Investigation on Releasing of a Stuck Drill String by Means of a Mechanical Jar

¹ Department of Higher Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, 15 Karpatska St., 76019 Ivano-Frankivsk, Ukraine
² Department of Oil and Gas Equipment, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, 15 Karpatska St., 76019 Ivano-Frankivsk, Ukraine

^* Corresponding author e-mail: kgl.imp.nan@gmail.com

Received: 9 October 2016
Accepted: 10 July 2017

Abstract

Purpose. In this article the most important part is dedicated to the research of elimination of accident that is caused by drill string sticking during the process. That is why it is necessary to develop a mathematical model of the mechanic system: travelling system + drill string + mechanical jar + rock, to develop a computer model for numerical calculation of dynamic characteristics of firing gear. The aim is to use the results of the research and to work out recommendations for expediency of jar application. Methods. For description of the drill string we are using synthesis of the wave theory and theory of the local distortions. For mathematical modeling of firing device we are offering the use of the combined method that combines static solutions of the theory of elasticity for contact zone of drill string and method of a plain wave of Saint-Venant. We solved systems of differential equations using the methods of mathematical physics. An algorithm of the numerical decision which mounted in the computing environment were used at simulation of the longitudinal impact to the stuck drill pipe. In this article we designed a wave chart of the equation system of the drill pipe and conducted step-by-step calculation of a collision momentum. We also designed a computer program for numerical modeling of the drill pipe mechanism with firing gear. We also designed a method of calculation of main dynamic characteristics of firing device that will help analyze and prove the performance of the mechanical jar. A wave diagram was built that shows the impact forces and speeds on the boundary surfaces of the sections of the drill string. There were calculated main dynamic characteristic of mechanical the jar. Originality. Authors also developed a dynamic mathematical model that combined elastic vibrations of continual system of loose part drill pipe, impact mechanisms and discrete movements of a given drill pipe. The process of a mechanical jar work that considers elastic deformations of contact areas was not published by researchers. Practical implications. Received results could be used for further research and perfection of existing engineering methods of modeling and calculations of drill pipes at the stage of their designing and their construction.