Safety and reliability evaluation of casing in ultra-deep well based on uncertainty analysis of extrusion load

The extrusion load on casing in ultra-deep well is uncertain, which limits the application of safety factor method. Therefore, the evaluation method of collapsing safety and reliability on casing during drilling in ultra-deep wells is put forward. Based on the extrusion load model in ultra-deep well considering the diversity of strength parameters of casing and the integrity of formation-cement sheath-casing system, the uncertainty distribution functions of collapse strength and extrusion load on casing are derived by introducing probability and statistics theory. Then, the theory of “stress-strength interference” is applied to obtain the reliability R, confidence interval and reliability-safety factor n_R of casing. Taking multiple ultra-deep wells in the Kuqa block of the Tarim Oilfield as an example, the collapse safety and reliability analysis on casing is carried out. Several conclusions are made based on the oilfield statistics. The traditional safety factor is greater than the reliability-safety factor. The surface casing and the production casing are both safer than the technical casing. More accurate original data can narrow the confidence interval width of n_R and reduce the collapse risk of technical casing. The change in reliability is consistent with the change of the reliability-safety factor. For technical casing, when R is greater than 0.50 and 0.92, n_R is greater than 1.0 and 1.1 respectively. For production casing, when R is greater than 0.98, n_R is greater than 1.1. For each type of casing, affected by the uncertainty of the extrusion load on casing, when the extrusion load exceeds a certain value (but this value is less than the casing strength), the reliability begins to decrease. The larger the standard deviation of extrusion load is, the more obvious the influence on reliability change will be. Compared with the traditional design safety factor, the change of the anti-collapse safety degree of the casing can be more intuitively displayed by the reliability, which could provide an important supplement for the selection of traditional design safety factor during drilling operations.