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Two Dimensional Application Example, Comparison of MODFLOW 6 Transport with MT3DMS
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 9 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-p09"
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()
data_path = pl.Path(f"../data/{example_name}")
data_path = data_path if data_path.is_dir() else pl.Path.cwd()
# Settings from environment variables
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 = "meters"
time_units = "seconds"
# Model parameters
nlay = 1 # Number of layers
nrow = 18 # Number of rows
ncol = 14 # Number of columns
delr = 100.0 # Column width ($m$)
delc = 100.0 # Row width ($m$)
delz = 10.0 # Layer thickness ($m$)
top = 0.0 # Top of the model ($m$)
prsity = 0.3 # Porosity
k1 = 1.474e-4 # Horiz. hyd. conductivity of fine grain material ($m/sec$)
k2 = 1.474e-7 # Horiz. hyd. conductivity of medium grain material ($m/sec$)
inj = 0.001 # Injection well rate ($m^3/sec$)
ext = -0.0189 # Extraction well pumping rate ($m^3/sec$)
al = 20.0 # Longitudinal dispersivity ($m$)
trpt = 0.2 # Ratio of horiz. transverse to longitudinal dispersivity ($m$)
perlen = 2.0 # Simulation time ($years$)
# Additional model input
hk = k1 * np.ones((nlay, nrow, ncol), dtype=float)
hk[:, 5:8, 1:8] = k2
laytyp = icelltype = 0
# Active model domain
ibound = np.ones((nlay, nrow, ncol), dtype=int)
ibound[0, 0, :] = -1
ibound[0, -1, :] = -1
idomain = np.ones((nlay, nrow, ncol), dtype=int)
icbund = 1
# Boundary conditions
# MF2K5 pumping info
qwell1 = 0.001
qwell2 = -0.0189
welspd = {0: [[0, 3, 6, qwell1], [0, 10, 6, qwell2]]} # Well pumping info for MF2K5
cwell1 = 57.87
cwell0 = 0.0
spd = {
0: [[0, 3, 6, cwell1, 2], [0, 10, 6, cwell0, 2]],
1: [[0, 3, 6, cwell0, 2], [0, 10, 6, cwell0, 2]],
} # Well info 4 MT3D
# MF6 pumping information
wellist_sp1 = []
# (k, i, j), flow, conc
wellist_sp1.append([(0, 3, 6), qwell1, cwell1]) # Injection well
wellist_sp1.append([(0, 10, 6), qwell2, cwell0]) # Pumping well
#
wellist_sp2 = []
# (k, i, j), flow, conc
wellist_sp2.append([(0, 3, 6), qwell1, cwell0]) # Injection well
wellist_sp2.append([(0, 10, 6), qwell2, cwell0]) # Pumping well
spd_mf6 = {0: wellist_sp1, 1: wellist_sp2}
# Transport related
sconc = 0.0
ath1 = al * trpt
dmcoef = 0.0 # m^2/s
# Time variables
perlen = [365.0 * 86400, 365.0 * 86400]
steady = [False, False]
nper = len(perlen)
nstp = [365, 365]
tsmult = [1.0, 1.0]
#
sconc = 0.0
c0 = 0.0
botm = [top - delz]
mixelm = -1
# Solver settings
nouter, ninner = 100, 300
hclose, rclose, relax = 1e-6, 1e-6, 1.0
percel = 1.0 # HMOC parameters
itrack = 2
wd = 0.5
dceps = 1.0e-5
nplane = 0
npl = 0
nph = 16
npmin = 2
npmax = 32
dchmoc = 1.0e-3
nlsink = nplane
npsink = nph
nadvfd = 1
Model setup
Define functions to build models, write input files, and run the simulation.
[3]:
def build_models(sim_name, mixelm=0, silent=False):
print(f"Building mf2005 model...{sim_name}")
mt3d_ws = os.path.join(workspace, sim_name, "mt3d")
modelname_mf = "p09-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,
perlen=perlen,
itmuni=1,
lenuni=2,
steady=steady,
)
# Instantiate basic package
strt = np.zeros((nlay, nrow, ncol), dtype=float)
strt[0, 0, :] = 250.0
xc = mf.modelgrid.xcellcenters
for j in range(ncol):
strt[0, -1, j] = 20.0 + (xc[-1, j] - xc[-1, 0]) * 2.5 / 100
flopy.modflow.ModflowBas(mf, ibound=ibound, strt=strt)
# Instantiate layer property flow package
flopy.modflow.ModflowLpf(mf, hk=hk, laytyp=laytyp)
# Instantiate well package
flopy.modflow.ModflowWel(mf, stress_period_data=welspd)
# Instantiate solver package
flopy.modflow.ModflowPcg(mf)
# Instantiate link mass transport package (for writing linker file)
flopy.modflow.ModflowLmt(mf)
# Transport
print(f"Building mt3d-usgs model...{sim_name}")
modelname_mt = "p09-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,
mxstrn=86400,
nper=nper,
perlen=perlen,
timprs=[perlen[0], 2 * perlen[1]],
dt0=0,
)
# 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,
)
# 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
print(f"Building mf6gwt model...{sim_name}")
name = "p09-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 initial conditions package for flow model
strt = np.zeros((nlay, nrow, ncol), dtype=float)
strt[0, 0, :] = 250.0
xc = mf.modelgrid.xcellcenters
for j in range(ncol):
strt[0, -1, j] = 20.0 + (xc[-1, j] - xc[-1, 0]) * 2.5 / 100
flopy.mf6.ModflowGwfic(gwf, strt=strt, filename=f"{gwfname}.ic")
# Instantiating MODFLOW 6 node-property flow package
flopy.mf6.ModflowGwfnpf(
gwf,
save_flows=False,
icelltype=icelltype,
k=hk,
k33=hk,
save_specific_discharge=True,
filename=f"{gwfname}.npf",
)
# Instantiate storage package
sto = flopy.mf6.ModflowGwfsto(gwf, ss=1.0e-05)
# Instantiating MODFLOW 6 constant head package
# MF6 constant head boundaries:
chdspd = []
