Peng-Robinson Cubic Equation Of State Research Articles

Predicting solvation energies of free radicals and their mixtures: A robust approach coupling the Peng-Robinson and COSMO-RS models

Detailed kinetic models are valuable tools for a clear understanding of the dynamics of complex reacting systems based on radical-chain mechanisms, such as combustion and oxidation. Gas-phase automatic kinetic generators, such as EXGAS, RMG, MAMOX, NetGen, REACTION, and GENESYS can be used to establish a detailed network of reaction pathways and the rates associated with each reaction. The range of applications of these gas-phase kinetic generators can be extended to liquids through diffusional and solvation corrections directly applied to the gas-phase thermo-kinetic data. In this work, a flexible framework is proposed for the calculation of the solvation correction involving closed-shell (i.e., non-free radical) and open-shell (i.e., free radicals) molecules. This novel model relies on the Peng-Robinson cubic equation of state (EoS) combined with a quantum-based continuum solvation model (COSMO-RS) through an advanced mixing rule. Unlike most predictive equations of state, the proposed model requires only pure compound inputs: critical temperature (Tc,i), critical pressure (Pc,i), acentric factor (ωi), and the screening charge distribution (σ-profile). These inputs were obtained for C/H/O free radicals using group corrections applied to the known values of the associated closed-shell molecules (parent molecules). The resulting EoS is able to provide fast predictions of solvation quantities of closed-shell molecules and C/H/O free radicals with a mean unsigned error of around 0.30 kcal/mol. The great advantage of this method is that it allows high-throughput computation of solvation quantities in pure solvents and mixtures at any temperature (including the supercritical domain), which could enable the simulation of complex oxidation kinetics in a wide range of applications.

DNS of a non-premixed CH4/O2 flame in a supercritical CO2 environment

3D Direct Numerical Simulation (DNS) is performed to investigate turbulent non-premixed methane oxy-combustion in a CO2-rich environment at supercritical conditions (300 bar). The study focuses on a shear-layer configuration typical of slot burners, where the central slot carries the fuel and the oxidant mixture O2/CO2 flows on both sides of the central jet. The simulation solves the compressible Navier–Stokes equations coupled with the translated volume formulation of the Peng–Robinson cubic equation of state (VTPR-EoS), utilizing a reduced 23-species kinetic scheme derived from the ARAMCO 2.0 complete mechanism. The extremely high pressure results in turbulent scales smaller than those observed at lower pressures. Both premixed and diffusion flame zones are identified, with heat primarily released in non-premixed rich regions, leading to a CO mass fraction of up to 0.55. The flow exhibits uphill (counter-gradient) diffusion for both CO2 and H2O, primarily influenced by the interaction of binary diffusion coefficients and individual species chemical potential gradients. Values in the range of 2.52−2.62 are obtained for the fractal dimension of temperature iso-surfaces. Mixture fraction probability density functions (PDFs) are compared with the standard presumed β−PDF, revealing an underestimation of mixing. Differently from flames at atmospheric pressures, the Dufour effect in the energy diffusion flux, is not negligible. Furthermore, fugacity coefficients must be considered in the calculation of chemical species kinetic rates.

Measurements of saturation pressures for the novel refrigerant R1132(E)

R1132(E) (trans-1,2-difluoroethylene, C2H2F2) is a potential next generation refrigerant to be utilized in air conditioning applications. This hydrofluoroolefin (HFO) refrigerant possesses an extremely low-GWP value below 1 and it is an excellent candidate for replacing R32 in blends such as R410A, which are subjected to local and international greenhouse gas regulations for limiting global warming. Two isochoric apparatus were used to measure the saturation pressures of R1132(E) from 240 K to its critical temperature. At the critical temperature, the critical pressure of R1132(E) was also directly measured. Twenty-four saturation pressures including the critical point were used for optimizing a Wagner-type equation representing the saturation pressure curve. The absolute average deviation of the saturation pressures of R1132(E) predicted by the model using the fitted parameters and the experimental data is 0.02%. The optimized Wagner-type equation of saturation pressures is used for determining the acentric factor of R1132(E) as 0.2433, which is further utilized for the prediction of the saturation pressures using the Peng-Robinson cubic equation of state within an absolute average deviation of 0.31%.

