Modified Peng-Robinson Equation Research Articles

Evaluation of attraction terms in equations of state on the prediction of solubility of some biomolecules in supercritical carbon dioxide

In the present work, effect of the attraction terms of four recently modified Peng–Robinson equations of state on the prediction of solubility of caffeine, cholesterol, uracil and erythromycin was studied. The attraction terms of two of these equations are linear relative to the acentric factor and for the other two are exponential. It is found that the later show less deviation. Also interaction parameters for the studied systems are obtained and the percentage of average absolute relative deviation (%AARD) in each calculation is displayed.

Solubility of lycopene in supercritical CO 2 fluid as affected by temperature and pressure

For extraction efficiency, it is important to determine the lycopene solubility for optimum extraction technology and highest resulting yield. The temperature range of 50–80 °C and pressure range of 200–400 bars were used to measure the solubility of lycopene from tomato processing residue materials during supercritical fluid extraction. Single-pass flow method, off-line solute analysis, and subsequently HPLC quantitative analysis were the procedures followed for the lycopene extraction. The resultant calculated solubilities were on the lower scale as then ranged in the magnitude of 10 −6. Under supercritical conditions, increasing solubility of lycopene is stimulated by an increase in temperature and pressure. The highest solubility obtained was 1.9 × 10 −6 mol fraction at a pressure of 250 bars and at a temperature of 80 °C. Above these conditions, distinct signs of thermal degradation were observed. The efficiency calculated based on the experimental data was compared with the modified Peng–Robinson Equation of State. The correlated results through modelling show reasonably fair agreement with the experimental data. Through comparison of results produced by experimental methods and modelling, it was determined that the most favourable conditions for high solubility of lycopene in supercritical CO 2, for this particular method of analysis, were at 60 and 70 °C.

Liquid-vapor thermodynamic equilibrium in Fischer-Tropsch synthesis products

A modified Peng-Robinson equation of state is used to develop the methods for calculating the liquid-vapor thermodynamic equilibrium in Fischer-Tropsch synthesis products. The critical thermodynamic parameters of paraffin and olefin hydrocarbons with a number of carbon atoms higher than 20 are determined using the correlations proposed in the present paper. The calculated results are compared with literature data and the data obtained in the Integrated Research and Development Center.

Evaluation of Static Thermophysical Properties of the Ternary Molten Salt System Li, Na and Be/F Based on the Modified Peng-Robinson Equation

Evaluation of Static Thermophysical Properties of the Ternary Molten Salt System Li, Na and Be/F Based on the Modified Peng-Robinson Equation

Calculation of solubility of methimazole, phenazopyridine and propranolol in supercritical carbon dioxide

The calculation of solid-fluid equilibrium at high pressure is important in the modeling of separation of biomolecules from food and pharmaceutical products. In this study, three equations of state along with three mixing rules are used to calculate the solubility of methimazole, phenazopyridine and propranolol, as three representative drugs, in supercritical carbon dioxide. The equations of state are: Peng–Robinson (PR), Pazuki and others and a modified PR equation. Mixing rules are VdW 1, VdW 2 and Adachi–Sugie. It is shown that Pazuki equation along with VdW 2 mixing rule is more accurate than other equations. Interaction parameters for studied systems are obtained and the percentage of average absolute relative deviation (%AARD) in calculation is displayed. Also, we use Mendez-Santiago–Teja equation to check the consistency of experimental data.

Estimation of thermodynamic properties of the ternary molten salt system, LiF-NaF-BeF2, by the modified Peng-Robinson equation

The molten salt reactor (MSR), which is one of the generation IV reactors, can meet the demand of transmutation and breeding. The thermodynamic properties of the molten salt system like LiF-NaF-BeF2 influence the design and construction of the fuel salt and coolant in the MSR for the new generation. In this paper, the equation of state of the ternary system 15%LiF-58%NaF-27%BeF2, over the temperature range from 873.15 to 1 073.15 K at one atmosphere pressure, is described using a modified Peng-Robinson (PR) equation. The densities of the ternary system and its components are estimated by this equation directly, and compared with the experimental data. Based on the equation of state, the other thermodynamic properties such as the enthalpy, entropy and heat capacity at constant pressure are estimated by the residual function method and the fugacity coefficient method respectively. The densities calculated by PR equation are highly in agreement with the experimental data, and the enthalpy, entropy and heat capacity evaluated by the two different methods are consistent with each other. It can be concluded that the modified PR equation can be applied to evaluate the density of the molten salt system, and it is recommended that it be used as the basis to estimate the enthalpy, entropy and heat capacity of the molten salt system.

