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The extension of the translated–consistent Peng–Robinson (tc-PR) equation of state (EoS) to mixtures has been investigated. For this purpose, advanced EoS/aresE,γ mixing rules are used to combine t...

International audience; The computation of solvation energies has many uses in several fields, such as design of separation processes, pharmacology and drug-design, and kinetic modeling. These applications require thermodynamic models capable of accurately predicting solvation energies, accounting for the temperature dependency of this property, and which are fast and robust. Within this framework, we compared two COSMO-based continuum solvation models (COSMO-RS and COSMO-SAC-dsp) with two versions of predictive cubic equations of state well-acknowledged for their efficiency (PSRK and UMR-PRU). For this purpose, a large experimental set of 65,000 datapoints extracted from the COMPSOL databank was considered. Comparisons between computed and experimental data were performed for Gibbs solvation energy and, for the first time in the literature, for both entropy and enthalpy of solvation simultaneously. For simpler binary mixtures, in which hydrogen bonding does not take place, all models were capable of providing accurate predictions, with average absolute deviations below 0.3 kcal/mol regarding the solvation Gibbs energy. For more complex associating mixtures, COSMO-RS showed the best correlation between experimental and calculated data, especially for aqueous systems; among EoS, it is observed that the PSRK model offers the best accuracy.

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International audience; Combined cooling, heating, and power (CCHP) systems enable the simultaneous supply of electricity, heating, and cooling, thus meeting the major energy needs of humans in a single device. Conventional CCHP systems consist of the combination of a prime mover, heating, and cooling system, each of them operating with a thermodynamically suitable working fluid. Recently, novel CCHP cycles, based on the use of a single working fluid for the whole operation, have been proposed. Since the choice of the working fluid represents a design challenge in the development of such technologies, in this work, a product design approach for the selection of suitable working fluids for emergent CCHP applications is presented. A database search is implemented to screen about 60 000 structures included in the DDB, the Design Institute for Physical Properties, and the NIST TDE databases. The screening considers thermodynamic, process-related, constructional, safety, and environmental constraints. Moreover, the tc-PR equation of state is used to ensure the quality of the calculation of thermophysical properties and the performance assessment of promising working fluids. This study shows that flammable fluids such as vinylacetylene or HFC-152 have a good potential for CCHP applications. In the case of reinforced safety restrictions, HCFO-1233zd(E) seems to be an interesting candidate since it is nonflammable and nontoxic.

In carbon capture processes based on chemical absorption, the solution used for absorbing carbon dioxide plays a central role and must be carefully selected. It is expected to have the potential to capture large amounts of carbon dioxide on the one hand, and to be fully regenerated at the lowest energy price on the other hand. As a continuation of a study initiated by Coulier et al. some years ago, the present work focuses on the measurement and modeling of thermodynamic properties of aqueous solvents containing methylpiperidines (a class of amines), potentially usable in carbon capture processes and leading to liquid–liquid phase split in process conditions. To complete liquid–liquid equilibrium (LLE), excess enthalpy and excess heat capacity data previously measured by Coulier et al. for the N-methylpiperidine + water and 2-methylpiperidine + water systems, LLE data, and excess-enthalpy data were measured for the 3-methylpiperidine + water and 4-methylpiperidine + water systems. To model all these data,...

The chemistry underlying liquid-phase oxidation of organic compounds, the main cause of their aging, is characterized by a free-radical chain reaction mechanism. The rigorous simulation of these phenomena requires the use of detailed kinetic models that contain thousands of species and reactions. The development of such models for the liquid phase remains a challenge as solvent-dependent thermokinetic parameters have to be provided for all the species and reactions of the model. Therefore, accurate and high-throughput methods to generate these data are required. In this work, we propose new methods to generate these data, and we apply them for the development of a detailed chemical kinetic model for n-butane autoxidation, which is then validated against literature data. Our approach for model development is based on the work of Jalan et al. [J. Phys. Chem. B 2013, 117, 2955-2970] who used Gibbs free energies of solvation [ΔsolvG(T)] to correct the data of the gas-phase kinetic model. In our approach, an equation of state (EoS) is used to compute ΔsolvG as a function of temperature for all the chemical species in the mechanism. Currently, ΔsolvG(T) of free radicals cannot be computed with an EoS and it was calculated for their parent molecule (H-atom added on the radical site). Theoretical calculations with the implicit solvent model were performed to quantify the impact of this assumption and showed that it is acceptable for radicals in n-butane and probably in all n-alkanes. New rate rules were proposed for the most important reactions of the model, based on theoretical calculations and the literature data. The developed detailed kinetic model for n-butane autoxidation is the first proposed model in the literature and was validated against the experimental data from the literature. Simulations showed that the main autoxidation products, sec-butyl hydroperoxides and 2-butanol, are produced from H-abstractions from n-butane by sec-C4H9OO radicals and the C4H9OO + C4H9OO reaction, respectively. The uncertainty of the product ratio ("butanone + 2-butanol"/"2-butoxy + 2-butoxy") of the latter reaction remains high in the literature, and our simulations suggest a 1:1 ratio in n-butane solvent.

