Reference Correlation for the Viscosity of Carbon Dioxide

Molecular Dynamics Simulation on Thickening and Solubility Properties of Novel Thickener in Supercritical Carbon Dioxide

Supercritical CO2 has wide application in enhancing oil recovery, but the low viscosity of liquid CO2 can lead to issues such as poor proppant-carrying ability and high filtration loss. Therefore, the addition of thickening agents to CO2 is vital. Hydrocarbon polymers, as a class of green and sustainable materials, hold tremendous potential for acting as thickeners in supercritical CO2 systems, and PVAc is one of the best-performing hydrocarbon thickeners. To further improve the viscosity enhancement and solubility of PVAc, here we designed a novel polymer structure, PVAO, by introducing CO2-affine functional groups to PVAc. Molecular dynamics simulations were adopted to analyze viscosity and relevant solubility parameters systematically. We found that PVAO exhibits superior performance, with a viscosity enhancement of 1.5 times that of PVAc in supercritical CO2. While in the meantime, PVAO maintains better solubility characteristics than PVAc. Our findings offer insights for the future design of other high-performance polymers.

Simulation and Data-Driven Modeling of the Transport Properties of the Mie Fluid

This work reports the computation and modeling of the self-diffusivity (D*), shear viscosity (η*), and thermal conductivity (κ*) of the Mie fluid. The transport properties were computed using equilibrium molecular dynamics simulations for the Mie fluid with repulsive exponents (λr) ranging from 7 to 34 and at a fixed attractive exponent (λa) of 6 over the whole fluid density (ρ*) range and over a wide temperature (T*) range. The computed database consists of 17,212, 14,288, and 13,099 data points for self-diffusivity, shear viscosity, and thermal conductivity, respectively. The database is successfully validated against published simulation data. The above-mentioned transport properties are correlated using artificial neural networks (ANNs). Two modeling approaches were tested: a semiempirical formulation based on entropy scaling and an empirical formulation based on density and temperature as input variables. For the former, it was found that a unique formulation based on entropy scaling does not yield satisfactory results over the entire density range due to a divergent and incorrect scaling of the transport properties at low densities. For the latter empirical modeling approach, it was found that regularizing the data, e.g., modeling ρ*D* instead of D*, ln η* instead of η*, and ln κ* instead of κ*, as well as using the inverse of the temperature as an input feature, helps to ease the interpolation efforts of the artificial neural networks. The trained ANNs can model seen and unseen data over a wide range of density and temperature. Ultimately, the ANNs can be used alongside equations of state to regress effective force field parameters from volumetric and transport data.

Diffusion and Gas Flow Dynamics in Partially Saturated Smectites

Clays and clay rocks are considered good natural and engineered barriers for deep geological disposal of nuclear waste worldwide. Metal corrosion and organic waste degradation in underground repositories generate significant amounts of gas that should be able to migrate through the multibarrier system to avoid potential pressure buildup, which could be compromising the integrity of the barriers and host rocks. The gas is expected to accumulate in larger pores and eventually form an interconnected network. Under such conditions, the migration of gas molecules takes place both in pore water films and gas-filled macropores. Therefore, mass fluxes depend on the distribution of gas molecules between the water-rich and gas-rich phases and their mobility in both compartments. Classical molecular dynamics (MD) simulations were employed to investigate the mobilities of He, H₂, CO₂, Ar, and CH₄ in a Na-montmorillonite mesopore as a function of the degree of saturation, as well as evaluate the hydrodynamic behavior of the pore fluid in partially saturated clays. The diffusivity of the gas molecules was determined by observing the asymptotic behavior of the mean square displacement in the gas-rich phase and at the gas-water interface. The partition coefficient and Gibbs free energy were analyzed to investigate the transfer of gas molecules between the gas-rich and water-rich phases by observing the molecular trajectories as they cross the vapor-liquid interface. The results revealed that the diffusion coefficient in the gas phase increased with increasing gas-filled pore width and converged asymptotically toward the diffusion coefficient in the bulk state. It could be shown that the diffusion coefficient of gas molecules dissolved in the water films remained constant as long as the interacting water surface was in the bulk-liquid-like phase. This behavior changes in very thin water films. It was observed that the partitioning coefficient of gas molecules at the solid-liquid interface is nearly the same as that in the bulk-liquid-like phase. Partitioning is observed to be strongly dependent on the temperature and gas molecular weights. In the second part of the study, nonequilibrium molecular dynamics (NEMD) simulations were performed to investigate the mobility of gases in pressure-driven decoupled gas-phase dynamics (DGPD) and coupled gas and water phase dynamics (CGWPD) in a partially saturated Na-montmorillonite slit mesopore. The dynamic viscosity of the gas phase was calculated from NEMD simulations and indicated that the viscosity of the gas phase was almost the same in both methods (DGPD and CGWPD). The average slip length for gas molecules at the gas-water interface was also calculated, revealing that the slip-free boundary condition assumed in continuum models is generally invalid for microfluidics and that a slip boundary condition exists at the microscale for specific surface interactions. Finally, a Bosanquet-type equation was developed to predict the diffusion coefficient and dynamic viscosity of gas as a function of the average pore width, gas mean-free path, geometric factor, and thickness of the adsorbed water film.

