Thermodynamic Derivative Properties Research Articles

Modeling the thermodynamic properties of cyclic alcohols with the SAFT-γ Mie approach: application to cyclohexanol and menthol systems

Cyclic alcohols are commonly found in natural and synthetic products and are involved in many biological processes. An ability to model their thermodynamic properties is of interest in food, flavouring, and pharmaceutical manufacturing, particularly for mixtures for which available experimental data are limited. Good examples are mixtures including menthol, a naturally occurring cyclic alcohol widely used in the food and pharmaceutical industries, well-known for its cooling-sensation properties and its role in the discovery of the TRPM8 receptor. Here, we extend the SAFT-γ Mie group-contribution method to model cyclic alcohols, by introducing a new cCHOH group (c for cyclic) composed of two identical Mie segments. Three association sites (two electronic sites of type e and one hydrogen site of type H) are also included to mediate hydrogen bonding. New parameters that characterise the group interactions (one new like interaction and 26 new unlike interactions) are developed and are employed to determine the thermophysical properties (vapour pressure, saturation density, vaporisation enthalpy, and second-order thermodynamic derivative properties) of pure cyclic alcohols, and mixture properties (vapour–liquid equilibria, liquid–liquid equilibria, solid–liquid equilibria, density, and excess enthalpy) of cyclic alcohols in several solvents. The quality of the model is evaluated by comparing predictive calculations with experimental data of 76 systems: six pure fluids and 70 binary mixtures, selected from a large range of solvent families: cyclic, linear, and branched alkanes, 1-alcohols, 2-alcohols, 2-ketones, esters, aromatic compounds, water, and carbon dioxide. Very good overall agreement is found, including for the prediction of solid–liquid solubility, which confirms the transferability of the new group parameters. Together with previously developed parameters, these open the way for the prediction of the thermodynamic properties of further complex mixtures.

Implementation of PC-SAFT for Predicting thermodynamic properties of pure refrigerants and vapor-liquid equilibria of refrigerants binary mixtures.

A new approach to evaluate PC-SAFT molecular parameters based on pure components critical properties was proposed in our previous paper. In this study, the performance of the proposed approach is verified through its application to the calculation of vapor pressure, saturated density, saturated enthalpy, heat of vaporization, isobaric heat capacity, and speed of sound for propane, butane, isobutane, R22, R23, R32, R116, R125, R134a, R143a, and R1234yf. In general, the results have shown that the new approach is better than the existing one when applied in predicting second-order thermodynamic derivative properties, and it has much less overall percent average absolute deviations than the existing method. However, the main limitation on the accuracy is that underestimated liquid densities. The PC-SAFT is also applied to predict vapor-liquid equilibria of eleven binary refrigerant mixtures, including R23 – R22, R23 – R134a, R23 – R143a, R23 – R227ea, R32 –Isobutane, R32 – Propane, R116 – Butane, R116 – 134a, R116 – R143a, R125 – R1234yf, and Propane – R227ea. The obtained results show that the new approach provides very good predictions of the vapor-liquid equilibria and the critical properties of mixtures, while the existing approach tends to overestimate these quantities.

Crossover PC-SAFT equations of state based on White's method for the thermodynamic properties of CO2, n-alkanes and n-alkanols

In order to improve the prediction accuracy of the thermophysical properties of fluid in near critical region, in this work, White's renormalization group (RG) corrections were applied to construct the crossover PC-SAFT EoS (simplified as PC-SAFT-RG). We first fit the three parameters introduced by the crossover process to the experimental data, then the phase behavior as well as derivative properties in the critical region and outside the critical region for several fluids such as CO2, n-alkanes and n-alkanols were investigated using the PC-SAFT EoS and the PC-SAFT-RG. Our results show that the PC-SAFT-RG is able to modify the behavior of the PC-SAFT EoS in the critical region and revert to classic behavior outside the critical region. The PC-SAFT-RG improves the PC-SAFT EoS's performances on the second derivative thermodynamic properties, with the average absolute relative deviations (AADs) of 9.96%, 6.99% and 3.91% for isobaric heat capacity, isochoric heat capacity and speed of sound respectively.

