Special Issue "Thermodynamics: Modeling and Simulation"

A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Chemical Systems".

Deadline for manuscript submissions: 31 August 2020.

Special Issue Editors

Dr. Andrew S. Paluch
Website
Guest Editor
Department of Chemical, Paper and Biomedical Engineering, Miami University, Oxford, OH 45056, USA
Interests: thermodynamics, phase-equilibrium, molecular simulation, separation processes
Dr. Juan Carlos Araque
Website
Guest Editor
School of Engineering, Benedictine College, USA
Interests: thermodynamics; process simulation; molecular dynamics simulations; Monte Carlo simulations and methods; statistical mechanics; structure and dynamics of ionic liquids; molecular modeling of DNA, copolymers, and nanoparticle systems

Special Issue Information

Dear Colleagues,

From its origins as a field of study during the Industrial Revolution to model and optimize the process of converting heat to work, thermodynamics remains central to the design and optimization of a wide range of chemical and biological processes, and the improvement of the welfare of society, from the design of novel, green refrigerants and solvents, the removal of emergent contaminants from wastewater, to the formulation of novel pharmaceuticals and beyond.

In this Special Issue, “Thermodynamics: Simulation and Modeling”, we highlight and celebrate the latest developments in thermodynamics research. Topics include but are not limited to the following:

  • Thermodynamic models for process modeling, simulation, optimization, and control: equations of state, excess Gibbs free energy models, and related methods;
  • Property prediction for early stage process development and design: molecular simulation, electronic structure calculations, and group-contribution methods;
  • Molecular thermodynamics for process intensification.

We welcome contributions in the form of full-length articles, short communications, and reviews.

Dr. Andrew S. Paluch
Dr. Juan Carlos Araque
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Processes is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Please note that for papers submitted after 30 June 2020 an APC of 1500 CHF applies. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • thermodynamics
  • phase-equilibrium
  • separation processes
  • process simulation
  • molecular simulation
  • equation of state
  • excess Gibbs free energy

Published Papers (15 papers)