Predicting the essential oil composition in supercritical carbon dioxide extracts from hop pellets using mathematical modeling

Supercritical fluid extraction from hops (Humulus lupulus L.) can be used to extract essential oil for the flavoring of beer. With a special focus on the oil composition being linked to the hop aroma, the influence of pressure and temperature on the extraction kinetics of seven oil components (β-myrcene, α-humulene, β-caryophyllene, 2-methylbutyl isobutyrate, undecanone, linalool, and α-pinene) is analyzed and modeled in this article. Supercritical CO₂ extraction from hop pellets was conducted at pressure-temperature combinations of 90/100/110 bar and 40/45/50 °C. The extract composition over time, analyzed by gas chromatography, was used for the parameterization of two existing mechanistic models: an internal-mass-transfer-control (IMTC), and a broken-and-intact-cells (BIC) model. The IMTC model was found to effectively describe most extraction kinetics and hence applied in this study. In contrast to previous studies, the IMTC model parameters were not only fitted to individual extraction curves from different experiments but also correlated to temperature and pressure as a further step towards model-based prediction. Using the parameterized model, the extract composition was predicted at 95 bar/48 °C, 105 bar/42 °C, and 105 bar/48 °C. Extraction yields were found to be higher at lower temperatures and higher pressures in general. The sensitivity towards pressure was observed to differ between components and to be particularly higher for β-myrcene compared with α-humulene. Changes of the essential oil composition with a variation in pressure and temperature were predicted correctly by the model with a mean relative deviation from experimental data of 11.7% (min. 1.2%, max. 36.2%).

Dynamic Crossover in Fluids: From Hard Spheres to Molecules

We propose a simple and generic definition of a demarcation reconciling structural and dynamic frameworks when combined with the entropy scaling framework. This crossover line between gas- and liquid-like behaviors is defined as the curve for which an individual property, the contribution to viscosity due to molecules' translation, is exactly equal to a collective property, the contribution to viscosity due to molecular interactions. Such a definition is shown to be consistent with the one based on the minima of the kinematic viscosity. For the hard sphere, this is shown to be an exact solution. For Lennard-Jones spheres and dimers and for some simple real fluids, this relation holds very well. This crossover line passes nearby the critical point, and for all studied fluids, it is well captured by the critical excess entropy curve for atomic fluids, emphasizing the link between transport properties and local structure.

Diffusion of the carbon dioxide-ethanol mixture in the extended critical region

The effect of traces of ethanol in supercritical carbon dioxide on the mixture's thermodynamic properties is studied by molecular simulations and Taylor dispersion measurements. This mixture is investigated along the isobar p = 10 MPa in the temperature range between T = 304 and 343 K. Along this path, the mixture undergoes two transitions: First, the Widom line is crossed, marking the transition from liquid-like to gas-like conditions. A second transition occurs from the supercritical gas-like domain to a subcritical gas. The Widom line crossover entails inflection points for most of the studied properties, i.e. density, enthalpy, shear viscosity, Maxwell-Stefan and intradiffusion coefficients. On the other hand, the transition between the super- and subcritical regions is found to be generally smooth, an observation that is qualitatively confirmed by experimental Taylor dispersion measurements. Dedicated atomistic simulations show the presence of microheterogeneities due to ethanol self-association along the investigated path, which lead to the mixture's anomalous behavior in its extended critical region.

