Perturbed-chain Statistical Associating Fluid Theory Model Research Articles

Bubble Point Measurements of cis-1,1,1,4,4,4-Hexafluorobutene [R-1336mzz(Z)] + trans-1,2-Dichloroethene [R-1130(E)] mixtures

Saturation pressures of pure R-1336mzz(Z) and R-1130(E) and bubble point pressures of three R-1336mzz(Z)/1130(E) blends were measured from 265 K to 360 K. For each pure refrigerant or refrigerant blend, a total of twenty unique saturation pressures or bubble points were measured. In total 100 unique state points were obtained. Presently, no Helmholtz-energy-explicit type equation of state (EoS) is available for R-1130(E). While an extended corresponding states EoS for R-1130(E) is available to estimate the properties of the R-1336mzz(Z)/1130(E) blend, this model does not resolve the azeotropic behavior of the mixture. Therefore, the perturbed-chain statistical-associating fluid theory (PC-SAFT) EoS is used to model the vapor–liquid equilibria of the R-1336mzz(Z)/1130(E) blend. PC-SAFT model parameters are reported, and the overall performance of the model is characterized by deviations from the experimental data.

PC-SAFT model and experimental explicating interaction of binary and ternary systems of 2-ethoxyethanol, methylcyclohexane and N-methylcyclohexylamine

In this project upon measurements of density ρ, speed of sound u, and refractive index nD, the excess molar volumes VmE, deviations in isentropic compressibility ΔKs, and in refractive index ΔnD, were calculated for the whole range of composition and temperatures of T = (298.15–308.15–318.15)K for binary and ternary systems of 2-ethoxyethanol, methylcyclohexane, and N-methylcyclohexylamine. Results correlated with the Redlich-Kister and Cibulka equations. The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state was used to predict density and there was a good agreement between calculated and experimental density. Intermolecular interactions between like and unlike molecules were discussed for the systems. It seems that study provides useful insights into the properties and behavior of these mixtures, which could have potential applications in various fields such as chemistry and materials science.

Density Measurements and PC-SAFT Modeling for Beef Tallow Fatty Acid Methyl Esters (FAME Mixture) + Alkane up to 70 MPa

Biodiesel is mainly constituted by fatty acid alkyl esters, and the effect of adding alkane compounds is of great importance in order to analyze the changes in the thermophysical properties under high pressure that is of relevance in diesel engines. This work is aimed at the study of density behavior of two systems formed by beef tallow fatty acid methyl esters (FAME mixture) + alkane (decane or dodecane) in the temperature range of 303–393 K and in the pressure range of 0.2–68.29 MPa. Experiments were carried out by means of two vibrating tube densimeters with an expanded uncertainty in density of 0.7 kg·m–3. Transesterification of waste beef tallow by using methanol at supercritical conditions was used to obtain biodiesel. The FAME mixture was constituted by methyl tetradecanoate, methyl hexadecanoate, methyl octadecenoate, and methyl (Z)-octadec-9-enoate. Density behavior was correlated using the Tammann–Tait equation and modeled with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Density correlation deviations using the Tammann–Tait equation were found to be less than 0.05% and 4.15 kg·m–3 for the average absolute deviation (AAD) and standard deviation (STD), respectively. The PC-SAFT modeling yielded an AAD = 0.11% and an STD = 1.15 kg·m–3. The behavior for density and the derived thermodynamic properties were explained in terms of the fatty acid methyl ester content.

P-T-x Measurement and Modeling of Methane + Propane + Methanol or 2,2′-[Ethane-1,2-diylbis(oxy)] Di(ethan-1-ol) and Methane + Propane + Methanol + 2,2′-[Ethane-1,2-diylbis(oxy)] Di(ethan-1-ol) Systems

Limited phase equilibria data exist for multicomponent systems encountered in the natural gas processing industry. To address this gap, bubble point measurements were performed for methane + propane + methanol; methane + propane + (2,2′-[ethane-1,2-diylbis(oxy)] di(ethan-1-ol) or triethylene glycol); methane + propane + methanol + triethylene glycol systems in the temperature range of 283.16 to 323.16 K and a pressure range of 0.78 to 13.79 MPa. A visual synthetic high-pressure cell comprising a sapphire tube of 33 cm3 working volume was used. The new experimental P-T-x data were modeled using the Cubic Plus Association (CPA) model and the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) model. Model correlations with the CPA model yielded better results than those with the PC-SAFT model, with a maximum absolute average relative deviation in pressure of 6.97% and 7.33%, respectively. The CPA model predictions based on binary parameters alone do not adequately describe phase behavior of multicomponent systems.