Peng-Robinson Cubic Equation of State Based on Key Group Contribution and Calculation of Nitrogen Gas Solubility in MMA Dimer

Previously authors have reported facts that nitrogen (N2) and oxygen solubilities in styrene is the same as those in benzene and divinylbenzene at 303 K. Though the three compounds have an atomic composition, (CH)n (n=6, 8 and 10), the gas solubilities are thought to depend on the number of aromatic carbons in the solution. Then, authors named it ‘a key group in solubility’. In this research, the key group was investigated for N2 solubility in methyl methacrylate (MMA) and its dimer, ethylene glycol dimethacrylate (EGDMA). Therefore, the calculations were carried out by Peng-Robinson (PR) equation of state based on group contribution methods. The experimental data employed were those of Lai et al., where N2 solubility are reported in MMA at 303 K. The N2 solubility in EGDMA was assumed to be double of that in MMA at 303 K, because EGDMA has two MMA units in the molecule. Two types of group contribution methods were proposed to calculate N2 solubility in EGDMA. One was for the critical temperature and pressure proposed by Joback and Reid. Using these properties, the attractive and excluded volume parameters in PR equation were evaluated for EGDMA. Other was similar to a method proposed by Orbey and Sandler. The excluded volume parameter in PR equation can be evaluated from those of MMA by multiplying the number of repeating units, and the attractive by multiplying the squared number. Instead of the method, the powers were proposed to be 3/4 and 3/2 for the excluded volume and attractive perimeters, respectively. The powers were come from a scaling theory by de Gennes. The binary parameter for N2 – EGDMA was also set to k12 = 0.224, which was the same as that for N2 –MMA. The calculated N2 solubility in EGDMA was far smaller than the hypothetical N2 solubility in EGDMA at 303 K. Otherwise, to reproduce the hypothetical N2 solubility, a quite different value, k12 = -0.044, was necessary for the method by Joback and Reid. The results suggested that a key group for gas solubility will not be accepted in MMA.

Hydrogen solubility in bio-based furfural and furfuryl alcohol at elevated temperatures and pressures relevant for hydrodeoxygenation

Biomass conversion into fuels and added-value chemicals, in high yield and with good selectivity, is still a great issue and an attractive research topic. The design and the optimization of defunctionalisation processes require accurate kinetic models that take into account the solubility of various gases in the bio-based chemicals present in the process.Some of the promising platform bio-based compounds that can be further converted to valuable chemicals are furfural and furfuryl alcohol. Hydrogen solubility in furfural and furfuryl alcohol was studied at three temperatures from the range (323.15–423.15) K and at pressures up to 25 MPa. Hydrogen dissolves better in furfural than in furfuryl alcohol, for about 15 %.The obtained experimental data were modelled using the Soave-Redlich-Kwong and Peng-Robinson cubic equations of state, as well as the PC-SAFT equation of state. The parameters of the PC-SAFT equation of state for pure compounds were defined for furfural and furfuryl alcohol. The binary interaction parameters, crucial for the prediction of phase-equilibrium behaviour, were determined for both examined systems. The interaction parameters obtained for the cubic equations of state were temperature dependent, while the interaction parameters optimized for the PC-SAFT equation of state were almost the same at all three temperatures for each studied system. The average absolute percentage deviations between the measured equilibrium pressures and those calculated using the mentioned models were under 4 %.

Density data for carbon dioxide (CO2) +trans-1,3,3,3-tetrafluoroprop-1-ene (R-1234ze(E)) mixture at temperatures from 283.32 to 353.02K and pressures up to 10MPa

The densities of CO 2 -R1234ze(E) (trans-1,3,3,3-tetrafluoroprop-1-ene) binary mixture were measured using VTD densitometer, Anton Paar DMA 512, in the gas, liquid and supercritical phases. Four compositions of mixtures: 21.3% CO 2 + 78.7% R1234ze(E), 40% CO 2 + 60% R1234ze(E), 59.6% CO 2 + 40.6% R1234ze(E) and 79.4% CO 2 + 20.6% R1234ze(E) were studied at seven temperatures between 283.32 K and 353.02 K and pressures up to 10 MPa. The data were well correlated using the Peng-Robinson cubic equation of State using the Wong Sandler mixing rules involving the NRTL activity coefficient model, and the fundamental Helmholtz equation of state using the Kunz and Wagner mixing rules involving Helmholtz energy. The experimental and correlated phase compositions were compared. Both two models were adjusted on the VLE data, but the Helmholtz model is more accurate to the prediction of density than the Peng-Robinson model.

