Liquid Activity Coefficient Model Research Articles

Kinetics of cashew apple drying through mechanistic models and analysis of the effects of drying conditions on the retention of bioactive compounds

AbstractGlobal cashew nut production is nearly 4 million tons per year, valued at 7 billion US dollars. Remarkably, almost the entire cashew apple crop, amounting to 20 million tons annually, goes to waste. However, the cashew apple contains valuable nutraceutical compounds, including tannins, polyphenols, and carotenoids, estimated to be worth 150 million US dollars annually. Due to the highly perishable nature of cashew apples, degradation is a significant issue. In response, the current work has established drying as an effective preservation technique for these bioactive components. The effect of drying temperature on bioactive compounds has been thoroughly investigated. The non‐random two liquid (NRTL) activity coefficient model effectively captures the thermodynamics of the drying process. To facilitate the selection and design of drying equipment, two mechanistic mass transfer models were developed. The first model employs the Maxwell‐Stefan framework to account for internal diffusion, with external mass transfer resistance appearing as a boundary condition. While this model works well for products like grapes, it proved inadequate for explaining the drying behaviour of cashew apples. Consequently, a second model was developed, postulating rapid moisture transport by capillary action within the cashew apple. This model effectively captures the effects of a wide range of operating conditions, using only external mass transfer resistance as the tuneable kinetic parameter. This mechanistic model is more suitable for dryer design compared to conventional phenomenological models like the logarithmic model and the two‐term exponential model.

Comparison of solubility of trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) and trans-1,1,1,4,4,4-hexafluoro-2-butene (R1336mzz(E)) in two lubricants: An experimental study

Trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) and trans-1,1,1,4,4,4-hexafluorobut-2-ene (R1336mzz(E)) are environmentally friendly working fluids with low global warming potential (GWP) that can be used in compression refrigeration and heat pump systems. In this study, a solubility measurement system was established to assess the solubility of R1234ze(E) and R1336mzz(E) in polyalkylene glycol ether (PAG) and polyol ester (POE) at temperatures (283.15–323.15 K). The Henry's constants for four binary systems R1234ze(E)/PAG, R1336mzz(E)/PAG, R1234ze(E)/POE, and R1336mzz(E)/POE were analyzed and compared. Additionally, The non-random two liquid (NRTL) activity coefficient model was applied to correlate the solubility data in this study. The results indicate that R1234ze(E) exhibits higher solubility in PAG lubricant, while R1336mzz(E) is more easily dissolved in POE lubricant. Moreover, the solubility of R1336mzz(E) in both PAG and POE lubricants shows greater sensitivity to pressure and temperature changes compared to R1234ze(E). The results reported in this study can serve as a valuable guide for the choice of suitable lubricants for R1234ze(E) and R1336mzz(E) in different applications.

Investigating the effect of blending of diamine and alkanolamine for CO2 capture: Experiment and thermodynamic modeling of CO2-AEEA-DEA-H2O system

This study reports the experimental data on CO2 solubility in aqueous aminoethylethanolamine (AEEA) and diethanolamine (DEA) under different amine blending ratios (9:21, 15:15 and 21:9 wt% AEEA: DEA, respectively and remaining 70 wt% being the water), CO2 partial pressure up to 477.4 kPa and temperatures up to 393.15 K. The complex nature of AEEA diamine and DEA was thermodynamically modeled to evaluate the behavior of aqueous blend of AEEA and DEA for CO2 capture. The electrolyte nonrandom two liquid (electrolyte NRTL) activity coefficient model is used to incorporate the nonideality of the system. The system of blended aqueous AEEA and DEA contained twelve equilibrium equations, three mass balance equations, one charge balance equation and one hydronium ion-based polynomial. These equations were simultaneously solved by using an inhouse built MATLAB code to determine the CO2 loading, CO2 cyclic capacity, pH, heat of absorption, activity coefficients and concentration of seventeen species in the system. Model results have been compared with literature and inhouse experimental data, which are in a good agreement. Furthermore, study reports activity coefficients, mole fractions of seventeen species, dependence of CO2 loading on temperature, pressure and concentration of individual amine. The Absolute average deviation percent in the model and experimental data for AEEA, DEA and their blend are 9.90%, 7.61% and 8.55%, respectively for CO2 loading.

