Fickian Diffusion Coefficients Research Articles

On the structure of continuum thermodynamical diffusion fluxes—A novel closure scheme and its relation to the Maxwell–Stefan and the Fick–Onsager approach

This paper revisits the modeling of multicomponent diffusion within the framework of thermodynamics of irreversible processes. We briefly review the two well-known main approaches, leading to the generalized Fick–Onsager multicomponent diffusion fluxes or to the generalized Maxwell–Stefan equations. The latter approach has the advantage that the resulting fluxes are consistent with non-negativity of the partial mass densities for non-singular and non-degenerate Maxwell–Stefan diffusivities. On the other hand, this approach requires computationally expensive matrix inversions since the fluxes are only implicitly given. We propose and discuss a novel and more direct closure which avoids the inversion of the Maxwell–Stefan equations. It is shown that all three closures are actually equivalent under the natural requirement of positivity for the concentrations, thus revealing the general structure of continuum thermodynamical diffusion fluxes. As a special case, the new closure also gives rise to a core-diagonal diffusion model in which only those cross-effects are present that are necessary to guarantee consistency with total mass conservation, plus a compositional dependence of the diffusivity. This core-diagonal closure turns out to provide a rigorous fundament for recent extensions of the Darken equation from binary mixtures to the general multicomponent case. As an outcome of our investigation, we also address different questions related to the sign of multicomponent thermodynamic or Fickian diffusion coefficients. We show rigorously that, in general, the second law requires positivity properties for tensors and operators rather than for scalar diffusivities.

Diffusivities in Binary Mixtures of Cyclohexane or Ethyl Butanoate with Dissolved CH4 or R143a Close to Infinite Dilution

This work is part of a series of studies focusing on binary mixtures consisting of a liquid with a dissolved gas close to infinite dilution. A particular focus is on the study of the influence of molecular characteristics on mutual or self-diffusivity. Heterodyne dynamic light scattering (DLS) experiments and equilibrium molecular dynamics (EMD) simulations are applied to determine the Fick diffusion coefficient D11 and the self-diffusion coefficient of the gas solute in the mixture Dself,1. Often, the latter is referred to in the literature as the intradiffusion coefficient, which is equal to D11 in the limit of infinite dilution. Both DLS and EMD simulations are applied in macroscopic thermodynamic equilibrium at or close to saturation conditions. In the present study, mixtures of methane (CH4) or the refrigerant 1,1,1-trifluoroethane (R143a) dissolved in cyclohexane or ethyl butanoate are investigated at temperatures T between 303 and 423 K. The average expanded experimental uncertainty (coverage factor k = 2) of D11 from DLS experiments is 10%, and the average expanded statistical uncertainty (k = 2) of Dself,1 from EMD simulations is 6.4%. Unexpectedly, D11 in mixtures of CH4 dissolved in cyclohexane or ethyl butanoate essentially matches within uncertainties at a given T, and mixtures of cyclohexane with R143a show smaller D11 values in comparison to ethyl butanoate with R143a.

Hyperhydration of Cancers: A Characteristic Biophysical Trait Strongly Increasing O2, CO2, Glucose and Lactate Diffusivities, and Improving Thermophysical Properties of Solid Malignancies.

Cancers are complex, heterogeneous, dynamic and aggressive diseases exhibiting a series of characteristic biophysical traits which complement the original biological hallmarks of cancers favouring progressive growth, metastasis, and contributing to immune evasion and treatment resistance. One of the prevalent differences between most solid tumors and their corresponding, healthy tissues is a significantly higher water content (hyperhydration) in cancers. As a consequence, cancers have distinctly higher (Fick's) diffusion coefficients D [cm2s-1] for the respiratory gases O2 and CO2, the key substrate glucose, and for the oncometabolite lactate. In addition, cancers have (a) clearly increased specific heat capacities cp [Jg-1K-1], thus representing high-capacity-tissues upon therapeutic heating induced by electromagnetic irradiation, and (b) higher thermal conductivities k [Wm-1K-1], i.e., increased abilities to conduct heat. Therefore, in diffusion analyses (e.g., when describing critical O2 and glucose supplies or CO2 removal, and the development of hypoxic subvolumes) and for modeling temperature distributions in hyperthermia treatment planning, these specific cancer-related data must be considered in order to reliably reflect oncologic thermo-radiotherapy settings.

