第2章污染诊断-表皮分析

污染诊断-表皮分析第二章表皮组成1.污染表皮sd2.部分完井与井斜，sc+θ3.射孔表皮，sp4.拟表皮（所有与相和流速有关的表皮）∑spseudopseudopθcdsssss1.近井地带污染表皮地层污染带对压力分布的影响污染表皮污染外边界(rs)与井筒(rw)间的稳态压降理想状况（无污染）真实状况（污染带渗透率ks）wsidealwfsrrkhqppln2,wssrealwfsrrhkqppln2,污染表皮污染造成的附件压降表皮系数定义为近井地带由于污染造成的稳态附加压降wswssrealwfidealwfrrkhqrrhkqppln2ln2,,skhqps2污染表皮，Hawkin公式由于理想井底压力与真实井底压力间的差值由表皮效应引起所以求解表皮S：wswssrrkhqrrhkqskhqln2ln22wssrrkksln1realwfidealwfsppp,,例：污染k和距离对表皮影响rw=0.1m，污染距离距井壁（rs=1m）1）k/ks=5and10，分别计算表皮2）如果要求k/ks=5的表皮等于k/ks=10的情形，污染半径应满足什么要求？例：污染k和距离对表皮影响1)用Hawkin公式计算表皮2）k/ks=10的S=21.58，用Hawkin公式计算k/ks=5的污染半径58.211.01.1ln110:01k/kFor59.91.01.1ln15:5k/kForssssmeerrskksws03.22)1.0(1558.211例2：污染带影响A=640acres(re=2980ft)rw=0.328ft污染带深3ft(rs=3.328ft)k/ks=10。比较消耗在污染带的压降与总压降比。例2：污染带影响稳态流动总压降:污染带压降：skhqps2srrkhqppwewfln2例2：污染带影响污染带压降与总压降比：例1中，k/ks=10S=20.9.污染带压降为总压降比：2lnln2sewfewwqspskhrpprqssrkhr70.09.20328.02980ln9.20wfsppp2.部分完井与井斜表皮射开厚度小于油层厚度Skinduetoconvergenceofflowlinestotheopensection表皮增加1)射开厚度与油藏厚度比降低2)完井位置skewness(i.e.完井段远离油层中部)井斜表皮slant井不完全垂直产生负表皮（增加产能）表皮效应随井斜角度增加计为：s部分完井与井斜表皮,,,部分完井表皮模型模型Cinco-Leyetal.(1975),半解析，查表,spe5589Papatzacos(1987spe13956)BessonSPE20965部分完井表皮模型Cinco-Leyetal.(1975),半解析，查表,spe5589部分完井表皮模型Cinco-Leyetal.(1975),半解析，查表,spe5589部分完井表皮模型Cinco-Leyetal.(1975),半解析，查表,spe5589部分完井表皮模型Cinco-Leyetal.(1975),半解析，查表,spe5589例3：部分完井表皮rw=0.328ft，H=33ft.射开8ft，射孔中部距油藏底部29。计算一下情形的部分完井表皮和井斜表皮：Case1:直井Case2:井斜45oCase3:直井re/rw=1000（其他条件相同）Case4:井斜45ore/rw=1000（其他条件相同）例3：Cinco-Ley等人模型hD=h/rw=33/0.328=100zw/h=29/33=0.875hw/h=8/33=0.25Case1:(θ=0o):Sc=8.6Case2:(θ=45o):Sc=8.6&Sθ=-2.7,Sc+θ=6hD=1000andallotherratiosthesame:Case3:(θ=0o):Sc=15.7Case4:(θ=45o):Sc=15.7&Sθ=-5.4,Sc+θ=10.3部分完井表皮Muskat表皮油藏中部部分完井表皮部分完井表皮Papatzacos(1987spe13956)部分完井表皮Papatzacos部分完井表皮部分完井表皮部分完井表皮井斜表皮BessonSPE20965各向同性各向异性井斜表皮例3：模型比较ModelCase1Case2Case3Case4Cinco-Ley8.66.015.710.3Papatzacos12.810.020.017.53.射孔完井表皮Wellradius,rwPerforationradius,rperfPerforationlength,lperfAngleofperforationphasing,θDistancebetweenperforation,hperf(inverselyproportionaltoperforationdensity)射孔完井射孔完井射孔表皮组成KarakasandTariq(1988,spe18247)推导了半解析公式sp：sH=planefloweffectsV=verticalconvergingeffectswb=wellboreblockageeffectwbVHpssss射孔表皮)(lnwwHrrs0for)(0for4)(perfperflralrww射孔表皮CalculationofSV.ToobtainSV,twodimensionlessvariablesmustbecalculatedVHDkklhhperfperf12perfperfHVDkkhrr射孔表皮Verticalpseudo-skinSVWithbDbDaVrhs11021lnaraaD21brbbD部分完井表皮模型射孔表皮CalculationofSwb.ForthecalculationofSwb,adimensionlessquantityiscalculatedfirstlyperfThenwDrcwbecs21Theconstantc1andc2canbeobtainedfromTable5-3射孔表皮EXAMPLEPerforationskineffectrw=0.328ft,SPF=2,Rperf=0.25in.