PR Equation Of State Research Articles

Generalization of the Wong-Sandler mixing rule to a generic cubic equation of state: Examples of use for systems of industrial interest (Hydrogen, CCUS, refrigeration)

Cubic equations of state (EoS) remain the most widely used models in chemical engineering, and their predictive capabilities are highly dependent on mixing rules (MR). Considered as one of the most accurate, Wong Sandler's (WS) MR, have been generalized in this work, to allow its use with all 2-parameter (PR, SRK, …) and 3-parameter (PT, mPT, NEOS, …) cubic EoSs. The procedure for implementing the generalized WS MR is presented and tested with PR, PT and its variants (mPT and NEOS) on vapor-liquid equilibrium (VLE) and density data on various classes of mixtures for different types of use (hydrogen, CCUS, refrigeration). The results clearly show the benefits of this type of MR, especially around the critical point and for density data without considering volume translation frequently used with PR and SRK EoS.

Solubility of o-toluidine in supercritical carbon dioxide at high-temperatures and high-pressures

In many technological applications the solubility (VLE data) of materials (solid or liquids) in SC CO2 is required. It is essential to understand the solubility and other properties of o-toluidine in the SC CO2 due to their technological importance. This paper presents a new isothermal VLE data for SC CO2 (1)+ o-toluidine (2). Thus, the main purpose of the present work is to experimental study of the VLE properties (solubility, PTxy relationship) of o-toluidine (one of the technologically important compound) in the SC CO2 needs for variety industrial applications. The measurements were made at four selected isotherms of (313.15, 333.15, 353.15, and 373.15) K over the pressure range from (1.24 to 31.44) MPa. A high-temperature and high-pressure optical cell has been used to measure of the phase equilibrium properties (PTxy) of the binary CO2 (1)+ o-toluidine (2) mixture. The combined expanded absolute and relative uncertainty of the temperature, pressure, and the phase concentration measurements at 0.95 confidence level with a coverage factor of k = 2 is estimated at 0.15 K, 0.2 %, and 3 %, respectively. The critical point parameters of the mixture in the PC−TC projection have been estimated using the measured VLE data. The shape of the critical curve behavior indicates that CO2 (1) + o-toluidine (2) mixture belongs to the Type III according to the Konynenburg and Scott classification. PR and PC-SAFT equation of state (EoS) were successfully applied to model the phase equilibria (qualitative point of view) for the SC CO2 (1) + o-toluidine (2) mixture at the measured experimental temperatures. From a quantitative point of view, the best choice (among the models used) was PR EoS. The critical curves predicted with PR and PC-SAFT EoS confirmed that the mixture is classified as Type III phase behavior.

Isothermal VLE (PTxy) measurements and modeling of the high-pressure and high-temperature phase behavior of SC CO2 + aniline mixture using the PC-SAFT and PR equations of state

This paper presents a new experimental VLE (PTxy) property data of aniline in the near and supercritical CO2 at four selected isotherms of (313.15, 333.15, 353.15, and 443.15) K over the pressure range from (0.8 to 32.4) MPa using a high-temperature and high-pressure (HTHP) optical cell. Samples were taken from both equilibrium phases and analyzed using gravimetric technique. The critical property data (PC−TC) have been estimated based on measured VLE data for SC CO2 +aniline mixture. The PC-SAFT and PR equations of state (EoS) were successfully applied to model the phase equilibrium (PTxy) behavior of CO2 +aniline mixture. The present experimental VLE data and the critical curves behavior predicted from both EoS indicates that the phase diagram of the CO2 +aniline mixture belongs to Type III according to classification Konynenburg and Scott.

