Contents

F23 Exercise Set 2

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Purpose :

Apply selected analytical models for conservative (non-reactive) transport

Assessment Criteria :

Completion, results plausible, format correct, example calculations shown.

Problem 1 (Problem 6-1, pg. 567)

Chloride (\(Cl^{-}\)) is injected as a continuous source into a 1-D column 50 centimeters long at a seepage velocity of \(10^{-3}~\frac{cm}{s}\). The effluent concentration measured at \(t=1800~s\) from the start of the injection is \(0.3\) of the initial concentration, and at \(t=2700~s\) the effluent concentration is measured to be \(0.4\) of the initial concentration.

Determine:

  1. Sketch the system.

  2. The longitudinal dispersivity.

  3. The dispersion coefficient.

  4. The volumetric flow rate through the column.

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Problem 2 (Problem 6-2, pg. 567)

Chloride (𝐶𝑙−) is injected as a continuous source into a 1-D column. The system has Darcy velocity of \(5.18 \times 10^{-3}~\frac{in}{day}\), a porosity of \(n=0.30\), and longitudinal dispersivity of \(5 m\).

Determine:

  1. Sketch the system.

  2. The ratio \(\frac{C}{C_0}\) at a location 0.3 meters from the injection location after 5 days of injection.

  3. The ratio \(\frac{C}{C_0}\) at a location 0.3 meters from the injection location after 5 days of injection, if the dispersivity is 4 times larger (\(20 m\)).

  4. Comment on the difference in results.

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Problem 3 (Problem 6-3, pg. 587)

The estimated mass from an instantaneous release of benzene is \(107 \frac{kg}{m^2}\) of a 1-D aquifer system. The aquifer has a seepage velocity of \(0.03 \frac{in}{day}\) and a longitudinal dispersion coefficient of \(9 \times 10^{-4}\frac{m^2}{day}\)

Determine:

  1. Sketch the system.

  2. Plot a concentration profile at \(t = 1~\text{year}\) for \(x = 0\) to \(x = 50\) inches, in 1-inch increments.

  3. Plot a concentration history at \(x=v\times (1~\text{year})\) (this value stays constant) for \(t = 0\) to \(t = 2 \) years in \(\frac{1}{12}\)-year increments.

  4. The maximum concentration at \(t = 1~\text{year}\) and its location.

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