International audience; The perturbed chain-statistical associating fluid theory (PC-SAFT) equation of state (EoS) is applied, and its performance is assessed using a reliable free-to-access benchmark thermodynamic database developed by the authors. A total of 200 non-electrolytic binary systems are included in the database, which are divided into nine groups according to the associating character of the components, that is, their ability to be involved in a hydrogen bond. The properties based on which the assessment is performed include two-phase vapor–liquid and liquid–liquid equilibrium, three-phase vapor–liquid–liquid equilibrium, critical point, azeotropic point, enthalpy of mixing, and heat capacity of mixing data. A specific procedure for the calculation of deviations between model predictions and experimental data and for grading the thermodynamic model is applied based on a previously published proposed methodology. The PC-SAFT EoS is implemented with classical mixing rules, no induced association scheme, and no regressed binary interaction parameters. The results are discussed, and specific characteristics of model performance with respect to different families of mixtures are analyzed

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International audience; Using a synthetic method, the phase behavior of the CO2 (1) + cyclooctane (2) binary system was for the first time experimentally studied between 292.95 K and 373.55 K. In this temperature range, the bubble- and dew-point pressures, ranging from 13.2 to 183.4 bar were measured for carbon dioxide mole fractions between 0.1014 and 0.9701. A total of 96 experimental data points were acquired. The experimental data were obtained using a high-pressure cell by visual observation of phase transitions. These measurements made it possible to conclude that the studied binary system probably exhibits a type V phase behavior in the classification scheme of Van Konynenburg and Scott. In particular, the experimental temperature of the suspected lower critical end point (LCEP) was found to be 303 K. Despite the complexity of the phase behavior, the experimental data could be accurately correlated with the Peng-Robinson equation of state combined with sophisticated mixing rules that either involve temperature-dependent binary interaction parameters (kij(T)) or that embed the residual part of the Wilson activity coefficient model.

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Parameterization is defined as the method used to assign values to component-dependent parameters of an Equation of State (EoS). For SAFT-type EoS, historically, little attention has been paid to t...

International audience; In the last two centuries, equations of state (EoSs) have become a key tool for the correlation and prediction of thermodynamic properties of fluids. They not only can be applied to pure substances as well as to mixtures but also constitute the heart of commercially available computer-aided-process-design software. In the last 20 years, thousands of publications have been devoted to the development of sophisticated models or to the improvement of already existing EoSs. Chemical engineering thermodynamics is thus a field under steady development, and to assess the accuracy of a thermodynamic model or to cross-compare two models, it is necessary to confront model predictions with experimental data. In this context, the importance of a reliable free-to-access benchmark database is pivotal and becomes absolutely necessary. The goal of this paper is thus to present a database, specifically designed to assess the accuracy of a thermodynamic model or cross-compare models, to explain how it was developed and to enlighten how to use it. A total of 200 nonelectrolytic binary systems have been selected and divided into nine groups according to the associating character of the components, i.e., their ability to be involved in a hydrogen bond (the nature and strength of the association phenomena are indeed considered a measure of the complexity to model the thermodynamic properties of mixtures). The methodology for assessing the performance of a given model is then described. As an illustration, the Peng− Robinson EoS with classical van der Waals mixing rules and a temperature-dependent binary interaction parameter (k ij) have been used to correlate the numerous data included in the proposed database, and its performance has been assessed following the proposed methodology.

