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ex-gwt-hecht-mendez.py.
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Hecht-Mendez 3D Borehole Heat Exchanger Problem
The purpose of this script is to (1) recreate the 3D heat transport example first published in Groundwater in 2010 titled, “Evaluating MT3DMS for Heat Transport Simulation of Closed Geothermal Systems,” and (2) compare MF6-GWT solutions to the published MT3DMS solution.
Note: The original problem employed the FHB boundary package to specify heads on the left and right boundaries. For this script, the same boundary conditions are achieved using the specified head option within the .bas package (specifies -1 for ibound which locks in the starting heads and constant heads)
Within the script that generates and runs the model, a user seeking to compare MODFLOW results with MT3D-USGS may do so by setting the parameter runMT3D equal to True on (or near). The correct line of script to adjust will look similar to scenario(1, runMT3D=False, silent=False).
For the first simulated scenario with a Peclet value of 1.0, simulated fits to the analytical solution can be improved by refining the temporal resolution of the simulation.
Initial setup
Import dependencies, define the example name and workspace, and read settings from environment variables.
[1]:
import os
import pathlib as pl
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
from scipy.special import erf, erfc
# 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.
name = "hecht-mendez"
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 = root / "data" / name if root 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"
# Set scenario parameters (make sure there is at least one blank line before next item)
# This entire dictionary is passed to _build_models()_ using the kwargs argument
parameters = {
"ex-gwt-hecht-mendez-a": {
"peclet": 0.0,
"gradient": 0.0,
"seepagevelocity": 0.0,
"constantheadright": 14,
},
"ex-gwt-hecht-mendez-b": {
"peclet": 1.0,
"gradient": 1.2e-4,
"seepagevelocity": 3.7e-6,
"constantheadright": 13.964,
},
"ex-gwt-hecht-mendez-c": {
"peclet": 10.0,
"gradient": 1.2e-3,
"seepagevelocity": 3.7e-5,
"constantheadright": 13.64,
},
}
# Scenario parameter units
# add parameter_units to add units to the scenario parameter table that is automatically
# built and used by the .tex input
parameter_units = {
"peclet": "$unitless$",
"gradient": "$m/m$",
"seepagevelocity": "$m/s$",
"constantheadright": "$m$",
}
# Model parameters
nlay = 13 # Number of layers
nrow = 83 # Number of rows
ncol = 247 # Number of columns
delr = "varies" # Column width ($m$)
delc = "varies" # Row width ($m$)
width = 200 # Simulation width ($m$)
length = 300 # Simulation length ($m$)
delz = 1.0 # Layer thickness ($m$)
top = 13.0 # Top of the model ($m$)
satthk = 13.0 # Saturated thickness ($m$)
hk = 8.0e-3 # Horizontal hydraulic conductivity($m/s$)
vk = 8.0e-3 # Vertical hydraulic conductivity($m/s$)
T0 = 285.15 # Initial temperature of aquifer ($K$)
prsity = 0.26 # Porosity
al = 0.50 # Longitudinal dispersivity ($m$)
trpt = 0.1 # Ratio of horizontal transverse dispersivity to longitudinal dispersivity
