超深井套管外挤载荷的不确定性分析方法

Uncertainty Analysis Method of Casing Extrusion Load of Ultra-Deep Wells

摘要: 针对超深井复杂地层参数信息具有随机性的特点，提出了一定置信水平下超深井复杂地层外挤载荷的不确定性分析方法。在考虑地层–水泥环–套管系统完整性的超深井套管外挤载荷模型的基础上，引入概率统计理论，对外挤载荷不确定性进行参数敏感性分析，统计各参数的分布形式，推导出外挤载荷的不确定性分布状态及分布函数，并以库车地区多口井为例，进行了超深井套管外挤载荷的不确定性分析。结果表明：地层弹性模量、地层泊松比的随机性为超深井外挤载荷不确定性的主要影响因素；不确定性分析方法得到的超深井套管外挤载荷当量密度剖面不是单一曲线，而是具有一定置信水平的区间；与不确定性分析方法计算结果相比，传统单值计算方法得到的套管外挤载荷或偏大或偏小，根据套管层次不同而有所差异；套管外挤载荷的不确定性分析方法可以有效地避免传统套管设计方法造成的过安全或欠安全，可为套管抗挤安全系数的选取提供依据。

Abstract: With the consideration of the randomness of complex geologic parametersfor ultra-deep wells, an uncertainty analysis method is presented for the extrusion load on casing in ultra-deep wells through complex formation at a certain confidence level. Based on the extrusion load model for casing in ultra-deep wells and the prerequisite of integrity of formation-cement ring-casing, the probability and statistics theory is introduced and the sensitivity analysis on the uncertainty of extrusion load of casing is conducted. The distribution types of each formation parameters are determined statistically. The distribution type and distribution function of the extrusion load of casing are derived. Then, the uncertainty analysis of the extrusion load of casing is carried out on several ultra-deep wells in Kuqa block as case study. Several conclusions are made regarding to the field trial result. The randomness of formation elasticity modulus and formation Poisson’s ratio is the main influence factor. Compared with the result of uncertainty analysis, an error exists in the result of traditional single valued calculation method. The error varies with different casing program and can be positive or negative. The application of uncertainty analysis of extrusion load of casing provides proof for the accurate determination of casing collapse safety factor. Thus, the over engineering design and under engineering design as a result of tradition casing design will be avoided.