Layout optimization of large-scale oil–gas gathering system based on combined optimization strategy
Introduction
The oil–gas gathering system is a pipeline network system that accounts for a significant proportion of investment in oil–gas fields development and construction [1], [2]. Therefore, it is an effective way to reduce the cost of oilfield construction by applying the optimization theory to determine the optimal layout of oil–gas gathering system. Oil–gas gathering system layout optimization is a kind of network structure optimization problem with multiple constraints, nonlinearity, discrete and continuous variables coupling each other [3]. It is also a kind of mixed integer nonlinear programming problem (MLNLP) and has been proved to be a NP-hard problem, which is a problem to be solved urgently in the field of operations research [4]. Liu and Chen [5] established a multi-objective fuzzy optimization mathematical model by considering the fuzzy information existing in the layout optimization of oil–gas gathering system. Marcoulaki et al. [6], Baeza et al. [7] and Sanaye and Mahmoudimehr [8] proposed the route optimization mathematical models of pipelines and solved the models by applying different methods, respectively. Wang et al. [9] and Lucena et al. [10] adopted the heuristic optimization method based on the chain matrix and the genetic algorithm to obtain the optimal solutions of the layout optimization models for the submarine pipelines, respectively. Rodrigues et al. [11] and Wei et al. [12] established the mathematical models for oil gathering system and gas gathering system layout optimization with minimum total construction cost, respectively. Uster and Dilaveroğlu [13] and Zhu et al. [14] applied the branch and bound method and dominance degree model to optimize the layout of the natural gas pipelines, respectively. The published papers above mainly aimed at small-scale oil–gas gathering pipeline networks or trunk pipelines with relatively simple structures, with the several hundreds of variables at most. However, for large-scale oil–gas gathering system with complex topology structures and the property of multi-level management, the dimension of the optimization problem can be up to several thousands or even more, which increase sharply as the number of gathering network nodes becomes larger. To the best of our knowledge, there are few articles about such a large-scale structural optimization. In addition, on the basis of effectively dealing with high-dimensional coupled discrete and continuous variables, collaboratively processing set partition [15], facility location [16], minimum spanning tree [17], shortest path optimization [18] and other sub problems are also required. These sub-problems include NP-complete problems, which further aggravate the difficulty of solving. Moreover, due to the process differences between oil gathering system and gas gathering system, the optimization models and methods for one medium cannot be readily applied to another medium, which limits the application of the models and methods. As a result, optimization models and solving methods in the existing articles cannot be directly applied to the layout optimization of oil–gas gathering system with large-scale.
The solution methods of MINLP problem [19] can be divided into deterministic optimization methods and stochastic optimization methods. When solving the MINLP problem, the deterministic solution methods such as the branch and bound method, the outer approximation method, the extended cutting plane method, etc., need to ensure the convexity of the model, and the calculation time increases sharply as the dimension of the problem becomes larger, which is not suitable for solving the large-scale layout optimization problem in this paper. The stochastic optimization methods can realize parallel computing without gradient information of models and are powerful methods in solving high-dimensional MINLP optimization problems [20]. Among the existing stochastic optimization methods, the particle swarm optimization algorithm has good performance for both the discrete and continuous optimization problems [21], [22], [23], but it is easy to fall into local optima when solving high-dimensional optimization problems. Many scholars have improved the traditional particle swarm optimization algorithm to enhance the global search ability of the algorithm. Shi and Eberhart [24], Feng et al. [25], Nasiri et al. [26], and Amoshahy et al. [27] improved the inertia weight of particle swarm optimization, and put forward the fuzzy adaptive inertial weight, chaotic inertial weight, time-varying inertial weight and flexible inertial weight, respectively. Kennedy and Mendes [28], Mendes et al. [29], Wang et al. [30] and Bonyadi et al. [31] adjusted the topology of the standard PSO algorithm, and proposed Ring, Four cluster, Pyramid, dynamic tournament and time-adaptive topology, respectively. Adding operators or techniques is another effective way to improve the performance of PSO algorithm. Li et al. [32] introduced weighted particles to modify the search direction, and used fuzzy reasoning to adjust the attraction factor and inertial weight to increase the possibility of finding the optimal solution. Kundu et al. [33] proposed perturbation operator based on dimensional mean, aging guideline and nonlinear time-varying acceleration coefficient to improve the algorithm's ability to jump out of local optima. Li et al. [34] enhanced the global exploration and local exploitation capability by embedding a reverse predictor and repulsive force. Integrating other intelligent algorithms to form a new hybrid algorithm is also the preferred way to improve the PSO algorithm. Li et al. [35] combined the local search phase of PSO algorithm and global search phase of ABC algorithm, and proposed the PS-ABC algorithm. Sahoo et al. [36] proposed a hybrid algorithm based on PSO and GA, and applied it to the reliability optimization problems. Pandit et al. [37] developed the PSO-DE algorithm based on the information sharing of particle swarm optimization algorithm and differential evolution algorithm. Chen et al. [38] merged the particle swarm optimization with the fireworks algorithm, and proposed the PS-FW algorithm.
