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

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 equat...

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Bibliographic Details
Published in:Mathematical problems in engineering 2017-01, Vol.2017 (2017), p.1-8
Main Authors: Yan-feng, Bai, Heng-bin, Qiu, Yu-ming, Liu, Liu, Yongwang
Format: Article
Language:English
Subjects:
Algorithms
Ant colony optimization
Artificial intelligence
Drilling
Engineering
Genetic algorithms
Horizontal wells
Information science
Jacobi matrix method
Jacobian matrix
Mathematical problems
Matrix methods
Methods
Newton methods
Nonlinear equations
Outflow
Petroleum engineering
Petroleum production
Researchers
Searching
Transport
Variables
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2017/7898647