An Equation of State for Associating Fluids

The Phase Equilibria of Natural Gas Hydrate in the Presence of 1,3-Dimethylcyclohexane and Octyl-β-D-glucopyranoside

The thermodynamic effect of octyl-β-D-glucopyranoside (OGP) on the formation of methane-1,3-dimethylcyclohexane (DMCH) hydrate was studied in this work. The thermodynamic equilibrium hydrate formation pressures between 275.15 K and 283.15 K were measured by the isothermal pressure search method. Different OGP aqueous solutions (0, 0.1, and 1 wt%) were used in this work. The experimental results show that OGP had no obvious thermodynamic inhibition on methane-DMCH hydrate formation when its concentration was low (0.1 wt%), whereas it had an inhibition on methane-DMCH hydrate formation when its concentration was high (1 wt%). The phase equilibrium hydrate formation pressure of the methane-DMCH-OGP system is about 0.1 MPa higher than that of the methane-DMCH system. The dissociation enthalpies of methane hydrate in different solutions remained uniform, which indicates that OGP was not involved in methane-DMCH hydrate formation. This phenomenon is explained from the perspective of the molecular structure of OGP. As a renewable and biological nonionic surfactant, the concentration of OGP in the liquid phase is low, so OGP can be added to the methane-DMCH system without significant thermodynamic inhibition.

Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations

H2-CO2 mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H2-CO2 mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H2 due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO2, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO2 content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO2-H2-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO2 and H2 in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO2 in NaCl brine decreased in the ternary system compared to the binary CO2-NaCl brine system, the solubility of H2 in NaCl brine increased less in the ternary system compared to the binary H2-NaCl brine system. The cooperative effect of H2-CO2 enhances the H2 solubility while suppressing the CO2 solubility. The water content in the gas phase was found to be intermediate between H2-NaCl brine and CO2-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO2-H2 mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H2-CO2 mixtures.

Impact of nanopore confinement on phase behavior and enriched gas minimum miscibility pressure in asphaltenic tight oil reservoirs

Miscible gas injection in tight/shale oil reservoirs presents a complex problem due to various factors, including the presence of a large number of nanopores in the rock structure and asphaltene and heavy components in crude oil. This method performs best when the gas injection pressure exceeds the minimum miscibility pressure (MMP). Accordingly, accurate calculation of the MMP is of special importance. A critical issue that needs to be considered is that the phase behavior of the fluid in confined nanopores is substantially different from that of conventional reservoirs. The confinement effect may significantly affect fluid properties, flow, and transport phenomena characteristics in pore space, e.g., considerably changing the critical properties and enhancing fluid adsorption on the pore wall. In this study, we have investigated the MMP between an asphaltenic crude oil and enriched natural gas using Peng-Robinson (PR) and cubic-plus-association (CPA) equations of state (EoSs) by considering the effect of confinement, adsorption, the shift of critical properties, and the presence of asphaltene. According to the best of our knowledge, this is the first time a model has been developed considering all these factors for use in porous media. We used the vanishing interfacial tension (VIT) method and slim tube test data to calculate the MMP and examined the effects of pore radius, type/composition of injected gas, and asphaltene type on the computed MMP. The results showed that the MMP increased with an increasing radius of up to 100 nm and then remained almost constant. This is while the gas enrichment reduced the MMP. Asphaltene presence changed the trend of IFT reduction and delayed the miscibility achievement so that it was about 61% different from the model without the asphaltene precipitation effect. However, the type of asphaltene had little impact on the MMP, and the controlling factor was the amount of asphaltene in the oil. Moreover, although cubic EoSs are particularly popular for their simplicity and accuracy in predicting the behavior of hydrocarbon fluids, the CPA EoS is more accurate for asphaltenic oils, especially when the operating pressure is within the asphaltene precipitation range.

