Question

An accidental spill results in a total volume Vo = 100 gallons of a toxic liquid chemical entering the upper portion of an unconfined aquifer. The aquifer has a porosity η = 0.25 and a hydraulic conductivity K = 10-3 m/s. The density of the liquid chemical is € ρℓ = 1200 kg/m3 and sorption to solids is negligible. Groundwater samples show that the chemical quickly dissolved in the groundwater, forming a "blob" with a total volume (soil and porewater) Vb = 105 m3 .

a) What is the minimum volume of porewater (or volume of the voids) that must be pumped out to remove the contamination?

b) What is the concentration of the chemical in the porewater within the "blob" immediately after dissolution in the groundwater, i.e. neglecting any degradation?

c) The aquifer water table has a constant slope given by Δh/L = 1/1000. The "blob" is moving with the groundwater. As it moves, the chemical is degraded by reaction at a rate given by a firstorder reaction coefficient kr = 1/yr. How far will the "blob" move before the concentration is reduced to 1% of the initial value (i.e. the value immediately after dissolving in the groundwater as in part (b))?

Answer 1

Volume of the toxic liquid, V_o = 100 gallons or 0.3785 m³

Volume of blob (soil and porewater), V_b = 105 m³

Porosity, = 0.25

Hydraulic Conductivity, K = 10^-3 m/s

Density of the liquid chemical, l = 1200 kg/m³

We have to determine the volume of water that must be pumped out to remove the contamination

The volume of porewater = Volume of blob - volume of chemical

= 105 m³ - 0.3785 m³ =104.6215 m³

Concentration of Chemical = mass of chemical /volume of solution

Mass of chemical = volume Xdensity

= 0.3785 m³ x 1200 kg/m³ = 454.2 kg or 454.2 L

Thus, concentration of the liquid = 454.2 L/104.6215 m³

   ⁼ 4.3413 L/m³ or 4.3413 kg/m³