Properties Of Pure Substances Research Articles

Implementation of solvation free energy framework to predict the vapor-liquid equilibrium behaviors for the water–hydrazine and ethanol–water azeotropic systems

An azeotrope is a special vapor–liquid equilibrium in which the composition of two coexisting phases is equal. Due to its strong deviation from the Raoult’s law, it poses a great challenge to the simple distillation process and the understanding of fundamental molecular mechanisms. In this study, we calculated the coupling work of solute species based on the solvation free energy framework to predict the vapor–liquid equilibrium (VLE) behavior and azeotrope point of mixtures. Two prototypical binary mixtures: the negative water-hydrazine and positive ethanol–water azeotrope were investigated using molecular dynamic simulations and the OPLS-AA force field. All the simulations were performed with the TIP3P water model, because it has a good capability to represent enthalpy properties. The molecular models of hydrazine and ethanol have been re-parameterized to reproduce the density and solvation free energy properties of pure substance. Using free energy perturbation simulation, the coupling work of each substance was studied against liquid mixture composition. The coupling work is also translated to x-y or T-x-y phase diagrams for comparison with available experimental data. The tendency of two azeotropes is that the more volatile components experience the less pronounced coupling work changes in their local environments as the azeotropes form. The coupling work is also divided into van der Waals and Coulomb contributions to investigate the interactions between particles. Lithium Chloride was investigated as an entrainer for the separation of ethanol–water system. The coupling works of binary mixtures were calculated at different salt concentrations to study the salt-out effect for the violate species and salt-in effect for the less violate species. By adding LiCl, it was found that the azeotrope point was efficiently eliminated at a salinity 0.05 mol fraction at 1 bar. All the results show that the simulation methodology of coupling work are reliable for calculating the liquid–vapor equilibrium behavior. This method is also valuable for selecting and designing new extractants for distillation process.

FeOs: An Open-Source Framework for Equations of State and Classical Density Functional Theory

In this work, we present an open-source software package, referred to as FeOs─Framework for Equations of State and Classical Density Functional Theory. FeOs is a collection of interfaces and data types that can be used (1) to implement thermodynamic equations of state and Helmholtz energy functionals for classical density functional theory, and (2) to compute thermodynamic properties of pure substances and mixtures, phase equilibria, and interfacial properties such as surface tensions and adsorption isotherms. The framework is written in the Rust programming language with a complete Python interface and is designed with a focus on usability and extensibility. It is openly available on GitHub (https://github.com/feos-org/feos). Equations of state can be implemented in Rust, yielding performant code, or as a Python class, which is useful for prototyping and with less emphasis on execution speed. In both cases, the user has to implement a single function: the Helmholtz energy. FeOs then uses generalized (hyper-) dual numbers to evaluate the Helmholtz energy as well as the required exact partial (higher-order) derivatives. Using this type of automatic differentiation delivers performance without the need for implementing any analytical derivatives. The performance is further enhanced by a caching mechanism that avoids duplicate model evaluations. Together with the core interfaces and functionalities for equations of state and classical density functional theory, we provide implementations for multiple models such as the PC-SAFT equation of state (with homo- and heterosegmented group contribution methods) and Helmholtz energy functionals (including segment-based functionals). To showcase a selection of FeOs’ features, an example study of the adsorption of biogas in porous media using the PC-SAFT functional is provided.

Modeling of thermodynamic processes using the properties of matter presented in the form of spreadsheets

New thermodynamic cycles are developed in which the working fluid used cannot be considered as an ideal gas. This applies to oxy-fuel combustion cycles. In these cycles, oxygen is separated from the air prior to combustion. The combustion chamber is supplied with fuel and pure oxygen. The required temperature at the outlet of the combustion chamber is achieved by supplying some other substances from which it is easy to separate the CO2 formed during the combustion of the fuel. Commonly, CO2, or H2O, or their mixture is used as such substances. Thus, there are no exotic substances in the composition of the working fluid, but such a range of parameters is chosen for such cycles that the working fluid at certain points of the cycle can be both gaseous and liquid, or in a supercritical state. To model thermodynamic processes in such cycles, it is unacceptable to use the polytropic equation of ideal gases. A technique for integrating differential equations describing the state of the working fluid is proposed. This technique is based on the presentation of the thermodynamic properties of pure substances that make up the working fluid in the form of spreadsheets. The proposed technique is implemented in a software-computing module.