A comparison among three equations of state in predicting the solubility of some solids in supercritical carbon dioxide

Equations of state play an important role in chemical engineering designs, and they have assumed an expanding role in the study of the phase equilibria of fluids and fluid mixtures. In this report, a modified Peng-Robinson equation of state by Danesh et al., a modified Peng-Robinson equation of state by Gasem et al., and the Mansoori-Mohsen Nia-Modarress equation of state are used to predict the solubility of some solids in supercritical carbon dioxide. The systems studied were binary mixtures containing supercritical carbon dioxide with Ascorbic acid, Ascorbyl palmitate, Butyl hydroxyl anisole, Dodecyl gallate and Propyl gallate. Interaction parameters for the studied systems are obtained and the percentage of average absolute relative deviation (%AARD) in each calculation is displayed.

Measurements of isothermal vapor–liquid equilibrium of binary methanol/dimethyl carbonate system under pressure

By a static total pressure method, an equilibrium still with a viewing window was employed to measured isothermal vapor–liquid equilibrium data for methanol (1)–dimethyl carbonate (2) binary system from 337.35 to 428.15 K, as well as the lotus of azeotrope changing with pressure. The static total pressure method requires no analysis of phase composition, while the influence of vapor phase quantity must be considered under pressure. The system quantity ( n T) and composition ( z 1) of feedings and volume data ( V G) of equilibrium vapor phase were taken directly from the experiments. The fugacity coefficients of vapor phase were calculated from the experimental p– V G– T data, and correlated by the modified Peng–Robinson equation of state, which can be applied for both vapor and liquid phases. The isothermal equilibrium vapor and liquid compositions were then directly computed based on mass balance and a model-free method of calculation y from T, p and feeding composition z 1. The experimental data were also correlated with the modified Peng–Robinson equation of state and bubble point calculations. The correlated results showed that the maximum average relative deviation for experimental composition y 1 was 0.0174, and for total pressure p calc was 2.74%. The azeotrope of the binary system at different temperatures was also determined, which is consistent with the literature data.

Vapor-liquid equilibrium of UO2(NO3)2•2TBP and supercritical carbon dioxide mixture

Experimental studies were carried out with a high-pressure apparatus on the vapor-liquid equilibria of two binary mixtures of supercritical fluid C02 (SF-CO2) and tri-n-butylphosphate (TBP) complex with UO2(NO3)2 as well as SF-CO2 and TBP complex with nitric acid. In the experiments, the phase transitions resulting from pressure increase were observed by direct visualization. The measurements were performed at 313.15 to 333.15 K for CO2-TBP(HNO3)1.8(H2O)0.6 and at 323.15 K for CO2-UO2(NO3)2.2TBP. The transition pressures from two phases, i.e. vapor and liquid phases to a single phase were obtained at molecular fraction of TBP ranging from 5×10-4 through 2.5×10-1. The data were successfully correlated using the modified Peng-Robinson equation of state with the classical quadratic mixing rules. The temperature dependence of the pressures of phase transition was well reproduced with the correlation for CO2-TBP(HNO3)1.8(H2O)0.6. An interesting and practically important finding is that the organic solution, UO2(NO3)2.2TBP, where U concentration is 0.5 mol dm-3 forms a single phase with any amount of SF-CO2 when mixed under more than 13 MPa at 323.15 K.

