UNIFAC Research Articles

Extending UNIFAC models for solid-liquid equilibria prediction and design of eutectic solvent systems

Although eutectic solvents (ESs) have received considerable attention as sustainable process fluids for various applications, discovering novel ESs remains challenging as computational methods for predicting the formation of eutectics are still scarce. In the present work, both the original and modified UNIFAC models are evaluated and extended for predicting the solid–liquid equilibria (SLE) of ES systems. The applicability of the two versions of UNIFAC models is first evaluated based on the SLE of 25 ES systems composed of only conventional components. Motivated by the good evaluation results, the SLE of 50 ES systems involving one salt component are employed to extend the UNIFAC models to include novel salt-component-related functional groups. The obtained models cover widely-reported salt components of choline/tetraalkylammonium chloride/bromide and conventional components of fatty alcohols and fatty/dicarboxylic/α-hydroxy acids. A theoretical design of novel ESs in a large scale is performed with the best-performing model extension, wherein four designed ES systems are validated experimentally.

UNIFAC residual marine fuels stability prediction from NMR and elemental analysis of SARA components

This paper focuses on the development of theoretical approaches to predict the stability of very low-sulfur residual marine fuel (VLSFO) and is based on molecular weight, CHNS-, SARA-, NMR analysis, and the UNIFAC model. The main issue of using the UNIFAC model is to determine the group composition of marine fuel components in the UNIFAC representation. According to the data obtained, we developed a method for calculating UNIFAC pseudo-components group composition for residual and distillate petroleum products. The hyperparameters used in this model were the asphaltenes’ heat of fusion and melting point. The melting point was successfully estimated using a regression formula that took into account the molecular weight and C/H ratio. The heat of fusion was calculated using the optimization method. The resulting model makes it possible to estimate the influence of the VLSFO component’s parameters on the shape and position of the metastability line in ternary systems. The reliability of the developed model was confirmed by comparing the calculated and experimental data on the example of the VLSFO sedimentation stability diagram in the system of hydrotreated diesel fuel - catalytic cracking light gasoil - visbreaking residue. Based on the developed model it is possible to predict the stability of the residual marine fuel of a given composition. The application of this model is intended to greatly simplify the development of the stable VLSFO composition that meets the requirements of ISO 8217:2017.

Comparison of excess molar enthalpies predicted by UNIFAC model and COSMO-SAC theory with experimental data for some binary mixtures

In this work, the UNIFAC model and COSMO-SAC theory have been applied for prediction of the excess molar enthalpies of some binary mixtures. The predicted values of excess molar enthalpies via both theories show good agreement with the experimental data reported in literature for the mixtures containing polar and non-polar components, with relative errors less than 30%.

Phase Equilibrium Properties of Binary Systems (Furfural + Ethanol or Butan-2-ol) at Several Temperatures

The vapor pressures of the binary mixtures (furfural + ethanol) and (furfural + butan-2-ol) along with the pure component ethanol were measured using the static apparatus for VLE measurements (static device) between temperatures of 283 and 363 K. The generated results from this work were correlated using semi-empirical correlations as described by the Antoine equation. The excess Gibbs function was computed at assorted constant temperatures and applied to fit a fourth-order Redlich–Kister equation utilizing the Barker’s technique, as these two systems in study exhibited positive deviations in GE at all temperatures studied over the whole composition range. The Modified UNIFAC (Do) model, UNIQUAC model, and the NRTL model together with the Peng-Robinson-Sheng-Lu equation of state (PRSL EoS) were also employed, and excellent results were observed in the modeling of the total pressure. The Redlich–Kister equation was applied successfully for modeling the thermodynamic excess properties.

Predicting Temperature‐Dependent Activity Coefficients at Infinite Dilution Using Tensor Completion

AbstractKnowledge of thermodynamic properties of mixtures is essential in many fields of science and engineering. However, the experimental data is usually scarce, so prediction methods are needed. Matrix completion methods have proven to be very successful in predicting thermodynamic properties of binary mixtures. In this approach, the experimental data is organized in a matrix whose rows and columns correspond to the two components, and whose entries indicate the value of the studied thermodynamic property at fixed conditions. In the present work, we extend the concept to tensor completion methods (TCMs). This allows to account for the variation of the studied property depending on the chosen conditions. The feasibility is demonstrated by applying a TCM to predict activity coefficients at infinite dilution. The third dimension of the tensor is used to describe the influence of the temperature. The TCM is shown to yield better predictions than the well‐established UNIFAC method. Furthermore, the proposed TCM is able to learn and unveil the physical law describing the temperature dependence of activity coefficients from the scarce experimental mixture data only.