trpv = 0.1 # Ratio of vertical transverse dispersivity to longitudinal dispersivity
rhob = 1961.0 # Aquifer bulk density ($kg/m^3$)
sp1 = 2.103e-4 # Distribution coefficient ($m^3/kg$)
perlen = 12960000.0 # Simulation time ($seconds$) (=~150 days)
# Additional model input
delr = (
3 * [10.0]
+ 2 * [8.0]
+ 2 * [4.0]
+ 2 * [2.0]
+ 4 * [1.0]
+ 8 * [0.5]
+ 1 * [0.1]
+ 200 * [0.5]
+ 10 * [1.0]
+ 2 * [2.0]
+ 2 * [4.0]
+ 2 * [8.0]
+ 8 * [10.0]
+ 1 * [15.9]
)
delc = (
6 * [10.0]
+ 1 * [8.0]
+ 2 * [4.0]
+ 2 * [2.0]
+ 10 * [1.0]
+ 20 * [0.5]
+ 1 * [0.1]
+ 20 * [0.5]
+ 10 * [1.0]
+ 2 * [2.0]
+ 2 * [4.0]
+ 1 * [8.0]
+ 6 * [10.0]
)
botm = [top - delz * k for k in range(1, nlay + 1)]
laytyp = icelltype = 0
# Starting Heads:
strt = np.ones((nlay, nrow, ncol), dtype=float) * 14.0
# Active model domain
ibound = np.ones((nlay, nrow, ncol), dtype=int)
ibound[:, :, 0] = -1 # left side
ibound[:, :, -1] = -1 # right side
idomain = 1
# Transport related
icbund = np.ones((nlay, nrow, ncol))
icbund[:, :, 0] = -1
# Starting concentrations:
sconc = T0
# Dispersion
ath1 = al * trpt
atv = al * trpv
dmcoef_arr = 1.84e-6 # m^2/s
# From the Hecht-Mendez manuscript:
# "The 3D analytical solutions A4 and A5 consider a semi-infinite medium and
# therefore they neglect upgradient spreading. Accordingly, for consistency,
# thermal conductivity and dispersivity are set to zero in the area upgradient
# from the source in MT3DMS"
# dmcoef_arr = np.ones((nlay, nrow, ncol)) * 1.84e-6 # m^2/s
# dmcoef_arr[:, 0:82, 0:21] = 0.0
# Time variables
nstp = 1
transport_stp_len = 60000 # seconds simulated per transport step (16.66 hr)
ttsmult = 1.0
# Advection
mixelm = -1
percel = 1.0
# Boundary condition (BHE: "Borehole Heat Exchanger")
# Note: The manuscript is a bit different than the actual model input file. In
# the manuscript, it states, "The BHE for the 3D scenarios is
# represented as [a] point source by three cells within the three middle
# layers (sixth, seventh, and eighth layers)." However, the model input
# file that was obtained from Hecht-Mendez only included the 7th layer.
# So, for now, the script will mimic the original MT3DMS input and omit
# layers 6 and 8 as stated in the text.
ssm_bhe = [[7 - 1, 42 - 1, 22 - 1, -1.434e-5, 15]]
mf6_bhe = [[(7 - 1, 42 - 1, 22 - 1), -1.434e-5]]
# Reactive transport related terms
isothm = 1 # sorption type; 1=linear isotherm (equilibrium controlled)
sp2 = 2.0 # w/ isothm = 1 this is read but not used
rhob = 1.7 # g/cm^3
sp1 = 0.176 # cm^3/g (Kd: "Distribution coefficient")
# Transport observations
cobs = [(7 - 1, 42 - 1, k - 1) for k in range(22, 224, 2)]
# Solver settings
nouter, ninner = 100, 300
hclose, rclose, relax = 5e-5, 1e-8, 1.0
Model setup
Define functions to build models, write input files, and run the simulation.
[3]:
def hechtMendez_SS_3d(
x_pos, To, Y3d, Z3d, ath, atv, Fplanar, va, n, rhow, cw, thermdiff
):
"""
Calculate the analytical solution for changes in temperature three-
dimensional changes in temperature using transient solution provided in
the appendix of Hecht-Mendez et al. (2010) as equation A5. Note that for
SS conditions, the erfc term reduces to 1 as t -> infinity and the To/2
term becomes T.
