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ex-gwt-mt3dms-p06.py.
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MT3DMS Problem 6
The purpose of this script is to (1) recreate the example problems that were first described in the 1999 MT3DMS report, and (2) compare MF6-GWT solutions to the established MT3DMS solutions.
Ten example problems appear in the 1999 MT3DMS manual, starting on page 130. This notebook demonstrates example 6 from the list below:
One-Dimensional Transport in a Uniform Flow Field
One-Dimensional Transport with Nonlinear or Nonequilibrium Sorption
Two-Dimensional Transport in a Uniform Flow Field
Two-Dimensional Transport in a Diagonal Flow Field
Two-Dimensional Transport in a Radial Flow Field
Concentration at an Injection/Extraction Well
Three-Dimensional Transport in a Uniform Flow Field
Two-Dimensional, Vertical Transport in a Heterogeneous Aquifer
Two-Dimensional Application Example
Three-Dimensional Field Case Study
Initial setup
Import dependencies, define the example name and workspace, and read settings from environment variables.
[1]:
import os
import pathlib as pl
from pprint import pformat
import flopy
import git
import matplotlib.pyplot as plt
import numpy as np
from flopy.plot.styles import styles
from modflow_devtools.misc import get_env, timed
# Example name and workspace paths. If this example is running
# in the git repository, use the folder structure described in
# the README. Otherwise just use the current working directory.
example_name = "ex-gwt-mt3dms-p06"
try:
root = pl.Path(git.Repo(".", search_parent_directories=True).working_dir)
except:
root = None
workspace = root / "examples" if root else pl.Path.cwd()
figs_path = root / "figures" if root else pl.Path.cwd()
# Settings from environment variable
write = get_env("WRITE", True)
run = get_env("RUN", True)
plot = get_env("PLOT", True)
plot_show = get_env("PLOT_SHOW", True)
plot_save = get_env("PLOT_SAVE", True)
Define parameters
Define model units, parameters and other settings.
[2]:
# Model units
length_units = "feet"
time_units = "days"
# Model parameters
nlay = 1 # Number of layers
nrow = 31 # Number of rows
ncol = 31 # Number of columns
delr = 900.0 # Column width ($ft$)
delc = 900.0 # Row width ($ft$)
delz = 20.0 # Layer thickness ($ft$)
top = 0.0 # Top of the model ($ft$)
prsity = 0.35 # Porosity
dum1 = 2.5 # Length of the injection period ($years$)
dum2 = 7.5 # Length of the extraction period ($years$)
k11 = 432.0 # Horizontal hydraulic conductivity ($ft/d$)
qwell = 1.0 # Volumetric injection rate ($ft^3/d$)
cwell = 100.0 # Relative concentration of injected water ($\%$)
al = 100.0 # Longitudinal dispersivity ($ft$)
trpt = 1.0 # Ratio of transverse to longitudinal dispersitivity
# Additional model input
perlen = [912.5, 2737.5]
nper = len(perlen)
nstp = [365, 1095]
tsmult = [1.0, 1.0]
k11 = 0.005 * 86400 # established above, but explicitly writing out its origin here
sconc = 0.0
c0 = 0.0
dt0 = 56.25
dmcoef = 0
ath1 = al * trpt
botm = [top - delz] # Model geometry
k33 = k11 # Vertical hydraulic conductivity ($m/d$)
icelltype = 0
mixelm = -1
strt = np.zeros((nlay, nrow, ncol), dtype=float)
# Active model domain
ibound_mf2k5 = np.ones((nlay, nrow, ncol), dtype=int) * -1
ibound_mf2k5[:, 1 : nrow - 1, 1 : ncol - 1] = 1
idomain = np.ones((nlay, nrow, ncol), dtype=int)
icbund = 1
# Boundary conditions
# MF2K5 pumping info:
qwell = 86400.0
welspd = {
0: [[0, 15, 15, qwell]], # Well pumping info for MF2K5
1: [[0, 15, 15, -qwell]],
}
cwell = 100.0
spd = {
0: [0, 15, 15, cwell, 2], # Well pupming info for MT3DMS
1: [0, 15, 15, 0.0, 2],
}
# MF6 pumping information
# (k, i, j), flow, conc
spd_mf6 = {0: [[(0, 15, 15), qwell, cwell]], 1: [[(0, 15, 15), -qwell, 0.0]]}
# MF6 constant head boundaries:
chdspd = []