The present paper aims to enhance the awareness of users of thermodynamic models on the impact that their accuracy may have in designing and operating units for the purification and compression of CO2-streams produced from capture technologies. After providing a review on the composition of streams produced by coal- or gas-fired plants with post-/pre-/oxy-combustion CO2 capture, coupled with different purification technologies, the paper quantifies the influence of equations of state accuracy in designing and operating CO2 purification and compression units. A comparison is made between the results obtained from the cubic Peng-Robinson model combined with either classical vdW1f (van der Waals one fluid) mixing rules (i.e. the standard Peng-Robinson equation of state) or with recently optimized advanced mixing rules incorporating residual-excess-Helmholtz-energy ( a res E, γ ) models ( EoS / a res E, γ mixing rules). In detail, EoS / a res E, γ mixing rules combine the residual contribution of the Wilson a E , γ model and the formulation proposed by Lorentz, for the mixture co-volume term. It is shown that the improved accuracy of “PR + EoS / a res E, γ mixing rules” in the representation of vapour-liquid equilibrium properties of CCS mixtures, with respect to the standard PR EoS, may lead to the design of a halved-height stripping column for the reduction of the oxygen content in the captured CO2 stream. Moreover, the paper shows the effect of the applied thermodynamic model on the definition of the pressurization level of the captured fluid and on the computed power required for its compression.

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In this study, the thermodynamic behaviour of NO + SO2 mixtures has been investigated by means of molecular simulation, experiment and equation of state modelling. Quantum chemical calculation were performed to investigate possible chemical reactions between NO and SO2. Molecular simulations were based on Monte Carlo and Molecular Dynamics techniques using force fields available in the literature. Validation of simulated vapour liquid data for NO + SO2 binary mixtures was performed on the basis of proposed new experimental data, and new sets of parameters were optimized for the PPR78 EoS. We then moved our focus on the solubility of some gases (SOx, NOx, CO2, O2, N2) in water and brines studied by molecular simulations. We first compared performances of some combinations of salt and water intermolecular potentials in terms of density and osmotic pressure predictions. We then studied the evolution of Henry constant values for gases in brines considering various salt concentrations and temperatures.

International audience; The composition of the captured CO 2 mixture may considerably vary both qualitatively and quantitatively depending on the sources, the selected technologies for purification... Many other compounds could be co-captured at various concentration levels and their potential co-storage along with CO 2 could be considered. Since these compounds may change the behavior of the CO 2 rich mixture, operators of the whole CCTS chain therefore wait for Jerome Corvisier et al. / Energy Procedia 114 (2017) 3322-3334 3323 clear recommendations in terms of admissible concentration levels for the various co-injected impurities while regulators need tools allowing them to formulate these recommendations. The SIGARRR project aims at conducting precise geochemical simulations to model the long-term behavior of co-injected gases within CO 2 storage sites based on a combination of experimental and numerical approaches, to ensure the reliability of numerical simulations. Within this context and the recent improvements in both processes and geochemical codes, this paper presents the water solubility precise calculations for CO 2 and most of the potential impurities N 2 , O 2 , Ar, CO, H 2 S, SO 2 , CH 4 , H 2 and the brine solubility relatively accurate geochemical simulations for CO 2 , N 2 , O 2 and CH 4 as well.

International audience; As renewables are progressively displacing thermal plants in the power generation scene worldwide, the vocation of stationary Gas Turbines (GT) is deeply evolving. In this irreversible move GT plants are called upon to become cycling units with increasingly variable load profiles. This is dictated by the need to compensate for the fluctuations of renewable energy sources and secure the spinning reserve that is indispensable for the stability of the grids. This new scenario creates a serious challenge for gas turbine designers and operators in terms of investment policy, plant management and equipment lifetime. Indeed, operating a gas turbine at part, variable load requires reducing its firing temperature and possibly its air flow. While part load operation entails efficiency losses with respect to the full load mode, load variations cause maintenance penalties due the premature component ageing tied namely with thermal and low cycle fatigue effects on machine materials. As far as efficiency is concerned, an exergy analysis of a contemporary, air-based Brayton cycle is useful for quantifying and comparing the losses incurred by the various engine components. Such study reveals the high sensitivity of compressor efficiency to load decreases. Among possible countermeasures , heating the air at the compressor intake represents a simple mitigation measure, as it enables reducing the air flow rate while preserving to some extent the efficiency of the compressor and consequently GT efficiency.

International audience; The vaporization of drops of highly vaporizable liquids falling inside a cryogenic environment is far from being a trivial matter as it assumes harnessing specialized thermodynamics and physical equations. In this paper, a multi-component falling droplet evaporation model was developed for simulating the spray cooling process. The falling speed of the sprayed droplets was calculated with the momentum equations considering three forces (gravity, buoyancy and drag) applied to a droplet. To evaluate the mass and heat transfer between the sprayed droplet and the surrounding gas phase, a gaseous boundary film of sufficient thinness was assumed to envelope the droplet, while the Peng-Robinson equation of state was used for estimating the phase equilibrium properties on the droplet’s surface. Based on the relevant conservation equations of mass and energy, the key properties (such as temperature, pressure and composition) of the liquid and gas phases in the tank during the spray process could be simulated. To conclude, the simulation algorithm is proposed.