Response of Soil Respiration Rates to Soil Temperature and Moisture at Different Soil Depths of Caragana korshinskii Plantation in the Loess-Hilly Region

It is of great significance to clarify the influence of soil temperature and moisture on soil respiration rate and its characteristics in ecologically fragile regions under the background of climate change for the accurate assessment and prediction of carbon budgets in this region. The average CO2 concentration and soil temperature and moisture at different soil depths (10, 50, and 100 cm) were measured using a CO2 analyzer and temperature and moisture sensors. The soil respiration rate was calculated using Fick's first diffusion coefficient method. The dynamic characteristics of soil temperature, soil moisture, and soil respiration rate in different soil depths were explored, and the response of soil respiration rate to soil temperature and moisture were further analyzed. The results showed that the diurnal variation in soil respiration rate decreased significantly with the increase in soil depth (P<0.05), and the peak time lagged behind. Soil respiration rate in adjacent soil depths (10, 50, and 100 cm) lagged 1 h from top to bottom. The monthly variation in soil respiration rate was a multi-peak curve, in which the maximum soil respiration rates of 10, 50, and 100 cm soil depths were on July 25th, August 6th, and August 10th, reaching 13.96, 2.96, and 1.47 μmol·(m2·s)-1, respectively. The effect of soil temperature on soil respiration rate decreased with the increase in soil depth. Soil temperature at 50 cm and below had no significant effect on soil respiration rate (P>0.05). The fitting index of 10 cm soil depth was the best (R2=0.96), but the fitting indexes of 50 cm and 100 cm soil depths were poor (R2=0.00 and R2=0.01, respectively). The temperature sensitivity coefficient Q10 decreased with the increase in soil depth. Soil moisture in different soil depths had significant effects on soil respiration rate (P<0.05), and the quadratic fitting indicated that 50 cm (R2=0.35)>10 cm (R2=0.22)>100 cm (R2=0.31). The combined effects of soil temperature and moisture in different soil depths could explain 96%, 6%-50%, and 22%-24% of soil respiration rate, respectively. In summary, the effects of soil temperature and moisture at different soil depths of the Caragana korshinskii plantation in the loess-hilly region on soil respiration rate differed. The soil respiration rate of the 10 cm soil depth was affected by the comprehensive effect of soil temperature and moisture; however, the relative contribution of soil temperature was higher, and soil moisture at and below a soil depth of 50 cm was the key factor. These results could help improve predictions on the impact of future climate change on the carbon cycle of terrestrial ecosystems in the region and provide a theoretical basis for greenhouse gas regulation in the future.

An improved method for measuring the concentration dependence of Fick diffusion coefficient based on Boltzmann equation and cylindrical liquid-core lenses

Liquid diffusion coefficient that depends on solution concentration (D(C))11D(C): Liquid diffusion coefficient that depends on solution concentration is an important basic data for calculating mass transfer rate and studying mass transfer process. To measure the D(C) of glucose aqueous solution, the spatial and temporal profiles of the experimental concentration (Cexpt(x,t)s)22Cexpt(x,t)s: Spatial and temporal profiles of the experimental concentration during diffusion process have been measured on the base of a combination liquid-core cylindrical lens. In theoretical analysis aspect, based on the analytical method proposed by Hall and the graphic method adopted by Matano and Sauer-Freise et al., Boltzmann-Matano (BM)33BM: Boltzmann-Matano semi-analytical method is proposed and used to solve the D(C) equation, the D(C) of glucose aqueous solution is calculated with the obtained Cexpt(x,t)s. In addition, using the Finite-Difference Time-Domain (FDTD)44FDTD: Finite-Difference Time-Domain method, the distribution functions of diffusion concentration (CFDTD(x,t)s)55CFDTD(x,t)s: Concentration profile calculated by FDTD method under different D(C) correlations are calculated and compared with the Cexpt(x,t)s. The results indicate that the BM semi-analytical method can be used to correctly measure the liquid diffusion coefficient, which has the advantages such as stable and reliable measurement results, high precision, fast speed, and it can avoid the error caused by determining the “Matano” plane. The profile calculated by FDTD method provides an effective verification for the correctness of the measured D(C) as comparing with the experimental profile.