Measurement and Correlation of the Liquid-Liquid Equilibria of Tertiary-Butyl Alcohol – Water – Benzene System at 30°C and 1 Atmosphere Pressure

The Liquid-Liquid equilibria of Tertiary-Butyl Alcohol – Water – Benzene System were measured experimentally at 30°C and 1atm pressure. The experimental binodal curve compositions were obtained using the cloud point method. The compositions of the two equilibrium phases were analysed using Agilent 7820A series Gas Chromatograph. The consistency of the experimental data was determined using the Hand, Othmer-Tobias and Bachman- Brown correlation equations while the plate point was determined using the Treybal’s method. The effectiveness of the solvent in the extraction was determined by calculating the distribution coefficients and separation factors. The experimental tie-line data were correlated with the Universal Quasi-Chemical (UNIQUAC) and Non-Random Two Liquid (NRTL) activity coefficient models. Also, the deviation between the experimental and calculated equilibrium compositions were calculated using the root mean squared deviation equation. The UNIQUAC predicted data gave a closer resemblance to the experimental.

Isothermal vapour-liquid equilibrium data for environmentally friendly binary system {R1234ze(E) + R245fa}

A static analytical device was used in this investigation to collect the vapor pressures of R245fa and R1234ze(E), as well as the vapor liquid equilibrium (VLE) data of their combination, when the temperature was altered from T = 293.15 K to T = 323.15 K. According to the existing literature, no informative data about this combination exists in this temperature range. We also present the uncertainty of the acquired temperature, pressure, and molar fraction of the experimental equipment for the scientific accuracy of the data. The phase equilibrium values were regressed by two models (Peng-Robinson EoS + van der Waals rule model and the Peng-Robinson EoS + Huron-Vidal rule with non-random two liquid activity coefficient model), respectively, to compare their correlation results, which shows that the performances of both models are satisfactory, with the second model being more appropriate because the deviation of pressure correlation is smaller. Zeotropic behaviors have been found during the temperature range.

Ethylene Glycol을 이용하여 폐 유기용제로부터 고순도 Methylene Chloride 회수를 위한 추출증류공정의 전산모사 및 공정 최적화

The purpose of this study was to investigate the simulation and optimization of extraction distillation process for recovery of high purity methylene chloride (MC) from waste organic solvent using ethylene glycol (EG). NRTL liquid activity coefficient model was adopted for phase equilibrium calculations and PRO/Ⅱ, a commercial process simulator, was used to simulate the extractive distillation process. Based on the analysis results, it turned out that the optimum feed stage for introducing raw materials (Waste organic solvent) into the extractive distillation column (T-01) is the 60th stage. As a result of analyzing the heat duty of re-boiler and the purity of MC, the MC recovery flow rate, the water concentration, etc. to select the optimum feed stage and the optimum inflow flow rate of ethylene glycol (EG), it turned out that the optimum feed stage of EG is the fifth stage and the optimum inflow flow rate of EG is 1,8000 kg/hr. As a result of analyzing the purity of MC and the recovery flow rate of MC according to the reflux ratio of the extractive distillation column (T-01), it was found that when the reflux ratio is 3.5, the purity of methylene chloride could be maintained 0.997 as mass fraction and the recovery flow rate of MC is maximum. As a result of analyzing the optimum feed stage for introducing the heavy stream flowing out from the bottom of the extraction solvent column (T-01) into the solvent recovery column (T-02), it turned out that the optimum feed stage of the heavy stream is the 60th stage. It was analyzed that the optimum distillate to feed ratio (D·F) of the solvent recovery column (T-02) was 0.10 and the optimum reflux ratio is 0.30, respectively.

