Solid-liquid Equilibrium Research Articles

Solid-Liquid Equilibrium Behavior and Data Correlation of Furosemide in 12 Pure Solvents from 283.15 to 323.15 K

Solid-Liquid Equilibrium Behavior and Data Correlation of Furosemide in 12 Pure Solvents from 283.15 to 323.15 K

Solubility of N-Acetyl-L-glutamine in twelve Mono-solvents: Characterization, Determination, Analysis, and model correlation

In this work, the solid–liquid equilibrium solubility and solvent effects of N-acetyl-L-glutamine in twelve mono-solvent systems (water, methanol, ethanol, n-propanol, n-butanol, isobutanol, sec-butanol, acetonitrile, acetone, ethyl acetate, 2-butanone, methyl acetate) were reported at the pressure of 101.2 kPa (at T = 283.15–––323.15 K). Among the twelve mono-solvents, the solubility increased with the increase of absolute temperature, the order is: water > methanol > ethanol > sec-butanol > n-propanol > 2-butanone > isobutanol > acetone > methyl acetate > ethyl acetate > n-butanol > acetonitrile. The modified Apelblat model, Wilson model, NRTL model and UNIQUAC model were employed to correlate the experimental solubility, and the fitting results of the four models were all satisfactory. In addition, through comparison of the average ARD and RMSD values of the four models, the modified Apelblat model achieved the best correlation result. Hirshfeld surface analysis (HS) and molecular electrostatic potential surface (MEPS) were used to determine the internal interactions within N-acetyl-L-glutamine solutions. The Hansen solubility parameters (HSPs) and the coverage Pearson correlation coefficients (PCC) heatmap were utilized to assess the solvents’ capability and to elucidate its ability to dissolve N-acetyl-L-glutamine. Furthermore, mixing thermodynamic characteristics of N-acetyl-L-glutamine in selected solvents were calculated by the NRTL model, which revealed that the mixing process was spontaneous and entropy-driven. These experimental results could be utilized for the purification, crystallization, and industrial applications of N-acetyl-L-glutamine as well as similar substances.

Application of the van’t Hoff equation to phase equilibria

van’t Hoff and Clausius–Clapeyron equations correspond to chemical and phase equilibria, respectively, but the Clausius–Clapeyron equation can be also a result of the application of van’t Hoff equation to the liquid–vapor or solid–vapor phase equilibrium of pure substances. Moreover, the application of van’t Hoff to gas–liquid and solid–liquid equilibrium data makes it possible to obtain enthalpies of dissolution. Examples based on published experimental data are included for all cases.

Measurement, correlation and thermodynamic analysis of the solubility of dicyandiamide in three binary solvents

Dicyandiamide (DCD) is an important chemical raw material. The solid–liquid equilibrium solubility of DCD in three kinds of binary solvent mixtures (N,N-dimethylformamide (DMF) + ethanol, DMF + acetonitrile, DMF + acetone) at T = (283.15–323.15) K was determined by gravimetric method. The thermodynamic parameters of DCD dissolution in solvents were studied. The solubility of DCD in the three groups of binary mixed solvents increases with the increase of temperature. In three binary mixed solvents, the solubility of DCD increases monotonically with the increase of DMF composition. The modified Apelblat model, van’t Hoff model, λh model, the nonrandom two-liquid (NRTL) model and the Apelblat-Jouyban-Acree model were used to correlate the solubility data. The results show that the modified Apelblat model have the best correlation with the solubility of DCD. The calculation of thermodynamic parameters during the dissolution process indicates that dissolution is exothermic and driven by both enthalpy and entropy. This work can provide reference for improving the crystallization process of DCD, as well as for improving the chemical production process using DCD as raw material.

A novel algorithm for asphaltene precipitation modeling in shale reservoirs with the consideration of capillary pressure during the CCUS processes