Parameters
----------
x_pos : float or ndarray
x position
To : float or ndarray
initial temperature of the ground, degrees K
Y3d : float or ndarray
dimension of source in y direction for 3D test problem
Z3d : float or ndarray
dimension of source in z direction for 3D test problem
ath : float or ndarray
transverse horizontal dispersivity
atv : float or ndarray
transverse vertical dispersivity
Fplanar : float or ndarray
energy extraction (point source)
va : float or ndarray
seepage velocity
n : float or ndarray
porosity
rhow : float or ndarray
desity of water
cw : float or ndarray
specific heat capacity of water
thermdiff : float or ndarray
molecular diffusion coefficient, or in this case thermal
diffusivity
"""
# calculate transverse horizontal heat dispersion
Dy = ath * (va**2 / abs(va)) + thermdiff
t2 = erf(Y3d / (4 * np.sqrt(Dy * (x_pos / va))))
Dz = atv * (va**2 / abs(va)) + thermdiff
t3 = erf(Z3d / (4 * np.sqrt(Dz * (x_pos / va))))
# initial temperature at the source
To_planar = Fplanar / (abs(va) * n * rhow * cw)
sln = To + (To_planar * t2 * t3)
return sln
def hechtMendezSS(x_pos, y, a, F0, va, n, rhow, cw, thermdiff):
"""
Calculate the analytical solution for changes in temperature three-
dimensional changes in temperature for a steady state solution provided in
the appendix of Hecht-Mendez et al. (2010) as equation A4
Parameters
----------
x : float or ndarray
x position
y : float or ndarray
y position
a : float or ndarray
longitudinal dispersivity
F0 : float or ndarray
energy extraction (point source)
va : float or ndarray
seepage velocity
n : float or ndarray
porosity
rhow : float or ndarray
desity of water
cw : float or ndarray
specific heat capacity of water
thermdiff : float or ndarray
molecular diffusion coefficient, or in this case thermal
diffusivity
"""
# calculate transverse horizontal heat dispersion
Dth = a * (va**2 / abs(va)) + thermdiff
t1 = F0 / (va * n * rhow * cw * ((4 * np.pi * Dth * (x_pos / va)) ** (0.5)))
t2 = np.exp((-1 * va * y**2) / (4 * Dth * x_pos))
sln = t1 * t2
return sln
def hechtMendez3d(x_pos, t, Y, Z, al, ath, atv, thermdiff, va, n, R, Fplanar, cw, rhow):
"""
Calculate the analytical solution for three-dimensional changes in
temperature based on the solution provided in the appendix of Hecht-Mendez
et al. (2010) as equation A5
Parameters
----------
x : float or ndarray
x position
t : float or ndarray
time
Y : float or ndarray
dimension of the source in the y direction
Z : float or ndarray
dimension of the source in the z direction
al : float or ndarray
longitudinal dispersivity
ath : float or ndarray
transverse horizontal dispersivity
atv : float or ndarray
transverse vertical dispersivity
thermdiff : float or ndarray
molecular diffusion coefficient, or in this case thermal
diffusivity
va : float or ndarray
seepage velocity
n : float or ndarray
porosity
R : float or ndarray
retardation coefficient
Fplanar : float or ndarray
energy extraction (point source)
cw : float or ndarray
specific heat capacity of water
rhow : float or ndarray
desity of water
"""
To_planar = Fplanar / (va * n * rhow * cw)
Dl = al * (va**2 / abs(va)) + thermdiff
numer = R * x_pos - va * t
denom = 2 * np.sqrt(Dl * R * t)
t1 = (To_planar / 2) * erfc(numer / denom)
Dth = ath * (va**2 / abs(va)) + thermdiff
t2 = erf(Y / (4 * np.sqrt(Dth * (x_pos / va))))
Dtv = atv * (va**2 / abs(va)) + thermdiff
t3 = erf(Z / (4 * np.sqrt(Dtv * (x_pos / va))))
sln = t1 * t2 * t3
return sln
def build_mf2k5_flow_model(
sim_name,
peclet=0.0,
gradient=0,
seepagevelocity=0,
constantheadright=14,
silent=False,
):
print(f"Building mf2005 model...{sim_name}")
mt3d_ws = os.path.join(workspace, sim_name, "mt3d")
modelname_mf = "hecht-mendez"
# 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,
perlen=perlen,
nstp=nstp,
itmuni=4,
lenuni=1,
steady=True,
)
# Instantiate basic package
strt[:, :, -1] = constantheadright
flopy.modflow.ModflowBas(mf, ibound=ibound, strt=strt)
# Instantiate layer property flow package
flopy.modflow.ModflowLpf(mf, hk=hk, layvka=0, vka=vk, laytyp=laytyp)
# Instantiate solver package
flopy.modflow.ModflowPcg(
mf,
mxiter=90,
iter1=20,
npcond=1,
hclose=hclose,
rclose=rclose,
relax=relax,
nbpol=2,
iprpcg=2,
mutpcg=0.0,
)
# Instantiate link mass transport package (for writing linker file)
flopy.modflow.ModflowLmt(mf)
# Instantiate output control (OC) package
spd = {
(0, 0): ["save head"],
}
oc = flopy.modflow.ModflowOc(mf, stress_period_data=spd)
return mf
def build_mf6_flow_model(
sim_name,
peclet=0.0,
gradient=0,
seepagevelocity=0,
constantheadright=14,
silent=False,
):
print(f"Building mf6gwf model...{sim_name}")
gwfname = "gwf-" + name
sim_ws = os.path.join(workspace, sim_name, "mf6gwf")
sim = flopy.mf6.MFSimulation(sim_name=gwfname, sim_ws=sim_ws, exe_name="mf6")
# Instantiating MODFLOW 6 time discretization
tdis_rc = []
tdis_rc.append((perlen, 1, 1.0))
flopy.mf6.ModflowTdis(sim, nper=1, 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[:, :, -1] = constantheadright
flopy.mf6.ModflowGwfic(gwf, strt=strt, filename=f"{gwfname}.ic")
# Instantiating MODFLOW 6 node-property flow package
flopy.mf6.ModflowGwfnpf(
gwf,
save_flows=True,
k33overk=False,
icelltype=laytyp,
k=hk,
k33=vk,
save_specific_discharge=True,
save_saturation=True,
filename=f"{gwfname}.npf",
)
# Instantiate storage package
flopy.mf6.ModflowGwfsto(gwf, ss=0, sy=0, filename=f"{gwfname}.sto")
# Instantiating MODFLOW 6 constant head package
# MF6 constant head boundaries:
chdspd = []
