水驱开发效果评价图版

郭印龙2007年5月目录一、公式推导二、图版制作水平油层忽略毛管力情况下，莱弗里特简化分流方程rwrowoowowwKKBBf11相对渗透率比值－含水饱和度关系wbSrwroeaKK含水－含水饱和度关系wwoowowwbSeaBBf1111、含水－采出程度理论关系式推导油藏一定，fw仅与Kro/Krw比值有关油藏一定，Kro/Krw比值仅与Sw有关23平均含水饱和度－采出程度SwiRSoiSw平均含水饱和度－出口端含水饱和度SorSwSw13132出口端含水饱和度－采出程度SorSwiRSoiSw131231、含水－采出程度理论关系式推导出口端含水饱和度是采出程度的函数456含水－采出程度关系SorSwiRSoibeaBBfwwoowow13123111、含水－采出程度理论关系式推导将⑥式代入③式并整理得结论：⑦式即为所求，说明油藏一定，含水率fw仅是采出程度R的函数，应用⑦式，可制作fw-R理论图版72213123131231312313123123fw'231｝｛即：｝｛SorSwiRSoibSorSwiRSoibSorSwiRSoibSorSwiRSoibaeBBaeBBbSoibSoiaeBBaeBBdRdfwoowwoowwoowwoowowowowoww结论：⑧式即为所求，表示含水上升率－采出程度之间的函数关系，应用⑧式，可制作fw’-R理论图版82、含水上升率－采出程度理论关系式推导将⑦式对R微分，整理得⑧式：)1(2311123123'221312313123wwoiwwoiwoowwoowffbSffbSaeBBaeBBbSoidRdffwSorSwiRSoibSorSwiRSoibowoww｝｛)1(23'wwoiwffbSf即：93、含水上升率－含水率理论关系式推导将⑦式变形并代入⑧式得：结论：⑨式即为所求，表示含水上升率－含水率之间的函数关系，应用⑨式，可制作fw’-fw理论图版当采出程度在含水率为fw时变化dR，对应的累积采油量变化为NdR，累积采液量的变化值为dLp，则有dLpfwNdR)1(dRfwNdLp1dRfwNfwdWp1N－地质储量，104tWp－从投产到采出程度为R时的累积产水量，104tdRfwNfwdWpWpWpR00110111213代入74、存水率－采出程度理论关系式推导(1)、求累积产水量4、存水率－采出程度理论关系式推导dReowBwawoBoNdRaewoBoBwowNdRaewoBoBwowNdRSorSwiRSoibawoBoBwowNdRfwNdRfwNfwdWpWpRbRbRbRRWpRSorSwiRSoiSorSwiRSoiSorSwiRSoie0230230230000131131131111131231111111323223131231312313123131023bSoiRSorSwibSorSwibSorSwiRSoibSorSwiRSoieeowBwabSoiwoBoNeeowBwabSoiwoBoNdReowBwawoBoNWpRb4、存水率－采出程度理论关系式推导1322313123bSoiRSorSwibeeowBwabSoiwoBoNWp即：4、存水率－采出程度理论关系式推导结论：式即为所求，表示累积产水量－采出程度之间的函数关系，应用式，可进一步求出存水率与采出程度的理论关系式1414在注采平衡（即注采比为1）的条件下,累积产液量的地下体积应等于累积注入量Wi，故存水率推导如下：ReewBwabSoiwoRBNReeowBwabSoiwoBoNeeowBwabSoiwoBoN132132132112313123231312323131234、存水率－采出程度理论关系式推导(2)、求存水率ReewBwabSoiwoRCbSoiRSorSwib1322313123即：154、存水率－采出程度理论关系式推导结论：式即为所求，表示存水率－采出程度之间的函数关系，油藏一定，存水率仅与采出程度有关，应用式，可制作C－R理论图版1515目录一、公式推导二、图版制作1、图版制作流程(1)、确定常数值：应用相对渗透率曲线确定Sor、Soi、Siw、a、b值；查《油田开发基础数据表》确定Bo、Bw、μo、μw、ρo值(2)、根据理论关系式计算fw、fw’、C理论值(3)、计算油藏实际fw、fw’、C实际值(4)、应用excel制表作图功能，将以上数据列表成图00.10.20.30.40.50.60.70.80.910.20.30.40.50.60.70.80.9SwKr/fwkrokrwfw(1)、确定常数值魏岗油田典型相渗曲线可以读取：Sor＝0.276Soi＝0.69Swi＝0.31Swkrokrwfwkro/krw0.311000.35250.81630.00630.0588129.57140.4350.51470.020.434425.7350.5410.1060.0520.85532.0384620.560.05910.05910.916910.60.0260.0760.97310.3421050.66880.00730.1210.99560.0603310.719800.164610典型相渗曲线对应试验数据当Sw＝0.3525时，Kro/Krw＝129.5714；当Sw＝