# Loop through the left & right sides.
for i in np.arange(nrow):
chdspd.append([(0, i, 0), strt[0, i, 0]])
chdspd.append([(0, i, ncol - 1), strt[0, i, ncol - 1]])
# Loop through the top & bottom while omitting the corner cells
for j in np.arange(1, ncol - 1):
chdspd.append([(0, 0, j), strt[0, 0, j]])
chdspd.append([(0, nrow - 1, j), strt[0, nrow - 1, j]])
chdspd = {0: chdspd}
# Solver settings
nouter, ninner = 100, 300
hclose, rclose, relax = 1e-6, 1e-6, 1.0
percel = 1.0 # HMOC parameters
itrack = 3
wd = 0.5
dceps = 1.0e-5
nplane = 1
npl = 0
nph = 16
npmin = 2
npmax = 32
dchmoc = 1.0e-3
nlsink = nplane
npsink = nph
# Time discretization
tdis_rc = []
tdis_rc.append((perlen, nstp, 1.0))
Model setup
Define functions to build models, write input files, and run the simulation.
[3]:
def build_models(sim_name, mixelm=0, silent=False):
mt3d_ws = os.path.join(workspace, sim_name, "mt3d")
modelname_mf = "p06-mf"
# Instantiate the MODFLOW model
mf = flopy.modflow.Modflow(
modelname=modelname_mf, model_ws=mt3d_ws, exe_name="mf2005"
)
# Instantiate discretization package
# units: itmuni=4 (days), lenuni=2 (m)
flopy.modflow.ModflowDis(
mf,
nlay=nlay,
nrow=nrow,
ncol=ncol,
delr=delr,
delc=delc,
top=top,
botm=botm,
nper=nper,
nstp=nstp,
perlen=perlen,
itmuni=4,
lenuni=1,
)
# Instantiate basic package
flopy.modflow.ModflowBas(mf, ibound=ibound_mf2k5, strt=strt)
# Instantiate layer property flow package
flopy.modflow.ModflowLpf(mf, hk=k11, laytyp=icelltype)
# Instantiate well package
flopy.modflow.ModflowWel(mf, stress_period_data=welspd)
# Instantiate solver package
flopy.modflow.ModflowSip(mf)
# Instantiate link mass transport package (for writing linker file)
flopy.modflow.ModflowLmt(mf)
# Transport
modelname_mt = "p06-mt"
mt = flopy.mt3d.Mt3dms(
modelname=modelname_mt,
model_ws=mt3d_ws,
exe_name="mt3dusgs",
modflowmodel=mf,
)
# Instantiate basic transport package
flopy.mt3d.Mt3dBtn(
mt,
icbund=icbund,
prsity=prsity,
sconc=sconc,
nper=nper,
perlen=perlen,
dt0=dt0,
obs=[(0, 15, 15)],
)
# Instatiate the advection package
flopy.mt3d.Mt3dAdv(
mt,
mixelm=mixelm,
dceps=dceps,
nplane=nplane,
npl=npl,
nph=nph,
npmin=npmin,
npmax=npmax,
nlsink=nlsink,
npsink=npsink,
percel=percel,
itrack=itrack,
wd=wd,
)
# Instantiate the dispersion package
flopy.mt3d.Mt3dDsp(mt, al=al, trpt=trpt, dmcoef=dmcoef)
# Instantiate the source/sink mixing package
flopy.mt3d.Mt3dSsm(mt, stress_period_data=spd)
# Instantiate the GCG solver in MT3DMS
flopy.mt3d.Mt3dGcg(mt)
# MODFLOW 6
name = "p06-mf6"
gwfname = "gwf-" + name
sim_ws = os.path.join(workspace, sim_name)
sim = flopy.mf6.MFSimulation(sim_name=sim_name, sim_ws=sim_ws, exe_name="mf6")
# Instantiating MODFLOW 6 time discretization
tdis_rc = []
for i in range(nper):
tdis_rc.append((perlen[i], nstp[i], tsmult[i]))
flopy.mf6.ModflowTdis(sim, nper=nper, perioddata=tdis_rc, time_units=time_units)
# Instantiating MODFLOW 6 groundwater flow model
gwf = flopy.mf6.ModflowGwf(
sim,
modelname=gwfname,
save_flows=True,
model_nam_file=f"{gwfname}.nam",
)
# Instantiating MODFLOW 6 solver for flow model
imsgwf = flopy.mf6.ModflowIms(
sim,
print_option="SUMMARY",
outer_dvclose=hclose,
outer_maximum=nouter,
under_relaxation="NONE",
inner_maximum=ninner,
inner_dvclose=hclose,
rcloserecord=rclose,
linear_acceleration="CG",
scaling_method="NONE",
reordering_method="NONE",
relaxation_factor=relax,
