Jun Zhou , Liuling Zhou , Gungchun Ling *, Shoo Wng , Tintin Fu ,Xun Zhou , Jinghong Peng

a Petroleum Engineering School, Southwest Petroleum University, Chengdu, PR China

b CNPC Beijing Oil and Gas Control Center, Beijing, PR China

ABSTRACT Underground natural gas storage(UNGS)is an important part of the natural gas supply system to ensure a balanced energy supply.The surface system, as an important part of the gas storage, undertakes the functions of gas injection and gas production of the gas storage, and its investment economy is of vital importance.In fact, the UNGS surface pipeline network has two-way injection and production characteristics, which is different from the one-way production characteristics of conventional oil&gas gathering and transportation systems.This paper takes the minimum investment of the pipeline network as the objective function, considers the gas injection and gas withdrawal flow conditions and esablishes a mixed integer non-linear programming model (MINLP) for the surface pipeline network of the UNGS to optimize its pipeline layout and diameter parameters.Constraints including the well affiliation, the number of stations, the gathering radius, the processing capacity and the flow/pressure equilibrium equations, are also taken into consideration.Taking an UNGS in China as an example, the results of the optimal structure and diameter of the pipeline network, as well as the pipe flow, node pressure, and maximum/minimum flowrate during gas injection and gas withdrawal are obtained.Finally, the effects of constraints such as processing capacity and radius on the structure layout and investment of the UNGS are analyzed, verifying the reliability and effectiveness of the model.

Keywords:Optimal design Pipeline network Natural gas storage Injection and withdrawal

1.Introduction

Natural gas is a competitive and widely used energy source.It emits much less carbon dioxide than coal and releases less dust,sulfur dioxide and nitrogen oxides.In the era of low-carbon economy,in order to control pollution and carbon emissions,the natural gas industry has developed rapidly.And UNGSs are playing an increasingly important role in the natural gas supply and demand chain [1].In 1915, a depleted natural gas reservoir in Ontario,Canada underwent the first successful underground gas storage[2].The original and main purpose of UNGS was to meet peak demand changes.There are four types of UNGS: oil reservoir, gas reservoir,salt cavern and aquifer.There are currently 672 UNGSs in operation worldwide, including 498 depleted oil fields, 77 aquifers, and 97 salt caves [3,4], of which the UNGSs in Europe usually account for 13-27%of annual natural gas consumption[5].It is expected that in the next one to two decades, the global demand for UNGS peak shaving will further increase.According to the prediction of the International Gas Union[6],by 2030,the peak demand of the UNGS will reach 5030×108m3,and 183 UNGSs to add 1406×108m3of active gas capacity will be needed.The development of UNGS in China began in the early 1990s.After more than 20 years of development,the domestic UNGS has played a key role in balancing the pressure and flow of gas pipelines and regulating regional gas supply.China’s peak shaving capacity of UNGS accounts for only 3%of natural gas sales,far below the global average of 11%[7].In China,natural gas will continue to increase in the medium and long term,and the demand for UNGS working gas volume will reach 550 ×108m3because of the urgent needs of air pollution control, accelerated urbanization,and carbon emission reduction.Obviously,the construction of UNGS in China has a long way to go.With the expansion of UNGS construction scale, especially the rapid development of UNGS in China, the rationality and economic value of UNGS ground equipment are becoming increasingly prominent.

The UNGS surface pipeline network is an intermediate transfer between the wellbore and the external pipeline.The process of natural gas injection and production is performed on the surface.Therefore, the surface injection pipeline is an important part of UNGS surface engineering construction.According to the geometry of the surface pipeline network in the gas field,the topology of the surface pipeline network can be divided into four types: tree,star,ring and a combination type of two level pipeline network forms as star-star,star-tree,etc.[8,9].In a single-stage pipeline network,if it has a tree-like topology, each well is first collected into a branch pipeline, and different wells are collected into the main pipeline through the branch pipeline;In the case of a star-shaped structure,each well is individually connected to the gas gathering station via a pipeline; in the case of a ring-shaped topology, each well is connected to a ring-shaped pipeline,and natural gas is then transferred to the gas gathering station through the pipelines.If it is a twostage topology, the wells will be collected to the gas gathering station through the lower layer pipeline network, and then to the processing plant (center station) through the gas gathering stations.The rational construction of the ground pipeline network is directly related to the construction efficiency and benefits.Therefore, optimizing the ground system is the key to reducing development costs [8].Compared with gas field pipeline network construction, UNGS surface pipeline network construction has the characteristics of injection-production cycle and high investment,and its investment of UNGS surface pipeline network is determined by the topology of the pipeline network.If the pipeline topology is given, different options combine many variables, such as the number and location of facilities, pipe length, etc., resulting in different costs for each aspect.Therefore,in order to minimize the investment in the surface pipeline network of the UNGS, the optimization of the pipeline network design must determine the optimal location and number of platforms, the location of the center station, the connection mode between the wells and the platforms,and consider the various requirements and limitations of the system, such as hydraulic condition.Surface pipeline network investment makes up for a large proportion of the entire construction investment,but less attention is paid to the optimization design of the UNGS ground pipeline network.Therefore,we need to optimize the UNGS surface pipeline network layout plan with the least investment.