Применение модели UNIFAC в расчете физико-химических свойств экотоксикантов для технологических и экоаналитических целей

Modern development vector of environmental monitoring leads to elaboration of analytical methods for qualitative and quantitative analysis of different ecotoxicants. Many studies face the lack of information on isomers and homologues of already studied compounds. This problem cannot always be solved experimentally due to the difficulty of separating or synthesizing certain compounds; the use of group theories of solutions will help partly; using them, solubility in water or partition coefficient between two immiscible solvents is calculated for ecotoxicants. These parameters are important for solving the analytical and ecological problems. The partition coefficient in the octanol – water system is associated with a possibility of accumulation of different compounds in living organisms; the partition coefficient in the hexane – acetonitrile system can be used in gas chromatographic analysis. Solubility in water is closely associated with accumulation of ecotoxicants in water bodies, as well as with their ability to be transferred. This paper presents the capabilities of the UNIFAC model for solving physicochemical problems using the example of calculating the properties of real ecotoxicants on the basis of the available thermodynamic data. All the obtained calculated values were compared with those determined experimentally. In the case of pyrene derivatives, solubility data were obtained for the first time using a correlation group model to calculate the heat of fusion and melting temperature.

Enhancing R410A blend separation by using ionic liquids: From UNIFAC model extension, solvent design to molecular dynamics simulation

The selective separation of refrigerants could facilitate their reclamation and reduce emissions of hydrofluorocarbons (HFC) with high global warming potential. R410A, a near azeotropic mixture comprising equimass difluoromethane (R-32) and pentafluoroethane (R-125), is required to be phased out and shortly replaced by more efficient and sustainable refrigerants. Under this background, the recovery of R-32 and R-125 by using ionic liquids (ILs) as the solvent is considered as a promising approach. In this work, the rational selection of ILs for enhancing the R410A separation is presented. To this end, 873 refrigerant-in-IL solubility data (573 for R-32, 300 for R-125) are firstly adopted for the extension of the UNIFAC-IL model to cover the R410A system. With the obtained UNIFAC-IL model, a computer-aided IL design (CAILD) task is cast as a mixed-integer nonlinear programming (MINLP) problem, which is solved to identify three top-ranked ILs. Following that, molecular dynamics (MD) simulations of the selected IL-refrigerant systems are conducted, which well elucidate the reliability of the CAILD results.

Screening of Absorbents for Viscose Fiber CS2 Waste Air and Absorption–Desorption Process

Screening of absorbents is essential for improving the removal rate of carbon disulfide (CS2) waste air by absorption. In this work, the UNIFAC model in Aspen Plus was utilized to calculate the excess Gibbs function and absorption potential of the binary system of CS2 with various alcohols, ethers, esters, amines, and aromatic hydrocarbons. The results were used to quantitatively compare the efficiency of each solvent for CS2 absorption. The theoretical predictions were then verified by absorption experiments in a packed tower. The results showed that the performance of various solvents to CS2 roughly followed the order of esters < alcohols < amines < heavy aromatics < glycol ethers. Meanwhile, N-methyl-2-pyrrolidone (NMP) is the optimal absorbent for CS2 waste air treatment. Additionally, the process parameters of absorption and desorption of NMP were optimized. The results illustrated that the average mass removal efficiency of CS2 by NMP is 95.2% under following conditions: liquid–gas ratio of 3.75 L·m−3, a temperature of 20 °C, and inlet concentration lower than 10,000 mg·m−3. Under the conditions of 115 °C, 10 kPa, and a desorption time of 45 min, the average desorption rate of CS2 is 99.6%, and the average water content after desorption is 0.39%. Furthermore, the recycled lean liquid can maintain an excellent CS2 purification effect during the recycling process.