Theoretical and practical investigation of ion-ion association in electrolyte solutions

In this study, we present a new equation of state for electrolyte solutions, integrating the statistical associating fluid theory for variable range interactions utilizing the generic Mie form and binding Debye-Hückel theories. This equation of state underscores the pivotal role of ion-ion association in determining the properties of electrolyte solutions. We propose a unified framework that simultaneously examines the thermodynamic properties of electrolyte solutions and their electrical conductivity, given the profound impact of ion pairing on this transport property. Using this equation of state, we predict the liquid density, mean ionic activity coefficient, and osmotic coefficient for binary NaCl, Na2SO4, and MgSO4 aqueous solutions at 298.15 K. Additionally, we evaluate the molar conductivity of these systems by considering the fraction of free ions derived from our equation of state in conjunction with two advanced electrical conductivity models. Our results reveal that, while ion-ion association has a minimal influence on the modification of the predicted properties of sodium chloride solutions, their impact on sodium and magnesium sulfate solutions is considerably more noticeable.

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.

Viscosity of Ionic Liquids: Theories and Models

Ionic liquids (ILs) offer a wide range of promising applications due to their unique and designable properties compared to conventional solvents. Further development and application of ILs require correlating/predicting their pressure-viscosity-temperature behavior. In this review, we firstly introduce methods for calculation of thermodynamic inputs of viscosity models. Next, we introduce theories, theoretical and semi-empirical models coupling various theories with EoSs or activity coefficient models, and empirical and phenomenological models for viscosity of pure ILs and IL-related mixtures. Our modelling description is followed immediately by model application and performance. Then, we propose simple predictive equations for viscosity of IL-related mixtures and systematically compare performances of the above-mentioned theories and models. In concluding remarks, we recommend robust predictive models for viscosity at atmospheric pressure as well as proper and consistent theories and models for P-η-T behavior. The work that still remains to be done to obtain the desired theories and models for viscosity of ILs and IL-related mixtures is also presented. The present review is structured from pure ILs to IL-related mixtures and aims to summarize and quantitatively discuss the recent advances in theoretical and empirical modelling of viscosity of ILs and IL-related mixtures.

Binding Debye-Hückel theory for associative electrolyte solutions

This study presents a new equation of state (EOS) for charged hard sphere fluids that incorporates ion-ion association. The EOS is developed using the Debye-Hückel (DH) theory, reference cavity approximation, and Wertheim's theory. Predictive accuracy is evaluated by comparing the model's predictions with Monte Carlo simulations for various charged hard-sphere fluids. The assessment focuses on mean ionic activity coefficient, individual ionic activity coefficient, and osmotic coefficients. The results demonstrate good agreement between the model and simulations, indicating its success for different electrolyte systems. Incorporating ion-ion association improves accuracy compared to the DH theory. The importance of the cavity function and ion-dipole interactions is emphasized in accurately representing structural properties. Overall, the developed EOS shows promising predictive capabilities for charged hard sphere fluids, providing validation and highlighting the significance of ion-ion association in thermodynamic predictions of electrolyte solutions.

Aqueous Solid Formation Kinetics in High-Pressure Methane at Trace Water Concentrations

Natural gas containing trace amounts of water is frequently liquefied at conditions where aqueous solids are thermodynamically stable. However, no data are available to describe the kinetics of aqueous solid formation at these conditions. Here, we present experimental measurements of both solid formation kinetics and solid-fluid equilibrium for trace concentrations of (12 ± 0.7) ppm water in methane using a stirred, high-pressure apparatus and visual microscopy. Along isochoric pathways with cooling rates around 1 K·min^-1, micron-scale aqueous solids were observed to form at subcoolings of (0.3-8.6) K, relative to an average equilibrium melting temperature of (253 ± 1.9) K at (8.9 ± 0.08) MPa; these data are consistent with predicted methane hydrate dissociation conditions within the uncertainty of both the experiment and model. The 36 measured formation events were used to construct a cumulative formation probability distribution, which was then fitted with a model from Classical Nucleation Theory, enabling the extraction of kinetic and thermodynamic nucleation parameters. While the resulting nucleation parameter values were comparable to those published for methane hydrate formation in bulk-water systems, the observed growth kinetics were distinctly different with only a small percentage of the water in the system converting into micron-scale solids over the experimental time scale. These results may help explain how cryogenic heat exchangers in liquefied natural gas facilities can operate for long periods without blockages forming despite being at very high subcoolings for aqueous solids.

