Optimization model establishment and optimization software development of gas field gathering and transmission pipeline network system

Abstract

To minimize total construction investment of the gas field gathering and transmission pipeline network, the mathematic model for optimization design of the gathering and transmission pipeline network of the gas field is established, which takes the pipeline network topology layout, pipe diameter, wall thickness and electric tracing power as the decision variants and the pipeline hydraulic equilibrium, thermodynamic equilibrium and actual process requirements as the constraint conditions. Based on the structural features of the model, the mathematic model is decomposed into the pipeline network topology optimization and parameter optimization problem. The hybrid optimization solution strategy is proposed including multiple layers, punishment function and intelligent optimization algorithm. Based on the above work, 7 kernel program classes are developed with the aid of C++ Builder development platform, OLE DB database connection technology and Map Objects component technology. Based on these classes, the gathering and transmission pipeline network layout demonstration, process computing and optimization design is implemented via computers, thus the gathering and transmission pipeline network optimization design platform is developed. This software is used to optimize design of the gathering and transmission pipeline network in a block of Daqing oil field. Compared to the artificial design scheme, the optimization scheme can save 13.9% of the investment cost.

Keywords

Pipeline network optimization topology optimization parameter optimization software natural gas gathering

1 Introduction

The gas field gathering and transmission pipeline network undertakes the mission of gathering, processing, storing and transporting the gas produced by the gas well and play an important role in ensuring normal development and production of the gas field. The investment on this system is huge, including construction cost of the pipeline networks and intermediate processing stations. This system is also a huge energy dissipation system and its loss is dominant in production energy consumption of the gas field. Now the gathering and transmission pipeline network is designed according to the experiences. The design quality is directly affected by the experiences and work state of the designer, so it is difficult to get the optimal scheme. The optimization theory has been better applied in the project in recent years. Many scholars have optimized the design of the oil gas pipeline networks based on the optimization theory. The Operations Research Center of America University of California studies operation optimization problem of the gas transmission pipeline network. Colorado Interstate Gas Transmission Co., Ltdstudies and develops the pipeline network operation optimization software [1]. America EI Paso applies the dynamic programming method to design the natural gas pipeline and develops out TRANSPORT optimization software [2]. America SSI Software Co., Ltd [3] optimizes the gas transmission trunk of the natural resource pipeline company by using the self-developed gas transmission pipeline network operation optimization software. The actual operation results indicate that this pipeline can reduce 1–5% energy consumption after optimization. Professor Yang Liu [4] studies the design optimization problem of the oil gas gathering and transmission pipeline network by using the fuzzy optimization theory, processes the constraints such as temperature and pressure as the fuzzy constraint, establishes the mathematic model for optimization, and proposes the optimization solution method. Later, a series of research on design optimization of the oil gas gathering and transmission system is consecutively carried out [5, 6]. In 1999, Sun team [7] developed out the “gas pipeline operation advisor” software system. This system aims to meet the user requirements, minimize the overall operation cost, and assist technicians to optimize the pipeline network system. Hui Liu [8] proposes a dynamic programming algorithm (TDDP) based on the tree decomposition and compares the TDDP algorithm with the genetic algorithm with the virtual pipeline network as the design object. The results indicate that TDDP algorithm has higher computing efficiency and optimal results. Dianlong Tian [9] studies the city gas transmission and distributed pipeline network, establishes the gas transmission and distribution pipeline network optimization mode with the pipeline network engineering cost minimization as the target function under certain layout, and selects the adaptive ant swarm algorithm for solution. The actual optimization results indicate that the optimization scheme can reduce 9.36% investment compared to the old design scheme.

On the whole, research on the design optimization of the old oil gathering and transmission pipeline network is relatively limited and the main research focuses on establishment of efficient solution algorithms. The intelligent optimization algorithms such as genetic algorithm, ant swarm algorithm and simulation annealing algorithm are successfully applied. For the natural gas collection and transmission pipeline network, the design optimization of the gas gathering pipeline should consider more factors due to big differences between the medium property and crude oil, higher design pressure of the gas gathering and transmission pipeline network and difference gathering and transmission flow. Now no uniform optimization model and solution algorithm is available. This paper investigates the gas gathering and transmission pipeline network, couples the process computing, topology optimization and parameter optimization of the gas gathering and transmission pipeline network, studies how to establish mathematic model and efficient solution algorithm of the pipeline network optimization, and develops the “Optimization design platform for natural gas gathering and transmission pipeline network” based on it in order to improve design efficiency of gas gathering and transmission pipeline network.

