变井径环空分形表征及其对固井顶替效率的影响  

Fractal characterization of variable well diameter annulus and its effect on cementing displacement efficiency

作　　者：张景富[1] 秦南欣欣 公海峰 王建成 谢帅 朱胡佳 ZHANG Jingfu;QIN Nanxinxin;GONG Haifeng;WANG Jiancheng;XIE Shuai;ZHU Hujia(Key Laboratory of Enhanced Oil Recovery,Ministry of Education,Northeast Petroleum University,Daqing,Heilongjiang 163318,China)

机构地区：[1]东北石油大学提高油气采收率教育部重点实验室,黑龙江大庆163318

出　　处：《东北石油大学学报》2023年第3期56-68,I0005,I0006,共15页Journal of Northeast Petroleum University

基　　金：国家自然科学基金项目(51474074);黑龙江省自然科学基金项目(E201334)。

摘　　要：为分析井径非线性变化对油气井注水泥顶替效率的影响,利用W-M分形函数、体积填充等理论,研究变井径环空几何形态表征及注水泥顶替效率计算,建立实测井径曲线的分形函数特征参数计算方法及变井径环空顶替流动分析模型,开展注水泥顶替流动数值模拟。结果表明:变井径环空的顶替效率低于均匀井径环空的顶替效率;标度参数、分形维数增大,井壁壁面凸起、凹陷高度增大,不规则程度增高,顶替效率降低;高标度参数、高分形维数范围内,顶替效率降低幅度高,顶替效率相对变化率大;顶替注入流速增大,顶替效率相对变化率减小;井斜角增大,顶替效率相对变化率增大;计算顶替效率时,当标度参数、分形维数低于阈值时,可将井眼环空近似考虑为均匀井径环空,而当标度参数、分形维数较高时,采用均匀井径环空简化处理会造成很大偏差;工程中,应注意处理计算模型选择及有效解决顶替效率问题。该结果为解决注水泥顶替效率计算的准确性、推进科学化固井设计与施工提供基础。To analyze the effect of nonlinear change of well diameter on cementing displacement efficiency of oil and gas well.Using W-M fractal function,volume filling and other basic theories,the geometric characterization of variable-diameter annulus and the calculation of cementing displacement efficiency were studied.The fractal function characteristic parameter calculation method of measured well diameter curve and the analysis model of variable-diameter annulus displacement flow were established to carry out numerical simulation of cementing displacement flow.The results show that the displacement efficiency of variable diameter annulus is lower than that of uniform diameter annulus,with the increase of scale parameters and fractal dimension,the height of bulge and sag on the wall surface increases,the degree of irregularity increases,and the displacement efficiency decreases.In the range of high scale parameters and high shape dimension,the displacement efficiency decreases greatly and the relative change rate of displacement efficiency is large.With the increase of displacement flow rate,the relative change rate of displacement efficiency decreases.With the increase of well inclination angle,the relative change rate of displacement efficiency increases.When the scale parameter and fractal dimension are lower than the threshold value,the approximation of borehole annulus can be considered as uniform annulus.However,when the scale parameter and fractal dimension are higher,the simplification of uniform annulus will cause great deviation.It is necessary to properly handle the calculation model selection and effectively solve the displacement efficiency problem in engineering.The results provide a basis for solving the accuracy of calculation of cementing displacement efficiency and promoting scientific cementing design and construction.

关 键 词：变井径 分形函数 数值模拟 固井 顶替效率 标度参数 分形维数 

分 类 号：TE256[石油与天然气工程—油气井工程]