Experimental and thermodynamic investigation of gemifloxacin solubility in supercritical CO2 for the production of nanoparticles

The effective use of the supercritical technology in the production of new pharmaceutical formulations with greater bioavailability requires the determination of the solubility of pharmaceutical substances in supercritical CO2 (scCO2) at different conditions. In the current work, the solubility of an antibacterial compound, Gemifloxacin, was measured at various temperatures (308 to 338 K), and pressures (120 to 300 bar). This compound has a poor solubility in scCO2 (0.02 × 10−4 to 0.67 × 10−4 mole fraction or 0.0156 to 0.5891 g.kg−1). Furthermore, some popular empirical models and three thermodynamic approaches (SRK and PR equations of state, and the regular solution model) were applied to correlate and predict the solubility of Gemifloxacin in scCO2. The regular solution model with temperature-dependent solubility parameter (mean AARD% = 2.32–4.34) and the SRK-based model (mean AARD% = 7.47), exhibited the highest accuracy in fitting the experimental data.

Measurement of the solubility and density of the saturated solution of 3-aminophenol in different pure solvents from 283.1 to 323.1 K: Correlative to pure predictive thermodynamic modeling and molecular dynamic simulation

The solubility of 3-aminophenol was measured in water, isopropanol, ethyl acetate, chloroform, and tert-butyl methyl ether (MTBE) from 283.1 to 323.1 K at atmospheric pressure. In addition, the density of pure solvents and the saturated 3-aminophenol solutions was measured. The experimental solubility data were correlated and predicted using four types of thermodynamic models, including correlative (Wilson, NRTL, and UNIQUAC), semi-predictive (NRTL-SAC, and UNIQAUC-SAC), predictive group contribution methods (UNIFAC, and UNIFAC-DMD), and pure predictive COSMO-SAC model. The NRTL-SAC and UNIQUAC-SAC as semi-predictive models were used to obtain 3-aminophenol conceptual segment numbers, and then, using the NRTL-SAC model, the solubility of 3-aminophenol was predicted in 58 FDA approved solvents in the pharmaceutical industry. The predictive models including UNIFAC and UNIFAC-DMD were also used to predict the 3-aminophenol solubility and compared with the experimental data. The results of the COSMO-SAC model have a large deviation from experimental data. In addition, the experimental solubility data were correlated using the PR equation of state with relative success. The segment-based models such as NRTL-SAC and UNIQUAC-SAC are suggested in the fast solvent screening procedure. Finally, the standard dissolution enthalpy (ΔdisH), the standard dissolution entropy (ΔdisS), and the standard dissolution Gibbs energy (ΔdisG) of 3-aminophenol in the selected solvents were calculated by the Van’t Hoff model and the Gibbs-Helmholtz equation. These values imply that the solubility of 3-aminophenol is an entropy-driven non-spontaneous endothermic process in all chosen single solvents. Using the molecular dynamic (MD) simulation the solvation free energy of 3-aminophenol was calculated. The order of the absolute value of free energy of solvation is as ethyl acetate > isopropanol > MTBE > water > chloroform which is consistent with the order of solubility data.

Improved vapor pressure prediction from PR + COSMOSAC EOS using normal boiling temperature

AbstractWe evaluate the predictive power of the PR + COSMOSAC Equation of State (EOS) for vapor pressure using a large dataset of 19,081 compounds. The PR + COSMOSAC EOS uses results of quantum mechanical solvation calculations to determine the energy and molecular volume parameters in the Peng‐Robinson EOS and thus does not require experimental critical temperature (Tc), pressure (Pc), and acentric factor (ω) as in the conventional approach. The prediction accuracy (average absolute relative deviation) is 141%, about seven times that of the PR EOS. A new approach is developed to improve the prediction accuracy from PR + COSMOSAC EOS by incorporating experimental normal boiling temperature. The prediction accuracy improves to 58%, about three times that of the PR EOS. The PR + COSMOSAC EOS is an effective method for vapor pressure prediction when no or just some experimental data is available.