Predicting Single-Substance Phase Diagrams: A Kernel Approach on Graph Representations of Molecules.

This work presents a Gaussian process regression (GPR) model on top of a novel graph representation of chemical molecules that predicts thermodynamic properties of pure substances in single, double, and triple phases. A transferable molecular graph representation is proposed as the input for a marginalized graph kernel, which is the major component of the covariance function in our GPR models. Radial basis function kernels of temperature and pressure are also incorporated into the covariance function when necessary. We predicted three types of representative properties of pure substances in single, double, and triple phases, i.e., critical temperature, vapor-liquid equilibrium (VLE) density, and pressure-temperature density. The accuracy of the models is nearly identical to the precision of the experimental measurements. Moreover, the reliability of our predictions can be quantified on a per-sample basis using the posterior uncertainty of the GPR model. We compare our model against Morgan fingerprints and a graph neural network to further demonstrate the advantage of the proposed method.

Estimation of vaporization properties of pure substances using artificial neural networks

Vaporization properties are important for equipment modeling and process control involving liquid-vapor equilibrium. The aim of this work was to obtain an Artificial Neural Network (ANN) to predict volume, internal energy, enthalpy, and entropy of vaporization, and the saturation pressure (or temperature) of several fluids. Two strategies were proposed: one using saturation temperature in the inputs and another using saturation pressure. Five physicochemical descriptors were used to distinguish each substance. All ANNs were trained using the Levenberg-Marquardt method. Nine outputs combination were evaluated to obtain the best model, which was determined by simulating a dataset not shown in the training/validation/test steps. The results showed that ANNs with three outputs presented higher accuracy. The best one (structure 4-40-40-3) predicted saturation pressure, internal energy and enthalpy of vaporization as outputs and presented relative errors as low as 0.02%. Finally, we showed that ANNs can be reliable for vaporization properties prediction.

Experimental Study of Electrical Properties of Pharmaceutical Materials by Electrical Impedance Spectroscopy

The physicochemical characterization of pharmaceutical materials is essential for drug discovery, development and evaluation, and for understanding and predicting their interaction with physiological systems. Amongst many measurement techniques for spectroscopic characterization of pharmaceutical materials, Electrical Impedance Spectroscopy (EIS) is powerful as it can be used to model the electrical properties of pure substances and compounds in correlation with specific chemical composition. In particular, the accurate measurement of specific properties of drugs is important for evaluating physiological interaction. The electrochemical modelling of compounds is usually carried out using spectral impedance data over a wide frequency range, to fit a predetermined model of an equivalent electrochemical cell. This paper presents experimental results by EIS analysis of four drug formulations (trimethoprim/sulfamethoxazole C14H18N4O3-C10H11N3O3, ambroxol C13H18Br2N2O.HCl, metamizole sodium C13H16N3NaO4S, and ranitidine C13H22N4O3S.HCl). A wide frequency range from 20 Hz to 30 MHz is used to evaluate system identification techniques using EIS data and to obtain process models. The results suggest that arrays of linear R-C models derived using system identification techniques in the frequency domain can be used to identify different compounds.

