Vapor-liquid equilibria for alcohol/hydrocarbon systems using the CPA Equation of state

The recently developed Cubic-Plus-Association Equation of State (CPA EoS) is extended in this study to binary systems containing one associating compound (alcohol) and an inert one (hydrocarbon). CPA combines the Soave-Redlich-Kwong (SRK) equation of state for the physical part with an association term based on perturbation theory. The classical van der Waals one-fluid mixing rules are used for the attractive and co-volume parameters, and b, while the extension of the association term to mixtures is rigorous and does not require any mixing rules. Excellent correlation of Vapor-Liquid Equilibria (VLE) is obtained using a small value for the interaction parameter (k_ij) in the attractive term of the physical part of the equation of state even when it is temperature-independent. CPA yileds much better results than SRK and its performance is similar to that of other association models, like the Anderko EoS, and the more complex SAFT and Simplified SAFT EoS.     

Application of the CPA equation of state to reservoir fluids in presence of water and polar chemicals

The complex phase equilibrium between reservoir fluids and associating compounds like water, methanol and glycols has become more and more important as the increasing global energy demand pushes the oil industry to target reservoirs with extreme or complicated conditions, such as deep or offshore reservoirs. Conventional equation of state (EoS) with classical mixing rules cannot satisfactorily predict or even correlate the phase equilibrium of those systems. A promising model for such systems is the Cubic-Plus-Association (CPA) EoS, which has been successfully applied to well-defined systems containing associating compounds. In this work, a set of correlations was proposed to calculate the CPA model parameters for the narrow cuts in ill-defined C₇₊ fractions. The correlations were then combined with either the characterization method of Pedersen et al. or that of Whitson et al. to extend CPA to reservoir fluids in presence of water and polar chemical such as methanol and monoethylene glycol. With a minimum number of adjustable parameters from binary pairs, satisfactory results have been obtained for different types of phase equilibria in reservoir fluid systems and several relevant model multicomponent systems. In addition, modeling of mutual solubility between light hydrocarbons and water is also addressed.     

Surface tension of chain molecules through a combination of the gradient theory with the CPA EoS

Despite the interest in systems containing non-associating compounds such as alkanes and fluoroalkanes or associating compounds like alkanols, their vapor–liquid interfaces have received little quantitative attention. Aiming at modeling the interfacial tensions of several families of chain molecules, a combination of the density gradient theory of fluid interfaces with the Cubic-Plus-Association (CPA) equation of state was developed. The density gradient theory is based on the phase equilibria of the fluid phases separated by the interface, for what an adequate equation of state is required.     

Effect of surface active sites on adsorption of associating chain molecules in pores: A Monte Carlo study

This work describes the adsorption behavior of associating and non-associating chains and their mixtures in pores with activated surfaces. The systems are studied using Gibbs ensemble Monte Carlo molecular simulations. Fluid molecules are modeled as freely jointed Lennard-Jones chains. Associating chains have, additionally, an associating square-well site placed in an end sphere. The pores are modeled as regular slit pores via an integrated Lennard-Jones potential (10-4-3); activation is achieved by placing specific association sites protruding from the surface. Two different solid-fluid interaction parameters are used, one of which corresponds roughly to alkanes on graphite, the other being a much weaker interaction. Adsorption isotherms are presented for several different cases: associating and non-associating chains confined within both neutral and activated walls. Mixtures of associating and non-associating chains are also considered. The effects of pore size, temperature and chain length are quantified. Selectivities obtained are in the range of those seen in adsorption experiments of alkane-alkanol mixtures.     

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 pvT$pvT$ 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.     

Application of the perturbed chain SAFT equation of state to complex polymer systems using simplified mixing rules

A simplified perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is applied to polymer systems that include a variety of non-associating (esters, cyclic hydrocarbons), polar (ketones) as well as associating (amines, alcohols) solvents. The solvent pure-component parameters that are not available in the literature are estimated by correlating vapor-pressure and liquid-density data. The performance of the simplified PC-SAFT is compared to the original PC-SAFT equation of state for polymer systems of varying complexity. It is shown that the applied simplification is not at the expense of the accuracy of equation of state, while the computational time and complexity are significantly reduced, especially for associating systems. With no binary interaction parameter, simplified PC-SAFT is successfully able to predict vapor–liquid equilibria of polymers with non-associating solvents. In the case of associating solvents, a small binary interaction parameter k_ij is usually needed for the satisfactory correlation of the experimental data.     

