分形理论及其在地层可钻性预测中的应用

FRACTAL THEORY AND IT’S APPLICATIONS ON ROCK DRILLABILITY FORECASTING

王培义 翟应虎 王克雄 王长东

Wang Peiyi Zhai Yinghu Wang Kexiong Wang Changdong

中国石油大学石油天然气工程学院, 北京 102249 中国石油天然气集团公司长城钻井公司, 北京 100724

为了及时方便地预测岩石的可钻性,首次用分形理论来描述岩石破碎过程,从而确定岩石的可钻性。介绍了分形、分维的基本概念及4种分维数的确定方法,阐述了岩石破碎的分形特征和岩石破碎碎块的分形度量方法。在室内实验基础上,确定了岩石破碎后的块度分布函数,计算了岩石破碎的分形维数,并分别采用直线、幂函数、对数、指数、多项式5种数学模型对实验数据进行了回归分析处理,结果表明直线回归方程综合指数最高,相关系数均在0.96以上。说明岩屑的分形维数与地层的抗钻特性参数(强度、硬度、可钻性等)有内在的联系,分形几何能很好地描述岩石破碎过程的不规则性和不确定性,分形维数是岩石微观结构、空隙结构、粉碎方式的综合反映,其在地层可钻性预测中的应用效果较好,预测误差小于12%。

The basic conception of fractal geometry and fractal dimension is introduced,and the methods for determining four kinds of values of fractal dimensions are defined.The fractal character of rock-crashing and fractal measurement methods of rock-crashing shiver are explained.Abnormity of rock-crashing can be described commendably by fractal geometry.Intensity,rigidity,drillability of rock and micro-structure,pore structure,crashing manner of rock are related to fractal dimension.Broken fragment distribution function is determined based on laboratory experiment.Broken fractal dimension of rock is calculated.Experiment data is regressed by five mathematics models such as beeline,power function,logarithm,exponential function and multinomial.As a result,the aggregate index of beeline regression equation is the biggest.The correlation parameter is more than 0.96.There is inherent relation between rock rigidity,intensity,drillability and rock fractal dimension.Furthermore,the applications of fractal dimension on rock drillability Forecasting is discussed preliminarily.

10.3969/j.issn.1000-7393.2005.06.007