1. A New Mathematical Method for Solving Cuttings Transport Problem of Horizontal Wells: Ant Colony Algorithm
- Author
-
Qiu Heng-bin, Liu Yu-ming, Bai Yan-feng, and Liu Yong-wang
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Article Subject ,General Mathematics ,Ant colony optimization algorithms ,lcsh:Mathematics ,General Engineering ,Process (computing) ,MathematicsofComputing_NUMERICALANALYSIS ,02 engineering and technology ,lcsh:QA1-939 ,Domain (mathematical analysis) ,Set (abstract data type) ,symbols.namesake ,Nonlinear system ,020901 industrial engineering & automation ,Singularity ,lcsh:TA1-2040 ,Jacobian matrix and determinant ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,020201 artificial intelligence & image processing ,lcsh:Engineering (General). Civil engineering (General) ,Variable (mathematics) ,Mathematics - Abstract
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.
- Published
- 2017