Thermodiffusion of CO2 in Water by Nonequilibrium Molecular Dynamics Simulations

The components of a fluid mixture may segregate due to the Soret effect, a coupling phenomenon in which mass flux can be induced by a thermal gradient. In this work, we evaluate systematically the thermodiffusion of the CO₂-H₂O mixture, and the influence of the geothermal gradient on CO₂ segregation in deep saline aquifers in CO₂ storage. The eHeX method, a nonequilibrium molecular dynamics simulation approach, is judiciously selected to simulate the phenomenon. At 350 K, 400 bar, and CO₂ mole fraction of 0.02 (aquifer conditions), CO₂ accumulates on the cold side, and the thermal diffusion factor is close to 1 in a number of force fields. The lower the temperature, the higher is the separation and the thermal diffusion factor. In colder regions, water self-association is stronger, whereas the CO₂-H₂O cross-association and the CO₂-CO₂ interactions enhance at higher temperatures. Thermodiffusion and gravitational segregation have opposite effects on CO₂ segregation. At typical subsurface conditions, the Soret effect is more pronounced than gravity segregation, and CO₂ concentrates in the top (colder region). Our work sets the stage to model the effect of electrolytes on CO₂ segregation in subsurface aquifers and other areas of interest.

Prediction method of solubility of carbon dioxide and methane during gas invasion in deep-water drilling

Gases that invade during deep-water oil and gas drilling may be concealed due to the gas dissolution effect, leading to increased well control risks. Accurate and rapid prediction of carbon dioxide and methane dissolution is of great significance for the prediction and control of wellbore pressure during gas invasion. In this study, 316 sets of carbon dioxide solubility data at 288.15 to 423.15 K and 0.1 to 100 MPa, and 266 sets of methane solubility data at 275.15 to 444.3 K and 0.1 to 68 MPa were used to train a machine learning algorithm. The machine learning prediction method for gas solubility was established with a support vector regression machine and a particle swarm optimisation algorithm. The kernel function and disciplinary parameters of the support vector regression machine were optimised using the experimental dataset. The solubility of CO₂ and CH₄ in water was measured using a gas solubility measurement device. The experimental and model analysis showed that the solubility of CO₂ varied in different phase states. At a given pressure, the solubility of CO₂ was highest in the liquid state, followed by the supercritical state, and then the gaseous state. The average absolute relative deviation percentages between the calculated values of the CO₂ and CH₄ solubility models and the experimental values were 2.57 and 8.20, respectively. The machine learning method is consistent with the high-precision Duan thermodynamic model for predicting the solubility of CO₂ and CH₄ in water and can be used to predict the gas solubility in deep water and deep oil and gas drilling.

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.

Modeling Binary and Multicomponent Systems Containing Supercritical CO2 with Polyethylene Glycols and Compounds Relevant to the Biodiesel Production

The CPA equation of state is applied to model binary, ternary, and multicomponent mixtures that contain CO₂ with polyethylene glycols or compounds relevant to biodiesel production, such as glycerol and various triglycerides. Effort has been made to evaluate the model performance on correlating both the liquid and the vapor phase compositions, which is a demanding task, revealing the model’s and parameters’ limitations, due to the rather low concentrations of heavy compounds in the vapor phase. Initially the model’s binary parameters, which in all cases were temperature independent, were estimated using experimental data for binary systems. Those parameters were used to predict the phase behavior of supercritical CO₂ containing ternary and multicomponent mixtures. Since no parameter was adjusted to ternary or multicomponent systems’ data, the reported CPA results for such mixtures are considered as pure predictions. This is the final part of a series of studies [Tsivintzelis et al. Fluid Phase Equilibria 430 (2016) 75–92 and 504 (2020) 112337] that complete the parameterization of the CPA equation of state for systems relevant to the biodiesel production, which allows the application of the model to multicomponent mixtures of the relevant processes.

