油层物理油藏工程-课件chap

SUNRen-yuanRoom648,EngineeringBuildingBNov.,2008ShandongProvincialExcellentCourse,20083.4RelativePermeabilityContentsShandongProvincialExcellentCourse,2008

Absolute,effectiveandrelativepermeabilities

Two-phaserelativepermeabilitycurve

Factorsaffectingrelativepermeabilitycurve

ApplicationofrelativepermeabilitydataDeterminationofrelativepermeabilitycurveShandongProvincialExcellentCourse,20081Absolute,effectiveandrelativepermeabilities

1.1Absolutepermeability(绝对渗透率):

Solution:Example1：Acylindricalrocksample:A＝4.9cm2,L＝3cm,△P=0.1MPa(1)100%saturatedwithbrine(μw=1mPa.s)，Qw=0.497cm3/s(2)100%saturatedwithoil(μo=2.99mPa.s)，Qo=0.166cm3/s.Calculatethepermeabilityofthisrocksample.brineoilShandongProvincialExcellentCourse,20081Absolute,effectiveandrelativepermeabilities

1.1Absolutepermeability(绝对渗透率)Absolutepermeabilityisafunctionoftheporestructureofreservoirrocksandindependentonthefluidused.Theabsolutepermeability(绝对渗透率)ofarockistheabilityoftherocktoallowafluidwithwhichitissaturatedtoflowthroughitspores.

ThreeassumptionsinapplyingDarcy’slawtocalculatetheabsolutepermeability?ShandongProvincialExcellentCourse,20081Absolute,effectiveandrelativepermeabilities

1.2Effectivepermeability(有效渗透率/相渗透率)Thepermeabilityofaporousmediumforonefluidduringasimultaneousflowofmultiphasefluids.QwQo

当岩石孔隙中饱和两种或两种以上流体时，岩石允许其中一种流体通过的能力，称为该相流体的有效渗透率或相渗透率。

ShandongProvincialExcellentCourse,2008Example:Thecoreissaturatedwithoil(30%)andbrine(70%).Theoilviscosityis2.99mPa·s.Underthesamepressuredifference,theflowratesofoilphaseandwaterphaseare0.02cm3/sand0.30cm3/srespectively.Effectivepermeabilitytowater:Effectivepermeabilitytooil:(kw+ko=0.1837+0.0366=0.2203μm2<

k=0.304μm2)

1.2Effectivepermeability(有效渗透率)ShandongProvincialExcellentCourse,2008Example:Thecoreissaturatedwithoil(50%)andbrine(50%).Theoilviscosityis2.99mPa·s.Underthesamepressuredifference,theflowratesofoilphaseandwaterphaseare0.05cm3/sand0.09cm3/srespectively.Effectivepermeabilitytowater:Effectivepermeabilitytooil:(kw+ko=0.055+0.0915=0.1465μm2<

k=0.304μm2)

1.2Effectivepermeability(有效渗透率)ShandongProvincialExcellentCourse,20081.2Effectivepermeability(有效渗透率)(1).Effectivepermeabilityisafunctionnotonlyoftheporestructureoftherockbutalsoofthefluidsaturations.(2).Thesumoftheeffectivepermeablitiestoallfluidsislessthantheabsolutepermeabilityoftherock.70%brine,30%oil:kw=0.1837,ko=0.0366,ko+kw=0.2203<k=0.30450%brine,50%oil:kw=0.0055,ko=0.0915,ko+kw=0.097<k=0.304ShandongProvincialExcellentCourse,20081.3Relativepermeability(相对渗透率)Theratiobetweentheeffectivepermeabilityandtheabsolutepermeability.Relativepermeabilitytowater:Relativepermeabilitytooil:

相对渗透率是指当岩石孔隙中饱和多相流体时，某一相流体的有效渗透率与岩石绝对渗透率的比值。ShandongProvincialExcellentCourse,20082Two-phaserelativepermeabilitycurvezoneA:

Sw

≤Swi,onlyoilflowsinthepores.zoneB:zoneC:Swi<Sw<1-SorOilandwaterflowsimultaneouslyintheporesSo

≤

SorOnlywaterflowsintheporesShandongProvincialExcellentCourse,20083Factorsaffectingrelativepermeabilitycurve3.1Effectsofwettability

Asthedegreeofrockpreferentialwettabilityforwaterdecreases,theoilrelativepermeabilityatagivensaturationdecreaseswhilethewaterrelativepermeabilityincreases.ShandongProvincialExcellentCourse,20083.1Effectsofwettability

Irreduciblewatersaturation:

water-wetSwc>20%

oil-wetSwc<15%ShandongProvincialExcellentCourse,20083.1Effectsofwettability

2)kro=krw@

Sw>50%forwater-wetrock

@

Sw<50%foroil-wetrockShandongProvincialExcellentCourse,20083.1Effectsofwettability

3)krw(Sor)<0.3

forwater-wetrock

>0.5foroil-wetrockShandongProvincialExcellentCourse,20083.2Effectsofsaturationhistory

Thewater(wettingphase)relativepermeabilitycurveisessentiallythesameinstronglywater-wetrockforbothdrainageandimbibitionprocesses.Atagivensaturation,thenonwettingphaserelativepermeabilityofarockisusuallylessforanimbibitioncurvethanforadrainagecurve.ShandongProvincialExcellentCourse,20083.3EffectofporestructureRockswithhighpermeabilityandgoodconnectionbetweenpores：thecurvecoversabroadregion.Connatewatersaturationislowandtheend-pointpermeabilitiesarehigh；ShandongProvincialExcellentCourse,20083.4Effectoftemperature