filename=f"{gwfname}.ims",
)
sim.register_ims_package(imsgwf, [gwf.name])
# Instantiating MODFLOW 6 discretization package
flopy.mf6.ModflowGwfdis(
gwf,
length_units=length_units,
nlay=nlay,
nrow=nrow,
ncol=ncol,
delr=delr,
delc=delc,
top=top,
botm=botm,
idomain=idomain,
filename=f"{gwfname}.dis",
)
# Instantiating MODFLOW 6 node-property flow package
flopy.mf6.ModflowGwfnpf(
gwf,
save_flows=False,
icelltype=icelltype,
k=k11,
k33=k33,
save_specific_discharge=True,
filename=f"{gwfname}.npf",
)
# Instantiating MODFLOW 6 storage package (steady flow conditions, so no actual storage, using to print values in .lst file)
flopy.mf6.ModflowGwfsto(gwf, ss=0, sy=0, filename=f"{gwfname}.sto")
# Instantiating MODFLOW 6 initial conditions package for flow model
flopy.mf6.ModflowGwfic(gwf, strt=strt, filename=f"{gwfname}.ic")
# Instantiating MODFLOW 6 constant head package
flopy.mf6.ModflowGwfchd(
gwf,
maxbound=len(chdspd),
stress_period_data=chdspd,
save_flows=False,
pname="CHD-1",
filename=f"{gwfname}.chd",
)
# Instantiate the wel package
flopy.mf6.ModflowGwfwel(
gwf,
print_input=True,
print_flows=True,
stress_period_data=spd_mf6,
save_flows=False,
auxiliary="CONCENTRATION",
pname="WEL-1",
filename=f"{gwfname}.wel",
)
# Instantiating MODFLOW 6 output control package for flow model
flopy.mf6.ModflowGwfoc(
gwf,
head_filerecord=f"{gwfname}.hds",
budget_filerecord=f"{gwfname}.bud",
headprintrecord=[("COLUMNS", 10, "WIDTH", 15, "DIGITS", 6, "GENERAL")],
saverecord=[("HEAD", "LAST"), ("BUDGET", "LAST")],
printrecord=[("HEAD", "LAST"), ("BUDGET", "LAST")],
)
# Instantiating MODFLOW 6 groundwater transport package
gwtname = "gwt_" + name
gwt = flopy.mf6.MFModel(
sim,
model_type="gwt6",
modelname=gwtname,
model_nam_file=f"{gwtname}.nam",
)
gwt.name_file.save_flows = True
# create iterative model solution and register the gwt model with it
imsgwt = flopy.mf6.ModflowIms(
sim,
print_option="SUMMARY",
outer_dvclose=hclose,
outer_maximum=nouter,
under_relaxation="NONE",
inner_maximum=ninner,
inner_dvclose=hclose,
rcloserecord=rclose,
linear_acceleration="BICGSTAB",
scaling_method="NONE",
reordering_method="NONE",
relaxation_factor=relax,
filename=f"{gwtname}.ims",
)
sim.register_ims_package(imsgwt, [gwt.name])
# Instantiating MODFLOW 6 transport discretization package
flopy.mf6.ModflowGwtdis(
gwt,
nlay=nlay,
nrow=nrow,
ncol=ncol,
delr=delr,
delc=delc,
top=top,
botm=botm,
idomain=idomain,
filename=f"{gwtname}.dis",
)
# Instantiating MODFLOW 6 transport initial concentrations
flopy.mf6.ModflowGwtic(gwt, strt=sconc, filename=f"{gwtname}.ic")
# Instantiating MODFLOW 6 transport advection package
if mixelm >= 0:
scheme = "UPSTREAM"
elif mixelm == -1:
scheme = "TVD"
else:
raise Exception()
flopy.mf6.ModflowGwtadv(gwt, scheme=scheme, filename=f"{gwtname}.adv")
# Instantiating MODFLOW 6 transport dispersion package
if al != 0:
flopy.mf6.ModflowGwtdsp(
gwt,
xt3d_off=True,
alh=al,
ath1=ath1,
filename=f"{gwtname}.dsp",
)
# Instantiating MODFLOW 6 transport mass storage package (formerly "reaction" package in MT3DMS)
flopy.mf6.ModflowGwtmst(
gwt,
porosity=prsity,
first_order_decay=False,
decay=None,
decay_sorbed=None,
sorption=None,
bulk_density=None,
distcoef=None,
filename=f"{gwtname}.mst",
)
# Instantiating MODFLOW 6 transport source-sink mixing package
sourcerecarray = [("WEL-1", "AUX", "CONCENTRATION")]
flopy.mf6.ModflowGwtssm(gwt, sources=sourcerecarray, filename=f"{gwtname}.ssm")
