Soave-Redlich-Kwong Equation Of State Research Articles

An extended corresponding states equation of state (EoS) for CCS industry

For a good design of all the processes in Carbon Capture and Storage, the thermodynamics of the CO2 and CO2 mixtures should be accurately predicted. Among these mixtures are CO2–water systems that are very difficult to deal with due to the polar nature. In this work we suggest a new extended corresponding states equation of state (EoS) that can handle polar mixtures. The new EoS uses the Bender Modified Benedict–Webb–Rubin EoS as a reference equation. NH3, R23 and R503 are used as reference fluids with parameters from Polt. The EoS presented uses the Soave–Redlich–Kwong EoS with Huron Vidal mixing rules based approach to compute the scale factors. The evaluation of the new EoS is done over a large set of experimental data. The results show very high accuracy in predicting both phase equilibrium and densities.

Solubility of carbon dioxide in three [Tf2N] ionic liquids

The solubility of carbon dioxide in three bis(trifluoromethylsulfonyl)imide-based ionic liquids: N-methyl-n-pentylpyrrolidinium bis(trifluoromethylsulfonyl)imide ([p(5)mpyrr][Tf2N]), 1-butyl-2,3-dimethylimidazolium bis(trifluoromethyl sulfonyl)imide ([bmmim][Tf2N]), and tributylmethylphosphonium bis(trifluoromethyl sulfonyl)imide ([P4441][Tf2N]) was measured at 298.15, 313.15, and 343.15K and pressures up to about 1.9MPa. The data were well correlated with the Soave–Redlich–Kwong equation of state (SRK-EoS). Henry's law constants for CO2 in the three ILs ([p(5)mpyrr][Tf2N], [bmmim][Tf2N], and [P4441][Tf2N]) at 298.15K were 3.1, 3.5, and 3.3MPa, respectively.

Effect of cation on the solubility of carbon dioxide in three bis(fluorosulfonyl)imide low viscosity ([FSI]) ionic liquids

The solubility of carbon dioxide in three bis(fluorosulfonyl)imide-based ionic liquids: N-propyl-n-methyl-piperidinium bis(fluorosulfonyl)imide ([p(3)mpip][FSI]), N-propyl-n-methyl-pyrrolidinium bis(fluorosulfonyl)imide ([p(3)mpyrr][FSI]) and N-propyl-n-methyl-n,n-dimethyl-ammonium bis(fluorosulfonyl)imide ([N4441][FSI]) was measured at (298.15, 313.15, and 343.15)K and pressure up to about 2MPa. The Henry's law constants for CO2 in the three ILs, ([p(3)mpip][FSI], [p(3)mpyrr][FSI] and [N4441][FSI]) at 298K are (4.1, 4.0, and 3.8)MPa respectively, indicating the negligible effect of change of cation precursors on CO2 solubility. Solubility of CO2 in the present ILs with [FSI] anion is comparable with those in the ILs containing a more fluorinated common anion, [Tf2N]. The solubility data were correlated well with the Soave–Redlich–Kwong equation of state (SRK-EoS).

Large-eddy simulation of supercritical fluid injection

Mixing is a key point for thrust and efficiency of combustion systems. It becomes crucial in the case Liquid Rocket Engines as large investments are involved. Besides, the pressure in liquid rocket combustion chamber often exceeding the critical point of loaded propellants, mixing becomes an important scientific issue as fluid properties differ from classical ideal gas assumption. In this study, two configurations are studied to evaluate the impact of subgrid models on mixing. Firstly, Mayer's experiments of trans- and super-critical nitrogen jet injection into a warm nitrogen atmosphere have been numerically investigated with a structured numerical code called SiTCom-B. SiTCom-B solves Direct Numerical Simulations and Large Eddy Simulations equations for perfect or real gas equation of states. In this study, Soave–Redlich–Kwong (SRK) and Peng–Robinson equation of state are used with appropriated thermodynamics relations and validated against NIST data. Three-dimensional LES are conducted for two cases (cases 3 and 4 in Mayer et al.'s reference [1]) with real-gas NSCBC treatment. Several sub-grid scale models are tested and the results are compared to experimental data for density on jet axis: a very good agreement is obtained on a light mesh (11.6 million of points) with the SRK equation of state and standard Smagorinsky model. Flow structures are evidenced with Schlieren snapshots. Secondly, the Mascotte test-bench from ONERA is simulated with SiTCom-B based on Soave–Redlich–Kwong equation of state and Smagorinsky models. The simulated non-reacting case is characterized by a very short liquid oxygen dense core because of the strong density and velocity gradients boosting mixing efficiency.