# Loop through the left & right sides for all layers.
for k in range(nlay):
for i in range(nrow):
# left-most column:
# (l, r, c), head, conc
chdspd.append([(k, i, 0), strt[k, i, 0], T0]) # left
# right-most column:
chdspd.append([(k, i, ncol - 1), strt[k, i, ncol - 1], T0])
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",
)
# 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"),
],
)
return sim
def build_mt3d_transport_model(
mf,
sim_name,
peclet=0.0,
gradient=0,
seepagevelocity=0,
constantheadright=14,
silent=False,
):
# Transport
print(f"Building mt3dms model...{sim_name}")
modelname_mt = "hecht-mendez_mt"
mt3d_ws = os.path.join(workspace, sim_name, "mt3d")
mt = flopy.mt3d.Mt3dms(
modelname=modelname_mt,
model_ws=mt3d_ws,
exe_name="mt3dms",
modflowmodel=mf,
)
# Instantiate basic transport package
if seepagevelocity == 0:
dt0 = 50000
else:
dt0 = 0.0
flopy.mt3d.Mt3dBtn(
mt,
icbund=icbund,
prsity=prsity,
sconc=sconc,
cinact=-1e10,
thkmin=0.01,
ifmtcn=-2,
nprs=2,
timprs=[864000, 12960000], # 10, 150 days
dt0=dt0,
obs=cobs,
chkmas=False,
perlen=perlen,
nstp=nstp,
tsmult=ttsmult,
mxstrn=20000,
)
# Instatiate the advection package
flopy.mt3d.Mt3dAdv(mt, mixelm=mixelm, percel=percel)
# Instantiate the dispersion package
flopy.mt3d.Mt3dDsp(
mt, multiDiff=True, al=al, trpt=trpt, trpv=trpv, dmcoef=dmcoef_arr
)
# Instantiate the source/sink mixing package
ssmspd = {0: ssm_bhe}
flopy.mt3d.Mt3dSsm(
mt, mxss=nrow * ncol * 2 + len(ssm_bhe), stress_period_data=ssmspd
)
# Instantiate the reaction package
flopy.mt3d.Mt3dRct(mt, isothm=isothm, igetsc=0, rhob=rhob, sp1=sp1, sp2=sp2)
# Instantiate the GCG solver in MT3DMS
flopy.mt3d.Mt3dGcg(mt, mxiter=100, iter1=50, isolve=1, ncrs=1, cclose=1e-7)
def build_mf6_transport_model(
sim_name,
peclet=0.0,
gradient=0,
seepagevelocity=0,
constantheadright=14,
silent=False,
):
# Instantiating MODFLOW 6 groundwater transport package
print(f"Building mf6gwt model...{sim_name}")
gwtname = "gwt-" + name
sim_ws = os.path.join(workspace, sim_name, "mf6gwt")
sim = flopy.mf6.MFSimulation(sim_name=gwtname, sim_ws=sim_ws, exe_name="mf6")
# MF6 time discretization is a bit different than corresponding flow simulation
tdis_rc = None
if peclet == 1.0:
# use tsmult to and hardwired number of steps to make it run fast
tdis_rc = [(perlen, 25, 1.3)]
elif peclet == 10.0:
transport_stp_len = 1.296e5 * 3
nstp_transport = perlen / transport_stp_len
tdis_rc = [(perlen, nstp_transport, 1.0)]
flopy.mf6.ModflowTdis(
sim, nper=len(tdis_rc), perioddata=tdis_rc, time_units=time_units
)
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,
atv=atv,
diffc=dmcoef_arr,
pname="DSP-1",
filename=f"{gwtname}.dsp",
)