New Model to Predict Infinite Dilution Activity Coefficients Based on (∂p/∂x) T,x → 0.

Accurate prediction of infinite dilution activity coefficient (γ∞) is essential for the calculation of phase equilibria, solubility, and related properties in molecular thermodynamics. Here, we propose a new model to accurately predict the value of γ∞. It is applicable to calculate γ∞ for compounds in aqueous solution at different temperatures. The model is based on the relationship of (∂p/∂x) T,x→0 with γ∞ and temperature at low pressure. First, we introduce the new idea of using the group contribution method to estimate (∂p/∂x) T,x→0 and then obtain the activity coefficient of a solute at infinite dilution in water based on the relationship between (∂p/∂x) T,x→0 and γ∞. The accuracy of this model is verified using experimental data from 46 systems and more than 450 data points. The result shows that the total average relative deviation of the predicted values from the experimental values for training data is 4.73%. Besides, we test the applicability of the model using solutes that are not part of the training data set. The result shows that the model is satisfactory for the prediction of testing data. Compared with other models, the results prove that the developed model outperforms the UNIFAC model, the modified UNIFAC model, and previous predictive models for aqueous systems. The final equation with only simple arithmetic is more easily applied in engineering practices.

How to rationally screen refrigerant/ionic liquids for thermal cooling: A multi-criteria approach based on machine learning

Absorption heat pumps (AHPs) for thermal cooling show great potential in utilizing renewable and waste heat towards carbon neutrality. AHPs using ionic liquids (ILs) as absorbents have attracted considerable attention for avoiding the shortcomings of traditional working fluids. To develop absorption technologies with high efficiency, compactness, and flexibility, a multi-criteria approach coupling the property models based on machine learning and UNIFAC methods, cycle models, and heat exchanger models is proposed to screen the optimum refrigerant/ILs. In terms of cycle performance, heat transfer performance, hydraulic resistance, and applicable range, the comprehensive performance of 214 novel refrigerant/ILs is estimated to identify suitable candidates. Six indicators are selected to compare the working pairs comprehensively: H2O/[OMIM][OAc] performs the best in terms of coefficient of performance (0.815), pumping power (0.071 W), and supply-side applicable operating ratio (76.8%), while NH3/[DBIM][Tf2N] yields the lowest saturation temperature drop (0.157 K) and the highest demand-side applicable operating ratio (64.9%). Within the studied IL-based working fluids, NH3/[DBIM][Tf2N] in the generator exhibits the highest heat transfer coefficient of 0.476 kW/(m2·K). Considering the trade-off between heat transfer performance and hydraulic resistance, satisfactory solution velocities are recommended for different working fluids with a saturation temperature drop limit of 2.2 °C. Based on the Pareto optimization, H2O/[OMIM][OAc] is highly recommended for industrial applications because of its crystallization-free nature, high COP, and compact system size. The proposed multi-criteria approach achieves large-scale screening of optimum ILs for highly efficient, compact, and flexible thermal cooling.

Droplet evaporation of alcohol-biodiesel blends

Despite recent research on blends of biodiesel with higher alcohols in Diesel engines, no information on their behaviour as single droplets is available. This work presents experimental data on the droplet evaporation of blends of biodiesel with 1-propanol and 1-pentanol and compares them to the results of numerical models of droplet evaporation. The phase equilibrium of the non-ideal mixture of alcohol with biodiesel was modelled using activity coefficients calculated from the UNIFAC method, which was shown to accurately reproduce experimental VLE data from the literature. Droplet evaporation experiments were performed for 1-propanol/biodiesel and 1-pentanol/biodiesel blends at temperatures of 450 °C and 700 °C. The numerical modelling compared two different liquid phase models: well-mixed and diffusion-limited. The diffusion-limited model was found to best represent the droplet evaporation process, particularly early in the droplet lifetime. Internal boiling and bubble formation were observed for all mixtures, driven by the large difference in boiling point between the alcohol and biodiesel components (around 200˚C). The diffusion-limited model was also able to roughly predict the conditions under which bubble formation could occur.

