Capabilities and Limitations of an Association Theory for Chemicals in Liquid or Supercritical Solvents

The cubic-plus-association (CPA) model is an equation of state (EoS) that combines the Soave–Redlich–Kwong (SRK) equation with the association term from Wertheim’s theory as used in statistical associating fluid theory (SAFT). In the form used here, the CPA EoS does not include separate terms for the polar and quadrupolar contributions. The capabilities and limitations of the CPA model when it is applied to mixtures with nonpolar and polar chemicals, as well as associating (hydrogen-bonding) compounds are illustrated. Three case studies are considered, all of which are of industrial relevance. The capabilities of the model are illustrated in the first two case studies: the phase behavior of mixtures used in the oxidation of 2-octanol in supercritical CO₂ and the investigation of systems containing acetone, methanol, water, chloroform, and methyl acetate. In each case, both correlations of vapor–liquid and liquid–liquid equilibria for binary systems and predictions for multicomponent mixtures are presented. Finally, the limitations of the CPA model are illustrated in the last case study, which focuses on the modeling of mixtures containing aromatic acids, such as benzoic and terephthalic acid. We also include a detailed discussion of the capabilities and limitations of the model in context and related to previous investigations. Finally, results are compared to observations from studies with other association models

Modeling Water Containing Systems with the Simplified PC-SAFT and CPA Equations of State

Numerous studies have been presented for modeling of water containing systems with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS), and more than 20 water parameter sets have been published with emphasis on different applications. In this work, eight of these sets and new estimated parameters with different association schemes are systematically compared on describing properties of pure water, the liquid–liquid equilibria (LLE) of water with hydrocarbons, and the vapor–liquid (VLE) and/or vapor–liquid–liquid equilibria (VLLE) of water with 1-alcohols. An interactive procedure is further proposed for including the LLE of water with hydrocarbons into the pure fluid parameter estimation. The results show that it is possible for PC-SAFT to give an accurate description of the LLE of water and hydrocarbons while retaining satisfactory accuracy for both vapor pressure and saturated liquid density of water. For the aforementioned aqueous systems, the PC-SAFT correlations using the newly developed parameters are compared with the corresponding correlations of the cubic plus association EOS. The two models show comparable results for phase equilibria, and both of them fail to describe second-order derivative properties of water, i.e., residual isochoric heat capacity and speed of sound. The ability of the models to predict the monomer (free site) fractions of saturated pure water is investigated and discussed from various aspects. The results suggest that more experimental or theoretical studies are needed

Comparison of the Debye–Hückel and the Mean Spherical Approximation Theories for Electrolyte Solutions

The thermodynamics of electrolyte solutions has been investigated by many scientists throughout the last century. While several theories have been presented, the most popular models for the electrostatic interactions are based on the Debye–Hückel and mean spherical approximation (MSA) theories. In this paper we investigate the differences between the Debye–Hückel and the MSA theories, and comparisons of the numerical results for the Helmholtz energy and its derivatives with respect to temperature, volume and composition are presented. The investigation shows that the nonrestricted primitive MSA theory performs similarly to Debye–Hückel, despite the differences in the derivation. We furthermore show that the static permittivity is a key parameter for both models and that in many cases it completely dominates the results obtained from the two models. Consequently, we conclude that the simpler Debye–Hückel theory may be used in connection with electrolyte equations of state without loss of accuracy

Modeling of Dielectric Properties of Aqueous Salt Solutions with an Equation of State

The static permittivity is the most important physical property for thermodynamic models that account for the electrostatic interactions between ions. The measured static permittivity in mixtures containing electrolytes is reduced due to kinetic depolarization and reorientation of the dipoles in the electrical field surrounding ions. Kinetic depolarization may explain 25–75% of the observed decrease in the permittivity of solutions containing salts, but since this is a dynamic property, this effect should not be included in the thermodynamic modeling of electrolytes. Kinetic depolarization has, however, been ignored in relation to thermodynamic modeling, and authors have either neglected the effect of salts on permittivity or used empirical correlations fitted to the measured static permittivity, leading to an overestimation of the reduction in the thermodynamic static permittivity. We present a new methodology for obtaining the static permittivity over wide ranges of temperatures, pressures, and compositions for use within an equation of state for mixed solvents containing salts. The static permittivity is calculated from a new extension of the framework developed by Onsager, Kirkwood, and Fröhlich to associating mixtures. Wertheim’s association model as formulated in the statistical associating fluid theory is used to account for hydrogen-bonding molecules and ion–solvent association. Finally, we compare the Debye–Hückel Helmholtz energy obtained using an empirical model with the new physical model and show that the empirical models may introduce unphysical behavior in the equation of state

Modeling of Dielectric Properties of Complex Fluids with an Equation of State

The static permittivity is a key property for describing solutions containing polar and hydrogen bonding compounds. However, the precise relationship between the molecular and dielectric properties is not well-established. Here we show that the relative permittivity at zero frequency (static permittivity) can be modeled simultaneously with thermodynamic properties. The static permittivity is calculated from an extension of the framework developed by Onsager, Kirkwood, and Fröhlich to associating mixtures. The thermodynamic properties are calculated from the cubic-plus-association (CPA) equation of state that includes the Wertheim association model as formulated in the statistical associating fluid theory (SAFT) to account for hydrogen bonding molecules. We show that, by using a simple description of the geometry of the association, we may calculate the Kirkwood <i>g</i>-factor as a function of the probability of hydrogen bond formation. The results show that it is possible to predict the static permittivity of complex mixtures over wide temperature and pressure ranges from simple extensions of well-established theories simultaneously with the calculation of thermodynamic properties

