Question 8 of 8: Sorption-Controlled Extent of a BTEX Wastewater Spill

Question B-3: Sorption-Controlled Extent of a BTEX Wastewater Spill (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. Total spilled wastewater volume (3 tank cars), BTEX concentration, soil bulk density, total porosity, gravimetric water content, fraction of organic carbon, and the sorption distribution coefficient.

Find. (i) the volume of soil wetted (contaminated) by the spill; (ii) the depth of penetration at the restricted footprint; (iii) how a higher sorption affinity would change the outcome; (iv) a remediation approach.

Approach. Mass-balance the spilled liquid volume into the soil's available (not already water-filled) pore space to get the wetted soil volume, then divide by the stated footprint for depth; use the retardation factor built from K_d to frame the sorption-affinity discussion.

1. Total spill volume. $$V_{spill} = 3\times 70{,}000\ \text{L} = 210{,}000\ \text{L} = 210\ \text{m}^3$$
2. BTEX mass released (context for part iii): $$M_{BTEX} = V_{spill}\times C = 210{,}000\ \text{L}\times 325\ \tfrac{\text{mg}}{\text{L}} = 68.25\ \text{kg}$$
3. Available porosity ahead of the wetting front. The soil already holds some pore water, so only the unoccupied porosity can accept the spill: $$\theta_w = w\times\frac{\rho_b}{\rho_w} = 0.15\times\frac{1{,}300}{1{,}000} = 0.195, \qquad n_{eff} = n-\theta_w = 0.50-0.195 = 0.305$$
4. Volume of soil wetted by the spill. $$V_{soil} = \frac{V_{spill}}{n_{eff}} = \frac{210\ \text{m}^3}{0.305} \approx \boxed{689\ \text{m}^3}$$
5. Penetration depth at the restricted footprint. $$d = \frac{V_{soil}}{A} = \frac{689\ \text{m}^3}{40\ \text{m}^2} \approx \boxed{17.2\ \text{m}}$$

(iii) Effect of a higher sorption affinity. The retardation factor built from the given K_d quantifies how much of the contaminant is captured on the soil rather than moving with the wetting front: $$R = 1+\frac{\rho_b}{n}K_d = 1+\frac{1.3\ \text{kg/L}}{0.50}\times1.8\ \tfrac{\text{L}}{\text{kg}} = 5.68$$ A chemical with a higher affinity for sorption (a larger K_d, equivalently a larger K_oc at the same f_oc, or a higher f_oc×K_oc product) produces an even larger R. Physically, more of the released mass partitions instantaneously onto the immobile soil solids close to the source rather than travelling with the infiltrating liquid, so the plume/wetted volume the mass actually reaches is smaller and shallower than the values computed above — but the soil concentration retained near the source is correspondingly higher. This is a double-edged outcome for remediation: a smaller footprint is easier to delineate, but a strongly-sorbed contaminant desorbs slowly and requires many more pore volumes of flushing to remove, which is precisely why the question frames part (i) as “sorption kinetics governs” — the contaminated volume, not just the plume length, is what a sorption-controlled spill is really defined by.

(iv) Remediation approach. Excavation and off-site disposal or thermal desorption is appropriate for the shallow, near-source zone where concentrations are highest and the material is accessible; below that, soil vapour extraction is well suited to the volatile BTEX fraction in this still-unsaturated silt loam. Because BTEX is readily biodegradable aerobically, enhanced bioremediation (biosparging/bioventing, paralleling Question B-2) is an effective polishing step for residual mass left by excavation and SVE, with in-situ chemical oxidation reserved for zones where a faster destruction timeline is required. Given the spill is on active farmland, the remediation plan also needs to evaluate the direct soil-contact and crop-uptake exposure pathways (not just groundwater), and BC Environmental Management Act spill-reporting and notification requirements are triggered at this release volume. A long-term monitoring well network confirms that any downgradient dissolved-phase mass continues to attenuate to acceptable levels before the land is returned to agricultural use.