Problem 1 (Problem 6-7, pg. 588)¶
An instantaneous release of biodegradable constituients occurs in a 1-D aquifer. Assume the mass released is $1.0 ~kg$ over a $10~m^2$ area normal to the flow direction, $\alpha_l = 1.0~m$, the seepage velocity is 1.0 $\frac{m}{day}$, and the half-life of the decaying constituient is 33 years.
Determine:
- The maximum concentration at 100 meters from the source.
- Plot a concentration history (annual intervals) for a 40 year period from release date for a location 100 meters from the source.
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Problem 2 (Problem 6-9, pg. 589)¶
An unintentional discharge from a point source introduced $10~kg$ of contaminant mass to an aquifer. The seepage velocity is $0.1~\frac{ft}{day}$ in the $+x$ direction. The longitudinal dispersion coefficient is $D_x = 0.01 \frac{ft^2}{day}$ the transverse dispersion coefficients are $D_y = D_z = 0.001 \frac{ft^2}{day}$.
Determine:
- Calculate the maximum concentration at $x=100~ft$ and $t=5~years$.
- Calculate the concentration at $(x,y,z,t) = (200~ft,5~ft,2~ft,5~years)$
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Problem 3 (Problem 6-10, pg. 589)¶
Apply the Domenico and Schwartz (1998) planar source model (pg. XXX) to a case of a continuous source that has been leaking contaminant into an aquifer for 15 years. The source had a width $Y=6~m$ and depth $Z=6~m$. The source concentration is $10~\frac{mg}{l}$. The seepage velocity is $0.057~\frac{m}{day}$. The longitudinal, transverse, and vertical dispervities are $1~m$,$0.1~m$, and $0.01~m$ respectively.
Determine:
- The contaminant concentration history at a location $x=200~m$ from the source using 1-year increments for 30 years.
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Problem 4¶
The following table has data from a column test with bromide (conservative) and chromium (sorbed). The porosity of the soil was 0.485, the bulk density was 1.85 g/cc, velocity was 0.244 cm/min, and the column was 25.4 cm long with a diameter of 2.54 cm.
| Time (min) | Bromide $\frac{C}{Co}$ | Chromium $\frac{C}{Co}$ |
|---|---|---|
| 0 | 0.000 | 0.000 |
| 15 | 0.000 | 0.000 |
| 30 | 0.005 | 0.000 |
| 45 | 0.003 | 0.000 |
| 60 | 0.013 | 0.000 |
| 75 | 0.075 | 0.000 |
| 90 | 0.137 | 0.000 |
| 105 | 0.530 | 0.000 |
| 120 | 0.841 | 0.000 |
| 135 | 1.000 | 0.000 |
| 150 | 1.000 | 0.000 |
| 165 | 1.000 | 0.009 |
| 180 | 1.000 | 0.186 |
| 195 | 1.000 | 0.595 |
| 210 | 1.000 | 0.791 |
| 225 | 1.000 | 0.875 |
| 240 | 1.000 | 0.913 |
| 255 | 1.000 | 0.946 |
| 270 | 1.000 | 0.946 |
| 285 | 1.000 | 1.000 |
| 300 | 1.000 | 1.000 |
| 315 | 1.000 | 1.000 |
| 330 | 1.000 | 1.000 |
| 345 | 1.000 | 1.000 |
| 360 | 1.000 | 1.000 |
Determine:
- The dispersivity in cm
- The retardation coefficient for $Cr$.
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Problem 5¶
A batch isotherm test was performed with several 1-L solutions of the chemical of interest and one soil type, 20 g in each solution container. The initial and final solution concentrations are shown in the table. Fit the linear, Freundlich, and Langmuir isotherm equations to this data.
| Initial Concentration (mg/L) | Equilibrium Concentration (mg/L) |
|---|---|
| 7.10 | 6.71 |
| 4.53 | 4.18 |
| 1.89 | 1.63 |
| 1.31 | 1.10 |
| 1.03 | 0.85 |
Determine:
- The Linear isotherm equation for these data (i.e. fit the isotherm model to the data), plot the isotherm and data
- The Freundlich isotherm equation for these data, plot the isotherm and data
- The Langmuir isotherm equation for these data, plot the isotherm and data
- Which isotherm model produces the best fit for these data?
Show calculations and identify all fitted parameter values.
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