Solubility of light hydrocarbons and their mixtures in pure water under high pressure

New solubility data of methane, ethane, n-butane and their mixtures in pure water are obtained at 344.25 K, from 2.5 to 100 MPa. The results agree well with those of the literature in the case of pure hydrocarbons in water, but differ significantly for hydrocarbon mixtures. In contrast to the conclusion reached by Amirijafari and Campbell [B. Amirijafari, J. Campbell, Solubility of gaseous hydrocarbon mixtures in water, Soc. Pet. Eng. J. (1972) 21–27.], the experimental solubility data of methane–ethane mixtures shows an ideal solution behavior, while the solubility data of methane–n-butane mixtures shows a weaker non-ideality than that observed by McKetta and Katz [J.J. McKetta, D.L. Katz, Methane–n-butane–water system in two-and three-phase regions, Ind. Eng. Chem. 40 (1948) 853–863]. The pure hydrocarbon solubility data are satisfactorily correlated using the Soreide and Whitson modification [I. Soreide, C.H. Whitson, Peng–Robinson predictions for hydrocarbons, CO2, N2, and H2S with pure water and NaCl brine, Fluid Phase Equilib. 77 (1992) 217–240] of the Peng–Robinson equation of state.     

Prediction of vapor–liquid and liquid–liquid equilibria for polymer systems: Comparison of activity coefficient models

A large number of equations of state and activity coefficient models capable of describing phase equilibria in polymer solutions are available today, but only a few of these models have been applied to different systems. It is therefore useful to investigate the performance of existing thermodynamic models for complex polymer solutions which have not yet been widely studied. The present work studies the application of several activity coefficient models [P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, New York, NY, 1953; T. Oishi, J.M. Prausnitz, Estimation of solvent activities in polymer solutions using a group-contribution method, Ind. Eng. Chem. Process Design Dev. 17 (1978) 333; H.S. Elbro, A. Fredenslund, P. Rasmussen, A new simple equation for the prediction of solvent activities in polymer solutions, Macromolecules 23 (1990) 4707; G.M. Kontogeorgis, A. Fredenslund, D. Tassios, Simple activity coefficient model for the prediction of solvent activities in polymer solutions, Ind. Eng. Chem. Res. 32 (1993) 362; C. Chen, A segment-based local composition model for the Gibbs energy of polymer solutions, Fluid Phase Equilib. 83 (1993) 301; A. Vetere, Rules for predicting vapor–liquid equilibria of amorphous polymer solutions using a modified Flory–Huggins equation, Fluid Phase Equilib. 97 (1994) 43; C. Qian, S.J. Mumby, B.E. Eichinger, Phase diagrams of binary polymer solutions and blends, Macromolecules 24 (1991) 1655; Y.C. Bae, J.J. Shim, D.S. Soane, J.M. Prausnitz, Representation of vapor–liquid and liquid–liquid equilibria for binary systems containing polymers: applicability of an extended Flory–Huggins equation, J. Appl. Polym. Sci. 47 (1993) 1193; G. Bogdanic, J. Vidal, A segmental interaction model for liquid–liquid equilibrium calculations for polymer solutions, Fluid Phase Equilibria 173 (2000) 241] and activity coefficient from equations of state [F. Chen, A. Fredenslund, P. Rasmussen, Group-contribution Flory equation of state for vapor–liquid equilibria en mixtures with polymers, Ind. Eng. Chem. Res. 29 (1990) 875; M.S. High, R.P. Danner, Application of the group contribution lattice—fluids EOS to polymer solutions, AIChE J. 36 (1990) 1625]. The evaluation of these models was carried out both at infinite dilution and at finite concentrations and the results compared to experimental data. Furthermore, liquid–liquid equilibrium predictions for binary polymer solutions using six activity coefficient models are compared in this work. The parameters were estimated for all the models to achieve the best possible representation of the reported experimental equilibrium behavior.     

Binary interaction parameter kij for calculating the second cross-virial coefficients of mixtures

The binary interaction parameters, k_ij, of 119 mixtures were determined by fitting the second cross-virial coefficients of mixtures with correlations for pure compounds [L. Meng, Y.Y. Duan, L. Li, Fluid Phase Equilib. 226 (2004) 109–120; L. Meng, Y.Y. Duan, Fluid Phase Equilib., 258 (2007) 29–33] and classical mixing rules. The mixtures included nonpolar/polar (associated), polar/polar, quantum/nonpolar (quantum) binaries. Very simple correlations for k_ij of H₂O/n-alkane, CO/nonpolar and quantum/nonpolar (quantum) binaries were successfully developed. The results show that the present correlations can accurately predict the second cross-virial coefficients.     