This article first summarizes the research status of the optimization design of UNGS surface gas injection and withdrawal network(Section 2).Next,introduce the injection and production/withdrawal process of the gas storage, and the shape of the gas storage network (Section 3).Then, a comprehensive optimization model of the UNGS surface pipeline network is proposed (Section 4), and the solution method of the model is introduced after that(Section 5).Taking an on-site UNGS in China as an example,different pipeline network layout schemes and pipe diameters are obtained, and the influence of constraints such as processing capacity and radius on the layout is analyzed, which verified the reliability and effectiveness of the model(Section 6).Finally,the full text is summarized in Section 7.

2.Literature review

Geological evaluation, drilling technology, and surface facilities related to UNGS have been studied by many scholars.At present,the evaluation of UNGS has formed a relatively mature technology system.These technologies provide a mighty support for the building and the safe operation of UNGSs.As there are many types of UNGSs, Verga [2] analyzed the physical characteristics and economics of the depleted oilfields, aquifers and salt caverns, and proposed a methodological approach for designing and operating UNGSs.In order to find an address where an UNGS can be established, Demirel et al.[10] considered the main criteria including cost, time, availability, risk, social factors, and environmental factors, and used the Choquet integral fuzzy based multi-criteria decision-making method to select the appropriate site for UNGS.In addition, Yang et al.[11] experimentally obtained the mechanical properties and permeability of the salt cave, and analyzed the underground geology of the salt cave is feasible, and evaluated the stability of cavern by 3D geo-mechanical numerical simulations.

Due to the large investment of UNGS, the literature on its economy is extensive[12].Modjtahedi and Movassagh[13]and Mu[14] emphasized that storage has an impact on the volatility and level of gas prices.In addition, Budny et al.[15] proposed the economic feasibility of pipeline storage and underground reservoir storage solutions.In recent years, risk analysis of well integrity failure has attracted attention.Lavasani et al.[16] carried out a fuzzy comprehensive risk assessment model for offshore oil wells.Recently,Lavasani et al.[17]established a model based on fuzzy FTA for risk analysis of abandoned well leakage.Unlike ordinary gas wells,UNGS gas storage wells have some notable attributes or risk characteristics [18-22].In order to ensure UNGS’s safe operation,Zhao et al.[1] built a model for integrity failure risk analysis of UNGS gas storage wells,which can effectively deal with uncertainty in risk calculations.But so far, the research on the integrity risk of UNGS gas wells has received little attention.Numerical simulation is also an important research direction that can evaluate the design and safety of UNGS underground structures.There are relatively many research results on UNGS in salt rock.Wang et al.[23]verified the analytical model of UNGS salt cavern shape optimizing with 3D geo-mechanical simulation, and pointed out that both numerical and analytical solutions are useful in salt cavern design.However,most scholars have focused on the underground part of UNGS,and there is little research on the pipeline network of ground engineering.Only Peng et al.[24] conducted a hydraulic simulation analysis using an actual UNGS ground pipeline network as an example.Yu et al.[25]analyzed the reliability of the UNGS surface pipeline network.At present, no scholar has studied the optimal design of UNGS surface pipeline network.