Irreduciblewatersaturationincreasesandtheresidualoilsaturationdecreaseswithincreasingtemperature,thecurvemovestotheright.ShandongProvincialExcellentCourse,20084DeterminationofrelativepermeabilitycurveRelativepermeabilityDirectmethods:

steady-statemethodUnsteady-statemethodIndirectmethods:EmpiricalequationCapillarypressuredataFieldproductiondataShandongProvincialExcellentCourse,20084.1Steady-statemethod(稳态法)(1)Rocksampleissaturatedwithbrine,measuretheabsolutepermeability；(2)Oilandwaterisinjectedintorocksamplewithafixedratio,thefluxrateismeasuredwhenthesteadystateisreached.(3)Theoil-waterratioischanged,andstep(2)isrepeated.4.1.1Stepsforsteady-statemeasurementShandongProvincialExcellentCourse,2008DeterminationofSwMaterialbalancemethodThevolumeofwaterflowingin–thevolumeoffluidflowingout=changeoffluidvolumeinthecore2)Weightingthecoresample3)Electricresistivity4.1Steady-statemethodShandongProvincialExcellentCourse,20084.1.2Endeffect(末端效应)Toeliminate:HighflowrateThree-sectioncoreassembly4.1Steady-statemethodShandongProvincialExcellentCourse,20084.1.2Endeffect(末端效应)4.1Steady-statemethod

Beforewettingphaseflowstooutsurface,thecapillarypressureisactiveforceforwettingfluiddrivingnonwettingfluid.Butwhenitmovestooutletsurface,themeniscuschangesdirection,therefore,thecapillarypressureisaresistanceforwettingfluidtoflowout.Asaresult,thesaturationofwettingphaseneartheoutletfaceisgreatthanthenormaldistribution,thisphenomenoniscalledendeffect.Thetimeforwettingphasetocomeoutoftheoutletfaceisdelayedbytheendeffect.

末端效应实质是多孔介质中两相流动在出口末端的一种毛管效应，其特点是：(a)距离多孔介质出口末端端面一定距离内湿相饱和度过高；(b)出口端见湿相出现短暂的滞后。ShandongProvincialExcellentCourse,2008swkrokrw0.32100.4790.3420.0320.4970.2480.0410.5250.1590.0540.5570.0960.0690.5880.060.0860.6260.0360.1080.6550.0240.1280.680.0180.1470.6990.0140.1620.7250.010.1850.79800.2624.1Steady-statemethodShandongProvincialExcellentCourse,20084.2Unsteady-statemethod(非稳态法)(1)Therocksampleissaturatedwithbrine,mountedintothecoreholderandheatedtotherequiredtemperature.(2)Determinetheabsolutepermeabilityusingbrine,andthendisplacedbyoiltoirreduciblewatersaturation,agedforsomehours.(3)Thecoreisdisplacedbybrineatconstantrate,recordthepressuredifferenceacrossthecore,theoilandbrineflowrate,thecumulativeoilandbrineproductionatdifferenttime,untilthewatercutreaches100%.

4.2.1Stepsforunsteady-statemeasurementShandongProvincialExcellentCourse,20084.2Unsteady-statemethod(非稳态法)4.2.2DatatreatmentShandongProvincialExcellentCourse,20084.3Capillarypressuremethod4.3.1Calculatetheabsolutepermeabilityfromcapillarypressuredata4.3.2Calculatetherelativepermeabilityfromcapillarypressuredata4.4Empiricaleauations4.5Calculatefromfielddata4.6ProbabilitymodelsforthreephaserelativepermeabilityShandongProvincialExcellentCourse,20085.1determinationthewatercut(产水率)

Watercutisdefinedasthefractionoftotalproductionwhichiswater.===Fractionalflowequation(分流量方程)5ApplicationsofrelativepermeabilitydataShandongProvincialExcellentCourse,20085.1DeterminationthewatercutShandongProvincialExcellentCourse,20085.1DeterminationthewatercutAtearlystage,whenwatersaturationislow,thewatercutrisesslowly,andthenitrisesrapidlyaswatersaturationincreases.Whenwatersaturationishighatlaterstage,therisingrateinwatercutwillslowdownagain.ShandongProvincialExcellentCourse,20085.2Determineoffreewatersurfacea-freewaterlevel(自由水面)Pc=0b–100%watersaturationlevel(100%含水面),water-oilcontact(WOC)c–100%waterproductionlevel(100%产水面)d–irreduciblesaturationlevel.ShandongProvincialExcellentCourse,20085.2Determinethefluiddistributioninthetransitionzone1–theoreticalwater-oiltransitionzone.2–practicalwater-oiltransitionzone.ShandongProvincialExcellentCourse,20085.2Determinethefluiddistributioninthetransitionzone1)

(Pc)r~Swh~Sw2)depthoffreewaterlevel=depthoflevelc–h1Thicknessofwater-oiltransitionzone=h2-h1knownShandongProvincialExcellentCourse,20085.3ThetransitionzoneinlayeredreservoirsShandongProvincialExcellentCourse,2008Example3.4.3ShandongProvincialExcellentCourse,20085.4Estimatetheoilrecovery(原油采收率)Oilrecoveryistheratioofcumulat