Effect of polarity on prediction of second order derivative thermodynamic properties of refrigerants

In this research, the SAFT-VR Morse has been extended to polar system by considering the dipolar interactions between non-spherical molecules. The second order derivative thermodynamic properties of refrigerants such as speed of sound, specific heat capacity and Joule-Thomson coefficient have been predicted and compared to PPC-SAFT EoS. The model parameters have been obtained using vapor pressure and saturated liquid density data of pure refrigerants. Using obtained model parameters the aforementioned properties have been predicted in the vapor, liquid, saturation and supercritical phases. The effect of polar contribution on model prediction performance has been studied. The results show that, the polar contribution can be neglected without losing model accuracy. The obtained average error of the polar PC-SAFT and polar SAFT-VR Morse is very close to their original versions. As well, the PPC-SAFT EoS gives accurate results compared to SAFT-VR Morse and its polar version, especially in the case of Joule-Thomson coefficient prediction.

Modeling thermophysical properties of several liquid adipates

The densities and several derived thermodynamic properties of 6 liquid adipates were correlated and predicted through a proposed perturbed hard-chain equation of state (PHC EoS) containing a term of Yukawa tail. The adipates under study comprised the diesters of methyl and ethyl types. The EoS was constructed through correlating it with densities and isothermal compressibilities of studied systems in 288–403 K range and pressure at 0.1Mpa. Then the EoS was applied to predict densities and several first derivative thermodynamic properties including isobaric expansivities, thermal pressure coefficients and internal pressure values for pressures up to 140 MPa. The average absolute relative deviations (AARD) of densities and isothermal compressibilities were found to be 0.21 % and 8.58 %, respectively. Then, the rest of derived thermodynamic properties of the aforementioned systems were predicted and compared with a Tait-type equation cited in literature. Further, a rough hard-sphere-chain (RHSC) model in conjunction with the proposed EoS has been successfully employed to correlate and predict the viscosities of 4 selected liquefied adipates, for which the experimental values were available in the literature. The model could correlate/predict 1075 experimental viscosity data points of the above-mentioned adipates in 283–373 K range and pressures up to 65 MPa with the AARD of 2.14 %. The accuracy of the results from the RHSC-based model has also been compared with those obtained from other RHS-based model of literature.

Prediction of second order derivative thermodynamic properties of ionic liquids using SAFT-VR Morse equation of state

The variable range statistical associating fluid theory (SAFT-VR) equation of state (EoS) based on the Morse potential was used to describe the second order derivative thermodynamic properties of ionic liquids. The isothermal compressibility coefficient, heat capacities, thermal expansion coefficient, isentropic compressibility coefficient, thermal pressure coefficient, and speed of sound of ionic liquids were predicted up to high pressure and temperature. In this regard, the ionic liquids were considered long chain molecules with two associating sites on cation and anion. The model parameters were obtained by fitting the experimental liquid density data. The average deviation of the calculated liquid density was about 0.09%. The predicted results were compared to the ePC-SAFT EoS to evaluate the capability of the SAFT-VR Morse model. The performance of SAFT-VR Morse EoS was comparable with ePC-SAFT, especially in the heat capacity coefficient and the speed of sound. The average deviation of predicted the isothermal compressibility coefficient, thermal expansion coefficient, isochoric heat capacities, isobaric heat capacities, thermal pressure coefficient, isentropic compressibility coefficient, and speed of sound are 6.46%, 8.32%, 8.18%, 9.55%, 8.10%, 2.67%, and 2.98%, respectively. Obtained results prove that SAFT-VR Morse can be used efficiently to predict second order derivative thermodynamic properties of ionic liquid over a wide range of pressure and temperature.

Modeling the density and the second-order thermodynamic derivative properties of imidazolium-, cyano-based ionic liquids using the SAFT-γ EoS

The knowledge of the thermophysical properties is essential to develop industrial processes involving ionic liquids (ILs). In the present research, the SAFT-γ group contribution (GC) technique is performed to estimate the density and the second-order thermodynamic derivative properties of some imidazolium-, cyano-based ILs (with either [SCN], [DCA], [TCM] or [TCB] anions). The density and the second-order derivatives including isothermal and isentropic compressibility coefficients, thermal expansion and thermal pressure coefficients, isochoric and isobaric heat capacities, and speed of sound are determined for the mentioned ionic liquids within a temperature range of 262–412 K and at pressures up to 200 MPa. The SAFT-γ predictions of the density and the second-order derivatives are compared with some accessible experimental data. The results demonstrate that the SAFT-γ equation can estimate the thermophysical properties of the studied ILs with good accuracy.