0.6688时，Kro/Krw＝0.060331，代入②式，得：669606b24a060331.05714.1296688.03525.0＝＝解得：bbaeae项目数值Sor0.276Soi0.69Swi0.31Bw1Bo1.097a669606b24μo6.85μw0.47ρo0.86结合基础数据则有(2)、计算fw、fw’、C理论值与实际值，并成图RfwRfw00.0281.227.6410.0363.3127.9520.0465.1938.0630.0606.8839.0940.0768.5534.9350.09810.3842.2660.1251245.9570.16113.5553.4480.20614.9959.4390.26416.3365.2100.33817.766.25110.43319.0369.31120.55420.2972.08130.70921.5374.03140.90822.7178.71151.16123.9378.29161.48325.1679.95171.89326.481.86182.41427.6179.81193.07426.9280.91203.90727.9981.03214.95429.0281.73226.26330.0483.37237.89031.0484.32249.89531.8685.822512.34032.6986.482615.28833.9484.592718.78935.0986.122822.87536.1287.96理论实际由⑦式计算fw理论值魏岗油田fw-R关系图0102030405060708090100010203040506070Rfw理论实际(2)、计算fw、fw’、C理论值与实际值，并成图由⑧式计算fw’理论值魏岗油田fw’-R关系图Rfw’Rfw’00.0071.2210.0093.3115.127529620.0125.198.3712627530.0156.880.9456535440.0198.55-3.869192250.02410.386.2592929460.031123.5319358270.04013.557.546483980.05114.996.4669814890.06516.336.68527733100.08417.71.19709333110.10719.033.56779783120.13720.293.4216172130.17521.532.45914164140.22322.716.16343362150.28523.93-0.536642160.36325.162.09286753170.46126.42.40881613180.58527.61-2.6308296190.74026.921.46744467200.93327.990.16232532211.17029.020.99089474221.45830.042.33710432231.80531.041.38186128242.21531.862.67661872252.68732.691.15000136263.21733.94-2.2085386273.79035.091.9423908284.38236.122.57258219理论实际01234567801020304050607080R01234567801020304050607080Rfw'理论实际(2)、计算fw、fw’、C理论值与实际值，并成图由⑨式计算fw’理论值魏岗油田fw’-fw关系图fwfw’fwfw’00.0007.6410.24627.9515.12820.48738.068.371330.72339.090.945740.95434.93-3.86951.18042.266.259361.40145.953.531971.61753.447.546581.82859.436.46792.03465.26.6853102.23666.251.1971112.43269.313.5678122.62372.083.4216132.80974.032.4591142.99178.716.1634153.16778.29-0.537163.33879.952.0929173.50581.862.4088183.66679.81-2.631193.82380.911.4674203.97481.030.1623214.12181.730.9909224.26383.372.3371234.39984.321.3819244.53185.822.6766254.65886.481.15264.77984.59-2.209274.89686.121.9424285.00887.962.5726理论实际0123456789100102030405060708090100fwfw’理论实际(2)、计算fw、fw’、C理论值与实际值，并成图由式计算理C论值魏岗油田C－R关系图15CRCR099.9901.22199.9883.3167.831299.9875.1974.674399.9856.8871.391499.9828.5568.344599.97910.3865.264699.9761260.479799.97