# Loop through the top & bottom sides.
for j in np.arange(ncol):
# l, r, c, head, conc
chdspd.append([(0, 0, j), 250.0, 0.0]) # Top boundary
hd = 20.0 + (xc[-1, j] - xc[-1, 0]) * 2.5 / 100
chdspd.append([(0, 17, j), hd, 0.0]) # Bottom boundary
chdspd = {0: chdspd}
flopy.mf6.ModflowGwfchd(
gwf,
maxbound=len(chdspd),
stress_period_data=chdspd,
save_flows=False,
auxiliary="CONCENTRATION",
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,
alh=al,
ath1=ath1,
filename=f"{gwtname}.dsp",
)
# Instantiating MODFLOW 6 transport mass storage package
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"),
("CHD-1", "AUX", "CONCENTRATION"),
]
flopy.mf6.ModflowGwtssm(
gwt,
sources=sourcerecarray,
print_flows=True,
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")],
filename=f"{gwtname}.oc",
)
# 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 = (7, 5)
def plot_results(mf2k5, mt3d, mf6, idx, ax=None):
mt3d_out_path = mt3d.model_ws
mf6.simulation_data.mfpath.get_sim_path()
# Get the MT3DMS concentration output
fname_mt3d = os.path.join(mt3d_out_path, "MT3D001.UCN")
ucnobj_mt3d = flopy.utils.UcnFile(fname_mt3d)
conc_mt3d = ucnobj_mt3d.get_alldata()
# Get the MF6 concentration output
gwt = mf6.get_model(list(mf6.model_names)[1])
ucnobj_mf6 = gwt.output.concentration()
conc_mf6 = ucnobj_mf6.get_alldata()
hk = mf2k5.lpf.hk.array
# Create figure for scenario
with styles.USGSPlot() as fs:
sim_name = mf6.name
plt.rcParams["lines.dashed_pattern"] = [5.0, 5.0]
levels = np.arange(0.2, 10, 0.4)
stp_idx = 0 # 0-based (out of 2 possible stress periods)
# Plot after 8 years
axWasNone = False
if ax is None:
fig = plt.figure(figsize=figure_size, dpi=300, tight_layout=True)
ax = fig.add_subplot(1, 2, 1, aspect="equal")
axWasNone = True
ax = fig.add_subplot(1, 2, 1, aspect="equal")
cflood = np.ma.masked_less_equal(conc_mt3d[stp_idx], 0.2)
mm = flopy.plot.PlotMapView(ax=ax, model=mf2k5)
mm.plot_array(hk, masked_values=[hk[0, 0, 0]], alpha=0.2)
mm.plot_ibound()
mm.plot_grid(color=".5", alpha=0.2)
cs = mm.plot_array(cflood[0], alpha=0.5, vmin=0, vmax=3)
cs = mm.contour_array(conc_mt3d[stp_idx], colors="k", levels=levels)
plt.clabel(cs)
plt.xlabel("Distance Along X-Axis, in meters")
plt.ylabel("Distance Along Y-Axis, in meters")
title = "MT3D - End of SP " + str(stp_idx + 1)
letter = chr(ord("@") + idx + 1)
styles.heading(letter=letter, heading=title)
if axWasNone:
ax = fig.add_subplot(1, 2, 2, aspect="equal")
cflood = np.ma.masked_less_equal(conc_mf6[stp_idx], 0.2)
mm = flopy.plot.PlotMapView(ax=ax, model=mf2k5)
mm.plot_array(hk, masked_values=[hk[0, 0, 0]], alpha=0.2)
mm.plot_ibound()
mm.plot_grid(color=".5", alpha=0.2)
cs = mm.plot_array(cflood[0], alpha=0.5, vmin=0, vmax=3)
cs = mm.contour_array(conc_mf6[stp_idx], colors="k", levels=levels)
plt.clabel(cs)
plt.xlabel("Distance Along X-Axis, in meters")
plt.ylabel("Distance Along Y-Axis, in meters")
title = "MODFLOW 6 - End of SP " + str(stp_idx + 1)
letter = chr(ord("@") + idx + 2)
styles.heading(letter=letter, heading=title)
if plot_show:
plt.show()
if plot_save:
fpth = figs_path / "{}{}".format(
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(mf2k5, mt3d, sim, idx)
Compares the standard finite difference solutions between MT3D and MF6.
[6]:
scenario(0, silent=True)
Building mf2005 model...ex-gwt-mt3dms-p09
Building mt3d-usgs model...ex-gwt-mt3dms-p09
Building mf6gwt model...ex-gwt-mt3dms-p09
run_models took 1933.80 ms