2 Mathematic model

2.1 Optimize mathematic model

Based on the well position coordinate, gas output, well hole temperature and external transmission pipeline interface coordination in the gas gathering system, with the total investment minimum of the gas gathering and transmission pipeline network as the target and the number and position of intermediate processing station, node-node connection relation and pipeline diameter and wall thickness parameter as the decision parameter, the optimize mathematical mode of the gas field gathering and transmission pipeline network is established. $\begin{matrix} OPTMS : D, δ, γ, e, P, M, U \\ Min \\ F (D, δ, γ, e, P, M, U) \\ = F_{z} (D, δ, γ, M) + F_{p} (D, δ, γ, e, P, U) \end{matrix}$ (1) $\begin{matrix} F_{z} = \sum_{i = 1}^{N} \sum_{j = 1}^{m_{i}} f_{ij} (γ_{ijk}, D_{ijk}, δ_{ijk}), \\ k = 1, 2, Λ, m_{i - 1} \end{matrix}$ (2) $F_{p} = \sum_{i = 1}^{N} \sum_{j = 1}^{m_{i}} \sum_{k = 1}^{m_{i - 1}} ξ_{ijk} γ_{ijk} f (D_{ijk}, δ_{ijk}, e_{ijk}, P_{ijk})$ (3) $\begin{matrix} ξ_{ijk} = \sqrt{{(x_{1}^{j} - x_{0}^{k})}^{2} + {(y_{1}^{j} - y_{0}^{k})}^{2}}, \\ i = 1, 2, Λ, N_{P}, \\ j = 1, 2, Λ, m_{i}, k = 1, 2, Λ, m_{i - 1} \end{matrix}$ (4) $s . t . φ_{i} (D, δ, γ, e, P, M, U) \leq 0, i = 1, 2, Λ, N_{φ}$ (5) $\sum_{k = 1}^{m_{i - 1}} γ_{ijk} = 1 i = 1, 2, Λ, N_{p}, j = 1, 2, Λ, m_{i}$ (6) $\begin{matrix} γ_{ijk} \in {0, 1} i = 1, 2 Λ, N, j = 1, 2, Λ, m_{i}, \\ k = 1, 2, Λ, m_{i - 1} \end{matrix}$ (7) $M_{\min} \leq M \leq M_{\max}$ (8) $v (D, δ) \leq v_{\max}$ (9) $U \in U_{0}$ (10) $δ \geq δ_{0}$ (11) $D \in S_{D}$ (12) $e \in S_{e}$ (13) $P \in S_{p}$ (14)

In this target function, F_z is the total construction cost of intermediate nodes in the gas gathering system, f_ij is the construction cost of the node j at ith level, which is related to the processing capacity of the nodes and specification of pipes connected with nodes. F_p is the total construction cost of the pipelines of the gas gathering system, including steel cost, electric tracing cost, cathode protection cost and construction cost. f (D_ijk, δ_ijk, e_ijk, P_ijk) is the construction cost of the unit pipe length and is related to the pipe diameter, wall thickness, material and electric tracing power. ξ_ijk is the length of the pipeline between the node j at ith level and subordinate node k and is determined by the node coordinate.

In the decision variants, D is the outer diameter vector of the pipes between nodes at different levels, δ is the wall thickness vector of the pipe, γ is the connection relation vector of nodes at different levels and the value is 0 or 1, P is the electric tracing power vector, M is the dimension vector of the intermediate nodes, U is the position coordinate vector of the intermediate node and e is the unit mass cost vector of the pipe, which depends on the material.

