Abstract: The method and formula of simplifying double bent PDM to equivalent single bent PDM is presented and the integrated equations applied to DKO and DTU are derived and a step equivalent method of simplifying double bent(mutibent) PDM to single bent PDM is provided.The difference and relationship between the deflecting force of bit and limiting curvature,build-up rate,etc in concept is discussed in this paper through limiting curvature method.These methods and results can be used to explain doubtful points of theory existed and to guide the design of structure and behavior of double bent(mutibent) PDM assembly in horizontal drilling.

Key words: horizontal well, double bent PDM, equivalent problem, limiting curvature, build-up rate

摘要： 提出了把双弯钻具简化为等效单弯钻具的方法和公式,建立了适用于同向、反向双弯的统一表达式,并给出了把三弯(多弯)钻具简化为单弯钻具的分步等效方法.通过极限曲率法论述了钻头侧向力与极限曲率、造斜率等概念间的联系和区别.这些方法和成果可以解释所存在的理论疑点并用于指导水平井双弯(多弯)钻具的结构和性能设计.

关键词: 水平井, 双弯钻具, 等效问题, 极限曲率, 造斜率