Since the large-scale oil–gas gathering system involves lots of coupled decision variables, although the improved particle swarm optimization algorithm has certain global search ability, when the algorithm is applied directly to solve the problem, there is no guarantee that the algorithm will converge within the specified time [39]. Therefore, it may be feasible to attempt to solve the layout optimization problem of large-scale oil–gas gathering system by combining several effective methods. In this paper, a mathematical model for layout optimization of large-scale oil–gas gathering systems is established. A modified particle swarm optimization algorithm is put forward, which involves the Cauchy perturbation operator, Gaussian mutation operator and adjustment operator by probability. Based on the Poincare theorem, the convergence theorem of stochastic optimization algorithm is put forward, and the global convergence of the modified particle swarm optimization algorithm is proved. Compared with other existing famous intelligent algorithms, numerical experiments demonstrated the performance of the proposed algorithm. The grid dissection set partition method with linear polynomial complexity is proposed, and the initial values of solution process are optimized. The concept of fuzzy set of adjacent position is proposed, and the dimension of the layout optimization model is effectively reduced by solving fuzzy set of adjacent position. Finally, based on the modified particle swarm optimization algorithm, the grid dissection method, the solution method by fuzzy set of adjacent position and the efficient constraint handling method, the combined optimization strategy is proposed.
The rest of paper is organized as follows. The network topology of the oil–gas gathering system is described in Section 2. Section 3 introduces the layout optimization mathematical model for large-scale oil–gas gathering system. In Section 4, the modified particle swarm optimization algorithm and stochastic optimization algorithm convergence theorem are described, and the performance and convergence of the algorithm is analyzed. The details of the grid dissection method, including its theoretical basis, the main steps and complexity analysis are introduced in Section 5. Section 6 illustrates the concept of fuzzy set of adjacent position, and solution method of connection mode between wells and stations based on fuzzy set of adjacent position is also described in this section. The details of the combined optimization strategy are introduced in Section 7. In Section 8, a real-world example is described and the conclusion is drawn in Section 9.
