni system was thermodynamically elucidated in a self-consistent way. The obtained thermodynamic description was confirmed to be reliable by measuring phase equilibria at relatively low temperatures. Our current thermodynamic evaluation can describe the phase stabilities over a wide temperature range and provide a reliable thermodynamic factor for the diffusion mobility optimization. For the face-centered cubic (FCC) phase in the investigated alloy system, optimization of diffusion mobilities was accomplished with the CALPHAD method. Interdiffusivities were extracted based on the composition-distance profiles of diffusion couples investigated herein. Through comprehensive diffusion behavior comparisons, our proposed diffusion mobilities were confirmed.

Geometric and Hydrophilic Effects of Oxirane Compounds with a Four-Carbon Backbone on Clathrate Hydrate Formation.

The physicochemical properties of clathrate hydrates are influenced by the chemical nature and three-dimensional (3D) geometry of the added molecules. This study investigates the effects of five oxirane compounds: cis-2,3-epoxybutane (c23EB), trans-2,3-epoxybutane (t23EB), 1,2-epoxybutane (12EB), 1,2,3,4-diepoxybutane (DEB), and 3,3-dimethylepoxybutane (33DMEB) on CH4 hydrate formation. Despite having a four-carbon backbone, these compounds differ in their 3D geometries. The structures and stabilities of CH4 hydrates containing each compound were analyzed using high-resolution powder diffraction, solid-state 13C NMR, and phase equilibrium measurements. The experimental results revealed that c23EB, 12EB, and 33DMEB act as sII/sH hydrate formers and thermodynamic promoters, whereas t23EB and DEB have opposite roles. These results were analyzed in relation to the 3D geometries and relative stabilities of various rotational isomers using DFT calculations. Hydrate structure was influenced by both the length and thickness of the added compounds. Moreover, an appropriate level of (not excessive) hydrophilicity induced by an oxirane group appeared to enhance the thermodynamic stability of the hydrates. This study provides insights into how the chemical nature of additives influences the structure and stability of clathrate hydrates.

Water Activity and Phase Equilibria Measurements and Model Simulation for the KCl–BaCl2–H2O System at 323.15 K and 0.1 MPa

Water Activity and Phase Equilibria Measurements and Model Simulation for the KCl–BaCl2–H2O System at 323.15 K and 0.1 MPa

Thermodynamic modeling of the Al–Co–W, Al–Ni–Ta and Co–Ni–W ternary systems

Thermodynamic descriptions of the Al–Co–W, Al–Ni–Ta and Co–Ni–W ternary systems are the foundation for developing thermodynamic database and material design for the Ni-based alloys. In the present work, the Al–Co–W, Al–Ni–Ta and Co–Ni–W systems were optimized based on the reliable experimental data by means of the CALPHAD method. The liquid, γ (Fcc_A1) and β (Bcc_A2) phases were described as substitutional solution model, and the γ’ (Fcc_L12), B2 (Bcc_B2), μ (Co7W6) and Ni3Ta phases were described with sublattice models. The Co3W phase was treated as a stoichiometric compound due to the limited homogeneity range in the Al–Co–W system and described as (Co, Ni)3W in the Co–Ni–W system. The self-consistent thermodynamic parameters for the Al–Co–W, Al–Ni–Ta and Co–Ni–W systems were obtained. Comprehensive comparisons between the calculated results and measured phase equilibrium data show that most experimental information is satisfactorily accounted for by the present thermodynamic description.

