1. Permeability Determination
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.

2. 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

3. 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

4. Non-Darcy Flow - Klinkenberg Effect
As pmean, gas permeability approaches absolute permeability

5. Non-Darcy Flow - Klinkenberg Effect
Klinkenberg correction for kair depends on mean flowing pressure
correction ratio shown is for pmean = 1 atm

6. Non-Darcy Flow - Klinkenberg Effect
Klinkenberg correction for kair is more important for low absolute permeability

7. 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
Determining permeability using a gas is similar to the method using a liquid. However, some extra terms are required to account for the changes in gas properties.
Since gas has very low viscosities relative to liquids, it is often preferable because it helps speed up the core testing. For low-permeability rocks, the time reduction can be very significant.

8. Non-Darcy Flow - Turbulence
Recalling Darcy’s equation for gas flow, (zg )=Constant
For laboratory flow experiments we can assume T=Tsc and z=1
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)

9. Non-Darcy Flow - Turbulence
Slope = k m
(p12- p22)
2 L
q psc A
Darcy
flow
Non-Darcy
Determining permeability using a gas is similar to the method using a liquid. However, some extra terms are required to account for the changes in gas properties.
Since gas has very low viscosities relative to liquids, it is often preferable because it helps speed up the core testing. For low-permeability rocks, the time reduction can be very significant.

10. Non-Darcy Flow - Forchheimer Equation
Forchheimer proposed a flow equation to account for the non-linear effect of turbulence by adding a second order term
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)

11. 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
intercept = (1/kabs); absolute permeability
(1/kgas), (1/md)
Slope = [(brg,sc)/(mgA)]
Intercept = [1/kabs]
qg,sc

12. Non-Darcy Flow - Forchheimer Equation
Non-Darcy Coefficient, b, is an empirically determined function of absolute permeability
For Travis Peak (Texas)
NOB=Net Overburden