Experimental measurement and thermodynamic modeling of Chlorothiazide solubility in supercritical carbon dioxide

Chlorothiazide, with the brand name Diuril, is used as a diuretic as well as an antihypertensive drug. This medicine with very slight solubility in water and low permeability is categorized in the class IV of Biopharmaceutical Classification System (BCS) and possess low bioavailability. Therefore, enhancement of the drug solubility would be of great importance to reduce its dosage and consequently side effects. Decrement of Chlorothiazide particles size to micro/nano scale using a supercritical carbon dioxide (scCO2)-based method can be an efficient approach to enhance its bioavailability and therapeutic efficiency. To select and design a proper supercritical micronization/nanonization method, solubility of Chlorothiazide in scCO2 should be determined which is conducted in this work by gravimetric method. In this study, solubility of Chlorothiazide in scCO2 was obtained at various operating conditions (308–338K and 130–290 bar). It was found between 0.417 × 10−5 to 1.012 × 10−5 mol mol−1 (mole fraction) for Chlorothiazide. Moreover, the obtained values were correlated through five empirical models (Chrastil, Mendez-Santiago and Teja (MST), Kumar- Johnston (K-J), Bartle, and Garlapati-Madras), as well as SRK and PR equations of state. All of the mentioned models have shown satisfactory correlation accuracy for the drug solubility. Meanwhile, the K-J model with the minimum AARD% value of 3.15 and the PR-EoS with the mean AARD% value of 6.51 have the highest precision to fit the experimental data. Also, the extrapolative ability of the mentioned empirical models to predict the Chlorothiazide solubility outside the considered range of operating conditions was investigated.

Compressed liquid densities for cyclopentane/n-heptane mixtures from 293.15 K to 363.15 K at pressures up to 70 MPa

The compressed liquid densities of pure cyclopentane, n-heptane and its binary mixtures were measured with the vibrating-tube densimeter. The temperature ranges were from 293.15 K to 363.15 K and the pressures up to 70 MPa. The density data were correlated with the Tammann-Tait equation. The excess molar volumes, isothermal compressibility and isobaric thermal expansivity were calculated and discussed. In addition, the SRK and PR equation of state and the corresponding volume-translation equations were used to predict the densities of the mixtures, and the predictive accuracy was analyzed.

Vapor-liquid equilibrium experiment and prediction of excess property of new working pair CO2-[BMP][Tf2N] in absorption refrigeration system: Expérience d'équilibre vapeur-liquide et prédiction de la propriété excédentaire de la nouvelle paire de travail CO2-[BMP][Tf2N] dans un système de réfrigération à absorption

Solubility of CO2 in ionic liquids (ILs) is of great importance in absorption refrigeration system as new working pairs. Vapor-liquid equilibrium (VLE) of CO2 in [BMP][Tf2N] (1-butyl-1-methyl-pyrrolidine bis(trifluoromethylsulfonyl)imide) is carried out experimentally using the experiment system at temperature range 303.15 K-363.15 K. The experimental results show that the solubility of CO2 in [BMP][Tf2N] can reach up to 0.1235–0.5324 (molar fraction) within temperature range 283.15∼363.15 K and pressure range of 0.2∼5 MPa. The solubility of CO2 in [BMP][Tf2N] increases with increase of temperature and pressure. The VLE data of CO2-[BMP][Tf2N] binary system is correlated with two models (SRK equation of state +WS mixing rule +UNIFAC activity coefficient model and PR equation of state +WS mixing rule +UNIFAC activity coefficient model). The excess Gibbs free energy (GE), excess enthalpy (HE) and excess entropy (SE) of the system are obtained and the interaction parameters kij is regressed based on the VLE of CO2-[BMP][Tf2N] binary system. The variation trend of GE, HE and SE are obtained with temperature, pressure and molar fraction of CO2. The calculation results show that the accuracy of SRK equation of state is slightly higher than that of PR equation of state in CO2-[BMP][Tf2N] binary system. The accuracy of SRK equation of state and PR equation of state decreases with increase of temperature and pressure.

Maximum Liquefaction of Gases Revisited

Joule-Thomson liquefiers are the commonest machines to liquefy gases. Over the years, countless number of articles have been published on the subject. Dozens of 1st and 2nd law analyses were carried out on Joule-Thomson liquefaction cycles. And yet an aspect of purely theoretical interest seems to have passed unnoticed, namely: for a given volume of gas, what conditions should be fulfilled to achieve maximum liquefaction without considering engineering details of design equipment and the highly irreversible character of work-consuming devices, heat exchangers, heat leaks and the throttling process. This work addressed this issue by applying the 1st law analysis and elementary calculus prescriptions to a simple Linde-Hampson liquefying process. The same approach could be applied to other liquefying cycles. As is well-known, for a given mass flow rate of a gas, maximum fraction liquefied occurs when the pre-cooling temperature, Ti , and initial pressure, Pi , lie on the inversion curve. It has been proved that this is only true if an additional condition is fulfilled. Expressions for it were derived for the van der Waals, RKS and PR equations of state.