Liquid-liquid phase equilibrium measurement and thermodynamic modeling for the separation of n-hexane and methanol with four solvents

To solve the problem of generating n-hexane in the industrial production of methanol, four common and inexpensive solvents {dimethyl sulfoxide, 1,2-propanediol, furfuryl alcohol, and furfural} were chosen as extractants to separate n-hexane and methanol. The liquid–liquid equilibrium (LLE) data of n-hexane + methanol +{dimethyl sulfoxide, 1,2-propanediol, furfuryl alcohol, or furfural} were measured at 303.2 K and 101.3 kPa. The extraction performance of four extractants was evaluated by the distribution coefficient (D) and separation factor (S). At the same time, NRTL and UNIQUAC models were used to fit the experimental LLE data to obtain regression parameters. The reliability of the binary interaction parameters was verified by the mixed surface analysis based on Gibbs energy topology. The root mean square deviation (RMSD) of the NRTL and UNIQUAC models are less than 0.0040 and 0.0057, respectively, indicating that the NRTL and UNIQUAC models are suitable for the study of this system. Furthermore, the interaction energy between extractant and methanol molecules was analyzed by the DMol3 module and the effect difference of liquid–liquid extraction was explained from the perspective of interaction energy using σ-Profile.

ß-Damascenone Highly Diluted in Hydroalcoholic Mixtures: Phase Equilibrium Measurements, Thermodynamic Modeling, and Simulation of a Batch Distillation

ß-Damascenone is a carotenoid-derived compound that plays a key role in the characteristic aroma of wines and distilled spirits. Despite the valuable contribution of this compound to the flavor quality of alcoholic beverages, little is known about its volatility and its vapor–liquid equilibrium behavior in hydroalcoholic mixtures of different compositions. Such information is essential to be able to choose the right thermodynamic model for ß-damascenone when using a distillation process simulation software to gain a better understanding of the behavior of ß-damascenone during spirit distillation. In this context, this work presents new experimental VLE data for ß-damascenone highly diluted in ethanol + water mixtures. The measurements were carried out in a recirculation ebulliometer operating at 101.3 kPa for ethanol mass fractions between (0.10 and 0.79) g·g–1. Activity coefficient model NRTL was used to correlate the experimental data and binary interaction parameters. The parameters obtained for the NRTL model were employed to simulate a laboratory-scale batch distillation of a model solution of ß-damascenone, ethanol, and water. The simulation results were well fitted to experimental data. This approach can be further extended to other compounds that contribute to the aroma of distilled spirits, and the results can be transferred to simulate larger scale distillations.

Vapor–Liquid Equilibrium Measurements for Aqueous Mixtures of NH3+ MDEA + CO2and KOH + MDEA

Isothermal vapor–liquid equilibrium measurements were performed for aqueous solutions containing N-methyl diethanolamine (MDEA), MDEA + ammonia (NH3), MDEA + potassium hydroxide (KOH), MDEA + carbon dioxide (CO2), NH3 + CO2, and MDEA + NH3 + CO2. The experiments were carried out between 310 and 390 K and 0.07 and 34 bar using a static synthetic apparatus. Overall, 202 data points are reported in terms of total volume, total number of moles, temperature, and pressure. The experimental results for MDEA(aq), NH3(aq) + CO2(aq), and MDEA(aq) + CO2(aq) are in good agreement with the calculations done using the Extended UNIQUAC model within the studied range. The data presented in this work are also comparable to previously published measurements. This work reports for the first time VLE measurements for aqueous mixtures of MDEA + NH3 and MDEA + KOH. These data suggest that the interactions between MDEA(aq) and NH3(aq) or K+(aq) ions have a minor effect on the equilibrium pressures. Consequently, other physical properties are needed to describe the thermodynamic state of these systems, such as heat capacity, heat of dilution, and other phase equilibrium measurements. The isothermal VLE measurements for solutions containing NH3(aq) showed a pressure minimum that was confirmed by model estimates and by other works done in similar conditions. As a consequence, it is not possible to estimate the partial pressure of CO2 based on the difference between the pressure at equilibrium conditions and the partial pressure of the lean solvent. This paper demonstrates that this common approach to determining the partial pressure of gases may introduce a bias in these values. The dissolution of CO2 into MDEA(aq) + NH3(aq) mixtures changes the speciation of the system, leading to an increase in the concentration of their protonated species (MDEAH+(aq) and NH4+(aq), respectively). For this reason, the interaction between these charged species must be determined in order to perform reliable phase equilibrium calculations. Ultimately, the measurements reported in this work can be used for thermodynamic modeling of CO2 capture solvents to ensure accurate results in process simulation.