High-pressure vapor–liquid equilibria of systems containing ethylene glycol,water and methane: Experimental measurements and modeling

This work presents new experimental phase equilibrium measurements of the binary MEG–methane and the ternary MEG–water–methane system at low temperatures and high pressures which are of interest to applications related to natural gas processing. Emphasis is given to MEG and water solubility measurements in the gas phase. The CPA and SRK EoS, the latter using either conventional or EoS/G^E mixing rules are used to predict the solubility of the heavy components in the gas phase. It is concluded that CPA and SRK using the Huron–Vidal mixing rule perform equally satisfactory, while CPA requires fewer interaction parameters.     

Modeling of the carbon dioxide solubility in imidazolium-based ionic liquids with the tPC-PSAFT equation of state

In this work, an equation of state (EoS) is developed to predict accurately the phase behavior of ionic liquid + CO2 systems based on the truncated perturbed chain polar statistical associating fluid theory (tPC-PSAFT) EoS. This EoS accounts explicitly for the dipolar interactions between ionic liquid molecules, the quadrupolar interactions between CO2 molecules, and the Lewis acid-base type of association between the ionic liquid and the CO2 molecules. Physically meaningful model pure-component parameters for ionic liquids are estimated based on literature data. All experimental vapor-liquid equilibrium data are correlated with a single linearly temperature-dependent binary interaction parameter. The ability of the model to describe accurately carbon dioxide solubility in various 1-alkyl-3-methylimidazolium-based ionic liquids with different alkyl chain lengths and different anions at pressures from 0 to 100 MPa and carbon dioxide fractions from 0 to 75 mol % is demonstrated. In all cases, good agreement with experimental data is obtained.     

Application of a new simplified SAFT to VLE study of associating and non-associating fluids

A new equation of state based on the Statistical Associating Fluid Theory (SAFT) is presented to study the phase behavior of associating and non-associating fluids. In the new equation of state, the hard sphere contribution to compressibility factor of the simplified version of the SAFT (SSAFT) is replaced with that proposed by Ghotbi and Vera. The Ghotbi–Vera SSAFT (GV-SSAFT) was also extended to study the phase behavior of associating and non-associating mixtures. The GV-SSAFT like the SSAFT equation of state has three adjustable segment parameters for non-associating fluids and five parameters for associating fluids. The experimental data of liquid densities and vapor pressures for pure fluids studied in this work were used to obtain the best values for the parameters of the GV-SSAFT. The results obtained from the GV-SSAFT for liquid densities and vapor pressures of pure associating and non-associating fluids were compared with those obtained from the SSAFT equation of state. The results showed that the GV-SSAFT similar to the SSAFT can accurately correlate the experimental data of liquid density and vapor pressure for systems studied. On the other hand the results obtained from two SAFT-based equations of state are almost identical. In order to show capability of the GV-SSAFT and SSAFT equations of state, they were used to directly calculate heat of vaporization for a number of pure associating and non-associating fluids. Slightly better results for heat of vaporization comparing to the experimental data were obtained from the GV-SSAFT EOS than those obtained from the SSAFT. The GV-SSAFT was also used to study the VLE phase behavior for a number of binary associating and non-associating mixtures. The results also showed that the GV-SSAFT can be successfully used to study the phase behavior of mixtures studied in this work.     