Transport properties of binary Lennard-Jones mixtures: Insights from entropy scaling and conformal solution theory

The relation of transport properties and the molecular interactions in binary mixtures was studied. The self-diffusion coefficient, Maxwell–Stefan as well as Fickian mutual diffusion coefficient, shear viscosity, and thermal conductivity of liquid binary simple mixtures were therefore sampled using molecular dynamics simulations. The mixtures were described by the Lennard-Jones potential. The molecular interaction parameters were chosen such that a large variety of mixture behavior was covered. The two components had the same size parameter in all cases, but different dispersion energies. Moreover, the cross-interaction parameter used in the modified Lorentz-Berthelot combination rule was varied such that the resulting mixtures showed different types of phase behavior: ideal, high- and low-boiling azeotrope. The results are discussed using conformal solution theory as a link between the molecular interactions in the mixtures and the macroscopic properties. Moreover, the applicability of Rosenfeld’s entropy scaling is tested. Despite the important differences of the studied mixtures regarding their molecular interactions and the large pressure, temperature, and composition range considered, a practically monovariate relation of these properties with respect to the configurational entropy is observed. Yet, the quality of the approximation differs for the studied properties.

Water Sorption in Glassy Polyvinylpyrrolidone-Based Polymers.

Polyvinylpyrrolidone (PVP)-based polymers are excellent stabilizers for food supplements and pharmaceutical ingredients. However, they are highly hygroscopic. This study measured and modeled the water-sorption isotherms and water-sorption kinetics in thin PVP and PVP-co-vinyl acetate (PVPVA) films. The water sorption was measured at 25 °C from 0 to 0.9 RH, which comprised glassy and rubbery states of the polymer-water system. The sorption behavior of glassy polymers differs from that in the rubbery state. The perturbed-chain statistical associating fluid theory (PC-SAFT) accurately describes the water-sorption isotherms for rubbery polymers, whereas it was combined with the non-equilibrium thermodynamics of glassy polymers (NET-GP) approach to describe the water-sorption in the glassy polymers. Combined NET-GP and PC-SAFT modeling showed excellent agreement with the experimental data. Furthermore, the transitions between the PC-SAFT modeling with and without NET-GP were in reasonable agreement with the glass transition of the polymer-water systems. Furthermore, we obtained Fickian water diffusion coefficients in PVP and in PVPVA from the measured water-sorption kinetics over a broad range of humidities. Maxwell-Stefan and Fickian water diffusion coefficients yielded a non-monotonous water concentration dependency that could be described using the free-volume theory combined with PC-SAFT and NET-GP for calculating the free volume.

Controlled Drug Release of Smart Magnetic Self-Assembled Micelle, Kinetics and Transport Mechanisms

Magnetic nanocarriers have been extensively used as a potential drug release system for breast cancer therapy. This work investigates drug release kinetics and transport mechanisms of dasatinib (DAS) anticancer drugs encapsulated in nanomagnetic self-assembled micelles. The drug release kinetics of DAS from the nanomagnetic micelles (NMM) was predicted by fitting the drug release experimental data to four different empirical models at pH values 7.4 and 5. Moreover, a simple mathematical model that can predict the drug release from bulk eroding polymer matrices has been developed using the COMSOL Multiphysics® program. The diffusional egress of the DAS release through the NMM was carried out by evaluating the diffusion coefficients inside NMM using Fick's second law and diffusion coefficients in the solution utilizing the Stokes-Einstein equation. The results revealed that NMM exhibited a superior sustained drug release rate in acidic conditions compared to the neutral state. The Peppas-Sahlin and COMSOL models gave the best fitting for the experimental drug release data and eroding matrices obtained from free DAS, DAS-micelles, and DAS-magnetic micelles at both pH values with correlation coefficients reached to 0.99. The transport mechanisms results showed a Fickian diffusion mechanism controlled with the highest diffusion coefficients of NMM in acidic conditions, while a significant relaxation contribution was observed at the neutral state.

Measuring and Modeling Water Sorption in Amorphous Indomethacin and Ritonavir

The amorphous state of an active pharmaceutical ingredient (API) enhances its water solubility compared to its crystalline state. However, it is well known that amorphous substances can absorb significant amounts of water therewith inducing API recrystallization. This work explores methods to obtain reliable information about water sorption in amorphous APIs and its modeling. Experimental water-sorption curves over a broad humidity range were obtained by measuring the mass increase of well-defined films of amorphous APIs. Water-sorption isotherms modeled using perturbed-chain statistical associating fluid theory (PC-SAFT) showed better accordance with the experimental data than those obtained using the Flory-Huggins model. Crank's diffusion equation was used to describe the water-sorption kinetics providing Fickian diffusion coefficients of water in indomethacin and in ritonavir. Stefan-Maxwell diffusion coefficients were obtained by converting Fickian diffusion coefficients using water activity coefficients obtained from PC-SAFT. Finally, the free-volume theory was applied to explain the persistent water concentration dependency of the Stefan-Maxwell diffusion coefficients.