Thermophysical characterization of terpenoid based hydrophobic deep eutectic solvent and its Vapour-Liquid equilibrium studies with furfural

The sustainable transition to cleaner production techniques over the last decade has projected deep eutectic solvents as alternative solvents to replace toxic volatile organic solvents especially in green extraction technologies. However, processes based on such newly developed solvents pose hindrances in industrial applicability due to lack of sufficient data for process design and scale up. Prospectively, a new hydrophobic deep eutectic solvent (HDES) that has been utilized for the selective extraction of biomass derived furfural from its aqueous solutions composed of thymol and 1-tetradecanol in 2:1 M ratio has been subjected to exhaustive thermo-physical characterization and phase equilibrium measurements in the present study. The various physico-chemical properties of the HDES such as density, viscosity, ionic conductivity as well as refractive index and acidity were measured as a function of temperature from 293.15 K to 333.15 K and suitably correlated. The thermal limit of operation for the HDES was analyzed through thermo-gravimetric analysis while its structural characterization was conducted by Fourier transform infrared spectroscopy. A modified Othmer type ebulliometer was used for the vapour pressure measurements of the HDES from 2.4 to 10.4 kPa and the experimental data was fit to the Antoine and Clark-Glew equations. Further, the isobaric vapour liquid equilibrium data at different sub-atmospheric pressures for the HDES and furfural system was generated and data regression using the non-random two liquid (NRTL) model was used to derive the optimized binary interaction parameters.

Extractive distillation of ethyl acetate-ethanol-water ternary system using deep eutectic solvent (DES): A techno economic and energy assessment

The extractive distillation (ED) process has been established as a commercially viable process that can be used to break the azeotropic systems. The present study investigates the performance and feasibility of conventional solvent (glycerol) and choline chloride-glycerol based deep eutectic solvent (DES) as entrainers for the separation of ethyl acetate-ethanol-water ternary mixture through ED. A comprehensive approach is proposed with phase-equilibrium measurements and process simulation through Aspen Plus for different entrainer to feed ratio (E/F). Optimization of the process is based on performance indicators such as Total Annual Cost, CO2 emissions, and Specific Energy Consumption. A sequential iterative algorithm was used to find the optimum E/F in distillation trains. The performance analysis has shown a reduction of 45.89% in global TAC with DES as an entrainer. The combined entrainer requirement for the dehydration was 268.3 kmol/h and 118.86 kmol/h with glycerol and DES respectively. The process sees a 58.21% total energy saving with a 15% and 44.5% reduction in Specific Energy Consumption and CO2 emissions respectively as compared to glycerol as an entrainer. The study provides a comparison and proves that DES is an effective entrainer to break the azeotropic point as a low-cost and eco-friendly alternative to conventional solvents.

Methane + neo-pentane system: VLE measurements, modeling of the phase diagram including solid phases

New measurements of isothermal vapor–liquid equilibrium for the (CH4 + neoC5H12) system have been carried out using a static-analytic method for temperatures from 213 K up to 345 K and pressures up to 13 MPa. The method of Ungerer et al. has been used to extrapolate the VLE data to the critical-points region.Measured VLE data have been compared with literature values and used for investigating the low-temperature phase equilibrium behavior of the system (temperatures lower than the triple-point temperature of neo-pentane down to 213 K) where literature SVE data and thermodynamic models are in partial disagreement.Measured VLE data agree with literature VLE data and low-temperature VLE calculated from predictive models (PPR78 and PSRK EoSs). The new phase equilibrium measurements obtained at temperatures lower than the triple point temperature of neoC5H12 have allowed solving the discrepancy between literature data and model predictions and determining the global phase diagram of the system following the van Konynenburg and Scott’s and the Kohn and Luks’ classifications.