The SAFT and cubic models are often compared in the open literature. Usually, limitations and strengths of both types of equations of state (EoSs) are ascribed to their theoretical foundations. Lit...

Most of the Statistical Associating Fluid Theory (SAFT) and cubic equations of state (EoS) for nonassociating pure components obey the three-parameter corresponding-state law, meaning that the know...

More than 40 years after their publication, updated versions of the generalized Soave α-function ( α ( T r , ω ) = [ 1 + m ( ω ) ( 1 − T r 0.5 ) ] 2 ) suitable for the Redlich-Kwong (RK) and Peng-Robinson (PR) equations of state (EoS) are proposed in this work. The new mathematical expressions of m R K ( ω ) and m P R ( ω ) have been determined by correlating the optimal m values, fitted on vapor pressures ( P s a t ) and/or enthalpies of vaporization ( Δ v a p H ) and/or saturated-liquid heat capacities ( c P , l i q s a t ) against the acentric factor ω . The correlations determined in this study can be considered as broad-based and sound since they were established for 1721 pure compounds belonging to many different chemical families (hydrocarbons, halogenated, oxygenated, sulfur, nitrogen compounds …) for which experimental data were available. Significant improvements on the reproduction of vapor pressures were obtained for the PR EoS with respect to the original version. The updated SRK EoS achieved similar average deviations for the three properties of interest ( P s a t , Δ v a p H and c P , l i q s a t ), in comparison with the original SRK equation. A substantial improvement is however noticeable for heavy molecules with an acentric factor larger than 0.9.

This paper describes the numerical method implemented in Gaztransport & Technigaz specific-purpose thermal and thermodynamic code for complex physical phenomena in Liquefied Natural Gas (LNG) carrier tanks. The code is zero-dimensional and is used for LNG industrial applications and research activities in several fields related to Boil-off Gas (generation, consumption, optimization, etc.). The set of equations considered consists of the LNG and NG mass and energy conservation equations completed with equation of state and equations for LNG aging modeling. An explicit time-marching scheme with multiple-order methods is used. Specific effort has been put into the fast computation of the thermodynamic and transport properties of LNG. The implemented physical approaches have been validated by operational data. Better management of Boil-off represents a significant operational challenge for players in the LNG chain. Industrial applications illustrate important aspects of physical modeling such as saturation properties, thermal layer and sloshing. These examples also demonstrate the capability of the code to tackle a large variety of LNG carrier operating conditions and tank geometries.

Solvation Gibbs energies are basically defined as a chemical potential change when transferring a fixed molecule from a perfect gas to a real liquid mixture. This quantity is of special interest for many practical applications as it quantifies the degree of affinity of a solute for its solvent. Few methods are currently available in the literature for the prediction of solvation Gibbs energies. In this article, a new approach is proposed: the use of a predictive cubic equation of state (EoS). The UMR-PRU (Universal Mixing Rule Peng-Robinson UNIFAC) EoS has been selected for its known capacity to semi-predict behaviors of complex systems including polar and associating compounds (by semi-prediction, it is meant that the EoS predicts binary interaction parameters but requires pure-component properties as input parameters). UMR-PRU predictions have been compared to experimental data extracted from the extensive CompSol database (containing around 22 000 pure component data and 70 000 binary data). Accurate predictions were obtained (a mean absolute deviation of 0.36 kcal/mol was obtained for all the binary data). Finally, when using a fully-predictive approach (i.e. pure-component EoS parameters are predicted from group-contribution methods), the prediction accuracy is roughly preserved.

Thermal engines, and in particular closed power cycles, are currently a focus of attention of many researches mainly because they represent the only way to exploit renewable thermal energies. To contribute to boosting the exploitation of available thermal sources, this work investigates the higher potential offered by a complementary technology, based on the use of reactive working fluids instead of inert ones: the here-called “thermo-chemical” engine. Such a power cycle enables the simultaneous conversion of thermal and chemical energies into power. With a theoretical approach, we analyse engine performances considering different stoichiometries and thermodynamic characteristics of reactive fluids and different operating conditions. It is shown that the use of specific equilibrated reactions occurring in the gaseous phase might lead to extremely powerful and highly efficient energy conversion systems, in the whole current domain of application of power cycles. Moreover, we demonstrate that, differently from classical thermal machines, a thermo-chemical engine allows for the efficient and powerful exploitation of low temperature heat sources and high temperature cold sinks which in general characterize renewable thermal energies.

