Impact of Low- or High-Permeability Inclusion on Free Convection in a Porous Medium

Abstract

Density-driven free convection in porous media is highly affected by large-scale heterogeneity, typical of which are low- or high-permeability inclusions imbedded in homogeneous porous media. In this research, we applied the modified Elder problem to investigate the impact of low- or high-permeability inclusions on the migration of a dense, unstable salt plume. Sensitivity analyses were conducted in terms of the permeability contrast, the effective area (the area of the inclusion beneath the source zone), and the distance of the inclusion from the source zone, all of which were found to play a significant role in controlling the total mass flux released from the source into the media. Results show that (1) a high-permeability inclusion has stronger effects than low-permeability inclusion, due to significantly unbalanced solute distributions caused by accelerated solute transport, (2) the inclusion with a larger effective area has more potential to influence free convection, (3) free convection is more sensitive to the low-/high-permeability inclusion vertically closer to the source zone, and (4) free convection is more susceptible to the low-permeability inclusion horizontally closer to the source zone. For high-permeability inclusions, the inclusion horizontally closer to the source zone influences the transport process more significantly at the early stage, and conversely, the inclusion far from the source zone has a later impact. The results obtained could offer significant implications for understanding unstable density-driven flow and solute transport in porous media with structured heterogeneity.

Paleo‐Hydrogeological Modeling to Understand Present‐Day Groundwater Salinities in a Low‐Lying Coastal Groundwater System (Northwestern Germany)

“…Free convection following vertical seawater infiltration is likely an important mechanism driving fast salinization of the groundwater system, particularly at the early stages of the simulation period when the coastline was quickly shifting landward (Kooi et al., 2000). Vertical seawater infiltration velocities were in the order of meters to tens of meters per year, which agrees with high rates of free convection reported for numerical studies (Xie et al., 2011; Yan et al., 2019) as well as field sites characterized by highly permeable geology (Delsman et al., 2014; Post & Kooi, 2003). The fast vertical salinization process linked to marine transgression implicates permeable sandy coastal groundwater systems that paleo‐modeling domains do not necessarily have to be extended until the position of the paleo‐coastline at the model start.…”

Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning

“…Among the newest advancements in the Elder problem, we can outline the following studies. Yan et al (2019) [20] applied the modified Elder problem to investigate the impact of permeability inclusions on the migration of an unstable salt plume. Shafabakhsh et al (2019) [21] investigated the fractured Elder problem, that is, the influence of different fracture networks on the Elder problem using the finite element method (FEM).…”

Numerical Analysis of the Effect of Heterogeneity on CO2 Dissolution Enhanced by Gravity Driven Convection

“…Studies on heterogeneous fields are usually limited to qualitative analysis of the effect of heterogeneity Yan et al, 2019;Wang et al, 2021;. Heterogeneity in permeability plays an important role in onset, growth, maintenance and decay of the GDC and the dissolution rate .…”

“…It is found that GDC depends to a large extent on properties of the formation (e.g., the permeability and porosity) and of the brine phase (e.g., the relation between brine density and concentration of dissolved CO 2 , viscosity and molecular diffusion coefficient) . For instance, researchers find a linear relation between the dissolution rate and the intrinsic permeability for isotropic homogeneous media Studies on heterogeneous fields are usually limited to qualitative analysis of the effect of heterogeneity Yan et al, 2019;Wang et al, 2021;. Heterogeneity in permeability plays an important role in onset, growth, maintenance and decay of the GDC and the dissolution rate .…”