# Instantiating MODFLOW 6 transport output control package
flopy.mf6.ModflowGwtoc(
gwt,
budget_filerecord=f"{gwtname}.cbc",
concentration_filerecord=f"{gwtname}.ucn",
concentrationprintrecord=[("COLUMNS", 10, "WIDTH", 15, "DIGITS", 6, "GENERAL")],
saverecord=[("CONCENTRATION", "LAST"), ("BUDGET", "LAST")],
printrecord=[("CONCENTRATION", "LAST"), ("BUDGET", "LAST")],
)
# Instantiate observation package (for transport)
obslist = [["bckgrnd_cn", "concentration", (0, 15, 15)]]
obsdict = {f"{gwtname}.obs.csv": obslist}
obs = flopy.mf6.ModflowUtlobs(gwt, print_input=False, continuous=obsdict)
# Instantiating MODFLOW 6 flow-transport exchange mechanism
flopy.mf6.ModflowGwfgwt(
sim,
exgtype="GWF6-GWT6",
exgmnamea=gwfname,
exgmnameb=gwtname,
filename=f"{name}.gwfgwt",
)
return mf, mt, sim
def write_models(mf2k5, mt3d, sim, silent=True):
mf2k5.write_input()
mt3d.write_input()
sim.write_simulation(silent=silent)
@timed
def run_models(mf2k5, mt3d, sim, silent=True):
success, buff = mf2k5.run_model(silent=silent, report=True)
assert success, pformat(buff)
success, buff = mt3d.run_model(
silent=silent, normal_msg="Program completed", report=True
)
assert success, pformat(buff)
success, buff = sim.run_simulation(silent=silent, report=True)
assert success, pformat(buff)
Plotting results
Define functions to plot model results.
[4]:
# Figure properties
figure_size = (6, 4.5)
def plot_results(mt3d, mf6, idx, ax=None):
mt3d_out_path = mt3d.model_ws
mf6_out_path = mf6.simulation_data.mfpath.get_sim_path()
mf6.simulation_data.mfpath.get_sim_path()
# Get the MT3DMS observation output file
fname = os.path.join(mt3d_out_path, "MT3D001.OBS")
cvt = mt3d.load_obs(fname) if os.path.isfile(fname) else None
# Get the MODFLOW 6 concentration observation output file
fname = os.path.join(mf6_out_path, list(mf6.model_names)[1] + ".obs.csv")
mf6cobs = flopy.utils.Mf6Obs(fname).data
# Create figure for scenario
with styles.USGSPlot():
sim_name = mf6.name
plt.rcParams["lines.dashed_pattern"] = [5.0, 5.0]
if ax is None:
fig = plt.figure(figsize=figure_size, dpi=300, tight_layout=True)
ax = fig.add_subplot(1, 1, 1)
x = cvt["time"] / 365.0
y = cvt["(1, 16, 16)"]
# Pare down the list length to clean plot
x_pare = x[::20]
y_pare = y[::20]
ax.plot(x_pare, y_pare, label="Upstream FD", marker="^")
# Add MF6 output
x_mf6 = mf6cobs["totim"] / 365.0
y_mf6 = mf6cobs["BCKGRND_CN"]
x_mf6_pare = x_mf6[::20]
y_mf6_pare = y_mf6[::20]
ax.plot(
x_mf6_pare,
y_mf6_pare,
label="MODFLOW 6",
marker="x",
linestyle=":",
)
plt.xlim(0, 10)
plt.ylim(0, 100.0)
plt.xlabel("Time, in years")
plt.ylabel("Normalized Concentration, in percent")
plt.legend()
title = "Calculated Concentration at an Injection/Pumping Well"
letter = chr(ord("@") + idx + 1)
styles.heading(letter=letter, heading=title)
if plot_show:
plt.show()
if plot_save:
fpth = figs_path / f"{sim_name}.png"
fig.savefig(fpth)
Running the example
Define and invoke a function to run the example scenario, then plot results.
[5]:
def scenario(idx, silent=True):
mf2k5, mt3d, sim = build_models(example_name, mixelm=mixelm)
if write:
write_models(mf2k5, mt3d, sim, silent=silent)
if run:
run_models(mf2k5, mt3d, sim, silent=silent)
if plot:
plot_results(mt3d, sim, idx)
# Compares the standard finite difference solutions between MT3D and MF6
scenario(0)
run_models took 6665.45 ms
