There are many compressor stations along longdistance natural gas pipelines. Natural gas can be transported using different boot programs and import pressures, combined with temperature control parameters. Moreover, different transport methods have correspondingly different energy consumptions. At present, the operating parameters of many pipelines are determined empirically by dispatchers, resulting in high energy consumption. This practice does not abide by energy reduction policies. Therefore, based on a full understanding of the actual needs of pipeline companies, we introduce production unit consumption indicators to establish an objective function for achieving the goal of lowering energy consumption. By using a dynamic programming method for solving the model and preparing calculation software, we can ensure that the solution process is quick and efficient. Using established optimization methods, we analyzed the energy savings for the XQ gas pipeline. By optimizing the boot program, the import station pressure, and the temperature parameters, we achieved the optimal energy consumption. By comparison with the measured energy consumption, the pipeline now has the potential to reduce energy consumption by 11 to 16 percent.
Gas pipelines are the bond that connects gas production and consumption; therefore, their operation must be safe, smooth, and effective. In 1961, a US gas pipeline company collaborated with IBM to simulate and optimize the operation of gas pipelines [
In 1983, Goldberg introduced a genetic algorithm, which was one of the most popular optimization algorithms of the time, to optimize the operation of a natural gas pipeline [
In this paper, we aim to characterize longdistance natural gas pipeline operation management. For a given throughput, with the minimum pipeline operation energy consumption as the goal, the gas pipeline optimal operation model can be established. This model is solved using a dynamic programming method to obtain the best operation scheme and the minimum energy consumption for the natural gas pipeline.
Natural gas pipeline systems are complicated. They are composed of pipelines, stations, compressors, fluids, external environmental factors, and other components. Based on the Chinese policy for energy savings and emission reduction and the premise of the transportation quantity plan (intake quantity or delivery quantity), the pipeline operation department must configure each station's compressors and determine the operating parameters for each station to reach the lowest energy consumption for the pipeline system.
To study the minimum energy consumption of a natural gas pipeline system, we need to establish a corresponding mathematical model. A reasonable and accurate mathematical model is the key to obtaining the best results.
During operation, the pipeline’s main energy consumption is from the compressor’s drive. Therefore, we established an objective function as the goal for minimum production unit consumption, which is expressed as
The power consumption
The gas consumption
The turnover
The power of the compressor depends on the compression ratio, flow rate, and temperature. Because the inbound traffic of the compressor station is known, the power of the compressor can be simplified into a function of the pressure ratio and temperature. The compressor inlet and outlet temperatures depend on the compression ratio; therefore, the optimization variables can be converted into the compression ratio and thus can be converted into the outbound pressure. The optimization variables of the optimization model, that is, the outbound pressures and the boot number, can be expressed as
To guarantee the safe operation of the pipeline and the devices, both the operation parameters of the pipelines and the operation parameters of the devices must be within the permitted range. Namely, the parameters must be satisfied with a series of constraint conditions.
The head curve is calculated according to
The efficiency curve is calculated according to
The buzz curve is calculated according to
The stagnation curve is calculated according to
From (
The mathematical model can be written in the standard form for optimization models as
The gas pipeline branch is simplified to a point. The operation process of the pipeline can be regarded as a multistage process. Thus, we can use a dynamic programming algorithm to distribute the optimal ratio of the compressor stations (i.e., the optimal discharge pressure).
Suppose the number of compressor stations is
The algorithm for solving the model is composed of the following components: “determine the state space,” “recursive between stations,” “recursive within the station,” and “backtracking algorithm.”
In the dynamic programming algorithm, a certain compressor station out of all of the feasible discharge pressures is the state space. The upper boundary of the state space can give the design pressure of the pipeline. The lower boundary, also called the lowest discharge pressure, is difficult to determine. If it is too large, it will increase the unnecessary computation; however, if it is too small, it may miss the optimal solution. We calculated the lowest discharge pressure for the previous compressor station with the limitations of the lowest discharge pressure of this compressor station.
The compressor with the gas turbine or motor drive performs stepless speed regulation, so that the discharge pressure of the compressor station can be within the scope of feasible continuous change. Thus, we must process the state space to obtain the finite state point. In this paper, the outlet pressure range of each compressor station is divided into 300 points to determine the compression ratio of the space.
When the pipeline is running with low throughput, the station operation plan is always run more economically than with a low compression ratio. This must be taken into consideration for circumstances where the pressure is above the permitted level for one of the compressor stations. By setting each station’s entrance pressure as part of the state space, the state transition will not leak.
Recursion between stations is a calculation through which the entrance condition of the next compressor station is determined by the outlet condition of the current compressor station, which mainly involves hydraulic and thermodynamic calculation between stations. On the basis of a certain outlet pressure of the compressor station, (
Taking the recursive between stations shown in Figure
The recursive process.
The recursive within the station gives the outlet station’s operation based on the compressor station’s inlet operation, which is dominated by the state transfer. For the state before the transfer, in addition to determining the state space, the feasible compression ratio range of compression for every inlet condition should also be obtained, based on the constraint conditions of the decision variables.
Taking the recursive within the station shown in Figure
Use the same method to calculate the total energy consumption from
After the completion of the recursive within the station, we will obtain all of the total energy costs corresponding to several inlet conditions in the terminal station. To obtain the operation program within the minimum energy consumption limit to meet the terminal station’s pressure, backtracking of the whole scheme is required.
Backtracking is performed according to the compression station’s inlet and outlet operations recorded in the optimal program to determine the optimal operation scheme of the pipeline. Backtracking starts from the gate station’s optimal inlet condition, according to every state transfer’s recorded results, to find out every compressor station’s outlet condition corresponding to the last station’s outlet condition.
The length of the pipeline is 3840 km, the design capacity is 170 × 10^{8} Nm^{3}/year, the design pressure is 10 MPa, and the diameter is
Elevation and mileage of the XQ gas pipeline.
There are 40 stations in the XQ gas pipeline, including 22 compressor stations and 18 distribution stations, as listed in Table
Equipment at each station.
Station  Compressor  Drive type  

