Thermodynamic Model Parameters Research Articles

Separation of 2-ethoxyethanol from wastewater by four esters: Correlation of LLE thermodynamic modeling, influence of molecular structure, and investigation of component interactions

To prevent the wastewater containing 2-ethoxyethanol (2EE) from causing environmental pollution and economic waste, liquid–liquid extraction was used to recover 2-ethoxyethanol from wastewater in this study. The liquid–liquid equilibrium behavior of water + 2-ethoxyethanol + four solvents (propyl acetate, isopropyl acetate, n-butyl acetate, and isobutyl acetate) was investigated at 303.2 K and atmospheric pressure. The distribution coefficient (D) and separation factor (S) were used to compare and discuss the extraction efficiency of each system. The results indicated that all esters could effectively separate 2-ethoxyethanol from water. Among them, isobutyl acetate exhibited the highest values for D and S, demonstrating its superior separation capability. The experimental data were correlated with the thermodynamic model and interaction parameters were obtained. These parameters were verified using the GUI-MATLAB tool, and all four systems passed validation, confirming the reliability of the obtained binary interaction parameters. Furthermore, the root mean square deviation (RMSD) was used to assess the deviation between the experimental and regression values. The RMSD values for the NRTL and UNIQUAC models were 0.008 and 0.007, respectively. The interactions between 2-ethoxyethanol and water or esters were explored using σ-Profile, and it was found that esters with a branched chain structure provided better extraction. To explain the properties of the extractants microscopically, the interaction energies between 2-ethoxyethanol molecules and water or ester molecules, as well as the non-bonding energies of 2-ethoxyethanol in different media, were calculated.

Thermodynamic re-optimization of the CaO–SiO2 system integrated with experimental phase equilibria studies

CaO–SiO2 is the key system in ferrous and non-ferrous metallurgy, ceramic manufacture, cement production, and other applications. A number of discrepancies and gaps in knowledge has been identified and resolved since the last thermodynamic optimization of this system. This study reports new experimental phase equilibria data measured using recent advances in equilibration, sample quenching, and Electron Probe X-ray Microanalysis (EPMA) technique. An updated self-consistent set of thermodynamic model parameters is provided. Most importantly, these updates are integrated with a complete re-assessment of the 20-component Cu–Pb–Zn–Fe–Ca–Si–O–S–Al–Mg–Cr–Na–As–Sn–Sb–Bi–Ag–Au–Ni–Co system directly relevant to applications in the ferrous and non-ferrous metallurgical industries. To obtain a large single set of model parameters, significant advances were made in the computational approach, with a focus on simultaneous parallel optimization of binary and ternary model parameters using an experimental dataset combining binary, ternary, and multicomponent information. The Modified Quasichemical Formalism is used for the liquid slag phase. Thermodynamic properties of solid phases and liquid endmembers are completely revised following the recommendations for the third generation of CALPHAD databases. Other notable changes include the revision of the melting temperature of CaO, justified by extrapolations from the multicomponent systems, as well as a physically realistic heat capacity function for metastable SiO2 below the glass transition temperature. These updated properties expand the areas of application of the database to amorphous and partially crystallized slags at ambient temperatures, such as thermodynamics and kinetics of leaching of toxic elements in an aqueous environment. The fundamental limitations of the existing Modified Quasichemical Formalism are also discussed, along with strategies for addressing them.

Phase equilibrium data prediction and process optimizationin butadiene extraction process

