Factors AffectingPermeability DeterminationNon-Darcy FlowSome figures in this section are from Fundamentals of Core Analysis, Core Laboratories, 1989.Some slides in this section are from !"# $!%F Short Course otes, 1999.Some slides a&&ear to ha'e been obtained from un(no)n &rimarysources that )ere not cited by !"#. ote that some slides ha'e a notes section. Air Permeability MeasurementMeasurement of permeability in the laboratory is most commonly done with airConvenient and inexpensiveProblem: low values of mean flowing pressure downstream pressure, patm upstream pressure, ust a few psi higher than patmAt low mean flowing pressure, gas slippage occurs!iameter of flow path through porous media approaches the "mean free path# of gas moleculesmean free path is a function of molecule si$emean free path is a function of gas density%ncreasing mean flowing pressure results in less slippage as pmean, we obtain absolute &e'uivalent li'uid( permeability )on*!arcy +low * ,as -lippage.i'uid flow and gas flow at high mean flowing pressure is laminar!arcy/s .aw is validflow velocity at walls is $eroAt low mean flowing pressure gas slippage occurs)on*!arcy flow is observedflow at walls is not $ero0lin1enberg developed a method to correct gas permeability measured at low mean flowing pressure to e'uivalent li'uid permeability )on*!arcy +low * 0lin1enberg 2ffect As pmean, gas permeability approaches absolute permeability )on*!arcy +low * 0lin1enberg 2ffect 0lin1enberg correction for 1air depends on mean flowing pressure correction ratio shown is for pmean 3 4 atm )on*!arcy +low * 0lin1enberg 2ffect 0lin1enberg correction for 1air is more important for low absolute permeability Non-Darcy Flow - High Flow Rates %n the field, gas wells exhibit non*!arcy flow at high flow rates At high flow velocity, inertial effects and turbulence become important, and cause non*!arcy flow inertial effect )on*!arcy +low * 5urbulence 6ecalling !arcy/s e'uation for gas flow, &$g (3Constant+or laboratory flow experiments we can assume 535sc and $34 +or !arcy flow, plotting &'g,sc psc(7A vs8 &p49*p99(7&9.( results in straight line8 line passes through origin :when 'g,sc 3;, then &p49*p99(3;< slope 3 17 g behavior departs from straight line under turbulent flow conditions &high flow velocity(( )9994g scscsc g,p p= $ 94p 55.A 1' =( )9.p ppA=1'9994sc gsc g,= Non-Darcy Flow - TurbulenceSlope =

!!"p#$- p$$%$ &' pscADarcy flowNon-Darcyflow )on*!arcy +low * +orchheimer 2'uation+orchheimer proposed a flow e'uation to account for the non*linear effect of turbulence by adding a second order term)ote that unit corrections factors would be re'uired for non*coherent unit systems8As flow rate decreases, we approach !arcy/s .aw &9nd order term approaches $ero(9ggg gA'> ?A'1=dsdp+= )on*!arcy +low * +orchheimer Plot@ased on +orchheimer/s 2'uation a plotting method was developed to determine absolute permeability even with )on*!arcy effects &471gas( vs8 'g,sc 1gas determined from !arcy/s .aw &incorrectly assuming !arcy flow( and is a function of 'g,sc intercept3 &471abs(A absolute permeability*1+(gas,, *1+md,-nterce&t . /1+(abs0Slo&e . /*g,sc,+*gA,01g,sc )on*!arcy +low * +orchheimer 2'uation)on*!arcy Coefficient, , is an empirically determined function of absolute permeability+or 5ravis Pea1 &5exas(N()=Net (*erbur+en