AARD Values Research Articles

Predicting ionic liquid efficiency as steel corrosion inhibitor under static hydrochloric acid immersion using group contribution method

As a novel corrosion inhibitor, ionic liquid has garnered a growing amount of interest. Different electrodes, such as carbon steel, stainless steel, aluminium, copper, magnesium, and others; different electrolytes, such as hydrochloric acid, sulfuric acid, nitric acid, and seawater; different condition operations at different temperatures and tribological properties; and various techniques, such as weight loss (WL), potentiodynamic polarization (PDP), and electro impedance spectroscopy (EIS), have been investigated. Due to the large number of cations and anions, this conventional laboratory study may not be completed anytime soon. Therefore, IL as a corrosion inhibitor must be investigated further. The purpose of this study is to conduct a more comprehensive analysis of IL as a corrosion inhibitor in 1 M HCl immersion on carbon steel using the group contribution method. Cations and anions were divided into 29 functional groups (FG) of cations and 17 functional groups (FG) of anions using 74 IL and 760 WL data points collected from various studies. Training and test set results have R2 values of 0.639 and AARD values of 14.9%; validation set results have R2 values of 0.319 and AARD values of 14.4%; and the overall data point evaluation has R2 values of 0.324 and AARD values of 14.3%.

Solubility of famotidine in supercritical carbon dioxide: Experimental measurement and thermodynamic modeling

In the current study, the solubility of famotidine (FAM) in supercritical carbon dioxide (scCO₂) was experimentally determined for the first time. The FAM solubility in scCO₂, expressed as mole fraction, at different temperatures (308 − 338 K) and pressures (12 − 30 MPa) was found to be in the range of 1.40 × 10−6 to 1.11 × 10−4. Due to the low solubility of FAM in scCO₂, the gas anti-solvent and supercritical anti-solvent processes can be a good option to generate the nano/micro size particles of this drug. The experimental solubility data were correlated by the density-based models of Bartle et al., Méndez-Santiago and Teja (MST), Jouyban et al. and Hozhabr et al., by the non-cubic equation of state PC-SAFT, and by the two versions of the Estévez et al. model (ECM-PR and ECM-RK). According to the modeling results, the Estévez et al. model showed the highest accuracy with AARD values of 9.92 (ECM-PR) and 10.70 (ECM-RK). The empirical models also yielded satisfactory outcomes to the correlation of the solubility of FAM in scCO₂.

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.

On the Analysis and Assessment of First-Order Group Contribution Models for the Calculation of Normal Boiling Point and Critical Properties of Pure Compounds

The thermodynamic properties of pure compounds are relevant data for process systems engineering. Different first-order group contribution models have been reported in the literature to calculate these properties and they are also widely employed in commercial process simulators. However, they may have some limitations and, consequently, a reliable comparison of these models is required to analyze their performance and to determine the best alternative for the calculation of pure compound properties. This paper reports the implementation and evaluation of several first-order group contribution models to calculate the normal boiling point and critical properties (temperature, pressure, and volume) of pure compounds. The performance of these models was characterized and compared for several compound families using a standardized approach to determine their group contributions and parameters. An artificial neural network model was also applied and assessed to improve the estimations obtained with the best group contribution models. Results showed that the calculation of critical temperature was challenging for several compound families where AARD values ranged from 0.05 to 56.28%, while the group contribution models were more accurate to estimate the critical volume with AARD values ranging from 0.48 to 35.99%. This study allows us to identify the limitations and gaps of this type of thermodynamic models with the objective of improving its performance for the calculation of pure compound thermodynamic properties. The findings of this study can help to enhance the capabilities of thermodynamic models for the calculation of the normal boiling point and critical properties of pure compounds, which are relevant for the process systems engineering of new operations and products.