In response to the lack of reliable physical parameters in the process simulation of the butadiene extraction, a large amount of phase equilibrium data was collected in the context of the actual process of butadiene production by acetonitrile. The accuracy of five prediction methods, UNIFAC, UNIFAC-LL, UNIFAC-LBY, UNIFAC-DMD, and COSMO-RS, applied to the butadiene extraction process was verified using partial phase equilibrium data. The results showed that the UNIFAC-DMD method had the highest accuracy in predicting phase equilibrium data for the missing system. COSMO-RS predicted multiple systems showed good accuracy. And a large number of missing phase equilibrium data were estimated using the UNIFAC-DMD method and COSMO-RS method. The predicted phase equilibrium data were checked for consistency. The NRTL-RK and UNIQUAC thermodynamic models were used to correlate the phase equilibrium data. Industrial device simulations were used to verify the accuracy of the thermodynamic model applied to the butadiene extraction process. The simulation results showed that the average deviations of the simulated results using the correlated thermodynamic model from the actual values were less than 2% compared to that using the commercial simulation software Aspen Plus and its database. The average deviation was much smaller than that of the simulations using the Aspen Plus database (>10%), indicating that the obtained phase equilibrium data are highly accurate and reliable. The best phase equilibrium data and thermodynamic model parameters for butadiene extraction are provided. This improves the accuracy and reliability of the design, optimization and control of the process, and provides a basis and guarantee for developing a more environmentally friendly and economical butadiene extraction process.

Efficient thermodynamic model optimization and uncertainty quantification via integration of combinatorial materials chip and Bayesian approach

Combinatorial materials chips (CMC) are composition spread thin-films deposited on a substrate that can rapidly determine the compositional-temperature information of ternary phase diagrams by high-throughput characterization. In this study, phase boundary information determined by CMC from the recent studies was used as input to optimize the thermodynamic model parameters by ESPEI based on Bayesian approach. The uncertainties in the model were also quantified. Fe–Cr–Ni and Fe–Co–Ni systems were chosen as examples to demonstrate the effectiveness of process. The newly optimized phase diagrams are in good agreement with the experimental results. It is also verified that the model can be effectively optimized by the dense CMC phase boundary data only without including the scattered experimental data. Moreover, the uncertainty in the model is reduced with the addition of CMC data. Finally, probability distributions of various phase combinations in the phase diagram were calculated, providing confidence intervals for material design.

Extractive distillation of tetrahydrofuran–ethanol azeotropic mixture with ionic liquid as extractant

AbstractBACKGROUNDThe tetrahydrofuran–ethanol azeotrope cannot be separated by common distillation, but can be effectively separated by extractive distillation. Extractive distillation can be simulated by Aspen Plus software. The minimum annual cost of the process can be calculated to assess ionic liquid separation ability. The interaction energy can be used to explain the separation mechanism.RESULTSThe non‐random two‐liquid model parameters of ternary mixtures for tetrahydrofuran and ethanol containing tributylmethylammonium acetate or 1‐octyl‐3‐methylimidazolium acetate were obtained. Thermodynamic property databases of tributylmethylammonium acetate, 1‐hexyl‐2,3‐dimethylimidazolium acetate and 1‐octyl‐3‐methylimidazolium acetate were established. Based on the thermodynamic model parameters and properties, the sequential iterative method was used to determine the best operating conditions and minimum total annual cost the of extractive distillation process. The interaction energy was calculated to explain the separation mechanism.CONCLUSIONSThe separation performance of tributylmethylammonium acetate is better than that of 1‐hexyl‐2,3‐dimethylimidazolium acetate or 1‐octyl‐3‐methylimidazolium acetate. The selection and design of the ionic liquids can be conducted in terms of the interaction energy. © 2023 Society of Chemical Industry (SCI).

Thermodynamic assessment of La–Fe–Si systems

The phase equilibria of the La–Fe–Si system were investigated using a combination of experimental and thermodynamic modeling methods. The isothermal cross-section of the La–Fe–Si ternary system in the (Fe, Si)-rich region at 1373 K was experimentally investigated using electron probe microanalysis (EPMA) and X-ray diffraction (XRD). Based on the experimental results and literature reports of the La–Fe–Si system, the thermodynamic model parameters of the system were optimized using the CALPHAD method. The intermediate compounds in the La–Si binary system and ternary compounds in the La–Fe–Si ternary system were described via sublattice models. The calculated thermodynamic and phase equilibria data were in good agreement with the experimental data, providing a foundation for the development of a multi-component thermodynamic database for LaFeSi-based alloys.