Application of group contribution SAFT equation of state (GC-SAFT) to model phase behaviour of light and heavy esters

The group contribution SAFT approach developed for pure compounds in an earlier work [S. Tamouza, J.-P. Passarello, J.-C. de Hemptinne, P. Tobaly, Fluid Phase Eq. 222–223 (2004) 67] is here extended for the treatment of ester series. Parameters for groups CH₂ and CH₃ previously determined were reused for the alkyl chains while new parameters were determined for COO and HCOO groups. The polarity of these molecules was taken into account by the addition to the equation of state (EOS) of a dipole–dipole interaction term due to Gubbins and Twu [K.E. Gubbins, C.H. Twu, Chem. Eng. Sci. 33 (1978) 863]. This term requires an additional parameter, the dipole moment which was correlated to the COO chemical group position in the ester chain.Three different versions of SAFT were used here to test the validity of the method: the original SAFT [W.G. Chapman, G. Jackson, K.E. Gubbins, M. Radosz, Ind. Eng. Chem. Res. 29 (1990) 1709], VR-SAFT [A. Gil-Villegas, A. Galindo, P.J. Whitehead, S.J. Mills, G. Jackson, A.N. Burgess, J. Chem. Phys. 106 (1997) 4168] and PC-SAFT [J. Gross, G. Sadowski, Fluid Phase Eq. 168 (2000) 183; J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40 (2001) 1244]. In all three cases, similar and encouraging results are obtained. Reasonable predictions are found on heavy esters that were not included in the regression database.     

Improvements to a new equation of state for pure components

In a recent work [Fluid Phase Equilib. 194–197 (2002) 401], Kedge and Trebble presented a non-cubic equation of state (EOS) including a near-critical correction term. The evaluation of that equation was limited initially to matching fluid properties of methane. In this work, we investigate the impact of incorporating a Carnahan–Starling (CS) repulsive term [J. Chem. Phys. 51 (2) (1969) 635] into the non-cubic equation. The CS term improves the fit of the critical isotherm and it is shown to improve the fit of the entire PVT space. Anomalies in the fit of temperature dependence in the EOS parameters in the near-critical region are also reduced. We also demonstrate in this work how the new correction term serves to flatten the top of the vapor–liquid coexistence curve. The new term is compared to the exponential term in Soave’s modification of the BWR equation (SBWR) [Ind. Eng. Chem. Res. 34 (1995) 3981] which achieves a similar effect in a slightly different way.     

Extended corresponding states model for fluids and fluid mixtures: II. Application to mixtures and natural gas systems

We report an extended corresponding states model optimised for accurate prediction of the thermodynamic properties and vapour–liquid equilibria of natural gases and similar mixtures. The corresponding states model uses methane as the reference fluid and employs shape factors for pure components that were reported recently [Fluid Phase Equilib. 204 (2002) 15]. The van der Waals one-fluid model is used for mixtures and, in this paper, we report two alternative temperature- and density-dependent correlations of the binary interaction parameters. Model ECSmixS1 was optimised for 19 binary systems in the wide domain 90≤T (K)≤670 with p (MPa)≤510 and is suitable for the prediction of both liquid- and gas-phase thermodynamic properties and for the solution of vapour–liquid equilibrium problems. Model ECSmixS2 was specialised for increased accuracy in the natural gas ‘custody transfer’ interval 270≤T (K)≤330 with p (MPa)≤12 and is intended for gas-phase thermodynamic properties only. For mixtures of the major components of natural gas, we obtain with Model ECSmixS1 an overall average absolute deviation (AAD) of 0.12% in calculated densities, an AAD of 0.16% in calculated speeds of sound and an AAD of 1.8% in bubble pressure. With Model ECSmixS2, we obtained improved AADs of 0.03% in density and 0.03% in speed of sound. These results compare very favourably with other commonly used mixture models. The present model may be systematically improved or extended by introducing new or improved correlations of the binary parameters.     

Improvements to a new equation of state for pure components

In a recent work [Fluid Phase Equilib. 194–197 (2002) 401], Kedge and Trebble presented a non-cubic equation of state (EOS) including a near-critical correction term. The evaluation of that equation was limited initially to matching fluid properties of methane. In this work, we investigate the impact of incorporating a Carnahan–Starling (CS) repulsive term [J. Chem. Phys. 51 (2) (1969) 635] into the non-cubic equation. The CS term improves the fit of the critical isotherm and it is shown to improve the fit of the entire PVT space. Anomalies in the fit of temperature dependence in the EOS parameters in the near-critical region are also reduced. We also demonstrate in this work how the new correction term serves to flatten the top of the vapor–liquid coexistence curve. The new term is compared to the exponential term in Soave’s modification of the BWR equation (SBWR) [Ind. Eng. Chem. Res. 34 (1995) 3981] which achieves a similar effect in a slightly different way.     

