Solution to Exercise 4
4) A regional unconfined sand aquifer was developed during 1990. As a result of the extraction of water the water table dropped about 40 m over a 1 square km area. If the porosity is 34% and the specific retention is 12%, how much water (m3) was withdrawn from the impacted area? How might this volume differ if the aquifer were a 100 m thick confined sand with water at a temperature of 8°C?
Calculate the volume by using Equation 48 of this book.
| Volume of Unconfined Water Drained = SyA∆h |
where:
| Volume | = | volume drained from an unconfined aquifer over an area, A, for a water table elevation change of ∆h (L3) |
| Sy | = | specific yield (dimensionless) |
| A | = | area over which the water table changes (L2) |
| ∆h | = | change in water table elevation (L) |
Sy can be determined as ne – Sr as shown by Equation 13 of this book.
 |
| Volume of Unconfined Water Drained = (0.34 – 0.12) 1000m 1000m 40m |
| Volume from Unconfined Aquifer = 8,800,000 m3 = 8.8 million m3 |
If the aquifer were a 100-meter thick confined sand
| Ss = ρg (α + neβ) |
where:
| Ss | = | specific storage (1/L) |
| α | = | compressibility of the aquifer solid structure (T2L/M) |
| ne | = | effective porosity (dimensionless) |
| β | = | compressibility of water (T2L/M) |
Use a compressibility value for sand found in Table 4 and a density for 8°C water from Figure 28 in this book.
 |
 |
Equation 49 of this book is used to determine storativity:
 |
Equation 50 of this book determines the volume.
| Volume of Confined Water Drained = SAΔh |
| Volume of Confined Water Drained = 4×10-3 1000m 1000m 40m |
| Volume of Confined Water Drained = 160,000m3 |