Vapor-liquid equilibrium for the {R-OH + R-palmitate} systems at 50.3 and 101.3 kPa

Fossil sources of energy become focus of many debates due to the pollution caused by them. In this scenario, renewable fuels, as biodiesel, are studied to improve their production efficiency and become more competitive with fossil fuels and even substitute them. Biodiesel, produced by the transesterification reaction, is constituted by a mixture of fatty acid esters and needs to be separated from its reactional solution in order to be commercialized. To improve the separation processes, the thermodynamic behavior of the mixtures involving components of the biodiesel needs to be known. Aiming this, the vapor–liquid equilibrium (VLE) of the methanol + methyl palmitate and ethanol + ethyl palmitate systems was analyzed at 50.3 and 101.3 kPa and the experimental data were submitted to a thermodynamic consistency test and thermodynamic modeling with the Peng-Robinson (PR), Group Contribution Volume Translated Peng-Robinson (GC-VT-PR) and the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) equations of state. Experimental data were considered thermodynamically consistent, and the modeling showed good results in terms of the lowest relative deviations of temperature and vapor mole fraction obtained with the GC-VT-PR and PC-SAFT models.

Estimating the solubility of salsalate in supercritical CO2 via PC-SAFT modeling using its experimental solubility data in organic solvents

In this work, a methodology was studied for estimating the solubility of salsalate, an active pharmaceutical ingredient of non-steroidal anti-inflammatory drugs, in supercritical CO2 (scCO2) using the experimental data of its solubility in organic solvents and perturbed-chain statistical associating fluid theory (PC-SAFT)-based modeling. This type of modeling is more predictive than conventional semi-empirical correlation models and cubic-type equations of state. The PC-SAFT pure-component parameters of salsalate were determined by fitting its solubility data in organic solvents, which were newly measured in this work. The PC-SAFT parameters obtained thus were then applied to estimate the solubility of salsalate in scCO2. This approach can adequately reproduce the experimental values of the isothermal and isobaric solubilities of salsalate in scCO2 over a wide range of temperatures and pressures even when the binary interaction parameter (kij) is set to zero.

Water Sorption in Glassy Polyvinylpyrrolidone-Based Polymers.

Polyvinylpyrrolidone (PVP)-based polymers are excellent stabilizers for food supplements and pharmaceutical ingredients. However, they are highly hygroscopic. This study measured and modeled the water-sorption isotherms and water-sorption kinetics in thin PVP and PVP-co-vinyl acetate (PVPVA) films. The water sorption was measured at 25 °C from 0 to 0.9 RH, which comprised glassy and rubbery states of the polymer-water system. The sorption behavior of glassy polymers differs from that in the rubbery state. The perturbed-chain statistical associating fluid theory (PC-SAFT) accurately describes the water-sorption isotherms for rubbery polymers, whereas it was combined with the non-equilibrium thermodynamics of glassy polymers (NET-GP) approach to describe the water-sorption in the glassy polymers. Combined NET-GP and PC-SAFT modeling showed excellent agreement with the experimental data. Furthermore, the transitions between the PC-SAFT modeling with and without NET-GP were in reasonable agreement with the glass transition of the polymer-water systems. Furthermore, we obtained Fickian water diffusion coefficients in PVP and in PVPVA from the measured water-sorption kinetics over a broad range of humidities. Maxwell-Stefan and Fickian water diffusion coefficients yielded a non-monotonous water concentration dependency that could be described using the free-volume theory combined with PC-SAFT and NET-GP for calculating the free volume.

Bubble Point Measurements of Three Binary Mixtures of Refrigerants: R-32/1234yf, R-32/1234ze(E) and R-1132a/1234yf.