Genesis and evolution of hydrocarbons entrapped in the fluorite deposit of Koh-i-Maran, (North Kirthar Range, Pakistan)

The exceptional development of coeval hydrocarbon and aqueous fluid inclusions (FI) in fluorite from the MVT-type ore deposit of Koh-i-Maran, Baluchistan (North Kirthar range, Pakistan), provides samples which are representative of the ore-forming fluid and which support the hypothesis of petroleum migration in the province. Primary brines at 125°C (10 wt% equ. NaCl) and secondary CH 4-rich brines at 135°C (7 wt% equ. NaCl), are recognised to be associated with oil migration in the fluid inclusions. They support the model of a per ascensum MVT (Mississippi Valley Type) stratabound hydrothermal deposit. A pressure–temperature path of 120–125°C to 165–200 bars is calculated from microthermometric data and PVT modelling of hydrocarbon FI using the modified Peng–Robinson Equation of State (IFP software) from primary cogenetic inclusions (oil and brines). The composition of gas and oil fractions is obtained by a combination of Synchrotron FTIR microanalysis and gas chromatography performed on individual fluid inclusions. The oil entrapped as a coeval primary fluid phase is a light aliphatic normal oil in the range C 8–C 35 with a high CO 2 content. The brown solid phase found systematically in the oil is probably asphaltene resulting from precipitation after trapping of the heavy fraction, which commonly occurs by decreasing pressure and temperature and\\or by CO 2 injection. Later CH 4-rich brine influx probably modified part of the oil in the primary fluid inclusions because degraded oil is observed within such inclusions. Biomarkers obtained by GC-MS analysis indicate a terpane distribution quite similar to the nearest oil seepage in the Gokurt area. This result and the high CO 2 content of organic fluid inclusions indicate a restricted/confined sedimentary environment for the source rock, which could correspond to the Eocene Carbonate formation with type-II organic matter. A possible additional input of gas from the Sambar formation is suggested as feasible. The link between the fluid inclusion data and the geodynamic evolution lead us to propose a circulation of basinal fluids driven mainly by the fault system during dewatering in the foredeep. In Pakistan, they are coeval to major compressional NW–SE Oligocene episode in the thrust belt. The origin of the fluorine may be found in the basin sediments as well as near the basement. The brines originated in salt structures recognized in eocambrian at the decollement level, the source rock was already mature.

A Theoretical Model to Simulate Supercritical Fluid Extraction: Application to the Extraction of Terpenes by Supercritical Carbon Dioxide

The ternary system CO 2 -limonene-citral was chosen as a model system in order to study the extraction of terpenes from lemon oil using supercritical carbon dioxide. Extractions were performed at several pressures and temperatures to evaluate the influence of these parameters on the separation efficiency. Extract composition was monitored by capillary gas chromatography. A theoretical model, based on a modified Peng-Robinson equation of state, was used to simulate the thermodynamic and mass transfer aspects of the extraction column. The critical parameters and the acentric factors of limonene and citral were estimated by group contribution methods. The method developed by Abdoul et al., which allows the calculation of binary interaction parameters (k ij ), was applied to terpenic compounds. The extraction experiments were simulated using this model, and the extraction profiles were accurately reproduced.

High-pressure (vapor+liquid) equilibrium in binary mixtures of (carbon dioxide+water or acetic acid) at temperatures from 313 to 353 K

Experimental results for the high-pressure (vapor+liquid) equilibrium of binary systems of carbon dioxide+(either water or acetic acid) are reported for temperatures from 313 to 353 K and pressures between 1 and 14 MPa. The experimental results are correlated using the modification of Melhem et al. [G.A. Melhem, R. Saini, B.M. Goodwin, A modified Peng–Robinson equation of state, Fluid Phase Equilibr. 47(1989) 189] for the Peng–Robinson equation of state and the mixing rule of Panagiotopoulos and Reid [A.Z. Panagiotopoulos, R.C. Reid, Equations of state: theories and applications, in: K.C. Chao, R.L. Robinson (Eds.), ACS Symposium Series, vol. 300, American Chemical Society, Washington, DC 1986 pp. 571]. The correlation of the experimental data for (carbon dioxide+water) required temperature-dependent binary interaction parameters. Correlating the data for (carbon dioxide+acetic acid) was not very successful as long as the dimerization of acetic acid was neglected. However, including dimerization resulted in a reliable correlation and even a successful prediction of the high-pressure (vapor+liquid) equilibrium from pure component data alone.

