Acentric Factor Research Articles

Solubility of Methane in Ionic Liquids for Gas Removal Processes Using a Single Multilayer Perceptron Model

In this work, four hundred and forty experimental solubility data points of 14 systems composed of methane and ionic liquids are considered to train a multilayer perceptron model. The main objective is to propose a simple procedure for the prediction of methane solubility in ionic liquids. Eight machine learning algorithms are tested to determine the appropriate model, and architectures composed of one input layer, two hidden layers, and one output layer are analyzed. The input variables of an artificial neural network are the experimental temperature (T) and pressure (P), the critical properties of temperature (Tc) and pressure (Pc), and the acentric (ω) and compressibility (Zc) factors. The findings show that a (4,4,4,1) architecture with the combination of T-P-Tc-Pc variables results in a simple 45-parameter model with an absolute prediction deviation of less than 12%.

Study on separation of methanol and dimethyl carbonate azeotropic system with deep eutectic solvents

Dimethyl carbonate (DMC) is an important diesel and gasoline additive that is also a low-toxic and environmentally friendly chemical raw material. However, it will form an azeotrope with methanol (MeOH) during the actual chemical production process. Therefore, separating high-purity DMC from the azeotrope is of significance. In extractive distillation, deep eutectic solvents (DESs) have demonstrated superior separation performance as green extractants. This study calculated the σ-profiles of DMC, MeOH, and DESs by the COSMO-SAC model to examine the most appropriate DES for the MeOH and DMC separation. Eventually, DES1(1:2 choline chloride (ChCl): malonic acid (MA)), DES2(1:2 ChCl: urea), DES3(1:2 ChCl: glycerol (G)), DES4(1:2 ChCl: ethylene glycol (EG)), DES5(1:2 ChCl: pyruvic acid (PA)) were designated as preferred extractants. The vapor pressures of five DESs at different temperatures were determined using a thermogravimetric analyzer, while their critical properties, normal boiling points, and acentric factors were predicted. The vapor–liquid equilibrium (VLE) data measured for DMC + MeOH + DESs ternary systems at 101.3 kPa showed that the addition of 15 mol % of any of the five DESs could successfully break the azeotrope and DES2 achieved a higher degree of separation in the MeOH-DMC binary azeotrope compared to the other DESs evaluated. The binary interaction parameters between MeOH/DMC and DESs were calculated through the NRTL (Non-Random Two-Liquid) model, and the fitting results were found to be consistent with the experimental data. The mechanism of the MeOH-DMC separation by DES2 was elucidated through quantum chemical (QC) calculations. The improved independent gradient model (IGMH) and the theory of atoms in molecules (AIM) demonstrated that the stronger interaction between DES2 and MeOH molecules is the key for DES2 to break the azeotrope of the system.

Use of Thermodynamically Consistent Phase Equilibrium Data to Obtain a Generalized Padé-Type Model for the Henry’s Constants of Gases in Ionic Liquids

A generalized Padé-type expression is proposed for Henry’s constant of gases in ionic liquids. The constants are determined using an equation of state, and generalized expressions for the Henry’s constants of the gases in the ionic liquids are proposed. The solute gases included in the study were oxygen, hydrogen, and carbon monoxide in three solvent ionic liquids ([MDEA][Cl], [Bmim][PF6], and [Hmim][TF2N]). The Valderrama–Patel–Teja equation of state with the mixing rules of Kwak and Mansoori are employed to correlate the solubility data, to examine the thermodynamic consistency of the experimental data, and to determine the fugacity (fi) for each concentration (xi) of the solute gas in the liquid phase. From these data, the fugacity coefficients (fiL/xi) are determined to obtain Henry´s constant as Hi = lim(fiL/xi) when xi→0. The calculated Henry’s constants are correlated in terms of the temperature and acentric factor of the gases to finally obtain a generalized expression for Henry´s constant, Hi.

Application of thermodynamics at different scales to describe the behaviour of fast reacting binary mixtures in vapour-liquid equilibrium

