Establishment and solution of a mathematical model of the drillstring vibration and analysis of dynamic release force during an up-jar operation in a vertical well

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (20) : 62-74.

WEI Qiang1，LI Zifeng1，ZHANG Jie1,2

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Abstract

In this paper, a mathematical model of the drillstring vibration in the process of an up-jar operation in vertical wells was established and solved. The three stages of the drillstring vibration were described, and a mathematical model was made to explain them during an up-jar operation. ① During the tensile energy storage stage, the static analysis of the drillstring was carried out. ② During the pressure relief stage, the Eigenfunction Function Expansion Method was used to find an analytical solution. ③ During the impact stage, the compact difference method was used to solve the mathematical model. After processing with the low-pass filtering method, the dynamic release force discovered using the aforementioned method is in good agreement with the corresponding analytical solutions and Abaqus results. The relationship between the jar initiation tensions, the up-jar’s location, the drilling fluid viscosity, the effective distance of the mandrel, and the dynamic release force were investigated.

Key words

Drillstring-sticking / Release operation / Drilling up-jar / Tube-to-tube axial impact / Drillstring vibration / Mathematical modelling / Drilling fluid damping / Dynamic release force

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WEI Qiang1, LI Zifeng1, ZHANG Jie1, 2. Establishment and solution of a mathematical model of the drillstring vibration and analysis of dynamic release force during an up-jar operation in a vertical well[J]. Journal of Vibration and Shock, 2024, 43(20): 62-74

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