Transcript Document
PERMEABILITY
Flow of Liquids in Porous Media
Linear Flow, Incompressible Liquid
• 1-D Linear Flow System
•
•
•
•
•
•
•
•
steady state flow
incompressible fluid, q(0s L) = constant
d includes effect of dZ/ds (change in elevation)
A(0s L) = constant
Darcy flow (Darcy’s Law is valid)
k = constant (non-reactive fluid)
single phase (S=1)
isothermal (constant )
A
q
L
1
2
Linear Flow, Incompressible Liquid
• Darcy’s Law:
A
q
L
1
2
q
k dΦ
vs
A
μ ds
kA
q ds
dΦ
μ
2
L
kA
q ds
dΦ
μ 1
0
kA
1 2
q
μL
• q12 > 0, if 1 > 2
• Use of flow potential, , valid for horizontal, vertical or inclined
flow
Radial Flow, Incompressible Liquid
• 1-D Radial Flow System
•
•
•
•
•
•
•
•
•
steady state flow
incompressible fluid, q(rws re) = constant
horizontal flow (dZ/ds = 0 = p)
A(rws 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
rw
re
Radial Flow, Incompressible Liquid
• Darcy’s Law:
q
q
k dΦ
vs
A
μ ds
q
k
dr dp
2π rh
μ
rw
1
2π kh
q dr
r
μ
re
rw
re
• qew > 0, if pe > pw
pw
dp
pe
2π kh
pe p w
q
μ ln(re /rw )
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 lbmft/lbfs2)
Flow Potential - Darcy’s Experiment
Discuss ABW, Fig. 2-26 (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
Flow Potential - Example Problem
Discuss ABW, Example 2-8 (pg. 75)
Solve this problem using flow potential
Permeability Units
Discuss ABW, Example 2-9 (pg. 79)
2 conversion factors needed to illustrate
permeability units of cm2
cp Pas
atm Pa