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Research

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Open AccessFeature PaperArticle
Assessment of the SM12, SM8, and SMD Solvation Models for Predicting Limiting Activity Coefficients at 298.15 K
Processes 2020, 8(5), 623; https://doi.org/10.3390/pr8050623 - 22 May 2020
Abstract
The SMx (x = 12, 8, or D) universal solvent models are implicit solvent models which using electronic structure calculations can compute solvation free energies at 298.15 K. While solvation free energy is an important thermophysical property, within the thermodynamic modeling [...] Read more.
The SMx (x = 12, 8, or D) universal solvent models are implicit solvent models which using electronic structure calculations can compute solvation free energies at 298.15 K. While solvation free energy is an important thermophysical property, within the thermodynamic modeling of phase equilibrium, limiting (or infinite dilution) activity coefficients are preferred since they may be used to parameterize excess Gibbs free energy models to model phase equilibrium. Conveniently, the two quantities are related. Therefore the present study was performed to assess the ability to use the SMx universal solvent models to predict limiting activity coefficients. Two methods of calculating the limiting activity coefficient where compared: (1) the solvation free energy and self-solvation free energy were both predicted and (2) the self-solvation free energy was computed using readily available vapor pressure data. Overall the first method is preferred as it results in a cancellation of errors, specifically for the case in which water is a solute. The SM12 model was compared to both the Universal Quasichemical Functional-group Activity Coefficients (UNIFAC) and modified separation of cohesive energy density (MOSCED) models. MOSCED was the highest performer, yet had the smallest available compound inventory. UNIFAC and SM12 exhibited comparable performance. Therefore further exploration and research should be conducted into the viability of using the SMx models for phase equilibrium calculations. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Numerical Simulation for the Combustion Chamber of a Reference Calorimeter
Processes 2020, 8(5), 575; https://doi.org/10.3390/pr8050575 - 13 May 2020
Abstract
This paper focuses on the numerical modeling of the effect of the height of a combustion chamber on the development of a reference calorimeter whose objective is to measure the calorific value of natural gas. The impacts of temperature, velocity, and mass fraction [...] Read more.
This paper focuses on the numerical modeling of the effect of the height of a combustion chamber on the development of a reference calorimeter whose objective is to measure the calorific value of natural gas. The impacts of temperature, velocity, and mass fraction on the exhaust gases were evaluated by varying the height of the combustion chamber. The eddy dissipation concept (EDC) approach was used to model combustion with two different chemical kinetic mechanisms: one with three steps, called the three-step mechanism defined by default in the software used, and second skeletal model, which consists of 41 steps, through the ChemKin-import file with 16 species. The main result of this study is the selection of a combustion chamber height for the reference calorimeter that produces the best performance in the combustion process, which is 70 mm, as well as the main differences in using a three-step mechanism and a skeletal model to simulate an oxy-fuel combustion reaction. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Combined Analysis of Parameter Sensitivity and Exergy for Natural Gas Liquefaction in Cryogenic Fuel Production Process
Processes 2020, 8(5), 561; https://doi.org/10.3390/pr8050561 - 10 May 2020
Abstract
Compared with conventional natural gas, liquefied natural gas has the advantages of easier storage and transportation, more safety, less indirect investment, better peak regulation, and environmental protection. This paper studies the large-scale cryogenic propane precooled mixed refrigerant (C3MR) liquefied natural gas (LNG) process. [...] Read more.
Compared with conventional natural gas, liquefied natural gas has the advantages of easier storage and transportation, more safety, less indirect investment, better peak regulation, and environmental protection. This paper studies the large-scale cryogenic propane precooled mixed refrigerant (C3MR) liquefied natural gas (LNG) process. The phase equilibrium of the liquefaction process is calculated by the Peng-Robinsonstate equation using ASPEN. A numerical model for the thermal process simulation of the liquefaction process is established by MATLAB. Based on Active X technology, data invocation between software is realized, which overcomes the problem of process variable changes under limited degrees of freedom. The minimum sum of the propane precooling amount for the compressor energy consumption is used as the objective function, the control variate method is used to address the liquefaction process model, and the parameter sensitivity analysis is performed and combined with the exergy analysis. The effects of multiple parameters (e.g., the pressures and temperatures) on the process performance are analyzed and discussed. The results indicate that the combined analysis of the parameter sensitivity and exergy adopted in this paper are able to increase the system performance and reduce the exergy loss of equipment. The maximum reduction of the throttling loss of the process is 60.14%, and the total exergy loss is reduced by 25.8%. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Modeling of Novel Thermodynamic Cycles to Produce Power and Cooling Simultaneously
Processes 2020, 8(3), 320; https://doi.org/10.3390/pr8030320 - 09 Mar 2020
Abstract
Thermodynamic cycles to produce power and cooling simultaneously have been proposed for many years. The Goswami cycle is probably the most known cycle for this purpose; however, its use is still very limited. In the present study, two novel thermodynamic cycles based on [...] Read more.
