Experimental Phase Equilibrium Data Research Articles

Experimental investigation and thermodynamic assessment of the Ag–Cr–Y and Ag–Cu–Y ternary systems

The phase equilibria of the Ag–Cr–Y system were investigated by a combination of key experiments and thermodynamic modeling. Eleven ternary alloys were prepared to determine the isothermal sections of the Ag–Cr–Y system at 500, 600 and 800 °C, by means of X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDS). No ternary compound was found in the Ag–Cr–Y system. Based on the experimental phase equilibria data, thermodynamic assessment of the Ag–Cr–Y and Ag–Cu–Y systems was performed by the CALPHAD (CALculation of PHAse Diagrams) method. Two ternary compounds τ1 and τ2 in the Ag–Cu–Y system with the compositions of Ag3Cu12Y5 and (AgxCu2-x)Y (x: 22.9–43.1 at.%) were described by two sublattice model (Ag, Cu)4Y1 and (Ag, Cu)2Y1, respectively. A set of self-consistent thermodynamic parameters of the two systems were obtained. Most of the reliable experimental data can be well reproduced by the present thermodynamic modeling.

What does the NRTL model look like? Determination of boundaries for different fluid phase equilibrium regions

AbstractThe adequate correlation of experimental phase equilibrium data by using any thermodynamic model represents a key point for the rigorous design of the chemical processes. However, this data correlation process remains a challenging problem, due to the high nonlinearity of the models used and the consequent problems of convergence. The present work analyzes the nonrandom two‐liquids mode (NRTL) model to check the relation between the values of the binary interaction parameters and the corresponding phase equilibria that the NRTL model can or cannot reproduce. Additionally, in the case of the LLE, empirical equations have been established as a function of the nonrandomness parameter, to model the trajectory of the different miscibility boundaries observed. These functions can be used as constraints in the experimental data correlation procedure to reduce the search space and guarantee the consistency of the obtained binary interaction parameters with the experimental behavior of the system under study.

Integrated experimental and thermodynamic modeling study of phase equilibria in the ‘CuO0.5’-MgO-SiO2 system in equilibrium with liquid Cu metal for characterizing refractory-slag interactions

An integrated experimental and thermodynamic modeling study of the phase equilibria in the ‘CuO0.5’-MgO-SiO2 system in equilibrium with liquid Cu metal has been undertaken to better understand the reactions between MgO-based refractories and liquid slag in copper converting and refining processes. New experimental phase equilibria data at 1250–1680 °C were obtained for this system using a high-temperature equilibration of synthetic mixtures with predetermined compositions in silica ampoules or magnesia crucibles, a rapid quenching technique, and electron probe X-ray microanalysis of the equilibrated phase compositions. The system has been shown to contain primary phase fields of cristobalite (SiO2), tridymite (SiO2), pyroxene/protoenstatite (MgSiO3), olivine/forsterite (Mg2SiO4), periclase (MgO), and cuprite (Cu2O). Three regions of 2-liquid immiscibility were found—two in the high-silica range of compositions above the cristobalite primary phase field (close to ‘CuO0.5’-SiO2 and MgO–SiO2 binaries) and one in the low-SiO2, high-‘CuO0.5’ compositional region above the periclase and olivine phase fields. The results obtained in this study indicate that silica in high-copper refining slags likely led to olivine and pyroxene phase formation, increased solubility of MgO in liquid slag, and decline in the performance of MgO-based refractories. New experimental data were used in the development of a thermodynamic database describing this pseudo-ternary system.

Binary mixture phase equilibria for the vinyl laurate, vinyl methacrylate and vinyl propionate under high pressure carbon dioxide

The experimental phase equilibrium data of binary mixtures of vinyl laurate, vinyl methacrylate, and vinyl propionate in supercritical CO2 fluid is reported at high pressure starting from 3.92 MPa to 23.55 MPa and temperature varying from 313.2 K to 393.2 K with a static-type high pressure apparatus. It is observed that the solubility of binary mixtures considered in present study increases with temperature at constant pressure. Furthermore, at constant pressure, the critical point of the mixtures moves higher as temperature increases. Besides, the type I phase curve is exhibited by all the binary mixtures considered.The experimental bubble pressure data is correlated with Ghoderao-Dalvi-Narayan (GDN) and Peng-Robinson (PR) equations of state by the using Van der Waals single fluid mixing rules with two adaptable interaction factors. The pressure-composition (P-x) isotherms are obtained for the binary systems (carbon dioxide + vinyl laurate), (carbon dioxide + vinyl methacrylate), and (carbon dioxide + vinyl propionate) at several temperatures varying from 313.2 K to 393.2 K. A good fit to the experimental data is obtained with GDN equation of state performing better than PR equation of state.