PρT parameterization of SAFT equation of state: developing a new parameterization method for equations of state

The lack of a transparent and universal parameterization method is one of the main problems in developing SAFT-type equations of state and it's an obstacle in their way of becoming an industrial equation of state. Usually, vapor-pressure and saturated liquid density data with a local optimization algorithm are used to parameterize SAFT-type equations of state. In addition to the ambiguity in the data selection process, using a local optimization method reduces the accuracy of the estimated parameters. Therefore, in this paper, a new method for calculating the adjustable parameters of SAFT or any equations of state with several parameters is presented. By providing a clear and explicit data selection procedure, including data categorization, comparison, and validation, integrated with the use of a combination of global and local optimization methods, the new methodology achieves the best possible parameters set for the equation of state. The proposed computational program for fitting parameters is based on the use of the Differential evolution algorithm as the main process and the Levenberg-Marquardt algorithm as the post-process along with applying one (or two) hyperparameter. Afterward, a wide range of pressure-temperature-density data has been used to estimate the parameters of 60 non-associating and associating pure compounds. Then, the SAFT equation of state with the new parameters, so-called PρT-SAFT-HR, is applied to predict pressure (P), temperature (T), density (ρ), vapor-pressure (Psat), saturated vapor density (ρvapsat), saturated liquid density (ρliqsat), critical point, isochoric heat capacity (cv), isobaric heat capacity (cP), speed of sound (u), isothermal compressibility (κT), and isobaric thermal expansivity (αP). All properties are calculated with the PρT-SAFT-HR equation of state, and the results are compared with experimental data and SAFT-HR and the average absolute percentage deviation is reported for all of them. In total, 19460 experimental and pseudo-experimental data were used to reparameterization the SAFT equation of state, and more than 74,000 data were validated to calculate thermodynamic properties. The results showed a significant improvement in predicting second-order thermodynamic derivative properties. In general, PρT-SAFT-HR performs better than SAFT-HR, and in some cases, such as pressure, speed of sound, isothermal compressibility, and isobaric thermal expansivity, the results have been significantly improved, and the average absolute deviation of PρT-SAFT-HR has been much less than SAFT-HR.

Thermal Pressure in the Laser‐Heated Diamond Anvil Cell: A Quantitative Study and Implications for the Density Versus Mineralogy Correlation of the Mantle

AbstractThermal pressure is an inevitable thermodynamic consequence of heating a volumetrically constrained sample in the diamond anvil cell. Its possible influences on experimentally determined density‐mineralogy correlations are widely appreciated, yet the effect itself has never been experimentally measured. We present here the first quantitative measurements of the spatial distribution of thermal pressure in a laser‐heated diamond anvil cell (LHDAC) in both olivine and AgI. The observed thermal pressure is strongly localized and closely follows the distribution of the laser hotspot. The magnitude of the thermal pressure is of the order of the thermodynamic thermal pressure (αKTΔT) with gradients between 0.5 and 1.0 GPa/10 μm. Remarkably, we measure a steep gradient in thermal pressure even in a sample that is heated close to its melting line. This generates consequences for pressure determinations in pressure‐volume‐temperature (PVT) equation of state measurements when using an LHDAC. We show that an incomplete account of thermal pressure in PVT experiments can lead to biases in the coveted depth versus mineralogy correlation. However, the ability to spatially resolve thermal pressure in an LHDAC opens avenues to measure difficult‐to‐constrain thermodynamic derivative properties, which are important for comprehensive thermodynamic descriptions of the interior of planets.

Second-Order Thermodynamic Derivative Properties of Ionic Liquids from ePC-SAFT: The Effect of Partial Ionic Dissociation

Ionic liquids (ILs) are potentially suitable compounds as replacements for organic solvents in chemical processes and play an important role in reducing the production of toxic compounds. In this w...

Modeling Thermodynamic Derivative Properties and Gas Solubility of Ionic Liquids with ePC-SAFT

In this work, the ion-specific electrolyte perturbed-chain statistical associating fluid theory (ePC-SAFT) was extended to predict the second-order thermodynamic derivative properties and gas solub...

Observations regarding the first and second order thermodynamic derivative properties of non-polar and light polar fluids by perturbed chain-SAFT equations of state

This paper focuses on the second order derivative properties of some pure components, as the most significant challenges to develop the equations of states. For this reason, PC-SAFT equation of state has been used to predict derivative properties of n-alkanes, such as heat capacities, the speed of sound and Joule-Thomson coefficient in the wide temperature and pressure ranges up to 20 MPa. The performance of this model is evaluated against experimental data so that a good agreement with predicted properties can be observed except near the critical point and in some cases, near the coexistence phases. Furthermore, this study has tried to demonstrate the capability of polar sPC-SAFT equation of state to estimate the saturated pressure, liquid density and the speed of sound for light alcohols. Therefore, the system-dependent parameters of this model have been reassigned. The results have been compared with the available literature data and have shown a very good agreement.