Gas sorption and diffusion in perfluoro(butenyl vinyl ether) based perfluoropolymeric membranes

Amorphous glassy perfluoropolymers are characterized by high fractional free volume and hydrocarbon phobicity which means that they perform at the upper bound for several gas pairs. In this study, the sorption of a range of pure gases in Cytop® and a CyclAFlorTM random copolymer of perfluoro(butenyl vinyl ether) (PBVE) and perfluoro(2,2-dimethyl-1,3-dioxole) (PDD) are studied for the first time at different temperatures. The Non-Equilibrium Lattice Fluid (NELF) model is used to model the sorption isotherms in Cytop®, after the determination of the Sanchez-Lacombe model parameters from literature data of the polymer volumetric behavior. The Dual Mode Sorption model is used to model the sorption isotherms in Poly(50%PBVE-co-50%PDD). These results and previously published permeability data are then used within a transport model to determine the diffusivity and activation energy of diffusion for a range of gases within these polymers. The CyclAFlor™ copolymer is shown to have a higher CO2 diffusivity than Cytop®, while maintaining comparable CO2/CH4 diffusivity selectivity. Molecular Dynamics (MD) simulations are performed as a comparison, to calculate the Fickian diffusion coefficients at 35 °C. The diffusion coefficients obtained from MD are consistent with those calculated by the transport model for He and H2 but deviate for larger penetrants (i.e. CO2 and CH4). The results confirm the superior performance of the CyclAFlor™ copolymer for gas separation applications, with greater CO2 solubility and diffusivity than comparable polymers.

Mutual diffusion coefficients of dimethyl carbonate + n-heptane and dimethyl carbonate + isooctane from 288.15 K to 318.15 K

The mutual diffusion coefficients of dimethyl carbonate + n-heptane and dimethyl carbonate + isooctane binary systems were measured at temperatures from 288.15 K to 318.15 K with the mass fraction of dimethyl carbonate from 0.05 to 0.95 under atmospheric pressure. All the mutual diffusion coefficients we reported are Fick diffusion coefficients, which were measured by the digital holographic interferometry. The expanded relative uncertainty for the measured mutual diffusion coefficients is estimated to 2.4% with the level of confidence of 0.95 (coverage factor k = 2). Moreover, a theoretical model (UNIDIF) of mutual diffusion coefficients for dimethyl carbonate + n-heptane and dimethyl carbonate + isooctane binary mixtures was given by fitting the experimental results, and the adjustable parameters and infinite dilution diffusion coefficients of these two solutions were given. The influences of temperature and composition on the mutual diffusion coefficients were discussed.

Fick and Maxwell-Stefan Diffusion Coefficients in the Ternary Liquid Mixture of Acetone-Methanol-Chloroform

Fick diffusion coefficients are calculated by means of molecular simulation for liquid mixtures containing acetone, methanol and chloroform at 1 atm and 298 K for different compositions. For this means, Maxwell-Stefan (MS) diffusion coefficients were calculated using physical properties of the components and thermodynamic factors, Γ, using three different models of Wilson, NRTL and UNIQUAC. Because of the lack of experimental data for Fick diffusivities for ternary system, the validity of the model was tested by comparing Fick diffusivities obtained for binary subsystems with experimental data for acetone- chloroform system. The results were in good agreement. So the Fick coefficients, Maxwell-Stefan diffusion coefficient and the thermodynamic factors were predicted for the ternary mixture as well as its binary subsystems by molecular simulation in a consistent manner. The presented ternary diffusion data should facilitate the development of aggregated predictive models for diffusion coefficients of polar and hydrogen-bonding systems and allows for an efficient and consistent prediction of multicomponent Fick diffusion coefficients from molecular models.

The Mathematics of Quasi-Diffusion Magnetic Resonance Imaging

Quasi-diffusion imaging (QDI) is a novel quantitative diffusion magnetic resonance imaging (dMRI) technique that enables high quality tissue microstructural imaging in a clinically feasible acquisition time. QDI is derived from a special case of the continuous time random walk (CTRW) model of diffusion dynamics and assumes water diffusion is locally Gaussian within tissue microstructure. By assuming a Gaussian scaling relationship between temporal (α) and spatial (β) fractional exponents, the dMRI signal attenuation is expressed according to a diffusion coefficient, D (in mm2 s−1), and a fractional exponent, α. Here we investigate the mathematical properties of the QDI signal and its interpretation within the quasi-diffusion model. Firstly, the QDI equation is derived and its power law behaviour described. Secondly, we derive a probability distribution of underlying Fickian diffusion coefficients via the inverse Laplace transform. We then describe the functional form of the quasi-diffusion propagator, and apply this to dMRI of the human brain to perform mean apparent propagator imaging. QDI is currently unique in tissue microstructural imaging as it provides a simple form for the inverse Laplace transform and diffusion propagator directly from its representation of the dMRI signal. This study shows the potential of QDI as a promising new model-based dMRI technique with significant scope for further development.