Phase equilibrium measurements and thermodynamic modeling of {CO2 + diethyl succinate + cosolvent} systems

This work reports experimental phase equilibrium data for the binary systems {CO2(1) + diethyl succinate(2)} and {CO2(1) + ethyl acetate(2)}, and for the ternary systems {CO2(1) + diethyl succinate(2) + ethanol(3)} and {CO2(1) + diethyl succinate(2) + ethyl acetate(3)}. The experiments for the binary system {CO2(1) + diethyl succinate(2)} were carried out at temperatures ranging from 308 K to 358 K, and temperatures ranging from 303 K to 343 K for {CO2(1) + ethyl acetate(2)} as well as for all ternary systems. Only vapor-liquid equilibria were observed for all systems. The experimental measurements were carried out in a high-pressure variable-volume view cell containing a movable piston, which allows pressure control inside the cell. Binary and ternary systems were modeled with the Peng-Robinson cubic equation of state with the van der Waals quadratic mixing rule (vdW2). The presence of a cosolvent (ethanol and ethyl acetate) decreased the saturation pressures of either bubble or dew points compared to the binary system CO2 + diethyl succinate, increasing the solubility of diethyl succinate in CO2.

A hybrid analytical method for evaluating thermodynamic properties of mixtures by the Peng-Robinson equation of state

A new analytical hybrid method for calculating enthalpy difference in mixtures is presented in this paper. The method is based on the Peng-Robinson cubic equation of state (PR CEOS), it is a combination of two common enthalpy calculation methods, and it does not require any experimental data. The α function of the PR CEOS for every component is selected among several models. The new hybrid method results of 8 different mixtures are compared to data from the REFPROP™ database, and a satisfying agreement is obtained.

Experimental solubility of carbon dioxide and hydrogen sulfide in 2,2′-thiodiglycol

The solubility of acid gases such as CO2 and H2S in 2,2-thiodiglycol (TDG) were measured by static method so called isochoric saturation within the temperature range (303.15–353.15) K by steps of 10 K and pressure up to 1.2 MPa. To calculate the absorption behaviour of gases, density of 2,2-thiodiglycol at the related temperature range was measured with Anton Paar SVM 3000, as well. The outcome solubility data were modelled using Stryjek-Vera modification of Peng-Robinson cubic equation of state (PRSV EoS), and thermodynamic solubility quantities at infinitely diluted solution in 2,2-thiodiglycol were reported.

Direct numerical simulation on auto-ignition characteristics of turbulent supercritical hydrothermal flames

Hydrothermal flames occur in aqueous environments at conditions above the critical point of water. Due to the lack of reliable diagnostics applicable to high-pressure, high density-gradient and corrosive environments in hydrothermal flames, the auto-ignition characteristics of hydrothermal flames are still unclear. The objective of this study is to provide a fundamental understanding of auto-ignition process in non-premixed hydrothermal flames in terms of homogeneous ignition calculations and a two-dimensional (2D) direct numerical simulation. To model the real-fluid effects, the Peng-Robinson cubic equation of state with consistent formulas for thermodynamic properties and Chung's high-pressure methods for transport properties are implemented. The homogeneous ignition results indicate that the correlation of the ignition delay time with the mixture fraction in the current study is quite different from those reported in canonical conditions and there is no well-defined “most reactive” mixture fraction. In the DNS, a hydrothermal flame in a 2D mixing layer with pseudo-turbulence is simulated. Auto-ignition occurs independently and ignition kernels form at locations where the local mixture fraction varies from 0.80 to 0.85, lower than the stoichiometric mixture fraction (0.911). The ignition kernels evolve to edge flames that propagate at a mean displacement speed of 1.286 m/s. A compact structure of edge flames is observed, which lacks a rich premixed branch in contrast with the classic triple flame structure. An analysis in terms of species profiles and flame index is carried out to reveal the dynamics of the edge flames.

