Question 7 of 8: TCE Migration and Pump-and-Treat Remediation

Question B-2: TCE Migration and Pump-and-Treat Remediation (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Find. (i) baseline travel time for TCE to clear the building footprint; (ii) pump-and-treat clean-up time; (iii) options to accelerate extraction beyond the aquifer’s maximum pumping rate.

Approach. The given flow values are treated as Darcy flux (specific discharge); converting to seepage velocity via porosity gives the true average linear groundwater velocity for part (i). For part (ii), pump-and-treat clean-up time is a mass-balance problem: the total TCE mass present must be removed at the rate the extracted water carries it out, using the flow through the spill zone’s cross-section (3 m × 4 m, perpendicular to the 10 m flow path) at the elevated pumping rate.

1. Part (i) — seepage velocity and travel time. Seepage (average linear) velocity: $v_s=q_1/n=0.03/0.30=0.10\ \text{m/d}$. Time to migrate the length of the spill zone (10 m, the dimension along the flow path) and clear the building footprint: $t=\dfrac{L}{v_s}=\dfrac{10}{0.10}=\boxed{100\ \text{d}}$.
2. Part (ii) — extraction flow rate. At the elevated Darcy flux $q_2=0.30$ m/d through the 3 m×4 m cross-section: $Q=q_2\,A_{cross}=0.30\times(3\times4)=\boxed{3.6\ \text{m}^3/\text{d}}$.
3. Total TCE mass present. Using the unaccounted spill volume and TCE’s specific gravity: $m_{TCE}=V_{TCE}\times SG=3000\ \text{L}\times1.47\ \text{kg/L}=\boxed{4410\ \text{kg}}$.
4. Mass-removal rate and clean-up time. At the extracted concentration $C_2=250$ mg/L and flow $Q=3.6\ \text{m}^3/\text{d}=3600\ \text{L/d}$: removal rate $=C_2\,Q=250\times3600=900{,}000\ \text{mg/d}=900\ \text{g/d}$. Time to remove the full 4,410 kg: $t=\dfrac{4{,}410{,}000\ \text{g}}{900\ \text{g/d}}=4900\ \text{d}\approx\boxed{13.4\ \text{years}}$.

Part (iii) — accelerating extraction beyond the pumping-rate ceiling. Since the aquifer’s hydraulic transmissivity caps a single well’s achievable flow at 0.3 m/d, further acceleration has to come from methods that do not depend on raising bulk groundwater flow through one well: install additional extraction wells to increase the total hydraulic capture without exceeding any one well’s individual pumping-rate limit; add in-situ enhancement — air sparging/soil vapour extraction to exploit TCE’s volatility and strip it directly from groundwater and the unsaturated zone, or in-situ chemical oxidation (e.g., permanganate) to destroy TCE in place rather than relying solely on pump-out; enhanced reductive dechlorination (electron-donor injection with bioaugmentation) to biologically degrade TCE in place; and pulsed (rather than continuous) pumping, which allows sorbed/back-diffused TCE mass in lower-permeability zones to re-equilibrate into the mobile pore water between pumping cycles, improving the mass recovered per unit of water extracted and mitigating the classic pump-and-treat "tailing" problem that the 13.4-year estimate above already hints at.