High-pressure phase behavior of the quaternary system (carbon dioxide + dichloromethane + ε‒caprolactone + poly(ε‒caprolactone): Experimental data and PC-SAFT modeling

The phase behavior of the system containing carbon dioxide + dichloromethane + ε- caprolactone + poly(ε-caprolactone) was studied in order to get important information to understand the polymerization reaction in a high-pressure system. The experiments were performed using a variable-volume view cell over the temperature range from 323.15 to 353.15 K. The mass ratio between dichloromethane: (ε- caprolactone + poly(ε-caprolactone)) mixture was kept fixed at 1:1 with different poly(ε-caprolactone) mass fractions (reaction conversion) from 0.0 up 15.0 wt%. The mass composition of supercritical carbon dioxide varied in relation to the dichloromethane + ε- caprolactone + poly(ε-caprolactone) mixture from 60.0 to 77.5 wt% on dichloromethane free basis. Phase transitions of vapor-liquid bubble point type (VLE-BP) and liquid-liquid (LLE) were verified and lower critical solution temperature (LCST) behavior in P-W and P-T diagrams was observed. The experimental results were modeled using the PC-SAFT EoS, providing a positive representation of the experimental phase equilibrium data.

Thermodynamic modeling of calcium carbonate scale precipitation: aqueous Na+-Ca2+-Cl–-HCO3–-CO32–-CO2 system

To allow for accurate calculations of calcium carbonate scaling in highly saline produced waters, we present a comprehensive thermodynamic model based on the electrolyte nonrandom two-liquid (eNRTL) activity coefficient equation for the aqueous Na+-Ca2+-Cl–-HCO3–-CO32–-CO2 system. The eNRTL binary interaction parameters for the H2O:(Na+-CO32–) pair, the H2O:(Na+-HCO3–) pair, the (Na+-Cl–):(Na+-CO32–) pair, and the (Na+-Cl–):(Na+-HCO3–) pair are identified in this work via the regression of thermodynamic, calorimetric, and phase equilibria experimental data. The binary interaction parameters associated with the H2O:(Na+-Cl–) pair, the CO2:(Na+-Cl–) pair, the H2O:(Ca2+-Cl–) pair, and the (Na+-Cl–):(Ca2+-Cl–) pair are retrieved from the literature. The remaining binary interaction parameters are retrieved from Aspen Plus or set to zero. In addition, the solubility product constants are identified for Na2CO3•10H2O(s), Na2CO3•7H2O(s), Na2CO3•H2O(s), Na2CO3•NaHCO3•2H2O(s), Na2CO3•3NaHCO3(s), and CaCO3(s) via regression of solubility data. The model is capable of accurately calculating all phase equilibria and calorimetric properties at temperatures up to 473.15 K and salt concentrations up to saturation.

Structure-H hydrate of mixed gases: Phase equilibrium modeling and experimental validation

Clathrate hydrates are solid ice-like compounds that entrap the gas or liquid molecules into their cavities of hydrogen-bonded water molecules. As compared to commonly available sI and sII structures of clathrate hydrate, the sH-type is reported to possess more stability and gas uptake capacity. Despite copious implications of the sH-type hydrates of mixed gases in gas storage and separation, the phase equilibrium modeling to predict their formation condition is rarely available in the literature due to inaccurate estimation of the interactions between the guest components. In this view, we develop a novel methodology using the Wong-Sandler mixing rule extended for the three-parameter Patel-Teja equation of state, in association with the statistical thermodynamics based van der Waals and Platteeuw model to define the hydrate phase. This apart, the solubility of the help gases in water is estimated using the Patel-Teja model instead of the empirical correlations. It is observed that the proposed formulation is capable of predicting the experimental phase equilibrium data with a range of 1.389–2.812 %AARD for a variety of sH hydrates (i.e., neohexane, methylcyclopentane, isopentane, 2,2-dimethylpentane and a recently discovered first vapor phase heavy former tetrafluorocyclobutane) having methane, nitrogen or carbon dioxide as their co-guest.

