Thermodynamic Properties Of Pure Fluids Research Articles

Further Results on a Generalized van der Waals Model

A generalized van der waals model is considered to study the thermodynamic properties of pure fluids. Analytical solution of the equivalent cubic equation of state is presented and the critical properties in the general form are derived. The fluctuations of number of particles are calculated in the grand canonical ensemble by using three quantities (scaled variance omega (N), skewness Ssigma, and kurtosis ksigma ^2). The critical behavior of these quantities is investigated in terms of the dimensionless particle number density and temperature for different models. It is found that the fluctuations have a singular behavior close to the critical point.

Predictions of thermodynamic properties of pure fluids, refrigerants, and binary mixtures using modified Peng-Robinson equation of state

Predictions of thermodynamic properties of pure fluids, refrigerants, and binary mixtures using modified Peng-Robinson equation of state

A Comparative Study between Two Methods for Calculating the Thermodynamic Properties of Pure Fluids in an Energy System

A Comparative Study between Two Methods for Calculating the Thermodynamic Properties of Pure Fluids in an Energy System

Predicting the Coefficients of Antoine Equation Using the Artificial Neural Network (TECHNICAL NOTE)

Neural network is one of the new soft computing methods commonly used for prediction of the thermodynamic properties of pure fluids and mixtures. In this study, we have used this soft computing method to predict the coefficients of the Antoine vapor pressure equation. Three transfer functions of tan-sigmoid (tansig), log-sigmoid (logsig), and linear were used to evaluate the performance of different transfer functions to redict the coefficients of the Antoine vapor pressure equation. The critical pressure, critical temperature, critical volume, molecular weight, and acentric factor were considered as the input variables and the Antoine equation coefficients showed by the symbols A, B, and C were considered as the output variables. The results of this study indicated that the linear transfer function had a better performance than other transfer functions and the topology of 5-6-3 with Levenberg–Marquardt learning algorithm and linear transfer function had the best performance for prediction of these coefficients.

Machine learning for predicting thermodynamic properties of pure fluids and their mixtures

Establishing a reliable equation of state for largely non-ideal or multi-component liquid systems is challenging because the complex effects of molecular configurations and/or interactions on the thermodynamic properties must generally be taken into account. In this regard, machine learning holds great potential for directly learning the thermodynamic mappings from existing data, thereby bypassing the use of equations of state. The present study outlines a general machine learning framework based on high-efficiency support vector regression for predicting the thermodynamic properties of pure fluids and their mixtures. The proposed framework is adopted in conjunction with training data obtained from a high-fidelity database to successfully predict the thermodynamic properties of three common pure fluids. The predictions demonstrate extremely low mean square errors. Moreover, little loss in the prediction accuracy is obtained for ternary mixtures of the pure fluids at the cost of a modest increase in the volume of training data provided by state-of-the-art molecular dynamics simulations. Our results demonstrate the promising potential of machine learning for building accurate thermodynamic mappings of pure fluids and their mixtures. The proposed methodology may pave the way in the future for the rapid exploration of novel or complex systems with potentially exceptional thermodynamic properties.

A five-parameter cubic equation of state for pure fluids and mixtures

A five parameter cubic equation of state, named 5PGDN is presented for the prediction of thermodynamic properties of pure fluids and mixtures. A new alpha function is proposed with two compound specific parameters which are estimated by matching experimental saturation vapor pressure data at two fixed temperatures Tr=0.5,0.7. We have cast three of the five parameters in terms of the remaining two parameters. The 5PGDN uses the critical temperature, the critical pressure, the critical compressibility factor, and two parameters of the alpha function to calculate thermodynamic properties such as saturated vapor pressure, liquid and vapor density, enthalpy of vaporization, sound velocity, heat capacity at constant pressure and volume. The 5PGDN is further used for the prediction of bubble point pressure and vapor mole fraction of several binary mixtures. The accuracy of 5PGDN is demonstrated by comparing results with the Patel-Teja (PT), Haghtalab-Kamali-Mazloumi-Mahmoodi (HKM1) and Ghoderao-Dalvi-Narayan (4PGDN1) equations of state.