Hydrate phase equilibrium determination and thermodynamic modeling of CO2 + epoxy heterocycle + water systems

Ethylene oxide (EO), 1,3-propylene oxide (PO), tetrahydrofuran (THF), 1,3-dioxolane (1.3-DX), 1,4-dioxane (1,4-DX) and 1,3,5-trioxane (s-TO) were selected to investigate their thermodynamic promotion effects on CO2 hydrate formation. New hydrate phase equilibrium data of carbon dioxide + epoxy heterocycles + water systems were determined employing an isochoric temperature-search method in the temperature range of (273.15 to 295.35) K and the pressure range of (0.4 to 4.5) MPa. Results showed that the presence of epoxy heterocycles significantly increased the hydrate formation temperature substantially compared with that of pure CO2 hydrate. Under the same conditions, the phase equilibrium temperature of CO2 hydrate under the action of the additive was from low to high: PO < 1,4-DX < 1,3-DX < s-TO < EO < THF. CO2 hydrate dissociation enthalpies with different epoxy heterocycles were also calculated from Clausius–Clapeyron equation to infer their stabilities and the structures formed. It was found that the estimated enthalpy of dissociation was consistent with the superiority sequence obtained from the phase equilibrium data, illustrating that the water-soluble sII clathrate former of THF had the highest hydrate promoting effect. Moreover, Chen-Guo model, associated with a modified Joshi empirical activity model and PR equation of state was proposed further to predict hydrate phase equilibrium. Satisfactory agreement was observed between predictions and experimental data. Analysis of the results confirmed that the proposed thermodynamic model worked well in describing phase behavior of complex hydrates and the maximum relative error of the pressure was less than 8.5%.

Reliable estimate of minimum miscibility pressure from multiple possible EOS models for a reservoir oil under data constraint

Multiple Equation of State (EOS) models are possible for a reservoir oil if limited laboratory data is used in the EOS model development; each EOS model has its own predicted minimum miscibility pressure (MMP) value with unknown reliability. This article presents a novel approach to estimate a reliable MMP value using the multiple MMP values calculated from multiple EOS models developed with limited laboratory data such as bubble point and density at bubble point. MMP predicted using the proposed approach has better accuracy than the estimated MMP from an EOS model developed using a large set of data at the regression stage. Each possible EOS model for a reservoir oil has a specific set of values of total Gibbs free energy of mixing (g) at bubble point and predicted MMP for a given injection gas. The MMP estimate is developed using the trend of g versus MMP (predicted) from multiple EOS models in the proposed approach. The AARD in MMP prediction for 22 oils is 5.21% using SRK EOS and 6.65% using PR EOS, which is lower than the earlier approach (7.6%) that uses all PVT, swelling test, and multi-contact test data in EOS model development.

Method for prediction of liquid-vapor critical points in binary mixtures: geometrical-EOS model

A new method for predicting the Liquid- Vapor critical point of binary mixture, is presented, which is based in geometrical distances. Actually, the method is based on the minimization of the distance between the experimental and calculated values of the critical temperatures and critical pressures. The SRK and PR equations of state along with classical mixing rules of van der Waals were used as thermodynamic models to calculate the critical point of a given mixture. The proposed method requires that the mixture parameters a, b, and the covolume ε = b/v of each equation of state be determined at each iteration by solving the resulting cubic equation. For nine binary mixtures containing: hydrocarbon derivatives, carbon dioxide and alcohols are studied. The AARE of the calculated values is about 0.86% for critical temperature and 2.07% for critical pressure. Good agreements are found between the calculated results and experimental data. The technique is a general purpose one and can be applied in connection with other thermodynamic models.