Simulation of Organic Liquid Products Deoxygenation by Multistage Countercurrent Absorber/Stripping Using CO2 as Solvent with Aspen-HYSYS: Thermodynamic Data Basis and EOS Modeling.

In this work, the thermodynamic data basis and equation of state (EOS) modeling necessary to simulate the fractionation of organic liquid products (OLP), a liquid reaction product obtained by thermal catalytic cracking of palm oil at 450 °C, 1.0 atmosphere, with 10% (wt.) Na2CO3 as catalyst, in multistage countercurrent absorber/stripping columns using supercritical carbon dioxide (SC-CO2) as solvent, with Aspen-HYSYS was systematically investigated. The chemical composition of OLP was used to predict the density (ρ), boiling temperature (Tb), critical temperature (Tc), critical pressure (Pc), critical volume (Vc), and acentric factor (ω) of all the compounds present in OLP by applying the group contribution methods of Marrero-Gani, Han-Peng, Marrero-Pardillo, Constantinou-Gani, Joback and Reid, and Vetere. The RK-Aspen EOS used as thermodynamic fluid package, applied to correlate the experimental phase equilibrium data of binary systems OLP-i/CO2 available in the literature. The group contribution methods selected based on the lowest relative average deviation by computing Tb, Tc, Pc, Vc, and ω. For n-alkanes, the method of Marrero-Gani selected for the prediction of Tc, Pc and Vc, and that of Han-Peng for ω. For alkenes, the method of Marrero-Gani selected for the prediction of Tb and Tc, Marrero-Pardillo for Pc and Vc, and Han-Peng for ω. For unsubstituted cyclic hydrocarbons, the method of Constantinou-Gani selected for the prediction of Tb, Marrero-Gani for Tc, Joback for Pc and Vc, and the undirected method of Vetere for ω. For substituted cyclic hydrocarbons, the method of Constantinou-Gani selected for the prediction of Tb and Pc, Marrero-Gani for Tc and Vc, and the undirected method of Vetere for ω. For aromatic hydrocarbon, the method of Joback selected for the prediction of Tb, Constantinou-Gani for Tc and Vc, Marrero-Gani for Pc, and the undirected method of Vetere for ω. The regressions show that RK-Aspen EOS was able to describe the experimental phase equilibrium data for all the binary pairs undecane-CO2, tetradecane-CO2, pentadecane-CO2, hexadecane-CO2, octadecane-CO2, palmitic acid-CO2, and oleic acid-CO2, showing average absolute deviation for the liquid phase () between 0.8% and 1.25% and average absolute deviation for the gaseous phase () between 0.01% to 0.66%.

A solid solution modeling approach somehow analogous to the EoS approach for fluids: Application to equilibria involving fluid phases and solid solutions

In the present work, a modeling approach applicable over wide ranges of temperature and pressure to the representation of the thermodynamic properties of pure components in solid state is extended to the case of solid solutions. The resulting Solid Solution (SS) modeling Approach (SSA) makes possible to avoid, for multicomponent systems, the inconsistent assumption of solid precipitation in pure state. The SSA here proposed accounts in a straightforward way for the effects of temperature, pressure and SS composition on the thermodynamic properties of the SS. Modeling results are shown for the binary systems Ar(argon)+CH4(methane) and CH4 + n-C20H42 (n-eicosane) in wide ranges of conditions. The agreement between the calculation results obtained for the particular form of the SSA tested in this work and the experimental phase equilibrium data is good for the systems studied. The results in this work indicate that the proposed SSA is able to properly capture the patterns of the phase behavior of the studied mixtures.

Thermodynamic assessment of the Ni-Co-M1 (M1 = Re, Ru) and Ni-Re-M2 (M2 = W, Ta) superalloy systems over the whole composition

The phase equilibria of the Ni-Co-M1 (M1 = Re, Ru) and Ni-Re-M2 (M2 = W, Ta) ternary systems were thermodynamically assessed by the CALPHAD (CALculation of PHAse Diagrams) method based on the thermodynamic descriptions of the constitutive binary systems and experimental phase equilibria data available in the literature. The solution phases, i.e., fcc(Co, Ni), hcp(Co, Re, Ru) and bcc(Co, W, Ta), were described using substitutional solution model and the binary phases σ(ReW), χ(Re3W), χ(Re3Ta), NiTa2, μ(NiTa), Ni2Ta and Ni3Ta with the solubilities of the third element were modeled by the sublattice models. A set of self-consistent thermodynamic parameters for each ternary system was finally obtained. Some representative isothermal sections and liquidus projections were calculated. Comparisons between the calculated results and experimental data show that almost all the reliable experimental data were satisfactorily reproduced by the present modeling.