Phase Behavior of Heavy-Oil/Propane Mixtures

Summary The phase behavior of heavy-oil/propane mixtures was mapped from temperatures ranging from 20 to 180°C and pressures up to 10 MPa. Both vapor/liquid (VL1) and liquid/liquid (L1L2) regions were observed. Saturation pressures (VL1 boundary) were measured in a Jefri 100-cm3 pressure/volume/temperature (PVT) -cell and blind-cell apparatus. The propane content at which a light propane-rich phase and a heavy bitumen-rich (or pitch) phase formed (L1/L1L2 boundary) was visually determined with a high-pressure microscope (HPM) while titrating propane into the bitumen. High-pressure and high-temperature yield data were measured using a blind-cell apparatus. Here, yield is defined as the mass of the indicated component(s) in the pitch phase divided by the mass of bitumen in the feed. A procedure was developed and used to measure propane-rich-phase and pitch-phase compositions in a PVT cell. Pressure/temperature and pressure/composition phase diagrams were constructed from the saturation-pressure and pitch-phase-onset data. High-pressure micrographs demonstrated that, at lower temperatures and propane contents, the pitch phase appeared as glassy particles, whereas at higher propane contents and temperatures, it appeared as a liquid phase. Ternary diagrams were also constructed to present phase-composition data. The ability of a volume-translated Peng-Robinson cubic equation of state (CEOS) (Peng and Robinson 1976) to match the experimental measurements was explored. Two sets of binary-interaction parameters were tested: temperature-dependent binary-interaction parameters (SvdW) and composition-dependent binary-interaction parameters (CDvdW). Models derived from both types of binary-interaction parameters matched the saturation pressures and the L1L2 boundaries at one pressure but could not match the pressure dependency of the L1L2 boundary or the measured L1L2 phase compositions. The SvdW model could not match the yield data, whereas the CDvdW model matched yields at temperatures up to 90°C.

Modelos basados en termodinámica clásica para predecir las propiedades de biodiésel

Objective: To obtain a model based on the classical Peng-Robinson equation of state (PR-EOS) to evaluate the initial thermodynamic expressions (first- and second-derivative properties) in biodiesel. Methodology: A modified temperature dependence was used to transform the volume of the Peng-Robinson cubic equation of state to predict the thermophysical properties of biodiesel. The fuel studied is composed of five fatty acid methyl esters (methyl palmitate, stearate, oleate, linoleate and linolenate), which are the primary constituents of biodiesel. Results: The results showed that the approach presented in this work can improve the prediction of secondorder properties (isentropic bulk modulus, heat capacities and speed of sound) if the accuracy of the primary properties is maintained (vapor pressure and liquid density). Study limitations: Biodiesel is highly corrosive and is used in mixtures with other fuels such as gasoline; however, the model is only applicable to the properties of biodiesel and not mixtures. Originality: Two concepts in the Peng-Robinson equation are used: the α(T) function and volume transformation. The second concept was implemented because second-order thermodynamic properties need accurate densities and derivatives with respect to the total volume. Additionally, the α(T) function was selected through a systematic search among a wide range of reported correlations. Conclusions: The proposed thermodynamic model can predict, with only a few experimental data, properties that have an impact on the representation of spray, atomization and combustion events in diesel engines.

Predictive method of hydrogen solubility in heavy petroleum fractions using EOS/GE and group contributions methods

Hydrogen solubility in heavy petroleum fractions was modelled with Peng-Robinson cubic equation of state combined with the UNIFAC solution model (EoS/GE) through a modified Huron-Vidal mixing rule (MHV1). As critical properties and molecular structure of heavy petroleum fractions are entering parameters in this thermodynamic model, the thermodynamic characterization procedure by contribution of functional groups proposed by Carreón-Calderón et al. (2012) was taken as starting point in order to develop a predictive method for estimating hydrogen solubility in such fractions. The functional groups considered in the original work were reviewed and modified, improving predictions and avoiding adjustment of model parameters. Besides, a procedure of mass distribution for the hydrogen-carbon ratio (HCR) of the petroleum fraction is proposed so that the hydrogen solubility can be estimated when more than one heavy petroleum fraction is present. This approach was tested with twelve heavy petroleum fractions in a wide range of pressure and temperature. These fractions include coal liquids, refinery products and a bitumen from Athabasca. The total average deviation was about 15%.