Impact of turbine impeller blade inclination on the batch sorption process

Batch sorption is a practical process used to remove various species from the wastewater. It is affected by different parameters such as initial concentrations, temperature, pH, surface area, coexisting ions, and mixing that need to be known for batch reactor design. Although reaction mixture in batch processes needs to be well-mixed, and there are many papers regarding sorption, mixing parameters are rather neglected. Therefore, the aim of this work was to analyse the impact of the turbine impeller blades inclination and baffle presence on sorption kinetics in the uncovered batch reactor. This impact was studied using copper (II) ions sorption on zeolite NaX particles. The experiments were conducted in the baffled and unbaffled reactor equipped with the four-blade turbine placed close to the vessel base. To determine the influence of impeller blades inclination on hydrodynamics and sorption kinetics, the blades inclination varied from 30° to 90°. A transient multiphase computational fluid dynamics model was developed to gain valuable insight into complex flow kinetics. The Ritchie model, Mixed surface reaction and diffusion-controlled sorption kinetic model, and Weber-Morris model were used for the kinetic analysis of the experimental kinetic data. According to Ψ and AARD values, the reaction is kinetic controlled regardless of the impeller blades inclination. The process is the fastest if the impeller with a blades inclination of 90° is used and in the baffled reactor. Concurrently, the energy consumption is the lowest for this impeller, regardless of the presence of the baffles.

An extraction-based facile method for measuring the solubility of organic solid compounds in supercritical carbon dioxide

Due to its dual gas- and liquid-like properties, supercritical carbon dioxide (scCO2) is considered an excellent solvent for dissolving precursors and penetrating nanoscale pores. After subsequent calcination, uniformly dispersed metal or metal oxide nanoparticles or nanowires can be obtained. Organometallic salts are commonly used precursors in this method because they usually have high solubility in scCO2. Therefore, solubility data are essential for the controllable synthesis of such nanocomposites. This work establishes a facile and accessible method for measuring the solubility of organic solids in scCO2. The solubilities of copper acetylacetonate and cobalt acetylacetonate were obtained at temperatures of 313–333 K and pressures of 11–24 MPa. And the solubilities were within 2.3 × 10−2 to 14.1 × 10−2 g/L for Cu(acac)2 and 6.9 × 10−2 to 13.4 × 10−2 g/L for Co(acac)2. The experimental data were fitted to the semi-empirical model with the AARD values of 4.58% and 2.14% for Cu(acac)2 and Co(acac)2, respectively, and the obtained equations could be used to predict solubility of the same systems in the experimental range.

New solubility and heat of absorption data for CO2 in blends of 2-amino-2-methyl-1-propanol (AMP) and Piperazine (PZ) and a new eNRTL model representation

New data comprising CO2 partial pressure, total pressure, and the heat of absorption of CO2 for over aqueous solution of 3 mol/dm3 AMP and 1.5 mol/dm3 PZ and total pressure and heat of absorption for different mol ratios of AMP/PZ (3.0/0.0, 0.0/1.5, 0.5/4.0, 1.5/3.0, 2.25/2.25, 3.0/1.5, 4.0/0.5) are presented as functions of CO2 loading and temperature.Measured solubility data and selected data reported in the literature were used in the regression of binary interaction energy parameters in the quaternary system (AMP/PZ/H2O/CO2) using the eNRTL model. The equilibrium constants and binary interaction energy parameters from our previous work on the ternary systems of AMP/H2O/CO2 and PZ/H2O/CO2 were used without refitting.Good agreement with the literature was observed for the total pressure data over aqueous solutions of 3.0 mol/dm3 AMP and 1.5 mol/dm3 PZ, and the CO2 partial pressure and heat of reaction data over aqueous solutions of 3.0 mol/dm3 AMP+1.5 mol/dm3 PZ at different loadings and temperatures. The results reflect that the new data are consistent with reported data from the literature.The modeling results show that the eNRTL model represents the data well with AARD values of 13.1% for total pressure and 20.9% for CO2 partial pressure. The volatility of AMP and PZ as function of loading and temperature and published speciation data for AMP/AMPH+, PZ/PZH+/PZH22+, PZCO2−/PZH+CO2−, PZ(CO2−)2 and HCO3−/CO32− were also well predicted.Only the heat of absorption data over an aqueous solution of 3.0M AMP+1.5M PZ from this work can be compared with literature data, and good agreement is observed. The eNRTL model also predicts satisfactorily the experimentally obtained heat of absorption data for all different ratios of AMP/PZ. Individual reaction contributions show that when the AMP/PZ ratio increases, the predicted total heat of absorption goes toward the single solvent AMP system where only protonated AMP is the main contributor. When the AMP/PZ ratio decreases, the predicted total heat of absorption also approaches the single solvent PZ system where the protonated PZ, PZ-monocarbamate and zwitterion reactions play important roles. In systems with high PZ-concentration, the contribution of the zwitterion, protonated PZ and PZ-carbamate cancel each other at high loadings.