Section snippets
Network topology of oil–gas gathering system
Multi-layer star (MS) network system and multi-layer star-tree network system are the most common pipeline network systems in oil–gas fields. In the MS network system, the low-layer nodes are radially connected with the high-layer nodes, which is widely used in the development of onshore oil fields [5] and offshore oil fields [8]. In the MST network system, the well nodes and station nodes are connected radially, and the station nodes are connected in tree-like structures, which are commonly
The objective function
Taking the minimum total construction cost as the objective function, the mathematical model of oil–gas gathering system layout optimization is established. The total construction cost includes pipelines construction cost and stations construction cost. The objective function is as follows:where, U denotes the geometric position vector of the station nodes, η
Modified particle swarm global optimization algorithm
Particle swarm optimization (PSO) algorithm is an effective algorithm to solve the MINLP problem. However, for the large-scale layout optimization model of the oil–gas gathering system proposed in Section 3, the decision variables can amount to thousands for only hundreds of wells, and thousands of equality constraints and inequality constraints are also formed. When the standard PSO algorithm is applied to solve the model, it is easy to fall into local optima, and even does not converge when
Grid dissection set partition method
The MPSO algorithm has high accuracy and fast convergence speed for solving the high-dimensional optimization problems, but in its practical application for the optimization model in Section 2, the common problem of the stochastic optimization algorithm should be considered. The randomly generated initial values of intelligent algorithms often cover a large number of infeasible solutions, resulting in slow convergence speed of the algorithm. A reasonable optimization for the initial value of
Solution method by fuzzy set of adjacent position
On the basis of the initial solution given by the grid dissection set partition method, determining the connection mode of the pipeline network and the geometric position of the stations are the key to solving the model. For the layout optimization model of a large-scale oil–gas gathering system, the dimension can reach thousands or even tens of thousands, in which the design variables of the connection mode between the wells and the stations account for the overwhelming proportion. If the
Combined optimization strategy
Based on the idea of hierarchical optimization, the layout optimization model of large-scale oil–gas gathering system is decomposed into two layers of optimization problems: design-layer optimization and layout-layer optimization. Combined with the MPSO algorithm, grid dissection set partition method and solution method by FSAP proposed in this paper, a combined optimization strategy is put forward.
Application and discussion
In an oilfield, a new gathering system needs to be planned and designed. There are 661 new oil wells in the oil field, and the average yield of each well is 20.2 t/d. The average wellhead pressure is 0.61 MPa and the average temperature comes up to 22.5 °C. The location distribution of the wells is shown in Fig. 10. The new layout of the pipeline network involves 60–70 metering stations, 11–16 transfer stations, and 1 central processing station. The layout optimization model and combined
Conclusion
In this paper, a layout optimization mathematical model is established, which is a MINLP model and can be generally applied to both the large-scale oil gathering system and gas gathering system. In order to solve the model, the MPSO algorithm is proposed, in which the adaptive Cauchy perturbation operator, the Gauss mutation operator and the adjustment operator by probability are put forward. Based on the Poincare cycle theorem, the convergence theorem of the stochastic optimization algorithm
Acknowledgments
This study was supported by National Natural Science Foundation of China [grant numbers 51674086, 51534004].
Yang Liu received his Ph.D. degree in Computational Mechanics from Dalian University of Technology, China, in 1988. He became a professor in 1994 and went to the University of Houston as a senior visiting scholar in 1998. Currently, he is a professor and doctoral supervisor at School of Petroleum Engineering, Northeast Petroleum University. He has published more than 100 academic articles. His current research focuses on petroleum engineering optimization, stochastic optimization algorithms,
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Cited by (0)
Yang Liu received his Ph.D. degree in Computational Mechanics from Dalian University of Technology, China, in 1988. He became a professor in 1994 and went to the University of Houston as a senior visiting scholar in 1998. Currently, he is a professor and doctoral supervisor at School of Petroleum Engineering, Northeast Petroleum University. He has published more than 100 academic articles. His current research focuses on petroleum engineering optimization, stochastic optimization algorithms, structural optimization and network system optimization.
Shuangqing Chen received his Ph.D. degree in Petroleum and Natural Gas Engineering from Northeast Petroleum University, China, in 2018. Currently, he is a lecturer at School of Petroleum Engineering, Northeast Petroleum University. His interests include the stochastic optimization algorithms, system optimization, complex layout design and oil–gas engineering optimization.
Bing Guan received her Master's degree in Oil and Gas Well Engineering from Northeast Petroleum University, China, in 2016. Currently, she is a Ph.D. candidate at School of Petroleum Engineering, Northeast Petroleum University. Her research interests include rock mechanics, laser - rock interaction and parameters optimization.
Ping Xu received his Ph.D. degree in Management Science and Engineering from Harbin Engineering University, China, in 2009. Currently, he is a professor and doctoral supervisor at School of Economics and Management, Northeast Petroleum University. His current research focuses on management system engineering and optimization, technical economy and management of petroleum engineering, modern management theory and method, project management and optimization of oil–gas engineering.