The use of reactive working fluids in thermodynamic cycles is currently being considered as an alternative to inert working fluids, because of the preliminarily attested higher energy-efficiency potential. The current needs to simulate their use in thermodynamic cycles, which may operate in liquid, vapour or vapour-liquid state, are an accurate real-fluid equation of state and ideal gas thermochemical properties of each molecule constituting the mixture, to calculate the equilibrium constant. To this end, the appeal to a multi-scale theoretical methodology is paramount and its definition represents the objective of the present work. This methodology is applied and validated on the system N2O4 ⇌ 2NO2. Firstly, the equations solved for simultaneous two-phase and reaction equilibrium are presented. Secondly, ideal gas thermochemical properties of N2O4 and NO2 are computed at atomic scale by quantum mechanics simulations. Then, to apply the selected cubic equation of state, pure-component properties of the species forming the reactive mixture (critical point coordinates and acentric factor) are required as input. However, these properties are not measurable, since NO2 and N2O4 do not exist in nature as pure components. To get around this difficulty, the methodology relies on molecular Monte Carlo simulations of the pure N2O4 and NO2, as well as on the reactive N2O4 ⇌ 2NO2, enabling the determination of those missing pure-component properties and thus the calculation, on a macroscopic scale, of the reactive mixture properties. Finally, the comparison of calculated mixture properties with available experimental data leads to validate the accuracy of the proposed methodology.

On some extended energy of graphs and their applications

In this paper, we established a relation between the extended energy of graphs such as the first and second Zagreb energy, Randi?c energy, reciprocal Randi?c energy, and the atom-bond connectivity energy with some thermodynamic properties of benzenoid hydrocarbons. We have seen that these indices are well correlated to the boiling point (BP), Kovats retention index (RI), entropy (S), enthalpy of formation (?Hf), octanol-water partition coefficient (logP), and acentric factor (?) of benzenoid hydrocarbons.

Degree-weighted Wiener index of a graph

<abstract><p>From geometric point of view, we introduced the Sombor-Wiener index of a graph and studied the basic properties of the new index. It was shown that the Sombor-Wiener index was useful in predicting the acentric factor of octane isomers. In addition, we proposed a degree-weighted Wiener index to generalize the Schultz index, the Gutman index, and the Sombor-Wiener index. Meanwhile, we gave the calculation formula of degree-weighted Wiener index for generalized Bethe trees.</p></abstract>

A Cubic Equation of State with a Repulsion Term

A new cubic equation of state (EoS) was proposed to address the lack of repulsion terms in conventional cubic EoSs, with a molar critical compressibility factor Zc = 0.273 and suitable for most molecular fluids. Similar to Soave-Redlich-Kwong (SRK) EoS, its α-function is related to the fluids’ acentric factors by fitting with 44 molecular fluids. Differently, the new EoS can pass the α-consistency test, confirming the robustness across all temperatures. With only three parameters (ac, b, m) to be determined, it is as convenient as the SRK EoS in application. But it is more accurate - tested against experimental data - for both single and multi-component fluids than SRK EoS.

Comprehensive study on deep eutectic solvent density based on various EoSs: SRK, PT, VTSRK, sPC-SAFT

In this communication, the capability of a two-parameter cubic equation of state (EoS) i.e. Soave-Redlich-Kwong (SRK) EoS to predict the density behavior of deep eutectic solvents (DESs) in the wide range of temperature conditions and at atmospheric pressure, was improved using the volume-translated concept. At first, the c-parameter of 139 DESs (1793 experimental data points) was obtained referring to volume-translated SRK (VTSRK) EoS. The obtained results were compared with the original SRK and Patel-Teja (PT) EoSs and sPC-SAFT (simplified perturbed chain statistical associating fluid theory) EoS. Afterward, three c-parameter correlations were recommended based on molecular weight and acentric factor (Case 1), acentric factor (Case 2), and critical compressibility factor (Case 3). The capability of recommended c-parameter correlations was investigated by density modeling of 67 new DESs systems (419 experimental data). The AARD% (average absolute relative deviation) of Case 1, Case 2, Case 3 and sPC-SAFT EoS was 4.24%, 3.24%,4.19% and 0.5677%, respectively.

Mathematical aspects and molecular descriptors for anti-tumour and anti-COVID drugs medications

The COVID-19 pandemic has significantly affected both the global economy and human health. COVID-19 is a single-stranded RNA virus that spreads through the inhalation of viral droplets. Its genome encodes four structural proteins: the envelop protein, spike protein, membrane protein, and nucleocapsid protein. The virus's capsid is a protein shell that contains a positive RNA strand that allows it to take control of human cell machinery. Currently, the only treatments for COVID-19 are preventative measures and immunization. Some of the anti-COVID and anti-cancer medications used to combat this virus include Camptothecin Polymer, Hyaluronic Acid-curcumin, and Hydroxychloroquine. Graphs are used extensively in chemical investigation to provide a mathematical model of molecules. The selection of graph invariants, formerly known as molecular structure descriptor's, is the mathematical modelling of chemical compounds’ physio-chemical, pharmacologic, and toxicological aspects. This paper presents a new technique to compute topological indices for three types of chemical networks for a few anti-COVID and anti-cancer medications. Our findings suggest that these indices show a strong association with the acentric factor and entropy, which make them effective in QSPR and QSAR analysis with high accuracy.