# Instantiating MODFLOW 6 transport mass storage package
Kd = sp1
flopy.mf6.ModflowGwtmst(
gwt,
porosity=prsity,
first_order_decay=False,
decay=None,
decay_sorbed=None,
sorption="linear",
bulk_density=rhob,
distcoef=Kd,
pname="MST-1",
filename=f"{gwtname}.mst",
)
# Instantiating MODFLOW 6 transport source-sink mixing package
sourcerecarray = [("CHD-1", "AUX", "CONCENTRATION")]
flopy.mf6.ModflowGwtssm(
gwt,
sources=sourcerecarray,
print_flows=True,
filename=f"{gwtname}.ssm",
)
flopy.mf6.ModflowGwtsrc(
gwt,
print_flows=True,
maxbound=len(mf6_bhe),
stress_period_data={0: mf6_bhe},
pname="SRC-1",
filename=f"{gwtname}.src",
)
# Instantiating MODFLOW 6 Flow-Model Interface package
flow_name = gwtname.replace("gwt", "gwf")
pd = [
("GWFHEAD", "../mf6gwf/" + flow_name + ".hds", None),
("GWFBUDGET", "../mf6gwf/" + flow_name + ".bud", None),
]
flopy.mf6.ModflowGwtfmi(gwt, packagedata=pd)
# 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"),
("CONCENTRATION", "STEPS", "15"),
("BUDGET", "LAST"),
],
printrecord=[("CONCENTRATION", "LAST"), ("BUDGET", "LAST")],
filename=f"{gwtname}.oc",
)
return sim
def write_mf2k5_models(mf2k5, mt3d, silent=True):
mf2k5.write_input()
mt3d.write_input()
def write_mf6_models(sim_mf6gwf, sim_mf6gwt, silent=True):
sim_mf6gwf.write_simulation(silent=silent)
sim_mf6gwt.write_simulation(silent=silent)
@timed
def run_models(sim_mf6gwf, sim_mf6gwt, mf2k5=None, mt3d=None, silent=True):
if mf2k5 is not None:
success, buff = mf2k5.run_model(silent=silent)
if mt3d is not None:
success, buff = mt3d.run_model(silent=silent)
success, buff = sim_mf6gwf.run_simulation(silent=silent)
success, buff = sim_mf6gwt.run_simulation(silent=silent)
assert success, buff
Plotting results
Define functions to plot model results.
[4]:
# Figure properties
figure_size = (5.5, 2.75)
def plot_results(
sim_mf6gwf,
sim_mf6gwt,
idx,
mf2k5=None,
mt3d=None,
ax=None,
peclet=0.0,
gradient=0,
seepagevelocity=0,
constantheadright=14,
):
if mt3d is not None:
mt3d_out_path = mt3d.model_ws
# Get the MT3DMS concentration output
fname_mt3d = os.path.join(mt3d_out_path, "MT3D001.UCN")
ucnobj_mt3d = flopy.utils.UcnFile(fname_mt3d)
times_mt3d = ucnobj_mt3d.get_times()
conc_mt3d = ucnobj_mt3d.get_alldata()
mf6_out_path = sim_mf6gwt.simulation_data.mfpath.get_sim_path()
# Get the MF6 concentration output
gwt = sim_mf6gwt.get_model("gwt-" + name)
ucnobj_mf6 = gwt.output.concentration()
times_mf6 = ucnobj_mf6.get_times()
conc_mf6 = ucnobj_mf6.get_alldata()
# Get the x location of the cell centroids
model_centroids_x = []
for i, (cum_pos, half_width) in enumerate(zip(np.cumsum(delr), np.divide(delr, 2))):
if i > 0:
model_centroids_x.append(cum_pos - half_width)
else:
model_centroids_x.append(half_width)