An extension of gases-brine mutual solubility models to include geochemical reactions: Modeling and applications

Accurate and quantitative numerical modeling of phase behavior and speciation of gas-water-rock systems is crucial for fluid and rock evolution analysis, and important in scientific research and engineering applications. In our previous work, mutual solubility models of series gases and brine have been developed for wide temperature, pressure and composition ranges. The gas components included CO₂, CH₄, H₂S, N₂ and O₂. The existing experimental data can be reproduced accurately. In this paper, the models are extended to include water-rock interactions by means of a full coupling with the open-source software package PHREEQC. With the new coupled model, the solubility of gases and various minerals can be correctly and reliably reproduced. The proposed numerical framework is properly implemented and it can be applied in different scenarios of gas-water-rock interactions. Three practical applications have been investigated: calculation of uranium in situ leaching, CO₂ geological storage and natural gas souring are provided in the paper. The application cases have additionally proven the stability and reliability of the proposed model.

Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state

A methodology for obtaining molecular parameters of a modified statistical associating fluid theory for variable-range interactions of Mie form (SAFT-VR Mie) equation of state (EoS) from ab initio calculations is proposed for non-associative species that can be modeled as single spherical segments. The methodology provides a strategy to map interatomic or intermolecular potentials obtained from ab initio quantum-chemistry calculations to the corresponding Mie potentials that can be used within the SAFT-VR Mie EoS. The inclusion of corrections for quantum and many-body effects allows for an excellent, fully predictive description of the vapor-liquid envelope and other bulk thermodynamic properties of noble gases; this description is of similar or superior quality to that obtained using SAFT-VR Mie with parameters regressed in the traditional way using experimental thermodynamic-property data. The methodology is extended to an anisotropic species, methane, where similar levels of accuracy are obtained. The efficacy of using less-accurate quantum-chemistry methods in this methodology is explored, showing that these methods do not provide satisfactory results, although we note that the description is nevertheless substantially better than those obtained using the conductor-like screening model for describing real solvents (COSMO-RS), the only other fully predictive ab initio method currently available. Overall, the reliance on thermophysical data is completely dispensed with, providing the first extensible, wholly predictive SAFT-type EoSs.

Three-Phase Equilibrium Calculations of Water/Hydrocarbon/Nonhydrocarbon Systems Based on the Equation of State (EOS) in Thermal Processes

A simple and novel approach is proposed to represent the mutual solubility of water and hydrocarbon components based on equations of state at high temperatures in thermal recovery processes. Sϕreide and Whitson modifications are applied to the Peng-Robinson (PR) equation of state (EOS) so that all components, including the water component, can exist in all phases, reasonably representing gas solubility in water and water solubility in hydrocarbon phases. We propose an algorithm to assign binary interaction parameters (BIPs) for aqueous and nonaqueous phases. The water vapor pressure helps select initial K-values for stability analysis so that the aqueous phase can be split out first if present. The algorithm is tested by a wide range of variations in pressure, temperature, and composition. The results show the robustness of the algorithm and the effects of temperature and overall water mole fraction on phase behaviors in steam flooding processes.

Impact of Asphaltene Precipitation and Deposition on Wettability and Permeability

Asphaltene precipitation and deposition have been a formation damage problem for decades, with the most devastating effects being wettability alteration and permeability impairment. To this effect, a critical look into the laboratory studies and models developed to quantify/predict permeability and wettability alterations are reviewed, stating their assumptions and limitations. For wettability alterations, the mechanism is predominantly surface adsorption, which is controlled by the asphaltene contacting minerals as they control the surface chemistry, charge, and electrochemical interactions. The most promising wettability alteration evaluation techniques are nuclear magnetic resonance, ζ potential, and the use of high-resolution microscopy. The integration of such techniques, which is still missing, would reinforce the understanding of asphaltene interaction with rock minerals (especially clays), which holds the key to developing a strategy for modeling wettability alteration. With regard to permeability impairment, surface deposition, pore plugging, and fine migration have been identified as the dominant mechanisms with several models reporting the simultaneous existence of multiple mechanisms. Existing experimental findings showed that asphaltene deposition is non-uniform due to mineral distribution which further complicates the modeling process. It also remains a challenge to separate changes due to adsorption (wettability changes) from those due to pore size reduction (permeability impairment).