Tight and shale reservoirs have markedly expanded their role in global oil and gas production. However, the overall recovery from these reservoirs is suboptimal, leaving much of the shale oil unrecovered. CO2 flooding is a promising enhanced oil recovery (EOR) technique that can improve oil extraction and simultaneously facilitate carbon capture, utilization, and storage (CCUS). However, this method presents challenges, notably the precipitation and deposition of asphaltene, which risks plugging the nanoporous structure characteristic of shale reservoirs. Given that the nanopore sizes in these reservoirs align closely with asphaltene particle dimensions, the risk of pore and throat blockages during gas injection is pronounced. Although various asphaltene precipitation models have been proposed, there is still a lack of robust algorithms accounting for the substantial influence of capillary pressure on asphaltene precipitation in these nanopores. In this study, a novel three-phase vapor–liquid-asphaltene equilibrium calculation algorithm coupled with capillary effect is developed. The algorithm is first validated by comparing with the experimental data of the Px phase diagram and asphaltene precipitation amount. The validated algorithm is then used to conduct example calculations to demonstrate the robustness of the new algorithm and to examine the impact of capillarity on the three-phase vapor–liquid-solid (VLS) equilibria. Computation results show that capillary pressures in nanopores substantially modify the three-phase VLS equilibria, causing shifts in saturation pressure and influencing asphaltene precipitation. Generally, asphaltene precipitation in nanopores occurs at a lower pressure and gas injection concentration. The smaller pore sizes intensify these effects, but the impact diminishes as pressure increases. Additionally, the gas composition also greatly affects asphaltene precipitation. The results reveal that this new algorithm is robust across different conditions, offering an innovative approach that reliably predicts asphaltene precipitation considering the effect of capillary pressures, paving the way for improved EOR and CCUS in shale reservoirs.

Insight into the dissolution behavior of valsartan (form E) in twelve pure solvents: Solubility, modelling and molecular simulation

Valsartan is an angiotensin II receptor antagonist used to treat hypertension. Crystals of valsartan were prepared and the stability of the valsartan (form E) at different solvents and temperatures was investigated. The solid-liquid equilibrium solubility of valsartan (form E) in twelve pure solvents was determined by a dynamic method at the temperature from 278.15 K to 323.15 K. Among the solvents used in the experiment, the solubility of valsartan (form E) was found to be highest in methanol and lowest in acetonitrile. In straight-chain alcohols, the solubility decreases with the increase of carbon chain length. The modified Apelblat model, λh model and NRTL model were used to correlate the solubility data. The thermodynamic properties of the mixing process such as Gibbs free energy, enthalpy and entropy were estimated by applying the NRTL model. The KAT-LSER model was adopted to explore solvent effects. Hirshfeld surface analysis and molecular electrostatic potential (ESP) were employed to visualize close contacts and charge distribution of valsartan and solvents. In addition, molecular dynamics (MD) simulation was performed to calculate intermolecular interactions between solute and solvent. Radial distribution function (RDF) and the mean square displacement (MSD) analyses were also carried out to explore molecular association and molecular diffusion.

Experimental solubility of FeCO3 in aqueous 3–20 wt% KCl at 25–80 °C

FeCO3 is a mineral, present in both industrial and natural systems. While the solubility of FeCO3 is determining for CO2 storage, and driving for corrosion, it is not well understood. For the development of rigorous modelling, there is a lack of adequate experimental data under relevant conditions to model carbonated systems containing iron.In this work, the solid-liquid equilibrium (SLE) of the ternary system FeCO3-KCl-H2O was measured at atmospheric pressure at temperatures from 25 to 80 °C. The FeCO3 solubility was studied in aqueous KCl solutions from 3 to 20 wt%. 73 new solubility data points for the systems FeCO3–KCl–H2O are presented together with 73 oxidation data points. Results showed that less than 5% of FeCO3 is oxidized in the electrolyte system. The equilibrium concentration of FeCO3 was obtained after 5–10 days with the fastest equilibrium kinetics obtained at the highest temperature, 80 °C. Temperature had a minor impact on the FeCO3 solubility in aqueous KCl solutions. However, the FeCO3 solubility seemed to slightly decrease with temperature. The solubility data was fitted to a first-order rate equation with molality as driving, to obtain kinetic insights. The dissolution rate decreases as a function of KCl concentrations. In some cases, it was 75 % lower than in NaCl. A rate constant of approximately 0.2 1/day was obtained for most experiments. The FeCO3 solubility and kinetic data obtained in this work will allow for a deeper understanding and better prediction of CO2 corrosion and mineralization, suitable for CO2 storage.

Prediction of wax disappearance temperature: a review

Wax deposition in pipelines is a recurring problem in the oil industry. Therefore, several studies have analyzed the phenomenon and predicted the wax disappearance temperature (WDT). This variable represents the exact solid-liquid equilibrium point. Such information is an effective aid in decision-making regarding pipelines and production facilities. However, the study of paraffin deposition is highly dependent on conducting experiments, which are typically costly and can make this type of analysis impractical. The increasing progress of models based on machine learning techniques has been an alternative to experimental and thermodynamic methods to predict this phenomenon. In the present study, a bibliographic review of the main authors on models for predicting kerosene deposition has been compiled.

