def test_homogeneous(self):
steady = af.thiem(
rad=self.rad,
r_ref=self.r_ref,
transmissivity=self.t_gmean,
rate=self.rate,
h_ref=self.h_ref,
)
transient = af.theis(
time=self.time,
rad=self.rad,
storage=self.storage,
transmissivity=self.t_gmean,
rate=self.rate,
r_bound=self.r_ref,
h_bound=self.h_ref,
)
self.assertTrue(inc(steady, self.delta))
for rad_arr in transient:
self.assertTrue(inc(rad_arr, self.delta))
for time_arr in transient.T:
self.assertTrue(dec(time_arr, self.delta))
self.assertAlmostEqual(np.abs(np.max(steady - transient[-1, :])),
0.0,
places=4)
def test_create(self):
# create the field-site and the campaign
field = wtp.FieldSite(name="UFZ", coordinates=[51.3538, 12.4313])
campaign = wtp.Campaign(name="UFZ-campaign", fieldsite=field)
# add 4 wells to the campaign
campaign.add_well(name="well_0", radius=0.1, coordinates=(0.0, 0.0))
campaign.add_well(name="well_1", radius=0.1, coordinates=(1.0, -1.0))
campaign.add_well(name="well_2", radius=0.1, coordinates=(2.0, 2.0))
campaign.add_well(name="well_3", radius=0.1, coordinates=(-2.0, -1.0))
# generate artificial drawdown data with the Theis solution
self.rad = [
campaign.wells["well_0"].radius, # well radius of well_0
campaign.wells["well_0"] - campaign.wells["well_1"], # dist. 0-1
campaign.wells["well_0"] - campaign.wells["well_2"], # dist. 0-2
campaign.wells["well_0"] - campaign.wells["well_3"], # dist. 0-3
]
drawdown = ana.theis(
time=self.time,
rad=self.rad,
storage=self.storage,
transmissivity=self.transmissivity,
rate=self.rate,
)
# create a pumping test at well_0
pumptest = wtp.PumpingTest(
name="well_0",
pumpingwell="well_0",
pumpingrate=self.rate,
description="Artificial pump test with Theis",
)
# add the drawdown observation at the 4 wells
pumptest.add_transient_obs("well_0", self.time, drawdown[:, 0])
pumptest.add_transient_obs("well_1", self.time, drawdown[:, 1])
pumptest.add_transient_obs("well_2", self.time, drawdown[:, 2])
pumptest.add_transient_obs("well_3", self.time, drawdown[:, 3])
# add the pumping test to the campaign
campaign.addtests(pumptest)
# plot the well constellation and a test overview
campaign.plot_wells()
campaign.plot()
# save the whole campaign
campaign.save()
# test making steady
campaign.tests["well_0"].make_steady()
# -*- coding: utf-8 -*-
import numpy as np
from matplotlib import pyplot as plt
from anaflow import theis
time = [10, 100, 1000]
rad = np.geomspace(0.1, 10)
head = theis(time=time, rad=rad, storage=1e-4, transmissivity=1e-4, rate=-1e-4)
for i, step in enumerate(time):
plt.plot(rad, head[i], label="Theis(t={})".format(step))
plt.legend()
plt.tight_layout()
plt.show()
time_labels = ["10 s", "10 min", "10 h"]
time = [10, 600, 36000] # 10s, 10min, 10h
rad = np.geomspace(0.05, 4) # radial distance from the pumping well in [0, 4]
var = 0.5 # variance of the log-conductivity
len_scale = 10.0 # correlation length of the log-conductivity
anis = 0.75 # anisotropy ratio of the log-conductivity
KG = 1e-4 # the geometric mean of the conductivity
Kefu = KG * np.exp(
var * (0.5 - aniso(anis))) # the effective conductivity for uniform flow
KH = KG * np.exp(-var / 2.0) # the harmonic mean of the conductivity
S = 1e-4 # storage
rate = -1e-4 # pumping rate
L = 1.0 # vertical extend of the aquifer
head_Kefu = theis(time, rad, S, Kefu * L, rate)
head_KH = theis(time, rad, S, KH * L, rate)
head_ef = ext_theis_3d(time, rad, S, KG, var, len_scale, anis, L, rate)
time_ticks = []
for i, step in enumerate(time):
label_TG = "Theis($K_{efu}$)" if i == 0 else None
label_TH = "Theis($K_H$)" if i == 0 else None
label_ef = "extended Theis 3D" if i == 0 else None
plt.plot(rad,
head_Kefu[i],
label=label_TG,
color="C" + str(i),
linestyle="--")
plt.plot(rad,
head_KH[i],
