三重介质油藏压力动态分析的边界元法

油藏形状对井底压力动态响应有着显著的影响,为了研究任意形状三重介质油藏的压力动态,本文首先建立了由基岩系统、裂缝系统和溶洞系统组成的任意形状的三重介质油藏试井解释模型.利用Laplace变换和边界元方法获得油藏内任意点的压力,进而由杜哈美原理得到了考虑井筒储存和表皮效应的井底压力.讨论了介质间窜流、弹性储容比、复杂边界以及油藏内存在不渗透区域等因素对压力响应的影响.分析表明,溶洞—裂缝窜流系数越大,半对数压力曲线上第一个过渡段出现得越早,双对数压力导数曲线上第一个下凹部分出现得越早;基岩—裂缝窜流系数和溶洞—裂缝窜流系数类似,只是其影响压力响应曲线的第二个过渡段;裂缝弹性储容比的大小控制着第一个过渡段持续时间的长短,表现为压力曲线上第一个过渡段台阶的宽窄和压力导数曲线上第一个凹兜的深浅;油藏的边界条件对油藏的压力动态存在明显影响,与定压边界条件相比,分段定压边界条件明显延迟了压力导数曲线下掉的时间;不渗透区域的存在使得压力导数曲线上第二个凹兜变浅,晚期径向流段抬升,偏离了0.5水平线.

Boundary element method for the analysis of the transient pressure of triple porosity reservoir

The effect of the shape of reservoir boundaries on the well-bore pressure response is evident.The conventional analytical methods can only be used to calculate the well-bore pressure response in regularly shaped reservoirs.A mathematical model for the well test interpretation of arbitrary shaped triple porosity reservoirs(composed of basement rock system,fracture system and solution cavity system) is established and transformed to the modified Helmholtz equation.The well-bore pressure in which skin effect and well-bore storage are considered is obtained by using boundary element method and Duhamel principle.The effects of interporosity flow parameter among basement rock system,fracture system and solution cavity,dimension fracture storage parameter,boundary shape and impermeable barriers in reservoir on the pressure response curve are discussed.It is shown that,the greater the interporosity flow factor between solution cavity system and fracture system,the earlier the first transition section on semilogarithmic pressure curve and the first concavity on double-logarithmic pressure derivative curve appear;the greater the interporosity flow factor between basement system and fracture system,the earlier the second transition section in semilogarithmic pressure curve and the first concavity in double-logarithmic pressure derivative curve appear;the dimension fracture storage parameter controls the duration of the first transition section in semilogarithmic pressure curve,that is,the length of the transition section and the depth of the first concavity in double-logarithmic pressure derivative curve;the boundary conditions of reservoir has obvious influence on the pressure response,compared with constant-pressure boundary condition,sectional constant-pressure boundary condition obviously postpones the time of pressure derivative curve dropping;the existence of impermeable barriers makes the second concavity in the pressure derivative curve shallow and makes late radial-flow section rise and deviate 0.5 horizontal line.