Solution Exercise 1

1. Loading calculation

Estimate of the hydraulic gradient in aquifer: (80 m – 60 m) / 200 m = 0.1

Divide the sulphate plume into 3 zones, as shown below.

Zone I

Assume average sulphate concentration in Zone I of 200 mg/L

Given the distance from the divide to the stream, estimate the width of Zone I as 53 m

Cross-sectional area of flow at the stream: 53 m x 10 m = 530 m²

Zone II

Assume average sulphate concentration in Zone II of 300 mg/L

Given the distance from the divide to the stream, estimate the width of Zone II as 33 m

Cross-sectional area of flow at the stream: 33 m x 10 m = 330 m²

Zone III

Assume average sulphate concentration in Zone III of 200 mg/L

Given the distance from the divide to the stream, estimate the width of Zone III as 63 m

Cross-sectional area of flow at the stream: 66 m x 10 m = 660 m²

Loading to stream is the product of the volumetric discharge (q=Kai) and concentration

Loading to stream in Zone I =

(5×10^-4 m/s) (530 m²) (0.1) (200 mg/L) (1000 L/m³) = 5300 mg/s ≅ 460 kg/d

Loading to stream in Zone II =

(5×10^-4 m/s) (330 m²) (0.1) (300 mg/L) (1000 L/m³) = 4950 mg/s ≅ 430 kg/d

Loading to stream in Zone III =

(5×10^-4 m/s) (660 m²) (0.1) (200 mg/L) (1000 L/m³) = 6600 mg/s ≅ 570 kg/d

Total sulphate load carried to stream is approximately 1460 kg/d

2. Key assumptions

A number of simplifying assumptions have been made to derive this estimate. Other than those related to the reliability of the hydraulic conductivity estimate and the contouring of the sulphate plume, the key assumptions are:

• The hydraulic head gradient in the direction of groundwater flow within this unconfined aquifer is linear between the topographic divide and the stream.
• There is no bypass flow beneath the stream course, all the groundwater moving in this section of the aquifer discharges into the stream bed.
• To compute a representative concentration value for each zone, it was assumed there is a linear concentration profile across the width of each zone, between the contours. Because the maximum concentration in the monitoring well was only slightly higher than the bounding concentration contours defined by the vertically-averaged concentration, an average concentration of 300 mg/l was adopted for Zone II.
• The spread of contaminants beyond the 100 mg/L contours is minimal and can be neglected, some compensation for that is provided by ignoring the background concentration of the aquifer.

Return to Exercise 1