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ESS 454
Homework set #5
1. Fetter Chapter 7 1 2. Fetter Chapter 7 2 3. Fetter Chapter 7 3
(Figures attached)
Question 4 (Conductivity anisotropy, Darcy’s Law in 3 dimensions)
The hydraulic gradient in a horizontal aquifer has a trend of N30E and a magnitude of .001 m/m. The aquifer is 1 meter thick sandstone with a hydraulic conductivity measured in the rock as 5x10-‐5 m/s . The sandstone has vertical fractures running north-‐south with a spacing of 0.5 meters (2 fractures per meter) and an average fracture aperture (e) of 0.5 mm. The transmissivity (per unit fracture width) of a single fracture is given as
1. Express the hydraulic gradient as a vector using positive x as east and positive y as north and z is up.
2. What is the transmissivity of a single fracture (flow capacity per unit width)? 3. For water flow parallel to the fractures (N-‐S), what is the formation transmissivity?
(hint: look at page 100 in Fetter). What is the N—S hydraulic conductivity? 4. Construct a conductivity tensor for the aquifer. In words explain what the non-‐zero
elements of the tensor describe. 5. For the given hydraulic gradient, determine the flow rate per unit area of aquifer
and the direction of flow. Compare this direction with the gradient direction. 6. If the fractures ran N30W, determine the hydraulic conductivity tensor. (hint, the
new tensor will be “rotated” into a new coordinate system relative the original tensor. )
7. What is the aquifer flow rate and direction for the same (trending N30E) hydraulic gradient.
(one more question may be added)
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