Global Temporal and Geographic Stability of Brines on Present-day Mars

We combine experimentally verified constraints on brine thermodynamics along with a global circulation model to develop a new extensive framework of brine stability on the surface and subsurface of Mars. Our work considers all major phase changes (i.e., evaporation, freezing, and boiling) and is consistent, regardless of brine composition, so it is applicable to any brine relevant to Mars. We find that equatorial regions typically have temperatures too high for stable brines, while high latitudes are susceptible to permanent freezing. In the subsurface, this trend is reversed, and equatorial regions are more favorable to brine stability, but only for the lowest water activities (and lowest eutectic temperatures). At locations where brines may be stable, we find that their lifetimes can be characterized by two regimes. Above a water activity of ~0.6, brine duration is dominated by evaporation, lasting at most a few minutes per sol. Below a water activity of 0.6, brine duration is bound by freezing or boiling; such brines are potentially stable for up to several consecutive hours per sol. Our work suggests that brines should not be expected near or on the Martian surface, except for low eutectic water activity salts such as calcium or magnesium perchlorate or chlorate, and their (meta)stability on the surface would require contact with atmospheric water vapor or local ice deposits.

Entropy Scaling of Viscosity - II: Predictive Scheme for Normal Alkanes

In this work, a residual entropy value 6/10 of the way between the critical point and a value of -2/3 of Boltzmann's constant is shown to collapse the scaled viscosity for the family of normal alkanes. Based on this approach, a nearly universal correlation is proposed that can reproduce 95% of the experimental data for normal alkanes within ±18% (without removal of clearly erroneous data). This universal correlation has no new fluid-specific empirical parameters and is based on experimentally accessible values. This collapse is shown to be valid to a residual entropy half way between the critical point and the triple point, beyond which the macroscopically-scaled viscosity has a super-exponential dependence on residual entropy, terminating at the triple point. A key outcome of this study is a better understanding of entropy scaling for fluids with intramolecular degrees of freedom. A study of the transport and thermodynamic properties at the triple point rounds out the analysis.

Entropy Scaling of Viscosity - I: A Case Study of Propane

In this work, a broadly-applicable and simple approach for building high accuracy viscosity correlations is demonstrated for propane. The approach is based on the combination of a number of recent insights related to the use of residual entropy scaling, especially a new way of scaling the viscosity for consistency with the dilute-gas limit. With three adjustable parameters in the dense phase, the primary viscosity data for propane are predicted with a mean absolute relative deviation of 1.38%, and 95% of the primary data are predicted within a relative error band of less than 5%. The dimensionality of the dense-phase contribution is reduced from the conventional two dimensional approach (temperature and density) to a one-dimensional correlation with residual entropy as the independent variable. The simplicity of the model formulation ensures smooth extrapolation behavior (barring errors in the equation of state itself). The approach proposed here should be applicable to a wide range of chemical species. The supporting information includes the relevant data in tabular form and a Python implementation of the model.

Compressed-liquid Densities of the Binary Mixture Dimethyl Carbonate + Heptane at Three Compositions

Compressed-liquid densities of the binary system dimethyl carbonate + heptane have been measured with a vibrating-tube densimeter over the temperature and pressure ranges of 270 K to 470 K, and 1 MPa to 50 MPa at three compositions of the mixture. The measurements are part of an effort to better understand the molecular interactions of polar/non-polar mixtures. These types of mixtures often exhibit very non-ideal behavior. By measuring the mixture at three compositions and over a large range of temperature and pressure, the non-ideality can be assessed. There are no high-pressure liquid density data for this binary system in the literature, thus data reported here could only be compared to literature data at atmospheric pressure to establish their quality. The majority of literature data agree well with the presented results which have a maximum expanded uncertainty of 1.63 kg·m-3 (for the composition with the greatest mole fraction of dimethyl carbonate). The non-ideality for the mixture, in the temperature, pressure and composition range of this study was found to be minimal. This is rationalized by considering the molecular sizes, shapes, and charge distributions of the pure components and the attractive parts of their intermolecular force fields as they are reflected in the temperature ranges of their vapor pressure curves.

