Computational and Physical Performance of a Modified PC-SAFT Equation of State for Highly Asymmetric and Associating Mixtures

Prediction of water anomalous properties by introducing the two-state theory in SAFT

Water is one of the most abundant substances on earth, but it is still not entirely understood. It shows unusual behavior, and its properties present characteristic extrema unlike any other fluid. This unusual behavior has been linked to the two-state theory of water, which proposes that water forms different clusters, one with a high density and one with a low density, which may even form two distinct phases at low temperatures. Models incorporating the two-state theory manage to capture the unusual extrema of water, unlike traditional equations of state, which fail. In this work, we have derived the framework to incorporate the two-state theory of water into the Statistical-Associating-Fluid-Theory (SAFT). More specifically, we have assumed that water is an ideal solution of high density water molecules and low density water molecules that are in chemical equilibrium. Using this assumption, we have generalized the association term SAFT to allow for the simultaneous existence of the two water types, which have the same physical parameters but different association properties. We have incorporated the newly derived association term in the context of the Perturbed Chain-SAFT (PC-SAFT). The new model is referred to as PC-SAFT-Two-State (PC-SAFT-TS). Using PC-SAFT-TS, we have succeeded in predicting the characteristic extrema of water, such as its density and speed of sound maximum, etc., without loss of accuracy compared to the original PC-SAFT. This new framework is readily extended to mixtures, and PC-SAFT-TS manages to capture the solubility minimum of hydrocarbons in water in a straightforward manner.

Multiple insights call for revision of modern thermodynamic models to account for structural fluctuations in water

Modern thermodynamic models incorporate the concept of association (hydrogen bonding) and they can describe very satisfactorily many properties of water containing mixtures. They have not been successful in representing water's anomalous properties and this work provides a possible explanation. We have analyzed and interpreted recent experimental data, molecular simulation results, and two-state theory approaches and compared against the predictions from thermodynamic models. We show that the dominance of the tetrahedral structure implemented in modern thermodynamic models may be the reason for their failure for describing water systems. While this study does not prove the two-state theories for water, it indicates that a high level of tetrahedral structure of water is not in agreement with water's anomalous properties when used in thermodynamic models.

Hydrophobic polyamide nanofilms provide rapid transport for crude oil separation

Hydrocarbon separation relies on energy-intensive distillation. Membrane technology can offer an energy-efficient alternative but requires selective differentiation of crude oil molecules with rapid liquid transport. We synthesized multiblock oligomer amines, which comprised a central amine segment with two hydrophobic oligomer blocks, and used them to fabricate hydrophobic polyamide nanofilms by interfacial polymerization from self-assembled vesicles. These polyamide nanofilms provide transport of hydrophobic liquids more than 100 times faster than that of conventional hydrophilic counterparts. In the fractionation of light crude oil, manipulation of the film thickness down to ~10 nanometers achieves permeance one order of magnitude higher than that of current state-of-the-art hydrophobic membranes while retaining comparable size- and class-based separation. This high permeance can markedly reduce plant footprint, which expands the potential for using membranes made of ultrathin nanofilms in crude oil fractionation.

Diffusion Coefficients in Systems Related to Reservoir Fluids: Available Data and Evaluation of Correlations

Molecular diffusion determines the time to reach local equilibrium in a reservoir. It can be a main production mechanism in scenarios such as production from fractured reservoirs or tight formation. However, there is a lack of high-pressure diffusion coefficients for reservoir fluids and its related systems. Many correlations exist, but there is no consensus on their accuracy for these systems. We provide a systematic review of the available data for systems related to reservoir fluids, as well as a comprehensive comparison of five commonly used correlations for hydrocarbon mixtures, including the extended Sigmund, Riazi-Whitson, Leahy-Dios-Firoozabadi, Wilke–Chang, and the Hayduk–Minhas correlations. We collected extensive data of diffusion coefficients in binary mixtures related to petroleum fluids and established a database of over 80 binaries and 1600 data points. We also collected the data for gas diffusion in different oils and reservoir fluids, but the data in high-pressure live oils are extremely scarce. The five correlations were evaluated using the binary database, and a few selected correlations using the oil database. None of the correlations show consistent and dominant superiority for all the binary mixtures, although some are better for particular groups/regions. For oils and reservoir fluids, the composition information is often incomplete. Only a few sets allow a comparison between different correlations. Although some trends can be identified from the correlation evaluation, no conclusive recommendation is made for a particular model, due to the data scarcity. The findings underscore the need for more accurate measurement and modeling of gas diffusion in mixtures that are more representative of reservoir fluids at high pressures.

Dry Glass Reference Perturbation Theory Predictions of the Temperature and Pressure Dependent Separations of Complex Liquid Mixtures Using SBAD-1 Glassy Polymer Membranes

In this work we apply dry glass reference perturbation theory (DGRPT) within the context of fully mutualized diffusion theory to predict the temperature and pressure dependent separations of complex liquid mixtures using SBAD-1 glassy polymer membranes. We demonstrate that the approach allows for the prediction of the membrane-based separation of complex liquid mixtures over a wide range of temperature and pressure, using only single-component vapor sorption isotherms measured at 25 °C to parameterize the model. The model was then applied to predict the membrane separation of a light shale crude using a structure oriented lumping (SOL) based compositional model of petroleum. It was shown that when DGRPT is applied based on SOL compositions, the combined model allows for the accurate prediction of separation performance based on the trend of both molecular weight and molecular class.

