Problem Set 2 is based

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Problem Set 2 is based on a problem in the
MT3D manual also discussed in ZB, p. 228-231.
2D steady state flow in a confined aquifer
We want to predict the breakthrough curve at
the pumping well. The transport problem is
transient.
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Zone of low hydraulic conductivity
Peclet numbers 5 and 25
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GWV screen
Note the heterogeneity is not present in the
first column
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Units in MT3D see p. 6-8 in the manual
Concentration units do not have to be consistent
with the units used for other parameters. It is
permissible, for example, to use ft for the
system parameters and mg/l for concentration. How
ever, in that case the units calculated in the
mass balance will have inconsistent units and the
mass balance numbers will need to be manually
corrected.
Recommended use ppm mg/l ? gm/m3 That is, use
meters mass is reported in grams.
Mass c Q ?t
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NOTE. These results were produced using an old
version of MT3DMS. Please run again with the
latest version of the code.
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MT3DMS Solution Options
PS2
1
3
4
2
8
Central Difference Solution
Time step multiplier 1 41 time steps
Time step multiplier 1.2 13 time steps
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Courant number
See information on solution methodologies
under the MT3DMS tab on the course homepage for
more about these parameters.
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Boundary Conditions
---for flow problem ---for transport problem
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Head solution-- Flow problem is steady state
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Transport Problem
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Need to designate these boundary cells as
inactive concentration cells. Use zone 10 in the
diffusions properties menu of Groundwater Vistas.
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Cells in first row are in zone 10 in the
diffusion properties menu
This is necessary to prevent loss of mass through
the boundary by diffusion.
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Solution at t1 year
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Mass Balance Considerations in MT3DMS
Sources of mass balance information .out
file .mas file mass balance summary in GW Vistas
See supplemental information for PS2 posted on
the course homepage for more information on mass
balance options.
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Water Flow IN through upper boundary
injection well OUT pumping well
lower boundary
wells
IN - OUT ?S where ?S 0 at steady state
conditions
Mass Flux IN through injection well
changes in storage OUT pumping well
lower boundary changes in storage
Mass Balance states that Mass IN Mass
OUT where changes in mass storage are considered
either as contributions to mass IN or to mass OUT.
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From the .out file (TVD solution)
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Mass Storage Water
Consider a cell in the model
IN - OUT ?S where change in storage is ?S
S(t2) S(t1)
If IN gt OUT, the water level rises and there is
an increase in mass of water in the cell. IN
OUT ?S, where ?S is positive. Note that ?S is
on the OUT side of the equation.
If OUT gt IN IN ?S OUT, where ?S is
negative ?S is on the IN side of the equation.
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From the .out file (TVD solution)
?S
?S ? ?c (?x ?y ?z ?)
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Mass Storage Solute
IN - OUT ?S where change in storage is ?S
S(t2) S(t1)
If IN gt OUT, concentration in cell increases
and there is an increase in solute mass in the
cell. IN OUT ?S, where ?S is positive. Note
that ?S is on the OUT side of the equation. There
is an apparent sink inside the cell.
If OUT gt IN, the concentration in cell decreases
and there is a decrease in solute mass in the
cell. IN ?S OUT, where ?S is negative and
?S is on the IN side of the equation. There is
an apparent source inside the cell.
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From the .out file (TVD solution)
?S
IN OUT 0 (INsource?SIN) - (OUTsource
?SOUT) 0 ?SIN - ?SOUT ? Storage
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HMOC .mas file
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General form of the ADE
Expands to 9 terms
Expands to 3 terms
Where does the extra term come from?
(See eqn. 3.48 in ZB)
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Assume local chemical equilibrium (LEA)
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HMOC .mas file
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Mass Balance error for FD solutions should be
less than 1.
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MOC methods typically report high mass balance
errors, especially at early times.
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TVD Solution
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From the .out file (TVD solution)
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From the .out file (TVD solution)
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Last ?t 0.0089422 yr
Mass Flux (mass at t2 - mass at t1) / ?t