The UNGS surface system has a similar structure to the conventional oil&gas field pipeline network.Currently,there are many achievements in the optimization of the oil and gas field pipeline network.Wei et al.[26] divided the optimization problem of oil &gas gathering and transportation into two sub-problems of topology optimization and parameter optimization.In terms of topology optimization, in order to reduce the investment of the pipeline network,many scholars have considered the factors that affect the layout of the pipeline network and proposed a mathematical optimization model with the objective function of reducing the cost of the pipeline network.Zheng et al.[27]built a mixed-integer nonlinear programming (MINLP) model that takes into account the facilities and power costs of a centralized transmission network.However, the optimization model in this paper does not consider some limitation factors that may be encountered in the actual construction of the pipeline network, such as terrain obstacles.Zhang et al.[28]further considered the construction conditions and took the common star-shaped pipeline network and tree-like pipeline network topology as the research object, and established a comprehensive model including the constraints of the pipeline construction and taking into account the terrain impact.This model can make the layout optimal under various connection modes and thus minimize the investment of single-stage pipeline network.Similarly, Zhang et al.[29] considered the gathering radius and economic flowrate into the optimization of the offshore gathering pipeline network, and established a mixed integer linear programming(MILP)model.In order to optimize the pipeline network layout, scholars have raised various optimization strategies and algorithms.For the multi-layer pipeline network optimization problem,Liu et al.[30]decomposed the optimization problem into multiple sub-problems such as group optimization division and pipeline network layout optimization,and adopted particle swarm algorithm for optimization.Wei et al.[31]divided the optimization problem of the gathering and transportation system into positioning layer and distribution layer, and systematically combined genetic algorithm, simulated annealing algorithm and hierarchical optimization method to solve it.However, using the abovementioned layered strategy to optimize the model, the solution obtained is a local optimal solution, and the network layout with the lowest network cost cannot be obtained.There are also many research results on the optimization design of pipeline network diameter parameters.El-Mahdy et al.[32] developed a new algorithm based on genetic algorithm in order to determine the optimal pipeline size of the natural gas network, and applied it to a ringshaped natural gas network to reduce the cost of the network.But this model cannot solve the pipeline network with both layout parameters and pipeline parameters.Liu et al.[33] conducted a high-dimensional optimized mixed-integer nonlinear layout programming (MINLP) mathematical model that includes pipeline network structure parameters and pipe design parameters, which can be widely applied to large oil-gas gathering and transportation system.Most of the models studied above are designed for optimizing the layout and diameter of the gathering pipeline network of oil and gas fields, and they are not suitable for the optimization design of UNGS surface pipeline network.

In summary,most of the mathematical optimization models are only applicable to the oil&gas field gathering and transportation pipeline network.Because the UNGS has two-way gas injection and production processes, the UNGS surface pipeline network is different from the common oil&gas field pipeline network, and it needs to assume the function of bidirectional gas delivery.At present, there are very few optimization studies on the design and layout of the UNGS surface pipeline network.Therefore,in view of the characteristics of its pipeline network with bidirectional transportation function,a comprehensive mathematical optimization model with the total investment of UNGS ground pipeline network as the objective function is proposed.Moreover,we also consider various constraints of pipeline length,processing capacity of each station, pipe diameter, and some hydraulic conditions,such as node flow balance,pressure limitation,gas velocity,etc..Taking a salt cave in China as an example,the model is finally optimized and solved to obtain the global optimal layout structure and pipe diameter parameters of the surface pipeline network.

3.Process flow and pipeline network of UNGS

UNGS facility provides underground storage.Natural gas is thus stored at a depth in the cavities or porous rock.Wells are used to inject gas into the reservoir and to withdraw it afterwards into the transmission network.The surface installations are designed to process the gas prior to injection into the reservoir (filtering,metering, etc.) and to process it at the time of withdrawal (separating it from the water,desulphurisation,drying,etc.).The storage facility provides seasonal storage through injection and withdrawal process.

3.1.Injection and withdrawal process

In summer, the pipeline marketers bring more natural gas into the grid than their customers consume.Natural gas injection process is shown in Fig.1.Incoming natural gas is first filtered in order to prevent the dust it contains from damaging the facilities.The filtered gas then passes through a metering line which measures its volume, pressure and temperature.The composition of the gas is also analyzed.All the data is transmitted to the on-site control room for further processing.Before the natural gas can be injected,it must be compressed to achieve a higher pressure.The compressed natural gas is then forwarded to the platforms (four platforms in Fig.1).The gas flow rate is naturally regulated:all the wells are opened to enable the natural gas to be naturally distributed throughout the reservoir.

