Transcript Document

PERMEABILITY
Flow of Liquids in Porous Media
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 )
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
• q12 > 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(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
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
• qew > 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 lbmft/lbfs2)
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  Pas
 atm Pa