DSC Investigation and Thermodynamic Modeling of the Al–Sb–Sn System

The Al–Sb–Sn ternary system was studied by combining experimental measurement and thermodynamic modeling. The three vertical cross-sections of Al–SnSb, Sn–AlSb, and Sb–AlSn were measured by Differential Scanning Calorimetry (DSC). Based on the Calculation of Phase Diagram (CALPHAD) method, the thermodynamic modeling of the Al–Sb–Sn ternary system was carried out based on the evaluated experimental data by FactSage. A set of thermodynamic model parameters consistent with the experimental data was obtained.

Experiment and thermodynamic modelling of phase equilibria in PbO−“CuO0.5” and PbO−“CuO0.5”−“FeO1.5” slag systems with metal

The phase equilibria of the PbO−“CuO0.5” and PbO−“CuO0.5”−“FeO1.5” slag systems in equilibrium with solid metallic copper and/or liquid metallic lead−copper alloy were studied as part of the investigation of the 19-element PbO−ZnO−Cu2O−FeO−Fe2O3−CaO−SiO2−Al2O3−MgO−S−(As, Sn, Sb, Bi, Ag, Au, Ni, Cr, Co as minor elements) multicomponent slag/matte/metal/speiss system, supporting the operation and development of the existing and emerging pyrometallurgical processes. In the experimental portion of this study, samples underwent high temperature equilibration followed by quenching, after which the compositions in the liquid slag, solid oxide and metallic phases were directly measured by electron probe microanalysis (EPMA). Phase equilibria data on the massicot (PbO), spinel ((Fe, Cu)Fe2O4), cuprite (Cu2O), lead ferrite (Pb2+xFe2O5+x), magnetoplumbite (Pb1+xFe12−xO19−x), copper plumbite (Cu2PbO2), and delafossite (CuFeO2) primary phase fields were obtained between 688 and 1000 °C. A key finding of the experimental study of the PbO−“CuO0.5” subsystem was that the copper plumbite (Cu2PbO2) phase melted incongruently, contradicting previous studies that suggested it apparently decomposed below the binary eutectic temperature to form massicot (PbO) and cuprite (Cu2O). Based on the results of past and present experimental studies, a self-consistent set of thermodynamic model parameters describing all phases in the system was derived using the FactSage software package.

Computational fluid dynamics simulation and the experimental verification of protein adsorption on a hollow fiber membranes module

Immobilized metal affinity chromatography (IMAC) ensures the specific purification of proteins containing histidine tags through high affinity with transition metal chelators, which has various applications in biological protein separation. Most chromatographic separations currently use a fixed bed. In this form, internal flow pressure drops very sharply, accompanied by uneven solution flow, pore blockages, etc., all of which greatly reduce separation efficiency. Therefore, this study uses hollow fiber membranes (HFMs) with micron-scale inner diameters as a base, thus reducing operating pressure and significantly enhancing mass transmission. Batch adsorption experiments were performed using flat plate membranes to obtain the reaction's thermodynamic and kinetic model parameters for use in a dynamic column breakthrough simulation. The numerical simulation was based on a single HFM model and established a mathematical model for computational fluid dynamics (CFD) in ANSYS Fluent software. Model accuracy was validated by combining the simulation with experiments. The effects of different module and process parameters on the breakthrough curve were investigated by varying parameters such as flow rate, initial feed concentration, and HFM inner diameter. Design parameters and operating conditions contributing to module utilization were subsequently obtained.

Bayesian regression and model selection for isothermal titration calorimetry with enantiomeric mixtures.

Bayesian regression is performed to infer parameters of thermodynamic binding models from isothermal titration calorimetry measurements in which the titrant is an enantiomeric mixture. For some measurements the posterior density is multimodal, indicating that additional data with a different protocol are required to uniquely determine the parameters. Models of increasing complexity—two-component binding, racemic mixture, and enantiomeric mixture—are compared using model selection criteria. To precisely estimate one of these criteria, the Bayes factor, a variation of bridge sampling is developed.

