Section B — Two of Three Questions: 18-Env-B4 Site Assessment and Remediation, May 2014, Q6

Question B-1: Fe⁰ Permeable Reactive Barrier Sizing for a PCE Plume (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.

A zero-valent iron (Fe⁰) permeable reactive barrier (PRB) is installed as a wall of granular iron across the width and depth of the contaminant plume, oriented perpendicular to groundwater flow, so that the plume passes through it under its own natural gradient with no pumping (a purely passive, in-situ treatment train). PCE reacts abiotically at the iron surface: the iron corrodes ($\text{Fe}^0 \rightarrow \text{Fe}^{2+} + 2e^-$), and the released electrons reductively dechlorinate PCE, stripping chlorine atoms stepwise (or, more favourably, via beta-elimination that bypasses the more toxic intermediates) to non-chlorinated end products such as ethene and ethane. Because the reaction occurs at the iron surface, its rate is normalized to the surface area of iron presented to the water — the surface-area rate constant $k_{sa}$ supplied in this question — rather than to the iron's mass or the barrier's bulk volume directly.

Plan-view sketch: the PCE plume from the dry-cleaner source passes through a continuous Fe⁰ permeable reactive barrier installed across the full plume cross-section; abiotic reductive dechlorination on the iron surface reduces the concentration from 95 mg/L to below the 5 µg/L target by the downgradient compliance well.

Given. $C_0 = 95$ mg/L, $C_t = 5\ \mu\text{g/L} = 0.005$ mg/L, plume cross-section $A = 80$ m², groundwater (seepage) velocity $v = 0.12$ m/d, aquifer porosity $n = 0.35$, iron specific surface area $a_s = 1.0$ m²/g, $k_{sa} = 2.1\times10^{-3}$ L/(m²·h) with only 35% activity at the 10°C site temperature, safety factor SF = 3.

Find. The total mass of granular Fe⁰ (metric tons) required in the barrier.

Approach. Model the barrier as a plug-flow packed bed: water carrying PCE flows through a fixed mass of iron, and PCE degrades as a pseudo-first-order surface reaction. Integrating the mass balance along the flow path gives the classic packed-bed design equation $W = Q\ln(C_0/C_t)/(k_{sa}a_s)$ — the total iron mass needed depends only on the water flux, the required log-removal, and the rate parameters, not on the barrier's thickness (mass and thickness trade off against each other for a fixed iron packing density).

Temperature-corrected rate constant. $k_{sa,10^\circ C} = 0.35 \times 2.1\times10^{-3} = \boxed{7.35\times10^{-4}}\ \text{L/(m}^2\cdot\text{h)} = 1.764\times10^{-2}\ \text{L/(m}^2\cdot\text{d)}$.
Volumetric flow through the barrier. The given 0.12 m/d is the average linear (seepage) groundwater velocity; converting to the Darcy flux (specific discharge) that actually carries the water volume through the full cross-section uses the aquifer porosity: $v_{Darcy} = n\,v = 0.35 \times 0.12 = 0.042$ m/d. The volumetric flow is then $Q = v_{Darcy}A = 0.042 \times 80 = \boxed{3.36}\ \text{m}^3/\text{d} = 3360\ \text{L/d}$.
Required log-removal. $\ln(C_0/C_t) = \ln(95/0.005) = \boxed{9.85}$.
Iron mass, no safety factor. $W = \dfrac{Q\ln(C_0/C_t)}{k_{sa,10^\circ C}\,a_s} = \dfrac{3360 \times 9.85}{1.764\times10^{-2}\times1.0} = 1{,}876{,}600\ \text{g} = 1.877$ metric tons.
Apply the safety factor. $W_{design} = 3 \times 1.877 = \boxed{5.63}\ \text{metric tons of Fe}^0$.

Final Results
Quantity	Value
$k_{sa}$ at 10°C	$7.35\times10^{-4}$ L/(m²·h)
Darcy flux through barrier	0.042 m/d (Q = 3.36 m³/d)
Required log-removal, ln(C₀/Cᷯ)	9.85
Fe⁰ mass, no safety factor	1.877 t
Fe⁰ mass, design (SF = 3)	5.63 metric tons

Check: “groundwater velocity of 0.12 m/d” is read here as the average linear (seepage) velocity, converted to a Darcy flux via the given aquifer porosity to obtain the true volumetric flow through the barrier — the standard convention when a porosity value is supplied alongside a stated groundwater velocity. If instead 0.12 m/d were intended as the Darcy flux directly (no porosity correction), Q rises to 9.6 m³/d and the design Fe⁰ mass scales up to ≈16.1 metric tons; either reading uses every given number, so the assumption is stated explicitly rather than silently resolved.

Topic: Permeable reactive barrier (PRB) sizing via surface-area-normalized kinetics.

Key relations: $-r = k_{sa}a_s C$ (pseudo-first-order surface reaction); packed-bed design equation $W = Q\ln(C_0/C_t)/(k_{sa}a_s)$; Darcy flux $v_{Darcy}=nv_{seepage}$.

Why this works: because the reaction is first-order in contaminant concentration and the iron surface area presented per unit time of flow is what controls the rate, the required total catalyst (iron) mass is exactly analogous to sizing a packed-bed reactor for a target conversion — a design equation borrowed directly from chemical reaction engineering and validated for PRBs in the Battelle/EPA design guidance.

Common pitfall: confusing the surface-area rate constant $k_{sa}$ (per m² of iron) with a bulk first-order rate constant, or forgetting to apply the temperature correction and safety factor before sizing — both push heavily toward under-designing the barrier, since the un-corrected, no-safety-factor mass here is nearly 3× smaller than the design value.

Source: Gavaskar et al., Design Guidance for Application of Permeable Reactive Barriers (Battelle/EPA, 2000); Suthersan & Payne, Remediation Engineering, Ch. 6 (in-situ reactive treatment).

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

Section A — Three of Five Questions

Section B — Two of Three Questions

Question B-1: Fe⁰ Permeable Reactive Barrier Sizing for a PCE Plume (20 marks)