A four-parameter cubic equation of state for pure compounds and mixtures

A four parameter cubic equation of state, GDN-CEOS, is presented to describe thermodynamic properties of pure fluids and mixtures. We have cast three of the four parameters in terms of the remaining parameter and all the parameters are temperature independent. A new alpha function is proposed in the attractive term of the CEOS; which requires two compound-specific parameters determined from saturation vapor pressure data at two reduced temperature points Tr=0.5 and 0.7. Hence, the GDN CEOS has five inputs per substance: the critical temperature (Tc), the critical pressure (Pc), the critical compressibility factor (Zc) and two compound specific parameters (m, n) of the alpha function. The saturated vapor pressure and liquid density of 334 pure compounds, representing a large variety of functional groups, are predicted successfully. Other thermodynamic properties such as isobaric and isochoric heat capacities, sound velocity, compressed liquid density and enthalpy of vaporization have been calculated using GDN CEOS with remarkably good accuracy. The GDN CEOS is further applied to the prediction of bubble pressure and vapor mole fraction of several binary mixtures using the van der Waals one fluid mixing rules. The accuracy of GDN CEOS is demonstrated by comparing results with three well-known equations of state: Haghtalab-Kamali-Mazloumi-Mahmoodi (HKM1), Modified Peng Robinson (MPR) and Patel-Teja (PT) cubic equations of state.

The Extended Crossover Peng–Robinson Equation of State for Describing the Thermodynamic Properties of Pure Fluids

In this paper, a theoretical method has been introduced for developing the crossover Peng–Robinson (CPR) equation of state (EoS) which incorporates the non-classical scaling laws asymptotically near the critical point into a classical analytic equation further away from the critical point. The CPR EoS has been adopted to describe the thermodynamic properties of some pure fluids (normal alkanes from methane to n-butane and carbon dioxide) such as density, saturated pressure, isochoric heat capacity and speed of sound. Unlike the original method for the crossover transformation made by Chen et al. (Phys Rev A 42:4470–4484, 1990), we have proposed a procedure which adding an additional term into the crossover transformation to obtain the thermophysical properties at the critical point more exactly. It is shown that this new crossover method yields a satisfactory representation of the thermodynamic properties close to the critical point for pure fluids relative to the original PR EoS.

An Improvement to COSMO-SAC for Predicting Thermodynamic Properties

A modified COSMO-SAC model is presented to calculate thermodynamic properties of pure fluids and mixtures using statistical thermodynamics and the surface charge density of each compound obtained from a quantum mechanics (QM) calculation. The main differences from the previous models are that the new model includes a dispersion contribution in the mixture interaction, and is reparametrized using measured pure and mixture thermodynamic data simultaneously. With a single set of universal parameters, the new model provides higher accuracy than our previous models for predicting mixture thermodynamic properties while maintaining the same accuracy for pure compound thermodynamic properties. The overall root-mean-square deviation (RMSD) in the logarithms of partition coefficients for 992 octanol–water partitioning systems and 829 other solvent–water partitioning systems with this new model is reduced by about 10% compared to the results from previous models. Also, the agreement between the predicted and measure...

Comparative study of eight cubic equations of state for predicting thermodynamic properties of alkanes

AbstractPrecise descriptions of the thermodynamic properties of pure fluids require accurate definition of vapour–pressure and phase volumes as well as residual volumes, enthalpies and entropies. While carefully fitted multi‐parameter equations of state (EOS), such as Benedict–Webb–Rubin–Starling fulfil these requirements, cubic EOSs usually do not. On the other hand, cubic EOSs are widely used in the oil industry, due to their simplicity and reliability in most vapour–liquid equilibrium calculations. For thermal oil recovery processes and the natural gas industry, the choice of EOS becomes important for predicting thermodynamic properties, such as isobaric and isochoric heat capacities, sound velocity and the Joule–Thomson coefficient. In this study, eight cubic EOSs which most of them are used in commercial reservoir simulators are selected for evaluation of their capability in the prediction of second‐order derivative thermodynamic properties at different temperatures and pressures, using pure components frequently found in petroleum and natural gas mixtures. It is shown that none of the cubic EOSs could accurately predict all of the stated parameters, especially below the critical point. All EOSs failed to show the extrema in the derivative properties. However, among these equations the Yu–Lu and Schmidt–Wenzel EOSs were found to have more reliable predictions in most of the cases. © 2011 Canadian Society for Chemical Engineering

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.

Evaluation of co-volume mixing rules for bitumen liquid density and bubble pressure estimation

The Peng–Robinson cubic equation of state (CEOS) is widely used to predict thermodynamic properties of pure fluids and mixtures. The usual implementation of this CEOS requires critical properties of each pure component and combining rules for mixtures. Determining critical properties for components of heavy asymmetric mixtures such as bitumen is a challenge due to thermolysis at elevated temperatures. Group contribution (GC) methods were applied for the determination of critical properties of molecular representations developed by Sheremata for Athabasca vacuum tower bottoms (VTB). In contrast to other GC methods evaluated, the Marrero–Gani GC method yielded estimated critical properties with realistic, non-negative values, followed more consistent trends with molar mass and yielded normal boiling points consistent with high temperature simulated distillation data. Application of classical mixing rules to a heavy asymmetric mixture such as bitumen yields saturated liquid density and bubble pressure estimates in qualitative agreement with experimental data. However the errors are too large for engineering calculations. In this work, new composite mixing rules for computing co-volumes of asymmetric mixtures are developed and evaluated. For example, composite mixing rules give improved bubble point predictions for the binary mixture ethane + n-tetratetracontane. For VTB and VTB + decane mixtures the new composite mixing rules showed encouraging results in predicting bubble point pressures and liquid phase densities.