Number  Type  Model  Number  
1  Compressor  1  2  Gas 
2  Compressor  2  2  Gas 
3  Compressor  3  1  Gas 
4  Compressor  4  2  Gas 
5  Compressor  5  2  Gas 
6  Compressor  6  1  Gas 
7  Compressor  7  2  Gas 
8  Compressor  8  2  Gas 
9  Compressor  9  2  Electric 
10  Compressor  10  2  Gas 
11  Compressor  11  2  Gas 
12  Compressor  12  1  Gas 
13  Compressor  13  1  Gas 
14  Distribution  
15  Compressor  14  1  Gas 
16  Compressor  15  2  Gas 
17  Compressor  16  1  Gas 
18  Distribution  
19  Compressor  17  1  Gas 
20  Compressor  18  2  Electric 
21  Distribution  
22  Compressor  19  2  Electric 
23  Distribution  
24  Compressor  20  2  Electric 
25  Distribution  
26  Compressor  21  2  Electric 
27  Distribution  
28  Distribution  
29  Compressor  22  2  Gas 
30  Distribution  
31  Distribution  
32  Distribution  
33  Distribution  
34  Distribution  
35  Distribution  
36  Distribution  
37  Distribution  
38  Distribution  
39  Distribution  
40  Distribution 
There are two manufacturers for the compressors used in the XQ gas pipeline (GE and RR). Part of the compressor’s coefficients for (
Coefficients for the equation for the compressor performance curves.
Model 










1  −0.000282  −0.000393  0.000090  −0.001170  0.000144  4620  0.396  8310  1.44 
2  −0.001200  0.000167  0.000045  −0.001470  0.000332  3840  0.145  4910  0.533 
3  −0.000403  −0.000348  0.000064  −0.001440  0.000140  5920  0.412  10700  1.47 
4  −0.001200  0.000167  0.000045  −0.001470  0.000332  3840  0.145  4910  0.533 
5  −0.000390  −0.001090  0.000334  −0.002180  0.000392  3080  0.145  5970  0.585 
6  −0.000640  0.000012  0.000023  −0.000883  0.000141  5010  0.342  8520  1.26 
7  −0.000183  −0.001100  0.000314  −0.001990  0.000362  3260  0.173  6270  0.79 
8  −0.001190  0.000161  0.000042  −0.001450  0.000317  3610  0.149  4640  0.554 
9  −0.000644  −0.000679  0.000252  −0.001790  0.000324  2970  0.165  5340  0.504 
10  −0.001190  0.000161  0.000042  −0.001450  0.000317  3610  0.149  4640  0.554 
The maximum outbound pressure is 9.8 MPa, while minimum pitted pressure is 5 MPa. The minimum pitted temperature is 15°C, while the maximum outbound temperature is 65°C.
Take the parameters in May 2012 as an example for the optimization calculation. The pitted pressure of the first station is 6.5 MPa and the temperature is 15°C. Each station's gas transmission capacity is shown in Table
Transmission capacity, 10^{4} Nm³/d.
Station number  Injection volume  Distribution volume 