In the constraint conditions, the Equation (5) is the pipeline network performance constraint, which indicates that the constructed gas gathering and transmission pipeline network should meet the actual gas gathering process requirements, guarantee hydraulic power AND heat balance of the pipeline network, and make the gas well pressure, station in/out pressure and temperature within the permitted scope. The temperature at the end of the gas gathering pipe should keep 5°C higher than it of the hydrate generation temperature. The Equation (6) is the uniqueness constraint of the node membership relation. The Equation (7) is the value scope constraint of the variants. If the membership relation is available between nodes, the value is 1. Otherwise the value is 0. The Equation (8) is the dimension constraint of the intermediate nodes. M_max is the maximum dimension vector of the nodes and M_min is the minimum dimension vector of the nodes. The Equation (9) is the pipe flow speed constraint. v (D, δ ) is the actual flow speed vector of the pipeline and is determined by the gas volume, pipe diameter and wall thickness. v_max is the maximum flow speed vector permitted by the pipe. When the flow speed is too high, it will aggravate the impact on the pipe body or valve and corrosion, generally the pipe’s flow speed is within certain range. The Equation (10) is the value scope constraint of the geometric vector of the node coordinate. U₀ is the permitted coordinate range and the coordinate scope of the obstacles such as river and road should be eliminated. The Equation (11) is the wall thickness constraint of the pipe. δ ₀ is the permitted minimum wall thickness vector. The pipe’s wall thickness should not be too low and can meet the strength requirement. The Equation (12) is the value scope constraint of the pipe diameter. S_D is the optional pipe diameter scope, the Equation (13) is the unit price scope constraint of the pipe material, S_e is the unit price scope of the optional pipe material. The Equation (14) is the value scope constraint of the pipe electric tracing power and S_p is the optional electric tracing power scope.

2.2 Solution algorithm

The established optimization model includes the discrete design variant such as 0 and 1 variant, pipe diameter and wall thickness, and continuous design variants such as node coordinate, so this optimization problem is a hybrid variant design optimization problem. The target function and constraint conditions include non-linear functions, so it is difficult to solve the model directly and the heuristic algorithm should be used. First the hierarchical optimization solving algorithm is used to decompose the old optimization model into the pipeline network topology optimization and parameter optimization problem. For the pipeline network topology optimization, first we assume that the pipe material and pipe diameters are known and the weight ω_ijk indicate the unit cost difference of the connection pipes between node at different levels, so the old problem is simplified as the optimization problem of the number of the intermediate nodes, position coordinate and node connection relation in the gas gathering system. The mathematical mode of this optimization problem is expressed as follows: $\begin{matrix} OPTMS : & compute D, δ, e, P \\ Min & F_{1} (γ, M, U) = \sum_{i = 1}^{N} \sum_{j = 1}^{m_{i}} f_{ij} \\ + \sum_{i = 1}^{N} \sum_{j = 1}^{m_{i}} \sum_{k = 1}^{m_{i - 1}} ξ_{ijk} γ_{ijk} ω_{ijk} \end{matrix}$ (15) $\begin{matrix} s . t . & φ_{i} (D, δ, γ, e, P, M, U) \leq 0, \\ i = 1, 2, Λ, N_{φ 1} \end{matrix}$ (16) $\begin{matrix} \sum_{k = 1}^{m_{i - 1}} γ_{ijk} = 1 i = 1, 2, Λ, N_{p}, \\ j = 1, 2, Λ, m_{i} \end{matrix}$ (17) $\begin{matrix} γ_{ijk} \in {0, 1} i = 1, 2 Λ, N, \\ j = 1, 2, Λ, m_{i}, k = 1, 2, Λ, m_{i - 1} \end{matrix}$ (18) $M_{\min} \leq M \leq M_{\max}$ (19) $U \in U_{0}$ (20)

It is also difficult to solve this model. First the number M of the intermediate nodes is identified according to the gas output and actual process conditions of the studied gas gathering system to reduce the number of feasible solutions. Based on it, the node position and connection relation of adjacent nodes are optimized. Two problems can be regarded as optimal division problem of the set and optimization problem of geometric position. For the optimal division of the set, the dimension reduction planning method and greedy algorithm are used for solution. For the optimization problem of the geometric position, the non-linear features should be considered and the punishment function is used for solution. The optimization results can be obtained under any given number of the intermediate nodes by solving the optimization model, including the optimized node connection relation and optimization node’s coordinate. Based on it, the pipeline network parameters can be optimized. This optimization model can be expressed as follows: $\begin{matrix} OPTMS : & compute D, δ, e, P \\ Min & F_{2} (D, δ, e, P) \\ = \sum_{i = 1}^{N} \sum_{j = 1}^{m_{i}} f_{ij} (D_{ijk}, δ_{ijk}) + \sum_{i = 1}^{N} \sum_{j = 1}^{m_{i}} \sum_{k = 1}^{m_{i - 1}} \\ ξ_{ijk} γ_{ijk} f (D_{ijk}, δ_{ijk}, e_{ijk}, P_{ijk}) \end{matrix}$ (21) $s . t . φ_{i} (D, δ, e, P) \leq 0, i = 1, 2, Λ, N_{φ}$ (22) $v (D, δ) \leq v_{\max}$ (23) $δ \geq δ_{0}$ (24) $D \in S_{D}$ (25) $e \in S_{e}$ (26) $P \in S_{p}$ (27)

In the above optimization model, the pipe diameter, wall thickness, pipe material and electric tracing power are discrete variants and the routine optimization search algorithms are not applicable. if the enumeration method is used, the spare schemes are plentiful. E.g. each pipeline material has corresponding pipe diameter and wall thickness specification scheme. If they are enumerated one by one, the computing load is too huge, so the genetic algorithm is used to solve this model in order to improve the search speed of the optimal scheme much.