Cubic Plus GE (CPGE): Cubic equation of state with simple mixing rule plus excess Gibbs energy that satisfies low-density condition

The excess Gibbs energy calculated by activity coefficient model GE,M is added to a cubic equation of state. The additional term containing GE,M is obtained by a dimensional analysis. A simple mixing rule such as a/b = Σ(ai/bi)xi and b = Σbixi is adopted. The equation of state satisfies the low-density boundary condition that the second virial coefficient be quadratic in composition. The activity coefficient derived from the equation of state is expressed as the sum of Flory-Huggins term and interaction term, which has the same form as UNIQUAC, UNIFAC, and ASOG models at low pressure in liquid phase. Peng-Robinson equation of state was used for an example of cubic equation of state, and NRTL, CDSAP, and r-CDSAP models were adopted for GE,M for examples of activity coefficient models. The vapor-liquid equilibria for 2-propanol (1) + water (2), acetone (1) + water (2), benzene (1) + 2,2,4-trimethylpentane (2), methane (1) + pentane (2), and ethane (1) + heavy alkanes (2) systems were calculated to test the temperature dependency. The parameter values in the activity coefficient models were fitted to the experimental data of each binary system at the lowest temperature. Then, the vapor-liquid equilibria were calculated at higher temperatures with the parameter values. The calculated results at higher temperatures by the proposed model are better than those by Peng-Robinson + Wong-Sandler + NRTL mixing rule or Peng-Robinson + Huron-Vidal + NRTL mixing rule. The vapor-liquid equilibria for acetone (1) + acetonitrile (2) + benzene (3) + ethanol (4) system and its sub-binary and sub-ternary systems were calculated to test the estimation performance. The parameter values in the activity coefficient models were fitted to the experimental data of sub-binary systems. Then, the vapor-liquid equilibria for ternary and quaternary systems were estimated. The average deviations between the experimental data and the calculated results by the proposed model are 0.7% for pressure and 0.005 to 0.006 for mole fraction in vapor phase.

Predicting vapor-liquid equilibria of CO<sub>2</sub>+HFC binary mixtures by the PR EOS combined with a group contribution model

CO<sub>2</sub>+HFC binary mixtures have good performance and environmental friendliness and are considered good alternative working fluids in cooling and power cycle systems. The vapor-liquid phase equilibrium properties are key to the calculation of the enthalpy and entropy of mixtures, which is critical for the analysis of cooling and power cycle systems. To accurately predict the vapor-liquid equilibrium of CO<sub>2</sub> and HFC (R23, R32, R41, R125, R134a, R143a, R152a, R161, and R227ea) binary mixtures, a group contribution model based on the excess free energy (<i>G</i><sup>E</sup>) mixing rules (PR+MHV1+UNIFAC and PR+LCVM+UNIFAC) is established in this paper. The interaction parameters between groups such as -CO<sub>2</sub>, -Alkane, -CHF, and -CHF<sub>3</sub> are obtained by the vapor-liquid phase equilibrium experiment of CO<sub>2</sub> and HFC refrigerants, and these group parameters are critical for predicting their vapor-liquid phase equilibrium properties (the pressures and vapor phase molar fractions). The AARD<i>p</i> value calculated by the PR+LCVM+UNIFAC model is 5.53%, the value of AAD<i>y</i><sub>1</sub> is 0.0132, and the AARD<i>p</i> and AAD<i>y</i><sub>1</sub> values of the PR+MHV1+UNIFAC model are 7.40% and 0.0229, respectively. However, for the CO<sub>2</sub>+R32 system, the PR+MHV+UNIFAC prediction model can reproduce the experimental data with lower deviations, and the values of AARD<i>p</i> and AAD<i>y</i><sub>1</sub> are 1.53% and 0.0045, respectively. In summary, for CO<sub>2</sub>+HFC binary mixtures, the PR+LCVM+UNIFAC group contribution model can reproduce the experimental data with lower deviations, but for individual CO<sub>2</sub> binary mixtures (such as CO<sub>2</sub>+R32), the PR+MHV1+UNIFAC model also has unique advantages. According to the prediction results of the group contribution model, the PR+LCVM+UNIFAC model has significantly improved the calculation progress compared with the PR+MHV1+UNIFAC model used in the previous system.