Integrated phase equilibria experimental study and thermodynamic modeling of the Cr–Si–O, Fe–Cr–O and Fe–Cr–Si–O systems

Complete characterization of the Fe–Cr–Si–O system at high temperatures (700–2600 °C) is performed using integrated experimental and thermodynamic modeling research methodology. Experimental technique includes high-temperature equilibration, quenching and electron probe X-ray microanalysis (EPMA). Main challenges in the experiments are the choice of holding materials (substrate), fixing the oxygen partial pressure in a wide range, using the secondary standards for EPMA correction, overcoming slow reactions to achieve solid state equilibria. Thermodynamic modeling involves critical assessment of literature data, development of the mathematical models for the Gibbs energies of all phases in the system, and optimization of model parameters. The main modeling challenge is to obtain a self-consistent database, which requires a re-assessment of the Cr–Si–O and Fe–Cr–O sub-systems, and an accurate simultaneous description of all experimental data from literature and from the present study. There are several outcomes of the present study: a critical review of earlier work; a set of diagrams representing phase equilibria and distribution of elements among phases within the system; a set of thermodynamic model parameters for liquid and solid phases in the system. The results of the work will be applied to solve chemical engineering problems in pyrometallurgical production of copper, nickel and steel, recycling of waste electronics and designing refractory materials.

Dried Brown Seaweed's Phytoremediation Potential for Methylene Blue Dye Removal from Aquatic Environments.

The dried form of the brown seaweed Sargassum latifolium was tested for its ability to remove toxic Methylene Blue Dye (MBD) ions from aqueous synthetic solutions and industrial wastewater effluents. In a batch adsorption experiment, different initial concentrations of MBD (5, 10, 20, 30, and 40 mg L−1), sorbent dosages (0.025, 0.05, 0.1, 0.2, 0.3, 0.4, and 0.5 g L−1), contact time (5, 10, 15, 30, 60, 120 min), pH (3, 5, 8, 10, and 12), and temperature (30, 40, 50, 60 °C) were observed. Dried powder of S. latifolium was characterized before and after adsorption of MBD using different techniques, such as FTIR, SEM, UV visible spectral examination, and BET techniques. The BET surface area suggests the formation of S. latifolium was 111.65 m2 g−1, and the average pore size was 2.19 nm. The obtained results showed that at an MBD concentration of 40 mg L−1, the adsorption was rapid in the first 5, 10, and 15 min of contact time, and an equilibrium was reached in about 60 and 120 min for the adsorption. At the optimum temperature of 30 °C and the adsorbent dose of 0.1 g L−1, approximately 94.88% of MBD were removed. To find the best-fit isotherm model, the error function equations are applied to the isotherm model findings. Both Tempkin and Freundlich isotherm models could appropriate the equilibrium data, as well as the pseudo 2nd order kinetics model due to high correlation coefficients (R2). Thermodynamic and Freundlich model parameters were assessed and showed that the mechanism of the sorption process occurs by an endothermic and physical process. According to the results of the experiments, S. latifolium is a promising environmentally friendly approach for eliminating MBD from the aqueous solution that is also cost-effective. This technology could be useful in addressing the rising demand for adsorbents employed in environmental protection processes.

Bridging atomistic simulations and thermodynamic hydration models of aqueous electrolyte solutions.

Chemical thermodynamic models of solvent and solute activities predict the equilibrium behavior of aqueous solutions. However, these models are semi-empirical. They represent micro-scale ion and solvent behaviors controlling the macroscopic properties using small numbers of parameters whose values are obtained by fitting to activities and other partial derivatives of the Gibbs energy measured for the bulk solutions. We have conducted atomistic simulations of aqueous electrolyte solutions (MgCl2 and CaCl2) to determine the parameters of thermodynamic hydration models. We have implemented a cooperative hydration model to categorize the water molecules in electrolyte solutions into different subpopulations. The value of the electrolyte-specific parameter, k, was determined from the ion-affected subpopulation with the lowest absolute value of the free energy of removing the water molecule. The other equilibrium constant parameter, K1, associated with the first degree of hydration, was computed from the free energy of hydration of hydrated clusters. The hydration number, h, was determined from a reorientation dynamic analysis of the water subpopulations compared to bulk-like behavior. The reparameterized models [R. H. Stokes and R. H. Robinson, J. Solution Chem. 2, 173 (1973) and Balomenos et al., Fluid Phase Equilib. 243, 29 (2006)] using the computed values of the parameters lead to the osmotic coefficients of MgCl2 solutions that are consistent with measurements. Such an approach removes the dependence on the availability of experimental data and could lead to aqueous thermodynamic models capable of estimating the values of solute and solvent activities as well as thermal and volumetric properties for a wide range of compositions and concentrations.