Bubble point pressures of three binary mixtures at two compositions each have been measured utilizing a static method. The mixtures studied were: difluoromethane + 2,3,3,3 tetrafluoroprop-1-ene (R-32/1234yf), difluoromethane + (E)-1,3,3,3-tetrafluoroprop-1-ene (R-32/1234ze(E)) and 1,1-difluororethene + 2,3,3,3 tetrafluoroprop-1-ene (R-1132a/1234yf). For all the mixtures the minimum temperature measured was 270 K. The maximum temperatures measured for the R-32/1234ze(E), R-32/1234yf and R-1132a/1234yf mixtures were 360 K, 345 K and 325 K respectively. A total of 100 bubble point pressures are reported and compared to available literature data relative to the REFPROP database1. Additionally, the bubble point pressures obtained in this study are modeled using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. The PC-SAFT model parameters are reported as well as deviations of this work and literature data from the model.

Modeling solubility of CO2\u2013N2 gas mixtures in aqueous electrolyte systems using artificial intelligence techniques and equations of state

Determining the solubility of non-hydrocarbon gases such as carbon dioxide (CO2) and nitrogen (N2) in water and brine is one of the most controversial challenges in the oil and chemical industries. Although many researches have been conducted on solubility of gases in brine and water, very few researches investigated the solubility of power plant flue gases (CO2–N2 mixtures) in aqueous solutions. In this study, using six intelligent models, including Random Forest, Decision Tree (DT), Gradient Boosting-Decision Tree (GB-DT), Adaptive Boosting-Decision Tree (AdaBoost-DT), Adaptive Boosting-Support Vector Regression (AdaBoost-SVR), and Gradient Boosting-Support Vector Regression (GB-SVR), the solubility of CO2–N2 mixtures in water and brine solutions was predicted, and the results were compared with four equations of state (EOSs), including Peng–Robinson (PR), Soave–Redlich–Kwong (SRK), Valderrama–Patel–Teja (VPT), and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). The results indicate that the Random Forest model with an average absolute percent relative error (AAPRE) value of 2.8% has the best predictions. The GB-SVR and DT models also have good precision with AAPRE values of 6.43% and 7.41%, respectively. For solubility of CO2 present in gaseous mixtures in aqueous systems, the PC-SAFT model, and for solubility of N2, the VPT EOS had the best results among the EOSs. Also, the sensitivity analysis of input parameters showed that increasing the mole percent of CO2 in gaseous phase, temperature, pressure, and decreasing the ionic strength increase the solubility of CO2–N2 mixture in water and brine solutions. Another significant issue is that increasing the salinity of brine also has a subtractive effect on the solubility of CO2–N2 mixture. Finally, the Leverage method proved that the actual data are of excellent quality and the Random Forest approach is quite reliable for determining the solubility of the CO2–N2 gas mixtures in aqueous systems.

Development of a Computational Fluid Dynamics Compositional Wellbore Simulator for Modeling of Asphaltene Deposition

The asphaltene problem is a two-step process: (1) asphaltene precipitation, as predicted by the thermodynamic model, and (2) asphaltene deposition, the amount of which is estimated by the kinetic model. Asphaltene precipitation is a prerequisite but not a sufficient condition for deposition. Deposition is dependent on other factors such as surface properties, phase behavior, rheology, and flow patterns. As a result, in addition to understanding thermodynamic and kinetic models, it is critical to also understand flow models. In fact, multiphase flow modeling is at the core of simulation, and it must be coupled with thermodynamic and kinetic models. Numerous studies on modeling asphaltene deposition on pipe walls have been performed theoretically and experimentally, but a comprehensive theory to properly understand this phenomenon has not yet been presented. In thermodynamic modeling, the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state is used to predict the asphaltene phase behavior. In this study, we show that the proposed PC-SAFT model is more accurate than the solid model used in commercial software. Unlike prior research that neglected flow patterns or used empirical relations to model multiphase flow, this study simulates multiphase flow using separate momentum equations for each phase. Among the existing kinetic models, the Kurup model has been used to predict the asphaltene deposition profile in the wellbore due to its greater compatibility for computational fluid dynamics application. The results of the proposed model show good agreement with field case data of asphaltene deposition thicknesses along the wellbore tubing.

