Diffusion Foundations Vol. 27

Abstract: The discrete Frenkel-Kontorova model for the movement of a foreign atom in a solid, obtained in the local chains approximation, led to the movement of the atom in the Frenkel-Kontorova (F-K) soliton form. This model made it possible to reveal the structure of the F-K soliton, to design the shapes of nanostructures and to take into account their influence on the F-K soliton. The transition to field variables leads the Frenkel-Kontorova equation to the sine-Gordon equation for the displacement field of an atom having solutions also in the form of a soliton. This equation and its solution (soliton) contains coefficients depending on the shape and size of nanostructures. The transition to the sine-Gordon equation allowed us to use the results of Theodorakopoulos 's works related to the consideration of the interaction of elastic vibration modes with a soliton. This made it possible to calculate the diffusion coefficient of the soliton and find the dependence of the diffusion coefficient on the shape and size of nanostructures and temperature.

Abstract: Our research group is currently investigating a new kind of thermal desorption experiment (TDE), which uses a hydrogen isotope by loading-unloading process yielding transport parameters. Safety issues are limiting the hydrogen loading content to 3 % at 10⁵ Pa, while former experiments are using pure hydrogen for the loading process at nearly same pressure e. g. [1]. Especially the thermal elongation coefficient (TDE operating conditions 300° to 500 °C compatibility to stainless steel) forces to think about an alternative material of boron silicate glass for specimen containment, in this paper copper will be discussed. The analysis of TDE concerns the amount of hydrogen stored in the specimen, stored in the time variable gas phase as well as stored in the containment material. These three phases are coupled by phase equilibrium. The here developed analysis procedure can currently only be performed numerically for a two dimensional geometry. However a two dimensional analytical solution regarding the same boundary condition is currently under investigation. One part of the solution results of this problem can be compared to an additional analytical solution with simpler boundary conditions, e.g. a vanishing hydrogen amount inside the specimen containment observed in steady state. The numerical results will be used to check the suitability of several experimental scenarios, for example the usability of a copper based specimen containment. The approach currently practiced in many experiments is to simply subtract the zero rate of hydrogen without considering the phase equilibrium between the three mentioned phases. The main goal of this analysis procedure consists in the solution of the inverse problem, namely the extraction of the transport parameters like Sieverts ́-and diffusion-constant from a measured time dependent desorption pressure increase.

Abstract: Understanding scaling of enhanced oil/bitumen recovery processes is essential in moving laboratory scale experimental results to field scale. Scaling theory for thermal processes is well understood and has been applied to steam processes. However, scaling of hybrid steam (thermal) /solvent (mass transfer) processes is still not well defined nor well understood. This paper investigates the scaling behavior of hybrid steam/butane gravity drainage processes using reservoir simulation (commercial thermal compositional simulator CMG STARSTM). Previous research has used reservoir simulation to confirm scaling groups for waterflooding. A similar strategy was used in this study whereby the scaling of a hybrid (steam) solvent oil recovery process was examined using reservoir simulations at three different reservoir scales: lab scale, semi-field scale and field scale to examine the influence of the mass transfer mechanisms of diffusion and dispersion on the scalability of the process. In particular, the influence of butane solvent concentration on scaling a steam/butane gravity drainage process was investigated by considering several butane mole fraction concentrations injected with steam (1%, 2%, 5%, 7%, 10%, 15%, 21%, 25% and 50%). Temperature contours, and mole fraction contours of butane in both the oil and gas phases were examined for various solvent injection concentrations to examine scalability. Numerical results are provided with no diffusion and dispersion, diffusion only, dispersion only and with both diffusion and dispersion added to the simulations. Results confirmed scalability of the process with no capillary effects when the simulation results were non-dimensionalized, although there were some issues with material balance errors in some of the simulation results particularly at high solvent concentrations. For low injection concentrations, the contours were almost identical (indicating scalability) for the three scales for the operating condition studied. In addition, capillary effects were also studied, and similar to scaling thermal processes, the capillarity effects influenced scalability of the process under the conditions studied particularly at higher injection concentrations. Scalability using reservoir simulation was generally preserved with low injection concentrations, but unusual behavior was observed at higher injection concentrations (>5%). Oil recovery curves were non-dimensionalized to make comparisons amongst the three scales. The oil recovery curves displayed an unusual S-shaped behavior at higher injection concentrations when capillary effects were included especially for the lab and semi-field scales. In all cases when all of the mechanisms are included (diffusion, dispersion and capillary effects), Scale 1 shows a much faster recovery than Scale 3 which suggests that the lab scale might temporally overestimate the field scale recovery for this particular process scenario.