Solubility of carbon dioxide, methane, and ethane in 1-butanol and saturated liquid densities and viscosities

A designed pressure–volume–temperature (PVT) apparatus has been used to measure the (vapor+liquid) equilibrium properties of three binary mixtures (methane +, ethane +, and carbon dioxide + 1-butanol) at two temperatures (303 and 323)K and at the pressures up to 6MPa. The solubility of the compressed gases in 1-butanol and the saturated liquid densities and viscosities were measured. In addition, the density and viscosity of pure 1-butanol were measured at two temperatures (303 and 323)K and at the pressures up to 10MPa. The experimental results show that the solubility of the gases in 1-butanol increases with pressure and decreases with temperature. The dissolution of gases in 1-butanol causes a decline in the viscosity of liquid phase. The saturated liquid density follows a decreasing trend with the solubility of methane and ethane. However, the dissolution of carbon dioxide in 1-butanol leads to an increase in the density of liquid phase. The experimental data are well correlated with Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) equations of state (EOSs). SRK EOS was slightly superior for correlating the saturated liquid densities.

Phase behavior of mixture of supercritical CO2 + ionic liquid: Thermodynamic consistency test of experimental data

Various models have been applied composed of the Peng‐Robinson equation of state (PR‐EoS) and the Soave‐Redlich‐Kwong equation of state (SRK‐EoS) associated with three mixing rules including the following: Wong‐Sandler (WS), van der Waals one (vdW1), and van der Waals two (vdW2) for phase behavior modeling of mixtures of supercritical CO2 + different ionic liquids in vapor–liquid equilibrium (VLE) region. It has been found that the PR EoS implying the WS mixing rule can be used as a reliable thermodynamic model to perform a thermodynamic consistency test on the experimental data of phase behaviors of the supercritical CO2 + ionic liquid systems (19 commonly‐used ionic liquids have been studied). The results show that 40% of the experimental data seem to be thermodynamically consistent, 55.5% seem to be thermodynamically inconsistent, and 4.5% seem to be not fully consistent. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3892–3913, 2013

Assessment, measurement and correlation of (vapour + liquid) equilibrium of (carbon dioxide + butyl, isobutyl, and amyl formate) systems

In this work, three formates (butyl, isobutyl, and amyl formate) were considered as relative perfect CO2 absorption performance based on the excess Gibbs function as the thermodynamics criterion. An online static-analytical method was used to measure the (vapour + liquid) equilibrium (VLE) data for the CO2+butyl, isobutyl, and amyl formates under the pressure of (0.2 to 6)MPa and the temperatures at a range from (283.15 to 343.15)K. Then the VLE data were correlated by Peng–Robinson (PR) equation of state (EOS) with classic mixing rule, PR EOS with Wong–Sandler (WS) mixing rule and Soave–Redlich–Kwong (SRK) EOS with classic mixing rule. It is shown that SRK EOS is comparatively appropriate for CO2+butyl formate binary system. Both PR EOS with classic mixing rule and SRK EOS can be used to correlate the binary systems of CO2+isobutyl, amyl formate. It is found that the solubility order of three formates for CO2 from high to low is arranged as CO2+amyl formate>CO2+butyl formate>CO2+isobutyl formate, showing the system of CO2+amyl formate has the best absorption performance. By comparison, it indicates that formates have a greater solubility for CO2 than acetates on the condition of the same temperature and pressure. In addition, the thermophysical properties, mole absorption and mass absorptive amount of several industrial absorbents were assessed and the absorption performance of amyl formate for CO2 is better than other physical absorbents. Thus, the study concluded that amyl formate has potential research value as physical absorbent for CO2 capture.

Measurement and Correlation of α-Bisabolol Solubility in Near-Critical Carbon Dioxide

The solubility of (−)-α-bisabolol, ((−)-6-methyl-2-(4-methyl-3-cyclohexen-1-yl)-5-hepten-2-ol), a monocyclic sesquiterpene alcohol, in sub- and supercritical CO2 was measured at the temperatures (313.2, 323.2, and 333.2) K and pressures ranging from (7 to 12.5) MPa by a dynamic method. To the best of our knowledge, there are no previous measurements of α-bisabolol solubility in near critical CO2 reported in the literature. The solubility isotherms were in the crossover region; the maximum mole fraction of α-bisabolol in CO2, 9·10–3, was therefore at 313.2 K and 11.5 MPa, the maximum pressure applied at this temperature. The Soave–Redlich–Kwong equation of state (SRK-EoS) was employed to correlate the experimental data and an acceptable agreement was obtained. Furthermore, the thermophysical properties of the solute required by the modeling were estimated and reported.

