水平井油藏内三维势分布及精确产能公式

3D potential distribution and precise productivity equation of horizontal well.

过去常利用保角变换、等值渗流阻力以及Ｊｏｓｈｉ等人的方法研究水平井的产能公式。由于简化和回避了油藏中水平井的三维渗流本质，这些方法缺乏严格可信的理论基础。提出以三维渗流为前提的水平井产能评价研究方法，并给出它的一些应用。首先建立均质、各向异性油藏中线源水平井速度势方程，然后利用Ｇｒｅｅｎ函数方法分别导出水平无限大和底水驱油藏中水平井的三维势分布。在此基础上建立了一组新的水平井产能公式，这些公式的精度明显高于一些对三维流动简化后所得到的近似公式，后者往往低估了水平井的产能。此外，讨论了水平无限大油藏中势分布的某些重要特征，从理论上证实了水平井适应于垂向渗透性好的薄油层的开采。

The traditional productivity formulae of a horizontal well was established in literatures by use of conform transformation, equivalent flow resistance and Joshi's methods. Its reliability is doubtful due to simplifying 3D steady state fluid flow. This paper considers a method for studying productivity of the well, which is based on 3D potential equation for fluid flow with line sinks. A steady state fluid flow equation is established in a homogeneous anisotropy reservoir. Some steady state solutions of a horizontal well in a laterally infinite reservoir and a reservoir with bottom water drive are derived. Productivity of the well is studied and some new productivity equations are presented in these cases. Reliability of the equations is significantly better than other approximate formulae obtained by simplifying the 3D steady state fluid flow equation. The results demonstrate that the formulae can analyze low productivity of a horizontal well. From potential distributions within the laterally infinite reservoir, we can see that horizontal wells are suitable for thin, high vertical permeability reservoirs.