Groundwater Hydraulics: Heterogeneity, anisotropy and hydraulic conductivity

Question 1

True or False
Geological formations are usually uniform in composition, making their hydraulic properties consistent in space and direction.

Answer 1

False

Question 2

In heterogeneous formations, hydraulic conductivity K(x,y,z) is _______ constant.

Answer 2

not

Question 3

What does anisotropy in a geological formation refer to?
A) Dependence on direction
B) Independence of position
C) Both hydraulic conductivity being constant and varying

Answer 3

A) Dependence on direction

Question 4

What is the significance of transversely isotropic formations in hydrogeology?

Answer 4

They are layered formations where hydraulic conductivity is considered as having distinct horizontal and vertical components, typically K_x = K_y ≠ K_z

Question 5

True or False
A homogenous material has varying hydraulic conductivity
K values depending on its position within the geological formation.

Answer 5

False (Homogenous means
K is constant)

Question 6

In the equation for the hydraulic conductivity tensor
q=−K∇h, K represents the _______ tensor of the medium.

Answer 6

hydraulic conductivity

Question 7

How does the hydraulic conductivity tensor affect flow in anisotropic materials?
A) It is symmetric, meaning
k_{xy} = k_{yx}
​B) It allows for different conductivities in different directions
C) Both A and B

Answer 7

C) Both A and B

Question 8

True or False
The hydraulic conductivity tensor components k_{xy} and k_{yx} are different in an isotropic material.

Answer 8

False (They are equal and the material does not depend on direction)

Question 9

In layered geological formations, the equivalent vertical hydraulic conductivity
K_z is calculated using a _______ harmonic mean.

Answer 9

weighted

Question 10

What is the relationship between K_{xx} and K_{yy} in a transversely isotropic material?

Answer 10

K_{xx} and K_{yy} are equal, different from K_{zz}.

Question 11

True or False
Hydraulic conductivity in heterogeneous formations is represented by a weighted harmonic mean vertically and an arithmetic mean horizontally.

Answer 11

True

Question 12

The equation K_z = d[∑d_i/K_i]^-1calculates the equivalent vertical hydraulic conductivity using a _______ mean.

Answer 12

weighted harmonic

Question 13

Which mean is used to find horizontal hydraulic conductivity K_x in layered geological formations?
A) Arithmetic Mean
B) Geometric Mean
C) Harmonic Mean

Answer 13

A) Arithmetic Mean

Question 14

What is viscosity and how is it measured in fluids?

Answer 14

Viscosity is the measure of a fluid’s resistance to gradual deformation by shear stress or tensile stress. For pure water at 20°C, dynamic viscosity is measured as
1.002×10^−3 Pascal-seconds.

Question 15

True or False
Poiseuille’s Law describes the volumetric flow rate through a pipe as a function of the pipe’s radius, fluid viscosity, and pressure gradient.

Answer 15

True

Question 16

Total flow through a porous block containing N pipes of radius R can be expressed as Q = NQ’, where Q’ is the flow through a _____.

Answer 16

single pipe

Question 17

What property does the formula k = n_eR^2/8 estimate in a porous medium?
A) Hydraulic conductivity
B) Permeability
C) Viscosity

Answer 17

B) Permeability

Question 18

True or False
The kinematic porosity n_k is considered equal to the effective porosity n_e in scenarios where flow and storage properties are identical.

Answer 18

True

Question 19

Intrinsic permeability in geological formations is independent of the fluid’s properties and is denoted by the symbol ___.

Answer 19

k

Question 20

Explain the difference between Darcy velocity and pore water velocity in terms of porosity.

Answer 20

Darcy velocity refers to the velocity of groundwater flow through the entire cross-sectional area of a porous medium, including both solid and void spaces. Pore water velocity specifically refers to the velocity at which groundwater moves through the void spaces (porous areas) alone and is calculated as q=vn_e, with n_e representing effective porosity.

Question 21

How to find discharge Q?

Answer 21

Q = vNπR^2

Question 22

What are the units of K?

Answer 22

10^{-5} m/s or ~ 1 m/d

Question 23

What is k used in?

Answer 23

petroleum reservoir modelling

Question 24

What is 1 Darcy equivalent to?

Answer 24

1 darcy = 9.87×10^{−13} m^2 (or ~ 10^{−12} m^2)

Question 25

How can the effective porosity of a system be found (block)?

Answer 25

n_e = 𝜋NR^2/HB, where A = HB

Question 26

How can you calculate arithmetic mean?

Answer 26

K_A = 1/N∑K_i

Question 27

How can you calculate geometric mean?

Answer 27

K_G=exp(1/N∑lnK_i)

Question 28

What is the shear stress in a pipe equal to?

Answer 28

𝜏 = rdP/2dx