Binary Diffusion Coefficients Research Articles

Determination of binary diffusion coefficients between hot liquid solvents and bitumen with X-ray CT

Abstract The Steam Assisted Gravity Drainage (SAGD) process has been used for in-situ thermal bitumen recovery in Canada. Nevertheless, there are several drawbacks that could impair the SAGD performance. One of the main drawbacks of SAGD is nontrivial consumption of energy to generate steam. To curtail the consumption of steam, many SAGD variants have been proposed. For example, Vapor Extraction (VAPEX) was proposed as a solvent-based cold production method and Solvent-Assisted SAGD (SA-SAGD) was proposed as a solvent-assisted hybrid method. In those solvent-based/assisted methods, the dissolution of solvents in bitumen enhances the in-situ oil mobility. The speed of the mixing between solvents and bitumen in solvent-based/assisted recovery processes is dictated by dispersive mass flux which is proportional to the transverse dispersion coefficient. Diffusion coefficient, tortuosity and transverse dispersivity should be quantified to characterize the transverse dispersion coefficient. In this research, the diffusion coefficients of solvents in Athabasca bitumen were determined with X-ray computed tomography (CT). A medical X-ray CT scanner was used to capture the diffusion phenomenon occurring between fresh liquid solvents and bitumen. The experiments were designed to reproduce the in-situ high pressure, high temperature condition (3.5 MPa, 135C) where solvent and bitumen actually interact at the vapor chamber edge in the SA-SAGD process. Using our new °experimental system, we successfully measured molecular diffusion coefficients at the condition of the vapor chamber edge for the first time. In conclusion, the binary diffusion coefficients between solvents and bitumen were successfully measured at the condition where the mixing of solvents and bitumen actually occurs in the SA-SAGD process. The characterized diffusion coefficients will be input parameters for the reservoir simulation and semi-analytical models.

Binary Diffusion Coefficients for Gas Mixtures of Propane with Methane and Carbon Dioxide Measured in a Loschmidt Cell Combined with Holographic Interferometry

Binary diffusion coefficients D12 for the molecular gas systems propane–methane (C3H8–CH4) and propane–carbon dioxide (C3H8–CO2) have been measured with a Loschmidt cell combined with holographic interferometry at (293 and 313) K, between (0.05 and 0.5) MPa, and for different mixture compositions. Improved experimental and evaluation procedures already validated for the noble-gas system helium–krypton have been successfully adapted for the molecular gas systems. For the investigated mixtures, adsorption–desorption processes are superimposed on the diffusion process and increase the achievable uncertainties. This hinders reliable conclusions regarding a concentration dependency of the diffusion coefficient. D12 clearly increases with increasing temperature and decreasing pressure. At the same pressure, temperature, and C3H8 mole fraction, the diffusion coefficient is larger for C3H8–CH4 than for C3H8–CO2. For both systems, the presented diffusion coefficients are in reasonable agreement with available literature data. In particular, the pressure-dependent trend and the absolute values of D12 at a given temperature match with recent theoretical data based on ab initio calculations in the zero-density limit for both systems.

Water Sorption and Diffusivity in [C2C1im][BF4], [C4C1im][OAc], and [C4C1im][Cl

Measurements of in situ atmospheric water absorption and desorption in ionic liquids (ILs) (1-ethyl-3-methylimidazolium tetrafluoroborate [C2C1im][BF4], 1-butyl-3-methylimidazolium acetate [C4C1im][OAc], and 1-butyl-3-methylimidazolium chloride [C4C1im][Cl]) were made using a gravimetric microbalance at temperatures ranging from 283.15 to 315.15 K and relative humidity (RH) 0–70% at 101 kPa. Solubility data were well correlated using the nonrandom two-liquid (NRTL) activity model, and time dependent concentration data were used to determine the binary diffusion coefficients using one- and two-dimensional transport models of water in the IL–water systems. The solubility of water was highest in [C4C1im][OAc] (77.5 mol %), followed by [C4C1im][Cl] (68.6 mol %), and [C2C1im][BF4] (19.5 mol %) at equivalent conditions (303.15 K and 25.00% RH). The diffusion coefficients in order of increasing relative humidity ranged from 1.3 × 10–10 to 2.8 × 10–11 m2/s for [C2C1im][BF4], from 8.8 × 10–12 to 3.9 × 10–11 m2/s f...