Prediction of solid solute solubility in supercritical carbon dioxide with and without organic cosolvents from PSRK EOS

Solid solute solubility in supercritical carbon dioxide (ScCO2) with and without organic cosolvents provides important information for design and optimization of processes involving ScCO2 in industry. The accuracy of PSRK EOS in predicting solid solute solubility in ScCO2 with and without organic cosolvents is systematically investigated in this study. The first-principles thermodynamic model PR + COSMOSAC EOS and four well-known group contribution models are used to estimate critical properties and acentric factors for all solid solutes to overcome the lack of experimental critical properties for most investigated solid solutes. The results show that combining PSRK EOS with pure substance properties from a certain group contribution model provides the lowest overall deviations, but those from the first-principles thermodynamic model give greater accuracy for solutes with complicated molecular structures. In general, the PSRK EOS is able to provide useful solubility information, especially when no experimental data is available.

Methods for calculating equilibrium properties of pure substances, considering the critical point features

This paper deals with a fundamental equation of state for matter (FEoS). When constructing FEoS, the method of pseudocritical points (PCP) is used. The PCP method is based on the Benedek hypothesis and a new representation of the scale hypothesis of the critical point. We show the possibility to construct FEoS of argon based on the PCP method with the following characteristics: (i) FEoS is transformed into the virial equation of state in the region of small densities; (ii) FEoS is transformed into the Widom equation in the region of the critical point; (iii) FEoS has its working area with pressure (0 ≤ p/pc ≤ 740), density (0 ≤ p/pc ≤ 3.2) and temperature (83.8058 ≤ T ≤ 2300∼K) in. We compare FEOS with a number of known equations of argon state and discuss the results.

Toward generalized models for estimating molecular weights and acentric factors of pure chemical compounds

In this work, four prompt and robust techniques have been used to introduce new generalized models for estimation of the physical properties of pure substances, including molecular weight and acentric factor. These methods were developed based on radial basis function (RBF) neural networks, group method of data handling (GMDH), multilayer perceptron (MLP), and least square support vector machine (LSSVM) techniques. Models were introduced based on a set of experimental data including 563 pure compounds that were collected from available literature. Input parameters for estimation of molecular weight were considered as specific gravity and normal boiling point. Critical temperature, critical pressure and normal boiling point were selected as inputs for estimation of the acentric factor. Statistical and graphical error analyses normal boiling point revealed that all of the developed models are accurate. The designed RBF models give the most accurate results with an AAPRE of 5.98% and 1.92% for molecular weight and acentric factor, respectively. The developed GMDH models are in the form of simple correlations, which can be used easily in hand calculation problems without any need to computers. Comparison of the developed models with the available methods showed that all of the developed models are more accurate than the existing methods. Using the relevancy factor, the impact of each input parameter on the output results was determined. Additionally, to find out the applicability region of the developed models, and to demonstrate the reliability of the models, the Leverage method has been used. There are few data out of the applicability domain of the proposed models. All the statistical and graphical resolutions, demonstrate the reliability of the developed models in estimating the molecular weight and acentric factor.

Effective Critical Constants for Helium for Use in Equations of State for Natural Gas Mixtures

Most of the world’s helium supply is obtained by the cryogenic distillation of natural gas. Modeling the distillation conditions requires equations of state capable of predicting vapor–liquid equilibria over wide ranges of conditions. Equations of state, including cubic equations and multiparameter Helmholtz models, depend on the critical properties of pure substances for predicting various properties of multicomponent fluid mixtures. Predictions for helium are problematic as its critical point (5.195 K, 0.2275 MPa) is influenced strongly by quantum effects; large, empirical interaction parameters tend to be used in equations of state to compensate for these effects. Prausnitz and co-workers proposed an alternative approach using effective critical constants for quantum gases but demonstrated it for only three helium-containing binary mixtures. Here, we demonstrate that the use of an effective critical point at (11.73 K, 0.568 MPa) for helium substantially improves the prediction of VLE by the Peng–Robinson equation of state for 15 binary and 2 ternary mixtures, including the major components of natural gas. This effective critical point for helium was selected from a critical analysis of pTxy data for the (methane + helium) binary. The effective critical constants for helium are compatible with an acentric factor near zero, as expected for a small spherical molecule and similar to the acentric factors of heavy noble gases. The possibility of applying this approach to address recognized limitations of the GERG-2008 equation of state is discussed.