Thermodynamic modeling of the Te-X (X = Zr, Ce, Eu) systems

Thermodynamic descriptions of the tellurium-zirconium (Te-Zr), tellurium-cerium (Te-Ce) and tellurium-europium (Te-Eu) systems have been carried out using the CALPHAD (CALculation of PHAse Diagrams) method based on the experimental phase equilibria data available in the literature and the enthalpies of formation calculated by first-principles calculations in the present work. The liquid phase was described by the substitutional solution model for the Te-Zr and Te-Eu systems while the associated solution model for the Te-Ce system with CeTe as associate. The intermetallics Zr3Te, ZrTe, Zr5Te4, ZrTe3, ZrTe5, CeTe, Ce4Te7, CeTe2, Ce2Te5, CeTe3, Eu4Te7 and Eu3Te7 were treated as stoichiometric compounds while Zr1+xTe2, Ce3-xTe4 and Eu1-xTe were modeled by the sublattice model Te1/3(Zr, Va)1/3(Zr, Te)1/3, (Ce, Va)3/7Te4/7 and (Eu, Va)0.5Te0.5, respectively, on the basis of their homogeneity ranges and crystal structures. A set of self-consistent thermodynamic parameters for the Te-X (X = Zr, Ce, Eu) systems was obtained. Comparisons between the calculated results and experimental data available in the literature show that most reliable experimental information can be satisfactorily accounted for by the present modeling.

A new highly stable methane hydrate from the synergic mixture of common promoters: Experimental and modeling surveys

One of the main issues in flow assurance in offshore operations, specially at high pressure conditions as in deep pipelines is the formation of hydrates in the corners of pipelines that causes notable problems like pipe blockage followed by an explosion. Hydrate or gas hydrate is a bright solution for gas storage and transportation. Tetrabutylphosphonium bromide (TBPB) and tetrabutylammonium bromide (TBAB) are salts capable of tackling the thermodynamic and kinetic limitations of hydrate formation/dissociation conditions. In the present work, the effect of TBAB, TBPB and TBAB + TBPB mixture on CH4 hydrate dissociation condition was studied. All experiments were performed by pursuing a constant-volume pressure search technique with the step heating approach to study the effects of additive mixtures with different compositions. A mass fraction of 5%, 10% TBAB/TBPB was used. The experiments were conducted at 280–290.05 K and 1–5.5 MPa. In all the conducted experiments, the mixture had a promoting effect. After generating the accurate data of TBAB-TBPB-CH4 hydrate in water system, a thermodynamic prediction model was developed to investigate efficient hydrate-based applications. The hydrate phase was predicted on the basis of Chen and Guo's approach. Soave−Redlich−Kwong equation of state was applied to predict the required methane properties in the gas phase. The TBAB-TBPB activity coefficient and water activity in the electrolyte phase were obtained through the Bromley equations. The results of the proposed thermodynamic model showed that there is a satisfactory accordance between the experimental phase equilibrium data and the predicted data with an acceptable AARD % of 0.95%.

Modeling of the Interfacial Behavior of Carbon Dioxide + Methyl Myristate, Carbon Dioxide + Palmitate, and Carbon Dioxide + Methyl Myristate + Methyl Palmitate Mixtures Using CPA-EOS and Gradient Theory

This work presents the vapor–liquid equilibrium and the interfacial behavior modeling of binary and ternary CO $$_2$$ + ester mixtures, with the cubic plus association equation of state (CPA-EOS) combined with the density gradient theory. The binary mixtures, CO $$_2$$ + methyl myristate and CO $$_2$$ + methyl palmitate, were studied at temperatures from 313.15 K to 333.15 K, considering the ester molecules as non-associating and the carbon dioxide as non-associating or self-associating (2B scheme) molecule. Phase behavior was predicted with binary interaction parameters adjusted from binary mixture phase equilibrium experimental data. Results show than there are some points better represented by the associating scheme, but the overall trend shows that the CPA-EOS with the non-associating scheme for all the molecules is the best option for describing the phase equilibrium and calculating the interfacial tension for the CO $$_2$$ + ester binary mixtures. For this reason, the CO $$_2$$ + methyl myristate + methyl palmitate mixture at 313.15 K was modeled only with non-associating fluids. The AAD% for the calculated interfacial tensions, considering non-associating molecules in the mixture is 9.7 % for the CO $$_2$$ + methyl myristate mixture, 15.1 % for the CO $$_2$$ + methyl palmitate mixture, and 7.9 % for the CO $$_2$$ + methyl myristate + methyl palmitate mixture.