Hydrophobic interactions described using hetero-segmented PC-SAFT: 1. Alcohol/water mixtures

The hydrophobic effect plays a central role in aqueous systems containing molecules with hydrophobic moieties. Despite the relevance of this effect for chemical processes or pharmaceutical applications, modeling remains challenging even using molecular-based models such as different versions of the Statistical Associating Fluid Theory. This work shows the feasibility of hetero-segmented PC-SAFT for this purpose. This model was used as a group contribution method to build molecules from different functional groups, namely from CH2, CH3, and CH2OH groups. Saturated-liquid densities and vapor pressures of n-alkanes and n-alcohols as well as binary mixtures of these molecules were accurately described by this approach. The description of aqueous mixtures containing n-alkanes and n-alcohols was improved compared to state-of-the-art modeling by explicitly accounting for intermolecular interactions resulting in the hydrophobic effect. The so-obtained framework describes the two liquid−liquid equilibrium phases in mixtures of n-alkanes or n-alcohols with water equally well using a single set of transferable parameters. The model was also validated for vapor–liquid equilibria, solid–liquid equilibria, infinite-dilution properties, as well as octanol/water partition coefficients and showed quantitative agreement with experimental data.

Insights into solid–liquid equilibrium behavior of 2′,4′-Dichloro-5′-fluoroacetophenone

2′,4′-Dichloro-5′-fluoroacetophenone is a key intermediate in the preparation of ciprofloxacin hydrochloride, a broad-spectrum quinolone antibacterial drug. Wherein, crystallization and solid–liquid equilibrium thermodynamics play an irreplaceable role in the separation and purification of 2′,4′-Dichloro-5′-fluoroacetophenone. Therefore, in this work, the solubility of 2′,4′-Dichloro-5′-fluoroacetophenone was measured by dynamic method in eight different solvents and range from 273.15 K to 288.15 K. The results showed that the solubility of 2′,4′-Dichloro-5′-fluoroacetophenone increased with increasing temperature. Further analysis showed that the solubility of 2′,4′-Dichloro-5′-fluoroacetophenone increased with increasing carbon chain length in ester solvents. Single crystals of 2′,4′-Dichloro-5′-fluoroacetophenone were successfully prepared and the result reveals that the Cl⋯H, O⋯H, and F⋯H interactions dominated the packing and long-range order of the crystals. Then, different thermodynamic models were employed to describe the thermodynamic behavior of 2′,4′-Dichloro-5′-fluoroacetophenone. The calculated ARD% and RMSD values show that the correlation results are in good agreement with the experimental data, and the Van’t Hoff equation has the best regression performance. Finally, it is interesting to find that the contribution of entropy and enthalpy change to dissolution of 2′,4′-Dichloro-5′-fluoroacetophenone tends to be equal with increasing temperature.

Phase diagram and density of SiO2–H2O fluid across critical conditions

The SiO2–H2O binary system serves as a basis for understanding complex silicate-water systems. In this study, based on limited existing experimental data of solubility, we propose a new thermodynamic model for SiO2–H2O fluid by modifying the traditional non-random two-liquid model with a simplified polymerization reaction. This model is applicable from 773 K to the anhydrous quartz melting temperature and from 0.5 GPa to at least 2 GPa across the critical conditions. It can predict solid–liquid equilibrium and vapor–liquid equilibrium in good agreement with available experiments. The upper critical endpoint of the SiO2–H2O system is predicted to be at ~ 1.14 ± 0.18 GPa and 1344 ± 87 K. With the new model, we obtain a quantitative three-dimensional pressure–temperature–composition phase diagram of the SiO2–H2O fluid, which greatly facilitates the understanding of the complex phase behavior of this binary around the upper critical endpoint. In addition, since the model is based on the Gibbs free energy foundation, we further discuss the derived density variations of SiO2–H2O fluid along with its complex phase changes in typical geochemical processes.