Solid-liquid equilibrium using the SAFT-VR equation of state: Solubility of naphthalene and acetic acid in binary mixtures and calculation of phase diagrams

A solid-liquid equilibrium (SLE) thermodynamic model based on the SAFT-VR equation of state (EOS) is presented. The model allows for the calculation of solid-liquid phase equilibria in binary mixtures at atmospheric pressure. The fluid (liquid) phase is treated with the SAFT-VR approach, where molecules are modelled as associating chains of tangentially bonded spherical segments interacting via square-well potentials of variable range. The equilibrium between the liquid and solid phase is treated following a standard thermodynamic method that requires the experimental temperature and enthalpy of fusion of the solute. The model is used to calculate the solubilities of naphthalene and acetic acid in common associating and non-associating organic solvents and to determine the solid-liquid phase behaviour of binary mixtures with simple eutectics. The SAFT-VR pure component model parameters are determined by comparison to experimental vapour pressure and saturated liquid density data with the choice of association models according to the nature of the molecule; in addition, an unlike adjustable parameter (k_ij) is used to model the solutions. The solubility data of naphthalene and acetic acid in both associating and non-associating solvents are reproduced essentially within the accuracy of the experimental measurements. The phase boundaries and the position of the eutectic points in the binary mixtures considered are, in most cases, reproduced with the accuracy commensurate with the industrial applications. Overall, the results presented show that the SAFT-VR EOS can be used with confidence for the prediction of the SLE of binary systems at atmospheric pressure.     

Prediction of thermodynamic properties of some polymeric systems using an extended LJ potential-based equation of state up to high temperature–high pressure conditions

In this work, the extended Lennard-Jones potential-based equation of state (ELJ-based EoS) on which the effective near-neighbour pair interactions are LJ (12,6,3) type has been used to predict the specific volume and other thermodynamic properties of some semi-crystalline and liquid polymers and copolymers up to extremely high temperature–high pressure conditions. It seems that, at least in the dense regions, there are no upper- and lower-specific volume limitations in the applicability of the model for different polymeric systems. The parameters can be determined at any temperature for each compound using the temperature dependence of the parameters of ELJ-based EoS. The calculated parameters have been used to calculate the specific volume and other derived thermodynamic properties of different polymeric systems at any temperature and pressure. The ELJ-based EoS has been also compared with some previous studies.     

Use of normal boiling point correlations for predicting critical parameters of paraffins for vapour–liquid equilibrium calculations with the SRK equation of state

Correlations between normal boiling points and critical parameters (critical temperatures and critical pressures) and between normal boiling points and acentric factors of normal and branched paraffins in the range from C₇ to C₁₀₀ have been developed. These correlations can be used to quickly and easily compute critical properties that allow to reproduce closely, by means of the Soave–Redlich–Kwong (SRK) equation of state (EoS), the vapour pressure of pure compounds. In the range of 0.5–5 mmHg the values of vapour pressure calculated by means of the SRK EoS become less accurate and they can be improved using a different equation for the temperature-depending attractive parameter (i.e., the Mathias–Copeman alpha function) instead of the classical Soave function.     

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 Computationally Efficient Approach to Applying the SAFT Equation for CO2 + H2O Phase Equilibrium Calculations

The statistical associating fluid theory equation of state (EoS) is employed in a time efficient way for the correlation and prediction of vapor–liquid equilibrium of the CO₂ + H₂O binary system for the temperature (10–100 °C) and pressure (1–600 bar) ranges suitable for simulation of CO₂ geologic sequestration. The effective number of segments and energy parameter are correlated with the reduced temperature. Simple mixing rules are applied to obtain binary interaction parameters. Assigning a fixed H₂O composition in the mixing rule makes the phase equilibrium calculations relatively fast compared to other EoS’s. The results obtained by the model used were found to be in satisfactory agreement with the literature data.     

Measurement and modelling of bubble and dew points in the binary systems carbon dioxide + cyclobutanone and propane + cyclobutanone

The fluid phase behaviour for the binary systems carbon dioxide+cyclobutanone and propane+cyclobutanone has been determined experimentally, using Cailletet equipment. For both the systems bubble points have been determined for a number of isopleths covering the whole mole fraction range. Additionally, for the binary system carbon dioxide+cyclobutanone dew points and critical points could be observed for a number of overall-compositions rich in carbon dioxide. The temperature and pressure range were, respectively, from 278 to 369 K and from 0.1 to 14.0 MPa. Correlation of the experimental data of both systems has been performed using the Soave–Redlich–Kwong (SRK) equation of state. Satisfactory results have been achieved using only one binary interaction parameter.     