label=label_TH,
import numpy as np
from matplotlib import pyplot as plt
from anaflow import theis, neuman2004
time_labels = ["10 s", "10 min", "10 h"]
time = [10, 600, 36000] # 10s, 10min, 10h
rad = np.geomspace(0.05, 4) # radius from the pumping well in [0, 4]
var = 0.5 # variance of the log-transmissivity
len_scale = 10.0 # correlation length of the log-transmissivity
TG = 1e-4 # the geometric mean of the transmissivity
TH = TG*np.exp(-var/2.0) # the harmonic mean of the transmissivity
S = 1e-4 # storativity
rate = -1e-4 # pumping rate
head_TG = theis(time, rad, S, TG, rate)
head_TH = theis(time, rad, S, TH, rate)
head_ef = neuman2004(
time=time,
rad=rad,
trans_gmean=TG,
var=var,
len_scale=len_scale,
storage=S,
rate=rate,
)
time_ticks = []
for i, step in enumerate(time):
label_TG = "Theis($T_G$)" if i == 0 else None
label_TH = "Theis($T_H$)" if i == 0 else None
label_ef = "transient Neuman [2004]" if i == 0 else None
time = np.geomspace(10, 7200, 10)
transmissivity = 1e-4
storage = 1e-4
rad = [
campaign.wells["well_0"].radius, # well radius of well_0
campaign.wells["well_0"] -
campaign.wells["well_1"], # distance between 0-1
campaign.wells["well_0"] -
campaign.wells["well_2"], # distance between 0-2
campaign.wells["well_0"] -
campaign.wells["well_3"], # distance between 0-3
]
drawdown = ana.theis(
rad=rad,
time=time,
T=transmissivity,
S=storage,
Qw=prate,
)
### create a pumping test at well_0
pumptest = wtp.data.PumpingTest(
name="well_0",
pumpingwell="well_0",
pumpingrate=prate,
description="Artificial pump test with Theis",
)
### add the drawdown observation at the 4 wells
pumptest.add_transient_obs("well_0", time, drawdown[:, 0])
pumptest.add_transient_obs("well_1", time, drawdown[:, 1])
from matplotlib import pyplot as plt
from anaflow import theis, ext_theis_tpl
time_ticks = []
time_labels = ["10 s", "10 min", "10 h"]
time = [10, 600, 36000] # 10s, 10min, 10h
rad = np.geomspace(0.05, 4) # radial distance from the pumping well in [0, 4]
S = 1e-4 # storage
KG = 1e-4 # the geometric mean of the conductivity
len_scale = 20.0 # upper bound for the length scale
hurst = 0.5 # hurst coefficient
var = 0.5 # variance of the log-conductivity
rate = -1e-4 # pumping rate
KH = KG * np.exp(-var / 2) # the harmonic mean of the conductivity
head_KG = theis(time, rad, S, KG, rate)
head_KH = theis(time, rad, S, KH, rate)
head_ef = ext_theis_tpl(
time=time,
rad=rad,
storage=S,
cond_gmean=KG,
len_scale=len_scale,
hurst=hurst,
var=var,
rate=rate,
)
for i, step in enumerate(time):
label_TG = "Theis($K_G$)" if i == 0 else None
label_TH = "Theis($K_H$)" if i == 0 else None
label_ef = "extended Theis TPL 2D" if i == 0 else None
LINEAR_SOLVER=[2, 5, 1e-14, 1000, 1.0, 100, 4])
model.out.add_block( # point observation
PCS_TYPE="GROUNDWATER_FLOW",
NOD_VALUES="HEAD",
GEO_TYPE=["POINT", "owell"],
DAT_TYPE="TECPLOT",
)
model.tim.add_block( # set the timesteps
PCS_TYPE="GROUNDWATER_FLOW",
**generate_time(time) # generate input from time-series
)
model.write_input()
success = model.run_model()
print("success:", success)
# observation
point = model.readtec_point(pcs="GROUNDWATER_FLOW")
time = point["owell"]["TIME"]
head = point["owell"]["HEAD"]
# analytical solution
head_ana = ana.theis(time, obs, storage, transmissivity, rate=rate)
# comparisson plot
plt.scatter(time, head, color="k", label="simulated, r={:04.2f}m".format(obs))
plt.plot(time, head_ana, label="analytical solution")
plt.xscale("symlog", linthreshx=10, subsx=range(1, 10))
plt.xlim([0, 1.1 * time[-1]])
plt.xlabel("time in s")
plt.ylabel("head in m")
plt.legend()
plt.show()
# show mesh
model.msh.show()
def plotfitting3Dtheis(data, para, rad, time, radnames, prate, plotname):
"""Plot of estimation fitting with theis."""
