1、2013.112013.11陈军斌陈军斌 教授教授Professor Junbin ChenProfessor Junbin Chen2.1 2.1 三种基本渗流方式三种基本渗流方式 Three basic forms of percolationThree basic forms of percolation2.22.2 单相不可压缩液体的平面一维稳定渗流单相不可压缩液体的平面一维稳定渗流 Planar one-dimensional steady state percolation of Planar one-dimensional steady state percolation of
2、single-phase incompressible fluid single-phase incompressible fluid 2.3 2.3 单相不可压缩流体的平面径向稳定渗流单相不可压缩流体的平面径向稳定渗流 Planar radial steady state percolation of single-phase Planar radial steady state percolation of single-phase incompressible fluid incompressible fluid2.4 2.4 油井的不完善性油井的不完善性 Imperfect wellI
3、mperfect well2.5 2.5 稳定试井稳定试井 Systematic well testing Systematic well testing（Step rate testingStep rate testing）2.6 2.6 单相流体渗流的微分方程单相流体渗流的微分方程 Differential equation of single-phase fluid Differential equation of single-phase fluid percolation percolation2.12.1 三种基本渗流方式三种基本渗流方式 Three basic forms of
4、percolation Three basic forms of percolation平面一维渗流平面一维渗流planar one-dimensional percolationr平面径向渗流平面径向渗流planar radial percolation球面径向渗流球面径向渗流globe radial percolation2.1 2.1 三种基本渗流方式三种基本渗流方式 Three basic forms of percolationThree basic forms of percolation2.22.2 单相不可压缩液体的平面一维稳定渗流单相不可压缩液体的平面一维稳定渗流 Plana
5、r one-dimensional steady state percolation of Planar one-dimensional steady state percolation of single-phase incompressible fluid single-phase incompressible fluid 2.3 2.3 单相不可压缩流体的平面径向稳定渗流单相不可压缩流体的平面径向稳定渗流 Planar radial steady state percolation of single-phase Planar radial steady state percolatio
6、n of single-phase incompressible fluid incompressible fluid2.4 2.4 油井的不完善性油井的不完善性 Imperfect wellImperfect well2.5 2.5 稳定试井稳定试井 Systematic well testing Systematic well testing（Step rate testingStep rate testing）2.6 2.6 单相流体渗流的微分方程单相流体渗流的微分方程 Differential equation of single-phase fluid Differential eq
7、uation of single-phase fluid percolation percolation2.2 2.2 单相不可压缩液体的平面一维稳定渗流单相不可压缩液体的平面一维稳定渗流 Planar one-dimensional steady state percolation of single- Planar one-dimensional steady state percolation of single- phase incompressible fluid phase incompressible fluid 不可压缩流体不可压缩流体：体积不随着压力的变化而变化的流体，又称：
8、体积不随着压力的变化而变化的流体，又称刚性流体刚性流体。与之相反，。与之相反，称为称为可压缩流体可压缩流体。 Incompressible fluid Incompressible fluid ：the fluid that volume does not change with the the fluid that volume does not change with the change of pressurechange of pressure，also known as also known as rigid rigid fluidfluid. It is named as . It
9、 is named as compressible compressible fluid fluid on the contraryon the contrary. . 稳定渗流稳定渗流：压力、渗流速度等运动参数不随时间变化而变化，又被称为：压力、渗流速度等运动参数不随时间变化而变化，又被称为定常渗流定常渗流或或稳态渗流稳态渗流。与之相反，称为。与之相反，称为不稳定渗流不稳定渗流。 Steady state percolation Steady state percolation ：The motion parametersThe motion parameters，pressure pres
10、sure 、velocity velocity etc.etc.，do not change with time, also known as the steady state flow. It is do not change with time, also known as the steady state flow. It is named as named as unsteady state percolation unsteady state percolation on the contrary. on the contrary. 渗流场图渗流场图：由一组等压线和一组流线按照一定规
11、则构成的图形。：由一组等压线和一组流线按照一定规则构成的图形。 Percolation field diagram Percolation field diagram ：Graphics consisted of a set of isobar and Graphics consisted of a set of isobar and a group of streamline according to certain rules. a group of streamline according to certain rules. pepw2.2 2.2 单相不可压缩液体的平面一维稳定渗流单相
12、不可压缩液体的平面一维稳定渗流 Planar one-dimensional steady state percolation of single- Planar one-dimensional steady state percolation of single- phase incompressible fluid phase incompressible fluid 假设长为假设长为L L、宽为、宽为B B、厚度为、厚度为h h的水平条带状油层，刚性水压驱动，地层是均质、的水平条带状油层，刚性水压驱动，地层是均质、等厚、各向同性的。供给边界上的压力为等厚、各向同性的。供给边界上的压力为P