Abstract: We are focused to the numerical modelling of heat, contaminant and water transport in unsaturated porous media in 3D. The heat exchange between water and porous media matrix is taken into the account. The determination of heat energy transmission coefficient and matrix heat conductivity is solved by means of inverse problem methods. The mathematical model represents the conservation of heat, contaminant and water mass balance. It is expressed by coupled non-linear system of parabolic-elliptic equations. Mathematical model for water transport in unsaturated porous media is represented by Richard's type equation. Heat transport by water includes water flux, molecular diffusion and dispersion. A successful experiment scenario is suggested to determine the required parameters including heat transmission and matrix heat conductivity coefficients. Additionally we investigate contaminant transport with heat transmission and contaminant adsorption. The obtained experiments support our method suitable for solution of direct and inverse problems. This problem we have discussed previously in 1D model, but preferential streamlines in 1D thin tubes shadow accurate results in determination of required parameters. In our presented setting we consider a cylindrical sample which is suitable in laboratory experiments for inverse problems.

Abstract: The wide range of industrial applications is the main reason for an increased interest in dioxides such as HfO₂. In this study, classical molecular dynamic simulations were performed to calculate the lattice thermal conductivity of the cubic phase of HfO₂, over a temperature range of 100-3000 K, based on the Green-Kubo fluctuation method. In this research, the heat current autocorrelation function and lattice thermal conductivity were calculated in the a-direction. The lattice thermal conductivity of the cubic phase of HfO₂ was found to be a result of three contributions. These were the optical and acoustic short-range and long-range phonon modes. Comparisons between the results of the research and experimental data when available indicate good agreement. Keywords: lattice thermal conductivity, molecular dynamics, Green-Kubo formalism, heat current autocorrelation function, hafnium dioxid

Abstract: Following nuclear decay, a daughter atom in a solid will "stay in place" if the recoil energy is less than the threshold for displacement. At high temperature, it may subsequently undergo long-range diffusion or some other kind of atomic motion. In this paper, motion of ¹¹¹Cd tracer probe atoms is reconsidered following electron-capture decay of ¹¹¹In in the series of In₃R phases (R= rare-earth). The motion produces nuclear relaxation that was measured using the method of perturbed angular correlation. Previous measurements along the entire series of In₃R phases appeared to show a crossover between two diffusional regimes. While relaxation for R= Lu-Tb is consistent with a simple vacancy diffusion mechanism, relaxation for R= Nd-La is not. More recent measurements in Pd₃R phases demonstrate that the site-preference of the parent In-probe changes along the series and suggests that the same behavior occurs for daughter Cd-probes. The anomalous motion observed for R= Nd-La is attributed to "lanthanide expansion" occurring towards La end-member phases. For In₃La, the Cd-tracer is found to jump away from its original location on the In-sublattice in an extremely short time, of order 0.5 ns at 1000 K and 1.2 ms at room temperature, a residence time too short to be consistent with defect-mediated diffusion. Several scenarios that can explain the relaxation are presented based on the hypothesis that daughter Cd-probes first jump to neighboring interstitial sites and then are either trapped and immobilized, undergo long-range diffusion, or persist in a localized motion in a cage.