Question 7 of 8: Bioventing Air Flow and First-Order Remediation Time

Question B-2: Bioventing Air Flow and First-Order Remediation 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. Total hydrocarbon mass spilled (as hexane), soil composition and dry bulk density, porosity, gravimetric water content, initial soil concentration, oxygen-utilization rate for part (i), lab first-order rate constant for part (ii), and the target clean-up level.

Find. (i) the design air flowrate for bioventing; (ii) the field remediation time to reach the target concentration under the lab-derived first-order rate; (iii) whether that time is realistic.

Approach. For (i), convert the spill mass and concentration into the volume of soil affected, evaluate the air-filled porosity available to carry injected air, and apply the standard oxygen-utilization design equation; for (ii), apply first-order decay with the lab rate constant.

1. Volume of soil affected by the spill. The total mass spilled, divided by the measured soil concentration, gives the mass of dry soil carrying that concentration; dividing by bulk density converts to volume: $$m_{soil} = \frac{M_{HC}}{C_0} = \frac{10{,}000\ \text{kg}}{2.6\times10^{-3}} \approx 3.85\times10^{6}\ \text{kg}, \qquad V_{soil} = \frac{m_{soil}}{\rho_b} = \frac{3.85\times10^{6}}{1{,}410} \approx 2{,}728\ \text{m}^3$$
2. Air-filled porosity check. Converting the gravimetric water content to a volumetric basis and comparing it with the total porosity: $$\theta_w = w\times\frac{\rho_b}{\rho_w} = 0.25\times\frac{1{,}410}{1{,}000} = 0.353, \qquad \theta_a = n-\theta_w = 0.35-0.353 \approx 0$$

3. Design air flowrate (illustrative, θ_a = 0.10). The venting rate needed to replace consumed oxygen scales with the utilization rate and the air-filled soil volume available to hold it: $$Q_{air} = k_{O_2}\times\theta_a\times V_{soil} = 0.10\ \text{d}^{-1}\times 0.10\times 2{,}728\ \text{m}^3 \approx \boxed{27\ \text{m}^3/\text{d}}$$
4. Lab first-order rate constant. Recovering k from the given natural log: $$k = e^{\ln k} = e^{-3.688} \approx 0.0250\ \text{d}^{-1}$$
5. Field remediation time (part ii). Applying first-order decay $C = C_0e^{-kt}$ and solving for t at the target level: $$t = \frac{\ln(C_0/C_t)}{k} = \frac{\ln(2{,}600/200)}{0.0250} = \frac{\ln 13}{0.0250} \approx \boxed{103\ \text{days}}$$

(iii) Is the answer in (ii) realistic? Not as a field commitment. The lab rate constant comes from a controlled microcosm or column test with optimized temperature, moisture, nutrient supply and oxygen delivery — conditions the field essentially never matches. Field heterogeneity lets injected air bypass fine-grained, low-permeability zones (exactly the concern flagged above for this soil) rather than sweeping through them uniformly; seasonal temperature swings slow microbial kinetics substantially, since biodegradation rates typically follow a Q₁₀-type relationship that can halve the rate for every 10°C drop; and diffusion-limited oxygen and vapour transport through a fine-textured soil is inherently slower than in a well-mixed lab reactor. Field bioventing timelines are commonly two to five times longer than lab-derived first-order estimates as a result. The 103-day figure should therefore be treated as a best-case, lower-bound benchmark — not a design or contractual schedule — and a field pilot-scale respiration test should be run to derive a field-calibrated rate constant before committing to a remediation timeline.