Factors Affecting
Permeability Determination
Non-Darcy Flow
Some figures in this section are from “Fundamentals of Core Analysis,” Core Laboratories, 1989.
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.
Air Permeability Measurement
• Measurement of permeability in the laboratory is most commonly
done with air
– Convenient and inexpensive
– Problem: low values of mean flowing pressure
• downstream pressure, patm
• upstream pressure, just a few psi higher than patm
• At low mean flowing pressure, gas slippage occurs
– Diameter of flow path through porous media approaches the “mean free
path” of gas molecules
• mean free path is a function of molecule size
• mean free path is a function of gas density
– Increasing mean flowing pressure results in less slippage
• as pmean, we obtain absolute (equivalent liquid) permeability
Non-Darcy Flow - Gas Slippage
• Liquid flow and gas flow at high mean flowing pressure is laminar
– Darcy’s Law is valid
– flow velocity at walls is zero
• At low mean flowing pressure gas slippage occurs
– Non-Darcy flow is observed
– flow at walls is not zero
• Klinkenberg developed a method to correct gas permeability
measured at low mean flowing pressure to equivalent liquid
permeability
Non-Darcy Flow - Klinkenberg Effect
• As pmean, gas permeability approaches absolute permeability
Non-Darcy Flow - Klinkenberg Effect
• Klinkenberg correction for kair depends on mean flowing pressure
– correction ratio shown is for pmean = 1 atm
Non-Darcy Flow - Klinkenberg Effect
• Klinkenberg correction for kair is more important for low absolute
permeability
Non-Darcy Flow - High Flow Rates
• In the field, gas wells exhibit non-Darcy flow at high flow rates
• At high flow velocity, inertial effects and turbulence become
important, and cause non-Darcy flow
– inertial effect
Non-Darcy Flow - Turbulence
• Recalling Darcy’s equation for gas flow, (zg )=Constant
q g,sc
k A  Tsc 



L  T p sc 
 1

 2zμ
g

 2
 p1  p 22




• For laboratory flow experiments we can assume T=Tsc and z=1
q g,sc
k

μg

 A  p12  p 22


2L
 psc 

• For Darcy flow, plotting (qg,sc psc)/A vs. (p12-p22)/(2L) results in
straight line.
• line passes through origin [when qg,sc =0, then (p12-p22)=0]
• slope = k/ g
• behavior departs from straight line under turbulent flow conditions (high
flow velocity)
Non-Darcy Flow - Turbulence
Darcy
flow
Non-Darcy
flow
q psc
A
k
Slope = 
0
0
(p12- p22)
2L
Non-Darcy Flow - Forchheimer Equation
• Forchheimer proposed a flow equation to account for the nonlinear effect of turbulence by adding a second order term
 qg 
 dp μ g  q g 
   β ρ g  

ds
k A
A
2
– Note that unit corrections factors would be required for non-coherent unit
systems.
– As flow rate decreases, we approach Darcy’s Law (2nd order term
approaches zero)
Non-Darcy Flow - Forchheimer Plot
• Based on Forchheimer’s Equation a plotting method was
developed to determine absolute permeability even with
Non-Darcy effects
– (1/kgas) vs. qg,sc
• kgas determined from Darcy’s Law (incorrectly assuming Darcy flow)
and is a function of qg,sc
(1/kgas), (1/md)
– intercept = (1/kabs); absolute permeability
Slope = [(brg,sc)/(gA)]
Intercept = [1/kabs]
qg,sc
Non-Darcy Flow - Forchheimer Equation
• Non-Darcy Coefficient, b, is an empirically determined function of
absolute permeability
– For Travis Peak (Texas)
NOB=Net
Overburden