Investigating the phase diagram-ionic conductivity isotherm relationship in aqueous solutions of common acids: hydrochloric, nitric, sulfuric and phosphoric acid

The relationship between phase diagram features around the solid–liquid equilibrium region and ionic conductivity in aqueous solutions is not well understood over the whole concentration range as is the case for acidic aqueous solutions. In this work, we have studied the ionic conductivity (κ) as a function of molar fraction (x) and temperature (T) for four acid/water solutions namely, monoprotic hydrochloric acid (HCl) and nitric acid (HNO3), diprotic sulfuric acid (H2SO4) and triprotic phosphoric acid (H3PO4) along with their binary phase diagrams. The connection between the main features of the phase diagrams and the trends in the ionic conductivity isotherms is established with a new insight on the two pertinent dominant conductivity mechanisms (hopping and vehicular). Ionic conductivity at different temperatures were collected from literature and fitted to reported isothermal (κ vs. x) and iso-compositional (κ vs. T) equations along with a novel semi-empirical equation (κ = f (x, T)) for diprotic and triprotic acids. This equation not only has the best fit for acids with different valency; but also contains four parameters, less than any other similar equation in literature. This work is one of few that advances the understanding of the intricate relationship between structure and ionic transport in various acidic aqueous solutions.

Determination of Regorafenib monohydrate (colorectal anticancer drug) solubility in supercritical CO2: Experimental and thermodynamic modeling

In this study, the solubilities of Regorafenib monohydrate (REG), a widely used as a colorectal anticancer drug, in supercritical carbon dioxide (ScCO2) were measured under various pressures and temperature conditions, for the first time. The minimum value of REG in mole fraction was determined to be 3.06×10−7, while the maximum value was found to be 6.44×10−6 at 338 K and 27 MPa. The experimental data for REG were correlated through the utilization of two types of models: (1) a set of 25 existing empirical and semi-empirical models that incorporated 3–8 parameters according to functional dependencies, (2) a model that relied on solid-liquid equilibrium (SLE) and the newly improved association models. All of the evaluated models were capable of generating suitable fits to the solubility data of REG, however, the average absolute relative deviation (AARD) of Gordillo et al. model (AARD=13.2%) and Reddy et al. model (AARD=13.5%) indicated their superiority based on AARD%. Furthermore, solvation and sublimation enthalpies of REG drug were estimated for the first time.

Solid–Liquid Equilibrium and Thermodynamic Analysis of Transition Metal Complexes Supported by Bis(imino)pyridine in Different Solvents

Solid–Liquid Equilibrium and Thermodynamic Analysis of Transition Metal Complexes Supported by Bis(imino)pyridine in Different Solvents

Numerical modelling on coupled behavior of calcium leaching and chloride transport in cement-based materials by considering ion desorption

Concrete structures serving in water environment with rich chloride ions are subjected to the coupling action of calcium leaching and chloride corrosion. In this paper, a transport model of calcium and chloride ions coupled with the calcium solid-liquid equilibrium equation is proposed to simulate the behavior of calcium leaching and chloride penetration in concrete. In the model, the effect of free chloride ions bound by solid calcium and the release of bound chloride ions caused by the dissolution of solid calcium is considered. Secondly, the model is numerically solved by using the finite difference method of Crank-Nicolson scheme. Then, the experimental data of porosity and calcium silicon ratio, chloride concentration are compared to the calculated results to validate the model. Finally, a numerical simulation is conducted to analyze the evolution of ion concentration, solid calcium content and porosity of cement paste slice exposed to deionized water and accelerated dissolution solution. The results show that, the concentration of calcium ion decreases with corrosion time, while that of chloride ion increases. There are concentration gradient distributions of calcium and chloride ions in the slice. The higher the concentration of accelerated dissolution solution, the larger the porosity of cement paste and the higher the concentration of chloride ions in the paste. It indicates that, the calcium leaching accelerates the chloride penetration into concrete. In addition, the dissolution process of solid calcium, i.e. calcium hydroxide first dissolves followed by C-S-H gel, are presented.