Thermodynamic cycles to produce power and cooling simultaneously have been proposed for many years. The Goswami cycle is probably the most known cycle for this purpose; however, its use is still very limited. In the present study, two novel thermodynamic cycles based on the Goswami cycle are presented. The proposed cycles use an additional component to condense a fraction of the working fluid produced in the generator. Three cycles are modeled based on the first and second laws of thermodynamics: Two new cycles and the original Goswami cycle. The results showed that in comparison with the original Goswami cycle, the two proposed models are capable of increasing the cooling effect, but the cycle with flow extraction after the rectifier presented higher irreversibilities decreasing its exergy efficiency. However, the proposed cycle with flow extraction into the turbine was the most efficient, achieving the highest values of the energy utilization factor and the exergy efficiency. It was found that for an intermediate split ratio value of 0.5, the power produced in the turbine with the flow extraction decreased 23% but the cooling power was 6 times higher than that obtained with the Goswami Cycle. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessFeature PaperArticle
CFD Simulation of Forced Recirculating Fired Heated Reboilers
Processes 2020, 8(2), 145; https://doi.org/10.3390/pr8020145 - 22 Jan 2020
Cited by 1
Abstract
An advanced algorithm has been developed in order to analyze the performance of re-boiling process of crude oil flowing inside reboilers tubes. The proposed model is composed from Heptane fire heater and a tube array. The heat flux produced from burner is transferred [...] Read more.
An advanced algorithm has been developed in order to analyze the performance of re-boiling process of crude oil flowing inside reboilers tubes. The proposed model is composed from Heptane fire heater and a tube array. The heat flux produced from burner is transferred to the crude oil flowing inside the tube. The computational model is composed of two phases—Simulation of fire by using Fire Dynamics Simulator software (FDS) version 5.0 and then a nucleate boiling computation of the crude oil. FDS code is formulated based on CFD (Computational Fluid Dynamics) of fire heater. The thermo-physical properties (such as: thermal conductivity, heat capacity, surface tension, viscosity) of the crude oil were estimated by using empirical correlations. The thermal heat transfer to evaporating two-phase crude oil mixture occur by bubble generation at the wall (nucleate boiling) has been calculated by using Chen correlation. It has been assumed that the overall convective heat transfer coefficient is composed from the nucleate boiling convective coefficient and the forced turbulent convective coefficient. The former is calculated by Forster Zuber empirical equation. The latter is computed from the Dittus-Boelter relationship. In order to validate the nucleate boiling heat transfer coefficient, a comparison has been performed to nucleate boiling convective coefficient obtained by Mostinski equation. The relative error between the nucleate boiling convective heat-transfer coefficients is 10.5%. The FDS numerical solution has been carried out by using Large Eddy Simulation (LES) method. This work has been further extended to include also the structural integrity aspects of the reboiler metal pipe by using COMSOL Multiphysics software. It was found out, that the calculated stress is less than the ultimate tensile strength of the AISI 310 Steel alloy. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Diffusion in Binary Aqueous Solutions of Alcohols by Molecular Simulation
Processes 2019, 7(12), 947; https://doi.org/10.3390/pr7120947 - 12 Dec 2019
Abstract
Based on the molecular dynamics method, the calculations for diffusion coefficients were carried out in binary aqueous solutions of three alcohols: ethanol, isopropanol, and tert-butanol. The intermolecular potential TIP4P/2005 was used for water; and five force fields were analyzed for the alcohols. The [...] Read more.
Based on the molecular dynamics method, the calculations for diffusion coefficients were carried out in binary aqueous solutions of three alcohols: ethanol, isopropanol, and tert-butanol. The intermolecular potential TIP4P/2005 was used for water; and five force fields were analyzed for the alcohols. The force fields providing the best accuracy of calculation were identified based on a comparison of the calculated self-diffusion coefficients of pure alcohols with the experimental data for internal (Einstein) diffusion coefficients of alcohols in solutions. The temperature and concentration dependences of the interdiffusion coefficients were determined using Darken’s Equation. Transport (Fickian) diffusion coefficients were calculated using a thermodynamic factor determined by the non-random two-liquid (NRTL) and Willson models. It was demonstrated that for adequate reproduction of the experimental data when calculating the transport diffusion coefficients, the thermodynamic factor has to be 0.64. Simple approximations were obtained, providing satisfactory accuracy in calculating the concentration and temperature dependences of the transport diffusion coefficients in the studied mixtures. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessFeature PaperArticle
Energetic Analysis of Different Configurations of Power Plants Connected to Liquid Chemical Looping Gasification
Processes 2019, 7(10), 763; https://doi.org/10.3390/pr7100763 - 18 Oct 2019
Cited by 1
Abstract
In this article, a thermodynamic study was conducted on the energetic and exergy performance of a new configuration of liquid chemical looping gasification (LCLG) plant integrated with a power block to assess the overall performance of the system including exergy partitioned in syngas [...] Read more.
In this article, a thermodynamic study was conducted on the energetic and exergy performance of a new configuration of liquid chemical looping gasification (LCLG) plant integrated with a power block to assess the overall performance of the system including exergy partitioned in syngas and first law efficiency (FLE). LCLG is a relatively new concept for the production of high-quality synthetic gas from solid feedstock such as biomass. As the temperature and pressure of the looping system are high, there is thermodynamic potential to co-produce chemical products, power and heat. Hence, in the present work, three different configurations of a power cycle were thermodynamically assessed. In the first proposed power cycle, the produced syngas from the gasifier was combusted in a combustion chamber and the exhausted gases were fed into a gas turbine. In the second and third proposed power cycles, the hot air was directly fed into a gas turbine or was used to produce steam for the steam turbine combined cycle. The processes were simulated with Aspen Plus and Outotec HSC chemistry software packages. The influence of different operating parameters including temperature and pressure of the air reactor and type of oxygen carrier on the first law and exergy efficiency (exergy partitioned in synthetic gas) was assessed. Results showed that the FLE for the proposed gas turbine and steam turbine combined cycles was ~33% to 35%, which is within the range of the efficiency obtained for the state-of-the-art power cycles reported in the literature. Results also showed that lead oxide was a suitable oxygen carrier for the LCLG system, which can be integrated into a steam turbine combined cycle with an FLE of 0.45, while copper oxide showed an FLE of 0.43 for the gas turbine combined cycle. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Multi-Scale Multi-Field Coupled Analysis of Power Battery Pack Based on Heat Pipe Cooling