Multiple Solutions When Fitting Excess Gibbs Energy Models and Implications for Process Simulation

AbstractExcess Gibbs energy models are often fitted to binary experimental data of phase equilibria. Even in the case of two binary parameters fitted to two binary infinite‐dilution activity coefficients, multiple solutions for the parameters may occur. The present work shows that this is also true, if more data – like vapor‐liquid equilibrium data sets – is used. Chemical systems and conditions are identified that lead to multiple solutions. It is shown that the multiple solutions may lead to significantly different results when the models are used in simulation of separation processes.

Experimental study and thermodynamic optimization of the ZnO–FeO–Fe2O3–CaO–SiO2 system

Liquidus phase equilibrium experimental data from the present study for the ZnO-“Fe2O3”-CaO-SiO2 system in air, combined with phase equilibria and thermodynamic data from the literature on the ZnO-“Fe2O3”-CaO system in air and ZnO-“FeO”-CaO-SiO2 system in equilibrium with metallic Fe, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases in the ZnO–FeO–Fe2O3–CaO–SiO2 system. The modified quasichemical model is used for the liquid slag phase; spinel (Fe,Zn,Ca)tetr (Fe,Zn,Ca,Va)oct2O4, melilite Ca2(Fe2+,Fe3+,Zn)(Fe3+,Si)2O7 and olivine (Fe,Zn,Ca)I(Fe,Zn,Ca)IISiO4 are described with compound energy formalism; lime and wustite (monoxide) (Ca,Fe,Zn)O, zincite (Zn,Fe,Ca)O1+x, calcium-zinc ferrites Ca2Fe2O5-“CaZnO2” and CaFe4O7-“ZnFe4O7”, α- and α′-dicalcium silicate (Ca,Fe,Zn)2SiO4 and tricalcium silicate (Ca,Fe,Zn)3SiO5 and silicoferrite of calcium (SFC) Ca9Fe46SiO80–Ca12Fe40Si4O80 are described within Bragg-Williams formalism; for other phases, previous assessments have been adopted. The phase diagrams are back calculated with the optimized model parameters. Present study is a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe2O3-“Cu2O”-CaO-SiO2 system.

Thermodynamic re-modelling of the ternary B–Fe–Mo system based on novel experimental data

In the present paper, the complete ternary B–Fe–Mo system is thermodynamically re-modelled based on our own experimental results and novel information reported in literature. A few key experiments were performed with ternary B–Fe–Mo alloys in order to clarify the morphology and stability of the MoxFe3-xB phase and measure temperatures of invariant second-order equilibria caused by the ferro-to-paramagnetic transformation of Fe-rich phases. In samples Mo6Fe64B30 and Mo10Fe65B25 (in at.%) annealed at 1403, 1363, 1343, 1023 and 873 K considerable amounts of MoxFe3-xB boride were detected to form at the expense of A1(Fe) or A2(Fe) and Fe2B phases. EBSD results show that the area fraction of this boride is higher when the annealing temperature is lower and the annealing time is longer. The sample Mo6Fe64B30 annealed at 1363 K for 15 h reached three-phase state Mo2FeB2+Fe2B+MoxFe3-xB. The sample Mo10Fe65B25 annealed at 1343 K for 5 h + 1403 K for 45 min + 1023 K for 5 h and quenched in a liquid Ga-In eutectic alloy was almost a three-phase A2(Fe)+Mo2FeB2+MoxFe3-xB material, with only about 2 area % Fe2B. The elaborated thermodynamic description was applied to calculate selected phase equilibria and thermodynamic properties in order to provide a comparison between the calculated and experimental results. The calculations are shown to reproduce available experimental phase equilibria data well. Enthalpies of formation at 0 K of the compounds Mo2FeB2 and MoFe1.93B3.73 were calculated to be equal to −216.0 and −277.4 kJ mol−1, respectively. The present value for Mo2FeB2 matches with first-principles calculations result of Wang at al. (−219.0 kJ mol−1).