Temperature and Concentration Dependence of the Ionic Transport Properties of Lithium-Ion Battery Electrolytes

Lithium-ion battery performance at low temperatures or fast charge/discharge rates is determined by the intrinsic electrolyte transport and the thermodynamic properties of the commonly used binary electrolytes. For the development of future electrolyte solutions, a quantification of the ionic conductivity, the binary diffusion coefficient, the transference number, and the thermodynamic factor over a large concentration and temperature range is mandatory. In this study, we apply previously discussed and established methods for the determination of ionic conductivities and binary diffusion coefficients to two commonly used electrolyte systems (EC:DMC (1:1 w:w) and EC:EMC (3:7 w:w)) as well as to one EC-free electrolyte (EMC:FEC (19:1 w:w)). To quantify transference numbers and thermodynamic factors, we introduce a novel analysis scheme, so that we are ultimately able to report temperature (−10°C–+50°C) and concentration (0.1 M–3.0 M) dependent values as well as approximate relationships for transport and thermodynamic properties required for numerical battery models. Comparison with scarcely available literature data highlights that the hitherto reported concentration and temperature dependencies do not reflect the complexity of ionic transport properties, which will likely lead to imprecise predictions of, e.g., a lithium-ion battery's power limitations or the onset of lithium plating.

Cross second virial coefficient and dilute gas transport properties of the (H2O + CO2) system from first-principles calculations

The cross second virial coefficient and three dilute gas transport properties (shear viscosity, thermal conductivity, and binary diffusion coefficient) of mixtures of water (H2O) and carbon dioxide (CO2) were calculated with high accuracy for temperatures up to 2000 K using statistical thermodynamics and the kinetic theory of molecular gases, respectively. The required intermolecular potential energy surface (PES) for the H2O–CO2 interaction is presented in this work, while the like-species interactions were modeled using PESs from the literature. All three PESs are based on high-level quantum-chemical ab initio computations. The predicted values for the cross second virial coefficient are in satisfying agreement with the best experimental data. In the case of the transport properties, the calculated values should be more accurate than the few available data sets.

Coupled diffusion in aqueous citric acid + calcium citrate solutions

Taylor dispersion is used to measure ternary mutual diffusion in aqueous citric acid(1) + calcium citrate(2) solutions at 25 °C. Main diffusion coefficients D11 and D22 reach values 25% to 60% larger than the respective binary diffusion coefficients of aqueous citric acid and calcium citrate. Of additional interest, cross-coefficient D12 is large and negative, indicating that each mole of diffusing calcium citrate counter-transports up to two moles of citric acid. Nernst-Planck (NP) equations are used to relate the fluxes of the citric acid and calcium citrate components to the fluxes of the solution species: molecular citric acid (H3Cit) and its dissociation products (H+, H2Cit−, HCit2− and Cit3− ions), Ca2+ ions, and calcium complexes produced by ion association (CaCit−, CaHCit, CaH2Cit+). The NP analysis identifies key roles in the coupled diffusion of citric acid and calcium citrate played by ion association and by ion migration in the electric field generated by hydrogen-ion concentration gradients.