Processes 2019, 7(10), 696; https://doi.org/10.3390/pr7100696 - 03 Oct 2019
Abstract
Based on the study of the relationship between micro and macro parameters in the actual microstructure of the electrodes, a new multi-scale multi-field coupling model of battery monomer is established and the heat generation rate of the battery is obtained by detailed numerical [...] Read more.
Based on the study of the relationship between micro and macro parameters in the actual microstructure of the electrodes, a new multi-scale multi-field coupling model of battery monomer is established and the heat generation rate of the battery is obtained by detailed numerical simulation. According to the parameters of a certain electric vehicle and battery selected, the structure of the power battery pack and heat pipe cooling system is designed. Through multi-field coupling computational fluid dynamics simulation, the temperature difference of the battery pack is gained. By changing the fin spacing, the cooling scheme of the heat pipe is optimized, which ensures that the temperature difference is less than 5 K and the maximum temperature of the battery system is 306.26 K. It is found that increasing the discharge rate, the temperature difference increases rapidly. Increasing the air inlet velocity can improve the thermal uniformity of the battery pack, but changing the air inlet temperature only determines the range of temperature, it cannot improve the thermal uniformity. The method proposed and results gained can provide a reference for the research of heat management systems with heat pipe of lithium-ion power battery pack for vehicles. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Numerical Study of the Effects of Injection Fluctuations on Liquid Nitrogen Spray Cooling
Processes 2019, 7(9), 564; https://doi.org/10.3390/pr7090564 - 23 Aug 2019
Cited by 1
Abstract
Spray cooling with liquid nitrogen is increasingly utilized as an efficient approach to achieve cryogenic cooling. Effects of injection mass flow rate fluctuations on the evaporation, temperature distribution, and droplet distribution of a spray field were examined by employing a validated Computational Fluid [...] Read more.
Spray cooling with liquid nitrogen is increasingly utilized as an efficient approach to achieve cryogenic cooling. Effects of injection mass flow rate fluctuations on the evaporation, temperature distribution, and droplet distribution of a spray field were examined by employing a validated Computational Fluid Dynamics (CFD) numerical model. The numerical results indicated that injection fluctuations enhanced the volume-averaging turbulent kinetic energy and promoted the evaporation of the whole spray field. The strengthened mass and heat transfer between the liquid nitrogen droplets and the surrounding vapor created by the fluctuating injection led to a lower temperature of the whole volume. A relatively smaller droplet size and a more inhomogeneous droplet distribution were obtained under the unsteady inlet. The changes of the frequency and the amplitude of the fluctuations had little effects on the overall spray development. The results could enrich the knowledge of the relation between the inevitable fluctuations and the overall spray development and the cooling performance in a practical spray cooling system with cryogenic fluids. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Study on Wear Properties of the Flow Parts in a Centrifugal Pump Based on EDEM–Fluent Coupling
Processes 2019, 7(7), 431; https://doi.org/10.3390/pr7070431 - 09 Jul 2019
Abstract
By using EDEM–Fluent codes and coupling the continuous fluid medium with a solid particle discrete element, the solid–liquid two-phase flow field in a centrifugal pump was simulated under the same inlet conditions of the particle volume fraction and three flow conditions of 0.7 [...] Read more.
By using EDEM–Fluent codes and coupling the continuous fluid medium with a solid particle discrete element, the solid–liquid two-phase flow field in a centrifugal pump was simulated under the same inlet conditions of the particle volume fraction and three flow conditions of 0.7Qd, 1.0Qd and 1.3Qd. By introducing the Archard wear model, the wear was calculated, and the wear law was obtained for the pump flow parts such as the leading edge of the impeller blade, blade tip, blade pressure side, blade suction side, impeller shroud, hub and volute. The results demonstrate that the wear of volute is about 70% of the total wear of pump. The wear in the impeller mainly occurs in the blade leading edge, the junction of the hub and the trailing part of the blade pressure side, and the junction of the shroud and the rear part of the blade suction side. Under lower flow conditions, the wear in the impeller shroud is relatively considerable. As the flow rate increases, the wear in the blade pressure side and the hub increases significantly. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Finite Time Thermodynamic Optimization of an Irreversible Proton Exchange Membrane Fuel Cell for Vehicle Use
Processes 2019, 7(7), 419; https://doi.org/10.3390/pr7070419 - 03 Jul 2019
Cited by 1
Abstract
A finite time thermodynamic model of an irreversible proton exchange membrane fuel cell (PEMFC) for vehicle use was established considering the effects of polarization losses and leakage current. Effects of operating parameters, including operating temperature, operating pressure, proton exchange membrane water content, and [...] Read more.
