COTRA 1.0.1

A simple 1D contaminant transport simulation library

COntaminant TRAnsport code (COTRA)

This code is developed for academic purposes.
It numerically solves the Adsorption-Dispersion Equation in one dimension (1D).

Installation

You can install the package by:

pip install COTRA

Functions

Examples

You can find a complete example of all the features in the showcase.py file.

List of functions

• COTRA.run(Hydro_Dispersion, pore_velocity, porosity, bulk_density, Source_Time, Source_Intensity, Domain_Length, dx, Time_Span, dt, retardation, k_1, k_2)
  Solves the 1D Adsorption-Dispersion equation and saves the output as .npz files automatically.

• COTRA.CvS(files, *comments)
  Interactive plot of concentration profiles vs space at different times using a slider.

• COTRA.CvT(files, *comments)
  Interactive plot of concentration vs time at different positions using a slider.

• COTRA.animate(file_name)
  Creates an animation of the concentration profile evolving over time.

• COTRA.save_profile(file_name, point, domain='space')
  Exports the concentration profile either over time at a given space point or over space at a given time point, saving it into a CSV file.

Equation

The code solves the following coupled system:

$$ \frac{dC}{dt} = \frac{-v_p \frac{dC}{dx} + D \frac{d^2C}{dx^2} - S}{R} $$

$$ \rho \frac{ds}{dt} = \dot{a} n C - \dot{d} \rho s $$

Where:

• $C$= concentration in the fluid [g/L]
• $s$= sorbed concentration [g/kg]
• $v_p$= pore velocity [m/s]
• $D$= hydrodynamic dispersion coefficient [m²/s]
• $S$= source term
• $R$= retardation factor
• $n$= porosity [-]
• $\rho$= bulk density [kg/L]
• $\dot{a}$= adsorption rate
• $\dot{d}$= desorption rate

The adsorption rate can be defined with two models:

• Freundlich Model:
  $\dot{a} = k_1 \left( \dot{d} \frac{\rho}{n} \right) C^{\left( k_2 - 1\right)}$
• Linear Model:
  $\dot{a} = k_1 \left( \dot{d} \frac{\rho}{n} \right)$

Output

The solver automatically saves results in .npz format containing:

• t_full: full time array
• C_full: concentration over space and time
• Grid_Space: discretized spatial domain
• Domain_Length: total domain length
• Source_Intensity: intensity of the contaminant source

These files are used for further plotting, animation, and exporting data.