Understanding dynamics in coarse-grained models. III. Roles of rotational motion and translation-rotation coupling in coarse-grained dynamics.

This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.

Estimating CO2 solubility in ionic liquids by using machine learning methods

Ionic liquids (ILs) can be used to absorb a greater quantity of carbon dioxide (CO2) by adjusting the ratio of anions and cations.The methods to obtain CO2 solubility in ILs are as follows: Experiment, Equation of State (EOS) and Molecular dynamics simulation (MD). The experiment is time-consuming and labor-intensive, EOS requires critical parameters, and MD calculation is complicated. However, Machine Learning (ML) methods are embraced with high prediction accuracy and convenience by the chemical and petroleum industry. In this work, 1517 solubility data were collected based on 20 different ILs. Three different machine learning methods (Optimization (PSO), Grey Wolf Optimization (GWO) and Sparrow Search Algorithm (SSA) based on Support Vector Machine (SVR)), using acentric factor (ω), critical temperature (Tc), critical pressure (pc) of ILs accompanied by pressure (p), and temperature (T), as input parameters, were employed to predict CO2 solubility in ILs. Meanwhile, three error indexes (namely root mean square error (RMSE), correlation coefficient (R2) and average absolute relative deviation (AARD)), and the duration of time each specified model (PSO-SVR, GWO-SVR and SSA-SVR) takes in order to evaluate the effectiveness of each prediction model.Although the results show that the three different optimization models (PSO-SVR, GWO-SVR and SSA-SVR) have viable prediction effects, the performance of PSO-SVR model has high accuracy and is the lowest time-consuming among them with RMSE and R2 of 0.01881 and 0.9824, respectively. For the SSA-SVR, the estimated RMSE and R2 are respectively 0.01944 and 0.9824 while they are 0.01889 and 0.9822 for the GWO-SVR, respectively. The results imply that all of the models can give reliable predictions on the CO2 solubilities in ILs and the PSO-SVR model performs slightly better than the SSA-SVR and GWO-SVR models.

Assessment of the pseudopotential lattice-Boltzmann method for modeling multiphase fuel droplets

An improved pseudopotential lattice–Boltzmann model was proposed for simulating multiphase flow dynamics to describe fuel droplets, and its thermodynamic consistency was tested against the Peng–Robinson equation of state. The studied liquid fuels included paraffinic hydrocarbons with a different number of carbon atoms (C[Formula: see text]–C[Formula: see text]), methanol (CH[Formula: see text]OH), hydrogen (H[Formula: see text]), ammonia (NH[Formula: see text]), and water (H[Formula: see text]O). To improve accuracy and reduce the magnitude of the spurious currents, the multi-relaxation times collision operator was implemented and the forcing term was computed using the hybrid pseudopotential interaction force with an eighth-order isotropic degree. The pseudopotential lattice–Boltzmann model accurately predicted the equilibrium densities and captured satisfactorily the thermodynamic vapor-liquid coexistence curve given by the analytical solution of the Peng–Robinson equation of state for acentric factors ranging from [Formula: see text]0.22 to 0.56, keeping the maximum average error for the liquid and vapor branches below 0.8% and 3.7%, respectively. Nevertheless, Peng–Robinson was found to be insufficiently accurate to replicate the actual thermodynamic state, especially for H[Formula: see text]O and CH[Formula: see text]OH, for which the results strongly deviated from the experimental vapor-liquid equilibrium densities and reached average errors for the vapor phase of nearly 28%. Furthermore, the surface tension ([Formula: see text]) was retrieved using the multiphase pseudopotential lattice–Boltzmann results and served to verify the thermodynamic consistency of the pseudopotential lattice–Boltzmann with respect to the parachor model. Lastly, the pseudopotential lattice–Boltzmann model was also shown to predict accurately the transient behavior of oscillating droplets. Overall, the enhanced model satisfactorily predicted the properties and behavior of the substances for a wide range of conditions.