Effects of 2-Butanol Addition on Waste Cooking Oil Biodiesel Density: An Updated Experimental Measurement and Thermodynamic Modeling Study

Biodiesels will become the most popular alternative energy resource to fossil diesels; they can be used alone or blended with an oxygenated additive in any proportion. The properties of biodiesels strongly depend on the type of the fatty acid methyl esters (FAME) that compose them. The main objective of the present work is to investigate the influence of 2-butanol addition on the waste cooking oil biodiesel (WCOB), for this fact, the new experimental density data (952 points) of WCOB + 2-butanol binary mixtures over a wide range of composition [seven compositions; 0 ≤ (WCOB) mole fraction x ≤ 1] between 0.1 and 140 MPa and 298.15 and 393.15 K are presented. The experimental data were correlated using Tait and perturbed chain-statistical associating fluid theory (PC-SAFT) equations of state (EoS), to our knowledge, this is the first time that density measurements for the WCOB + 2-butanol mixture are correlated using the famous PC-SAFT EoS. The Tait equation predicts successfully the density with a global absolute average deviation (AAD) of 0.089%, while the PC-SAFT model correlates well the density with a very small global AAD of 0.223% in each composition. Furthermore, contrary to the Tait equation, the PC-SAFT model can explain some interactions between fluid molecules. From the experimental data, the excess volumes VE have been calculated and fitted using the Redlich-Kister equation with a very small global standard deviation of 7.49 × 10-5 cm3 mol-1, and VE show a positive and symmetric parabolic shape in all composition ranges. Finally, the isobaric thermal expansivity, αp, and the isothermal compressibility, κT, have been derived from the Tait equation and their observed trend was as expected.

PC-SAFT Modeling of Phase Equilibria Relevant for Lipid-Based Drug Delivery Systems

In this work we investigated the solubilities of 10 active pharmaceutical ingredients (APIs), namely, fenofibrate, ibuprofen, cinnarizine, carbamazepine, indomethacin, naproxen, griseofulvin, glibenclamide, felodipine, and praziquantel in the pharmaceutically relevant excipients tricaprylin, Lauroglycol FCC, Capryol 90, Kolliphor TPGS, ethanol, and monolaurin. API solubilities were either determined gravimetrically, with high-performance liquid chromatography, or with differential scanning calorimetry. Mutual solubilities in the three possible mixtures out of Kolliphor TPGS, tricaprylin, and carbitol as well as the vapor sorption of ethanol in tricaprylin were determined experimentally. The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) pure-component parameters for seven APIs were determined via fitting to vapor pressures and liquid densities or to solubilities in organic solvents. In total, 80 binary interaction parameters were fitted to the investigated binary mixtures. They can be used in the future to improve the accuracy of lipid-based drug delivery systems in-silico screenings with PC-SAFT.

Measurement and PC-SAFT Modeling of the Solubility of Gallic Acid in Aqueous Mixtures of Deep Eutectic Solvents

Deep eutectic solvents have appeared as potential solvents for improving the extraction of polyphenols from vegetable or fruit matrixes. Since gallic acid is abundant in these sources, it is considered as a typical standard for quantifying their total polyphenol content after extraction with solvents. However, there are no extensive studies on the solubility behavior of gallic acid in different solvents or deep eutectic solvents. Thus, in this work, the solubility of gallic acid is measured in pure water; aqueous solutions of different hydrogen bond donors such as ethylene glycol, levulinic acid, and glycerol; and aqueous mixtures of deep eutectic solvents using choline chloride as the hydrogen bond acceptor and ethylene glycol, levulinic acid, and glycerol as the hydrogen bond donors. All of the measurements were performed at 293.15, 303.15, and 313.15 K and at 101.3 kPa and were validated by comparing the solubility of gallic acid in water from the literature. Results suggest that a 50 wt % aqueous solution of deep eutectic solvent based on ethylene glycol or glycerol improves the gallic acid solubility compared with a 50 wt % aqueous solution of its corresponding hydrogen bond donor. The deep eutectic solvent containing levulinic acid acts as the best aqueous mixture for gallic acid dissolution. Nondissolved gallic acid was measured after equilibrium using powder X-ray diffraction, showing that its structure does not change upon mixing with all of the liquid mixtures. All of the solid–liquid equilibrium results were accurately modeled with perturbed-chain statistical associating fluid theory (PC-SAFT).