Extending the GC-SAFT-VR approach to associating functional groups: Alcohols, aldehydes, amines and carboxylic acids

The statistical associating fluid theory is a widely used molecular-based equation of state that has been successfully applied to study a broad range of fluid systems. It provides a framework in which the effects of molecular shape and interactions on the thermodynamics and phase behavior of fluids can be separated and quantified. In the original approach, molecules were modeled as chains composed of identical segments; the heterogeneity of molecules in terms of structure and functional groups was described implicitly through effective parameters. To overcome this limitation, in recent works [Peng et al. Fluid Phase Equilib. 227(2), 131 (2009); Ind. Eng. Chem. Res. 49(3), 1378 (2010)] the GC-SAFT-VR approach has been developed to extend the theory to model chains composed of segments of different size and/or energy of interaction and enable the development of a group-contribution approach within the SAFT-VR framework in which molecular heterogeneity and connectivity is explicitly accounted for. The parameters for several key functional groups (CH₃, CH₂, CH, CH₂CH, CO, C₆H₅, esters, ethers, cis-alkenes and trans-alkenes groups) were determined by fitting to experimental vapor pressure and saturated liquid density data for a number of small molecules containing the functional groups of interest and transferability of the parameters tested by comparing the theoretical predictions with experimental data for pure fluids not included in the fitting process and binary mixtures of both simple fluids and the VLE and LLE of small molecules in polymer systems. In this work, we further extend the applicability of the GC-SAFT-VR approach through the study of the vapor-liquid phase behavior of associating systems, such as linear and branched alcohols, primary and secondary amines, aldehydes, and carboxylic acids, and their mixtures. In the study of these new molecules several new functional groups (OH (linear and branched), HCO, NH₂, NH and COOH) are defined and their molecular parameters characterized. The transferability of the parameters is again tested by comparing the theoretical predictions with experimental data for pure fluids and binary mixtures not included in the fitting process. The GC-SAFT-VR approach is found to predict the phase behavior of the systems studied in most cases in good agreement with experimental data and accurately captures the effects of changes in structure and molecular composition on phase behavior.     

First-order mean spherical approximation for attractive, repulsive, and multi-Yukawa potentials

The first-order mean spherical approximation (FMSA) theory proposed by Tang et al. [Fluid Phase Equilib., 134, 21(1997)] is applied for studying several typical Yukawa fluids, including attractive, repulsive, and multi-Yukawa cases. The FMSA study is particularly advantageous in providing thermodynamics and structure information in a simple, analytical, and consistent manner. Comparisons with the latest reported computer simulation data for compressibility factor, internal energy, and radial distribution function show that FMSA performs very well and the performance is very close to the full MSA and to several other theories, developed individually for the above-mentioned cases or properties. The present study provides solid evidence to support FMSA applications to more complex fluids.     

Modification of Esmaeilzadeh–Roshanfekr equation of state to improve volumetric predictions of gas condensate reservoir

The Peneloux–Rauzy–Freze (PRF) method of improving volumetric predictions by introducing the volume shift into the equation of state, is applied to the Esmaeilzadeh–Roshanfekr equation of state (ER-EOS). The ER-EOS is a new three parameter equation of state that was developed in 2006 aiming to be applied to reservoir fluids. First, this equation of state was developed for pure hydrocarbons and then was extended to mixtures by using mixing rules [M. Bonyadi, F. Esmaeilzadeh, Fluid Phase Equilib. 260 (2007) 326–334]. The modified ER-EOS (mER-EOS) is expected to improve volumetric predictions of gas condensate by applying volume shift for heavy end(s). In this study, three gas condensate fluid samples taken from three wells in a real field in Iran, referred here as SA1, SA4 and SA8, as well as two samples from literature have been used to check the validity of the modified ER-EOS in calculating the PVT properties of gas condensate mixtures. Some experiments such as constant composition expansion (CCE), constant volume depletion (CVD) and dew point pressures are carried out on these samples. Relative volume and condensate drop-out in CCE and CVD tests were predicted by ER-EOS, mER-EOS, PR-EOS and SRK-EOS [D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1), (1976) 59–64; G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203]. Comparison results between experimental and calculated data indicate that the mER-EOS has smaller error than the ER-EOS, PR-EOS and SRK-EOS. By this modification, the total average absolute deviations of the predicted liquid saturation from CVD experiments and relative volume from CCE experiments are 13.17% and 0.99%, respectively.     