Mathematical modeling and topological graph description of dominating David derived networks based on edge partitions

Chemical graph theory is a well-established discipline within chemistry that employs discrete mathematics to represent the physical and biological characteristics of chemical substances. In the realm of chemical compounds, graph theory-based topological indices are commonly employed to depict their geometric structure. The main aim of this paper is to investigate the degree-based topological indices of dominating David derived networks (DDDN) and assess their effectiveness. DDDNs are widely used in analyzing the structural and functional characteristics of complex networks in various fields such as biology, social sciences, and computer science. We considered the FN*, {M}_{2}^{*}, and {HM}_{N} topological indices for DDDNs. Our computations' findings provide a clear understanding of the topology of networks that have received limited study. These computed indices exhibit a high level of accuracy when applied to the investigation of QSPRs and QSARs, as they demonstrate the strongest correlation with the acentric factor and entropy.

Studies on crystallization process for pharmaceutical compounds using ANN modeling and model based control

Solvent selection and Controlling of operating parameters play a crucial role in batch cooling crystallization process. Choosing a best solvent for crystallization process involves more experimentation and time. To overcome this problem, an Artificial Neural Network (ANN) model technique is used to predict the carbamazepine form Ⅲ solubility by considering the thermodynamic properties of different solvents i.e. critical temperature, critical pressure, temperature, molecular weight, and acentric factor. The ANN model was trained and evaluated for solubility at various input data sets using experimental solubility data available in the literature. The ANN model with 20 hidden neurons has given the R2 value of 0.9943 which shows that the developed ANN model can be used for the selection of best solvent for batch crystallization process. Further, to determine the optimal cooling profile of batch cooling crystallization process, a multi-objective optimization problem is formulated by considering objectives as minimizing the coefficient of variation (CV) and maximizing the Number mean size (NMS) of crystals subjected to population balance equations using “method of moments” technique. Two types of temperature strategies i.e., piece-wise constant and piece-wise linear are developed and solved using NSGA-Ⅱ dynamic optimization procedure. The optimal NMS value attained through piece-wise linear strategy was 197.1 µm. This value has been increased by 28.3 µm from the nominal case (without optimization) and the coefficient of variation has decreased from 0.951 to 0.76. Further, optimal NMS value attained through piece-wise constant strategy was 205 µm. The value has been increased by 36.2 µm and the coefficient of variation has decreased from 0.951 to 0.73. This proves that the crystal attributes can be improved by optimal cooling temperature profile obtained by multi-objective optimization framework. For implementing the optimal cooling profile an advanced model-based control, i.e., Generic Model Control (GMC) was developed. It was observed that the GMC controller has the good tracking profile with no offset with/without disturbances and small value of root mean square error (RMSE) of 0.0016 using piece-wise constant as set point temperature. Using piece-wise linear as set point temperature, the RMSE value was 0.0018. In particular, it is advantageous to operate the batch cooling crystallization process with piece-wise linear strategy for set point trajectory tracking problems.

Predicting Critical Properties and Acentric Factors of Fluids Using Multitask Machine Learning.

Knowledge of critical properties, such as critical temperature, pressure, density, as well as acentric factor, is essential to calculate thermo-physical properties of chemical compounds. Experiments to determine critical properties and acentric factors are expensive and time intensive; therefore, we developed a machine learning (ML) model that can predict these molecular properties given the SMILES representation of a chemical species. We explored directed message passing neural network (D-MPNN) and graph attention network as ML architecture choices. Additionally, we investigated featurization with additional atomic and molecular features, multitask training, and pretraining using estimated data to optimize model performance. Our final model utilizes a D-MPNN layer to learn the molecular representation and is supplemented by Abraham parameters. A multitask training scheme was used to train a single model to predict all the critical properties and acentric factors along with boiling point, melting point, enthalpy of vaporization, and enthalpy of fusion. The model was evaluated on both random and scaffold splits where it shows state-of-the-art accuracies. The extensive data set of critical properties and acentric factors contains 1144 chemical compounds and is made available in the public domain together with the source code that can be used for further exploration.

Comparative Evaluation of a Functions for the Soave-Redlich-Kwong Equation of State and the Peng-Robinson Equation of State to Predict Saturation Pressures for Gas(es)-Heavy Oil/Bitumen-Water Systems

