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Journal of Applied Mathematics
Volume 2014, Article ID 969465, 12 pages
http://dx.doi.org/10.1155/2014/969465
Research Article

A New Method for Predicting the Position of Gas Influx Based on PRP in Drilling Operations

1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China
2CNPC Key Lab for Tubular Goods Engineering, Southwest Petroleum University, Chengdu, Sichuan 610500, China

Received 6 December 2013; Accepted 7 March 2014; Published 16 April 2014

Academic Editor: Jong Hae Kim

Copyright © 2014 Xiangwei Kong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Accurately predicting the position of gas influx not only helps to analyze complex formation structure, but also can provide reference for taking effective measure, such as increasing mud density, increasing back pressure and casing packer, to suppress the gas influx. Predicting the accurate position of gas influx has been one of the urgent difficulties for drilling industry. With full consideration of the important factors such as the virtual mass force, viscous shear force, energy exchange, and narrow resistance, a new method for predicting the position of gas influx has been proposed based on pressure response time calculation. The gas equations of state (EOS), small perturbation theory, and the fourth-order Runge-Kutta method (R-K4) are adopted to solve the model. Also, the pressure response time plate (PRP) which presents the corresponding relationship between position of gas influx and wellhead parameters by several pressure wave response curves calculated by computer programming is given. The results showed that the PRP is unique at different well depth and gas influx rate, and the position of gas influx can be accurately determined by PRP with known wellhead parameters and detected response time. Therefore, without the help of downhole tools, the accurate mathematical method for predicting the position of gas influx is completely feasible.