Physics-based smart model for prediction of viscosity of nanofluids containing nanoparticles using deep learning

Abstract The traditional model-driven methods are not much efficient to predict the viscosity of nanofluids accurately. This study presents a novel approach of using physics-guided deep learning technique for predicting viscosity of water-based nanofluids from large dataset containing both experimental and simulated data of spherical oxide nanoparticles $\rm{Al2O3}$, $\rm{CuO}$, $\rm{SiO2}$, and $\rm{TiO2}$. Further, this study introduces a novel methodology of combining deep learning methods and physics-based models to leverage their complementary strengths. To the best of the author’s knowledge, theory-guided deep learning prediction model was never used to predict viscosity before. The theory-guided deep neural networks (TGDNN) model is trained by minimizing the mean square error (MSE) and regularization terms using Adam optimization technique. The investigations reveal that the values of R2, RMSE, and AARD% are, respectively, 0.999868, 0.001143, and 2.198887 on experimental testing dataset. The TGDNN model learns non-linear relationship among the input variables from the training data. Additionally, the results show that the proposed method performed better than the other well-known existing theoretical and computer-aided models to predict the viscosity in wide range with high level of accuracy.

Insights into the estimation of heavy metals ions sorption from aqueous environment onto natural zeolite

In this work, we present how soft computing approaches can be used to study the sorption performance of natural zeolite to eliminate heavy metals ions including Zn2+, Ni2+, Cd2+, and Pb2+, from aqueous environment. The models include least-squares support-vector machine (LSSVM), genetic programming (GP), particle swarm optimization-adaptive neuro-fuzzy inference system (PSO-ANFIS), and artificial neural network (ANN), as well as multivariate nonlinear regression (PNR). The inputs of the models are electronegativity, hydrated ionic radii (A), first ionization energy (E1, kJ/mol) and molecular weight (Mw, g/mol) of heavy metal ion, initial pH (pHi, mmol/l) and equilibrium pH (pHe, mmol/l) of solution, and Si concentrations in the aqueous phase (Sie, mg/l). The output of the models is ionic species sorbed per gram of zeolite, f, (mmol/g). The importance of initial concentration, pollutant molecular weight, and acidic functional groups in the sorption of heavy metals is emphasized by sensitivity analysis. Ion exchange variables are determined by the adsorption isotherm expressions: Redlich–Petersen (RP), Langmuir–Freundlich (LF), Dubinin–Radushkevich (DR), Toth (T), Lineweaver–Burk (LB), and modified Dubinin–Radushkevich (MDR). Here, we focus on the applications of smart techniques in modeling complicated sorption systems used in wastewater treatment and environmental pollution control. The % AARD values for LSSVM, GP, ANN, PNR (with 5 order of polynomial), PSO-ANFIS, LF, RP, T, DR, MDR, and LB are 0.77, 5.37, 2.47, 1.23, 1.59, 177.1, 15.1 4215.8, 159.3, 128.9, and 11.2, respectively. The results of the computational techniques are found better than the adsorption isotherms.