Aerogels may be synthesized by extracting the liquid solvent from an organogel using supercritical CO 2 . The mixture (CO 2 -solvent) leaving the autoclave should be separated and all the solvent in the sample should be recovered at the end of the extraction. This paper deals with a pilot-scale unit where CO 2 and the solvent, here toluene, are separated using a cascade of cyclone separators. During the separation, the toluene recovery rate during is below 65%. In order to determine the reasons behind this malfunction, a thermodynamic study and a hydrodynamic study (Computational Fluid Dynamics, CFD) of the mixture separation in the cyclones were carried out. According to CFD, cyclones allow an efficient mechanical separation of the liquid solvent and the gaseous CO 2 . On the other hand, the thermodynamic model revealed that under the actual operating conditions, a large fraction of the solvent remains in gaseous state and is carried away through the cyclone gas outlet, hence the poor overall separation performance.

This study highlights that α-functions used in cubic equations of state must be of class C2 i.e. that their first ( d α / d T ) and second ( d 2 α / d T 2 ) derivatives must exist and must be continuous, positive ( α > 0 ) , monotonically decreasing ( d α / d T 0 ) , convex ( d 2 α / d T 2 > 0 ) and also verify d 3 α / d T 3 0 , for any value of the temperature T. Our proposed “consistency test for α-functions” gathers all these conditions. The non-respect of one of them can entail low-accuracy prediction of binary phase diagrams involving at least one supercritical compound (this statement is illustrated through the case-studies of the CO2-argon and CO2-decane systems) as well as improper variations of pure-component supercritical properties ( h and c P ) with respect to the temperature. Finally, an extensive study of the mostly used α-functions described in the open literature is performed and shows that all of them fail this test. Some component-dependent α-functions may however pass this test but only if mathematical constraints are added to their parameters.

In a previous work, we showed that the incorporation of a temperature-dependent volume-translation parameter in an equation of state for pure components alters necessarily the prediction of 1-phase and 2-phase properties. On the contrary, if a temperature-independent volume translation parameter is used, most of the 1-phase and 2-phase properties are preserved. In the present study, the influence of the incorporation of a volume translation in an equation of state, on mixture properties (essentially phase equilibria and properties of mixing) is addressed. It is first assumed that the volume-translation parameter of a mixture ( c ) is related to mole fractions through a quadratic mixing rule involving mutual volume translation parameters ( c ij ). It is found that only a simple arithmetic-mean combining rule for c ij makes it possible to preserve phase equilibria. Using such a combining rule entails that the quadratic mixing rule for the c parameter degenerates to a linear mixing rule. Secondly, it is proved that properties of mixing ( g M , h M , s M , c P M …) are preserved if a linear mixing rule is used for the c parameter and altered otherwise.

In many textbooks of chemical-engineering thermodynamics, a gas mixture obeying the fundamental law pVm = RT is most often called ideal-gas mixture (in some rare cases, the term perfect-gas mixture can be found). These textbooks also define the fundamental concept of ideal solution which in theory, can be applied indifferently to liquid or gas mixtures but in practice, is nearly always introduced through the instance of liquid solutions. Undergraduate students are thus faced with different theoretical solution models that are all named “ideal” which can be a source of confusion. It is indeed often observed either that the connections between the concepts of perfect gas and ideal solution are missed by undergraduate students, or that they do not make any distinction between the concepts of gaseous ideal-solutions and perfect-gas mixtures. In this article, a simple example is proposed to pedagogically clarify all the misconceptions inherited from the multiple definitions of ideal mixtures and to explicate t...

Robust and fast methods for chemical or multiphase equilibrium calculation are routinely needed by chemical-process engineers working on sizing or simulation aspects. Yet, while industrial applications essentially require calculation tools capable of discriminating between stable and nonstable states and converging to nontrivial solutions, students are often introduced to the simplest and less efficient equilibrium-calculation methods. In this article, the Gibbs energy minimization technique is presented as a robust alternative way to perform phase-equilibrium calculations and is applied to the determination of 2-fluid phase equilibria in low-pressure binary systems. It is carefully explained how the combination of this technique with an efficient quasi-global minimization method makes it possible to derive a robust PT-flash algorithm. In the frame of project-based learning devoted to develop a tool for building complex phase diagrams, this approach was successfully tested with a group of 100 students.