Thermodynamic phase equilibria of wax precipitation in crude oils

Economic loss due to wax precipitation in oil exploitation and transportation has reached several billion dollars a year recently. Development of a model for better understanding of the process of wax precipitation is therefore very important to reduce the loss. In this paper, a new thermodynamic model for predicting phase equilibriums of crude oils is proposed. The modified SRK EOS and the UNIQUAC equations are used to describe the vapor, liquid phase and the wax, respectively. New correlations have been introduced to calculate the volume parameter, c, in SRK EOS and the heat of vaporization in UNIQUAC equation. The model can be used to describe the systems which contain paraffin, naphthene and aromatic fractions. New correlations for the enthalpies, temperatures of solid–solid transitions and fusion enthalpies of paraffins are established in this paper based on data obtained from open literature. By using the proposed modified model, the wax precipitation in hydrocarbon fluids has been predicted for three crude oil systems. The calculation results have been compared with experimental observations and those results obtained using regular solution models. It is found that wax precipitation in complex systems can be better predicted by using this new model.     

Vapor–liquid equilibria for pentafluoroethane + propane and difluoromethane + propane systems over a temperature range from 253.15 to 323.15 K

This paper provides vapor–liquid equilibrium (VLE) data obtained for two binary systems of pentafluoroethane (R125)+propane (R290) and difluoromethane (R32)+R290 over a temperature range from 253.15 to 323.15 K. The measurement of VLE was performed at isothermal conditions in a vapor recirculation apparatus. Both systems form azeotropes in the temperature range of this study. The experimental results were well correlated with the Peng–Robinson equation of state (PR EoS) using one parameter van der Waals one fluid model. The binary interaction parameters were optimized using the experimental data of bubble point pressure. A comparison with published experimental VLE data has been carried out by means of the PR equation of state.     

Extension of the associated perturbed anisotropic chain theory to mixtures with more than one associating component

The Associated Perturbed Anisotropic Chain Theory (APACT), a theory useful for calculation of equilibrium thermodynamic properties for fluid mixtures presented recently by Ikonomou and Donohue has been extended to treat multicomponent mixtures in which two or more components associate. Mixtures containing non-associating components (diluents) also can be treated. Association equilibria for each component hydrogen bonding to itself as well as for cross-association between associating components are considered. Following an approach similar to that used previously in the derivation of APACT, a closed-form equation of state has been derived. Preliminary results show that APACT does well in fitting phase equilibrium data for binary mixtures involving alcohols and water with small values of k_ij. The fits are not as good, however, for systems containing small molecules (water and methanol) and the reasons for this shortcoming are discussed.     

Predicting interfacial tension between water and nonpolar fluids from a Cahn-type theory

We propose an accurate method to predict interfacial tension between water and nonpolar fluids by using Cahn gradient theory. The only necessary elements are (i) a water contact energy function and (ii) an equation of state (EoS) for the nonpolar fluid, chosen here as the Peng-Robinson EoS. The contact energy, a function of the fluid (adsorbate) surface density, is related to interfacial tension (IFT) by means of the Gibbs adsorption equation. Examining a large number of IFT data, we observe that the water contact energy is a universal function of adsorbate's surface density when proper scaling variables are used: it depends neither on adsorbate nor on temperature. A corresponding-states principle appears to govern the interfacial behavior between water and any nonpolar compound that is sparingly soluble in water. A predictive method (without any adjustable parameter) is therefore available for estimating IFT between water and any nonpolar fluid, whether the fluid is in supercritical or in subcritical states. The method performs well when the adsorbate is sparingly soluble in water, but slightly overestimates IFTs when the adsorbate's solubility in water is significant (e.g., CO2 and H2S). A similar behavior should also hold for interfaces involving a solid substrate.