A finite time thermodynamic model of an irreversible proton exchange membrane fuel cell (PEMFC) for vehicle use was established considering the effects of polarization losses and leakage current. Effects of operating parameters, including operating temperature, operating pressure, proton exchange membrane water content, and proton exchange membrane thickness, on the optimal performance of the irreversible PEMFC are numerically studied in detail. When the operating temperature of the PEMFC increases, the optimal performances of PEMFC including output power density, output efficiency, ecological objective function, and ecological coefficient of performance, will be improved. Among them, the optimal ecological objective function increased by 81%. The proton film thickness has little effect on the output efficiency and the ecological of coefficient performance. The maximum output power density increased by 58% as the water content of the proton exchange membrane increased from 50% to the saturation point. The maximum output power density increases with the operating pressure. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Isosteric Heat: Comparative Study between Clausius–Clapeyron, CSK and Adsorption Calorimetry Methods
Processes 2019, 7(4), 203; https://doi.org/10.3390/pr7040203 - 10 Apr 2019
Cited by 5
Abstract
This work presents the calorimetric study of five adsorbents with different chemical and textural characteristics: MOF-199, MCM-41, SBA-15, activated carbon prepared from corn cob (GACKP) and graphite. These solids were used to establish the differences between isosteric heats evaluated by three different methods: [...] Read more.
This work presents the calorimetric study of five adsorbents with different chemical and textural characteristics: MOF-199, MCM-41, SBA-15, activated carbon prepared from corn cob (GACKP) and graphite. These solids were used to establish the differences between isosteric heats evaluated by three different methods: Clausius–Clapeyron (C-C), Chakraborty, Saha and Koyama (CSK) and Adsorption Calorimetry (A-Cal). The textural characterization results show solids that have values of specific surface area between 2271 m2·g−1 for the MOF-199 and 5.2 m2·g−1 for the graphite. According to the results obtained for the isosteric heats for each sample, the magnitude varies depending on the coverage of the adsorbate and the textural characteristics of each adsorbent. Solids with an organized structure have isosteric heat values that are coincident among the three methods. Meanwhile, heterogeneous solids such as activated carbon values evaluated by the CKS and C-C have a high dispersion method regarding the adsorption calorimetry method. The results obtained show that the adsorption calorimetry, being a direct experimental measurement method, presents less dispersed data. At low quantities, the isosteric heat of nitrogen adsorption decreased in the order MOF-199, GACKP, MCM-41, SBA-15 and Graphite. The order for the isosteric heats values was coherent with the surface characteristics of each of the solids, especially with the pore size distribution. Finally, throughout the coverage examined in this work, the isosteric heats for nitrogen adsorption determined by adsorption calorimetry (A-Cal) were larger than the evaluated by C-C and CSK indirect methods of vaporization. According to the results, it is shown that the adsorption calorimetry allows values of the isosteric heats of adsorption with an error of less than 2% to be established and also reveals the complex nature of the heterogeneity or homogeneity of the adsorbent. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Immersion Enthalpy of Activated Carbon–Cyclohexane and Activated Carbon–Hexane. Difference in the Solid–Liquid Interaction Enthalpy Due to the Structure of the Solvent
Processes 2019, 7(4), 180; https://doi.org/10.3390/pr7040180 - 28 Mar 2019
Abstract
The enthalpy of immersion for five activated carbons (with different surface chemistry) in cyclohexane and hexane was determined in order to observe the intensity of the solid–liquid interaction. The enthalpy of immersion was related to the properties of activated carbons, such as micropore [...] Read more.
The enthalpy of immersion for five activated carbons (with different surface chemistry) in cyclohexane and hexane was determined in order to observe the intensity of the solid–liquid interaction. The enthalpy of immersion was related to the properties of activated carbons, such as micropore volume, total basic groups content, and the EoWo product, that characterized each solid-liquid system. The values for the immersion enthalpy were between −21.2 and −91.7 J g−1 for cyclohexane and between −16.4 and −66.1 J g−1 for hexane. It showed greater interaction between the cyclohexane and the activated carbons and it was related to the properties of this adsorbate, such as molecular size and molecular arrangement. The difference in the enthalpy of immersion between the solvents per unit of micropore volume for the set of activated carbons was calculated obtaining a value of −487 J cm−3. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Open AccessArticle
Measurement and Correlation of the Solubility of β-Cyclodextrin in Different Solutions at Different Temperatures and Thermodynamic Study of the Dissolution Process
Processes 2019, 7(3), 135; https://doi.org/10.3390/pr7030135 - 05 Mar 2019
Abstract
A new improved formulation was studied to improve the rehydration properties of freeze-dried dumplings. To provide basic data for industrial applications, the solubility capabilities of β-Cyclodextrin in sucrose, NaCl, and a mixed solution were measured at temperatures ranging from 303.15 to 353.15 K [...] Read more.
A new improved formulation was studied to improve the rehydration properties of freeze-dried dumplings. To provide basic data for industrial applications, the solubility capabilities of β-Cyclodextrin in sucrose, NaCl, and a mixed solution were measured at temperatures ranging from 303.15 to 353.15 K using a laser monitoring method. The experimental values indicated that the solubility of β-Cyclodextrin in solvents increased with increasing temperature. The simplified Apelblat model, Apelblat model, and λh model were employed to analyze the experimental results using correlation tests. The relative average deviation (RAD) values between the experimental and calculated values were less than 0.095, 0.075, and 0.103 for the simplified Apelblat equation, Apelblat equation, and λh equation, respectively. Apparent thermodynamic analysis of β-Cyclodextrin dissolution was also performed at the mean temperature using the model parameters of Apelblat equation. Furthermore, thermodynamic properties of the solution process, including the enthalpy, entropy, and Gibbs free energy, were also calculated and analyzed. This study provides the basic data for applications in industrial production, and is specifically of great significance for the improved formulation of freeze-dried dumplings. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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Review

