对Joshi各向异性水平井产量公式的质疑、推导与对比

Query,Derivation and Comparison About Joshi's Production Rate Formula for Horizontal Well in Anisotropic Reservoir

水平井是提高油井产能的重要手段。近20多年来,在我国的陆上和近海地区,水平井钻井与开采技术取得了重大的发展,因而,采用什么方法能够可靠地计算水平井的产量已经成为一个重要课题。目前,国际上被推荐应用的方法有4种,即:Joshi方法、Borisov方法、Giger方法和Renard方法。最近,作者又提出了一种计算水平井产量的新方法。在各向同性的均质条件下,这5种方法的计算都能得到比较好的一致性。然而,对于各向异性条件下的水平井,尽管Joshi提出了2种校正方法,并得到了广泛的应用。经过研究认为,这2种校正方法没有理论上推导的依据,可以说是不正确的。通过理论上的分析与推导,得到了Joshi在各向异性条件下计算水平井的产量公式,同时,对其他几种水平井产量公式,统一地进行了各向异性的校正,也对影响产能的不同因素进行了计算。通过实例计算表明,只有正确考虑各向异性条件下,水平井产量的计算公式才是正确有效的。

In the past 20 years, major development has been made in horizontal drilling and production technologies applied to domestic onshore and offshore areas. How to reliably calculate the production rate by horizontal drilling process is becoming an important task to reservoir engineers. There are four methods widely applied at home and abroad at present： Joshi＇s method, Borisov＇s method, Giger＇s method and Renard-Dupuy＇s method. This paper presents a new method for it proposed by Prof. Yuanqian Chen. Under homogeneous conditions, satisfactory results can be all given by these methods. In anisotropic conditions, Joshi had given two modified methods which were widely used, but this study indicates that such modified methods have no basis from theoretic derivation, so the results are not correct. Adding theoretic analysis and derivation, this paper presents Joshi＇s production rate formula for horizontal well in anisotropic reservoir. Meanwhile, anisotropic corrections for other methods are made correspondingly, including calculations of different factors influencing individual productivity. Case study shows that the method proposed in this paper is proper and effective.