Effect of diffusing layer thickness on the density-driven natural convection of miscible fluids in porous media: Modeling of mass transport

Abstract

In this study, density-driven natural convection in porous media associated with Rayleigh-Taylor instability was visualized by X-ray computed tomography to investigate the effect of the thickness of the diffusing interface on convection. The thickness of the interface was changed by molecular diffusion with time, and the effective diffusivity in a porous medium was estimated. Compared with the thick interface, for the thin interface, many fine fingers formed and extended rapidly in a vertical direction. The onset time of natural convection increased proportionally with the thickness of the interface, being correlated with Rayleigh number and Péclet number. For the thinner initial interface, the finger number density increased more rapidly after onset and reached a higher value. Next, we discussed the mass transport in Rayleigh-Taylor convection to show how dispersion affects mass transport based on finger extension velocity and concentration in fingers. Increasing the interface thickness delayed the onset of convection, while the finger extension velocity remained the same. The reduced finger extension velocity changed nonlinearly with the Péclet number, reflecting the effect of dispersion. High transverse dispersion and longitudinal dispersion quickly reduced finger density. Transverse dispersion between ascending and descending fingers decreased the density; the density decreased linearly along the finger on both sides of the symmetric plane. As a result, the Sherwood number was proportional to the Rayleigh number, whereas the coefficient changed nonlinearly with Péclet number because of dispersion, reflecting the nonlinear dependences of the reduced velocity and the reduced density difference on Péclet number.

The Role of Water Flow and Dispersive Fluxes in the Dissolution of CO2 in Deep Saline Aquifers

“…As shown, the downwelling velocity linearly decays with Pe / Ra as with the fitted coefficients being A = − 0.166 ± 0.060 and B = 0.377 ± 0.032 (dashed line, R 2 = 0.79). We note that for three‐dimensional natural convection in a packed bed and in the absence of horizontal flow, Wang et al (2016) who also used a MEG solution (albeit doped with NaI) found that , while Wang et al (2018) who used a system of pure water and brine doped with NaI found that , in agreement with our results. The linear relation can be rearranged to represent the effect of the horizontal water velocity and the vertical gravitational velocity on the downwelling velocity of the fingers as …”

“…As seen in Figures 6a and 6b, the number of fingers decreases with time during the experiments. This was mostly due to the merging of small fingers into bigger ones during finger propagation, as observed in previous numerical and experimental studies (e.g., Riaz et al, 2006;Wang et al, 2018). The decrease in the maximum number of fingers with increasing water flow rate, shown in Figure 6b, is consistent with the simulations of Emami-Meybodi (2017) who found that a large horizontal velocity and the presence of high longitudinal dispersion lead to the formation of fewer fingers.…”

Three-Dimensional Interaction of Viscous Fingering and Gravitational Segregation in Porous Media

“…Two scans were then performed; one before the injection of the LVF ("before" scan) to reflect the initial condition and another after the injection ("after" scan). In both scans, the cylinder rotated 360 degrees in the space between the X-ray source and the detector panel, yielding 625 images in 78 s. Although the cylinder is placed vertically during the X-ray CT scan, the convection due to the density difference is negligible because the scan time is shorter than that for the onset of natural convection (>500 s), estimated with the same particles [30]. Under the assumption of well-developed convection, the maximum convection travel distance during the CT scan, estimated by the product of the Darcy velocity ∆ gk/µ 1 = 1.54 × 10 −4 m/s and the CT scan time is 1.2 cm, where ∆ is the density difference between the MVF and LVF, g is the gravitational acceleration, and µ 1 is the viscosity of the injected LVF.…”

Direct experimental observations of the impact of viscosity contrast on convective mixing in a three-dimensional porous medium

“…Whilst it may be the case the fingers reach the bottom before this happens, a lack of a constant flux was predicted from numerical simulations for Ra < 10 41,7,37 . Therefore, to compare cases, the maximum dissolution rate is used 9,38 .…”

“…At τ = 3 − 5 the BEG fingers have penetrated further into the domain than the MEG. However, the fingers are less concentrated and are less well-defined which indicates more dispersion has occurred, and the result of high transverse and longitudinal dispersion is the quick reduction and flattening of the concentration gradients 38 . This result is consistent with previous numerical works where it has been shown that the larger the mixing zone, the closer the fingering phenomenon behaviors like a purely dispersive system 23 .…”