adepy 0.2.0

Analytical solutions for solute transport in groundwater with Python

AdePy

AdePy contains analytical solutions for the advection-dispersion equation (ADE) describing solute transport in groundwater, written in Python.

Currently, all solutions shown in Wexler (1992) are provided as separate Python functions. These simulate 1D, 2D or 3D solute transport in uniform background flow for a variety of boundary conditions and source geometries. The solute may be subjected to linear equilibrium sorption and first-order decay. Additionally, solutions for instantaneous point pulse sources ("tracer slugs") are also provided for 1D, 2D and 3D transport, as well as the Multi-Process Non-Equilibrium (MPNE) 1D transport model described in Neville et al. (2000).

Since all equations are linear, superposition in time and space can be applied to create complex source geometries with time-varying source concentrations. Gauss-Legendre quadrature is used to solve the integrals which require numerical integration. Sequential or parallel first-order parent-daughter chain reactions are supported using the method described by Sun & Clement (1999).

To install

The released version can be installed using pip:

pip install adepy

To install the development version, download or git clone the GitHub repository locally. Then install using:

pip install -e <path/to/local/clone>

AdePy depends on NumPy, SciPy and Numba.

Documentation

Coming soon.

Available solutions

Module	Function	Dimensionality	Source geometry	Boundary type	Aquifer geometry	Reference
uniform	finite1()	1D	Inlet	Dirichlet	Finite	Wexler (1992)
	finite3()	1D	Inlet	Cauchy	Finite	Wexler (1992)
	seminf1()	1D	Inlet	Dirichlet	Semi-infinite	Wexler (1992)
	seminf3()	1D	Inlet	Cauchy	Semi-infinite	Wexler (1992)
	point1()	1D	Point	Cauchy	Infinite	Bear (1979)
	pulse1()	1D	Point	Pulse	Infinite	Bear (1979)
	mpne()	1D	Inlet	Dirichlet/Cauchy	Semi-infinite/finite	Neville et al (2000)
	point2()	2D	Point	Cauchy	Infinite	Wexler (1992)
	stripf()	2D	Finite Y at X=0	Dirichlet	Finite Y	Wexler (1992)
	stripi()	2D	Finite Y at X=0	Dirichlet	Semi-infinite	Wexler (1992)
	gauss()	2D	Gaussian along Y at X=0	Dirichlet	Semi-infinite	Wexler (1992)
	pulse2()	2D	Point	Pulse	Infinite	Bear (1979)
	point3()	3D	Point	Cauchy	Infinite	Wexler (1992)
	patchf()	3D	Finite Y and Z at X=0	Dirichlet	Finite Y and Z	Wexler (1992)
	patchi()	3D	Finite Y and Z at X=0	Dirichlet	Semi-infinite	Wexler (1992)
	pulse3()	3D	Point	Pulse	Infinite	Wexler (1992)

Example

The fate of a contaminant plume generated by continuous injection of a point source in an aquifer with uniform background flow is simulated. The source generates a plume which extends in three dimensions and migrates due to advection and mechanical dispersion. Molecular diffusion, linear sorption and first-order decay are neglected in this example.

More examples are available in the examples folder.

import numpy as np
import matplotlib.pyplot as plt

# 3D ADE solution of a continuous point source in uniform background flow
from adepy.uniform import point3 

# Source parameters ----
xc = 0   # x-coordinate of point source, m
yc = 0   # y-coordinate of point source, m
zc = 0   # z-coordinate of point source, m
c0 = 100 # injection concentration, mg/L
Q = 1    # injection rate, m³/d

# Aquifer parameters ----
v = 0.05  # uniform groundwater flow velocity in x-direction, m/d
al = 5    # longitudinal dispersivity, m
ah = 1    # horizontal transverse dispersivity, m
av = 0.1  # vertical transverse dispersivity, m
n = 0.2   # porosity, -

# Calculate and plot the concentration field after 1 year at z = 0 ----
t = 365   # output time, d
x, y = np.meshgrid(np.linspace(-10, 20, 100), 
                   np.linspace(-7.5, 7.5, 100))  # output grid x-y coordinates, m
z = 0     # output grid z-coordinate, m

c = point3(c0, x, y, z, t, v, n, al, ah, av, Q, xc, yc, zc) # simulated concentration, mg/L

plt.contour(x, y, c, levels=np.arange(100, 2501, 100))
plt.xlabel('x (m)')
plt.ylabel('y (m)')
plt.gca().set_aspect("equal")
plt.grid()

# Calculate and plot the concentration time series for 5 years at a location downstream ----
obs = (40, 0, 0)  # x-y-z coordinates of observation point, m
t = np.linspace(1, 5 * 365, 100)  # output times, d
cobs = point3(c0, obs[0], obs[1], obs[2], t, v, n, al, ah, av, Q, xc, yc, zc)

plt.plot(t, cobs)
plt.xlabel('Time (d)')
plt.ylabel('Concentration (mg/L)')

References

Wexler, E.J., 1992. Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow, USGS Techniques of Water-Resources Investigations 03-B7, 190 pp., https://doi.org/10.3133/twri03B7

Neville, C.J., Ibaraki, M., Sudicky, E.A., 2000. Solute transport with multiprocess nonequilibrium: a semi-analytical solution approach, Journal of Contaminant Hydrology 44-2, p. 141-159, https://doi.org/10.1016/S0169-7722(00)00094-2

Sun, Y., Clement, T.P., 1999. A Decomposition Method for Solving Coupled Multi–Species Reactive Transport Problems, Transport in Porous Media 37, p. 327–346, https://doi.org/10.1023/A:1006507514019