A new generalized model for predict speed of sound of refrigerants

In consideration of physical and chemical properties of pure substances, speed of sound is one of important quantity which can used to calculate many of other thermo-physical properties such as isothermal compressibility, Joule-Thomson coefficient, isobaric heat capacity and etc. These thermo-physical properties are the main parameters in industrial and chemical processes. Development of accurate models for thermodynamic properties computation such as speed of sound is well expected above all in those fields where very high performance calculations have to be reached. In this present work, a new generalized model as a function of reduced temperature and reduced density is proposed to correlate speed of sound of methane, ethane, propane and butane halogenated refrigerants. Speed of sounds have been calculated and compared with data reported in literatures for 5600 data points of 28 refrigerants, and the overall average absolute percentage deviation of 0.92%. The source of speed of sound data used in this study is the NIST Chemistry WebBook.

Comparative Method of Calculating the Thermodynamic Parameters of Some Uranium Hexafluoride Solutions

It is shown that the thermodynamics characteristics of uranium hexafl uoride solutions with volatile hexaand pentafl uoride elements are a consequence of the strictly symmetric confi guration of their molecular structure in the gaseous and liquid states. Simple methods are proposed for evaluating the properties of binary mixtures of elemental penta- and hexafl uorides. These methods are based on a comparison of the element–fl uorine bond length in the constituent molecules of system and the known enthalpy of mixing of one solution with the potential energy in the formation of a pair of unlike molecules of a different solution. Researchers looking for a universal method of deep purifi cation of uranium hexafl uoride have turned their attention to a rectifi cation method, for which there are no limitations on the depth of purifi cation, and a list of impurities to be removed, including metal impurities which are diffi cult to remove by means of water-extraction conversions of uranium concentrates and give volatile fl uorides (molybdenum, tungsten, ruthenium, technetium, and others). Moreover, its specifi c productivity is high, the energy consumption is low, and the separation effi ciency is high. These advantages are due to the special properties of uranium hexafl uoride as a working substance for rectifi cation: high density of liquid (more than 3.5 times higher than the density of water) and gaseous uranium hexafl uoride, low viscosity comparable to that of water, good wettability of the metals which are corrosion resistant to fl uoride media, and low heat of evaporation of liquid uranium hexafl uoride (less than 1/10th that of water). Deep purifi cation of uranium hexafl uoride raw material by rectifi cation has been used in the Republic of South Africa for several decades now [1]. In our country, we have experience in prolonged operation of a large-tonnage rectifi cation process for purifying sublimate and high-enrichment uranium hexafl uoride [2–4]. In order to develop a rectifi cation process, it is necessary to have information on the phase equilibrium of mixtures based on uranium hexafl uoride and to predict the properties of systems with which it is diffi cult to experiment. Computer methods of calculating steam-water systems have now been developed and are being improved; examples are models of local compositions Wilson, NRTL, UNIQUAC, equations of state SRK, Peng Robinson, and the group model UNIFAC, TTA [5–7]. They are based on the equation of thermodynamic equilibrium between coexisting phases and are generalizations of the Van-der-Waals equation of phase equilibrium, expressed in terms of partial properties [8]. Some forms of this equation are identical to a previously used van-Laar equation expressing the dependence of the coeffi cient of activity of a component on the composition of the solution [9]. Such methods of calculating the liquid–vapor equilibrium in nonideal systems take account of the effect of variable temperature and are convenient for modeling mixtures with an appreciable difference of the boiling temperature of pure components, making it possible to obtain good agreement between the computed and experimental parameters for some solutions. The application of a comparative method for calculating the properties of pure substances and solutions and the characteristics of phase and chemical equilibria is illustrated in the monograph [10]. In the present work, a method is proposed for fi nding parameters that can be used to calculate the vapor–liquid equilibria of mixtures of elemental hexa- and pentafl uorides by means of a comparative method.