Experimental studies on constant mass–volume depletion of gas-condensate systems

This paper presents a new empirical model to estimate dew point pressure Pd for gas condensate reservoirs as a function of routinely measured gas analysis and reservoir temperature. The proposed model was developed based on field and laboratory PVT analysis data of 202 gas-condensate fluid samples representing different gas reservoirs and a wide range of gas properties and reservoir temperatures. Statistical error analysis was used to determine the accuracy of the model. The evaluation shows that correlation coefficient, average relative error (ARE), and average absolute relative error (AARE) are 0.9896, −1.1% and 2.58%, respectively. In addition, results of the proposed model were compared with those published in the literature and ensured its success for capturing the physical trend of gas-condensate systems, and consequently is considered as the most reliable one for the petroleum industry. The accuracy of the model has been also compared to the Soave Redlich Kwong equation of state (SRK-EOS) and the Peng Robinson equation of state (PR-EOS). Gas condensate samples have been used to check the validity of the proposed model against EOS.

Measurements and predictions of density and carbon dioxide solubility in binary mixtures of ethanol and n-decane

The solubility of carbon dioxide (CO2) in binary mixtures of ethanol and n-decane has been measured using an in-house developed pressure-volume-temperature (PVT) apparatus at pressures up to 6MPa and two different temperatures (303.2 and 323.2K). Three different binary mixtures of ethanol and n-decane were prepared, and the densities of the prepared mixtures were measured over the studied pressure and temperature ranges. The experimental data of CO2 solubility in the prepared mixtures and their saturated liquid densities were then reported at each temperature and pressure. The solubility data indicated that the gas solubility reduced as the ethanol mole fraction in the liquid mixture increased. The dissolution of CO2 in the liquid mixtures resulted in the increase in the saturated liquid densities. The impact of gas dissolution on the saturated liquid densities was more pronounced at the lower temperature and lower ethanol compositions. The experimental solubility and density data were compared with the results of two cubic equations of state (EOSs), Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR). The modeling results demonstrated that both EOSs could predict the solubility data well, while the saturated liquid densities calculated with the PR EOS were much better than those predicted with the SRK EOS.

Experimental measurements and predictions of density, viscosity, and carbon dioxide solubility in methanol, ethanol, and 1-propanol

The solubilities of carbon dioxide in different alcohols, methanol, ethanol, and 1-propanol, were measured at two different temperatures (303.2 and 323.2)K and pressures up to 6MPa. The experimental data of saturated alcohol density and viscosity were also reported at each temperature and pressure. The solubility data shows that the solubility of carbon dioxide in alcohol increases with pressure and decreases with temperatures in the studied pressure and temperature ranges. The higher dissolution of carbon dioxide in alcohols resulted in increase in the saturated liquid densities and decrease in saturated liquid viscosities. The experimental solubility as well as saturated liquid density data were predicted with two cubic equations of state (EOS), Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK). The modeling results demonstrated that both equations of state correlated the solubility data well over the studied pressure and temperature ranges. However, the saturated liquid densities calculated with the SRK EOS were much better than those of PR EOS.

Solubility Measurements and Saturated Liquid Properties of Ternary Systems (Methane + Decane + Octadecane) at 295 K

Experimental vapor–liquid equilibrium (VLE) data have been measured for the ternary system (methane + decane + octadecane) at 295 K over the pressure range (1 to 8) MPa using a PVT apparatus that was designed in-house. Three different (decane + octadecane) binary mixtures were prepared, and the solubility and phase equilibria of these prepared mixtures with methane were studied. The experimental information of saturated liquid phase composition, density, and viscosity was reported at each pressure. The VLE data were correlated with the Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) equations of state (EOS's). The adjustment of binary interaction parameters and the volume translation technique has been employed to correlate the experimental compositions and densities. The adjusted binary parameters from the VLE data of binary pairs (methane + decane) and (methane + octadecane) were used to correlate the generated ternary VLE data. The calculated ternary VLE compositions were found to be in good agreement with the experimental data using the binary parameters from the VLE data of binary pairs for both EOS's. According to the results for the saturated liquid densities, more accurate predictions of the experimental data were obtained using the PR EOS than the SRK EOS.

