A 3‐D Semianalytical Solution for Density‐Driven Flow in Porous Media

Abstract

Existing analytical and semianalytical solutions for density-driven flow (DDF) in porous media are limited to 2-D domains. In this work, we develop a semianalytical solution using the Fourier Galerkin method to describe DDF induced by salinity gradients in a 3-D porous enclosure. The solution is constructed by deriving the vector potential form of the governing equations and changing variables to obtain periodic boundary conditions. Solving the 3-D spectral system of equations can be computationally challenging. To alleviate computations, we develop an efficient approach, based on reducing the number of primary unknowns and simplifying the nonlinear terms, which allows us to simplify and solve the problem using only salt concentration as primary unknown. Test cases dealing with different Rayleigh numbers are solved to analyze the solution and gain physical insight into 3-D DDF processes. In fact, the solution displays a 3-D convective cell (actually a vortex) that resembles the quarter of a torus, which would not be possible in 2-D. Results also show that 3-D effects become more important at high Rayleigh number. We compare the semianalytical solution to research (Transport of RadioACtive Elements in Subsurface) and industrial (COMSOL Multiphysics®) codes. We show cases (high Raleigh number) where the numerical solution suffers from numerical artifacts, which highlight the worthiness of our semianalytical solution for code verification and benchmarking. In this context, we propose quantitative indicators based on several metrics characterizing the fluid flow and mass transfer processes and we provide open access to the source code of the semianalytical solution and to the corresponding numerical models. SHAO ET AL.10,094

Application of GALDIT in Assessing the Seawater Intrusion Vulnerability of Jeju Island, South Korea

“…The results of this research may be used to develop a quantitative index for rational decision-making on policies and suggest the need for further improvements in groundwater management, with a stronger focus on easing groundwater use.2 of 17 index method. Numerical simulations reproduce the dynamics of groundwater flow and salt transport in the coastal aquifer and can incorporate site characteristics [2,[7][8][9][10][11][12]. However, despite their accuracy and usefulness, numerical simulations require a considerable amount of hydrogeologic data as input and a difficult calibration process, therefore substantial computing power is needed for data processing and modeling.An alternative vulnerability assessment method uses a steady-state analytical solution based on the sharp interface model with the Ghyben-Herzberg principle, where the mixing of freshwater and saltwater is neglected and instead a sharp interface is assumed [13].…”

“…2 of 17 index method. Numerical simulations reproduce the dynamics of groundwater flow and salt transport in the coastal aquifer and can incorporate site characteristics [2,[7][8][9][10][11][12]. However, despite their accuracy and usefulness, numerical simulations require a considerable amount of hydrogeologic data as input and a difficult calibration process, therefore substantial computing power is needed for data processing and modeling.…”

Unstable Density-Driven Flow in Fractured Porous Media: The Fractured Elder Problem

“…DDF in the pours matrix was governed by variable-density flow and mass transport equations [38]. The mass conservation was ensured by the continuity equation and the velocity based on Darcy's law using the freshwater head formulation are as follows:…”

Experiment and Numerical Simulation of Seawater Intrusion under the Influences of Tidal Fluctuation and Groundwater Exploitation in Coastal Multilayered Aquifers

“…It involves the variable density groundwater flow, which is difficult to simulate well. Two types of flow models were developed for seawater intrusion simulation, including the sharp interface models and mixing interface models [14,[19][20][21][22][23][24]. There are many analytical solutions for variable density flow models to solve the coupled seawater intrusion equations under special conditions [6,19,20,25].…”

“…As a consequence, the models may overestimate the actual penetration length of the seawater wedge [26]. Therefore, the analytical models of variable density flow including mixing between freshwater and seawater were provided considering the realistic condition [24,27]. However, the analytical solutions are often derived based on some hypothetical conditions.…”