A Fundamental Equation of State for Sulfur Hexafluoride (SF6) in Extended Equation of State Format

An innovative method for the regression of thermodynamic properties of pure fluids was recently proposed. The technique, indicated as an extended equation of state, adopts a framework similar to the extended corresponding states method, but a cubic equation is assumed instead of the equation of state of the reference fluid and the shape functions are expressed through a multilayer feedforward neural network. The use of a neural network assures a very high flexibility of the functional form to be regressed, so the resulting model reaches a representation accuracy which is comparable to that attained by the state-of-the-art multiparameter equations of state in the representation of the thermodynamic properties of a pure fluid. The technique was applied here to sulfur hexafluoride aiming at drawing its dedicated equation of state in a heuristic mode directly from the available experimental data. For sulfur hexafluoride (critical point is at Tc=318.7232K and Pc=3.754983MPa), experimental data of several properties in homogeneous states and of properties at phase equilibrium are available. The data approximately cover the range from the triple-point temperature at 223.6upto625K and for pressures up to 60MPa. The regression procedure was developed on a subset of well distributed density and vapor–liquid coexistence data, the so-called “training set,” and the model was successively validated for all the data sets, including the literature sources reporting values of isobaric heat capacity, speed of sound, and Joule–Thomson coefficient. The obtained results are satisfactory; in fact the proposed equation of state represents the available data within their experimental accuracy.

Effective intermolecular potentials in theoretical thermodynamics of pure substances and solutions

Effective potentials have been used extensively as model molecular interactions to account for the thermodynamic properties of pure fluids and solutions. Here we develop the concept of effective potential and apply it to a variety of properties in the dilute- and dense-fluid states. We show how a simple kind of potential, named Approximate Non-Conformal (ANC), can be used effectively to calculate accurately a variety of thermodynamic properties of fluid substances. We present evidence for properties in the gaseous state (second and third virial coefficients), for the liquid–vapour coexistence and critical properties ( T c, V c and P c). Most gaseous-phase properties are obtained within estimated experimental errors. The molecular features whose effects have been incorporated into the ANC effective potentials are overlap, dispersion, electrostatic (dipolar and quadrupolar) and many-body interactions, and steric features such as elongation Applications to a selection of non-polar substances noble gas molecules, diatomics and light alkanes highlight the main features of the theory. New results include Gibbs ensemble Monte Carlo simulations of ANC fluids, an effective potential to account for many-body forces, prediction of critical temperatures and volumes, and we also prove a general relation satisfied by the critical temperatures of many substances.

A multi-fluid nonrandom associating lattice fluid model

A lattice fluid theory valid from pure fluids to multi-component mixtures of molecules having any number of associating donor and acceptor groups formulated. Under the fundamental assumption that the intermolecular forces are divided into physical and chemical forces, the Veytsman statistics for associating contribution was combined with the multi-fluid nonrandom lattice fluid (MLF) equation of state developed recently by the present authors. The physical contribution is characterized by temperature independent molecular parameters representing close packed volumes of a mer, segment numbers and energy parameters of a pure fluid, and a binary interaction parameter for a binary mixture. The chemical part is represented by internal energy and entropy of associating system. The resulting multi-fluid nonrandom associating lattice fluid (MALF) equation of state was applied to describe thermodynamic properties of pure fluids and phase equilibrium of mixtures. The results for alkane–alcohol and alcohol–alcohol mixtures were found satisfactory for most systems when compared with the MLF and the statistical associating fluid theory (SAFT) model.

Generalized crossover description of the thermodynamic and transport properties in pure fluids: II. Revision and modifications

In our previous work [S.B. Kiselev, J.F. Ely, Fluid Phase. Equilib. 222–223 (2004) 149], we developed a generalized cubic (GC) EoS for pure fluids, which incorporates non-analytic scaling laws in the critical region and reproduces the thermodynamic properties of pure fluids with high accuracy, including the asymptotic scaling behavior of the isochoric heat capacity in the one- and two-phase regions. However, it appears that in some cases the GC EoS can give unphysical behavior when extrapolated to high temperatures and densities. In this work, we present a modification of the generalized cubic EoS, which in the critical region is physically equivalent to the GC EoS developed earlier, but is more reliable in its extrapolation to high temperatures.