(0.0208ft),Rperf=8in.(0.667ft),θ=180o,andkH/kV=10FromEq.5.0)667.0328.0)(5.0()(wrThenfrom405.0328.0ln.sH射孔表皮EXAMPLEPerforationskineffectFromEqandrememberingthathperf=1/SPFand2.3710667.05.0Dh027.0)1.01()5.0)(2(0208.0Dr271.30943.0)027.0log(025.2a894.18115.1)027.0)(0373.3(b射孔表皮EXAMPLEPerforationskineffect4.3027.037.210894.1894.0271.3Vs0.33328.0667.0328.0wDr0.1)106.2()33.0)(532.4(2eswbThetotalperforationskineffectisthen41.03.44.0ps射孔表皮与污染的综合影响射孔比污染半径短(lperfrs):射孔比污染半径长:用修正的射孔长度和半径计算&psodppwsspdskksssrrkksln1'ppdssssperfperfrkkll1'sswwrkkrr1''ps例4：射孔表皮计算rw=0.328ft，kH/kV=10，射孔2SPF,rperf=0.0208ft，lperf=0.667ft，计算如下情形表皮:Case1:Forθ=0o,60o,and180oθ=perforationphasingCase2:ForkH/kV=1withθ=180oθ=180o:1)Planeflowskin,sH:例4：射孔表皮计算2)Verticalconvergingskin,sV:3)Wellboreblockageskin,swb:Overallperforationskin,sp:5.0667.0328.05.0'wr4.05.0328.0lnHs5.0211SPFhperf37.210667.05.0Dh027.01.015.020208.0Dr271.30943.0027.0log025.2a894.18115.1027.00373.3b3.4027.037.210894.1894.0271.3Vs33.0328.0667.0328.0wDr1.0106.233.0532.42eswb41.03.44.0ps例4：射孔表皮计算Similarly,Forθ=0o,sH=0.3,sV=3.6,swb=0.4,hencesp=4.3.Forθ=60o,sH=-0.9,sV=4.9,swb=0.004,hencesp=4.Forθ=180oandkH/kV=1,sHandswbdonotchange,sV=1.2,hencesp=0.9.(comparetovalueof4forkH/kV=10)例4：射孔表皮计算，Case1060180例4：射孔表皮计算，Case2180例5：射孔密度影响Awellwithrw=0.328fthastypicalperforationcharacteristicsofrperf=0.0208ft,lperf=0.667ft,andθ=120o.Developatableofperforationskin,spversusperforationdensity(rangingfromSPFof0.5to4)forpermeabilityanisotropies,KH/KV=10,5and1.例5：射孔密度影响，kH/kV=105.0SPF2SPF4SPF例5：射孔密度影响spSPFkH/kV=10kH/kV=5kH/kV=10.520.815.37.119.66.93.024.12.80.932.31.50.341.50.90–Forhighperforationdensities(3to4SPF),skincontributionbecomessmall.–Forlowshotdensities,skineffectissubstantialinnormallyanisotropicformations.4.拟表皮与流速相关与多相相关4.拟表皮：与流速相关的表皮通常是高速气井（也可能是高速油井）由紊流造成表示为：whereD=非达西系数q=flowrateD典型值：orderof10-3Dqsdependentrate拟表皮：与流速相关的表皮对于高产气井，该表皮比其他表皮严重对于高产气井，试井得到拟表皮，s’or试井中改变产量来，隔离与速度相关的表皮确定D并预测与流速相关的表皮对产量的影响Dqss'wotFfss,'拟表皮：与流速相关的表皮interceptslopeDqss'拟表皮组分：与相相关的表皮油井：Ifpwfpb，析出气，如果气相不流动，降