# Saturated Mass Transport

## Overview

These benchmark compile 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. The benchmark source files can be found in Parabolic/ComponentTransport/SimpleSynthetics.

## 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 $10^{-5}$, intrinsic 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, $R=1$.

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

#### 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 $\alpha_t = 0.1 m$.

#### 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 $\beta_c = 1$.

#### Diffusion, Storage, Advection, and Decay

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

#### Changes With Inclusion of Non Boussinesq-Effects

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

This article was written by Marc Walther. If you are missing something or you find an error please let us know.
Generated with Hugo 0.122.0 in CI job 447067 | Last revision: April 14, 2024
Commit: [PL/TH2M] Extract MWpC part of W4 equation 4e84e6c  | Edit this page on