1  3552  0 
14  0  291 
15  1277  0 
21  0  35 
22  188  0 
23  0  158 
24  0  379 
25  219  220 
26  0  589 
27  0  55 
28  0  68 
29  0  130 
30  0  39 
31  0  351 
32  817  56 
33  0  522 
34  0  66 
35  0  416 
36  0  149 
37  0  183 
38  0  751 
39  0  508 
Optimal operation scheme.
Station number  Pitted pressure, MPa  Outbound pressure, MPa  Pitted temperature, °C  Outbound temperature, °C  Compressor boot program 

1  6.5  8.43  15  37.28  1 set 
2  6.41  9.08  6.61  35.87  2 set 
3  7.78  9.75  8.69  27.56  1 set 
4  8.5  8.5  6.32  6.32  0 set 
5  6.62  9.17  5.09  32.36  2 set 
6  8.17  9.78  8.24  23.14  1 set 
7  7.96  9.8  6.88  24.09  1 set 
8  8.73  8.73  6.73  6.73  0 set 
9  6.98  9.8  5.15  33.56  2 set 
10  8.54  8.54  6.35  6.35  0 set 
11  6.85  9.24  5.15  30.07  2 set 
12  8.43  9.8  9.73  22.27  1 set 
13  8.81  8.81  7.54  7.54  0 set 
15  7.84  9.76  5.18  23.15  1 set 
16  7.03  9.7  6.93  33.98  2 set 
17  8.05  9.8  11.8  28.32  1 set 
19  8.05  9.8  9.41  25.8  1 set 
20  7.95  9.74  9.44  26.35  1 set 
22  7.68  9.34  8.9  25.18  1 set 
24  7.5  9.26  8.36  25.87  1 set 
26  7.24  9.03  7.37  25.72  1 set 
29  6.29  7.84  5.24  23.39  1 set 
Energy consumption of the optimal operation scheme.
Turnover  452892.63 × 10^{7} Nm³·km 
Gas consumption  4154.5 × 10^{4} Nm³ 
Gas unit consumption  91.7 Nm³/(10^{7}Nm³·km) 
Production unit consumption  135.4 kgce/(10^{7}Nm³·km) 
Power consumption  4195 × 10^{4} kW·h 
Total energy consumption  61314.19 tce 
Power unit consumption  108.9 kW·h/(10^{7} Nm³·km) 
Using the same method to optimize the operation for 1–7 months in 2012, the energy consumption optimization results can be obtained. As shown in Table
XQ1 energy consumption.
Month  Production unit consumption, kgce/(10^{7} Nm³·km)  Turnover, 10^{7} Nm³·km 
Power consumption, 10^{4} kW 
Gas consumption, 10^{4} Nm³  

Optimal value  Measured value  Energy saving rate  Optimal value  Measured value  Deviation  Optimal value  Measured value  Deviation  
1  205.1  241.46  −15.07%  521623  5446  5302  2.72%  7540  8980  −16.04% 
2  210.1  237.6  −11.56%  496704  4944  5825  −15.12%  7391  8335  −11.33% 
3  236.0  283  −16.59%  476826.49  5267  6996  −24.71%  7976  9529  −16.30% 
4  147.0  174  −15.53%  452892.63  4449.69  5345  −16.75%  4594  4377  4.96% 
5  135.4  158.5  −14.58%  452892.63  4930.3  4195  17.53%  4154.5  5011  −17.09% 
6  148.6  171.2  −13.20%  463643.35  5024.59  5194  −3.26%  4716.23  5487  −14.05% 
7  157.4  187.3  −15.97%  486394.54  5049.2  4612  9.48%  5289.32  6424  −17.66% 
We can acquire the operating parameters through the SCADA systems of the pipeline, including the gas consumption and electricity consumption. Therefore, we can obtain the actual energy of the pipeline in Table
The data in Table
Energy analysis.
Our conclusions are as follows.
Based on a full understanding of actual demands of a pipeline company, we introduce production consumption indicators to establish an objective function of the minimum energy consumption of the gas pipeline and use dynamic programming to solve the model quickly and efficiently.
When setting the constraints, it is necessary to consider the pipeline, station, power equipment, topography, and climate and to simplify these constraints reasonably such that the mathematical model can accurately describe not only the energy consumption of crude oil pipeline but also the convenient mathematical operations.
According to the dynamic programming method, we compiled the natural gas pipeline running optimization software, which can be used to guide the natural gas pipeline running program analysis and optimize the energy savings. Through the optimization analysis of the XQ nature gas pipeline with the actual working condition, we discovered that the optimal operation scheme can reduce energy consumption by 11%~16%.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the special fund of China’s central government for the development of local colleges and universities—the project of National FirstLevel Discipline in Oil and Gas Engineering, the Scientific Research Cultivate Project of SWPU, the National Natural Science Foundation of China (no. 51174172), and a subproject of the National Science and Technology Major Project of China (no. 2011ZX05054).