Continuum-scale modelling of polymer blends using the Cahn-Hilliard equation: transport and thermodynamics

The Cahn-Hilliard equation is commonly used to study multi-component soft systems such as polymer blends at continuum scales. We first systematically explore various features of the equation system, which give rise to a deep connection between transport and thermodynamics-specifically that the Gibbs free energy of mixing function is central to formulating a well-posed model. Accordingly, we explore how thermodynamic models from three broad classes of approach (lattice-based, activity-based and perturbation methods) can be incorporated within the Cahn-Hilliard equation and examine how they impact the numerical solution for two model polymer blends, noting that although the analysis presented here is focused on binary mixtures, it is readily extensible to multi-component mixtures. It is observed that, although the predicted liquid-liquid interfacial tension is quite strongly affected, the choice of thermodynamic model has little influence on the development of the morphology.

Modeling of RAFT polymerization of MMA in supercritical carbon dioxide using the PC-SAFT equation of state

The PC-SAFT equation of state was applied to the study of RAFT polymerization of methyl methacrylate in supercritical CO₂.

Analysis of Thermodynamic Models for Simulation and Optimisation of Organic Rankine Cycles

Equations of state (EOSs) form the base of every thermodynamic model used in the design of industrial processes, but little work has been done to evaluate these in the context of such models. This work evaluates 13 EOSs for their accuracy, computational time and robustness when used in an in-house optimisation program that finds the maximum power output of an organic Rankine cycle. The EOSs represent popular choices in the industry, such as the simple cubic EOSs, and more complex EOSs such as the ones based on corresponding state principles (CSP). These results were compared with results from using the Groupe Européen de Recherches Gazières (GERG) EOS, whose error is within experimental uncertainty. It appears that the corresponding state EOSs find a solution to the optimisation problem notably faster than GERG without significant loss of accuracy. A corresponding state method which used the Peng–Robinson EOS to calculate the shape factors and a highly accurate EOS for propane as the reference EOS, was shown to have a total deviation of just 0.6% as compared to GERG while also being 10 times as fast. The CSP implementation was also more robust, being able to converge successfully more often.

Bond cooperativity and ring formation in hydrogen fluoride thermodynamic properties: A two-density formalism framework

In this work, we develop a thermodynamic perturbation theory using a two-density formalism framework to model the bond cooperativity effect for associating hard sphere and Lennard-Jones fluids. The theory predictions are compared with Monte Carlo simulation results and they are in excellent agreement. We incorporate bond angle dependent ring formation into the theory to calculate hydrogen fluoride thermodynamic properties. The liquid density and vapor pressure obtained by the theory are in good agreement with the experimental data. Comparing the thermo-physical properties of hydrogen fluoride calculated by this theory with previous studies reveals the importance of bond angle dependent ring formation and cooperative hydrogen bonding to capture its anomalous behavior especially in the vapor phase. The cooperativity ratio obtained in our model is close to the values reported by previous quantum studies.

A molecular equation of state for alcohols which includes steric hindrance in hydrogen bonding

In this paper, we develop the first equation of state for alcohol containing mixtures which includes the effect of steric hindrance between the two electron lone pair hydrogen bond acceptor sites on the alcohol's hydroxyl oxygen. The theory is derived for multi-component mixtures within Wertheim's multi-density statistical mechanics in a second order perturbation theory. The accuracy of the new approach is demonstrated by application to pure methanol and ethanol and binary ethanol/water mixtures. It is demonstrated that the new approach gives a substantial improvement in the prediction of the hydrogen bonding structure of both pure alcohol and alcohol/water mixtures, as compared to conventional approaches which do not include steric effects between the alcohol association sites. Finally, it is demonstrated that the inclusion of steric effects allows for more accurate binary phase equilibria and heats of mixing prediction with water.

A density functional theory for association of fluid molecules with a functionalized surface: fluid-wall single and double bonding

In this manuscript we extend Wertheim's two-density formalism beyond its first order to model a system of fluid molecules with a single association site close to a planar hard wall with association sites on its surface in a density functional theory framework. The association sites of the fluid molecules are small enough that they can form only one bond, while the wall association sites are large enough to bond with more than one fluid molecule. The effects of temperature and of bulk fluid and wall site densities on the fluid density profile, extent of association, and competition between single and double bonding of fluid segments at the wall sites versus distance from the wall are presented. The theory predictions are compared with new Monte Carlo simulation results and they are in good agreement. The theory captures the surface coverage over wide ranges of temperature and bulk density by introducing the effect of steric hindrance in fluid association at a wall site.

On the cooperativity of association and reference energy scales in thermodynamic perturbation theory

Equations of state for hydrogen bonding fluids are typically described by two energy scales. A short range highly directional hydrogen bonding energy scale as well as a reference energy scale which accounts for dispersion and orientationally averaged multi-pole attractions. These energy scales are always treated independently. In recent years, extensive first principles quantum mechanics calculations on small water clusters have shown that both hydrogen bond and reference energy scales depend on the number of incident hydrogen bonds of the water molecule. In this work, we propose a new methodology to couple the reference energy scale to the degree of hydrogen bonding in the fluid. We demonstrate the utility of the new approach by showing that it gives improved predictions of water-hydrocarbon mutual solubilities.

A density functional theory for colloids with two multiple bonding associating sites

Wertheim's multi-density formalism is extended for patchy colloidal fluids with two multiple bonding patches. The theory is developed as a density functional theory to predict the properties of an associating inhomogeneous fluid. The equation of state developed for this fluid depends on the size of the patch, and includes formation of cyclic, branched and linear clusters of associated species. The theory predicts the density profile and the fractions of colloids in different bonding states versus the distance from one wall as a function of bulk density and temperature. The predictions from our theory are compared with previous results for a confined fluid with four single bonding association sites. Also, comparison between the present theory and Monte Carlo simulation indicates a good agreement.