Linear relationships for modeling CO2 absorption in aqueous alkanolamine solutions in a thermodynamically consistent way

AbstractA thermodynamically consistent model for the carbon dioxide (CO2) absorption in aqueous alkanolamine system is of great importance in the research and development of a CO2 capture process. To facilitate the development of thermodynamic models, linear Gibbs free energy, enthalpy, and heat capacity relationships using well‐known amines as reference are used to correlate the standard reference state properties of ionic species with those of molecular species in the electrolyte system, which has been approved to provide a reliable and consistent way to estimate required parameters when there is minimal or no appropriate experimental data available. The proposed relationships have been applied to the development of an electrolyte nonrandom two liquid (NRTL) activity coefficient model for CO2 absorption in aqueous 1‐amino‐2‐propanol (A2P) solution, as an example to demonstration the methodology. With limited vapor–liquid equilibrium data and other thermodynamic properties, the parameters in the electrolyte NRTL model are identified with good accuracy.

Quaternary liquid-liquid equilibria measurements and NRTL modelling for the (Water + Ethanol + 2-Propanol + 2,2,4-Trimethylpentane) system at 298.2K to 328.2K

In this work, the influence of a second alcohol on the phase behaviour of (water + alcohol + entrainer) systems was investigated by measuring Liquid-Liquid Equilibrium (LLE) data for the quaternary system of (water + ethanol + 2-propanol + isooctane) under isobaric (0.1 MPa) conditions. Data were measured at three ethanol: 2-propanol ratios to characterise the quaternary system behaviour, and for the constituent ternary (water + ethanol + isooctane) and (water + 2-propanol + isooctane) systems at 298.2 K. The measured quaternary data exhibit an evolution in phase behaviour between the constituent ternary systems in both the miscibility and total alcohol distribution between the aqueous and organic phases. The individual alcohol behaviour highlights the differing intermolecular interactions occurring in the systems, resulting in an increased recovery of ethanol to the organic phase and 2-propanol to the aqueous phase in the quaternary system. Further, the influence of temperature on the quaternary system's phase behaviour was investigated by measuring the quaternary system's data at four temperatures (298.2 K, 308.22 K, 318.2 K, and 328.2 K).The ternary (water + alcohol + entrainer) LLE literature and experimental data were correlated well using the Non-Random Two Liquid (NRTL) activity coefficient model with binary interaction parameters (BIPs) incorporating linear temperature dependence. These BIPs acceptably predicted the quaternary system's total alcohol behaviour, but only qualitatively captured the correct individual alcohol behaviour.

Solubility of Phthalic Acid and o-Toluic Acid in Seven Organic Solvents: Experimental Measurement and Thermodynamic Modeling

In this study, the solubility of phthalic acid and o-toluic acid in propionic acid, N-methylformamide, N,N-dimethylformamide (DMF), N,N-dimethylacetamide (DMAC), dimethyl sulfoxide (DMSO), N-methylpyrrolidone (NMP), and acetonitrile are measured under atmospheric pressure (101.3 kPa) by the method of laser dynamics. The experimental temperature range is 286.35 to 338.75 K. The measured data shows that the solubility of phthalic acid and o-toluic acid increases with increasing temperature in the temperature range studied. The experimental data are correlated by the Apelblat model, the λh model, and the modified nonrandom two liquid activity coefficient model, and the calculated solubility is in agreement satisfactorily with the measured results. Akaike information criterion analysis results show that the Apelblat model was the most suitable model to correlate the solubility of phthalic acid in propionic acid, N-methylformamide, and DMSO and the solubility of o-toluic acid in propionic acid, DMSO, and NMP; the λh model was the most suitable model to correlate the solubility of phthalic acid in DMF and DMAC and the solubility of o-toluic acid in N-methylformamide and DMF; and the modified NRTL model was the most suitable model to correlate the solubility of phthalic acid in NMP and acetonitrile and the solubility of o-toluic acid in DMAC and acetonitrile.

Extractive desulfurization of dibenzothiophene from normal octane using deep eutectic solvents as extracting agent

