. A saline (salt) solution with a concentration of 370 mg/L is introduced into a 3.0-m-long sand column in which the pores are initially filled with distilled water. The solution drains through the column at an average linear velocity of 0.79 m/d and the longitudinal dispersivity of the sand column is 15 cm. In answering the following, assume there is no retardation of the saline solution and assume that molecular diffusion is not important.

a) How long will it take for the advective front to reach the effluent (end) of the column?

b) What is the concentration of salt in the effluent 4.1 days after flow begins? Use the full and abbreviated forms of the Ogata-Banks Solution. Do they give different answers?

2. The contents of a canal are leaking into a shallow aquifer. The water in the canal is suddenly polluted by a discharge of industrial waste that contains a non-degradable chemical and non-retarded chemical: 1,4-dioxane. The concentration of 1,4-dioxane in the canal is 0.90 mg/L. The aquifer has an average linear velocity of 1.25 ft/d.

a) Use the Xu and Eckstein relationship to estimate the longitudinal dispersivity for a plume length of 30 ft.

b) What is the concentration of 1,4-dioxane at a distance 75 ft from the discharge after 50 days? (D* = 1.0 ×10−9 m2/s). Assume the system can be approximated as 1-dimensional flow.

c) What is the concentration at a distance of 150 ft after 70 days?

d) In b) and c), are you behind or ahead of the advective front?

e) Plot the concentration as a function of time at a monitoring well that is directly downgradient of the discharge and 300 ft away. Be sure to use times that are large enough so that eventually, the plot reaches C = C0.

3. A manufacturing facility prints circuit boards using TCE. The TCE washwater spills into a shallow groundwater at a steady rate such that it creates a continuous source of 10.0 mg/L. The groundwater beneath the site has an average linear velocity of 1.0 ft/d. The fractional organic carbon content of the soil is 0.012. The bulk density of the soil is 1.6 g/mL. The porosity is 0.35 and effective porosity is 0.18.

a) What is the retardation coefficient for TCE in this system?

b) Estimate the longitudinal dispersivity using a plume length of 600 feet using the Xu and Eckstein relationship.

c) What is the concentration of TCE at a well 75 feet directly downgradient of the spill after 200 days? Use the full Ogata-Banks solution with retardation. Assume no degradation of TCE.

d) If the TCE did not adsorb to the soil what would the concentration be at this well after 200 days? Assume no degradation of TCE.

e) Recalculate the concentration at 200 days assuming TCE is retarded and degrades according to a first order rate with coefficient of 0.01 /d.

f) What is the concentration of TCE at this well once the plume has reached steady state? Assume retarded transport and that degradation of TCE at a first order rate with coefficient of 0.01 /d.