In winter,the consumers consume more natural gas than which is brought into the transmission network.After being stored in the reservoir rock or cavities,the natural gas cannot be withdrawn and re-injected directly into the transmission network, it must first undergo a specialized processing as shown in Fig.2.For the UNGSs containing acid gases, the presence of water, carbon dioxide and sulphurous compounds produces a sulphuric acid.This gaseous substance mixes with the natural gas.Since sulphuric acid is highly corrosive, it must first be removed from the gas.This operation takes place by the desulphurisation towers.During underground storage, the natural gas may not only absorb sulphuric acid.In porous rock and cavern storage, the gas also becomes saturated with water and must as a consequence be dried.This operation is carried out in drying towers at the main facility.A substance like triethyleneglycol absorb large quantities of water.Hence, the natural gas is dried after that.For condensate reservoirs, a dehydrogenation treatment unit should be set up to remove the heavier components in the natural gas to meet the requirements of the natural gas on the hydrocarbon dew point.When the natural gas leaves the above equipment,it may still be in a high pressure state.The pressure thus first has to be decreased to the transmission pipe pressure(pressure reduction).Before injecting the gas back into the transmission network, its volume, pressure, temperature and composition are analyzed.

Fig.2.Schematic diagram of natural gas withdrawal process.

3.2.Pipeline network

The injection and withdrawal processes are undertaken by the pipeline network.At present, UNGS generally adopts a pipeline network form as shown in Fig.3.When injecting gas,the pressurized gas from the center station is delivered to each platform through the gathering and distribution pipe(GDP),then distributed to each well through the production and injection pipe (PIP), and finally injected into underground.During gas withdrawal process,the gas of multiple wells is gathered on the platform through each PIP, and then transported to the center station through each GDP.The produced gas by all the wells is then processed and transmitted to the transmission network at the center station.In order to save the cost of land occupation and reduce the land purchase process,the platform is generally located at a well site, and the center station is also to be built at a location of a platform.

4.Mathematical model

4.1.Objective function

Pipeline network investmentFcomprises pipeline investment and facility investment.The former one includes the pipeline investment between wells and platforms, and the pipeline investment between platforms and central station.The latter includes platforms investment and central station investment.

Pipeline investment between wells and platformsfWPcan be expressed as Eq.(1).

Fig.3.Schematic diagram of pipeline network structure.

nis the number of wells.mis the number of platforms.Ai,jrepresents the connection relationship between welliand platformj, if connected,Ai,j=1,otherwise 0.Ci,jis the pipe price between welliand platformj.Li,jis the pipe length from wellito platformj,Li,j=xiandyiare the coordinates of welli.ajandbjare the coordinates of platformj.

Pipeline investment between platforms and the central stationfPScan be expressed as Eq.(2).

βkis the central station location decision variable,if central station is located at platform k, βk=1, otherwise 0.Cj,kis the pipe price between platform j and central station located at platform k.Lj,kis the pipe length from platform j to central station located at platform k,Lj,k=x and y are the coordinates of central station.

Facility investmentffacilityincludes platforms investment and central station investment,as shown in the Eq.(3).

The first item in Eq.(3)represents the platform investment,and the second item represents the central station investment.αjis the platform location decision variable,if the platform is located at wellj,αj=1,otherwise 0.fjis the platform cost located at wellj.fkis the central station cost located at platformk.

4.2.Constraint conditions

(1) Well affiliation constriants

Each well can and can only be connected to one platform, as shown in the Eq.(4).

(2) Central station number constraints

The UNGS ground system has only one central station,as shown in the Eq.(5).

(3) Length constraints

When the UNGS ground pipeline network is artificially implemented, the engineer will comprehensively consider factors such as the pressure drop of the pipeline,the radius of the power supply,and the convenience of field staff to manage multiple wells connected to the platform.The length of the pipeline from well to platform will be restricted during design.The maximum lengthR,as shown in the Eq.(6), referred to as L-Constraint.

(4) Flowrate balance constraints

The node flowrate and pipeline flowrate should be balanced.For PIP, the relationship between the pipeline flowduring gas injection and the wellhead node flowis shown in Eq.(7);During gas withdrawal process, as shown in the Eq.(8).For GDP, the relationship between the pipeline flowduring gas injection and the platformis shown in Eq.(9); during gas withdrawal, as shown in the Eq.(10).The node flow of the platform during gas injection and gas production are calculated by Eq.(11)and Eq.(12),respectively.The node flow of the center station during gas injection and gas withdrawal is equal to the total flowrate of the entire system,as shown in Eq.(13) and Eq.(14), respectively.

(5) Capacity constraints

Each platform has a maximum node capacity limit.The larger the platform capacity, the higher the equipment investment.The processing size of the capacity is generally given by the equipment specifications and the engineers’ experience, and the maximum capacity isqmax,as shown in the Eq.(15).The capacity constraint is referred to as C-Constraint.