Measuring effective diffusivity in porous media with a gasket-free, radial arrangement

A simple technique for measuring the effective diffusivity, and ultimately tortuosity, in porous media is presented. The method uses a custom-built apparatus, based on a radial geometry, which eliminates the need for any gaskets to seal the edge of the sample. This makes it particularly well suited for thin media such as films and layers. The experiment is based on the transient response of the oxygen concentration at the center of the sample as oxygen diffuses into an initially nitrogen filled domain from the sample perimeter. The analytical solution of Fick’s law for transient diffusion in cylindrical coordinates is fitted to the measured oxygen concentration profile to obtain the effective diffusivity. To validate the method, binary diffusion coefficients of N2-Air system were measured and the results show a close match and are consistent for a range of experimental parameters like flow rate and domain thickness. The classical study of diffusion in porous media based on sphere packing is revisited for further validation of the technique. The results show good agreement to the well-known Bruggeman correlation as well as to the experimental values reported in the literature. The new technique is further applied to other types of thin porous materials and the results indicate that the Bruggeman correlation generally underestimates the effective diffusivity of non-sphere packing.

Roles of CO2 and H2O in premixed turbulent oxy-fuel combustion

A series of Two-Dimensional Direct Numerical Simulation (2-D DNS) cases are performed to investigate the effects of CO2 and H2O on premixed turbulent oxy-fuel combustion (case oxy-H2O, case oxy-CO2) in a constant vessel. A DNS solver for low Mach reacting flow is developed based on open source code OpenFOAM. The chemical effects of CO2 and H2O are isolated by a pair of artificial species. 2-D DNS results shows the flame surface of oxy-CO2 case trends to be wrinkled with small convex and concave structures due to a lower laminar flame speed and a smaller effective Lewis number. Moreover, the response of flame surface to the curvature is different with corresponding dilute agent. Owing to the high binary diffusion coefficient between H2O and H, the negative curvature effect on fast diffusing species, e.g. H and H2, are enhanced in oxy-H2O, and results in a higher burning velocity. The effects of CO2 on H transport are contrary to the effects of H2O and the oxidation process is slowed due to the elementary reaction CO2 + H ⇔ CO + OH, which result in a more uniform Heat Release Rate (HRR) distribution on flame surface. In addition, chemical reaction pathway analysis is performed to elucidate the chemical effects of CO2 and H2O. It is found that CO2 and H2O will cool down the temperature of burnt region compared with N2. Finally, an alternative solution is raised to counteract the negative effect of CO2 on flame speed, which should be useful in the development and design of oxy-fuel combustion.

Thermophysical Properties of Gaseous H2S–N2 Mixtures from First-Principles Calculations

Abstract The cross second virial coefficient and three dilute gas transport properties (shear viscosity, thermal conductivity, and binary diffusion coefficient) of mixtures of hydrogen sulfide (H2S) and nitrogen (N2) were determined with high accuracy at temperatures up to 1200 K using statistical thermodynamics and the kinetic theory of molecular gases, respectively. The required intermolecular potential energy surface (PES) for the H2S–N2 interaction is presented in this work, while the H2S–H2S and N2–N2 PESs were reported previously. All three PESs are based on high-level quantum-chemical ab initio (i.e. first-principles) calculations. There is only very limited experimental information available on the second virial coefficients of H2S–N2 mixtures, and there appear to be no experimental data at all for the transport properties. Thus, the present predictions constitute a substantial increase in our knowledge of the thermophysical properties of this system, which are of practical relevance for modeling sour natural gas.

A shrinking core model for Nannochloropsis salina oil extraction using subcritical water

In this study, subcritical water extraction (SCWE) was used for dynamic extraction of crude oil of Nannochloropsis salina. The effect of three parameters including water temperature, flow rate and sample loading on the extraction efficiency was investigated and the whole process was simulated by using a two-phase mathematical model. Water temperature, flow rate and sample loading were varied from 150 to 200 °C, from 1 to 4 mL/min and from 1 to 4 g, respectively. The best operating conditions were selected to be 175 °C, 4 mL/min and 1 g and at those conditions, the fatty acids profile was compared with the Folch method. Because of the nature of the biomass and small particle sizes of the cells, a mathematical model based on the shrinking core model (SCM) was developed to evaluate the behavior of the extraction process. Kinetic parameters of the model incl. external film mass transfer coefficient (kf), solute-solvent binary diffusion coefficient (D12), axial dispersion coefficient (Dax) and effective diffusivity (De) in solid particle were determined. The later one was selected as the tuning parameter of the model and the others were attained from available correlations. The model predictions were in good agreement with experimental data.