Estimation of CO2 adsorption in high capacity metal−organic frameworks: Applications to greenhouse gas control

In recent decades, adsorption of high amounts of carbon dioxide (CO2) in metal-organic frameworks (MOFs) has recived attention and is studied broadly. As a main principle, most scientists have accepted that CO2 can be capured by MOFs in order to prevent atmosphere from green-house gas emissions. In the present work, the potential of Particle Swarm Optimization Adaptive Neuro-Fuzzy Inference System (PSO-ANFIS), Differential Evolution-ANFIS (DE-ANFIS), Radial Basis Function Artificial Neural Network (RBF-ANN) and Least Square Support Vector Machine (LSSVM) to estimate CO2 uptake in 13 different MOFs, as a function of the operational pressure (P) supplemented with the property of MOFs was investigated. The inputs of the models are temperature, pressure, surface area and pore volume of MOFs. An extensive databank containing 506 data gathered from the literature was used for models development. The obtained %AARD values for the developed models are 10.05, 36.6, 35.51 and 8.17 for LSSVM, PSO-ANFIS, DE-ANFIS and RBF models, respectively.The sensitivity analysis demonstrated that operational pressure and pore volume of MOFs are the most effective parameters on CO2 adsorbtion by MOFs. It is found that LSSVM model is an outstanding tool for estimating adsorption of CO2 in comparison with other models. The LSSVM model presents a decent method for estimating CO2 adsorption in the studied MOFs, which is straightforward, capable and cost-efficient.

The effect of alcohol–gasoline fuel blends on the engines’ performances and emissions

This research investigated artificial neural network (ANN) modeling to predict the exhaust emissions and engine performance. Different percentages of alcohol at various engine speeds and comparison ratios were used to obtain the required data for testing and training the proposed ANN. Six experimental datasets were used for the training process to develop an ANN model based on the standard program. Furthermore, the accuracy of the proposed model was evaluated by calculating the mean square error (MSE), regression coefficient (R2), and average absolute relative deviation (AARD%). The total values of AARD% for the proposed model were 10.50 and 15.45% for carbon monoxide and hydrocarbon emissions and 10.50 and 3.13% for torque and fuel consumption, respectively, which were acceptable errors compared with the experimental uncertainty.

Competitive Heavy Metal Removal from Binary Solution

The removal of copper and cobalt ions from binary metal solutions on zeolite NaX by ion exchange process was investigated. Experiments were conducted in unbaffled glass reactor with a Rushton turbine as a stirrer. The dependence of ion exchange kinetics and the amount exchanged were tested using different initial concentrations of metal ions in mixtures. The results obtained indicate that the removal efficiency depends on the initial heavy metal concentrations in binary solutions. Experimental kinetics data were analysed using Ritchie and Weber-Morris models. According to AARD values, the rate in this study was reaction-controlled.

Measurement and Thermodynamic Modeling of Ternary (Liquid + Liquid) Equilibrium for Extraction of Phenols from Alkane with Furfural

The extraction process as a kind of energy-saving and environmental protection technology can be used to separate phenols from low-temperature coal tar. The liquid–liquid equilibrium (LLE) data regarding ternary systems n-heptane + phenols + furfural were determined experimentally at 303.2, 323.2, and 343.2 K under the atmospheric pressure condition, where phenols refer to phenol, p-cresol, and 2,6-xylenol. The solvent extraction capacity was assessed by the solute distribution coefficient and selectivity. Othmer–Tobias and Bachman equations were utilized to validate the consistency of the measured data, which the linear correlation (R2) ≥ 0.99. Experimental LLE data were correlated utilizing the NRTL and UNIQUAC thermodynamic models with all of the RMSD and AARD values below 0.01, meaning that each ternary system is satisfactorily in agreement at temperatures studied and the NRTL model gives better agreement than the UNIQUAC model for ternary systems.