Rapid prediction of solvation free energy and vapor pressure of liquid and solid from molecular dynamics simulation

We show that the solvation free energy and vapor pressure, important thermodynamic properties of pure substances in liquid or solid states, can be obtained from short, about 20 ps, molecular dynamics simulations. The method combines the determination of free energy of a chemical in vacuum using the normal‐mode analysis (NMA, energy minimization), and in the condensed phase using the two‐phase thermodynamic (2PT) model. We have examined the calculation results for common liquids and solids, including water, alcohol, acid, aromatics, and alkanes. The results, referred to as 2PT‐NMA, is comparable to those calculated from thermodynamic integration (TI) for liquids, and is readily applicable to solids, where simple TI is not applicable. Furthermore, the free energy from 2PT‐NMA converges (20 ps) much faster than that from TI (1 ns). The new method could be a very useful tool for fast screening of condensed phase pressure from the trajectory of MD simulations. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2298–2306, 2015

Measurement of critical heat flux conditions under vacuum

AbstractDetermination of optimum conditions for waste oil (used motor oils, transformer oils) regeneration using vacuum distillation was attempted including the search for the optimum temperature difference between the heating surface and the boiling point of the liquid. Optimum temperature allowed the distillation equipment to operate at maximum performance. Equipment suitable for the measurement of boiling curves under atmospheric pressure and vacuum conditions was assembled. These curves were used to determine the optimum temperature difference of various substances including waste oils. Properties of pure substances, for example water, ethanol, hexane, heptane, isooctane, decane, or dodecane, were measured with this equipment under atmospheric pressure. Results of various liquids measurements under vacuum and atmospheric pressure are presented.

Prediction of thermo-physical properties of argon at cryogenic conditions using modified Benedict-Webb-Rubin equation of state

The present work aims to determine thermo-physical properties such as mass density, specific heat capacity, viscosity, enthalpy and thermal conductivity of argon at cryogenic temperatures and high pressures up to 20 MPa. The deviations from the ideal gas law led to development of many empirical models based on equation of state (EOS) such as van der Waals EOS, Benedict-Webb-Rubin (BWR) EOS, Peng-Robinson EOS, Soave-Redlich- Kwong, etc. to predict the properties of pure substances. The present paper describes the development of a simple computer program in MATLAB for prediction of the properties using Modified Benedict-Webb-Rubin (MBWR) equation of state.

Thermodynamics of wax formation in the fischer-tropsch synthesis products

A new method is suggested for calculating the thermodynamic equilibrium in a multicomponent multiphase system without chemical reactions. This method is based on ideas of statistical physics and non-equilibrium thermodynamics and includes numerical minimization of the Gibbs energy of the complex system. Component concentrations and the physically realizable roots of the equation of state are calculated as the steady state solutions of the set of ordinary differential equations that is implied by the procedure of seeking the probability maximum for the realization of the equilibrium distribution. The approach developed here is used to calculate the equilibrium distribution of the concentrations of vaporous, liquid, and solid substances in the Fischer-Tropsch synthesis products. A thermodynamic model of the formation of solid paraffins from the synthesis products is presented. The calculation of the properties of pure substances and liquid and gaseous products is based on the Lee-Kesler equation of state. The wax formation thermodynamics is considered in the regular solid solution approximation (Hildebrand-Scott model) and in the solid solution approximation taking into account the nonideality of the system (NRTL model). The calculated mass fractions of vaporous, liquid, and solid synthesis products are presented as a function of temperature for different values of the chain propagation constant.