Ternary liquid–liquid equilibria for 2-phenylethyl acetate + 2-phenylethanol + water and 2-phenylethyl acetate + acetic acid + water at atmospheric pressure

2-Phenylethyl acetate can normally be produced by the esterification of 2-phenylethanol with acetic acid via a reactive distillation process. The multiphase coexistence behavior is a component of esterification and is important for the design of the reactive distillation process. In this report, the ternary liquid–liquid equilibrium (LLE) results of 2-phenylethyl acetate + 2-phenylethanol + water and 2-phenylethyl acetate + acetic acid + water at 303.15, 323.15, and 343.15 K under atmospheric pressure are presented. The ternary LLE data regression results were obtained using NRTL and UNIQUAC models with an absolute average deviation (AAD%) value of less than 2 %. The determined binary interaction parameters were verified by the GUI-MATLAB tool. Furthermore, the results predicted by the UNIFAC model for the investigated ternary LLE systems are acceptable.

Separation of acrylonitrile from water by n-Alkanols: Effect of alkyl chain length on separation efficiency and correlation of thermodynamic models

In order to explore the separate effect of water and acrylonitrile, liquid–liquid equilibrium (LLE) data of water + acrylonitrile + {1-pentanol, 1-hexanol, 1-heptanol or 1-octanol} were measured, and the results were compared and discussed regarding the partition coefficients and separation factors. Through electrostatic potential and σ-profiles, it shows that the longer the alkyl chain length had a more favorable effect on the extraction of acrylonitrile. The experimental data were associated with the NRTL and UNIQUAC models, and the parameters required for each model were obtained. Furthermore, the predicted data estimated by the UNIFAC model were compared with experimental values, and the prediction effect of the model was verified. The above models' root mean square deviation (RMSD) was less than 0.0060, 0.0059, and 0.0117, respectively. The mixing surface analysis of Gibbs energy topology tested each system's parameters, proving the model parameters' availability.

Computer-aided naphtha liquid–liquid extraction: Molecular reconstruction, sustainable solvent design and multiscale process optimization

A new integrated sustainable solvent and process design framework is proposed based on GDP (generalized disjunctive programming) to separate the naphthenic and aromatic components from naphtha. First, the detailed molecular composition information of naphtha is obtained using a molecular reconstruction model based on feasible bulk properties. Two group-based virtual molecules are then presented to express naphtha components for the liquid–liquid extraction process design. Second, four separation performance indicators and eight SHE (safety, health and environment) metrics are screened and described for the sustainable solvent design on the basis of the UNIFAC model and functional groups. The solvent structures are modelled through the improvement of the octet rule. Last, a conceptual liquid–liquid extraction process is proposed and expressed as a CAMPD (computer aided molecular and process design) optimization problem combining with the rigorous process mechanism model, sustainable solvent design model and molecular information model of naphtha. Especially, GDP is tailored to express the discrete choices in the simultaneous optimization design of solvents and processes and address the challenge of the large-scale framework solution. Compared with the process using the traditional solvent sulfolane, the content of the separated naphthenic and aromatic components is improved by 10.37%. At the same time, the sustainability is enhanced according to SHE assessment.

Thermodynamic and kinetic aspects of the solvent-free liquid–liquid synthesis of tailor-made glyceride esters

Direct esterification between glycerol and carboxylic acids allows the design of different glycerides according to predetermined applications. Five carboxylic acids (caprylic, capric, lauric, stearic and oleic) which formed a bi-phasic system with glycerol were tested for esterification in a 1:1 M proportion. Two strategies were pursued: on one hand, homogeneous acid catalysis using sulfuric acid or p-toluenesulfonic acid at 100 °C and on the other hand, reactions catalyzed by immobilized lipase B from Candida antarctica at 65 °C. The selectivity and yield for MG was higher at lower temperature and with the use of the enzyme. Lauric acid was the carboxylic acid with the higher yield and selectivity to MG despite the catalyst used. The decrease in the mutual solubility between the carboxylic acid and glycerol seems to favor MG formation. The rate of reaction decreased with the increase in the molecular weight of the carboxylic acid used and the introduction of one unsaturation. From caprylic to lauric acid, the catalyst performance was: p-toluenesulfonic acid > lipase > sulfuric acid whereas for stearic and oleic acids the lipase was superior. Reactant accumulation at the interface is proposed to explain these results. The thermodynamic UNIFAC model was applied to calculate the initial activity coefficients and molar fractions in each phase. It was demonstrated that the thermodynamic activity of the species is a more convenient representation of the effective concentration for kinetic description of a liquid–liquid system. The equilibrium constant of lipase reaction was calculated with an expression based on the activity of compounds. The equilibrium constant for diglycerides formation decreased with the carbon chain length.