Among the most important causes of air pollution we may refer to hydrocarbon fuels with a large content of organosulfur compounds. These compounds must be removed to the level of standard concentration for which different techniques are commonly in use. Since, desulfurization of aromatic sulfur compounds, such as thiophenes, is not possible by common methods such as hydrodesulfurization, other methods should be considered. In recent years, scientists have focused on extractive desulfurization using Deep Eutectic Solvents (DES) as a new method for removing organosulfurs from hydrocarbon fuels. In this research, two new DESs are synthesized. As the model fuel, we used n-octane, and dibenzothiophene (DBT) was chosen as the organosulfur content with a 1000 ppm concentration. DESs were synthesized by mixing quaternary ammonium salts and trifluoroacetic acid in a heating method. The structures of DESs were confirmed by FTIR and H-NMR analyses. The extraction process was first carried out at temperatures ranging from 25 to 40 °C. The results showed that the best temperature was 35 °C. Then, the effect of fuel to DES mass ratio (i.e. different compositions of feed), on extraction efficiency was examined. For thermodynamic modeling of liquid–liquid equilibrium the Non Random Two Liquid (NRTL) activity coefficient model was implemented. The parameters of the NRTL model were correlated using the binary data obtained from solubility experiments. Finally, the adjusted parameters were used for predicting ternary phase equilibrium data obtained in this work. The root mean square deviation from experimental data was less than 0.11% for each solvent.

Solubility of benzoic acid in twelve organic solvents: Experimental measurement and thermodynamic modeling

The solubility of benzoic acid in 1,2-ethanediol, 3,6-dioxa-1-decanol, octane, 3-oxa-1,5-pentanediol, N,N-dimethylacetamide, 1,4-dimethylbenzene, 1,3-dimethylbenzene, 1,2-dimethylbenzene, propanoic acid, cyclohexanone, decahydronaphthalene, thiacyclopentane dioxide were measured by the laser dynamic method. The experimental temperature ranged from 286.15 K to 354.15 K. The results show that within the temperature range studied, the solubility of benzoic acid would increase with the gradually increasing of temperature. Meanwhile, three thermodynamic models (Apelblat model, λh model, the modified non-random two liquid (NRTL) activity coefficient model) were used to correlate the experimental data, and the calculated solubility agreed satisfactorily with the measured results. The result of Akaike Information Criterion (AIC) analysis showed that the Apelblat model was the best model to correlate the solubility of benzoic acid in N,N-dimethylacetamide, the λh model was the best model to correlate the solubility of benzoic acid in octane, and the modified NRTL model was the best model to correlate the solubility of benzoic acid in 1,2-ethanediol, 3,6-dioxa-1-decanol, 3-oxa-1,5-pentanediol, 1,4-dimethylbenzene, 1,3-dimethylbenzene, 1,2-dimethylbenzene, propanoic acid, cyclohexanone, decahydronaphthalene and thiacyclopentane dioxide. Furthermore, the thermodynamic functions (dissolution enthalpy, entropy, Gibbs energy) were obtained from the SLE data by using the van't Hoff equation.

Phase equilibrium and diffusivities of hydrofluorocarbons in a synthetic polyol ester lubricant

AbstractDetailed knowledge about the thermophysical properties of refrigerant/lubricant systems, such as solubility and diffusivity, are required for the design, operation, and long‐term reliability of heating, ventilation, air‐conditioning, and refrigeration equipment. Herein, vapor–liquid equilibrium of hydrofluorocarbons (HFCs) 1,1,1,2‐tetrafluoroethane (R‐134a), pentafluoroethane (R‐125), and difluoromethane (R‐32) in a polyol ester oil (ISO VG 32) were measured using a gravimetric microbalance at temperatures ranging from 248.15 to 348.15 K and up to 1.0 MPa of pressure. The experimental solubility data of each refrigerant/lubricant system were successfully modeled using the nonrandom two liquid activity coefficient model. A one‐dimensional diffusion equation was applied on time‐dependent absorption data to determine binary diffusion coefficients (D) for the refrigerants in the ISO VG 32 lubricant. Finally, Stokes–Einstein diffusing radius calculations support the hypothesis that HFCs dissolve into ISO VG 32 lubricant as individual molecules rather than associated complexes.

Liquid–Liquid Equilibrium for the Ternary Systems Water + 1-Butanol + 1-Hexanol or 1-Octanol at 303.15, 313.15, and 323.15 K

Liquid–liquid equilibrium data (LLE) of ternary systems {water + 1-butanol + 1-hexanol} and {water + 1-butanol + 1-octanol} were investigated at 303.15, 313.15, and 323.15 K at 101.3 kPa. The distribution coefficient (D) and selectivity factor (S) were calculated from experimental LLE data. Meanwhile, the effect of temperature on the two-phase zone of the two systems was discussed. The nonrandom two liquid and universal quasi-chemical activity coefficient models were used to regress experimental data sets and generate the relevant binary interaction parameters. Both thermodynamic models provided similar good descriptions for the studied systems with root mean square deviations between the calculated and experimental values less than 0.3%.