After the optimal pipe diameter, wall thickness and electric tracing parameters of the gas gathering system is identified, the weight of the node-node connection pipes at different levels can be identified again. Based on it, the topology optimization and parameter optimization of the pipeline network is performed again, so the topology optimization and parameter optimization of the pipeline network are coupled till the optimal scheme is obtained. The whole solution process is shown in Fig. 1.

3 Software development

3.1 Software implementation mechanism

3.2 Data management module

Based on Microsoft Access database development tool, the software background database is developed and four sub-databases store the pipeline network foundational data information, optimized result data information, spare device data information and process computing results data information. C++ language and OLE DB database connection technology are used to develop DAManager class, which can realize query, storage and editing operation of the background database data. DAManager class is the kernel of the software data management module and the functions on the data operations will be implemented via this class.

3.3 Graphic processing module

The kernel of the software graphic processing module is our independently developed GRManager class. The MapObjects component is used to combine the GIS tool software with GRManager class, so the software graphic processing module can fully utilize the GIS tool software to manage and analyze the space data. The gas gathering pipeline topology design can be optimized by using GIS-based functions, so the optimization results are more feasible and high-precision. GRManager class can communicate with DAManager class. The pipeline network can be adjusted and the parameters can be edited on the graphic interface. The DAManager clas can be saved to the software database.

3.4 Pipeline network optimization design module

Based on the established mathematic model and solving algorithm of the gas gathering and transmission pipeline network design optimization, the OPManager class is developed to optimize the design of the gas gathering and transmission pipeline network. Prior to optimization, the GRManager class can identify the foundational data information on the ground pipeline network and DAManager class will transfer the data to the OPManager class. Based on it, if the constraint conditions and initial design parameters of the pipeline network design optimization are given, the pipeline network design can be optimized. This module can directly communicate with the GRManager directly. The optimization results can display as the pipeline network layout drawing. Designers can adjust the artificial layout or directly output the pipeline network layout drawing based on it.

3.5 Process computing module of gas gathering pipeline

The hydraulic power and thermal power of the pipeline network will be computed to check feasibility of the optimized scheme and restrict the scope of the feasible solutions in design optimization, so CAManager class is developed. The core is the hydraulic power and thermal power computing model and solving algorithm of the gas gathering and transmission pipeline network. The hydraulic power and thermal power feature will affect each other when the gas is transmitted along the pipeline, so the hydraulic power and thermal power coupling solving algorithm of the gas transmission pipeline is developed and is embedded in CAManager class as the pipeline process computing module. In addition, this module can be used to directly perform process computing for the pipelines. This module will communicate with DAManager class to store the computing results.

3.6 Device optimal selection module

After the pipeline network layout scheme is identified, the type selection computing for the intermediate nodes such as main devices at the gas gathering station will be performed according to the processing capability of the intermediate nodes. These devices include heating furnace, gas and liquid separator, triethylene glycol dehydration device and torque system. The device type is selected according to certain mathematic model. For the heating furnace, the heat required by the natural gas should be computed to further identify the power of the heating furnace disc pipe. The diameter of the required separator will be computed according to the volume of the processing gas and staying time of gas in the separator. The computing data will be compared with data of the known type to identify the proper separator type. The type of the triethylene device is identified according to the processing capacity. The type of the torque device should be determined according to the torque diameter and height which is computed according to the processing capacity. All mathematical models for device type selection and solving algorithms will be implemented via the independently developed EQManager class. This class integrates the data communication function with the spare database and optimal result database.

3.7 Scheme budget module

The optimization design of the gas gathering and transmission pipeline network can get the pipeline network optimization design scheme including coordinate of gas gathering station, well-station connection relation, pipe diameter and wall thickness. To further improve operability of this scheme, the scheme budget should be determined. The ECManager class is independently developed to embed the expense composition information of the pipeline network budget and detailed economy computing model. The ECManager class divides the expense of the gas gathering and transmission pipeline network into 6 types. Each type is divided into multiple sub-types, so the detailed expense composition of the optimization design scheme can be obtained to guide the actual application of the scheme.