Impact of non-ideal transport modeling on supercritical flow simulation

The simulation of a supercritical fluid flow requires sophisticated models for real gas thermodynamic and non-ideal phenomena. They both are presently addressed through the simulation of a non-reacting and reacting high pressure H2/O2 splitter-plate configuration. In particular, the diffusion velocity of species is evaluated through the gradient of chemical potential (dlNI=Xl(∇μl)T) expressed with the Peng–Robinson equation of state, or with the classical low-pressure approach dlI=∇Xl, which only uses the gradient of the lth species molar fraction, Xl. In addition, the high pressure binary diffusion coefficients are estimated by the correction of Kurochkin et al. or with the Takahashi approach. The results for the non-reaction case are consistent with the literature for mean and rms values using dlI. The use of dlNI has a limited impact but the temperature profiles become steeper. In the reactive case, the two approaches lead to a difference of 50 K on the average temperature just downstream of the injector and about 100 K further downstream. A non-ideal transport is then required for the modeling of supercritical flow simulation.

Ab initio intermolecular potential energy surface for the CO2-N2 system and related thermophysical properties.

A four-dimensional potential energy surface (PES) for the interaction between a rigid carbon dioxide molecule and a rigid nitrogen molecule was constructed based on quantum-chemical ab initio calculations up to the coupled-cluster level with single, double, and perturbative triple excitations. Interaction energies for a total of 1893 points on the PES were calculated using the counterpoise-corrected supermolecular approach and basis sets of up to quintuple-zeta quality with bond functions. The interaction energies were extrapolated to the complete basis set limit, and an analytical site-site potential function with seven sites for carbon dioxide and five sites for nitrogen was fitted to the interaction energies. The CO2-N2 cross second virial coefficient as well as the dilute gas shear viscosity, thermal conductivity, and binary diffusion coefficient of CO2-N2 mixtures were calculated for temperatures up to 2000 K to validate the PES and to provide reliable reference values for these important properties. The calculated values are in very good agreement with the best experimental data.

Transport properties of methane, ethane, propane, and n-butane in water

In this work, we have estimated self diffusion coefficients along with the binary diffusion coefficients of mixtures of alkane (methane, ethane, propane and n-butane) in SPC/E water(H2O). Molecular dynamics study of a binary mixture of alkane gas and SPC/E water, with alkane as solute and water as solvent, have been carried out at different temperatures ranging from 283.15 K to 333.15 K. We have taken a dilute solution of 3 alkane (methane, ethane, propane and n-butane) molecules and 971 water molecules in a system. The role of interaction in the structure of the constituents of the system as a function of temperature is studied with the help of the radial distribution function (RDF) and the coordination numbers. The self-diffusion coefficient of the constituents of the mixture was calculated by using mean square displacement (MSD) and the binary diffusion coefficients of alkane in water have been calculated by using Darken’s relation. The results are then compared with the available experimental values. The values of self-diffusion coefficients of water from the present work come in good agreement with the experimental values within 9% error. The binary diffusion coefficients of ethane, methane, propane and n-butane lie in between the previous experimental values performed by Wise and Houghton, and Witherspoon and D. N. Saraf. The estimated values lie within 30% error to each of the previously reported experimental values. The dependence of the diffusion coefficients on temperature is approximated by Arrhenius-type exponential relationship.

On the relaxation of the Maxwell–Stefan system to linear diffusion

In this note, we rigorously prove the relaxation limit of the Maxwell–Stefan system to a system of heat equations when all binary diffusion coefficients tend to the same positive value.

Finite-Size Effects of Binary Mutual Diffusion Coefficients from Molecular Dynamics.