Development of CO2 utilized flame retardant finishing: Solubility measurements of flame retardants and application of the process to cotton

2,2′-oxybis-(5,5-dimethyl-1,3,2,-dioxaphosphorinane-2,2′-disulfide) (5060) and 9,10-dihydro-9-oxa-10-phosphaphenanthrene-10-oxide (DOPO) are widely used in the flame-retardant finishing of polymers due to their excellent fire protection properties and environmentally friendly characteristics. In this work, solubility of 5060 and DOPO were measured at pressures ranging from 16 to 24 MPa with different temperatures in supercritical CO2. With the rising of system pressure and temperature, the solubility of 5060 and DOPO increase, and DOPO exhibits a higher solubility than 5060 in the same supercritical CO2 fluid conditions. Moreover, five semi-empirical models, namely Chrastil equation, Mendez-Santiago-Teja equation, Kumar-Johnston equation, Garlapati-Madras equation as well as Sung-Shim equation, were used to correlate the experimental solubility of the flame retardants. The results showed that Sung-Shim model presents better fitting effect with the AARD values of 21.5% for 5060 and 12.2% for DOPO. In addition, experiments were also conducted with 5060 and DOPO to determine the feasibility of flame-retardant finishing in supercritical CO2.

Liquid–Liquid Equilibria for Ternary Systems n-Hexane + 1-Hexene + Furfural (or N,N-Dimethylformamide) at 298.2, 308.2, and 318.2 K

The liquid–liquid equilibrium (LLE) data of ternary systems n-hexane + 1-hexene + solvents (furfural and N,N-dimethylformamide) were determined experimentally at 298.2, 308.2, and 318.2 K under 101.3 kPa. The solvents’ extraction capacity was assessed by the solute distribution coefficient and selectivity. Othmer-Tobias and Hand equations were used to correlate the measured data to test the correlation of the experimental data, which the linear correlation is (R2) ≥ 0.99. Experimental LLE data was correlated utilizing the NRTL and UNIQUAC thermodynamic models with all of the RMSD and AARD values below 0.01 meaning that each ternary system satisfactory agreement at temperatures studied and the NRTL model gives a better agreement than the UNIQUAC model for ternary systems.

Investigation of boiling heat transfer coefficients of different refrigerants for low fin, Turbo-B and Thermoexcel-E enhanced tubes using computational smart schemes

The design and manufacture of highly efficient evaporators and heat exchangers in cooling machinery need an accurate estimation of the boiling heat transfer coefficient of the refrigerants. In the present study, the boiling heat transfer coefficients of different refrigerants were predicted using machine learning methods and were compared to the existing empirical correlations. For this purpose, four models of ANN, ANFIS, ELM and SVM were developed by using MATLAB functions. 320 data were collected on the boiling heat transfer coefficient of the refrigerants in the plain and enhanced (low fin, Turbo-B, Thermo excel-E) tubes. The percent deviation from the actual value was between − 2.05 and 1.36% for the ANN, − 4.97 and 8.72% for the ANFIS, − 38.11 and 83.01% for the ELM and − 17.35 and 78.37% for the SVM. The results show that the proposed ANN and ANFIS models are reliable models for predicting the boiling heat transfer coefficient. They have a better performance than the ELM and SVM models. The values of RMSE, AARD and R2 for the best model were 74 W m−2 K−1, 0.399% and 0.99993 for the ANN, 306 W m−2 K−1, 1.117% and 0.99883 for the ANFIS, 2163 W m−2 K−1, 15.539% and 0.94191 for the ELM and 2212 W m−2 K−1, 14.905% and 0.93921 for the SVM. The intelligent algorithms of ANN and ANFIS have more accurate predictions than empirical correlations.

Optimization of Glucoamylase Production by Humicola grisea MTCC 352 in Solid State Fermentation

In the industrial processing of starch, the thermostable glucoamylase is employed in saccharification step. The thermophilic fungi Humicola grisea has been used for the glucoamylase production in solid state fermentation. The extracellular glucoamylase is estimated using glucose oxidase – peroxidase assay method. The initial screening studies revealed that wheat bran is the best substrate among the studied agricultural residues. The fermentation parameters were optimized through the response surface approach. By using central composite design, the optimal values of four important parameters viz., mineral salt solution concentration, incubation period, initial moisture content and inoculum size for glucoamylase production were found to be 65 % (v/w), 80 h, 240 % (v/w) and 13 % (v/w) respectively. The experimental activity of 282 U/gds obtained was close to the predicted activity of 288 U/gds. A high R2 value (0.9741), P values lesser than 0.05 and AARD values (1.98 %) indicate the accuracy of the proposed model.