An alternative use of Kieffer’s lattice dynamics model using vibrational density of states for constructing thermodynamic databases

We use Kieffer’s model to represent the vibrational density of states (VDoS) and thermodynamic properties of pure substances in pressure–temperature space. We show that this model can be simplified to a vibrational model in which the VDoS is represented by multiple Einstein frequencies without significant loss of accuracy in thermodynamic properties relative to experimental data. The resulting analytical expressions for thermodynamic properties, including the Gibbs energy, are mathematically simple and easily accommodated in existing computational software for making thermodynamic databases. We show for aluminium, platinum, orthoenstatite and forsterite that thermodynamic properties can be represented with comparable accuracy as with Kieffer’s model with the same number of fitting parameters as in the Mie–Gruneisen–Debye model. We demonstrate that the method enables to achieve thermodynamic properties with superior accuracy relative to the Mie–Gruneisen–Debye method. The method is versatile in the sense that it allows incorporating dispersion of Gruneisen parameters. It is possible to extend the formalism to include other physical effects, such as intrinsic anharmonicity in the same way as in vibrational models based on Kieffer’s formalism.

Statistical Approach to Quality Control of Large Thermodynamic Databases

In chemistry and engineering, thermodynamic databases are widely used to obtain the basic properties of pure substances or mixtures. Large and reliable databases are the basis of all thermodynamic modeling of complex chemical processes or systems. However, the effort needed in the establishment, maintenance, and management of a database increases exponentially along with the size and scope of the database. Therefore, we developed a statistical modeling approach to assist an expert in the evaluation and management process, which can pinpoint various types of erroneous records in a database. We have applied this method to investigate the enthalpy, entropy, and heat capacity characteristics in a large commercial database for approximately 25,000 chemical species. Our highly successful results show that a statistical approach is a valuable tool (1) for the management of such databases and (2) to create enthalpy, entropy and heat capacity estimates for such species in which thermochemical data are not available.

IGE Model: An Extension of the Ideal Gas Model to Include Chemical Composition as Part of the Equilibrium State

The ideal gas (IG) model is probably the most well-known gas models in engineering thermodynamics. In this paper, we extend the IG model into an ideal gas equilibrium (IGE model) mixture model by incorporating chemical equilibrium calculations as part of the state evaluation. Through a simple graphical interface, users can set the atomic composition of a gas mixture. We have integrated this model into a thermodynamic web portal TEST (http://thermofluids.sdsu.edu/) that contains Java applets for various models for properties of pure substances. In the state panel of the IGE model, the known thermodynamic properties are entered. For a given pressure and temperature, the mixture's Gibbs function is minimized subject to atomic constraints and the equilibrium composition along with thermodynamic properties of the mixture are calculated and displayed. What is unique about this approach is that equilibrium computations are performed in the background, without requiring any major change in the familiar user interface used in other state daemons. Properties calculated by this equilibrium state daemon are compared with results from other established applications such as NASA CEA and STANJAN. Also, two different algorithms, an iterative approach and a direct approach based on minimizing different thermodynamic functions in different situation, are compared.

Rapid determination of entropy and free energy of mixtures from molecular dynamics simulations with the two-phase thermodynamic model

The two-phase thermodynamic (2PT) model is generalized to determine the thermodynamic properties of mixtures. In this method, the vibrational density of states (DoS), obtained from the Fourier transform of the velocity autocorrelation function, and quantum statistics are combined to determine the entropy and free energy from the trajectory of a molecular dynamics simulation. In particular, the calculated DoS is decomposed into a solid-like and a gas-like component through the fluidicity parameter, allowing for treatments for the anharmonic effects in fluids. The 2PT method has been shown to provide reliable thermodynamic properties of pure substances over the whole phase diagram with only about a 20 ps MD trajectory. Here we show how the 2PT method can be used for mixtures with the same degree of accuracy and efficiency. We have examined the 2PT determined excess Gibbs free energies of Lennard-Jones (LJ) mixtures over a wide range of conditions (1 ≤ T* ≤ 3, 0.5 ≤ P* ≤ 2.5, 1 ≤ σ(BB)/σ(AA) ≤ 2, and 1 ≤ ε(BB)/ε(AA) ≤ 2), including the change of the off-diagonal LJ interactions. The 2PT determined values are in good agreement with those from Widom insertion or thermodynamic integration (TI). Our results suggest that the 2PT method can be a powerful method for understanding thermodynamic properties in more complicated multicomponent systems.