Ten Years with the CPA (Cubic-Plus-Association) Equation of State. Part 1. Pure Compounds and Self-Associating Systems

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.

Atomic-Scale Insights into the Phase Behavior of Carbon Dioxide and Water from 313 to 573 K and 8 to 30 MPa

We performed molecular dynamics (MD) simulations of CO2 + H2O systems by employing widely used force fields (EPM2, TraPPE, and PPL models for CO2; SPC/E and TIP4P/2005 models for H2O). The phase behavior observed in our MD simulations is consistent with the coexistence lines obtained from previous experiments and SAFT-based theoretical models for the equations of state. Our structural analysis reveals a pronounced correlation between phase transitions and the structural orderliness. Specifically, the coordination number of Ow (oxygen in H2O) around other Ow significantly correlates with phase changes. In contrast, coordination numbers pertaining to the CO2 molecules show less sensitivity to the thermodynamic state of the system. Furthermore, our data indicate that a predominant number of H2O molecules exist as monomers without forming hydrogen bonds, particularly in a CO2-rich mixture, signaling a breakdown in the hydrogen bond network's orderliness, as evidenced by a marked decrease in tetrahedrality. These insights are crucial for a deeper atomic-level understanding of phase behaviors, contributing to the well-grounded design of CO2 injection under high-pressure and high-temperature conditions, where an atomic-scale perspective of the phase behavior is still lacking.

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.

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.

Effects of Gas Dissolution on Gas Migration during Gas Invasion in Drilling

Sour gas reservoirs (including CO₂ and H₂S) are vulnerable to gas invasion when drilling into reservoir sections. The high solubility of the invaded gas in drilling fluid makes the gas invasion monitoring "hidden" and "sudden" for later expansion, and the blowout risk increases. Accurate prediction of gas dissolution is highly significant for monitoring gas invasion. In this study, the gas-liquid flow control equations considering gas dissolution were established. Focusing on the gas dissolution effect, a solubility experiment for CO₂ and CH₄ in an aqueous solution was performed using a phase equilibrium device. The experimental and simulation results revealed that the addition of CO₂ can significantly increase gas dissolution, and the presence of salts decreases it. For solubility prediction of pure CH₄ and CO₂, the fugacity-activity solubility model, calculated using the Peng-Robinson equation of state, was more accurate than the Soave-Redlich-Kwong equation of state. The Soave-Redlich-Kwong equation of state has higher accuracy for the CO₂ and CH₄ gas mixture. If the gas dissolution effect is considered for wellbore gas-liquid flow, the time required for the mud pit gain to reach the early warning value increases. When the contents of CO₂ and H₂S in intrusive gases are higher, the time for mud pit gain change monitored on the ground increases, the concealment increases, and the risk of blowout increases.

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.

Midstream on a chip: ensuring safe carbon dioxide transportation for carbon capture and storage

Emerging technologies like enhanced oil recovery and carbon sequestration rely on carbon dioxide water content data to ensure that pipelines remain sub-saturated to avoid corrosion and hydrate flow assurance issues. To improve throughput and confidence in the hydrate phase equilibria data to avoid pipeline blockages, further research into the carbon dioxide water content must be conducted. However, the liquid carbon dioxide regime is experimentally difficult to study and the available data disagree between studies. This work aims to provide the critical and accurate data for liquid carbon dioxide for a high pressure range (13.8 to 103.4 bar) and temperature range (20 and -30 °C) utilizing a small volume microfluidic reactor (<20 microliter) coupled with Raman spectroscopy, which can reveal any phase metastability in the system. The small volume of the microfluidic system (<20 microliter) allowed experiments to be run in a few hours, compared to a whole week for prior larger scale measurements. The carbon dioxide water content results from this work agree well with both model predictions and available literature data in the gas region; however, once carbon dioxide was converted to liquid, the data showed a weak function of pressure, similar to model predictions and some previous data sets. The discrepancies between literature data are attributed to metastable phases present in the equilibrium cells, as the data is usually taken in the carbon dioxide near critical region, close to carbon dioxide's dew point, and near the hydrate phase transition. For these reasons, it is important to observe and qualify all phases in the cell, as was done in this novel study with in situ Raman spectroscopy coupled to Midstream on a chip, to ensure accurate water content of the carbon dioxide fluid phase is being measured.

