PERMEABILITY
Some slides in this section are from NExT PERF Short Course Notes, 1999.
Some slides appear to have been obtained from unknown primary
sources that were not cited by NExT. Note that some slides have a notes section.
Permeability
• Definition (ABW, Ref: API 27)
– … permeability is a property of the porous medium and
is a measure of the capacity of the medium to transmit
fluids
– … a measure of the fluid conductivity of the particular
material
• Permeability is an INTENSIVE property of a
porous medium (e.g. reservoir rock)
Sources for Permeability Determination
• Core analysis
• Well test analysis (flow testing)
– RFT (repeat formation tester) provides small well tests
• Production data
– production logging measures fluid flow into well
• Log data
– MRI (magnetic resonance imaging) logs calibrated via
core analysis
Examples, Typical PermeabilityPorosity Relationship
From Tiab and Donaldson, 1996
Darcy’s
Apparatus for
Determining
Permeability
A
h1-h2
q
A
h1
(Sand Pack Length) L
•Flow is Steady State
•q = KA (h1-h2)/L
•K is a constant of
proportionality
•h1>h2 for downward flow
q
h2
PERMEABILITY
• Darcy’s “K” was determined to be a
combination of
–
k, permeability of the sand pack (porous
medium, e.g. reservoir rock)
–
, viscosity of the liquid
k
K
μ
Review - Derived Units
• Consider Newton’s 2nd Law for constant
mass, F=ma
– SI Units are Absolute and Coherent
• Absolute: Force is a derived unit, 1 N = 1 (kg*m/s2)
• Coherent (consistent): No conversion constants
needed
– So:
F[N] = m[kg]*a[m/s2]
Review - Derived Units
• What if we want F to be in [lbf ]?
– Then, F[lbf]*4.448[ N/lbf] =
m[kg]*a[m/s2]
– Adding the conversion factor restores the
original formula (a true statement in SI units)
Review - Derived Units
• For: F in [lbf ], m in [lbm ], a in [ft/s2]
– Then, F[lbf ]*4.448222[N / lbf] =
m[lbm ]*0.4535924[kg/lbm] *
a[ft/s2]*0.3048[m/ft]
– Or, F[lbf ] = m[lbm ] * a[ft/s2] /
32.17405[(lbmft)/(lbf s2)]
– Remember: 1[N] / 1[kg*m/s2] = 1; dimensionless
Permeability
Dimensions & Units
• Permeability is a derived dimension
• From Darcy’s equation, the dimension of permeability is length squared
qμ L  L3 P  T L 1 1 
k
;  
  2    L2
A Δp  T 1 1 L P 
 
– This is not the same as area, even though for example, it is m2 in SI units
• See handout: Darcy, {SI}, and [Oilfield] units
• In Darcy and SI Units, this equation is coherent
– Oilfield units are non-coherent, a unit conversion constant is required
Darcy Units
• Permeability is a derived dimension based on Darcy’s
Equation
k = (q  L) / (A Dp)
• The unit of permeability is the Darcy [d]
– The oilfield unit is millidarcy [md]
• The Darcy is defined from Darcy’s Equation, where:
q [cm3/s]
 [cp]
L [cm]
A [cm2]
Dp [atm]
Differential Form - Darcy’s Law
• Darcy’s Equation rearranged as Darcy velocity (volumetric
flux)
vs = q/A = (k/) (Dp/L)
• This equation applies for any L,  as L0
vs = q/A = -(k/) (dp/ds)
where,
vs Darcy velocity, (volumetric flux)
s distance along flow path (0s  L), in the direction of
decreasing pressure (note negative sign)
• The differential form is Darcy’s Law
Flow Potential
• The generalized form of Darcy’s Law includes pressure
and gravity terms to account for horizontal or nonhorizontal flow
qs
k
vs 

A

 dp g dz 
 ds  c ds 
– The gravity term has dimension of pressure / length
• Flow potential includes both pressure and gravity terms,
simplifying Darcy’s Law
q
k  dΦ 
vs 
 
A
μ  ds 
  = p - gZ/c ; Z+; Z is elevation measured from a datum
  has dimension of pressure