Molecular dynamics simulations were performed for the prediction of the finite-size effects of Maxwell-Stefan diffusion coefficients of molecular mixtures and a wide variety of binary Lennard–Jones systems. A strong dependency of computed diffusivities on the system size was observed. Computed diffusivities were found to increase with the number of molecules. We propose a correction for the extrapolation of Maxwell–Stefan diffusion coefficients to the thermodynamic limit, based on the study by Yeh and Hummer (J. Phys. Chem. B, 2004, 108, 15873−15879). The proposed correction is a function of the viscosity of the system, the size of the simulation box, and the thermodynamic factor, which is a measure for the nonideality of the mixture. Verification is carried out for more than 200 distinct binary Lennard–Jones systems, as well as 9 binary systems of methanol, water, ethanol, acetone, methylamine, and carbon tetrachloride. Significant deviations between finite-size Maxwell–Stefan diffusivities and the corresponding diffusivities at the thermodynamic limit were found for mixtures close to demixing. In these cases, the finite-size correction can be even larger than the simulated (finite-size) Maxwell–Stefan diffusivity. Our results show that considering these finite-size effects is crucial and that the suggested correction allows for reliable computations.

Diffusion in ternary aqueous {L-dopa + (NaSO3) -β-cyclodextrin} solutions using the pseudo-binary approximation

Mass transport in (drug + cyclodextrin) solutions is investigated by using Taylor dispersion technique, monitored by differential refractometry, to measure ternary mutual diffusion in aqueous solutions of {L-dopa + (NaSO3)n-β-CD} (the sodium salt of sulfated β-cyclodextrin). The values of the binary mutual diffusion coefficients of both aqueous L-dopa and aqueous (NaSO3)n-β-CD solutions are close to each other differing only by a few per cent units. As a result, the eigenvalues for the matrix of the ternary Dik diffusion coefficients for aqueous {L-dopa(1) + (NaSO3)n-β-CD(2)} solutions are nearly identical, and the numerical analysis of the Taylor dispersion data may be ill-conditioned in view of the unreliable data obtained from their analysis. To overcome these difficulties, the pseudo-binary diffusion approximation is used to evaluate in a simple way this ternary system. The pseudo-binary diffusion coefficient values found, Dp1 and Dp2, are very close to the binary diffusion ones, being the cross-coefficients approached zero, within the experimental error. From the obtained results, and under the circumstances of this study, we may deduct that no interaction between L-dopa and NaSO3ßCD was determined.

Thermophysical properties of binary mixtures containing oxygen and noble gases

This work deals with the determination of reliable transport and equilibrium thermophysical properties of binary mixtures of O2 and the noble gases Ar, Kr, and Xe. The second virial coefficients B(T), the viscosities η(T), and the binary diffusion coefficients D12(T) were calculated for each mixture in the temperature range between 200 K and 1000 K using a a temperature dependent (n-6) Lennard-Jones intermolecular interaction potential model. The properties of the mixtures were obtained by using the Lorentz-Berthelot and Hohm-Zarkova-Damyanova mixing rules. Our results were compared to other theoretical and experimental data and acceptable agreement was found in all cases. Fitting formulae for the calculation of the intermolecular potential parameters and equilibrium and transport properties of the examined mixtures are recommended proposed.

Predicting the Kinetics of Ice Recrystallization in Aqueous Sugar Solutions.

The quality of stored frozen products such as foods and biomaterials generally degrades in time due to the growth of large ice crystals by recrystallization. While there is ample experimental evidence that recrystallization within such products (or model systems thereof) is often dominated by diffusion-limited Ostwald ripening, the application of Ostwald-ripening theories to predict measured recrystallization rates has only met with limited success. For a model system of polycrystalline ice within an aqueous solution of sugars, we here show recrystallization rates can be predicted on the basis of Ostwald ripening theory, provided (1) the theory accounts for the fact the solution can be nonideal, nondilute and of different density than the crystals, (2) the effect of ice-phase volume fraction on the diffusional flux of water between crystals is accurately described, and (3) all relevant material properties (involving binary Fick diffusion coefficients, the thermodynamic factor of the solution, and the surface energy of ice) are carefully estimated. To enable calculation of material properties, we derive an alternative formulation of Ostwald ripening in terms of the Maxwell–Stefan instead of the Fick approach to diffusion. First, this leads to a cancellation of the thermodynamic factor (a measure for the nonideality of a solution), which is a notoriously difficult property to obtain. Second, we show that Maxwell–Stefan diffusion coefficients can to a reasonable approximation be related to self-diffusion coefficients, which are relatively easy to measure or predict in comparison to Fick diffusion coefficients. Our approach is validated for a binary system of water and sucrose, for which we show predicted recrystallization rates of ice compare well to experimental results, with relative deviations of at most a factor of 2.

