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Item type:Publication, Access status: without files , A pore-scale resolved direct numerical simulation study for scaling analysis of the solutal convection in porous mediaUnderstanding the solutal convection is a crucial step towards accurate prediction of CO2 sequestration in deep saline aquifers. In this study, pore-scale resolved direct numerical simulations (DNS) are performed to analyse the scaling laws of the solutal convection in porous media. The porous media studied are composed of uniformly distributed square or circular elements. The Rayleigh numbers in the range 426 ≤ Ra ≤ 80 000, the Darcy numbers in the range 1.7 × 10−8 ≤ Da ≤ 8.8 × 10−6 and the Schmidt numbers in the range 250 ≤ Sc ≤ 104 are considered in the DNS. The main time, length and velocity scales affecting the solutal convection are classified as the diffusive scales (tI, lI and uI), the convective scales (tII, lII and uII) and the shut-down scales (tIII, lIII and uIII). These scales determine the pore-scale Rayleigh number RaK and the Rayleigh number Ra. Based on the DNS results, the scaling laws for the transient dissolution flux are proposed in the different regimes of convection. It is found that the onset time of convection (toc) and the period of the flux-growth regime (∆tfg) vary linearly with the convective time scale tII. The merging of the original plumes and the re-initiation of the new plumes start in the same period, resulting in the merging re-initiation regime. Horizontal dispersion plays an important role in plume merging. The dissolution flux F and the time since the onset of convection t∗ have an F/uII ∼ (t∗/tII)−0.2 scaling in the later stage of the merging re-initiation regime. This scaling is caused by the merging of the low-wavenumber plumes. It becomes more pronounced with decreasing porosity and leads to the nonlinear relationship between the Sherwood number Sh and Ra when the domain is not high enough for the plumes to fully develop. According to the DNS results, a regime is expected that is independent of both Ra and RaK, while the dimensionless constant flux Fcf /uII in this regime decreases with decreasing porosity. When the mean solute concentration reaches approximately 30 %, convection enters the shut-down regime. For large Ra, the dimensionless flux in the shut-down regime follows the scaling law F/uIII ∼ (t/tIII)−1.2 at large porosity (φ = 0.56) and F/uIII ∼ (t/tIII)−1.5 at small porosity (φ = 0.36 or 0.32). The study shows the significant pore-scale effect on the convection. The DNS cases in this study are mainly for simplified geometries and large RaK. This can lead to uncertainties of the obtained scaling coefficients. It is important to determine the scaling coefficients for real geological formations to predict a real CO2 sequestration process.Publicationtype: Journal Article28 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Nonlinear deterministic reconstruction and prediction of remotely measured ocean surface waves(Cambridge University Press (CUP), 2023-11-10); ; ; ; Algorithms for reconstructing and predicting nonlinear ocean wave fields from remote measurements are presented. Three types of synthetic observations are used to quantify the influence of remote measurement modulation mechanisms on the algorithms' performance. First, the observations correspond to randomly distributed surface elevations. Then, they are related to a marine radar model - the second type takes the wave shadowing modulation into account whereas the third one also includes the tilt modulation. The observations are numerically generated based on unidirectional waves of various steepness values. Linear and weakly nonlinear prediction algorithms based on analytical models are considered, as well as a highly nonlinear algorithm relying on the high-order spectral (HOS) method. Reconstructing surfaces from shadowed observations is found to have an impact limited to the non-visible regions, while tilt modulation affects the reconstruction more generally due to the indirect, more complex extraction of wave information. It is shown that the accuracy of the surface reconstruction mainly depends on the correct modelling of the wave shape nonlinearities. Modelling the nonlinear correction of the dispersion relation, in particular the frequency-dependent wave phase effects in the case of irregular waves, substantially improves the prediction. The suitability of the algorithms for severe wave conditions in finite depth and using non-perfect observations is assessed through wave tank experiments. It shows that only the third-order HOS solution predicts the right amplitude and phase of an emerging extreme wave, emphasizing the relevance of the corresponding physical modelling.Publicationtype: Journal Article13 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Numerical investigation of the possibility of macroscopic turbulence in porous media : a direct numerical simulation study(Cambridge University Press (CUP), 2015-02-02); ; ; When a turbulent flow in a porous medium is determined numerically, the crucial question is whether turbulence models should account only for turbulent structures restricted in size to the pore scale or whether the size of turbulent structures could exceed the pore scale. The latter would mean the existence of macroscopic turbulence in porous media, when turbulent eddies exceed the pore size. In order to determine the real size of turbulent structures in a porous medium, we simulated the turbulent flow by direct numerical simulation (DNS) calculations, thus avoiding turbulence modelling of any kind. With this study, which for the first time uses DNS calculations, we provide benchmark data for turbulent flow in porous media. Since perfect DNS calculations require the resolution of scales down to the Kolmogorov scale, often only approximate DNS solutions can be obtained, especially for high Reynolds numbers. This is accounted for by using and comparing two different DNS approaches, a finite volume method (FVM) with grid refinement towards the wall and a lattice Boltzmann method (LBM) with equal grid distribution. The solid matrix was simulated by a large number of rectangular bars arranged periodically. The number of bars in the solution domain with periodic boundary conditions was reduced systematically until a minimum size was found that does not suppress any large-scale turbulent structures. Two-point correlations, integral length scales and energy spectra were determined in order to answer the question of whether or not macroscopic turbulence can be found in porous media.Publicationtype: Journal Article145 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Analysis of a model for foam improved oil recovery(2014-07); ; ; ; During improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as 'pressure-driven growth' is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, 'pressure-driven growth' is shown to correspond to a special case of the more general 'viscous froth' model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such 'inherent' singularities can be readily incorporated into these numerical schemes.Publicationtype: Journal Article18