13、ePe，出口端为一排排液坑道，其压力为，出口端为一排排液坑道，其压力为PwPw。 Assuming there is a horizontal strip oil layer Assuming there is a horizontal strip oil layer，and its length is Land its length is L，width is Bwidth is B，height is hheight is h，the the reserviorreservior is rigid water drive is rigid water drive，and the fluid
14、 and the fluid and rock are incompressible. And the formation is homogeneousand rock are incompressible. And the formation is homogeneous，and and isotropic. The supply boundary pressure is isotropic. The supply boundary pressure is PePe，and the delivery end is an and the delivery end is an drainage
15、pit whose pressure is Pwdrainage pit whose pressure is Pw. .平面一维渗流平面一维渗流planar one-dimensional percolation2.2 2.2 单相不可压缩液体的平面一维稳定渗流单相不可压缩液体的平面一维稳定渗流 Planar one-dimensional steady state percolation of single- Planar one-dimensional steady state percolation of single- phase incompressible fluid phase
16、incompressible fluid LppdxdpweewexewwpppxLppppLxL()ewKA ppQLpepw00tLAALTdtdxQQewK ppQK dpvAdxL 达西定律达西定律Darcy law产量产量Production压力梯度压力梯度Pressure gradient压力分布压力分布Pressure distribution见水时间见水时间Breakthrough time2.1 2.1 三种基本渗流方式三种基本渗流方式 Three basic forms of percolationThree basic forms of percolation2.22.2
17、 单相不可压缩液体的平面一维稳定渗流单相不可压缩液体的平面一维稳定渗流 Planar one-dimensional steady state percolation of Planar one-dimensional steady state percolation of single-phase incompressible fluid single-phase incompressible fluid 2.3 2.3 单相不可压缩流体的平面径向稳定渗流单相不可压缩流体的平面径向稳定渗流 Planar radial steady state percolation of single-ph
18、ase Planar radial steady state percolation of single-phase incompressible fluid incompressible fluid2.4 2.4 油井的不完善性油井的不完善性 Imperfect wellImperfect well2.5 2.5 稳定试井稳定试井 Systematic well testing Systematic well testing（Step rate testingStep rate testing）2.6 2.6 单相流体渗流的微分方程单相流体渗流的微分方程 Differential equat
19、ion of single-phase fluid Differential equation of single-phase fluid percolation percolation2.3 2.3 单相不可压缩液体的平面径向稳定渗流单相不可压缩液体的平面径向稳定渗流 Planar radial steady state percolation of single- Planar radial steady state percolation of single- phase incompressible fluid phase incompressible fluid （1 1）地层是均质
20、等厚各向同性的；）地层是均质等厚各向同性的；The formation is homogeneousThe formation is homogeneous，isopachous isopachous and isotropicand isotropic； （2 2）地层内只有一种均质不可压缩液体在流动，且不考虑地层的压缩性；）地层内只有一种均质不可压缩液体在流动，且不考虑地层的压缩性；There is There is one kind of homogeneous and incompressible fluid flowing in formationone kind of homoge
21、neous and incompressible fluid flowing in formation； （3 3）流体与岩石无物理化学反应；）流体与岩石无物理化学反应；There is no physical and chemical action There is no physical and chemical action between fluid and rock.between fluid and rock. （4 4）油井为裸眼井，地层形状如图所示。）油井为裸眼井，地层形状如图所示。The production well is barefoot well The product
22、ion well is barefoot well and the shape of formation is shown as figure.and the shape of formation is shown as figure.平面径向渗流平面径向渗流planar radial percolation2.3 2.3 单相不可压缩液体的平面径向稳定渗流单相不可压缩液体的平面径向稳定渗流 Planar radial steady state percolation of single- Planar radial steady state percolation of single- ph
23、ase incompressible fluid phase incompressible fluid QK dpvAdr 达西定律达西定律Darcy law压力分布压力分布Pressure distributionrRRRppppeweweelnlnwwewewRrRRpppplnln产量产量Production2()lnewewKh ppQRR压力梯度压力梯度Pressure gradientrRRppdrdpwewe1ln平均地层压力平均地层压力Average pressure1(ln)22ewwRqppKhR见水时间见水时间Breakthrough time22()ewh RRTQ2.