Measurement and correlation for solubilities of succinic acid, glutaric acid and adipic acid in five organic solvents

In this study, the solid-liquid equilibrium (SLE) data of succinic acid (SA) and glutaric acid (GA) and adipic acid (AA) in N,N-dimethylformamide (DMF), N,N-dimethylacetamide (DMAC), dimethyl sulfoxide (DMSO), 1-Methyl-2-pyrrolidinone (NMP) and sulfolane were determined by using the method of dynamic laser at atmospheric pressure. The experimental SLE data indicates that within the temperature range studied (286.25–358.75 K), the solubilities of SA, GA and AA in above five solvents is proportional to the temperature. Meanwhile, three thermodynamic models (Apelblat model, λh model, the modified nonrandom two liquid (NRTL) activity coefficient model) were used to correlate the experimental data, the results show that the correlated data is generally consistent with the experimental data. The result of Akaike Information Criterion (AIC) analysis filter out the best model for every system. In addition, the thermodynamic functions (dissolution enthalpy, entropy, Gibbs energy) were obtained from the SLE data by calculating the van't Hoff equation.

110th Anniversary: The First Thermodynamic and Kinetic Analysis of Ammonia in Imidazolium-Based Ionic Liquids Using a Gravimetric Microbalance

The first vapor liquid equilibrium (VLE) measurements for the binary systems of ammonia (NH3) and three imidazolium-based ionic liquids (ILs) have been successfully measured using a gravimetric microbalance. ILs 1-butyl-3-methylimidazolium hexafluorophosphate ([C4C1im][PF6]), 1-butyl-3-methylimidazolium tetrafluoroborate ([C4C1im][BF4]), and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C2C1im][NTf2]) were measured at temperatures of 283.15, 298.15, 323.15, and 348.15 K and at pressures up to 0.7 MPa using the new Hiden XEMIS gravimetric microbalance. The VLE data were correlated using the Peng–Robinson equation of state and the Non-Random Two Liquid (NRTL) activity coefficient models. Both models are in excellent agreement with the experimental data. The Fickian diffusivities of NH3 in imidazolium-based ILs were obtained fitting experimental concentration to the one-dimensional (1D) mass diffusion equation, and found to be about 3 to 5 times lower than the diffusion of NH3 in water (H2O...

Thermodynamic analysis of EMISE–Water as a working pair for absorption refrigeration system

In this paper, thermodynamic analysis of novel ionic liquid 1 Ethyl-3-methylimidazolium ethyl sulphate (EMISE) as absorbent and water as green refrigerant for absorption refrigeration system (ARS) is performed. Thermodynamics excess properties like excess Gibbs free energy (GE), excess enthalpy (hE) and equilibrium Dühring’s plot (P-T-x1) of EMISE-H2O binary mixture are assessed using non-random two liquid (NRTL) activity coefficient model for composition x1 of 0.45–1. The performance of single effect ARS with SHE are mathematically modeled and simulated by applying first and second laws (exergy analysis) of thermodynamics. Simulated results of ARS are compared with other widely used working fluids and revealed higher COP of 0.66 for EMISE-H2O in comparison to NH3-H2O but lower than LiBr-H2O. In addition, the deviation in the COP and ECOP with the generator temperatures are compared for the evaporation temperature of 5, 10, 15 °C. Result showed noticeable difference between the optimum generator temperature based on COP and ECOP. This indicates the exergy analysis is used for evaluation of ARS and selection of heat source supply temperature obtained from waste heat and renewable solar energy.