Gas-Liquid Equilibrium Prediction of Ternary System (CO2-Ethanol-Water) at Moderate Pressures and Different Temperatures Using SRK-EOS

In this work, a thermodynamic model for the prediction of gas-liquid equilibrium at moderate pressures (up to 6 bar) and different temperatures (288-323 K) for the ternary system of carbon dioxide (1)-(2) mixture (ethanol-water) is established using Soave/Redlich/Kwong equation of state (SRK-EOS). Two different mixing rules were used to show the effect of the type of mixing rule. A comparison of experimental phase equilibrium data in the literature with the predicted results showed very good representation for one mixing rule and good for the other.

Modeling of solid–liquid equilibria for polyethylene and polypropylene solutions with equations of state

AbstractWe modeled solid–liquid equilibria (SLEs) in polyethylene and polypropylene solutions with a Soave–Redlich–Kwong (SRK) cubic equation of state (EOS) and a perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS. Two types of mixing rules were used with SRK EOS: The Wong–Sandler mixing rule and the linear combination of the Vidal and Michelsen mixing rules (LCVM), both of which incorporated the Bogdanic and Vidal activity coefficient model. The performance of these models was evaluated with atmospheric‐pressure and high‐pressure experimental SLE data obtained from literature. The basic SLE equation was solved for the equilibrium melting temperature instead of for the composition. The binary interaction parameters of SRK and PC‐SAFT EOS were estimated to best describe the experimental equilibrium behavior of 20 different polymer–solvent systems at atmospheric pressure and 31 other polymer–solvent systems at high pressure. A comparison with experimental data showed that SRK–LCVM agreed very well with the atmospheric SLE data and that PC‐SAFT EOS was more efficient in high‐pressure conditions. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

The vdW EoS hundred years later, yet younger than before. Application to the phase equilibria modeling of food-type systems for a green technology

The relevant applications that supercritical fluid extraction (SFE) has attained in the food industry in the last decades increased the interest in the development of thermodynamic models to represent the phase equilibria of systems comprising food-related substances and supercritical carbon dioxide (SCCO 2). The targets are twofold: (i) calculation of solid solubilities in SCCO 2 pure or with polar co-solvents (mainly ethanol in food applications), what directly affects the selectivity of one of the most applied processes, e.g. the semi-batch SFE of plant material, and (ii) calculation of vapor–liquid equilibrium compositions of liquid raw materials processed in countercurrent packed columns, what is straightforwardly related with the number of theoretical stages necessary to achieve the desired separation. Cubic equations of state derived from the equation proposed by van der Waals (vdW-type EoSs, e.g. Peng–Robinson and Soave–Redlich–Kwong EoS) are the most common thermodynamic models applied to achieve these objectives. In this work, the application of vdW-type EoSs to food-type substance + SCCO 2 is reviewed. More than 100 systems, comprising lipids, antioxidants, pigments, alkaloids, vitamins, etc. were investigated from 2003 up today. Even though phase equilibria modeling of SCCO 2 + food-related systems involves serious difficulties, the extensive and, in many cases, successful application of vdW-type EoSs demonstrates that though developed 100 years ago the van der Waals equation is lively and younger than before.

SRK equation of state: Predicting binary interaction parameters of hydrocarbons and related compounds

The parameter mixing rules of the Soave–Redlich–Kwong (SRK) equation of state are rewritten as Huron–Vidal mixing rules, where infinite-pressure activity coefficients are predicted by group contributions. Alkanes are treated as composed by one group type and aromatics by two types, aliphatic and aromatic. Hydrocarbon mixtures can be treated using one universal interaction parameter. Light compounds like methane, N 2, CO 2, H 2S, etc. are treated as separate groups; each one requires a pair of parameters for its interactions with aliphatic and aromatic groups. Group interaction parameters were determined from experimental VLE data. From them, binary interaction constants of the classical quadratic mixing rules can directly be derived.