Vapor-liquid equilibrium of binary systems with EoS/GE models at low pressure: Revisiting the Heidemann-Kokal Mixing Rule

In this work, a ϕ-ϕ approach is tested in the description of vapor-liquid equilibrium of 18 different binary systems by means of EoS/GE type models. These models combine the potentialities of the Peng-Robinson cubic equation of state and the UNIQUAC local composition model. The focus is on the Heidemann-Kokal Mixing Rule, whose derivation is presented. Systems including nonpolar - nonpolar, weakly polar - weakly polar, water - weakly polar, nonpolar - weakly polar, weakly polar - strongly polar and strongly polar - strongly polar compounds, besides systems involving immiscible components and carboxylic acids, were evaluated. Binary interaction parameters of the UNIQUAC model were estimated using a stochastic particle swarm algorithm, coupled to a Quasi-Newton deterministic algorithm. As a result, average deviations of less than 2% and 1% were obtained for vapor phase composition and bubble temperature or pressure correlation, respectively. The proposed modeling was efficient in the treatment of all evaluated systems and appears as a good alternative for the development of new models.

Density of carbon dioxide with impurities by Coriolis flow meter, oscillation-type densitometer and equations of state

Transporting CO2 from the capture plant to the storage site may encounter challenges in the flow metering due to the unusual physical properties of CO2 – especially when containing impurities. Building on the authors’ previous work on the effect of impurities in CO2 mixtures on the performance of Coriolis flow meters, in this work, the accuracy of the density measurements of CO2 mixtures was investigated using a Coriolis meter and a high-pressure Anton Paar densitometer. The measured density data were then compared to the Peng-Robinson cubic equation of state with CO2 volume correction (PR-CO2) as well as to the multi-parameter GERG-2008 equation of state. The Average Absolute Relative Deviations (AARD) of the density predictions with PR-CO2 and GERG EOSs from the measured densities with the Anton Paar densitometer are 1.2% and 1.0%, respectively. While the Coriolis meter density values were consistently lower than the actual value in the gas phase. A correlation was obtained to correct the measured densities in the gas phase by fitting the measured densities to the prediction values using PR-CO2 and GERG EoSs at elevated pressures and temperatures. The AARD was reduced from 26.1% to 2.3% using PR-CO2 and from 25.4% to 3.6% using GERG EoSs.

Phase equilibrium measurements and thermodynamic modelling for the systems involving valeric acid, ethanol, ethyl valerate and water plus CO2

This work reports phase equilibrium measurements for binary, ternary, quaternary and five components mixtures of CO2, ethanol, valeric acid, water and ethyl valerate at high pressures. Experiments were carried out using a high-pressure variable-volume view cell with operating temperatures ranging from 303.15K to 353.15K and pressures up to 15MPa. The CO2 mole fraction ranged from 0.4780 to 0.9412 for the binary system {CO2(1)+valeric acid(2)}, from 0.3801 to 0.9811 for {CO2(1)+ethyl valerate(2)}, from 0.5649 to 0.9193 for the ternary system {CO2(1)+ethanol(2)+valeric acid(3)} at an ethanol to valeric acid mole ratio of (3:1) and from 0.5907 to 0.9373 for {CO2(1)+ethanol(2)+ethyl valerate(3)} at an ethanol to ethyl valerate mole ratio of (1:1). For the quaternary {CO2(1)+ethanol(2)+water(3)+ethyl valerate(4)} and the five components system {CO2(1)+ethanol(2)+valeric acid(3)+water(4)+ethyl valerate(5)} fixed compositions were investigated at CO2 mole fraction of 0.7336 and 0.7211, respectively, while the mole ratio of other compounds were fixed at typical esterification conditions. For the systems investigated, vapour-liquid (VL), liquid-liquid (LL) and vapour-liquid-liquid (VLL) phase transitions were observed. The experimental data sets were successfully modeled using the Peng-Robinson cubic equation of state with the Boston-Mathias alpha function and using the van der Walls quadratic mixing rule. The PR-BM showed good performance in the prediction of the phase transitions for the ternary, quaternary and five components systems based on the binary interaction parameters obtained from the binary CO2+valeric acid, CO2+ethyl valerate and CO2+ethanol experimental data.