Diffusion of methane in supercritical carbon dioxide across the Widom line

Diffusion of methane diluted in supercritical carbon dioxide is studied by experiment and molecular simulation in the temperature range from 292.55 to 332.85 K along the isobars 9.0, 12.5 and 14.7 MPa. Measurements of the Fick diffusion coefficient are carried out with the Taylor dispersion technique. Molecular dynamics simulation and the Green-Kubo formalism are employed to obtain Fick, Maxwell-Stefan and intradiffusion coefficients as well as shear viscosity. The obtained diffusion coefficients are on the order of 10-8 m2/s. The composition, temperature and density dependence of diffusion is analyzed. The Fick diffusion coefficient of methane in carbon dioxide shows an anomaly in the near-critical region. This behavior can be attributed to the crossing of the so-called Widom line, where the supercritical fluid goes through a transition between liquid-like and gas-like states. Further, several classical equations are tested on their ability to predict this behavior and it is found that equations that explicitly include the density are better suited to predict the sharp variation of the diffusion coefficient near the critical region predicted by molecular simulation.

Probing the link between residual entropy and viscosity of molecular fluids and model potentials

This work investigates the link between residual entropy and viscosity based on wide-ranging, highly accurate experimental and simulation data. This link was originally postulated by Rosenfeld in 1977 [Rosenfeld Y (1977) Phys Rev A 15:2545-2549], and it is shown that this scaling results in an approximately monovariate relationship between residual entropy and reduced viscosity for a wide range of molecular fluids [argon, methane, [Formula: see text], [Formula: see text], refrigerant R-134a (1,1,1,2-tetrafluoroethane), refrigerant R-125 (pentafluoroethane), methanol, and water] and a range of model potentials (hard sphere, inverse power, Lennard-Jones, and Weeks-Chandler-Andersen). While the proposed "universal" correlation of Rosenfeld is shown to be far from universal, when used with the appropriate density scaling for molecular fluids, the viscosity of nonassociating molecular fluids can be mapped onto the model potentials. This mapping results in a length scale that is proportional to the cube root of experimentally measurable liquid volume values.

Wide-ranging Absolute Viscosity Measurements of Sub- and Supercritical 1,1,1-trifluoroethane (R143a)

The viscosity of 1,1,1-trifluoroethane (R143a) was measured with a piezoelectrically actuated, torsionally vibrating quartz sensor. The measurements extended over a temperature range from 300 K to 440 K with pressures to 68 MPa and covered states from the dilute gas to the compressed liquid. The influence of the drive voltage on the torsional displacement of the vibrator in fluid and in vacuum was systematically investigated. Since R143a is highly polar, the sample conductance and susceptance were also monitored with the sensor to detect possible electroviscous contributions in the measured viscosities. None were identified so that the estimated uncertainty of the measurements remains at 2 % at a 95 % confidence level (coverage factor k = 2). The results agree well within this margin with literature data that were determined with four other viscometric techniques.

Reference Values and Reference Correlations for the Thermal Conductivity and Viscosity of Fluids

In this paper, reference values and reference correlations for the thermal conductivity and viscosity of pure fluids are reviewed. Reference values and correlations for the thermal conductivity and the viscosity of pure fluids provide thoroughly evaluated data or functional forms and serve to help calibrate instruments, validate or extend models, and underpin some commercial transactions or designs, among other purposes. The criteria employed for the selection of thermal conductivity and viscosity reference values are also discussed; such values, which have the lowest uncertainties currently achievable, are typically adopted and promulgated by international bodies. Similar criteria are employed in the selection of reference correlations, which cover a wide range of conditions, and are often characterized by low uncertainties in their ranges of definition.