Computation of the Dissociation Temperature of TBAB Semiclathrate in an Aqueous Solution Using Molecular Simulations.

Quaternary ammonium salts such as tetra-n-butyl ammonium bromide (TBAB) are known to form semiclathrate hydrates. Since they form at much milder conditions compared to gas hydrates, they have evoked much interest in development of new technologies for gas storage and gas separations. In this work, we present a method to compute the phase equilibrium of TBAB semiclathrate. The TBAB molecule is modeled using OPLS-AA and GAFF force fields and the results from simulations are compared with experimental data to determine the ability of the force fields to accurately predict the semiclathrate phase equilibria. It was observed that the OPLS-AA force field outperforms the GAFF force field in predicting the experimental phase equilibrium data.

Power generation from waste heat: Ionic liquid‐based absorption cycle versus organic Rankine cycle

AbstractAspen Plus® simulations using the Peng‐Robinson (PR‐EOS) and the COSMO‐SAC models were performed to study absorption power cycles (APCs) using mixtures of R‐134a with two ionic liquids, [C2C1im][Tf2N] or [C6C1im][Tf2N], and compared against an R‐134a organic Rankine cycle (ORC) operating under similar conditions. The PR‐EOS results were in agreement with calculations from a PR model fitted to the R‐134a + IL experimental phase equilibrium data. The APCs have similar efficiencies and outperform the ORC by 3%–46%, with the largest differences observed when operating with lower grade (lower TH) heating sources, lower quality cooling (higher TL), and lower subcooling in the pump inlet stream. The PR‐EOS and the Conductor‐like Screening Model Segment Activity Coefficient (COSMO‐SAC) results follow similar trends, but numerical discrepancies are observed in the cycle efficiencies and stream flow rates and compositions due to differences in solubilities and enthalpy changes between both models, suggesting that improvements are needed to increase the accuracy of COSMO‐SAC for these systems.

Investigation on the Surface Tension and Viscosity of (dimethylsulfoxide + alcohol) Mixtures by Using Gradient Theory and Eyring’s Rate Theory

The present study has been dedicated to modeling the surface tension and viscosity of (dimethylsulfoxide + alcohol) mixtures. The self and cross-association have been considered for both alcohol and dimethylsulfoxide, and the Cubic-Plus-Association equation of state is applied to the phase equilibrium calculations. The binary interaction parameters are obtained according to the experimental phase equilibrium data, taking advantage of accurate description of the phase equilibrium. Then the gradient theory is used to describe the surface tension and interface of (dimethylsulfoxide + alcohol) mixtures. Moreover, the Eyring’s rate theory is used to model the viscosity of (dimethylsulfoxide + alcohol) binary system. For more accurate description of the viscosity, an adjustable parameter of the Eyring’s rate theory is fitted based on the experimental viscosity data. The results of this investigation show that the application of association performs well for modeling the surface tension and viscosity of (dimethylsulfoxide + alcohol) mixtures.

Experimental high-pressure phase equilibria of carbon dioxide/n-alkanes mixtures and model-parameters for solid-phase obtained from DSC thermograms

We provide high-pressure experimental phase equilibrium data for systems containing mixtures formed by CO2 and mixtures of n-alkanes (n-C10H22/n-C20H42, n-C10H22/n-C24H50, n-C10H22/n-C20H42/n-C24H50) with CO2 weight fractions of 55%, 65% and 75%, temperature ranging from 273 K to 363 K and pressures up to 55 MPa. The measured equilibrium data include vapor-liquid (VL), solid-liquid (SL), and solid-liquid-vapor (SVL) phase transitions. Additionally, calorimetric (DSC) measurements were carried out at atmospheric pressure for mixtures of n-C10H22 (solvent), n-C16H34, n-C20H42, and n-C24H50, with the temperature range from 253 K to 333 K. To describe the phase-equilibrium diagrams, the solid phases were modeling using the multiple-solid solutions approach, which employs the modified UNIQUAC equation to calculate the activity coefficients. The UNIQUAC-energy interaction parameter λij and the Poynting correction factor were used to take into account the n-alkane/n-alkane interactions and pressure effect in the solid-liquid equilibria. We used the Peng-Robinson equation of state to describe the liquid and vapor phases. The phase equilibrium predictive calculations were in good agreement with the measured phase-transition data considering the experimental uncertainty.