Fluids- Flow Through Porous Media

Question 1

Porosity

Answer 1

Fraction of a volume with empty space

Question 2

Permeability

Answer 2

Ability of a medium to permit a flow through it

Question 3

Darcy’s law equation

Answer 3

q=Ak(dh/dx)
q is volumetric flow rate
A is CSA
dh/dx is hydraulic gradient
k is coefficient of permeability (m/s) aka hydraulic conductivity

Question 4

Rearrangement of Darcy’s law for Darcy velocity

Answer 4

q/A=k(dh/dx)

Not real velocity

Question 5

Equation to get fluid speed from Darcy velocity

Answer 5

Fluid speed=Darcy velocity/porosity

Question 6

Is the real velocity faster or slower than the Darcy velocity?

Answer 6

Faster

Question 7

What is the electrical analogy for Darcy’s law

Answer 7

I=AσV/l

Question 8

Equation for hydraulic conductivity, k

Answer 8

k=κρg/μ
Where κ is permeability
ρ is density
μ is dynamic viscosity

Question 9

What does the Darcy’s law equation look like when hydraulic conductivity, k, is substituted?

Answer 9

q=A(κ/μ)(dP/dx)

dP comes from dP=ρg.dh

Question 10

Kozeny-Carman equation for pressure gradient

Answer 10

dP/dx=(180μV(1-ε)^2)/(φ^2Dp^2ε^2)
Where φ is sphericity (1 for perfect sphere)
Dp is particle diameter in m (averaged)
ε is porosity of the media

Question 11

Equation for permeability, κ, by combining Darcy’s law and Kozeny-Carman equation

Answer 11

Substitute for dP/dx
κ=(φDpε)^2/180(1-ε)^2
These are all particle properties

Question 12

Potential reason for inaccuracies when calculating using Darcy’s law etc

Answer 12

The diameter of the particles won’t all be the same