{"id":108,"date":"2021-03-27T17:46:30","date_gmt":"2021-03-27T17:46:30","guid":{"rendered":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/chapter\/solution-exercise-1\/"},"modified":"2021-04-05T00:56:14","modified_gmt":"2021-04-05T00:56:14","slug":"solution-exercise-1","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/chapter\/solution-exercise-1\/","title":{"raw":"Solution Exercise 1","rendered":"Solution Exercise 1"},"content":{"raw":"
\r\n

1. Loading calculation<\/em><\/p>\r\n

Estimate of the hydraulic gradient in aquifer: (80 m - 60 m) \/ 200 m = 0.1<\/p>\r\n

Divide the sulphate plume into 3 zones, as shown below.<\/p>\r\n

\"Figure<\/p>\r\n

Zone I<\/p>\r\n

Assume average sulphate concentration in Zone I of 200 mg\/L<\/p>\r\n

Given the distance from the divide to the stream, estimate the width of Zone I as 53 m<\/p>\r\n

Cross-sectional area of flow at the stream: 53 m x 10 m = 530 m2<\/sup><\/p>\r\n

Zone II<\/p>\r\n

Assume average sulphate concentration in Zone II of 300 mg\/L<\/p>\r\n

Given the distance from the divide to the stream, estimate the width of Zone II as 33 m<\/p>\r\n

Cross-sectional area of flow at the stream: 33 m x 10 m = 330 m2<\/sup><\/p>\r\n

Zone III<\/p>\r\n

Assume average sulphate concentration in Zone III of 200 mg\/L<\/p>\r\n

Given the distance from the divide to the stream, estimate the width of Zone III as 63 m<\/p>\r\n

Cross-sectional area of flow at the stream: 66 m x 10 m = 660 m2<\/sup><\/p>\r\n

Loading to stream is the product of the volumetric discharge (q=Kai) and concentration<\/p>\r\n

Loading to stream in Zone I =<\/p>\r\n

(5x10-4<\/sup> m\/s) (530 m2<\/sup>) (0.1) (200 mg\/L) (1000 L\/m3<\/sup>) = 5300 mg\/s \u2245 460 kg\/d<\/p>\r\n

Loading to stream in Zone II =<\/p>\r\n

(5x10-4<\/sup> m\/s) (330 m2<\/sup>) (0.1) (300 mg\/L) (1000 L\/m3<\/sup>) = 4950 mg\/s \u2245 430 kg\/d<\/p>\r\n

Loading to stream in Zone III =<\/p>\r\n

(5x10-4<\/sup> m\/s) (660 m2<\/sup>) (0.1) (200 mg\/L) (1000 L\/m3<\/sup>) = 6600 mg\/s \u2245 570 kg\/d<\/p>\r\n

Total sulphate load carried to stream is approximately 1460 kg\/d<\/p>\r\n

2. Key assumptions<\/em><\/p>\r\n

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:<\/p>\r\n\r\n