考虑各向异性和偏心距影响的水平井产量公式推导、对比与应用

Derivation,Comparison and Application of Horizontal Well Production Formula Considering Anisotropy and Eccentricity Effects

在水平井产量公式的应用中,经常会遇到各向异性和偏心距的问题,这一问题的解决涉及到计算结果的可靠性。目前,考虑各向异性和偏心距的水平井产量公式,均由Joshi提出。但Joshi只提供了公式的结果,而没有具体的推导过程,因此,很难判断公式的可靠性和正确性。在附录中,对考虑各向异性和偏心距的水平井产量公式,进行了推导,得到了新的结果和认识。通过Joshi和陈氏公式的实际应用表明:①各向异性对水平井产量的影响非常明显,而偏心距则影响较小;②Joshi的只考虑各向异性的水平井产量公式存在问题较大;(3)Joshi考虑各向异性和偏心距影响的水平产量公式,在对数的偏心距项中,不应该考虑非均质的影响,而且偏心距前应当是正号而不是负号。

In application of production rate formula for horizontal well, anisotropy and eccentricity should often be encountered, and dealing with this problem relates to the reliability of the calculated results. At present, such formulas considering these two factors were all proposed by Joshi. However, only the results from one factor or two factors were provided by Joshi without related concrete derivations, hence remaining the issues of reliability and validity of the formulas. In appendix of this paper, the production rate formulas for horizontal well considering anisotropy and eccentricity are re-deduced and new results and recognitions are obtained. The application of the formulas by Joshi and by Chen Yuan-qian indicates that： （1）the influence of anisotropy on horizontal well production rate is very obvious, and that of eccentricity on it is relatively small; （2）there exist big problems with the formula only considering eccentricity by Joshi; （3） in Joshi＇s formula considering these two factors, the influence of anisotropy should not be taken into account in the eccentricity term expressed by log form; moreover, the mark before the eccentricity should be plus sign but not minus sign.