A Benchmark Database for Mixed-Solvent Electrolyte Solutions: Consistency Analysis Using E‑NRTL

Modeling of thermodynamic properties of mixed-solvent electrolyte solutions is challenging. Reliable experimental data are essential for any model development and parametrization. In this work, a benchmark database for (water + methanol/ethanol + alkali halide) mixed-solvent electrolyte solutions is presented. The available experimental data of mean ionic activity coefficient (MIAC) and vapor–liquid equilibrium (VLE) are comprehensively collected and critically evaluated for 61 data sets of 23 solutions. The resulting benchmark database includes 1413 data records from 32 data sets for 13 solutions. The evaluated data sets of the relevant aqueous electrolyte solutions are also presented. A consistent E-NRTL model that satisfies the Gibbs–Duhem equation is utilized for analyzing the data, reconciling the MIAC and VLE data. Based on the database, recommended parameters are obtained for the E-NRTL model

Approach to Improve Speed of Sound Calculation within PC-SAFT Framework

An extensive comparison of SRK, CPA, and PC-SAFT for the speed of sound in normal alkanes has been performed. The results reveal that PC-SAFT captures the curvature of the speed of sound better than cubic EoS, but the accuracy is not satisfactory. Two approaches have been proposed to improve PC-SAFT’s accuracy for speed of sound: (i) putting speed of sound data into parameter estimation; (ii) putting speed of sound data into both universal constants regression and parameter estimation. The results have shown that the second approach can significantly improve the speed of sound (3.2%) prediction while keeping acceptable accuracy for the primary properties, i.e. vapor pressure (2.1%) and liquid density (1.5%). The two approaches have also been applied to methanol, and both give very good results

Capabilities and Limitations of Predictive Engineering Theories for Multicomponent Adsorption

Multicomponent adsorption of gas mixtures on diverse solid surfaces is important in many applications. However, there are still many questions on the practical applicability of the available theories, especially for polar systems. In this work, we consider three well-known theories suitable for the prediction of multicomponent adsorption with parameters obtained solely from correlating single gas/solid data. We have tested them over an extensive database with emphasis on polar systems (both gases and solids). The three theories are the multicomponent Langmuir, the ideal adsorbed solution theory (IAST), and the multicomponent potential adsorption theory (MPTA). We have not attempted to improve/modify the methods in any way but have used them in their original form, as the purpose of our work is to illustrate the capabilities and inherent limitations of the models for predicting multicomponent adsorption. We have ensured that the description of single gas/solid systems is as accurate as possible, but besides this, the calculations for multicomponent systems are straight predictions. The work revealed on one side that all three theories yield for some systems similar predictions, with IAST and MPTA performing overall better than the multicomponent Langmuir. On the other hand, it is also shown that all the three theories, despite the good results in some cases, have serious limitations particularly for water and to some extent also for certain polar solids. Both strengths and weaknesses of the three models are discussed

Ternary Vapor–Liquid Equilibrium Measurements and Modeling of Ethylene Glycol (1) + Water (2) + Methane (3) Systems at 6 and 12.5 MPa

Novel technologies in the field of subsea gas processing include the development of natural gas dehydration facilities, which may operate at high pressure due to their proximity to reservoirs. For the qualification and design of these processing units, ternary vapor–liquid equilibrium data are required to validate the thermodynamic models used in the design process. For this purpose, 16 new ternary data points were measured for ethylene glycol (1) + water (2) + methane (3) at 6.0 and 12.5 MPa with temperatures ranging from 288 to 323 K and glycol content above 90 wt %. Glycol in gas (<i>y</i>₁), water in gas (<i>y</i>₂), and methane solubility (<i>x</i>₃) were measured with relative experimental uncertainties (<i>u</i>_r(<i>x</i>) = <i>u</i>(<i>x</i>)/<i>|x|</i>) below 12%, depending on the type of data. The Cubic-Plus-Association (CPA) equation of state was used to model the data. Literature pure component and binary interaction parameters were used. It was found that the model provides a good qualitative description of the experimental data for <i>y</i>₁ and <i>y</i>₂, while a significant over-prediction occurs for <i>x</i>₃. The modeling errors for CPA ranged between 5–40% average absolute relative deviation

Cubic Plus Association Equation of State for Flow Assurance Projects

Thermodynamic hydrate inhibitors such as methanol, ethanol, (mono) ethylene glycol (MEG), and triethylene glycol (TEG) are widely used in the oil and gas industry. On modeling these compounds, we show here how the CPA equation of state was implemented in an in-house process simulator as an in-built model. To validate the implementation, we show calculations for binary systems containing hydrate inhibitors and water or hydrocarbons using the Cubic Plus Association (CPA) and Soave–Redlich–Kwong (SRK) equation of states, also comparing against experimental data. For streams containing natural gas and water, CPA was applied to calculate the loss of the inhibitor to the vapor phase as a function of temperature and pressure. Simulations of dehydration units using TEG were conducted, and the CPA results were compared with that of two commercial simulators which used their available thermodynamic packages for glycol applications, proving that the CPA calculations are in good agreement with these models and showing that this is an adequate way to simulate complex mixtures containing natural gas, water, and hydrate inhibitors