24、1 2.1 三种基本渗流方式三种基本渗流方式 Three basic forms of percolationThree basic forms of percolation2.22.2 单相不可压缩液体的平面一维稳定渗流单相不可压缩液体的平面一维稳定渗流 Planar one-dimensional steady state percolation of Planar one-dimensional steady state percolation of single-phase incompressible fluid single-phase incompressible fluid 2
25、.3 2.3 单相不可压缩流体的平面径向稳定渗流单相不可压缩流体的平面径向稳定渗流 Planar radial steady state percolation of single-phase Planar radial steady state percolation of single-phase incompressible fluid incompressible fluid2.4 2.4 油井的不完善性油井的不完善性 Imperfect wellImperfect well2.5 2.5 稳定试井稳定试井 Systematic well testing Systematic well
26、 testing（Step rate testingStep rate testing）2.6 2.6 单相流体渗流的微分方程单相流体渗流的微分方程 Differential equation of single-phase fluid Differential equation of single-phase fluid percolation percolation2.4 2.4 油井的不完善性油井的不完善性 Imperfect well Imperfect well打开程度不完善打开程度不完善Imperfect penetrating well(1)(1)不完善性分类不完善性分类 Cla
27、ssification of imperfect well Classification of imperfect well打开性质不完善打开性质不完善Imperfect characteristic well双重不完善双重不完善Double imperfect well2.4 2.4 油井的不完善性油井的不完善性 Imperfect well Imperfect well(2)(2)不完善井的研究方法不完善井的研究方法 Research method of imperfect wellResearch method of imperfect well 1 1）表皮系数）表皮系数 Skin f
28、actorSkin factor2()(ln)ewewKh ppQRSR 2 2）折算半径）折算半径 Converted radiusConverted radiusSwewRR e 3 3）流动效率（不完善系数）流动效率（不完善系数） The flow efficiencyThe flow efficiency（imperfect factorimperfect factor）lnlnewewRRRSR2.1 2.1 三种基本渗流方式三种基本渗流方式 Three basic forms of percolationThree basic forms of percolation2.22.2
29、单相不可压缩液体的平面一维稳定渗流单相不可压缩液体的平面一维稳定渗流 Planar one-dimensional steady state percolation of Planar one-dimensional steady state percolation of single-phase incompressible fluid single-phase incompressible fluid 2.3 2.3 单相不可压缩流体的平面径向稳定渗流单相不可压缩流体的平面径向稳定渗流 Planar radial steady state percolation of single-pha
30、se Planar radial steady state percolation of single-phase incompressible fluid incompressible fluid2.4 2.4 油井的不完善性油井的不完善性 Imperfect wellImperfect well2.5 2.5 稳定试井稳定试井 Systematic well testing Systematic well testing（Step rate testingStep rate testing）2.6 2.6 单相流体渗流的微分方程单相流体渗流的微分方程 Differential equati
31、on of single-phase fluid Differential equation of single-phase fluid percolation percolation2.5 2.5 稳定试井稳定试井 Systematic well testing Systematic well testing（Step rate testingStep rate testing） 试井试井：直接从实测的产量、压力数据反求地层参数，然后用所求得地层参数来预：直接从实测的产量、压力数据反求地层参数，然后用所求得地层参数来预测新的工作制度下的产量和压力。测新的工作制度下的产量和压力。 Well t
32、estWell test：The formationThe formation parameters is obtained by directly using the parameters is obtained by directly using the measured production and pressure data and then to predict the production measured production and pressure data and then to predict the production and pressure under new w
33、orking condition.and pressure under new working condition. 稳定试井稳定试井：试井过程中每一实测的压力、产量都不随时间变化的叫稳定试井。：试井过程中每一实测的压力、产量都不随时间变化的叫稳定试井。 Systematic well testSystematic well test：That every measured pressure and production do That every measured pressure and production do not change with time in the process o