Numerical Investigation of AdBlue Droplet Evaporation and Thermal Decomposition in the Context of NOx-SCR Using a Multi-Component Evaporation Model

To cope with the progressive tightening of the emission regulations, gasoline and diesel engines will continuously require highly improved exhaust after-treatment systems. In the case of diesel engines, the selective catalytic reduction (SCR) appears as one of the widely adopted technologies to reduce NOx (nitrogen oxides) emissions. Thereby, with the help of available heat from exhaust gas, the injected urea–water solution (UWS) turns inside the exhaust port immediately into gaseous ammonia (NH3) by evaporation of mixture and thermal decomposition of urea. The reaction and conversion efficiency mostly depend upon the evaporation and subsequent mixing of the NH3 into the exhaust gas, which in turn depends upon the engine loading conditions. Up to now, the aggregation of urea after evaporation of water and during the thermal decomposition of urea is not clearly understood. Hence, various scenarios for the urea depletion in the gaseous phase that can be envisaged have to be appraised under SCR operating conditions relying on an appropriate evaporation description. The objective of the present paper is therefore fourfold. First, a reliable multi-component evaporation model that includes a proper binary diffusion coefficient is developed for the first time in the Euler–Lagrangian CFD (computational fluid dynamics) framework to account properly for the distinct evaporation regimes of adBlue droplets under various operating conditions. Second, this model is extended for thermal decomposition of urea in the gaseous phase, where, depending on how the heat of thermal decomposition of urea is provided, different scenarios are considered. Third, since the evaporation model at and around the droplet surface is based on a gas film approach, how the material properties are evaluated in the film influences the process results is reported, also for the first time. Finally, the impact of various ambient temperatures on the adBlue droplet depletion characteristics as well as the effect of gravity is pointed out. The prediction capability of the model variants is assessed by comparing the achieved results to each other and with experimental data. It turns out that satisfactory agreement between experiment and numerical predictions is achieved for a wide range of operating temperatures by using correlations by “Wilke and Lee” for urea and by “Fuller et al.” for water. The results are essentially sensitive to gravity. From subsequent comparisons of different ways to account for the thermal decomposition in the gaseous urea, a significant difference is observed. Finally, the 1/3 film rule widely used for evaluating the material properties in the film shows accurate prediction of both evaporation and thermal decomposition regimes of urea.

Cross Second Virial Coefficients and Dilute Gas Transport Properties of the (CH4 + C3H8) and (CO2 + C3H8) Systems from Accurate Intermolecular Potential Energy Surfaces

Accurate values for the cross second virial coefficients and dilute gas shear viscosities, thermal conductivities, and binary diffusion coefficients of the (CH4 + C3H8) and (CO2 + C3H8) systems were determined at temperatures from (150 to 1200) K using state-of-the-art computational approaches. The cross second virial coefficients were calculated semiclassically using the Mayer-sampling Monte Carlo method, while the transport properties were computed by means of the classical trajectory approach in conjunction with the kinetic theory of molecular gases. The required intermolecular potential energy surfaces (PESs) for the CH4–C3H8 and CO2–C3H8 interactions are reported in this work, whereas those for the CH4–CH4, CO2–CO2, and C3H8–C3H8 interactions were taken from our previous work on the pure gases. All PESs are based on high-level quantum-chemical ab initio calculations and were fine-tuned to the best experimental data for the second virial and cross second virial coefficients. Overall, the agreement of ...