Fickian diffusion in CO2 injection: A two-phase compositional flow model with fully 3D unstructured gridding

We present numerical modeling of CO2 injection in lab and field scales using fully unstructured grids with Fickian diffusion. The focus is on CO2 injection because of its wide range of applications and environmental and economic benefits. We demonstrate predictions of experimental measurement results without tuning and/or adjustment of Fickian diffusion coefficients and flow parameters. The spatial and temporal discretization in the algorithm allows for accurate description of the physics of the flow. Unstructured gridding at the lab scale simulation increases accuracy of Fickian diffusion flux computations. In this work we also compare the efficiency and accuracy of our algorithm to two-point and multi-point flux approximations. A grid sensitivity analysis demonstrates low mesh dependency of the model.

Gases migration behavior of adsorption processes in coal particles: Density gradient model and its experimental validation

The injection of CO2 or N2 to displace CH4 in coal seams can improve coalbed methane (CBM) recovery. However, the migration pattern of these gases in the coal matrix is disputed as the Fick diffusion model is not fully applicable. In this work, the isothermal adsorption experiments of CO2, CH4 and N2 were first performed on four kinds of coal samples. A mathematical model of gas diffusive adsorption was then established based on a free gas density gradient (FGDG) drive, which was solved numerically by finite difference method (FDM). The microchannel diffusion coefficient (Dfg) that reflected the transport capacity of free gas in the coal matrix was determined through matching the simulation curves of cumulative gas adsorption with experimental data. Furthermore, the effects of gas type, coal rank and adsorption pressure on the microchannel diffusion coefficient were quantitatively investigated. The results show that (i) the simulation results of the gases are well consistent with the experimental data, indicating that the migration behavior of CO2, CH4 and N2 in coal particles conforms to the FGDG-driven model; (ii) the Dfg of CO2 is much higher than that of CH4 and N2, and the Dfg of a single gas shows an asymmetric U-shaped trend with the coal rank; (iii) compared with Fick's diffusion coefficient and Darcy's permeability coefficient, the Dfg is only related to the pore structure of the coal and gas properties, independent of the state parameters such as pressure and time. Therefore, the FGDG-driven model better explains the essence of gases migration behavior in the coal particles, and this model can be considered as an important aspect of CBM production calculation and prediction.

Diffusion in multicomponent aqueous alcoholic mixtures

The Fick diffusion coefficient matrix of the highly associating quaternary mixture water + methanol + ethanol + 2-propanol as well as its ternary and binary subsystems is analyzed with molecular dynamics simulation techniques. Three of the ternary subsystems are studied in this sense for the first time. The predictive capability of the employed force fields, which were sampled with the Green–Kubo formalism and Kirkwood–Buff integration, is confirmed by comparison with experimental literature data on vapor-liquid equilibrium, shear viscosity and Fick diffusion coefficient, wherever possible. A thorough analysis of the finite size effects on the simulative calculation of diffusion coefficients of multicomponent systems is carried out. Moreover, the dependence of the Fick diffusion coefficient matrix on the velocity reference frame and component order is analyzed. Their influence is found to be less significant for the main matrix elements, reaching a maximum variation of 19%. The large differences found for the cross elements upon variation of the reference frame hinder a straightforward interpretation of the Fick diffusion coefficient matrix with respect to the presence of diffusive coupling effects.

Fick Diffusion Coefficient in Binary Mixtures of [HMIM][NTf2] and Carbon Dioxide by Dynamic Light Scattering and Molecular Dynamics Simulations.

