各向异性油藏椭圆不定常渗流近似解

The elliptic transient flow of vertically fractured well in anisotropic reservoir.

在考虑平面渗透率各向异性的情况下 ,分析了垂直裂缝井的稳态渗流以及垂直裂缝井无限导流和有限导流的不定常渗流。得到了椭圆形边水油藏中垂直裂缝井稳态渗流近似产量公式和压力分布公式 ,并举例说明渗透率非均质变异系数对产量的影响 :当平均渗透率和其它参数不变时 ,非均质变异系数越小 ,稳态产量越大。在椭圆坐标内建立有限导流及无限导流垂直裂缝井渗流的控制方程 ,利用质量守恒定律得到压力影响半径与无因次时间的关系 ,得到近似压力分布公式以及相应的试井公式。非均质变异系数对典型试井曲线的影响为 :当平均渗透率和其它参数不变时 ,非均质变异系数增大 ,井底压差、压力导数增大 ,说明地层垂直于裂缝方向的渗透率越大越有利于生产。在双对数试井理论图版上 ,无限导流和有限导流垂直裂缝井的试井曲线早期斜率分别为 0 .5和 0 .2 5 ,垂直裂缝井的试井导数曲线在后期恒为 0 .5。图 4参

The authors analyze the steady flow and transient flow of vertically fractured wells with infinite conductivity or finite conductivity in anisotropic reservoirs. The flow in formation can be regarded as elliptic flow, and the flow in vertical fracture is linear for finite conductivity wells. First, the formulae of approximate steady production and pressure distribution are derived at elliptic coordinate, an example shows the influence of anisotropic coefficient ( K x/K y ) to production, that is to say that the bigger anisotropic coefficient is, the smaller production is, at condition of same average permeability. Then the approximate formulae of well testing are deduced by using average mass conversation, and some typical curves are drawn and analyzed. It shows that: the smaller anisotropic coefficient is, the more the well bore pressure is, and well testing curves go up. In log log coordinate system, the slopes of well testing curves of vertically fractured wells with infinite conductivity and finite conductivity respectively are 0.5 and 0.25 at initial time, at later period the derivatives of well testing curves are 0.5.