radarr = np.linspace(rad.min(), rad.max(), 100)
timarr = np.linspace(time.min(), time.max(), 100)
plt.style.use("default")
t_gen = np.ones_like(radarr)
r_gen = np.ones_like(time)
r_gen1 = np.ones_like(timarr)
xydir = np.zeros_like(time)
fig = plt.figure(figsize=(12, 8))
ax = fig.gca(projection="3d")
for ri, re in enumerate(rad):
r1 = re * r_gen
r11 = re * r_gen1
h = ana.theis(time=time,
rad=re,
T=np.exp(para[0]),
S=np.exp(para[1]),
Qw=prate).reshape(-1)
h1 = data[:, ri]
h2 = ana.theis(time=timarr,
rad=re,
T=np.exp(para[0]),
S=np.exp(para[1]),
Qw=prate).reshape(-1)
zord = 1000 * (len(rad) - ri)
ax.plot(
r11,
timarr,
h2,
label=radnames[ri] + " r={:04.2f}".format(re),
zorder=zord,
)
ax.quiver(
r1,
time,
h,
xydir,
xydir,
h1 - h,
alpha=0.5,
arrow_length_ratio=0.0,
color="C" + str(ri % 10),
zorder=zord,
)
ax.scatter(r1, time, h1, depthshade=False, zorder=zord)
for te in time:
t11 = te * t_gen
h = ana.theis(time=te,
rad=radarr,
T=np.exp(para[0]),
S=np.exp(para[1]),
Qw=prate).reshape(-1)
ax.plot(radarr, t11, h, color="k", alpha=0.1, linestyle="--")
ax.view_init(elev=45, azim=155)
ax.set_xlabel(r"$r$ in $\left[\mathrm{m}\right]$")
ax.set_ylabel(r"$t$ in $\left[\mathrm{s}\right]$")
ax.set_zlabel(r"$h/|Q|$ in $\left[\mathrm{m}\right]$")
ax.legend(loc="lower left")
# plt.tight_layout()
plt.savefig(plotname, format="pdf")
# -*- coding: utf-8 -*-
import numpy as np
from matplotlib import pyplot as plt
from anaflow import theis
time = np.linspace(10, 200)
rad = [1, 5]
# Q(t) = Q * characteristic([0, T])
lap_kwargs = {"cond": 3, "cond_kw": {"a": 100}}
head = theis(
time=time,
rad=rad,
storage=1e-4,
transmissivity=1e-4,
rate=-1e-4,
lap_kwargs=lap_kwargs,
)
for i, step in enumerate(rad):
plt.plot(time, head[:, i], label="Theis(r={})".format(step))
plt.title("The Stehfest algorithm is not suitable for this!")
plt.legend()
plt.tight_layout()
plt.show()
# -*- coding: utf-8 -*-
import numpy as np
from matplotlib import pyplot as plt
from anaflow import theis, thiem
time = [10, 100, 1000]
rad = np.geomspace(0.1, 10)
r_ref = 10.0
head_ref = theis(time,
np.full_like(rad, r_ref),
storage=1e-3,
transmissivity=1e-4,
rate=-1e-4)
head1 = theis(time, rad, storage=1e-3, transmissivity=1e-4,
rate=-1e-4) - head_ref
head2 = theis(time,
rad,
storage=1e-3,
transmissivity=1e-4,
rate=-1e-4,
r_bound=r_ref)
head3 = thiem(rad, r_ref, transmissivity=1e-4, rate=-1e-4)
for i, step in enumerate(time):
label_1 = "Theis quasi steady" if i == 0 else None
label_2 = "Theis bounded" if i == 0 else None
plt.plot(rad, head1[i], label=label_1, color="C" + str(i), linestyle="--")
plt.plot(rad, head2[i], label=label_2, color="C" + str(i))
plt.plot(rad, head3, label="Thiem", color="k", linestyle=":")
# Generate artificial drawdown data with the Theis solution
rate = -1e-4
time = np.geomspace(10, 7200, 10)
transmissivity = 1e-4
storage = 1e-4
rad = [
campaign.wells["well_0"].radius, # well radius of well_0
campaign.wells["well_0"] - campaign.wells["well_1"], # distance 0-1
campaign.wells["well_0"] - campaign.wells["well_2"], # distance 0-2
campaign.wells["well_0"] - campaign.wells["well_3"], # distance 0-3
]
drawdown = ana.theis(
time=time,
rad=rad,
storage=storage,
transmissivity=transmissivity,
rate=rate,
)
###############################################################################
# Create a pumping test at well_0
pumptest = wtp.PumpingTest(
name="well_0",
pumpingwell="well_0",
pumpingrate=rate,
description="Artificial pump test with Theis",
)
###############################################################################