Development of Compound Specific Cohesion Function Relationship for SRK Equation of State

Chemical industries have undergone a paradigm shift in the designing process in the last decade, and most of them now rely on process simulators for designing and optimisation. Simulators are heavily dependent on thermodynamic models for the proper outcome of any simulation problem, in general, and phase equilibrium problem, in particular. Equations of state (EOS) have gained wide popularity due to their simplicity. Cubic equations of state (CEOS) can very accurately predict various thermophysical properties with minimum requirement of data. One of the key factors for obtaining accurate results from CEOS is its temperature dependency of cohesion factor relationship. In the present study, a new compound specific cohesion factor relationship is proposed for the Soave Redlich Kwong (SRK) EOS. The new model was compared with the original SRK EOS and its modified versions for accuracy in estimating vapour pressure for a large number of compounds representing various classes of families. It was found that the new relationship works better for almost all the families considered, especially, improving the vapour pressure prediction in the range of reduced temperature below 0.7.

The Cubic-Two-State Equation of State: Cross-associating mixtures and Monte Carlo study of self-associating prototypes

A new equation of state for associating fluids has recently been presented by Medeiros and Tellez-Arredondo, the Cubic-Two-State Equation of State (CTS EoS) [Ind. Eng. Chem. Res. 47 (2008) 5723]. This equation arises from the coupling of the Soave–Redlich–Kwong EoS (SRK) with an association term from a two-state association model. The CTS EoS is polynomial in volume and it is able to describe vapor pressures and molar volume of associating fluids such as water, alcohol and phenol, among others. The equation is also able to describe the liquid–vapor equilibria of their mixtures with alkanes. In this paper, the physical and thermodynamic foundations of the CTS EoS are further investigated. In order to verify its applicability for cross-associating systems, the equation was employed in the prediction of phase equilibria behavior of binary alcohol–alcohol and water–alcohol mixtures. Very good agreement between predictions and experimental phase equilibria data was obtained with very simple combining rules and only one adjustable binary parameter. No additional parameters were necessary to describe ternary systems. With the purpose of checking the model's hypothesis and limitations, the two-state association term was coupled with the hard sphere Carnahan–Starling EoS, forming the CS-TS equation and the association characteristic parameters were determined theoretically for prototype association fluids. Monte Carlo NPT simulations of such fluids were performed and the results were compared with the equation's predictions. The CS-TS was able to describe qualitatively the p v T behavior of the prototype; nevertheless, it is not as accurate as those predictions obtained from the combination CS with Wertheim's association term. It seems that, when adjusting parameters of the CTS EoS to real substances, the discrepancies between the predicted and the real association contribution are dissipated among other adjustable parameters, specially on the dispersive term of the SRK equation. Finally, it is shown that CTS EoS isotherms can only have one or three real bigger roots than the co-volume for positive pressures, similar to cubic equations of state, and then it has the desirable form to describe vapor–liquid phase equilibria of associating compounds mixtures.

GAS-LIQUID EQUILIBRIUM PREDICTION OF CO2-ETHANOL SYSTEM AT MODERATE PRESSURES AND DIFFERENT TEMPERATURES

In this work, a thermodynamic model for the prediction of gas-liquid equilibrium at moderate pressures (up to 19 bar) and different temperatures (288-323 K) for the binary system of carbon dioxide (1)-ethanol (2) is established using Soave-Redlich-Kwong equation of state (SRK-EOS), Peng-Robenson equation of state (PR-EOS), and HYSYS program with same equations of state. Three different mixing rules were used to show the effect of the type of mixing rule.
 A comparison of experimental phase equilibrium data in the literature with the predicted results showed very good representation for some mixing rules and good for the others, also the comparison with the results obtained using simulation on HYSYS program exhibits good agreement up to 11 bar with a deviation of 4*10-4 - 2*10-4 %.

A novel equation of state (EOS) for prediction of solute solubility in supercritical carbon dioxide: Experimental determination and correlation

AbstractSolubility data of organophosphorous metal extractants in supercritical fluids (SCF) are crucial for designing metal extraction processes. We have developed a new equation of state (EOS) based on virial equation including an untypical parameter as BP/RT, reduced temperature and pressure for prediction of solute solubility in supercritical carbon dioxide (SC CO2). Solubility experimental data (solubility of tributylphosphate in SC CO2) were correlated with the two cubic equations of state (EOS) models, namely the Peng–Robinson EOS (PR‐EOS) and the Soave–Redlich–Kwong EOS (SRK‐EOS), together with two adjustable parameter van der Waals mixing and combining rules and our proposed EOS. The AARD of our EOS is significantly lower than that obtained from the other EOS models. The proposed EOS presented more accurate correlation for solubility data in SC CO2. It can be employed to speed up the process of SCF applications in industry.