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BALL MOTION EQUATION IN THE BALL SEALER FRACTURING

XIAO Hui1,LI Jie2,ZENG Jun3(1.State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,SouthwestPetroleum University,Chengdu,Sichuan 610500,China;2.Guanghan Shengyou Company Ltd.,DownholeService Company of Chuanqing Drilling Engineering Co.Ltd.,CNPC,Guanghan,Sichuan 618300,China;3.Borehole Subsidiary Company,Southwest Petroleum Bureau,SINOPEC,Deyang,Sichuan 618200)  
This paper presents the motion equation of ball in the downhole through force analysis.Aiming at ballmovement in sand carrier,this paper establishes the ball motion equation in sand carrier by analysis of the proppant'sinfluence on the ball motion.The trapezia and four order Runge-Kutta method are used to solve the ball motionequation.Example calculations are conducted on a field well according to the established motion equation.Theeffect of ball density,discharge,fluid viscosity and the ball final velocity is analyzed.The ball motion consist ofearly short acceleration and later uniform motion,and the discharge is the key factor influencing the ball motion.
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