Summary To accurately predict saturation pressures for gas(es)-heavy oil/bitumen-water systems, several α functions have been selected and evaluated at a reduced temperature (Tr) of 0.70 and 0.60 for the Soave-Redlich-Kwong equation of state (EOS) and Peng-Robinson (PR) EOS, respectively. More specifically, 164 data points of measured saturation pressures of gas(es)-heavy oil/bitumen-water systems are collected from the public domain, while all α functions developed for heavy oil-associated mixtures and water have been reviewed and selected. At Tr = 0.70, the former, including three existing α functions, as well as two newly developed α functions at Tr = 0.70 together with three new α functions at Tr = 0.60, and the latter, including two alpha functions, are used to evaluate saturation pressures for various gas(es)-heavy oil/bitumen-water systems under various conditions. The absolute average relative deviation (AARD) between the measured saturation pressures and their predicted ones is found to decrease with either an increase in the pseudocomponent (PC) number or redefining the acentric factor (ω) at Tr = 0.60 other than the conventional one at Tr = 0.70. In addition to validating our coded program, the CMG WinProp module, together with its default binary interaction parameters (BIPs) is used to, respectively, quantify saturation pressures of the aforementioned systems with an overall AARD of 27.34 and 28.39% for the PR EOS and SRK EOS. The recommended α function newly developed at Tr = 0.60 by Chen and Yang (2017) predicts saturation pressures more accurately with an overall AARD of 3.88 and 1.64% by, respectively, treating the heavy oil as one PC and six PCs.

Chemical Applicability of Second Order Sombor Index

In this paper, we introduce the higher-order Sombor index of a molecular graph. In addtition, we compute the second order Sombor index of some standard class of graphs and line graph of subdivision graph of 2D-lattice, nanotube and nanotorus of TUC_4C_8[p,q] and also we obtain the expressions of the second order Sombor index of the line graph of subdivision graph of tadpole graph, wheel graph, ladder graph and chain silicate network CSn. Further, we study the linear regression analysis of the second order Sombor index with the entropy, acentric factor, enthalpy of vaporization and standard enthalpy of vaporization of an octane isomers.

Prediction of solvation energies at infinite dilution by the tc-PR cubic equation of state with advanced mixing rule based on COSMO-RS as gE model

The prediction of solvation quantities is an important issue in several fields of chemical and process engineering. In this regard, this work was conducted to increase the prediction power of the equation-of-state (EoS) approach by coupling the tc-PR (translated-consistent Peng-Robinson) EoS with COSMO-RS (Conductor-like Screening Model for Real Solvents) as gE model through an advanced mixing rule. Since the only input parameter of the COSMO-RS model is the charge density (σ) profile of each molecule, the resulting EoS (called tc-PR/COSMO-RS) does not require any binary interaction parameter contrary to other predictive cubic EoS, such as VTPR, PPR78, PSRK, and UMR-PRU. This feature allows the quantification of solvation data of a great number of systems from readily available pure-component properties (critical temperature and pressure, acentric factor and σ -profile). Satisfactory results were obtained for the prediction of solvation Gibbs energy data that were extracted from the extensive CompSol database (the average absolute deviation is 0.30 kcal/mol). The proposed model represents a very flexible alternative for the prediction of solvation data, since it can deal with a large variety of solutes in either a pure or mixed solvent, and for the entire phase diagram (including the supercritical region).

On the Hyper Zagreb Index of Trees with a Specified Degree of Vertices

Topological indices are the numerical descriptors that correspond to some certain physicochemical properties of a chemical compound such as the boiling point, acentric factor, enthalpy of vaporisation, heat of fusion, etc. Among these topological indices, the Hyper Zagreb index, is the most effectively used topological index to predict the acentric factor of some octane isomers. In the current work, we investigate the extremal values of the Hyper Zagreb index for some classes of trees.

Thermo-economic performance limit analysis of combined heat and power systems for optimal working fluid selections

In previous works, we have proposed the thermodynamic performance limit analysis methodology for the organic Rankine cycle for analyzing the impact of working fluid properties on system performance. Here the concept is extended to the thermo-economic performance limits, and is applied to a combined heat and power system based on an organic Rankine cycle. Working fluids are characterized with 8 characteristic thermodynamic and transport properties based on a corresponding state model and a residual entropy scaling approach. The 8 fluid characteristic properties along with 3 system operational parameters are optimized using a multi-objective genetic algorithm; a Monte Carlo algorithm is further adopted to avoid sub-optimal convergences. As the result, the performance limits could be well represented by the trade-off (Pareto front) between the maximized thermal efficiency and minimized payback period. The impact of the fluid characteristic properties on both thermodynamic and economic targets is investigated and ultimately guided the choice of working fluids: low molar mass, low thermal conductivity scaling factor, high viscosity scaling factor and high critical pressure are always preferred. "Wet" working fluid is preferred for a high thermal efficiency while "dry" working fluid is favored for a short payback period. Critical temperature has the most profound impact, while ideal gas isobaric heat capacity and acentric factor have negligible impacts. The choice of working fluid, system design (e.g., recuperative effectiveness) and system operational parameters (e.g., evaporation temperature) highly depends on the given hot sources and the preferences to the thermodynamic and economic targets.