基于Python语言的钻井井壁突变失稳机理分析

Mechanism analysis of catastrophic instability of drilling shaft lining based on Python language

钻井井壁结构竖向失稳是一种渐变至突变的力学问题,如何将传统的力学模型与现代的数学方法相结合,达到对井壁结构失稳机制的定量研究,是钻井井壁结构竖向稳定性研究亟需解决的问题。钻井井壁悬浮下沉至井底时,井壁结构积累了一定量的弹性势能,此时的稳定平衡状态是动态的,井壁有可能发生倾斜、滑移,甚至失稳,需要加强监控和有效防治。基于突变理论原理和井壁悬浮下沉力学模型,建立钻井井壁竖向失稳的总势能函数和尖点突变模型。由突变模型的平衡曲面和分歧点方程,给出了井壁突变失稳的定量判定条件。结果表明:控制变量m,n的取值直接决定井壁的稳定平衡状态。当Δ>0时,控制变量(m,n)落在分歧点集外部,系统位于平衡曲面的上叶和下叶,井壁结构处于稳定平衡状态。当Δ<0时,控制变量(m,n)落在分歧点集内部,系统位于平衡曲面的中叶,井壁结构处于不稳定平衡状态。当Δ=0时,控制变量(m,n)落在分歧点集的边界上,井壁结构处于临界稳定平衡状态。进一步地由稳定平衡临界条件,建立了井壁满水和非满水竖向失稳临界深度计算公式。同时,为推广突变模型分析方法的工程应用,利用Python语言,确立了井壁稳定性分析和判定的流程,为监测预报和井型参数优化提供了理论依据。结合工程实例,计算后发现满水和非满水状态下建立的突变理论临界深度值较能量法临界深度值分别相差0.396%和7.15%。因此,基于突变理论的井壁结构稳定性研究方法可以有效地阐释井壁结构竖向失稳。

Vertical instability of drilling shaft lining is a mechanical problem with gradual change to abrupt change.How to combine tradi⁃tional mechanical model with modern mathematical methods to achieve quantitative research on this instability mechanism analysis is the theoretical innovation on vertical stability of drilling shaft lining structure and the research content of this paper as well.When the shaft suspended and sunk to the bottom of the well,a certain amount of elastic potential energy is accumulated.At this time,the state of stable equilibrium is dynamic,and the shaft may tilt,slip,or even lose stability.,and strengthened monitoring and effective prevention is neces⁃sary.In this paper,based on the theory of catastrophe and the mechanics model of shaft wall suspension and subsidence,the total poten⁃tial energy function and the cusp catastrophe model for vertical instability of shaft lining were established.According to the equilibrium sur⁃face and bifurcation point equation of the model,the quantitative determination conditions of the instability are given.The results show that the values of the control variables m and n directly determine the stable equilibrium state of the shaft wall.WhenΔ>0,the control variable(m,n)falls outside the bipartite point set,the system is located at the upper and lower blade of the equilibrium surface,and the shaft structure is in a stable equilibrium state.WhenΔ<0 the control variable(m,n)falls inside the bipartite point set,the system is located at the middle of the equilibrium surface,and the shaft structure is in an unstable equilibrium state.WhenΔ=0,the control variable(m,n)falls on the boundary of the bipartite point set and the structure is in a critical stable equilibrium state.Furthermore,based on thecritical condition of stable equilibrium,the critical depth formula of vertical instability of shaft lining full and non-full water is established.At the same time,in order to popularize the engineering application of the catastrophic model analysis method,the flow chart of instability analy⁃sis and judgment is established by using Python language,which provides the theoretical basis for monitoring and forecasting and well type parameter optimization.Combined with an engineering example,it is found that the critical depth based on catastrophe theory in this paper is 0.396%and 7.15%different from those obtained by energy method respectively under full water and non-full water condition.There⁃fore,the study method of shaft lining structure stability based on catastrophe theory can effectively explain the vertical instability of shaft lining structure.