Factors AffectingPermeability Determination

Non-Darcy FlowSome 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 primarysources that were not cited by NExT. Note that some slides have a notes section.

Measurement of permeability in the laboratory is most commonly done with airConvenient and inexpensiveProblem: low values of mean flowing pressuredownstream pressure, patmupstream pressure, just a few psi higher than patm

At low mean flowing pressure, gas slippage occursDiameter of flow path through porous media approaches the mean free path of gas moleculesmean free path is a function of molecule sizemean free path is a function of gas densityIncreasing mean flowing pressure results in less slippageas pmean, we obtain absolute (equivalent liquid) permeability

Air Permeability Measurement

Liquid flow and gas flow at high mean flowing pressure is laminarDarcys Law is validflow velocity at walls is zero

At low mean flowing pressure gas slippage occursNon-Darcy flow is observedflow at walls is not zero

Klinkenberg developed a method to correct gas permeability measured at low mean flowing pressure to equivalent liquid permeabilityNon-Darcy Flow - Gas Slippage

As pmean, gas permeability approaches absolute permeabilityNon-Darcy Flow - Klinkenberg Effect

Klinkenberg correction for kair depends on mean flowing pressurecorrection ratio shown is for pmean = 1 atmNon-Darcy Flow - Klinkenberg Effect

Klinkenberg correction for kair is more important for low absolute permeabilityNon-Darcy Flow - Klinkenberg Effect

Non-Darcy Flow - High Flow RatesIn the field, gas wells exhibit non-Darcy flow at high flow ratesAt high flow velocity, inertial effects and turbulence become important, and cause non-Darcy flowinertial effect

Recalling Darcys equation for gas flow, (zg )=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)

Non-Darcy Flow - Turbulence

Non-Darcy Flow - Turbulence

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 Darcys Law (2nd order term approaches zero)

Non-Darcy Flow - Forchheimer Equation

Based on Forchheimers Equation a plotting method was developed to determine absolute permeability even with Non-Darcy effects(1/kgas) vs. qg,sckgas determined from Darcys Law (incorrectly assuming Darcy flow) and is a function of qg,scintercept = (1/kabs); absolute permeabilityNon-Darcy Flow - Forchheimer Plot(1/kgas), (1/md)Intercept = [1/kabs]Slope = [(brg,sc)/(mgA)]qg,sc

Non-Darcy Coefficient, b, is an empirically determined function of absolute permeabilityFor Travis Peak (Texas)Non-Darcy Flow - Forchheimer EquationNOB=Net Overburden

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.

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.