Assessment of the liquid mixture density effect on the prediction of supercritical carbon dioxide volume expansion of organic solvents by Peng-Robinson equation of state

Volume expansion and liquid mixture density are key-factors to design particle precipitation processes from expanded organic solvents using supercritical fluids such as carbon dioxide. To predict volume expansion it is necessary to know the volume or the density of the liquid mixture that is in equilibrium with its vapor at a certain temperature, pressure and composition. However, equations of state that fail to accurately describe the liquid mixture density are used to predict the volume expansion and results are considered satisfactory. In this work we investigated why this occurs using vapor-liquid equilibrium data of 13 binary systems containing CO2 and an organic solvent at high pressures with wide spread application in supercritical anti-solvent particle precipitation processes. Peng-Robinson cubic equation of state was applied with quadratic (PR-QMR) and LCVM-UNIFAC mixing rules (PR-LCVM-UNIFAC), and Peneloux’s volume correction was adopted too (PR-QMR-Peneloux). The results show that there is an offset of terms during volume expansion calculation that explains why large deviations in the prediction of liquid mixture density from bubble pressure data can lead to small deviations in prediction of organic solvents volume expansion by carbon dioxide.

Phase equilibria of 3-methylstyrene, 4-methylstyrene, alpha-methylstyrene and a methylstyrene mixture in supercritical CO2

Phase equilibria of 3-methylstyrene, 4-methylstyrene, alpha-methylstyrene and a methylstyrene mixture (mainly 3-methylstyrene (60%mol) and 4-methylstyrene (40%mol)) in supercritical CO2 were measured using high-pressure variable-volume view cells based on the static synthetic method. The systems were investigated between 308 and 353K, with mass fractions of solute ranging continuously from 0.0275 to 0.65 and pressures up to 15MPa. The experimental data shows a linear relationship between the phase transition pressure and the system temperature at constant composition. When the solubilities are compared, the methylstyrene isomers show little yet significant differences between them with the methylstyrene mixture being the most soluble. As the temperature increases, a decrease in the difference between the phase transition pressures of the methylstyrene structural isomers were observed. Lastly, the experimental data were correlated with the Peng-Robinson cubic equation of state using one temperature-independent binary interaction parameter and satisfactory results were obtained in both low and high solute concentration regions.

Modeling of CO2 vapor-liquid equilibrium in Colombian heavy oil using SARA analysis

The solubility of CO2 in Colombian heavy oil was calculated using the Peng-Robinson cubic equation of state and the Lee-Kesler correlations. The crude was represented as a mixture of pseudo-components and for each one of them, the thermodynamic and critical properties were estimated. The results obtained in representing the oil with four, five and six pseudo-components show that all these representations produce similar results and therefore the use of four pseudo-components is sufficient and has a lower computational cost. Excellent results were obtained by comparing the experimental and calculated data. For this system, it is enough to have a complete characterization of the SARA analysis and to use four pseudo-components to adequately model the vapor-liquid equilibrium of CO2 -heavy oil.

ЧИСЕЛЬНЕ МОДЕЛЮВАННЯ РОЗПОДІЛУ ТЕМПЕРАТУРИ В ПОТОЦІ МЕТАНУ В ВИХРОВИЙ ТРУБІ РАНКА-ХІЛША

In present numerical research, the temperature separation in methane stream within a counter flow Ranque-Hilsch vortex tube was investigated. A complete three-dimensional geometry of the vortex tube was used to generate a high-density computational grid. A vortex tube with two tangential inlet nozzles, an axial cold stream outlet and a circumferential hot stream outlet was considered. Methane was used as a fluid along with Peng-Robinson cubic equation of state. Fluid properties like total temperature and total pressure were analyzed for a range of inlet mass flow rates and inlet total pressure values. Also the total pressure and total temperature distribution along the axial direction was investigated. The temperature separation effect is more significant for air then for methane at all investigated pressures. Created model can be used to design industrial vortex tubes for oil and gas industry where methane is a main product.