CE 4363/5363 Groundwater Transport Phenomena
Spring 2023 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.
In [1]:
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Problem 2 (Problem 6-2, pg. 567)

Chloride (πΆπ‘™βˆ’) 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.
In [2]:
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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.
In [3]:
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Solution Sketch

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