# Next subtract off the location of the BHE
model_centroids_x_BHE = [val - model_centroids_x[21] for val in model_centroids_x]
# Drop the negative locations to the left of the BHE
model_centroids_x_right_of_BHE = model_centroids_x_BHE[22:] # Does not include
# Analytical solution(s)
To = T0 # deg K (initial temperature of the ground)
Y3d = 0.1 # m
Z3d = delz # m
ath = al * trpt # m
atv = al * trpv # m
F0 = -60 # W/m
Fplanar = -600 # W/m^2
va = seepagevelocity
n = prsity # porosity
rhow = 1000.0 # density of water
cw = 4185.0 # heat capacity of water
thermdiff = 1.86e-6 # "molecular diffusion" representing heat
# conduction
x_pos = np.array(model_centroids_x_right_of_BHE)
ss_sln = hechtMendez_SS_3d(
x_pos, To, Y3d, Z3d, ath, atv, Fplanar, va, n, rhow, cw, thermdiff
)
t = 864000 # seconds (10 days)
Y = 0.1 # dimension of source in the y direction
Z = delz # dimension of source in the z direction
R = 2.59 # From Hecht-Mendez manuscript
tr_sln = hechtMendez3d(
x_pos,
t,
Y,
Z,
al,
ath,
atv,
thermdiff,
va,
n,
R,
Fplanar,
cw,
rhow,
)
# list of where to draw vertical lines
avlines = list(range(10)) + list(range(10, 110, 10))
# fill variables with analytical solutions
y_ss_anly_sln = ss_sln
y_tr_anly_sln = [285.15 + val for val in tr_sln]
# fill variables containing the simulated solutions
if mt3d is not None:
y_10_mt_sln = conc_mt3d[0, 6, (42 - 1), 22:]
y_150_mt_sln = conc_mt3d[-1, 6, (42 - 1), 22:]
y_10_mf6_sln = conc_mf6[0, 6, (42 - 1), 22:]
y_150_mf6_sln = conc_mf6[-1, 6, (42 - 1), 22:]
# Create figure for scenario
with styles.USGSPlot() as fs:
sim_name = sim_mf6gwt.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)
for xc in avlines:
ax.axvline(x=xc, color="k", linestyle=":", alpha=0.1)
ss_ln = ax.plot(
x_pos,
y_ss_anly_sln,
"r-",
label="Steady state analytical solution",
)
tr_ln = ax.plot(
x_pos, y_tr_anly_sln, "b-", label="Transient analytical solution"
)
if mt3d is not None:
mt_ss_ln = ax.plot(
x_pos, y_150_mt_sln, "r+", label="Steady state MT3DMS, TVD"
)
mt_tr_ln = ax.plot(x_pos, y_10_mt_sln, "b+", label="Transient MT3DMS")
mf6_ss_ln = ax.plot(x_pos, y_150_mf6_sln, "rx", label="Steady-state MF6-GWT")
mf6_tr_ln = ax.plot(
x_pos,
y_10_mf6_sln,
"bo",
markerfacecolor="none",
label="Transient MF6-GWT",
)
ax.set_xlim(1, 100)
ax.set_ylim(285.15 - 2.1, 285.15 + 0.5)
ax.set_xscale("log")
ax.set_xlabel("x-coordinate, in meters")
ax.set_ylabel("temperature, in Kelvins")
ax.legend()
plt.tight_layout()
if plot_show:
plt.show()
if plot_save:
letter = chr(ord("@") + idx + 1)
fpth = figs_path / "{}{}".format(
"ex-" + sim_name + "-" + letter,
".png",
)
fig.savefig(fpth)
Running the example
Define and invoke a function to run the example scenario, then plot results.
