1. PERMEABILITY Flow of Liquids in Porous Media.

2. Linear Flow, Incompressible Liquid
1-D Linear Flow System
steady state flow
incompressible fluid, q(0s  L) = constant
d includes effect of dZ/ds (change in elevation)
A(0s  L) = constant
Darcy flow (Darcy’s Law is valid)
k = constant (non-reactive fluid)
single phase (S=1)
isothermal (constant ) L q A 1 2

3. Linear Flow, Incompressible Liquid
Darcy’s Law:
q12 > 0, if 1 > 2
Use of flow potential, , valid for horizontal, vertical or inclined flow L q A 1 2

4. Radial Flow, Incompressible Liquid
1-D Radial Flow System
steady state flow
incompressible fluid, q(rws  re) = constant
horizontal flow (dZ/ds = 0   = p)
A(rws  re) = 2prh where, h=constant
Darcy flow (Darcy’s Law is valid)
k = constant (non-reactive fluid)
single phase (S=1)
isothermal (constant )
ds = -dr q re rw

5. Radial Flow, Incompressible Liquid
Darcy’s Law:
qew > 0, if pe > pw q re rw

6. Flow Potential - Gravity Term
 = p - gZ/c
Z+
Z is elevation measured from a datum
 has dimension of pressure
Oilfield Units
c = (144 in2/ft2)(32.17 lbmft/lbfs2)

7. Flow Potential - Darcy’s Experiment
Discuss ABW, Fig (pg. 68)
Confirm that for the static (no flow) case, the flow potential is constant (there is no potential gradient to cause flow)
top of sand pack
bottom of sand pack

8. Flow Potential - Example Problem
Discuss ABW, Example 2-8 (pg. 75)
Solve this problem using flow potential

9. Permeability Units Discuss ABW, Example 2-9 (pg. 79)
2 conversion factors needed to illustrate permeability units of cm2
cp  Pas
atm Pa