Solubility of dibenzothiophene in nine organic solvents: Experimental measurement and thermodynamic modelling

In this study, the solubility of dibenzothiophene (DBT) in N,N-dimethylformamide, 2-(2-butoxyethoxy)ethanol, n-propanol, n-octane, diethylene glycol,decahydronaphthalene, sulfolane, dimethyl sulfoxide and acetone, were measured by using the method of dynamic laser at atmospheric pressure. The experimental temperature ranged from 282.75 K to 341.15 K. The results show that within the temperature range studied, the solubility of DBT increased with increasing temperature. The experimental data were correlated by the Apelblat model, λh model and the modified non-random two liquid (NRTL) activity coefficient model, and the calculated solubility agree satisfactorily with the measured results. The result of Akaike Information Criterion (AIC) analysis showed that the Apelblat model was the best model to correlate the solubility of DBT in diethylene glycol, n-octane, sulfolane and decahydronaphthalene, the λh model was the best model to correlate the solubility of DBT in 2-(2-butoxyethoxy)ethanol and the modified NRTL model was the best model to correlate the solubility of DBT in N,N-dimethylformamide, acetone, dimethyl sulfoxide and n-propanol. Furthermore, the thermodynamic functions including dissolution enthalpy, entropy and Gibbs energy were obtained from the solubility data by using the van’t Hoff equation.

Measurement and Correlation for Solubilities of Adipic Acid, Glutaric Acid, and Succinic Acid in Dimethyl Adipate + Methanol Mixtures

The solubilities of adipic acid, glutaric acid, and succinic acid in dimethyl adipate + methanol solvent mixtures were measured by the method of dynamic laser under 101.3 kPa. The mass fraction of dimethyl adipate in the solvent mixtures ranged from 0.0 to 1.0, and the temperature ranged from 283.95 to 328.15 K. It was found that with the increase of mass fraction for dimethyl adipate in mixed solvents, the measured solubilities of adipic acid, glutaric acid, and succinic acid would decrease at the same temperature, and with the gradually increase of temperature the measured solubilities of adipic acid, glutaric acid, and succinic acid would increase at the constant proportion solvent mixtures. The experimental data were correlated by the Apelblat model, λh model, and the modified nonrandom two liquid activity coefficient model. Results showed that the largest values of relative average deviation and root-mean-square deviations obtained by the three models were 4.49% and 0.35%, respectively. The three mod...

Measurement and Correlation for Solubilities of Adipic Acid, Glutaric Acid and Succinic Acid in Acetic Acid + Cyclohexanone Mixtures

Under atmospheric pressure, the solubilities of adipic acid, glutaric acid, and succinic acid in acetic acid + cyclohexanone mixtures were measured respectively by using the laser dynamic method in which the temperature ranged from 298.55 to 340.85 K and the mass fraction of cyclohexanone in the binary solvent mixtures ranged from 0.0 to 1.0. The results showed that the solubilities of adipic acid, glutaric acid, and succinic acid in acetic acid + cyclohexanone solvent mixtures all increased with decreasing of the mass fraction of cyclohexanone in the solvent mixtures at the constant temperature, and with the gradually increasing of temperature the measured solubilities of adipic acid, glutaric acid and succinic acid in acetic acid + cyclohexanone solvent mixtures would increase at the constant proportion solvent mixtures. The λh equation and the nonrandom two liquid (NRTL) activity coefficient model were used to correlate the experimental solubilities, and the average relative deviation was lesser than 2...

Liquid-liquid equilibrium constant for acetic acid in an olive oil-epoxidized olive oil-acetic acid-hydrogen peroxide-water system

The liquid-liquid equilibrium constant for acetic acid in a quinary system olive oil-epoxidized olive oil-acetic acid-hydrogen peroxide-water was experimentally determined for temperatures and component ratios relevant for in situ epoxidation of plant oils. The values has the constant range from 1.52 to 2.73. To predict the equilibrium constant for acetic acid, the experimental data were correlated with UNIQUAC (universal quasi chemical) and NRTL (non-random two liquid) activity coefficient models. For simplified calculation of the phase equilibrium the insolubility of olive oil and epoxidized olive oil in the water, as well as insolubility of water and hydrogen peroxide in the olive oil and epoxidized olive oil, was assumed. The root mean square deviation (RMSD) of the experimental and calculated values of the liquid-liquid equilibrium constant for acetic acid is 0.1910 for the UNIQUAC model and 0.1815 for the NRTL model. For rigorous flash calculation, when the partitioning of all components between the phases was assumed, the RMSD for the NRTL model is 0.1749.