Contaminated Site Remediation and Groundwater Protection Exercises

These exercises practise first-pass calculations used in contaminated site remediation and groundwater protection. They connect groundwater gradients, Darcy flow, plume travel time, contaminant mass removal, excavation quantity, monitoring trend confidence, vapor intrusion screening, hydraulic capture, risk ranking, and closure evidence.

Assume simplified nominal values unless an exercise states otherwise. Real remediation decisions require a conceptual site model, verified hydrogeology, contaminant chemistry, exposure assessment, laboratory quality controls, field uncertainty, regulatory criteria, and responsible professional review.

How to Use These Exercises

For each problem:

1. define the source, pathway, receptor, and system boundary;
2. state whether the calculation is about flow, mass, exposure, monitoring, or closure;
3. keep concentration, volume, time, and area units consistent;
4. separate numerical screening from evidence confidence;
5. identify what field data would confirm or challenge the result.

The most common mistake is treating one concentration result as the site model. Remediation engineering depends on patterns: head, gradient, geology, chemistry, source behavior, pathways, receptors, and monitoring reliability.

For each result, state whether it supports conceptual site model update, exposure control, remedy sizing, performance monitoring, institutional control, or closure refusal. A subsurface calculation should identify which uncertainty would change the protective decision.

Exercise 1: Hydraulic Gradient Between Wells

Two monitoring wells are screened in the same aquifer. The upgradient well has hydraulic head h_1=102.4\ \text{m} and the downgradient well has hydraulic head h_2=101.8\ \text{m}. The distance between wells along the interpreted flow path is 60\ \text{m}.

Estimate the hydraulic gradient magnitude.

Solution

Head difference:

Hydraulic gradient:

Engineering Comment

The gradient is only meaningful if the wells represent the same hydrostratigraphic unit and the surveyed elevations are reliable. Preferential pathways, utility trenches, pumping, and seasonal changes can make the apparent gradient misleading.

Exercise 2: Darcy Flow Through a Control Plane

An aquifer zone has hydraulic conductivity K=3.0\times10^{-5}\ \text{m/s}, hydraulic gradient i=0.010, and effective cross-sectional flow area A=40\ \text{m}^2.

Estimate groundwater flow through the control plane.

Solution

Darcy flow:

Convert to cubic metres per day:

Engineering Comment

This is a bulk estimate. Heterogeneity, anisotropy, fractures, sand seams, well-screen placement, and uncertainty in hydraulic conductivity can change the true contaminant pathway by orders of magnitude.

Exercise 3: Plume Travel Time

Using K=3.0\times10^{-5}\ \text{m/s} and i=0.010, estimate average seepage velocity for effective porosity n_e=0.30. Then estimate travel time to a receptor 120\ \text{m} downgradient.

Solution

Darcy velocity:

Seepage velocity:

Convert to metres per day:

Travel time:

Engineering Comment

This estimate ignores sorption, degradation, dispersion, density effects, preferential pathways, and source persistence. It is a screening value for investigation planning, not proof of receptor protection.

Exercise 4: Pump-and-Treat Mass Removal

A pump-and-treat system extracts groundwater at Q=25\ \text{m}^3/\text{day}. Influent contaminant concentration is C=2.4\ \text{mg/L}. Assume treatment removes the contaminant from the extracted water.

Estimate contaminant mass removed per day and over 30 days.

Solution

Convert concentration:

Daily mass removal:

Thirty-day removal:

Engineering Comment

Mass removal should be compared with source mass and rebound behavior. A pump-and-treat system can remove dissolved mass while leaving a persistent source in soil, low-permeability zones, or non-aqueous phase liquid.

Exercise 5: Excavation Quantity for Contaminated Soil

A shallow source zone covers 35\ \text{m}\times20\ \text{m} and is excavated to depth 1.2\ \text{m}. The estimated bulk density of soil is 1.7\ \text{t/m}^3.

Estimate excavation volume and soil mass.

