Introduction to MODFLOW

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Introduction to MODFLOW
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General 3D equation used in MODFLOW
Block centered grid
?xi
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K values in the space between nodes is
calculated using the harmonic mean
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The default boundary condition is no flow.
(active nodes)
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No flow boundary
Imaginary nodes
K0
(i1)
(i,j,k)
K0
K0
0
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MODFLOW Grid
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Darcys law
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In general, conductance
KA/?L
Also leakance Kv/thickness resistance
thickness/Kv (resistance is an analytic element
term)
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Vertical Conductance Terms
MODFLOW uses special terms (VCONT) for vertical
conductance, which is required in 3D problems.
Modflow.exe requires the user to supply values
for the VCONT arrays. GW Vistas computes the
values in the VCONT arrays for you.
VCONT Kv/?z Conductance/(?x?y)
leakance
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Vertical conductance is defined using leakance,
or VCONT in MODFLOW language.
We also have horizontal conductance along
rows and along columns.
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See MODFLOW manual (p. 2-19) or 2nd ed. of
textbook by Domenico Schwartz (Eqn. 7.15) for
MODFLOWs FD equation
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Types of Layers (LAYCON array) Confined Unconfined
Convertible (Useful to think in terms of a
layer transmissivity.)
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Conductance
Confined layer transmissivity (KRi,j-1/2,k)(?vk)
Unconfined layer transmissivity
(KRi,j-1/2,k)(hi,j,k-BOTi,j,k)
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Input of Grid Spacing

• MODFLOW asks for values of horizontal grid
  spacing
• (i.e., ?r and ?c) but not vertical grid spacing
  (?v).

• Vertical grid spacing (?v) is calculated by
  MODFLOW
• from user supplied values of the bottom (BOT)
• of each layer. (GwVistas asks for both top and
  bottom of
• each layer.)

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Note that a top unconfined layer actually has no
top. The head value in the top layer could
potentially rise to infinity.
Land surface elevation is not used in MODFLOW,
except in the ET package.
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Examples of solution techniques that
combine matrix solution with iteration IADI
(see chapter 5 of WA) SSOR SIP PCG2 Used
in MODFLOW
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m1
Note m is time level and n is iteration level.
?t
m
m-1
Schematic of solution procedure
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The 3D eqn. with an implicit approximation generat
es a coefficient matrix with 7 diagonals
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Coefficient Matrix for a model with 2 rows, 3
columns, 2 layers. Matrix is sparse and symmetric.
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SSOR
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SSOR The coefficient matrix has 5 diagonals
Coefficient matrix is Symmetric and banded
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From MODFLOW manual
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MODFLOW88/96 Packages
required
required
head dependent BCs
1 is required
PCG2
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Input assembly for the BAS Package
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