Modeling and validation of carbon dioxide absorption in aqueous solution of piperazine + methyldiethanolamine by PC-SAFT and E-NRTL models in a packed bed pilot plant: Study of kinetics and thermodynamics

A pilot plant with a closed cycle of the absorption/desorption process has been taken into account for the simulation of carbon dioxide (CO2) capture by piperazine (PZ) + methyldiethanolamine (MDEA) solution using Aspen Plus rate-based model with all design and operational parameters such as the hydraulic specifications of absorber and stripper as well as inlet flue gas conditions which are present in a commercial gas-fired burner for heating houses. Metal FLEXIPAC 250Y has been considered as the packing type to apply the model to the proposed correlations on Aspen Plus for calculation of flooding and pressure drop. In order to simulate the process, a new property package has been developed by electrolyte non-random two-liquid (E-NRTL) model and perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state which are used for the calculation of activity and fugacity coefficients respectively. The model has been compared with some experimental data e.g. CO2 absorption efficiency and CO2 loading and demonstrated good agreement with them.

Evaluation of different thermodynamic models in predicting asphaltene precipitation: A comparative study

One of the major issues in the oil industry is asphaltene precipitation. Modeling asphaltene precipitation is still considered as a complex problem due to various characteristics of different heavy components existing in the crude oil. Thermodynamic models have been found as accurate models for studying asphaltene precipitation in the past few years and a great deal of effort has been devoted to model this process by using different empirical models and equations of state. In this study, the obtained results of asphaltene precipitation from different models based on perturbed-chain statistical associating fluid theory (PC-SAFT), cubic-plus-association (CPA), solid model, Flory-Huggins (FH), and the modified Flory-Huggins (MFH) are compared and their accuracy and reliability are analyzed in detail. For this purpose, twelve crude oil types with different characteristics and asphaltene precipitation behavior are used. Additionally, the performance of the introduced models in predicting asphaltene precipitation during gas injection into the studied oil is investigated. Results demonstrated that PC-SAFT and CPA models have the highest accuracy for both precipitation estimation and behavior trend prediction. Afterward, sensitivity analysis is performed by using Monte-Carlo algorithm for better understanding of the effect of different adjusting parameters, which were used during the tuning process, on each model outputs. Results indicated that cross-association energy between asphaltene and heavy component (HC), self-association energy of asphaltene, and binary interaction coefficient between asphaltene and CO2 are the most sensitive tuning variables for PC-SAFT, CPA, and solid models, respectively. Finally, the CPU times of various models for simulating this process were compared. This comparison showed that the PC-SAFT model has more computational time due to the involved iterative processes for phase equilibrium calculations.

Density and Viscosity for Binary Mixtures of the Ionic Liquid 1-Butyl-3-methylimidazolium Tetrafluoroborate with 2-Propanol, N,N-Dimethylacetamide and N,N-Dimethylformamide at 293.15–323.15 K: Experimental and PC-SAFT Modeling

For three binary mixtures composed of ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate ([Bmim][BF4]) with 2-propanol, N,N‑dimethylacetamide (DMA) and N,N‑dimethylformamide (DMF), the values of the experimental density and viscosity over the whole composition range for T = (293.15 to 323.15 K) are reported. Excess molar volume $$\mathop V\nolimits_{{\text{m}}}^{{\text{E}}}$$, partial molar volume $$\overline{{V_{i} }}$$, and the deviation in viscosity $$\Delta \eta$$ are calculated and explained in order to clarify the intermolecular interactions among the species in the mixtures. For all of the binary mixtures, the negative values of $$\mathop V\nolimits_{{\text{m}}}^{{\text{E}}}$$ and $$\Delta \eta$$ were fitted with the Redlich–Kister polynomial function. An increase in temperature decreases the values of $$\mathop V\nolimits_{{\text{m}}}^{{\text{E}}}$$ and increases the values of $$\Delta \eta$$. The results have been discussed regarding binary interaction forces and the formation of a complex between dissimilar molecules. For the correlation and prediction of the binary system densities, perturbed chain statistical associating fluid theory (PC-SAFT) was used. The results obtained from this theory are consistent with the experimental data.