Energy‐Efficient Biobutanol Recovery Process Using 1‐Heptanol Extraction

AbstractBiobutanol is an attractive fuel, owing to its abundant lignocellulose utilization and the similarity of its physical properties to those of gasoline. Biobutanol recovery from its fermentation broth is crucial for large‐scale production because of the high costs involved. Extraction considerably reduces the energy demand for distillation, which is extensively used for its recovery. A new solvent, 1‐heptanol, was used for extraction in this study, and its thermodynamic model parameters were derived based on liquid‐liquid equilibrium data obtained via molecular simulations and experimental measurements. The results of the process design obtained with commercial design software indicated that the energy requirement was significantly lower than those of previously reported processes with comparable investments.

Inverse chemical equilibrium problems: General formulation and algorithm

In a forward chemical equilibrium problem (FCEP), the state of minimum Gibbs energy for a chemical system is sought, in which temperature, pressure, elemental amounts, and thermodynamic model parameters are prescribed. We herein present a mathematical framework for characterizing and solving inverse chemical equilibrium problems (ICEP), a class of problems for which one or more of those prescribed conditions in a FCEP are unknown in advance. In an ICEP, complementary conditions must be imposed, which are referred to here as equilibrium constraints. Examples of ICEPs include those in which a certain property is known at equilibrium (e.g., volume is specified instead of pressure; enthalpy is specified instead of temperature; pH is specified instead of the amount of element H). The equilibrium constraints may also be specified by equations that govern the relationship between several equilibrium properties (e.g., the equations relating temperature, pressure, density, energy, and velocity of the gases produced during the detonation of an explosive).

Thermodynamics of liquid Pb–In–Sn alloys determined by vapour pressure measurements

Application of Knudsen method for studies of liquid Pb–In and Pb–In–Sn alloys in temperatures 868–1200 and 848–1219 K, respectively, provided experimental data which made it possible to characterize thermodynamic properties of liquid phase of Pb–In and Pb–In–Sn systems. The produced experimental data were used in the optimization procedure aimed at determination of parameters of thermodynamic models of the Pb–In and Pb–In–Sn systems, linking the measured mass change rates with the thermodynamic properties of these systems. The model applied in this procedure uses equations proposed by Pelton and Bale, modified in the scope of this study. They provide an extension of the standard “dilute interaction parameter formalism” to non-dilute solutions. Parameters of the equations were calculated during optimization procedure using the least square method where the author’s experimental database was supplemented with the data which characterize molar enthalpies of mixing of both examined liquid alloys.

Thermodynamics of order and randomness in dopant distributions inferred from atomically resolved imaging

Exploration of structure-property relationships as a function of dopant concentration is commonly based on mean field theories for solid solutions. However, such theories that work well for semiconductors tend to fail in materials with strong correlations, either in electronic behavior or chemical segregation. In these cases, the details of atomic arrangements are generally not explored and analyzed. The knowledge of the generative physics and chemistry of the material can obviate this problem, since defect configuration libraries as stochastic representation of atomic level structures can be generated, or parameters of mesoscopic thermodynamic models can be derived. To obtain such information for improved predictions, we use data from atomically resolved microscopic images that visualize complex structural correlations within the system and translate them into statistical mechanical models of structure formation. Given the significant uncertainties about the microscopic aspects of the material’s processing history along with the limited number of available images, we combine model optimization techniques with the principles of statistical hypothesis testing. We demonstrate the approach on data from a series of atomically-resolved scanning transmission electron microscopy images of MoxRe1-xS2 at varying ratios of Mo/Re stoichiometries, for which we propose an effective interaction model that is then used to generate atomic configurations and make testable predictions at a range of concentrations and formation temperatures.