Prediction of speed of sound and specific heat capacity of ionic liquids using predictive SAFT-based equation of state

In this work, the predictive PC-SAFT EoS has been developed to predict the speed of sound, the isochoric and isobaric heat capacity of ionic liquids (ILs) over a wide range of pressures and temperatures. In this new methodology, the segment number and diameter of ILs have been estimated using the surface area and molecular volume of the UNIFAC model. The segment energy and association energy parameters have been obtained using an inverse relationship between dispersion/association energy and segment diameter. The results show that the predictive PC-SAFT model can predict the specific isochoric and isobaric heat capacity of ILs up to high pressure, accurately. In the case of the speed of sound, the model performance is acceptable by considering using no adjustable model parameters. To check the model capability, the new model results have been compared to the electrolyte PC-SAFT EoS.

Vapor–Liquid Equilibrium in Binary and Ternary Azeotropic Solutions Acetonitrile-Ethanol-Water with the Addition of Amino Esters of Boric Acid

The effect of amino esters of boric acid (AEBA) on the conditions of vapor–liquid equilibrium in binary mixtures of acetonitrile–water, ethanol–acetonitrile and a three-component mixture of ethanol-acetonitrile-water was investigated. Residual curves and vapor–liquid phase equilibrium conditions (TPXY data) were experimentally measured at atmospheric pressure for a binary mixture of acetonitrile-AEBA and a triple mixture of acetonitrile-water-AEBA. Previously unknown energy binary parameters of groups B, CH2N with group CH3CN were determined for the UNIFAC model. The correction of the value of the binary parameter water—acetonitrile was carried out. On the basis of thermodynamic modeling, the degree of influence of AEBA on the relative volatility of acetonitrile in binary and ternary mixtures was analyzed. It is shown that the use of AEBA removes all azeotropic points in the studied mixtures. In this case, acetonitrile turns out to be a volatile component, and water is a non-volatile component in the entire concentration range.

Accurate Effective Diffusivities in Multicomponent Systems

Mass transfer is an omnipresent phenomenon in the chemical and related industries for which effective diffusivities (Di,eff) constitute a useful and simple mathematical tool, especially when dealing with multicomponent mixtures. Although several models have been published for Di,eff they generally involve simplifying assumptions that severely restrict their use. The current work presents the derivation of accurate analytical equations for Di,eff, which take into account the nonideal behavior of multicomponent mixtures. Additionally, it is demonstrated that for an ideal mixture the new model reduces to the well-known equations of Bird et al., which are the exact analytical solution for ideal systems. The procedure for Di,eff estimation is described in detail and exemplified with two chemical reactions: the liquid phase ethyl acetate synthesis and the high pressure gas phase methanol synthesis. Relative to the Bird et al. ideal equations the effective diffusivities calculated with the new model show differences up to 38% for ethyl acetate synthesis when using UNIFAC model to evaluate activity coefficients. For methanol synthesis, deviations from −23% to 22% are found using PC-SAFT equation of state (EoS) and from −49% to 24% when applying the Peng–Robinson EoS to estimate fugacity coefficients. Comparisons are also performed with the models by Wilke, Burghardt and Krupiczka, Kubota et al., and Kato et al. The worst results are achieved by the Wilke and Kubota et al. equations for the liquid phase and gas phase reactions, respectively. Furthermore, it is shown that substantial errors in effective diffusivity calculations may occur when deviations from the ideal behavior are unaccounted for. This can be avoided by adopting the new rigorous approach here presented.