Modeling high-pressure vapor–liquid equilibrium of limonene, linalool and carbon dioxide systems

The research reported in this study is focused on modeling high-pressure phase behavior for CO 2–limonene and CO 2–linalool. A modified Peng–Robinson equation of state was applied to calculate vapor–liquid equilibrium using five different mixing rules obtained by incorporating activity coefficient models. The methodologies proposed by Heidemann–Kokal, Wong–Sandler and LCVM were used coupled with NRTL, UNIQUAC and UNIFAC models. A comparative analysis of the generated models was done for the binary systems and the best model was chosen to describe phase behavior of the system CO 2–limonene–linalool. An isothermal flash calculation was applied to investigate selectivity and yield simultaneously for this ternary system in order to understand better the process parameters governing supercritical CO 2 deterpenation of citrus peel oil. The results showed that to obtain good separation between limonene and linalool at 50°C and pressures from 80 to 90 bar a high CO 2/oil ratio is needed. As this ratio decreases, the process can be operated at 60 and 70°C over the same pressure range with equivalent performance.

High-pressure apparatus for phase equilibria studies: solubility of fatty acid esters in supercritical CO 2

Starting from a screw-type manual pump, a high-pressure variable-volume view cell was designed to perform static measurements of equilibria involving CO 2 and fatty acid esters. Though the design of the cell allows both the upper and the lower phases to be sampled, the synthetic method was chosen for this study. The efficiencies of both the apparatus and the method were first checked through preliminary experiments related to a compound already studied, namely methyl oleate. The good agreement between our measurements and those published in the literature allowed us to study other compounds, more precisely the ethyl esters of myristic, palmitic and stearic acids. These measurements were obtained at three different temperatures, 313.15, 323.15 and 333.15 K, and at pressures ranging from 1 to 18 MPa. The data were correlated using the modified Peng–Robinson equation of state with the classical quadratic mixing rules. An interesting feature of the apparatus is its low consumption of substance for a rather large amount of acquired data.

Some physical chemical properties of α–ω dihydroperfluoropolyethers

This paper describes the physico-chemical characterization and some properties of several α–ω dihydroperfluoropolyethers. Characterization has been carried out on the following properties: vapour pressure, density and viscosity as a function of temperature, glass transition temperature, refractive index and dielectric constant. The boiling point T b and the vaporization enthalpy Δ H v (calculated from vapour pressure data by means of the Clausius–Clapeyron equation) increase with the number of the backbone atoms N; both T b and Δ H v are higher than the corresponding values for compounds with the non-polar chain end CF 3 and the difference decreases, but does not disappear, when the number of chain atoms is as large as 10–15. The cohesive energy density and the solubility parameter δ are also found to be larger. It is shown that the increase with respect to CF 3 terminated homologues has to be attributed, as expected, to the polar component due to the CF 2H end group. The p– V– T properties can be predicted through a modified Peng–Robinson equation, where the critical temperature and pressure are obtained by group contributions. The comparison with the experimental data shows that the best group contribution data are those reported by Joback. The density increases and the expansion coefficient decreases with increasing chain length, as expected; at the same chain length the density is lower for materials with a CF 2H end group; the difference decreases with increasing N. The viscosity also increases with molecular weight; its dependence on temperature is described by the well-known Arrhenius equation. The activation energy is a function of Δ H v, as predicted by the hole theory of Eyring for simple liquids. The glass transition temperatures are very low and depend both on the chain length and on the structure of the compound. While the refractive index is a weak function of chain length and structure, the dielectric constant is a strong function of both variables; a relationship between the dielectric constant and the polar component of the solubility parameter is suggested. Finally the group contributions of the CF 2H group to the molar volume, vaporization energy, molar refractivity and molar polarizability have been determined, so that these data can be used to predict properties of new molecules.

Experimental vapour pressures of 13 secondary and tertiary alcohols—correlation and prediction by a group contribution method

Vapour pressures were measured using the static method for thirteen secondary and tertiary alcohols over the pressure range of 0.2 to 2000 Pa. Antoine equations are given in addition to the experimental values. A modified Peng–Robinson equation of state in which the covolume and attractive term were calculated by a group-contribution method was developed for primary alcohols. The proposed model leads to good results and is applied to secondary and tertiary alcohols.