4 Computing example

The pipeline network optimization design software of the developed gas gathering system is used to optimize the design of the gas gathering pipeline in a block of Daqing oil field. The geographic information on this bock is shown as the Fig. 3. This block includes 23 gas wells. The gas output of single gas well is 15858∼32112 Nm3/d. The well opening temperature is 24°C∼40°C. Multiple gas gathering stations will be deployed to gather the natural gas generated by the distributed gas wells in the gas gathering pipeline. After the gas is separated from the liquid, the gas will be transmitted to the gas transmission pipeline via the gas gathering and transmission pipeline. There are multiple villages at the gas well, which are obstacles for the pipeline network layout. The pipeline network designed by the optimization software is shown as the Fig. 4. Total 4 gas gathering stations are deployed. The gas gathering station 4 is connected with the gas gathering station 3 in series and then connected with the external transmission pipeline interface. Other two gas gathering stations are directly connected with the external transmission pipeline interface. The parameter setup interface for software optimization computing is shown as the Fig. 5. The Figs. 6 and 7 show the optimized pipeline network results. The Fig. 8 shows the budge results of the optimization design scheme. To compare the computer optimization design results with the artificial design results, the results are shown as the Table 1. The optimization design can reduce the length of the gas collection and gathering pipeline much and save the investment cost of the pipeline network. Compared to the artificial design scheme, the total cost can reduce 13.9%.

5 Conclusions

With the minimal total investment of the gas field gathering transmission pipeline network as the target, this paper establishes the mathematical model of the gas field gathering and transmission pipeline network optimization design by using the parameters such as number and positions of intermediate stations, connection relation of different nodes, pipe diameter, wall thickness and electric tracing power of corresponding pipeline in the pipeline network as the decision variants.

The optimization design of the gas field gathering transmission pipeline network belongs to hybrid variant optimization design problem and its target function and constraint conditions include non-linear function. Based on the structural features of the model, this paper proposes the layered optimization method to decompose this problem into the pipeline network topology optimization and parameter optimization sub-problem and establishes corresponding solving algorithm for them.

Based on C++ builder program design platform, OLE-DB database connection technology and MapObjects technology, 7 kernel program classes are developed to implement the pipeline network layout demonstration, process computing and optimization design process of gas gathering system via computers and the “gas gathering system pipeline network optimization design platform” is developed.

The “gas gathering system pipeline network optimization design platform” is used to optimize the design of the gas gathering and transmission pipeline network in a block of Daqing oilfield and the optimized pipeline network layout, gas gathering station position, pipe diameter and wall thickness are given. Compared to the artificial design scheme, the optimization scheme can save 13.9% investment cost.

Footnotes

Acknowledgments

This paper is Supported by PetroChina Innovation Foundation (2014D-5006-0607).

References

Rachford

H.H.

, Transient Pipeline Calculations Improve Design, The Oil and Gas, 1972.

Wienecke, Computerized Optimization of Dispatching on a Gas Pipeline System, 1986.

Grelli

G.J.

and Gilmour

, Western U.S. gas pipeline optimization program, Oil & Gas Journal (1986).

Liu

, Fuzze optimization design of gathering transmission pipeline network system, Journal of Daqing Petroleum Institute2 (1992), 32–36.

Liu

and Zhao

H.J.

, Research on general planning scheme of low-penetration oil field ground project, Acta Petrolei Sinica21(2) (2000), 88–95.

Liu

and Guan

X.J.

, Multi-object optimization design of oil gas gathering transmission pipeline network system, Petroleum Planning and Design1 (2000), 26–28.

Sun

C.K.

, An integrated expert System/Operations research approach for optimization of natural gas pipeline operations, Engineering Applications of Artificial Intelligence3 (1999), 465–475.

, He

, Li

J.F.

, Fu

Z.Z.

and Xu

, TDDP algorithm for solving operation optimization problem of natural gas pipeline network, Petroleum Engineering Construction40(2) (2014), 6–10.

Tian

D.L.

, Hao

R.F.

and Yang

C.H.

, Application of improved ant swarm algorithm in gas transmission and distribution pipeline network optimization, 21(3) (2010), 19–22.