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18-Env-B4 Site Assessment and Remediation · May 2014

Question 7 of 8: Benzene Sorption and Retarded Plume Travel Time

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — May 2014 — 04-Env-B4 / Site Assessment and Remediation. 3 hours duration; open-book exam (any non-communicating calculator permitted). The paper is split into Section A (five questions, candidates asked to answer three) and Section B (three questions, candidates asked to answer two), each question worth 20 marks. All eight questions are solved below for completeness.

Reference texts. Suthersan & Payne, Remediation Engineering: Design Concepts (CRC Press); Gavaskar, Gupta, Sass, Janosy & O'Sullivan, Design Guidance for Application of Permeable Reactive Barriers for Groundwater Remediation (Battelle/EPA, 2000); ASTM E1527 Standard Practice for Phase I Environmental Site Assessments and ASTM E1903 Standard Practice for Phase II ESA; Mercer & Cohen (1990), “A review of immiscible fluids in the subsurface,” Journal of Contaminant Hydrology; Freeze & Cherry, Groundwater; Davis & Cornwell, Introduction to Environmental Engineering (6th ed.); Ontario Reg. 153/04 under the Environmental Protection Act (Record of Site Condition regime); BC Environmental Management Act — Contaminated Sites Regulation.

Section A — Three of Five Questions

Question B-2: Benzene Sorption and Retarded Plume Travel Time (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. $C_w = 700\ \mu\text{g/L} = 0.700$ mg/L (dissolved benzene); soil bulk density $\rho_b = 1450$ kg/m³; porosity $n = 0.42$; fraction organic carbon $f_{oc} = 1.5\%$; $K_{oc} = 85$ mL/g; groundwater (seepage) velocity $v = 0.00002$ km/h; target travel distance 2 km.

Find. The sorbed benzene concentration, the retardation factor, and the travel time for the (retarded) contaminant front to migrate 2 km.

Approach. Linear equilibrium sorption ($K_d=K_{oc}f_{oc}$) partitions benzene between water and soil organic carbon; the retardation factor built from $K_d$ then slows the effective contaminant velocity relative to the groundwater itself.

  1. Soil–water partition coefficient. $K_d = K_{oc}f_{oc} = 85\ \text{mL/g} \times 0.015 = \boxed{1.275}\ \text{mL/g}\ (=\text{L/kg})$.
  2. Sorbed concentration. Assuming local equilibrium, $C_s = K_d C_w = 1.275 \times 0.700 = \boxed{0.8925}\ \text{mg/kg soil}$ (equivalently ≈1.29 mg per litre of bulk aquifer material, using $\rho_b$).
  3. Retardation factor. $R = 1 + \dfrac{\rho_b K_d}{n} = 1 + \dfrac{1450\ \text{kg/m}^3 \times 1.275\times10^{-3}\ \text{m}^3/\text{kg}}{0.42} = \boxed{5.40}$.
  4. Contaminant (retarded) velocity. Groundwater velocity $v = 0.00002$ km/h $= 0.48$ m/d; the dissolved benzene front travels at $v_c = v/R = 0.48/5.40 = 0.0889$ m/d.
  5. Travel time for 2 km. $t = \dfrac{2000\ \text{m}}{0.0889\ \text{m/d}} = 22{,}500\ \text{d} = \boxed{61.6}\ \text{years}$.
Final Results
QuantityValue
Soil–water partition coefficient, $K_d$1.275 L/kg
Sorbed benzene concentration, $C_s$0.8925 mg/kg soil
Retardation factor, R5.40
Retarded (contaminant) velocity0.089 m/d
Travel time to reach 2 km≈61.6 years

A 61.6-year travel time is reasonable given benzene's modest but real retardation (R ≈ 5.4) in a sandy loam with 1.5% organic carbon — benzene is one of the more mobile BTEX constituents, so this is on the faster end of what sorption-retarded transport typically produces, yet still far slower than the bare groundwater velocity itself (which alone would cover 2 km in about 11.4 years). The long travel time has two direct implications for remediation strategy: first, there is no urgency to intercept the plume before it reaches a receptor 2 km away on this timescale — monitored natural attenuation (biodegradation, dispersion, and further sorption over decades) is a credible, defensible remedy here, since benzene is also readily biodegraded aerobically and the very slow advective transport gives ample residence time for attenuation to keep pace with the plume front. Second, it reframes source control as the dominant priority: because dissolved-phase transport is this slow, removing or containing the source (the leaking UST) has decades to arrest further plume growth, whereas any hydraulic containment or reactive barrier sized for the plume's leading edge could be deferred or scaled down relative to a fast-moving, poorly retarded contaminant.