Saturated Mass Transport

Project file on GitHub

Overview

This benchmark compiles a number of simple, synthetic setups to test different processes of saturated component transport of a solute.

The development of the equation system is given in this PDF. In the following, we present the different setups.

Problem description

We use quadratic mesh with \(0 < x < 1\) and \(0 < y < 1\) and a resolution of 32 x 32 quad elements with edge length \(0.03125 m\). The domain material is homogeneous and anisotropic. Porosity is \(0.2\), storativity is \(10^{-5}\), intrinic permeability is \(1.239 \cdot 10^{-7} m^2\), dynamic viscosity is \(10^{-3} Pa \cdot s\), fluid density is \(1 kg\cdot m^{-3}\), molecular diffusion is \(10^{-5} m^2\cdot s^{-1}\). If not stated otherwise, retardation coefficient is set to \(R=1\), relation between concentration and density is \(\beta_c = 0\), decay rate is \(\theta = 0\), and dispersivity is \(\alpha = 0\).

Boundary conditions vary on the left side individually for each setup; right side is set as constant Dirichlet concentration \(c=0\); top and bottom are no-flow for flow and component transport. Initial conditions are steady state for flow (for the equivalent boundary conditions respectively) and \(c=0\).

Model setups

Diffusion only / Diffusion and Storage

Left side boundary conditions for these two setups are pressure \(p=0\) and concentration \(c=1\). The Diffusion only setup results in the final state of the Diffusion and Storage setup. For the former, retardation is set to \(R=0\), while for the latter, \(R=1\).

The Diffusion only project file
The Diffusion and Storage project file

Diffusion, Storage, and Advection

Left side boundary conditions for this setup are pressure \(p=1\) and concentration \(c=1\).

The Diffusion, Storage, and Advection project file

Diffusion, Storage, Advection, and Dispersion

Left side boundary conditions for these setups are pressure \(p=1\) and concentration \(c=1\). The latter is once given over the full left side, and in a second setup over half of the left side. Longitudinal and transverse dispersivity is \(\alpha_l = 1 m\) and \(\alpha_t = 0.1 m\).

The Diffusion, Storage, Advection, and Dispersion project file
The Diffusion, Storage, Advection, and Dispersion Half project file

Diffusion, Storage, Gravity, and Dispersion

Boundary condition for this setup is pressure \(p=0\) for the top left corner and concentration \(c=1\) for half of the left side. Relation between concentration and gravity is \(\beta_c = 1\).

The Diffusion, Storage, Gravity, and Dispersion project file

Diffusion, Storage, Advection, and Decay

Left side boundary conditions for this setup are pressure \(p=1\) and concentration \(c=1\). Decay rate is \(\theta = 0.001 s^{-1}\).

The Diffusion, Storage, Advection, and Decay project file

Changes With Inclusion of Non Boussinesq-Effects

The changes to the original setup are described in this PDF.