[5]:
def scenario(idx, runMT3D=False, silent=True):
key = list(parameters.keys())[idx]
parameter_dict = parameters[key]
mf2k5 = build_mf2k5_flow_model(key, **parameter_dict) if runMT3D else None
mt3d = build_mt3d_transport_model(mf2k5, key, **parameter_dict) if runMT3D else None
sim_mf6gwf = build_mf6_flow_model(key, **parameter_dict)
sim_mf6gwt = build_mf6_transport_model(key, **parameter_dict)
if write:
if runMT3D:
write_mf2k5_models(mf2k5, mt3d, silent=silent)
write_mf6_models(sim_mf6gwf, sim_mf6gwt, silent=silent)
if run:
run_models(sim_mf6gwf, sim_mf6gwt, mf2k5=mf2k5, mt3d=mt3d, silent=silent)
if plot:
plot_results(
sim_mf6gwf,
sim_mf6gwt,
idx,
mf2k5=mf2k5,
mt3d=mt3d,
**parameter_dict,
)
# ### Two-Dimensional Transport in a Diagonal Flow Field
#
# Compares the standard finite difference solutions between MT3D MF 6
# when the Peclet number is 0
# Not simulated because no known analytical solution to compare to
# scenario(0, silent=False)
# Compares the standard finite difference solutions between MT3D MF 6
# when the Peclet number is 0
scenario(1, silent=False)
# Compares the standard finite difference solutions between MT3D MF 6
# when the Peclet number is 0
scenario(2, silent=False)
Building mf6gwf model...ex-gwt-hecht-mendez-b
Building mf6gwt model...ex-gwt-hecht-mendez-b
writing simulation...
writing simulation name file...
writing simulation tdis package...
writing solution package ims_-1...
writing model gwf-hecht-mendez...
writing model name file...
writing package dis...
writing package ic...
writing package npf...
writing package sto...
writing package chd-1...
INFORMATION: maxbound in ('gwf6', 'chd', 'dimensions') changed to 2158 based on size of stress_period_data
writing package oc...
writing simulation...
writing simulation name file...
writing simulation tdis package...
writing solution package ims_-1...
writing model gwt-hecht-mendez...
writing model name file...
writing package dis...
writing package ic...
writing package adv...
writing package dsp-1...
writing package mst-1...
writing package ssm...
writing package src-1...
writing package fmi...
writing package oc...
FloPy is using the following executable to run the model: ../../../../../../../.local/bin/modflow/mf6
MODFLOW 6
U.S. GEOLOGICAL SURVEY MODULAR HYDROLOGIC MODEL
VERSION 6.5.0 05/23/2024
***DEVELOP MODE***
MODFLOW 6 compiled Jul 4 2024 03:21:22 with GCC version 11.4.0
This software has been approved for release by the U.S. Geological
Survey (USGS). Although the software has been subjected to rigorous
review, the USGS reserves the right to update the software as needed
pursuant to further analysis and review. No warranty, expressed or
implied, is made by the USGS or the U.S. Government as to the
functionality of the software and related material nor shall the
fact of release constitute any such warranty. Furthermore, the
software is released on condition that neither the USGS nor the U.S.
Government shall be held liable for any damages resulting from its
authorized or unauthorized use. Also refer to the USGS Water
Resources Software User Rights Notice for complete use, copyright,
and distribution information.
MODFLOW runs in SEQUENTIAL mode
Run start date and time (yyyy/mm/dd hh:mm:ss): 2024/07/04 3:27:48
Writing simulation list file: mfsim.lst
Using Simulation name file: mfsim.nam
Solving: Stress period: 1 Time step: 1
Run end date and time (yyyy/mm/dd hh:mm:ss): 2024/07/04 3:27:50
Elapsed run time: 1.508 Seconds
Normal termination of simulation.
FloPy is using the following executable to run the model: ../../../../../../../.local/bin/modflow/mf6
MODFLOW 6
U.S. GEOLOGICAL SURVEY MODULAR HYDROLOGIC MODEL
VERSION 6.5.0 05/23/2024
***DEVELOP MODE***
MODFLOW 6 compiled Jul 4 2024 03:21:22 with GCC version 11.4.0
This software has been approved for release by the U.S. Geological
Survey (USGS). Although the software has been subjected to rigorous
review, the USGS reserves the right to update the software as needed
pursuant to further analysis and review. No warranty, expressed or
implied, is made by the USGS or the U.S. Government as to the
functionality of the software and related material nor shall the
fact of release constitute any such warranty. Furthermore, the
software is released on condition that neither the USGS nor the U.S.
Government shall be held liable for any damages resulting from its
authorized or unauthorized use. Also refer to the USGS Water
Resources Software User Rights Notice for complete use, copyright,
and distribution information.
