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A pore-scale resolved direct numerical simulation study for scaling analysis of the solutal convection in porous media
Publikationstyp
Journal Article
Date Issued
2024-11-25
Sprache
English
Author(s)
Jin, Yan
Journal
Volume
1000
Article Number
A21
Citation
Journal of Fluid Mechanics 1000: A21 (2024)
Publisher DOI
Scopus ID
Publisher
Cambridge University Press
Understanding 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.
Subjects
convection in porous media | porous media
DDC Class
620: Engineering