Adam Říčka
Department of Geological Sciences, Faculty of Science, Masaryk University,
Kotlarska 2, 611 37 Brno, Czech Republic
Applied Hydrogeology
Introduction to Modflow
The most widespread computer code for groundwater flow -
MODFLOW
Modflow versions: 88, 96, 2000 and 2005
Software packages with modflow code: PMWIN (version
96), Processing modflow Pro (version 96), Visual Modflow
(version 2000), GMS (version 2000)
PMWIN:
Finite differences, saturated flow, steady-state and transient flow,
water budget, inverse modelling (PEST, UCODE), transport advective
modelling (MT3D, MT3DMS, MOC3D), advective modelling
(PMPATH)
Modflow – introduction
New model – crate new folder choose
simple path (e.g. C:
Document: My model folder)
Grid creation – define modeled
area extent and consequently
define number and size of rows,
columns and layers
Define the layer type – preferable is
the confined/unconfined layer with
transmissivity varies
Modeled area discretization
Keep the mine basical principles and rules in the grid preaparation! (see previous
presentation)
PMWIN – Grid
Environment
Find out:
• Extent of modeled area discretized by grid
• Extent of the underlying map - set up the same size for the
worksheet
• Define X and Y coordinates – Universal Trasnverse
mercator – UTM – depiction of elipsoid’s parts in plan
Environment and Maps
Latitude – 60 zones
marked by numbers
Longitude – 20 zones
marked by letter of the
alphabet
PMWIN – Grid
• Define the left-lower and right-upper edge of the map
(Ctrl + left mouse button - decrease the map view, Shift + left mouse button –
increase the map view)
Environment
move and rotate the model grid to desired position according
to underlaid map
Environment and Maps
Maps
• Underlying map – vector map (DXF) or raster map (bmp,
jpg)
PMWIN – Grid
Define the boundary conditions –
assign number:
• Active cell = 1
• Inactive cell = 0 (II. type)
• Constant cell = -1 (I. type)
Define the top and bottom of layers:
• Manual – cell by cell or zonal input method
• Interpolation – Digitizer, Field interpolator
PMWIN – Grid
Input parameters – time, observations, starting
heads and hydraulic parameters
Time:
Steady state flow type - steady-state flow even for
several Stress periods
Transient flow type – time is discretizated to Time steps
in Stress periods
Choose time unit
Initial starting heads:
• Steady–state flow – require exactly determined
heads only in boundary conditions
• Transient flow – require exactly determined heads
in the whole model
PMWIN – Parameters
• Real-world coordinate system – UTM (The Universal
Transverse Mercator )
• Relative coordinate system – relative position of modeled
grid in the status bar
Boreholes and Observations - insert name, coordinate
system and observed hydraulic head
PMWIN – Parameters
Hydraulic parameters:
• Horizontal hydraulic conductivity – one or more values
• Vertical hydraulic conductivity – in the multi-layer model, the ratio of horizotnal
to vertical conductivity is vertical conductivity ranging from 3:1 to 10:1
• Anisotropy factor – the ratio of horizontal conductivity (or transmissivity) along
the x and y direction
• Vertical leakance – quasi-three dimensional models – replace the modeled
layer and represent semiconfining unit - resistance to the vertical flow
• Transmissivity – define in Layer Type → User specified or Calculated
Lz
L
cz
c
uz
u
K
Z
K
Z
K
Z
VCONT
)()(
2
)(
2
PMWIN – Parameters
Storage parameters - transient simualation – water is released from or taken
into storage within the porous material
• Specific storage (Ss) – volume of water released from storage within a unit
volume of porous material per unit decline in head
• Storage coefficient (S) – in the 2-D areal simulations, vertically averaged
parameter equal to the volume of water released per unit area of aquifer per unit
decline in head
• Specific yield – storage parameter of the unconfined aquifer, volume of gravity
drainaged water per volume of porous material
Effective porosity – advective modelling, from 1 % (fractured rocks) to 35 %
(coarse grained sand or gravel)
sbSS b = aquifer thickness
PMWIN – Parameters
MODFLOW – flow field
MOC3D, MT3D, MT3DMS – transport modeling
PEST, UCODE – automated parameter estimation
PMPATH –
advective modeling
PMWIN – Models
Flow packages - inflow and outflow to/from model and within the model
III. Type of boundary condition
Drain, GHB, Evapotranspiration,
Reservoir, River, Streamflow-
Routing
Sources and Sinks
Recharge, Well
Additional
Horizontal-Flow barriers
Density
Interbed Storage
Wetting Capability
PMWIN – Models
III. Type of boundary condition: flux across is dependent on the difference
between a user-supplied specified head on one side of the boundary and the modelcalculated
head on the other side
L = leakage rate
QL = volumetric flux
A = area of the cell
Kz´ = vertical hydraulic conductivity of the interface
b´ = thickness of the interface
hsource = head in the source reservoir
h = head in the aquifer
• Drain – water releases model
• GHB – simulation of the distant constant head boundary condition
• Evapotranspiration – water releases model in accordance with extinction depth
• River – upper limit for water inflow
• Streamflow Routing – allow hyraulic parameters of the stream channel flow
• Reservoir – similar to River package, allow simulate more reservoirs
)(// ´´
hhbKAQL sourcezL
PMWIN – Models
General Head Boundary - III. Type of boundary condition
LAKCb /.