Investigation of solutions of ethyl alcohol and the deep eutectic solvent of Reline for their volumetric properties

In this study, the deep eutectic solvent of choline chloride/urea, also known as Reline, was synthesized. Mixtures of Reline with ethanol were prepared covering the entire concentration range, and their densities were determined experimentally. Together with pure Reline and pure ethanol, this made a total of eleven systems, whose densities were measured over the temperature range of 293.15–333.15 K at pressure of 100 kPa. The volumetric properties of interest in the calculation of other derivative thermodynamic properties were determined for all of the investigated mixtures and temperatures. This included the correlation of density to temperature, as well as the excess molar volumes, partial molar volumes, partial molar volumes at infinite dilution, excess partial molar volumes, excess partial molar volumes at infinite dilution, and isobaric volume expansions. The excess molar volumes had negative values at all concentrations and temperatures. This led us to propose a possible molecular arrangement of the hydrogen bond network, placing Reline mainly in central positions, with the preference to be surrounded by ethanol molecules.

Prediction of thermodynamic properties of aqueous electrolyte solutions using equation of state

In this study, a predictive model is presented for estimation of second order thermodynamic properties of electrolyte solutions. In order to provide a comprehensive understanding, the capability of modified electrolyte PC‐SAFT up to high pressure and temperature has been studied. In addition to the first order derivative thermodynamic properties, the Gibbs free energy, enthalpy and heat capacity of aqueous electrolyte solutions at infinite dilution are predicted. Using new methodology, the dielectric constant is modified to keep the pressure, temperature, and ionic strength dependency. Our results show that the Born term has a significant contribution on prediction of second order derivative properties. Meanwhile the impact of temperature‐dependent solution dielectric constant on standard state heat capacity is studied. Finally, the isobaric heat capacity at various salt concentrations is predicted without any adjustable parameters. The results of this work indicate an acceptable agreement with experimental data especially at high pressure and temperature. © 2017 American Institute of Chemical Engineers AIChE J, 2017

SAFT-VR modelling of the surface and bulk properties of imidazolium and pyridinium based ionic liquids with ten different anions

Statistical associating fluid theory for potential of variable range has been used to provide an accurate thermophysical properties for 26 imidazolium and pyridinium-based families of ionic liquids (ILs) with different cationic structures combined with [PF6]−, [BF4]−, [NTf2]−, [Cl]−, [dca]−, [Triflate]−, [EtSO4]−, [lactate]−, [C(CN)3]− and [MeSO4]− anions. An appropriate set of molecular parameters were obtained by means of fitting the model predictions to experimental liquid densities over a wide temperature and pressure ranges. The overall absolute average relative deviation (AARD) between the calculated and experimental liquid densities is 0.12% over a wide range of temperature and pressure from 283 to 472K and 0.1–200MPa. The reliability and physical significance of the parameters were tested by calculation of thermodynamic derivative properties including isobaric thermal expansivity and isothermal compressibility of ILs. Moreover, the interfacial surface tension of ILs was calculated by density gradient theory (DGT) coupled with the SAFT-VR model. The results are in excellent agreement with the available experimental data.

Prediction of thermodynamic properties of sodium dodecyl sulfate aqueous solutions through the hetero-SAFT equation of state

A special version of statistical associating fluid theory (SAFT), the so-called hetero-segmented SAFT equation of state, has been extended to calculate the thermodynamic properties of sodium dodecyl sulfate aqueous solutions. The predicted properties were included the vapor pressure as well as second thermodynamic properties, such as speed of sound. Evaluation of the model has been done through comparison of the calculated vapor pressure with experimental data in the range of 298.15–313.15 K. The hetero-SAFT model is found to be able to correctly describe the thermodynamic derivative properties as well as pVT and VLE properties of ionic surfactant solutions.