Decision tree‐based modeling of CO2 equilibrium absorption in different aqueous solutions of absorbents

In absorption‐based CO2 removal processes, one of the most important parameters that must be determined is the equilibrium solubility of CO2 in solvents. This study is the first time to employ the extremely randomized trees, Extra Trees, methodology to develop an Extra Trees model for the CO2 loading capacity of various absorbents. The ability of the proposed decision tree‐based model in estimation of CO2 solubility values was compared to that of the previously presented models on the basis of the adaptive neuro‐fuzzy inference system (ANFIS), least squares version of the support vector machine (LSSVM), and artificial neural network (ANN), using error analysis. According to the obtained results, the presented Extra Trees model is able to estimate the CO2 loading capacity of solvents with an absolute relative deviation in percent (AARD%) equal to 0.15. The calculated values of AARD% for the literature models, i.e., LSSVM, radial basis function‐artificial neural network (RBF‐ANN), multilayer perceptron‐ANN (MLP‐ANN), and ANFIS, are 2.00, 10.03, 6.18, and 14.15, respectively. Hence, the developed Extra Trees model provides much higher robustness and accuracy in estimating/representing the solubility of CO2 in different aqueous solutions of solvents. © 2019 American Institute of Chemical Engineers Environ Prog, 38: S441–S448, 2019

Viscosity Reduction of Heavy Crude Oil by Dilution Methods: New Correlations for the Prediction of the Kinematic Viscosity of Blends

Dilution is one of the various existing methods in reducing heavy crude oil viscosity. In this method, heavy crude oil is mixed with a solvent or lighter oil in order to achieve a certain viscosity. Thus, precise mixing rules are needed to estimate the viscosity of blend. In this work, new empirical models are developed for the calculation of the kinematic viscosity of crude oil and diluent blends. Genetic algorithm (GA) is utilized to determine the parameters of the proposed models. 850 data points on the viscosity of blends (i.e. 717 weight fraction-based data and 133 volume fraction-based data) were obtained from the literature. The prediction result for the volume fraction-based model in terms of the absolute average relative deviation (AARD (%)) was 8.73. The AARD values of the binary and ternary blends of the weight fraction-based model (AARD %) were 7.30 and 10.15 respectively. The proposed correlations were compared with other available correlations in the literature such as Koval, Chevron, Parkash, Maxwell, Wallace and Henry, and Cragoe. The comparison results confirm the better prediction accuracy of the newly proposed correlations.

Predictive correlation between surface tension, density, and speed of sound of ionic liquids: Auerbach model revisited

In the current study, following the pioneering work of Auerbach a novel interrelationship has been presented between surface tension (σ), density (ρ), and speed of sound (u) of ILs. 2314 strictly experimental data points pertaining to 48 ILs over an extended temperature range have been employed for the development and validation of this globally applicable predictive model. With AARD values of 1.11% and 1.62% for the training and test datasets, respectively, the new model addresses the systematic deviation of the original Auerbach model and also demonstrates more than a twofold increase in accuracy compared to two previously published models. By solely incorporating the readily available molecular weight of ILs it can be conveniently used for estimation of the speed of sound using surface tension and liquid density values at the temperature of interest. Additionally, the speed of sound is used to develop a semi-empirical relation for prediction of the thermal conductivity (λ) of ILs based on the Bridgman theory. The predicted values exhibit a satisfactory agreement with the experimental data with an AARD value of 1.32% for 75 data points corresponding to 11 ILs compared with a value of 5.45% for a similar previously published closed-form expression.