High Cb represents equivalent of constant head
PMWIN – MODFLOW
River - III. Type of boundary condition
W
KLW
C strriv,
)(, asstrriv hh
M
KLW
Q
K is vertical hydraulic conductivity of riverbed sediments, L is lenght of the river in
the cell, W is wide of the river and M is thickness of the rvierbed sediments
Sources and Sinks:
• Recharge – upper boundary condition
• Well - injection well + injected rate
- pumping well – pumped rate
Well in multi-layer model:
• Confined layer - divide of pumped/injected rate in model in accordance
with transmissivity of each layer
• Unconfined layer – to set a very large vertical hydraulic conductivity (e.g. 1
m/s) to all cells of the well
• Exact extraction rate from each penetrated layer – to set a minimal
pumped rate to the each layer (e.g. 1.10-10) and than use the water budget
calculator
T
T
QQ k
totalk
PMWIN – MODFLOW
Next flow packages:
• Horizontal-Flow barrier – thin impermeable geologic feature (fault, slurry wall),
impede the horizontal flow
• Density – approximation of density flow model without considering the salinity
distribution
• Interbed Storage – water volume released from storage by elastic adn inelastic
compaction of compressible fine-grained beds in a aquifer due to groundwater
extraction
• Wetting capability – the simulation of a rising water table into dry model cells
PMWIN – MODFLOW
Automated parameter calibration:
• Assign parameter number to calibrated value
• Calibrated value : hydraulic parameters, storage parameters, recharge and
boundary conditions III. type
• Output file PESTCTL.REC includes
optimized results
PMWIN – PEST, UCODE
Velocity Vectors
Streamline
Control panel
Information board
Position of the
mouse pointer –
real coordinates
Position of the
mouse pointer
– cell indices
Horizontal
pore velocity
at the cell
Head at
the cell
Vertical
pore
velocity
Current
stress
period
Current
time step
Number of
particles
Advective modeling - based on flow field from Modflow, 3-D demonstration of the flow
PMWIN – PMPATH
MOC3D – define the subrid for solute-transport equations
MT3D, MT3DMS – similar, solute-transport within Modflow grid with own boundary
conditions
Transport models:
• based on the flow field from modflow
• solute transport - advection, affected by disperzion, diffusion and retardation
Input parameters
• Initial Concentration and Source/Sink Concentration
• Advection (from Modflow)
• Disperzion:
Horizontal transverse dispersivity
Vertical transverse dispersivity
Longitudinal dispersivity
• Chemical reaction
The effective molecular diffusion coefficient
Sorption - Linear and unlinear Freundlich and Langmuir equilibrium
isotherm
Rdioactive decay or biodegradation - First order decay rate and First
order sorbed rate
PMWIN – MOC3D, MT3D, MT3DMS
• Digitizer – digitized points
• Field Interpolator – interpolation of digitized points to
the 3-D surface
• Field Generator – stochastic modeling – generate field
with heterogeneously-distributed hydraulic conducitivity
values
PMWIN – Tools
Results Extractor:
Resultant data sets in the sheet
Presentation:
Load resultant data sets
Graphs:
• Time dependent results
• Scatter diagram
PMWIN – Tools
Water Budget
• Check the quality of the simulation results
• Allow flow rates between all faces of model cell
• Zone – flow rate exchange across the cell
• Whole model – compare the discrepancy
Water balance Discrepancy:
• Recommended discrepancy < 1%
• Discrepancy > 1% denotes coarse grid, high closure
(convergence) criterium, too long time step
• Discrepancy > 10% denotes incorrect conceptual model
PMWIN – Tools
Anderson, M. P., Woessner, W. W. (1992): Applied Groundwater Modeling,
Simulation of Flow and Advective ransport.- Academic Press Inc., San Diego,
California.
Andersen, P. F. (1998): A manual of instructional problems for the U.S.G.S.
Modflow model.- Robert S. Kerr enviromental research laboratory office of
research and development U.S. enviromental protection agency, Oklahoma.
Hsing Chiang, W., Kinzelbach, W. (2000): 3D-Groundwater Modeling with
PMWIN.- Springer.
www.Wikipedia.com
References