Phase equilibrium for the binary mixture of 1,1,2,3,3,3-hexafluoro-1-propene (R1216) + propane (R290) at temperatures from 283.15 to 313.15 K

Based on the study of the mixture containing 1,1,2,3,3,3-hexafluoro-1-propene (R1216) and propane (R290) by a set of static-analytical type experimental apparatus, this paper presents a series of vapour-liquid equilibrium data at the temperature from 283.15 K to 313.15 K. It is the first time to report the VLE data at a temperature below 313.15 K. Moreover, the uncertainties of pressure, temperature, and mole fraction in this experiment were determinate. The PR equation of state (EoS) combined with the following two models respectively, the van der Waals (vdWs) mixing rule and the Huron-Vidal (HV) mixing rule relating to the non-random two-liquid (NRTL) activity coefficient model were used to correlate the experimental VLE data of the binary system. Two models all presented an extremely content correlation of the experimental data for the R290 + R1216 mixtures, and the second model is more suitable as the pressure's maximum average relative and absolute deviation are 0.003 and 0.0026, respectively, and the maximum average absolute deviation of the vapor phase mole fraction AAD(y) is 0.0045. Near azeotropic phenomenon occurred within the temperature range of the experiment when the proportion of R290 is about 0.6 to 0.7.

Calculation of thermodynamic properties of mixtures in two-phase equilibrium

Thermodynamic properties of mixtures in vapor-liquid equilibrium (VLE) were studied. Thermodynamic properties of the methane-ethane mixtures in VLE were calculated with highly accurate Helmholtz free energy equation of state GERG-2008, simplified GERG-2008 and common cubic PR equation of state (EOS). Results show that GERG-2008 has high accuracy in VLE calculations. However, simplified GERG-2008 and PR-EOS both work unsatisfactorily in VLE calculations.

Thermodynamic Property Calculation in Vapor-Liquid Equilibrium for Multicomponent Mixtures using Highly Accurate Helmholtz Free Energy Equation of State

Thermodynamic properties of multicomponent mixtures in phase equilibrium were studied. The tangent plane criterion was used for stability analysis, and the Gibbs energy minimization was employed for phase equilibrium calculation when the successive substitution didn't converge. Thermodynamic properties of a 12-component natural gas mixture in vapor-liquid equilibrium were calculated with highly accurate Helmholtz free energy equation of state GERG--2008, simplified GERG--2008 and common cubic Peng --- Robinson (PR) equation of state. Results show that in vapor-liquid equilibrium, GERG--2008 has high accuracy and works better than simplified GERG--2008 and PR-equation of state. Simplified GERG--2008 and PR-equation of state both work unsatisfactorily in vapor-liquid equilibrium calculation, especially near the saturation zone. The deviation function in GERG--2008 can significantly affect the accuracy of GERG--2008 when calculating thermodynamic properties of mixtures in vapor-liquid equilibrium

Phase Behavior and Physical Properties of Dimethyl Ether/Water/Heavy-Oil Systems Under Reservoir Conditions

SummaryPhase behavior and physical properties including saturation pressures, swelling factors (SFs), phase volumes, dimethyl ether (DME) partition coefficients, and DME solubility for heavy-oil mixtures containing polar substances have been experimentally and theoretically determined. Experimentally, novel phase behavior experiments of DME/water/heavy-oil mixtures spanning a wide range of pressures and temperatures have been conducted. More specifically, a total of five pressure/volume/temperature (PVT) experiments consisting of two tests of DME/heavy-oil mixtures and three tests of DME/water/heavy-oil mixtures have been performed to measure saturation pressures, phase volumes, and SFs. Theoretically, the modified Peng-Robinson equation of state (EOS) (PR EOS) together with the Huron-Vidal mixing rule, as well as the Péneloux et al. (1982) volume-translation strategy, is adopted to perform phase-equilibrium calculations. The binary-interaction parameter (BIP) between the DME/heavy-oil pair, which is obtained by matching the measured saturation pressures of DME/heavy-oil mixtures, works well for DME/heavy-oil mixtures in the presence and absence of water. The new model developed in this work is capable of accurately reproducing the experimentally measured multiphase boundaries, phase volumes, and SFs for the aforementioned mixtures with the root-mean-squared relative error (RMSRE) of 3.92, 9.40, and 0.92%, respectively, while it can also be used to determine DME partition coefficients and DME solubility for DME/water/heavy-oil systems.