Application of the SAFT-γ Mie group contribution equation of state to fluids of relevance to the oil and gas industry

The application of the SAFT-γ Mie group contribution approach [Papaioannou et al., J. Chem. Phys., 140 (2014) 054107] to the study of a range of systems of relevance to the oil and gas industry is presented. In particular we consider carbon dioxide, water, methanol, aromatics, alkanes, and their mixtures. Following a brief overview of the SAFT-γ Mie equation of state, a systematic methodology for the development of like and unlike group parameters relevant to the systems of interest is presented. The determination of group–group interactions entails a sequence of steps including: the selection of representative components and mixtures (in this instance carbon dioxide, water, methanol, aromatics, and alkanes); the definition of an appropriate set of groups to describe them; the collection of target experimental data used to estimate the group–group interactions; the determination of the group–group interaction parameters; and the assessment of the adequacy of the parameters and theoretical approach. The predictive capability of the SAFT-γ Mie group contribution approach is illustrated for a selection of mixtures, including representative examples of the simultaneous description of vapour–liquid and liquid–liquid equilibria, the densities of the coexisting phases, second derivative thermodynamic properties, and excess properties of mixing. Good quantitative agreement between the predictions and experimental data is achieved, even in the case of challenging mixtures comprising carbon dioxide and water, n-alkanes and water, and methanol and methane.

Analysis of Selected Thermodynamic Derivative Properties of Natural Gas Pipeline Flow Model

The thermodynamic derivatives based on fundamentals thermodynamic space and physical parameters of natural gas influences other variables of pipeline systems such as pressure, temperature, velocity, density, gas compressibility, etc. These variables are crucial for gas pipeline system knowledge and its accurate operation. Fundamental parameters are derived such as Joule-Thomson (J-T) coefficient, isothermal throttling coefficient and isentropic coefficient. They influence gas flow when during the expansion of natural gas in the pipeline, the gas cools down due to the J-T effect and due to the interaction between pipeline system and its surroundings to the conditions at which gas is saturated by water vapour (dew point), and gas is not able to keep excess humidity and its condensation and gas hydrate formation will occur. The article deals with analyses of selected thermodynamic derivatives in the range of chosen temperatures and pressures and also non-isothermal steady-state flow model for pipeline is presented.

Very fast averaging of thermal properties of crystals by molecular simulation.

Knowledge of approximate harmonic behavior of crystals is introduced into a new "mapped averaging" framework to yield alternative expressions for the thermodynamic properties of crystalline systems. The expressions separate the known harmonic behavior from residual averages, which thus encapsulate anharmonic contributions to the properties. With harmonic contributions removed, direct measurement of these anharmonic contributions by molecular simulation can be accomplished without contamination by noise produced by the already-known harmonic behavior. We show with application to the Lennard-Jones model that first-derivative properties (pressure, energy) can be obtained to a given precision via this harmonically mapped averaging at least 10 times faster than by using conventional averaging, and second-derivative properties (e.g., heat capacity) are obtained at least 100 times faster; in more favorable cases, the speedup exceeds a millionfold. Free-energy calculations are accelerated by 50 to 1000 times. Data obtained using these formulations are rigorous and not subject to any added approximation, and in fact are less sensitive to inaccuracies relating to finite-size effects, potential truncation, equilibration, and similar considerations. Moreover, the approach does not require any alteration in how sampling is performed during the simulation, so it may be used with standard Monte Carlo or molecular dynamics methods. However, the mapped averages do require evaluation of first and second derivatives of the intermolecular potential, for evaluation of first and second thermodynamic-derivative properties, respectively. Apart from its usefulness to simulation, the formalism developed here may constitute a basis for new theoretical treatments of crystals.

Modeling thermodynamic derivative properties of ionic liquids with ePC-SAFT

In this work, ePC-SAFT was extended to predict the second order thermodynamic derivative properties of pure ionic liquids (ILs), such as isothermal and isentropic compressibility coefficients, thermal pressure coefficient, heat capacities, speed of sound, thermal expansion coefficient and internal pressure. ePC-SAFT predictions were compared with available experimental data of imidazolium-based ILs. The pure-component ePC-SAFT parameters for the IL-cations [C2mim]+, [C4mim]+, [C6mim]+ and [C8mim]+, and IL-anions [BF4]−, [PF6]− and [Tf2N]− were taken from literature in order to predict the thermodynamic derivative properties. The pure-component ePC-SAFT parameters for the IL-cations [C3mim]+, [C5mim]+, [C7mim]+ and [C10mim]+ were predicted based on linear molecular-weight-dependent relations. These estimated ePC-SAFT parameters were verified by comparing so-predicted pure-IL density as well as predicted CO2 solubility in ILs with respective experimental data. Further, these parameters were used to predict the second order thermodynamic derivative properties. The comparison of model prediction with experimental data showed that ePC-SAFT predictions were reliable in a wide temperature and pressure range.