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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 7898647, 8 pages
Research Article

A New Mathematical Method for Solving Cuttings Transport Problem of Horizontal Wells: Ant Colony Algorithm

1School of Petroleum Engineering, China University of Petroleum, Qingdao 266580, China
2College of Energy Engineering, Yulin University, Yulin 719000, China
3Drilling Technology Research Institute, Shengli Petroleum Engineering Corporation, Sinopec, Dongying 257000, China
4Laojunmiao Oil Production Plant, Yumen Oilfield, Jiuquan 735000, China

Correspondence should be addressed to Liu Yongwang; moc.361@3002gnawgnoyuil

Received 19 March 2017; Revised 1 July 2017; Accepted 16 July 2017; Published 29 August 2017

Academic Editor: Jian G. Zhou

Copyright © 2017 Liu Yongwang 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.


Cuttings transport problem has long been recognized as one of the key difficulties in drilling horizontal wells, and the models in cuttings transport research are usually formulated with highly nonlinear equations set. When using Newton methods to solve real engineering problems with nonlinear equations set, the problems of result dependence on initial values, Jacobian matrix singularity, and variable outflow of its definition domain in iterations are three of the often-encountered difficulties. In this paper, the ant colony algorithm is applied to solve the two-layer cuttings transport model with highly nonlinear equations set. The solution-searching process of solving nonlinear equations set is transformed into an optimization process of searching the minimum value of an objective function by applying ant colony algorithm. Analyzing the results of the example, it can be concluded that ant colony algorithm can be used to solve the highly nonlinear cuttings transport model with good solution accuracy; transforming the solution-searching process of solving nonlinear equations set into an optimization process of searching the minimum value of the objective function is necessary; the real engineering problem should be simplified as much as possible to decrease the number of unknown variables and facilitate the use of ant colony algorithm.