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Open AccessFeature PaperReview
Experimental Data of Fluid Phase Equilibria- Correlation and Prediction Models: A Review
Processes 2019, 7(5), 277; https://doi.org/10.3390/pr7050277 - 10 May 2019
Cited by 4
Abstract
The examples of phase equilibria in binary systems, solid/liquid (SLE), liquid/liquid (LLE), vapor/liquid (VLE), as well as liquid/liquid equilibria in ternary systems mainly containing ionic liquids (ILs), or the infragrance materials, or pharmaceuticals with molecular organic solvents, such as an alcohol, or water, [...] Read more.
The examples of phase equilibria in binary systems, solid/liquid (SLE), liquid/liquid (LLE), vapor/liquid (VLE), as well as liquid/liquid equilibria in ternary systems mainly containing ionic liquids (ILs), or the infragrance materials, or pharmaceuticals with molecular organic solvents, such as an alcohol, or water, or hydrocarbons, are presented. The most popular correlation methods of the experimental phase equilibrium data are presented, related to the excess Gibbs free energy models such as Wilson, universal-quasichemical, UNIQUAC and non-random two-liquid model, NRTL as well as several popular theories for the modeling of the phase equilibria and excess molar enthalpy, HE in binary or ternary mixtures are presented: the group contribution method (Mod. UNIFAC) and modified UNIFAC model for pharmaceuticals and lattice theory based on non-random hydrogen bonding (NRHB). The SLE, LLE, or VLE and HE of these systems may be described by the Perturbed-Chain Polar Statistical Associating Fluid Theory (PC-SAFT), or a Conductor-like Screening Model for Real Solvents (COSMO-RS). The examples of the application of ILs as extractants for the separation of aromatic hydrocarbons from alkanes, sulfur compounds from alkanes, alkenes from alkanes, ethylbenzene from styrene, butan-1-ol from water phase, or 2-phenylethanol (PEA) from water are discussed on the basis of previously published data. The first information about the selectivity of extrahent for separation can be obtained from the measurements of the limiting activity coefficient measurements by the gas–liquid chromatography technique. This review outlines the main research work carried out over the last few years on direct measurements of phase equilibria, or HE and limiting activity coefficients, the possibility of thermodynamic modeling with emphasis on recent research achievements and potential for future research. Full article
(This article belongs to the Special Issue Thermodynamics: Modeling and Simulation)
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