A quasi-chemical nonrandom lattice fluid model for phase equilibria of associating systems

The contribution from Veytsman statistics for associating is combined with the quasi-chemical nonrandom lattice fluid (QLF) equation of state developed by the present authors. The physical contribution is characterized by temperature independent molecular parameters, representing close packed volume of a mer, segment numbers and energy parameters of a pure fluid, and a binary interaction parameter for a mixture. The chemical part is represented by the internal energy and entropy of the associating system. The resulting quasi-chemical nonrandom associating lattice fluid equation of state was applied to describe thermodynamic properties of pure fluids and phase equilibria of mixtures. The absolute chemical potentials which are derived from the canonical partition function are presented by using the fundament thermodynamic relations to consistently calculate phase equilibrium properties. The results for alkane–alkanol and alcohol–alkanol mixtures were found satisfactory for most systems when compared with the quasi-chemical nonrandom lattice fluid model and the statistical associating fluid theory model.

Generalized crossover description of the thermodynamic and transport properties in pure fluids

We have developed a generalized cubic (GC) EOS for pure fluids, which incorporates non-analytic scaling laws in the critical region and in the limit ρ→0 is transformed into the ideal gas equation EOS. The GC EOS contains 10 adjustable parameters and reproduces the thermodynamic properties of pure fluids with high accuracy, including the asymptotic scaling behavior of the isochoric heat capacity in the one- and two-phase regions. Unlike the crossover cubic EOS developed earlier [Fluid Phase. Equilibr. 147 (1998) 7], the GC EOS is based on the crossover sine model and can be extended into the metastable region for representing analytically connected van der Waals loops. In addition, using the GC EOS and the decoupled-mode theory (DMT) we have developed a generalized GC + DMT model, which reproduces the singular behavior of the thermal conductivity of pure fluids in and beyond the critical region. Unlike the DMT model based on the asymptotic crossover equation of state CREOS-97, the GC + DMT model is valid in the entire fluid state region at T≥ T b (where T b is the binodal temperature), and at ρ→0 reproduces the dilute gas contributions for the transport coefficients.

Extended corresponding states model for fluids and fluid mixtures: I. Shape factor model for pure fluids

We present a new and accurate extended corresponded states model for the prediction of thermodynamic properties of pure fluids. This model is based on shape factors expressed as functions of the reduced temperature and density, the acentric factor and the critical compression factor. Substance-dependent coefficients were optimised against volumetric, VLE and acoustic data for the light hydrocarbons from ethane to n-pentane, ethylene, nitrogen, carbon dioxide, oxygen, argon and carbon monoxide. With this model, fluid properties are estimated largely within their experimental uncertainty. The model was tested for reduced temperatures T r in the interval 0.52≤ T r≤3.33 and for reduced densities up to 2.8. The work reported here is a necessary precursor to the development of an extended corresponding states (ECS) equation of state for natural gas systems and mixtures of natural gas constituents.

An equation of state for R227ea from density data through a new extended corresponding states-neural network technique

A new and original method for the regression of thermodynamic properties of pure fluids has been recently proposed by Scalabrin et al. [1]. This is an extended corresponding states (ECS) technique in which the shape functions are expressed in a multi-layer feedforward neural networks (NN) framework. NN assure a very high flexibility of the functional form for the regression, reaching an accuracy which is comparable to that afforded by multi-parameter equations of state (EoS) in the representation of all the thermodynamic properties. The aim of the present work is to apply such a technique to 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea), one of the new generation of refrigerant fluids. A limited amount of experimental data has been published on this fluid over recent years. Although reliable, these data are sparse and the present method works better when fitting is achieved on regularly distributed data. Thus, a new experimental campaign was conducted at the Laboratoire de Thermodynamique, ENSMP, for the acquisition of a large number of PρT data between 253 and 393 K and up to 20 MPa. The regression procedure was carried out on a small subset of well-distributed density data, the so-called ‘training set’, and the model was then validated along all the data sets, including the literature data which report isobaric heat capacity, speed of sound and Joule–Thomson coefficient values. The accuracy of the method is evaluated for all the available properties, both in and outside the fitting range. It can be stressed that an accurate prediction of all thermodynamic properties is reached by fitting only a limited number of PρT data. This important result is due to the combination of an accurate multi-parameter EoS for the reference fluid R134a, with an improved version of the CS principle, incorporating modern NN techniques for mapping the two shape functions φ= φ( ρ, T) and θ= θ( ρ, T), which are characteristic of the ECS method.