Density variations of TMAO solutions in the kilobar range: Experiments, PC-SAFT predictions, and molecular dynamics simulations

We present measurements, molecular dynamics (MD) simulations, and predictions using Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) of the density of aqueous solutions in a pressure range from 1 bar to 5000 bar, a pressure regime that is highly relevant for both biochemical applications and the fundamental understanding of solvation. The accurate determination of density data of pressurized solutions remains challenging. We determined relative density changes from the variations in X-ray absorption through the sample and developed a new water parameter set for PC-SAFT modeling that is appropriate for high pressure conditions in the kilobar regime. As a showcase, we studied trimethylamine N-oxide (TMAO) solutions and demonstrated that their compressibility decreases with the TMAO content. This result is linked to the stabilizing effect of TMAO on the local H-bond network of water. Experiments and calculations, which represent two independent methods, are in very good agreement and are in accordance with results of force field molecular dynamics simulations of the same systems.

A comparative study of CPA and PC-SAFT equations of state to calculate the asphaltene onset pressure and phase envelope

The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) and the Cubic-Plus-Association (CPA) EoS have been widely applied to describe the asphaltene precipitation onset in crude oils because the association term of these models can appropriately account for the polar-polar interactions between asphaltene and resin molecules. In this study we have compared the PC-SAFT and CPA EoS capabilities in the calculation of the Asphaltene Precipitation Envelope (APE) of eight oils from the literature and discuss the physical meaning of the cross-association energy parameter between asphaltene and resin. For all oils the PC-SAFT EoS predicts an increase in the stability of the oil at higher temperatures with the consequent closure of the APE while the CPA model predicts a decrease in the stability at higher temperatures. For both models the fitted values of the cross-association energy parameter between asphaltene and resin show a dependency on temperature, but for PC-SAFT model this parameter has a clearer physical meaning. Results indicate that the PC-SAFT EoS is more accurate for APE calculations outside the experimental temperature range.

Density and Volumetric Properties of Binary Mixtures of CO2 + Hexadecane from (303.2 to 473.2) K and Pressures up to 50.0 MPa

Densities of CO2 + hexadecane binary mixtures were measured by the capillary high-pressure optical cell method at temperatures from 303.2 to 473.2 K and pressures up to 50.0 MPa with CO2 molar fractions x1 = 0, 0.2555, 0.3703, 0.7348, and 0.8645. The density and excess molar volume of CO2 + hexadecane mixtures are the positive correlation function of pressure and the negative correlation function of temperature. The dissolution of CO2 increases the density of mixtures at low temperatures and decreases the density of mixtures at high temperatures. The crossover temperature increases with increasing pressure. The perturbed-chain statistical associating fluid theory (PC-SAFT) parameters of pure substances were fitted, and the densities of CO2 + hexadecane mixtures can be calculated accurately with the PC-SAFT model.

Thermodynamic properties of hydrophobic deep eutectic solvents and solubility of water and HMF in them: Measurements and PC-SAFT modeling

Recently, hydrophobic deep eutectic solvents (DESs) were proposed as interesting solvents for biorefinery processes, such as the production of 5-hydroxymethylfurfural (HMF) from glucose in an aqueous environment. Physicochemical property data of hydrophobic DES + water/HMF systems are of utmost importance for process design. In this work, density and vapor pressure of eight different hydrophobic DESs, as well as water solubility and HMF solubility in these DESs were experimentally determined. The solubility was modeled using the pseudo-pure component approach within the framework of Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). New pure-component parameters for the eight hydrophobic DESs were obtained by fitting to measured density and vapor-pressure data, instead of to density data only. Based on these new pure-component parameters for the DESs, the solubilities of water and of HMF in the hydrophobic DESs were modeled in good agreement with the experimental data at 298 K and atmospheric pressure.