Solution

Excavation volume:

Soil mass:

Engineering Comment

Excavation planning also needs waste classification, dewatering, shoring, dust control, odor control, truck routing, confirmation sampling, stockpile management, worker protection, and disposal capacity.

Exercise 6: Monitoring Trend Signal-to-Noise

A monitoring well concentration decreases from 120\ \mu\text{g/L} to 95\ \mu\text{g/L} between two events. The estimated combined field and laboratory uncertainty for each result is approximately 15\ \mu\text{g/L}.

Estimate a simple signal-to-noise ratio using the concentration change divided by the uncertainty scale.

Solution

Concentration change:

Signal-to-noise ratio:

Engineering Comment

The apparent decrease is not strong evidence by itself. A trend decision should use more events, duplicate samples, detection limits, groundwater elevation, seasonal effects, sampling method, and whether nearby wells show consistent behavior.

Exercise 7: Vapor Intrusion Screening Ratio

A sub-slab vapor sample measures 1200\ \mu\text{g/m}^3. Indoor air concentration during the same period is 3.5\ \mu\text{g/m}^3.

Estimate the apparent attenuation factor:

Solution

Attenuation factor:

Engineering Comment

This screening ratio does not prove source attribution. Indoor products, outdoor air, building pressure, HVAC operation, foundation cracks, utility penetrations, and sampling duration can affect results. Vapor intrusion review needs multiple lines of evidence.

Exercise 8: Hydraulic Capture Ratio

A hydraulic containment system extracts 60\ \text{m}^3/\text{day} from a plume area. Groundwater flow through the interpreted capture plane is estimated as 48\ \text{m}^3/\text{day}.

Estimate the capture flow ratio.

Solution

Capture ratio:

Engineering Comment

The extraction rate is greater than the estimated through-flow, but capture is not proven by ratio alone. Hydraulic gradients, water levels, plume concentration trends, capture-zone modelling, well performance, and boundary uncertainty must be reviewed.

Exercise 9: Cap-Failure Risk Priority

A capped contaminated soil area has failure mode “cap damage allows infiltration through residual source material.” Initial scores are:

After adding inspections and access control, occurrence is estimated as O=2 and detection as D=2.

Find the initial and revised risk priority numbers.

Solution

Initial:

Revised:

Reduction:

Engineering Comment

The reduction is credible only if inspections are funded, access controls remain in place, repairs are timely, and future site users understand the cap restriction. Institutional controls are engineering controls only when maintained.

Exercise 10: Closure Evidence from Monitoring Network Condition

A closure review covers 46 monitoring wells. Forty-two have current survey control, and 39 are confirmed usable for representative sampling. The remaining wells are damaged, obstructed, or no longer representative.

Find the survey-control percentage and usable-well percentage.

Solution

Survey-control percentage:

Usable-well percentage:

Engineering Comment

Closure should not rely on a degraded monitoring network if damaged wells affect plume boundary, gradient, vapor pathway, source-zone, or receptor decisions. The evidence gap should be repaired, replaced, or explicitly justified.

Review Checklist

Before accepting a contaminated-site screening calculation, check:

• whether source, pathway, receptor, and hydrostratigraphic unit are defined;
• whether groundwater gradients are supported by surveyed, comparable wells;
• whether Darcy-flow and travel-time estimates acknowledge heterogeneity;
• whether mass removal is compared with source persistence and rebound;
• whether monitoring trends exceed data noise and seasonal variability;
• whether vapor intrusion uses multiple lines of evidence;
• whether containment performance is validated by gradients and concentration response;
• whether institutional controls, engineering controls, access restrictions, and maintenance obligations remain enforceable after closure;
• whether data gaps affect plume boundary, source mass, receptor exposure, or remedy performance rather than only documentation completeness;
• whether closure records prove that residual controls remain effective.

Good remediation engineering turns uncertain subsurface evidence into clear protective decisions: investigate further, control exposure, remove mass, contain migration, monitor performance, or withhold closure.