34、f well testing not change with time in the process of well testing 指示曲线指示曲线：每一稳定制度下的产量压差点在以产量为横坐标、压差为纵坐标的曲：每一稳定制度下的产量压差点在以产量为横坐标、压差为纵坐标的曲线。线。 Index curveIndex curve：Production pressure difference points under each steady Production pressure difference points under each steady statestate system are d
35、rawn on the chart which its X-coordinate is production system are drawn on the chart which its X-coordinate is production and the Y-coordinate is pressure differenceand the Y-coordinate is pressure difference. . QJ pn=1n1，不正常，不正常Q p2lnewKhJRSR2.1 2.1 三种基本渗流方式三种基本渗流方式 Three basic forms of percolation
36、Three basic forms of percolation2.22.2 单相不可压缩液体的平面一维稳定渗流单相不可压缩液体的平面一维稳定渗流 Planar one-dimensional steady state percolation of Planar one-dimensional steady state percolation of single-phase incompressible fluid single-phase incompressible fluid 2.3 2.3 单相不可压缩流体的平面径向稳定渗流单相不可压缩流体的平面径向稳定渗流 Planar radial
37、 steady state percolation of single-phase Planar radial steady state percolation of single-phase incompressible fluid incompressible fluid2.4 2.4 油井的不完善性油井的不完善性 Imperfect wellImperfect well2.5 2.5 稳定试井稳定试井 Systematic well testing Systematic well testing（Step rate testingStep rate testing）2.6 2.6 单相流
38、体渗流的微分方程单相流体渗流的微分方程 Differential equation of single-phase fluid Differential equation of single-phase fluid percolation percolation2.6 2.6 单相流体渗流的微分方程单相流体渗流的微分方程 Differential equation of single-phase fluid percolation Differential equation of single-phase fluid percolation(1)(1)单相流体渗流的连续性方程单相流体渗流的连续
39、性方程 Continuing equation of percolation of single-phase fluidContinuing equation of percolation of single-phase fluid()2xxvdxvx()2yyvdyvy()2zzvdzvzdiv0vt2.6 2.6 单相流体渗流的微分方程单相流体渗流的微分方程 Differential equation of single-phase fluid percolation Differential equation of single-phase fluid percolation(2)(2)
40、状态方程状态方程 State equation State equationd1dLLLVCVp 液体状态方程液体状态方程 liquid state equationliquid state equation1LdCdp0()0eLCpp 岩石状态方程岩石状态方程 Formation state equationFormation state equation11pfpdVdCVdpdp00fCppe 气体状态方程气体状态方程 Gas state equationGas state equationpZRTM2.6 2.6 单相流体渗流的微分方程单相流体渗流的微分方程 Differential
41、 equation of single-phase fluid percolation Differential equation of single-phase fluid percolation(3)(3)达西方程达西方程 Darcy equationDarcy equationxyzKpvxKpvyKpvz (4)(4)单相微可压缩液体渗流基本微分方程单相微可压缩液体渗流基本微分方程 Basic differential equation of single-phase compressible fluid Basic differential equation of single-ph
42、ase compressible fluid percolationpercolation222222()tKppppCxyzt2.6 2.6 单相流体渗流的微分方程单相流体渗流的微分方程 Differential equation of single-phase fluid percolation Differential equation of single-phase fluid percolation(5)(5)油藏边界条件和初始条件油藏边界条件和初始条件 Boundary condition and initial condition of reserviorBoundary con
43、dition and initial condition of reservior 第一类边界条件第一类边界条件 The first-kind boundary conditionThe first-kind boundary condition 第二类边界条件第二类边界条件 The second-kind boundary conditionThe second-kind boundary condition 初始条件初始条件 The initial condition The initial condition ()( , , )|( , , , )x,y,zp x y zf x y z t( , , )( , , , )x y zpf x y z tn00( , , )( , , , )|( , , , )tx y zDp x y z tp x y z t