MODFLOW runs in SEQUENTIAL mode
Run start date and time (yyyy/mm/dd hh:mm:ss): 2024/07/04 3:27:50
Writing simulation list file: mfsim.lst
Using Simulation name file: mfsim.nam
Solving: Stress period: 1 Time step: 1
Solving: Stress period: 1 Time step: 2
Solving: Stress period: 1 Time step: 3
Solving: Stress period: 1 Time step: 4
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Solving: Stress period: 1 Time step: 25
Run end date and time (yyyy/mm/dd hh:mm:ss): 2024/07/04 3:28:49
Elapsed run time: 59.926 Seconds
Normal termination of simulation.
run_models took 61466.37 ms
Building mf6gwf model...ex-gwt-hecht-mendez-c
Building mf6gwt model...ex-gwt-hecht-mendez-c
writing simulation...
writing simulation name file...
writing simulation tdis package...
writing solution package ims_-1...
writing model gwf-hecht-mendez...
writing model name file...
writing package dis...
writing package ic...
writing package npf...
writing package sto...
writing package chd-1...
INFORMATION: maxbound in ('gwf6', 'chd', 'dimensions') changed to 2158 based on size of stress_period_data
writing package oc...
writing simulation...
writing simulation name file...
writing simulation tdis package...
writing solution package ims_-1...
writing model gwt-hecht-mendez...
writing model name file...
writing package dis...
writing package ic...
writing package adv...
writing package dsp-1...
writing package mst-1...
writing package ssm...
writing package src-1...
writing package fmi...
writing package oc...
FloPy is using the following executable to run the model: ../../../../../../../.local/bin/modflow/mf6
MODFLOW 6
U.S. GEOLOGICAL SURVEY MODULAR HYDROLOGIC MODEL
VERSION 6.5.0 05/23/2024
***DEVELOP MODE***
MODFLOW 6 compiled Jul 4 2024 03:21:22 with GCC version 11.4.0
This software has been approved for release by the U.S. Geological
Survey (USGS). Although the software has been subjected to rigorous
review, the USGS reserves the right to update the software as needed
pursuant to further analysis and review. No warranty, expressed or
implied, is made by the USGS or the U.S. Government as to the
functionality of the software and related material nor shall the
fact of release constitute any such warranty. Furthermore, the
software is released on condition that neither the USGS nor the U.S.
Government shall be held liable for any damages resulting from its
authorized or unauthorized use. Also refer to the USGS Water
Resources Software User Rights Notice for complete use, copyright,
and distribution information.
MODFLOW runs in SEQUENTIAL mode
Run start date and time (yyyy/mm/dd hh:mm:ss): 2024/07/04 3:28:51
Writing simulation list file: mfsim.lst
Using Simulation name file: mfsim.nam
Solving: Stress period: 1 Time step: 1
Run end date and time (yyyy/mm/dd hh:mm:ss): 2024/07/04 3:28:53
Elapsed run time: 1.701 Seconds
Normal termination of simulation.
FloPy is using the following executable to run the model: ../../../../../../../.local/bin/modflow/mf6
MODFLOW 6
U.S. GEOLOGICAL SURVEY MODULAR HYDROLOGIC MODEL
VERSION 6.5.0 05/23/2024
***DEVELOP MODE***
MODFLOW 6 compiled Jul 4 2024 03:21:22 with GCC version 11.4.0
This software has been approved for release by the U.S. Geological
Survey (USGS). Although the software has been subjected to rigorous
review, the USGS reserves the right to update the software as needed
pursuant to further analysis and review. No warranty, expressed or
implied, is made by the USGS or the U.S. Government as to the
functionality of the software and related material nor shall the
fact of release constitute any such warranty. Furthermore, the
software is released on condition that neither the USGS nor the U.S.
Government shall be held liable for any damages resulting from its
authorized or unauthorized use. Also refer to the USGS Water
Resources Software User Rights Notice for complete use, copyright,
and distribution information.
MODFLOW runs in SEQUENTIAL mode
Run start date and time (yyyy/mm/dd hh:mm:ss): 2024/07/04 3:28:53
Writing simulation list file: mfsim.lst
Using Simulation name file: mfsim.nam
Solving: Stress period: 1 Time step: 1
Solving: Stress period: 1 Time step: 2
Solving: Stress period: 1 Time step: 3
Solving: Stress period: 1 Time step: 4
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Solving: Stress period: 1 Time step: 33
Run end date and time (yyyy/mm/dd hh:mm:ss): 2024/07/04 3:30:07
Elapsed run time: 1 Minutes, 13.900 Seconds
Normal termination of simulation.
run_models took 75650.29 ms