Unravelling the metal borides evolution in the transient liquid phase bonding of Ni-based alloys via high-throughput transmission electron microscopy and first-principles thermo-kinetic calculations

The understanding of temperature and time-dependent metal borides precipitation/dissolution is crucial for the design of the transient liquid phase (TLP) bonding process of Ni-based alloys. It however remains elusive despite substantial research efforts for many years mainly owing to the uncertainty on the precipitated metal borides and the complex thermo-kinetics in the process. In this paper, we have unambiguously constructed the micro/nanoscale map of the precipitated metal borides in the TLP bonded Ni-based Inconel 718 superalloy via a high-throughput transmission electron microscopy (TEM) analysis. Five types of metal borides were found to precipitate in the diffusion affected zone (DAZ) when the isothermal solidification is completed. They are the M5B3 with stacking faults, Ti-rich M3B4, and Nb-rich M3B4 at the grain boundaries as well as single-crystalline M5B3 and M3B2 inside the grains. Notably, the crystal structure of the faulted M5B3 was rationalized by a hybrid modelling approach integrating first-principles calculation and TEM experiments. The sublattice model, with the optimized thermodynamic model parameters, was used to reproduce the metal borides precipitation map in the TLP process using DICTRA software. Coupling with multiscale simulation and experimental data, the present work built a modified thermo-kinetic model, which enables the design of the TLP bonding process of Ni-based alloys that often involves complicated time-temperature schedules and the precipitation/dissolution of a variety of different phases. The strategy can be applied to the design of the brazing process of other alloys or hybrid materials such as ceramics and metal.

Application of modelling approaches of twin-screw compressors: thermodynamic investigation and reduced-order model identification

Refrigeration is an essential part of the food chain. It is used in all stages of the chain, from industrial food processing to final consumption at home. In these processes, mechanical refrigeration technologies are employed, where compressors increase gas pressure from evaporation to condensation. In industrial refrigeration systems, twin-screw compressors represent the most widely used technology. A detailed mathematical model of a twin-screw compressor has been developed in Simulink® using differential equations for energy and mass balances to simulate the compression cycle that includes suction, compression and discharge phases. Gas pressure and enthalpy can be calculated as time functions during the cycle. However, the computational times obtained limit the possibility to extend the use of the model in the development of control strategies for the whole refrigeration plant in its real operating conditions. Therefore, the detailed model has been used to train a simplified model developed in Matlab®: the simulated mass flow rate, shaft power and the fluid discharge temperature have been employed to identify several geometrical and thermodynamic parameters of the simplified model. The latter relies on non-linear algebraic equations and, thus, requires a very short computational time. A limited performance dataset has been used to train the model, and a different dataset to test it: the results of the models have been compared, and small errors in mass flow rate, shaft power and fluid discharge temperature have been observed.

Phase Equilibria and Minor Element Distributions in Complex Copper/Slag/Matte Systems

To address the increasing complexity of feed materials to pyrometallurgical processes, an integrated experimental and thermodynamic modeling research program is in progress to accurately characterize the multi-phase gas-slag-matte-speiss-metal-solids 17-component Cu/Pb-(Cu2O-PbO-ZnO-CaO-FeO-Fe2O3-SiO2)-(Al2O3-MgO)-S-(As-Bi-Sb-Sn-Ag-Au-Ni) system. New experimental data are used to continuously improve the thermodynamic database using FactSage. An example is provided on the slag-matte distributions of Bi, Pb, and Zn in equilibrium with tridymite in the Cu-Fe-O-S-Si system under copper smelting conditions. A closed system equilibration experimental technique with rapid quenching was used. Major element concentrations in phases were measured with electron probe x-ray microanalysis. A laser ablation inductively coupled plasma mass spectrum technique was used for determination of Bi, Pb, and Zn concentrations in slag. New experimental data contributed to the optimization of thermodynamic model parameters. Improved thermodynamic databases can be used to accurately predict the elemental distributions in multi-component systems; an example is given for the minor element distributions between slag and matte for industrial conditions.