Vapor–liquid equilibria for the binary system of carbon dioxide and 1,3-butadiene at 303, 313 and 333 K

In this work, the vapor–liquid equilibria for the binary system carbon dioxide—1,3-butadiene was measured at three temperatures, 303, 313 and 333 K. The measurements were carried out analytically in a recirculation apparatus. The experimental data were correlated with a modified Peng–Robinson equation of state and the Predictive Soave–Redlich–Kwong model. At 311 K, a parallel was drawn with the binary systems of n-butane, isobutane, 1-butene and carbon dioxide by means of the distribution coefficients K( i).

Critical points with the Wong-Sandler mixing rule—II. Calculations with a modified Peng-Robinson equation of state

This is the second of two papers in which critical point calculations in binary systems were performed utilizing cubic equations of state (EOS) combined with excess energy models using the Wong-Sandler mixing rule. In the first paper, a qualitative study of critical phase diagrams calculated using the simple van der Waals EOS combined with the NRTL model was made. In this paper, the Stryjek and Vera version of the Peng-Robinson EOS was also combined with the NRTL model and the resulting model was used in the computation of the critical loci of real systems. The binary interaction parameters of the model were estimated by correlating vapor-liquid equilibrium (VLE) data and, for some systems, successful predictions of the critical loci were obtained even when VLE data far from the critical point were used. To estimate parameters in systems for which the equation of state model may incorrectly predict a false liquid-liquid split, we used a penalty function approach based on the results of global stability tests. While the model studied here has been able to quantitatively predict the critical behavior of some non-ideal systems, involving compounds such as water, acetone and alkanols, only qualitatively correct behavior could be predicted for some highly asymmetric and non-ideal mixtures, such as water + n-dodecane.

AN IMPROVED PENG-ROBINSON EQUATION OF STATE WITH A NEW TEMPERATURE DEPENDENT ATTRACTIVE TERM

An improved form of the Peng-Robinson cubic equation of state has been proposed. The temperature dependence of the attractive term has been modified so as to accurately represent vapor pressures of several fluids with large acentric factors from triple point to close to the critical point. The prediction of saturated liquid volume is also improved by introducing volume translation term in the equation of state. Comparisons of theoretical results with experimental data are made for the vapor/liquid phase equilibria of 44 pure fluids including nonpolar, polar and associating fluids. Our results show that the modified Peng-Robinson equation of state can represent accurately saturated vapor pressures of the fluids investigated in this paper, and it is more accurate than the Peng-Robinson equation of state and its earlier modifications due to Stryjek and Vera (1986) and Twu et al. (1995rpar;. Incorporation of the volume translation term in the equation of state has been found to improve the accuracy of saturated liquid volume significantly.

Gas-liquid mass transfer in cyclohexane oxidation process using gas-inducing and surface-aeration agitated reactors

The equilibrium solubilities, C ∗ , and volumetric liquid-side mass transfer coefficients ( k L a) for gaseous nitrogen and oxygen in liquid cyclohexane were obtained in wide ranges of pressures (1–40 bar), temperatures (380–480 K) and mixing speeds (13.3–20 Hz) in gas-inducing (GIR) and surface-aeration (SAR) agitated reactors. The C ∗ values were calculated using a modified Peng-Robinson equation of state and the transient physical gas absorption technique was employed to obtain the mass transfer coefficients. The C ∗ values for both N 2 and O 2 were found to increase with the solute gas equilibrium partial pressure and temperature. Under the same operating conditions, O 2 appeared to be more soluble in cyclohexane than N 2. The k L a values for the two gases were found to increase strongly with mixing speed and slightly increase with pressure in both reactor types. k L a values for both gases appeared to slightly increase with temperature in the SAR while an opposite trend was observed in the GIR. k L a values for both gases in the GIR were higher than those in the SAR at higher mixing speeds (16.6 and 20.0 Hz). It appeared that k L a values in the SAR were controlled by the mass transfer coefficient, k L , whereas those in the GIR were controlled by the gas-liquid interfacial area. a. The effect of gas nature on k L a values in both reactors was insignificant. Two empirical correlations to predict k L a and gas holdup values for N 2 and O 2 in liquid cyclohexane in both reactor types with ±30% accuracy were developed.