Application of Generalized (Hyper-) Dual Numbers in Equation of State Modeling

The calculation of derivatives is ubiquitous in science and engineering. In thermodynamics, in particular, state properties can be expressed as derivatives of thermodynamic potentials. The manual differentiation of complex models can be tedious and error-prone. In this work, we revisit dual and hyper-dual numbers for the calculation of exact derivatives and show generalizations to higher order derivatives and derivatives with respect to vector quantities. The methods described in this paper are accompanied by an open source Rust implementation with Python bindings. Applications of the generalized (hyper-) dual numbers are given in the context of equation of state modeling and the calculation of critical points.

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.

Central-Moments-Based Lattice Boltzmann for Associating Fluids: A New Integrated Approach

Dynamic and thermodynamic behaviors of associating fluids play a crucial role in various science and engineering disciplines. Cubic plus association equation of state (CPA EOS) is implemented in a central-moments-based lattice Boltzmann method (LBM) in order to mimic the thermodynamic behavior of associating fluids. The pseudopotential approach is selected to model the multiphase thermodynamic characteristics such as reduced density of associating fluids. The priority of central-moments-based approach over multiple-relaxation-time collision operator is highlighted by performing double shear layers. The integration of central-moments-based LBM and CPA EOS is useful to simulate the dynamic and thermodynamic characteristics of associating fluids at high flow rate conditions, which is extended to high-density ratio scenarios by increasing the anisotropy order of gradient operator. In order to increase the stability of the model, a higher anisotropy order of the gradient operator is implemented; about 34 present reduction in spurious velocities is noticed in some cases. The type of gradient operator considerably affects the model thermodynamic consistency. Finally, the model is validated by observing a straight line in the Laplace law test. Prediction of thermodynamic behaviors of associating fluids is of significance in various applications including biological processes as well as fluid flow in porous media.

Energy Conservation in Absorption Refrigeration Cycles Using DES as a New Generation of Green Absorbents

Deep eutectic solvents (DESs) are emerging green solvents with very unique characteristics. Their contribution to atmospheric pollution is negligible, and they can be “designed” for desired properties. In this study, the feasibility of applying DESs (Reline, Ethaline, or Glyceline) as absorbents in absorption refrigeration cycles was investigated. The sophisticated cubic-plus-association (CPA) equation of state, considering the strong intermolecular interactions of such complex systems, was used to estimate the thermodynamic properties. At a fixed set of base case operating conditions, the coefficients of performance were calculated to be 0.705, 0.713, and 0.716 for Reline/water, Ethaline/water, and Glyceline/water systems, respectively, while the corresponding mass flow rate ratios were 33.73, 11.53, and 16.06, respectively. Furthermore, the optimum operating conditions of each system were estimated. To verify the feasibility, results were compared to literature systems, including LiBr/water and various ionic liquid/water systems. The results indicate that DES/water working fluids have the potential to be used in such cycles. Since DESs have the characteristic to be tuned (designed) to desired properties, including their solvent power and their enthalpies of absorption, much further research needs to be done to propose new DESs with higher energy efficiencies.

Hybridized method of pseudopotential lattice Boltzmann and cubic-plus-association equation of state assesses thermodynamic characteristics of associating fluids

It is crucial to properly describe the associating fluids in terms of phase equilibrium behaviors, which are needed for design, operation, and optimization of various chemical and energy processes. Pseudopotential lattice Boltzmann method (LBM) appears to be a reliable and efficient approach to study thermodynamic behaviors and phase transition of complex fluid systems. However, when cubic equations of state (EOSs) are incorporated into single-component multiphase LBM, simulation results are not well matched with experimental data. This study presents the utilization of cubic-plus-association (CPA) EOS in the LBM structure to obtain more accurate modeling results for associating fluids. An approach based on the global search optimization algorithm is introduced to find the optimal association parameters of CPA EOS for water and primary alcohols in the lattice units. The thermodynamic consistency is verified by the Maxwell construction and is also improved by the forcing scheme of [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)10.1103/PhysRevE.86.016709]. The spurious velocity is reduced with increasing isotropy in the gradient operator. Furthermore, an extended version of CPA EOS is introduced, which increases the system stability at low reduced temperatures. There is a very good match between the LBM results and experimental data, confirming the reliability of the model developed in the present study. The introduced approach has potential to be employed for simulating transport phenomena and interfacial characteristics of associating fluids in porous systems.