Question 6 of 8: Section B — Two of Three Questions

Question B-1: Toluene Wastewater Penetration into a Clay Retention Dyke (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) the depth of toluene penetration into the clay; (ii) the first remedial priority; (iii) a mobility classification for toluene in this soil.

Approach. With no exponent given, the Freundlich isotherm is taken as linear ($N=1$), so $K_f$ acts as a distribution coefficient $K_d$. The wastewater first wets the clay’s available (air-filled) pore space, defining a bulk water-infiltration front; toluene sorbs onto the clay as it migrates, retarding the dissolved toluene front relative to that water front by the standard retardation factor.

1. Available (air-filled) porosity. Volumetric water content already held by the clay: $\theta_w=w\rho_b/\rho_{water}=0.15\times1300/1000=0.195$. Available porosity for the spilled wastewater to occupy: $\theta_a=n-\theta_w=0.50-0.195=\boxed{0.305}$.
2. Bulk wetting-front (water) depth. The 25,000 L (25 m³) of wastewater infiltrates the available pore space over the confined 35 m² dyke floor: $d_{water}=\dfrac{V}{\theta_a A}=\dfrac{25}{0.305\times35}=\boxed{2.34\ \text{m}}$.
3. Retardation factor for toluene. With $K_d=K_f=0.2$ L/kg $=2\times10^{-4}\ \text{m}^3/\text{kg}$: $R=1+\dfrac{\rho_b}{n}K_d=1+\dfrac{1300}{0.50}\times2\times10^{-4}=1+0.52=\boxed{1.52}$.
4. Toluene penetration depth. Sorption retards the dissolved toluene front relative to the bulk water front by the factor $R$: $d_{toluene}=\dfrac{d_{water}}{R}=\dfrac{2.34}{1.52}=\boxed{1.54\ \text{m}}$.

Part (ii) — recommended first remedial step. Because the toluene front is retained within the top ∼1.5 m of the clay dyke — a shallow, well-defined, and readily accessible zone — excavation and off-site disposal (or ex-situ treatment such as land-farming/thermal desorption) of the impacted clay is the appropriate first remedial step, not a long-duration in-situ groundwater technology. The clay’s very low hydraulic conductivity would make in-situ pump-and-treat or flushing extremely slow, while a shallow, contained excavation can be completed quickly and confirmed by direct sampling of the open cut.

Part (iii) — mobility classification. $K_f=0.2$ L/kg is a very low distribution coefficient (toluene has only weak affinity for this clay’s organic carbon, consistent with its own modest $K_{oc}\approx150$ L/kg and the clay’s low $f_{oc}=1.5\%$), and the resulting retardation factor $R=1.52$ is close to 1 — toluene is only mildly retarded relative to the water itself. Toluene should therefore be classified as highly to moderately mobile in this soil chemically; the dominant restraint on its overall spread is not sorption but the clay’s own very low hydraulic conductivity, which limits how quickly any dissolved-phase toluene can migrate further once the initial wastewater volume has infiltrated.