A novel hybrid method for the calculation of methane hydrate-water interfacial tension along the three-phase (hydrate-liquid water-vapor) equilibrium line

We use a novel hybrid method to explore the temperature dependence of the solid-liquid interfacial tension of a system that consists of solid methane hydrate and liquid water. The calculated values along the three-phase (hydrate-liquid water-vapor) equilibrium line are obtained through the combination of available experimental measurements and computational results that are based on approaches at the atomistic scale, including molecular dynamics and Monte Carlo. An extensive comparison with available experimental and computational studies is performed, and a critical assessment and re-evaluation of previously reported data is presented.

Phase equilibria modeling of biorefinery-related systems: a systematic review

The search for sustainable ideas has gained prominence in recent decades at all levels of society since it has become imperative an economic, social, and environmental development in an integrated manner. In this context, biorefineries are currently present as the technology that best covers all these parameters, as they add the benefits of waste reuse, energy cogeneration, and fossil fuel substitution. Thus, the study of the various applicable biological matrices and exploring the technical capabilities of these processes become highly attractive. Thermodynamic modeling acts in this scenario as a fundamental tool for phase behavior predictions in process modeling, design, and optimization. Thus, this work aimed to systematize, using the PRISMA statement for systematic reviews, the information published between 2010 and 2020 on phase equilibria modeling in systems related to biorefineries to organize what is already known about the subject. As a result, 236 papers were categorized in terms of the year, country, type of phase equilibria, and thermodynamic model used. Also, the phase behavior predictions of different thermodynamic models under the same process conditions were qualitatively compared, establishing PC-SAFT as the model that best represents the great diversity of interest systems for biorefineries in a wide range of conditions.

An Accurate Model to Calculate CO2 Solubility in Pure Water and in Seawater at Hydrate–Liquid Water Two-Phase Equilibrium

Understanding of CO2 hydrate–liquid water two-phase equilibrium is very important for CO2 storage in deep sea and in submarine sediments. This study proposed an accurate thermodynamic model to calculate CO2 solubility in pure water and in seawater at hydrate–liquid water equilibrium (HLWE). The van der Waals–Platteeuw model coupling with angle-dependent ab initio intermolecular potentials was used to calculate the chemical potential of hydrate phase. Two methods were used to describe the aqueous phase. One is using the Pitzer model to calculate the activity of water and using the Poynting correction to calculate the fugacity of CO2 dissolved in water. Another is using the Lennard–Jones-referenced Statistical Associating Fluid Theory (SAFT-LJ) equation of state (EOS) to calculate the activity of water and the fugacity of dissolved CO2. There are no parameters evaluated from experimental data of HLWE in this model. Comparison with experimental data indicates that this model can calculate CO2 solubility in pure water and in seawater at HLWE with high accuracy. This model predicts that CO2 solubility at HLWE increases with the increasing temperature, which agrees well with available experimental data. In regards to the pressure and salinity dependences of CO2 solubility at HLWE, there are some discrepancies among experimental data. This model predicts that CO2 solubility at HLWE decreases with the increasing pressure and salinity, which is consistent with most of experimental data sets. Compared to previous models, this model covers a wider range of pressure (up to 1000 bar) and is generally more accurate in CO2 solubility in aqueous solutions and in composition of hydrate phase. A computer program for the calculation of CO2 solubility in pure water and in seawater at hydrate–liquid water equilibrium can be obtained from the corresponding author via email.