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Problem Set 2 is based on a problem in the MT3D manual; also discussed in Z&B, 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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Peclet numbers = 5 and 25 Zone of low hydraulic conductivity
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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 Recommended: use ppm= mg/l gm/m 3 That is, use meters; mass is reported in grams. Mass = c Q t 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. However, 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.
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Cs = 57.87 ppm Cs = 0
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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 1 2 3 4 PS#2
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Central Difference Solution Time step multiplier = 1 41 time steps Time step multiplier = 1.2 13 time steps
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See information on solution methodologies under the MT3DMS tab on the course homepage for more about these parameters. Courant number
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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 t=1 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 PS#2 posted on the course homepage for more information on mass balance options.
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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. Water Flow: IN= through upper boundary; injection well OUT= pumping well; lower boundary Mass Flux: IN= through injection well; changes in storage OUT= pumping well; lower boundary; changes in storage wells IN - OUT = S where S = 0 at steady state conditions
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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 > 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 > 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) SS 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 > 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 > 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) SS IN – OUT = 0 (INsource+ S IN ) - (OUTsource + S OUT )= 0 S IN - S OUT = Storage
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HMOC *.mas file q’ s =
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General form of the ADE: Expands to 9 terms Expands to 3 terms (See eqn. 3.48 in Z&B) Where does the extra term come from? q’ s =
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Assume local chemical equilibrium (LEA): Isotherms
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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) SS IN – OUT = 0 (INsource+ S IN ) - (OUTsource + S OUT )= 0 S IN - S OUT = Storage
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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
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