Influence factors on CO2 solubility in cycloalkanes and cycloalkane volume expansion: Temperature, pressure and molecular structure

In CO2 enhanced oil recovery process, the interactions between CO2 and oil components are complex since crude oil is a mixture of n-alkanes, cycloalkanes, aromatics, resin, asphaltene and other compounds. To investigate the effects of temperature, pressure and molecular structure on CO2 solubility in cycloalkanes and the resulting cycloalkane volume expansion, the solubility of near critical and supercritical CO2 in cyclopentane (CP), cyclohexane (CH), methylcyclohexane (MCH), methylcyclopentane (MCP) and ethylcyclohexane (ECH) and the volume expansion factor of cycloalkanes at diverse temperature and pressure were measured. It was observed that increasing temperature decreases CO2 solubility, while CO2 solubility increases with pressure increasing. Compared with CP and CH, it's harder for CO2 to dissolve in their methyl or ethyl substituents. For homologues, CO2 solubility decreases with carbon number increasing. The volume expansion factor and solubility have a same variation tendency with temperature, pressure and molecular structure. The experimental results of solubility were correlated with Fornari's model and PR equation of state with the maximum average absolute relative deviation (AARD) of 2.8% and 6.8%, respectively. The excess molar volume of CO2 + cycloalkane mixtures was calculated to be negative and increases with pressure.

Prediction of Carbon Dioxide Solubility in Monoethylene Glycol /Water Mixtures Employing SRK and PR-EOS with Two Different Mixing Rules

A thermodynamic models of binary system carbon dioxide (1) - mixture (monoethylene glycol (MEG)/water) (2) at pressure up to 5 bar and temperatures (288-348 K) are established using SRK and PR equation of state (EOS). Modified van der Waal’s and quadratic mixing rules are coupled with the two Equation of state. Prediction of carbon dioxide in pure water and MEG were studied as well using same equations. Average absolute deviation in liquid-phase compositions percentage AADx % used for adjustable parameter optimization. The predicted results are showed very good agreement with the experimental data in all the systems examined. Quadratic mixing rule in all systems gives AADx % lower than Modified van der Waal’s and the values differences can be ignored.

Modified Peng-Robinson equation of state for CO2/hydrocarbon systems within nanopores

Phase behavior of confined fluid demonstrates significant deviation from that of bulk fluid because of the strong molecule-wall interaction and geometric constraint in confined space, resulting in the inapplicability of the classical cubic equation of state (EOS). The objective of this work is to modify the Peng-Robinson EOS (PR EOS) with respect to both the attractive parameter and the covolume term to reflect the impact of molecule-wall interaction and geometric constraint, respectively. The modified PR EOS is applied to compute the phase diagrams of CO2+n-C4H10 and CO2+n-C10H22 binary mixtures, CO2+n-C4H10+n-C10H22 ternary mixture, and CO2+Eagle Ford condensate in nanopores. In this work, correlations of both critical temperature and critical pressure shift with nanopore sizes are proposed to compute the confined attractive parameter and the confined covolume in the modified PR EOS. The proposed EOS model is validated by both the critical temperature and the critical pressure shift data collected from literature. Results demonstrate that confinement effect in nanopores impose an overall shrinkage to the two-phase diagrams of all the CO2-hydrocarbon systems. The upper dew-point pressure of the Eagle Ford condensate sample is calculated to be 2972.6 psi, with a suppression of 27.56% compared to the bulk value of 4103.6 psi. Moreover, the size of the two-phase region in the ternary diagram and the minimum miscibility pressure also decrease in confined space, which is in favor of the miscible gas injection enhanced oil recovery with a higher possibility of achieving first contact miscibility.