Phase equilibrium measurements and correlation for {tetrafluoromethane (R14) + propane (R290)} system

In this work, a study on the (vapour + liquid) equilibrium (VLE) and (vapour + liquid + liquid) equilibrium (VLLE) for the tetrafluoromethane (R14) + propane (R290) system was carried out using an apparatus based recirculation method at temperatures ranging from (173.150–212.470) K. The uncertainties of the composition, temperature, and pressure were less than 0.005, 5 mK and 2% or 0.0008 MPa, respectively. All of the experimental data were correlated by the Peng–Robinson equation of state (PR EoS) with the Modified Huron–Vidal second-order (MHV2) mixing rule involving the non-random two-liquid (NRTL) activity coefficient model. The results show good agreement with the experimental data, and the maximum root mean square deviations for (R14 + R290) system are Rp =0.0239 MPa, Rx = 0.009, respectively.

High-pressure phase equilibrium and volumetric properties of pseudo-binary mixtures of stock tank oil + methane up to 463K

High-pressure phase equilibrium and volumetric properties of highly asymmetric mixtures related to reservoir fluids are critical to the development of high-pressure and high-temperature (HPHT) reservoirs. However, there is a lack of the relevant data and accurate modeling tools. In this work, we prepared asymmetric pseudo-binary mixtures of methane (CH4) + stock tank oil (STO) and systematically measured their phase equilibrium and densities at temperatures from (298.15 to 463.15) K and pressures up to 140 MPa. The methane mole fraction in these mixtures range from 0.20 to 0.61 for the density measurement, and from 0.20 to 0.81 for the phase equilibrium measurement. From the experimental densities, the isothermal compressibility values, as well as the pseudo-excess volumes, were determined. Moreover, phase envelopes, relative volumes, and liquid volume fractions below the saturation point were also measured. These data are valuable for evaluating and improving thermodynamic models for HPHT reservoir fluids. The experimental results were modeled by the Soave-Redlich-Kwong (SRK) equation of state (EoS), the Peng-Robinson (PR) equation of state, their volume translated versions SRK-VT and PR-VT, and the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). For density, SRK and PR gave large deviations of ~18% and ~8%, respectively, as compared with ~3% for PC-SAFT. Inclusion of volume translation reduced their deviations to the same level as that for PC-SAFT. For isothermal compressibility, all the models gave deviations of 20-30%, with PC-SAFT, SRK-VT and PR-VT being slightly better. The excess volumes calculated by SRK, PR and PC-SAFT were similar and close to the experimental values. The deviations in the calculated excess volumes resulted in only ~1% deviations in the calculated densities if the experimentally determined STO densities were used. It was illustrated that the small deviations could be utilized in the excess volume method to accurately estimate the high-pressure live oil densities from the high-pressure STO densities. This excess volume method gave ~1% density deviation on average for all the models, with PC-SAFT giving the smallest maximum deviation. The deviations in calculated saturation pressures were ~5% for all the models with the overall deviation for PC-SAFT being slightly smaller.

New Apparatus for CO2 Solubility Measurements From Total Pressure-composition Data

Carbon capture, utilization, and storage (CCUS) is among the selected strategies to restrain the effects of climate change in the near future. However, the amount of CO2 that is captured currently is much lower than the levels required for successful climate action. One key to unlock CCUS deployment is reducing the cost of captured CO2. The assessment of new technologies or different operating scenarios through process simulation rely on thermodynamic models that can reproduce the system’s properties. These models are fine-tuned based on accurate phase and chemical equilibrium measurements, especially vapor-equilibrium data. However, the measurement of such properties is often cumbersome and expensive. In this context, the goal of this work is to provide a reliable basis for thermodynamic modelling and process simulation of a CO2 absorption unit using a mixed salt solution. The work entails the commissioning and measurement of equilibrium data, which will be followed by the correlation of such properties using the extended UNIQUAC model. The developed model will be suitable for process simulations and should provide insights on energy consumption and cost of captured CO2.