Dynamic light scattering (DLS) experiments and equilibrium molecular dynamics (EMD) simulations were performed in the saturated liquid phase of the binary mixture of 1-hexyl-3-methylimidazolium bis(trifluormethylsulfonyl)imide ([HMIM][NTf2]) and carbon dioxide (CO2) to access the Fick diffusion coefficient (D11). The investigations were performed within or close to saturation conditions at temperatures between (298.15 and 348.15) K and CO2 mole fractions (xCO2) up to 0.81. The DLS experiments were combined with polarization-difference Raman spectroscopy (PDRS) to simultaneously access the composition of the liquid phase. For the first time in an electrolyte-based system, D11 was directly calculated from EMD simulations by accessing the Maxwell-Stefan (MS) diffusion coefficient and the thermodynamic factor. Agreement within combined uncertainties was found between D11 from DLS and EMD simulations for CO2 mole fractions up to 0.5. In general, an increasing D11 with increasing xCO2 could be observed, with a local maximum present at a CO2 mole fraction of about 0.75. The local maximum could be explained by an increasing MS diffusion coefficient with increasing xCO2 over the entire studied composition range and a decreasing thermodynamic factor at xCO2 above 0.7. Finally, PDRS and EMD simulations were combined to investigate the influence of the fluid structure on the diffusive process.

Diffusivities in Binary Mixtures of n-Hexane or 1-Hexanol with Dissolved CH4, Ne, Kr, R143a, SF6, or R236fa Close to Infinite Dilution

This work is a continuation of previous studies focusing on the influence of intermolecular interactions on the diffusive mass transport in mixtures consisting of liquids with dissolved gases by determining the Fick diffusion coefficient of the mixtures or self-diffusion coefficient of the gas solutes. Dynamic light scattering, Raman spectroscopy, and molecular dynamics simulations are applied to study the interplay between the liquid structure and diffusive mass transport in binary mixtures consisting of methane, neon, krypton, sulfur hexafluoride, and the two refrigerants R143a and R236fa dissolved in n-hexane or 1-hexanol. Experiments and simulations were performed at the macroscopic thermodynamic equilibrium close to infinite dilution of the solute at temperatures between 303 and 423 K. The obtained Fick diffusion coefficients increase with increasing temperature and are always smaller in mixtures based on 1-hexanol compared to those of n-hexane. For both solvents, a decreasing molar mass of the solutes leads to increasing Fick diffusion coefficients with the exception of methane and neon showing the opposite behavior. Next to a general discussion and comparison with the literature, the present diffusivity data are compared with values predicted by a semiempirical model, which was previously developed to predict mass diffusivities in binary mixtures consisting of n-alkanes or 1-alcohols with dissolved gases close to infinite dilution.

Fick diffusion coefficients via molecular dynamics: An alternative approach in the Fourier domain

Mutual diffusion coefficient data are required for several systems of scientific and engineering interest to properly describe mass transport phenomena over a wide range of pressures, temperatures, and compositions. In this work, we calculated Fick diffusion coefficients for some CO2 and n-alkane mixtures at high pressures using a new method, which we derived by introducing modifications to the Fourier Correlation Method (FCM) originally proposed by Nichols and Wheeler [I&EC Research, 54, 12,156–12,164 (2015)]. The modified FCM (mFCM) results were validated through comparisons with experimental data and with Fick coefficients calculated by employing well-established Molecular Dynamics methodologies. The new approach has some interesting advantages, such as providing Fick coefficients for molecular systems directly through a single equilibrium calculation, in contrast to traditional methods in which an extra calculation is needed to obtain the so-called thermodynamic factor. It is shown that the new approach considerably reduces the finite-size effect of the simulation box on the calculated diffusion coefficients, which are thus obtained in the thermodynamic limit.

Non–isothermal two–phase hydrogen transport in rock salt during cycling in underground caverns

For a good management and precise tracks of hydrogen quantities stored in salt caverns, this paper presents a study on hydrogen transport in rock salt during cycling. It provides a novel mathematical–numerical model that couples the cavern thermodynamics with the transport mechanisms of hydrogen in the saturated rock salt in a fully coupled thermo–hydraulic framework. Both the two–phase Darcian percolation and the Fickian diffusion are used to account for hydrogen migration in the interstitial brine of the rock salt. Due to the absence of experimental data, a parametric study is furnished. The effect of cycling within the cavern on the migration mechanisms is discussed in detail. Simulations have confirmed the dependency of the Darcian percolation on the model parameters. However, for similar applications, this dependency might be limited. The value of the Fickian diffusion coefficient affects indirectly the Darcian percolation. The two–phase percolation becomes more of a piston–like for very small values of the diffusion coefficient. On a real–scale typical cavern, and over a period of 40 years, simulations have proven that the quantity of hydrogen lost into the surrounding rock salt is unimportant. Besides, cycling renders this quantity more insignificant.