实钻造斜率的实用分析算法

A practical estimation algorithm for actual build-up rates

鲁港 李杉 杨云龙 王海涛 李雪松 孟庆安 陈俊宇 魏涛

LU Gang LI Shan YANG Yunlong WANG Haitao LI Xuesong MENG Qing’an CHEN Junyu WEI Tao

中国石油昆仑数智科技有限责任公司 中国石油渤海钻探工程有限公司定向井技术服务分公司 斯伦贝谢长和油田工程公司

CNPC Kunlun Digital Technology Co., Ltd., Beijing 100043, China Directional Drilling Company, CNPC Bohai Drilling Engineering Co., Ltd., Tianjin 300280, China SCP Oilfield Services Co., Ltd., A Schlumberger JV Company, Xi’an 710021, Shaanxi, China

为了根据现场有限的数据快速估算一个立柱(单根)的实际造斜率，建立了滑动钻进的数学模型。有2个滑动段的“复合+滑动+复合+滑动+复合”钻进模式，数学模型是一个九元非线性方程组。通过一系列数学变换，从该非线性方程组推导出一个只包含实际造斜率的一元非线性方程。从方程图像上看，该方程具有简单的凸凹性，适用于使用二分法求根。给出了完整的数值求解算法，当求出未知数实际造斜率之后，方程组的其他未知数能用解析计算公式简单地反向计算出来。使用理论模拟数据对算法进行验证，算法能正确求出唯一的造斜率；使用实际测斜数据和滑动记录数据对算法进行验证，算法能快速、正确给出实际造斜率的估算值。该算法为现场定向井工程师提供了一种新的计算辅助方法，在钻井现场快速估算实际造斜率时有较大的实用价值。

A mathematical model was built for slide drilling to rapidly estimate the actual build-up rate for a stand (joint) using limited on-site data. For the drilling mode of “compound + slide + compound + slide + compound” drilling (having two slide sections), the mathematical model is a nonlinear equation group with nine unknows. We managed to derive a nonlinear equation with only one unknown (the actual build-up rate) from the above nonlinear equation group via a series of mathematical transforms. The graph of the equation shows simple convexity-concavity and thus, applicability to the bisection method for solutions. The complete numerical solving algorithm was given for the derived equation, and the other unknows of the equation group can be inversely calculated simply using the analytical formulas. The presented algorithm was validated using the theoretical simulation data, which demonstrated that the algorithm can correctly deliver a sole value of the build-up rate. Moreover, the algorithm was validated using the actual inclinometer data and slide drilling records. It was indicated that the algorithm can rapidly and correctly estimate the actual build-up rate. This algorithm provides a new calculation aid for on-site directional drilling engineers and is highly practical for the on-site fast estimation of the build-up rate.

10.13639/j.odpt.202201035