Characterization of clathrate hydrate formed in H2 + CO2 + tetrahydropyran + water system as carbon capture materials

This paper reports the thermodynamic and crystallographic characterization of the clathrate hydrate formed in H2 + CO2 + tetrahydropyran (THP) + water system by phase equilibrium measurements and powder X-ray diffraction measurements with a goal of developing a hydrate-based carbon capture technology in an integrated coal gasification combined cycle. The four-phase [(H2 + CO2) gas + water liquid + THP liquid + hydrate] equilibrium conditions were measured with two series of gas compositions (around H2:CO2 = 0.7:0.3 and 0.9:0.1 in mole fractions) in the range of 2.64 MPa to 7.51 MPa. At around H2:CO2 = 0.7:0.3 in gas phase, the equilibrium temperatures in (H2 + CO2) gas + THP + water system are always higher by approximately 9 to 10 K compared to the equilibrium temperatures of H2 + CO2 + water system. This means that THP acts as the hydrate thermodynamic promoter. The equilibrium conditions in (H2 + CO2) gas + THP + water system, which is only considered with CO2 partial pressure, greatly agree with those in CO2 + THP + water system. Therefore, the equilibrium conditions in (H2 + CO2) gas + THP + water system would only depend on the partial pressure of CO2. Moreover, the crystallographic structure of the hydrate formed in H2 + CO2 + THP + water system was identified to be structure II, which is the same structure as the hydrate formed in H2 + CO2 + water system. These results can contribute to the study of a hydrate-based gas separation and carbon capture.

Thermodynamic re-assessment and liquidus projection of the Cu–Ni–Ti system

A critical thermodynamic re-assessment for the ternary Cu–Ni–Ti system was performed by means of the CALPHAD (CALculation of PHAse Diagram) approach, and a new set of self-consistent thermodynamic parameters for the Cu–Ni–Ti system was obtained. According to the reported crystal structures and homogeneity ranges, appropriate sublattice models were proposed for the τ4 and τ6 phases, which could achieve a better description than the previous stoichiometric compound model for phase compositions and primary phase regions. Three solid-state invariant reactions, CuTi + τ1 ↔ Cu4Ti3 + NiTi at 1074.86 K, Ni3Ti + NiTi + τ1 ↔ τ2 at 1074.39 K and NiTi + τ4 ↔ Ni3Ti + τ1 at 1175.11 K were predicted in the present work. Presently calculated liquidus projection eliminated the liquid miscibility gap of the Cu–Ni–Ti system on Cu–Ni side. Scheil reaction scheme of the entire composition range was also presented accordingly. Comparisons between the calculated results and the measured phase equilibria indicated that all the reliable experimental data were satisfactorily accounted for by the present modeling.

Sensitivity estimation for calculated phase equilibria

The development of a consistent framework for Calphad model sensitivity is necessary for the rational reduction of uncertainty via new models and experiments. In the present work, a sensitivity theory for Calphad was developed, and a closed‐form expression for the log‐likelihood gradient and Hessian of a multi‐phase equilibrium measurement was presented. The inherent locality of the defined sensitivity metric was mitigated through the use of Monte Carlo averaging. A case study of the Cr–Ni system was used to demonstrate visualizations and analyses enabled by the developed theory. Criteria based on the classical Cramér–Rao bound were shown to be a useful diagnostic in assessing the accuracy of parameter covariance estimates from Markov Chain Monte Carlo. The developed sensitivity framework was applied to estimate the statistical value of phase equilibria measurements in comparison with thermochemical measurements, with implications for Calphad model uncertainty reduction.

Measurement of Phase Equilibrium at High-Pressure Using Reflected Light

Measurement of Phase Equilibrium at High-Pressure Using Reflected Light