Question 3 of 8: Rail Tanker Derailment — PCE Release

Question A-3: Rail Tanker Derailment — PCE Release (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. Spill volume $V=10{,}000$ L PCE (a dense, non-aqueous-phase liquid — DNAPL); silty loam soil with gravimetric water content $w=15\%$, porosity $n=0.51$, bulk density $\rho_b=1375\ \text{kg/m}^3$; depth to the unconfined water table $z_{wt}=2.0$ m; a house 500 m away drawing from a private well into a separate confined aquifer 30 m below grade, with groundwater flow toward the house.

Find. Describe the fate of the released PCE, and estimate whether the vadose-zone soil can retain the release within the top 2.0 m before it reaches the water table.

Approach. Because PCE is denser than water (unlike a fuel/oil LNAPL), it behaves as a mobile DNAPL that sinks under gravity rather than floating; a first-order screening bound on whether it is retained in the unsaturated zone comes from comparing the spill volume to the soil’s own available (air-filled) pore volume down to the water table.

1. Describe DNAPL behaviour. As PCE drains from the punctured tank over 3.5 h, it infiltrates vertically under gravity through the silty loam. Because PCE is a DNAPL ($\rho \approx 1.62\ \text{g/cm}^3$, denser than both water and typical LNAPL fuels), it does not pool on the water table the way a fuel spill would; instead a fraction wets and is trapped in soil pores as it migrates (residual saturation), and any mobile excess continues past the water table into the saturated zone, sinking under gravity until it reaches a low-permeability layer or spreads laterally along the direction of any confining bed, forming DNAPL pools that act as a long-term source dissolving slowly into the groundwater (PCE’s aqueous solubility is low, ∼150–200 mg/L, so dissolution is a slow, persistent process rather than a rapid pulse). PCE is non-flammable (used industrially as a dry-cleaning/degreasing solvent), consistent with the “no explosion” statement, but its vapour is a chronic inhalation hazard (suspected carcinogen), so first responders still require SCBA/vapour monitoring even without a fire risk.
2. Compute the soil’s water-filled and air-filled porosity. Volumetric water content from the given gravimetric content and bulk density: $\theta_w = w\cdot\rho_b/\rho_{water} = 0.15\times 1375/1000 = \boxed{0.206}$. Air-filled (available) porosity: $\theta_a = n-\theta_w = 0.51-0.206=\boxed{0.304}$ — this is the pore space physically available to imbibe DNAPL as it infiltrates.
3. Retention capacity of the 2.0 m vadose zone. Treating the available porosity as the volume that must be filled before excess liquid can pass the water table, the retention capacity per unit surface area is $\theta_a \times z_{wt} = 0.304\times 2.0 = 0.6075\ \text{m}^3/\text{m}^2 = \boxed{607.5\ \text{L/m}^2}$.
4. Minimum footprint needed to fully retain the spill. Setting the spill volume equal to (retention capacity) × (footprint area): $A_{min} = V/(\theta_a z_{wt}) = 10{,}000\ \text{L}/607.5\ \text{L/m}^2 = \boxed{16.5\ \text{m}^2}$. A punctured rail tanker draining over 3.5 h at a derailment site (car length typically 15–18 m) will very plausibly pool over an area well in excess of this — so on a simple areal-average basis the vadose zone likely has enough capacity to retain the release above the water table.

That conclusion is optimistic, not assured: real DNAPL infiltration is dominated by fingering and preferential pathways (root channels, sand seams within the silty loam) rather than uniform lateral spreading, so a meaningfully smaller effective footprint can locally exceed capacity and let free-phase PCE reach the 2.0 m water table regardless of the areal average. The professional response therefore does not stop at this bounding calculation.

On the receptor side, the house’s private well draws from a separate confined aquifer 30 m below grade, below the unconfined aquifer the PCE enters at 2.0 m — the confining layer separating the two provides some protection provided it is intact, but the well’s own casing/annular seal is a plausible vertical conduit if improperly sealed, and should be inspected as part of the response. Because groundwater flow in the shallow (unconfined) system runs toward the house, and the house also has a septic tank (an additional subsurface receptor/pathway consideration and a reason to avoid cross-contamination of investigative and drinking-water sampling), a precautionary sampling of the private well and nearby shallow monitoring points is warranted immediately, independent of the outcome of Step 4 above.