Thermodynamic modeling of the solid-liquid equilibrium of two phenolic compounds in several solvents at temperatures ranging from 283.15 K to 323.15 K

The solubility of two natural phenolic compounds (vanillic acid (VA) and vanillin (V)) in four individual solvents (ethanol, butan-2-ol, ethylene glycol, and ethyl acetate) was measured using the gravimetric method from 283.15 to 323.15 K at atmospheric pressure. The optimization of the complexes between VA–solvents and V–solvents using the B3LYP theoretic technique and the 6-31+G (d, p) basis set indicated that the absolute value of interaction energy was higher, suggesting that the interaction between solute and the solvent was stronger. In addition, two excellent activity coefficient models (NRTL and Wilson) were used to correlate and evaluate the equilibrium solubility results. The highest relative average deviation and root-mean-square deviation values for VA are 4.36% and 3.09 × 10-3, respectively, and 3.35% and 5.52 × 10-3 for V. Furthermore, the excess enthalpy of the solution was determined on the basis of thermodynamic relations and the Wilson model. The findings indicate that the dissolution process was endothermic.
 KEY WORDS: Solid-liquid equilibrium, Vanillin, Vanillic acid, NRTL and Wilson models, Thermodynamic parameters
 Bull. Chem. Soc. Ethiop. 2024, 38(3), 799-810. 
 DOI: https://dx.doi.org/10.4314/bcse.v38i3.19 

Impact of supplementary cementitious materials on the solid–liquid equilibrium curve of calcium in cement hydrates

Impact of supplementary cementitious materials on the solid–liquid equilibrium curve of calcium in cement hydrates

Equilibrium solubility, solvent effect, and equation correlations of cyclosporine in twenty mono solvents and four binary mixtures

In this study, the solid–liquid equilibrium solubility of cyclosporine in 20 pure solvents and four binary mixtures at 298.15 K were determined using shake-flask technique. Solid-state characterization exhibited that no solvate formation or polymorphic transformation occurred during the dissolution of cyclosporine in any of the solvent systems investigated. The experimental solubilities of cyclosporine in 20 pure mono solvents were ranked as follows: DEGME (2.21 × 10−1) > ethanol (1.22 × 10−1) > NMP (1.15 × 10−1) = 1-butanol (1.15 × 10−1) > dichloromethane (1.07 × 10−1) > acetonitrile (1.02 × 10−1) > PEG 200 (9.78 × 10−2) > PEG 300 (9.12 × 10−2) > chloroform (8.98 × 10−2) > PEG 400 (8.11 × 10−2) > DMF (7.65 × 10−2) > 2-propanol (7.09 × 10−2) > 1-propanol (6.57 × 10−2) > methanol (6.14 × 10−2) > propylene glycol (6.08 × 10−2) > tetrahydrofuran (4.69 × 10−2) > DMSO (2.64 × 10−2) > acetone (1.28 × 10−2) > glycerol (1.35 × 10−5) > water (4.29 × 10−7). In the four binary solvents (DEGME + water, PEG 200 + water, PEG 300 + water, and PEG 400 + water), the mole fraction solubility of cyclosporine increased with increasing mass fractions of the four different organic solvents. Based on the Kamlet-Taft linear solvation energy relationship (KAT-LSER) model, the solubility of cyclosporine was mainly affected by the self-cohesiveness of the solvent, which is related to the interaction between the solvent and the solvent. Additionally, the solubility parameter was used to explain and understand the solubility of cyclosporine in four different binary solvents. To correlate the solubility data of cyclosporine, two models (the Yalkowsky Log-Linear and simplified CNIBS/R–K models) were applied. The calculated data based on two mathematical models and experimental mole fraction solubility data for cyclosporine could provide information for the separation, extraction, purification, crystallization, and selection of suitable a solvent system.

Solid–Liquid Equilibrium of GLA-NaCl System and Its Application for Separating GLA and NaCl

Solid–Liquid Equilibrium of GLA-NaCl System and Its Application for Separating GLA and NaCl

Crystallization risk of aromatic compounds in LNG production. Part II: The solubility of p-xylene in methane-rich mixtures down to cryogenic temperatures

New measurements of solubility of solid p-xylene in solvents methane and (90%mol/mol)methane + (10%mol/mol)ethane have been carried out using a cryogenic apparatus and adopting a static-analytic method for temperatures from 273 K down to 128 K at nominal pressures of 3 and 6 MPa. Measured solid-liquid and solid-vapor equilibria have been compared to literature values of solubility of solid p-xylene in methane-rich phases and to modeling results obtained by coupling a cubic equation of state and a model for the solid phase. Results confirm the conclusions reported in our previous study of this system that evidenced of a non-monotonic variation of the solubility of p-xylene with temperature when crossing the critical region of the solvent and that binary interaction parameters regressed on vapor-liquid equilibrium can be used for predicting the solubility at cryogenic conditions.