On the mean spherical approximation for the Lennard–Jones fluid

Subtle details on the mean spherical approximation (MSA) theory for the Lennard–Jones potential [Fluid Phase Equilib. 134 (1997) 21] are presented. In order to enhance the appreciation of the theory, the accuracy of the mapping method and the contact approximation used in the theory are demonstrated by comparing with the exact results at certain extreme conditions. Technical derivation of internal energy of the MSA is also fully displayed. In addition, the typographic errors appeared in [Fluid Phase Equilib. 134 (1997) 21] are also corrected in this work.     

Molecular simulation of vapor–liquid equilibria of toxic gases

In this paper, we derived the potential parameters for three toxic gases, hydrogen sulfide, phosgene and nitrous oxide, modeled by the effective Stockmayer potential model proposed by Gao et al. [Fluid Phase Equilib. 137 (1997) 87]. The vapor–liquid equilibria (VLE) of these substances have been extensively investigated over a wide range of temperatures by the Gibbs ensemble Monte Carlo (GEMC) technique. The simulated saturated densities and pressures are in good agreement with experimental data. The critical properties obtained by regression of the simulated data also agree well with the experimental values. The present work demonstrates that the effective Stockmayer potential can describe well the toxic gases concerned.     

On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols

Nagata, I., 1985. On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols. Fluid Phase Equilibria, 19: 153–174.Binary vapor—liquid and liquid—liquid equilibrium data for alcohol solutions includin one or two alcohols are correlated with the UNIQUAC associated solution theory (Nagata and Kawamura). The theory uses pure liquid association constants determined by the method of Brandani and a single value of the enthalpy of the hydrogen bond equal to ?23.2 kJ mol ^?1 for pure alcohols. For alcohol-active nonassociating component mixtures and alcohol—alcohol mixtures the theory involves additional solvation constants. The theory is extended to contain ternary mixtures with any number of alcohols. Ternary predictions of vapor—liquid and liquid—liquid equilibria are performed using only binary parameters. Good agreement is obtained between calculated and experimental results for many representative mixtures.     

Modelling LLE and VLE of methanol + n-alkane series using GC-PC-SAFT with a group contribution kij

The fluid phase diagrams (LLE and VLE) of methanol + n-alkane mixtures series (from C₄ up to C₁₆) were modelled using GC-PC-SAFT EOS (Tamouza et al., Fluid Phase Equilibria 222–223 (2004) 67–76) combined with a recent method for computing k_ij based on the London theory (NguyenHuynh et al., Industrial & Engineering Chemistry Research 47 (2008) 8847–8858). This latter method requires pure compound adjustable parameters: pseudo-ionization energies J that may be calculated by group contribution in the case of n-alkane series. J_alkane is calculated from group parameters JCH₃$J_{\text{C}{\text{H}}_3}$ and JCH₂$J_{\text{C}{\text{H}}_2}$.     

Analysis and applications of a group contribution sPC-SAFT equation of state

A group contribution (GC) method for estimating pure compound parameters for the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) is proposed in a previous work [A. Tihic, G.M. Kontogeorgis, N. von Solms, M.L. Michelsen, L. Constantinou, Ind. Eng. Chem. Res. 47 (2008) 5092–5101]. In this paper, an investigation of the predictive capability of the GC sPC-SAFT EoS through comparison of the method’s predictions for compounds with high molecular weights and several selected binary mixtures of industrial significance with experimental data such as thiols, sulphides and polynuclear aromatics is presented. Additionally, predictions of activity coefficient at infinite dilution for athermal systems are compared with the results using existing activity coefficient models. The results show that calculated pure compound parameters using the proposed GC method allow satisfactory representation of experimental data of investigated systems with the sPC-SAFT EoS. Moreover, the variety of functional groups in the available GC scheme ensures broad applications of the GC sPC-SAFT EoS.     

A saturated liquid density equation in conjunction with the Predictive-Soave–Redlich–Kwong equation of state for pure refrigerants and LNG multicomponent systems

An equation and a set of mixing rules for the prediction of liquid density of pure refrigerants and liquified natural gas (LNG) multicomponent systems have been developed. This equation uses the parameters of Mathias and Copeman [P.M. Mathias, T.W. Copeman, Fluid Phase Equilib. 13 (1983) 91–108] temperature dependent-term for the Predictive-Soave–Redlich–Kwong [T. Holderbaum, J. Gmehling, Fluid Phase Equilib. 70 (1991) 251–265] equation of state and hence it could be used together with this equation. The equation uses a characteristic parameter for each refrigerant; however, if it is not available, a value of zero is recommended. This model gives an average of absolute errors less than 0.42% for the prediction of liquid density of 28 pure refrigerants consisting of 2489 data points and 0.33% for 18 multicomponent LNG systems involving 132 data points. The model parameters were determined from pure component properties and reported. These parameters were then used without any adjustment to predict liquid density of multicomponent LNG mixtures and excellent results were obtained. The model was also compared with other available methods.