(6) Pressure balance constraints

The starting and ending pressure of the pipeline can be calculated by the pressure drop equation[34],ignoring the effect of the elevation difference.During the injection process,pipeline pressure drops of GDP and PIP are shown in Eq.(16) and Eq.(17), respectively.During the withdrawal process,the pipeline pressure drop of GDP and PIP are shown in Eq.(18) and Eq.(19), respectively.The compressibility factors in various equations, such as, can be obtained from the BWRS state equation [35]; the friction coefficients in various equations,such as,can be obtained from the Colebrook formula [36].

(7) Node pressure constraints

The node pressure must be within the allowable operating pressure range.During gas injection process, such as Eq.(20), the maximum pressureis determined by the maximum outlet pressure of the compressors, and the minimum pressure is generally determined by the requirements of the wellhead pressure at the initial stage of gas injection to ensure gas injected into the gas reservoir smoothly.During gas withdrawal process, there is a minimum pressurerequirement shown as Eq.(21) to guarantee that the UNGS supplies gas to the transimission network safely.The initial wellhead pressure is relatively high, and the maximum pressure after throttling is.

(8) Pipeline velocity constraints

The gas flow rate of the pipeline is within the economic flow rate range.Equation(22)shows the upper and lower bounds of the economic flow rate during gas injection.While Eq.(23)denotes the upper and lower limits of the economic flow rate during gas withdrawal process.

(9) Pressure drop constraints

The pressure drop per unit length needs to be within a given range.When injecting gas, represented as Eq.(24), and when extracting gas, shown as Eq.(25).

(10) Pipe diameter constraints

The pipe diameter is selected from a set of commercial pipe diameters, shown as Eq.(26).

Fig.4.Schematic of pipeline network with the variable descriptions.

(11) Variable value constraints

The binary variables are expressed as Eq.(27)-(29)。

To sum up, an optimization model for pipeline network layout can be described by:

Variables are labeled in the pipeline network diagram of Fig.4.

5.Optimization algorithm

The optimization model was solved by using GAMS softwareversion 24.8.2.The solutions obtained using the solver CONOPT 3 version 3.17C.The computer utilized has an Intel (R) Pentium (R)CPU G4560 3.50 GHz processor and 8 GB of random access memory(RAM).

6.Calculation results and analyses

6.1.Optimization results

The main function of UNGS in a salt cave natural gas in China is to ensure the reliability and safety of gas supply in nearby pipelines,and it is used for seasonal peak gas storage and emergency gas storage in gas-using areas.The UNGS total storage capacity is 11.79×108m3,effective working gas volume is 7.23×108m3,and bottom gas volume is 4.56×108m3.A single salt cavern gas storage has an effective volume of 20×104m3.The designed maximum gas injection capacity is 450 × 104m3/d; and the maximum peak shaving capacity is 600×104m3/d.The surface system contains 36 wells, and the coordinates of the wells are shown in Table 1.The composition of the inlet gas is shown in Table 2.The compressor configuration is selected according to the scale of gas injection.The displacement of the three units is 150×104Nm3/d,and the power of a single motor is 3400 kW.When injecting gas,natural gas enters injection and production stations via the transmission pipeline network for gas processing.In the station, the gas first enters the cyclone separator and the filter separator for metering, and then enters the compressor manifold, followed by the three compressors’ two-stage compression to 16.0 MPa, then cooled by the air cooler.After that the gas is divided into multiple streams by the manifold and sent it to the gathering pipeline network through GDPs,and finally injected it into each gas well through PIPs of the platform.During gas production, the gas from the gas well is throttled first at the wellhead.The initial wellhead pressure is 9-15 MPa,and the pressure after throttling is controlled to 8 MPa.The wellhead pressure gradully decreases as gas production progresses and control the center station inlet pressure not lower than 6 MPa.After being dehydrated in the center station,it meets the gas quality requirements and is exported to the transmission network after that.

Table 1 Well coordinates.

Table 2 Composition of inlet gas.

Table 3 Optimized parameters.

Table 4 Avaliable commercial pipe diameter.

The model of this paper is used to optimize the structure and diameter of the UNGS pipeline network.The optimized parameters are shown in Table 3, and the available commercial pipelines are shown in Table 4.The pipeline network layout optimization results are shown in Fig.5.The pipeline network diameter optimization results are shown in Table 5.The flowrate,pressure and gas veloity during gas injection and gas withdrawal are shown in Table 6.

Table 5 Pipeline network diameter optimization results.

6.2.Influence of different constraints on the structure of the pipeline network

As mentioned above, the optimal solution of the pipeline network can be obtained under the given constraints, but the pipeline network layout results are affected by many constraints,such as L-Constraint(Eq.(6)),and C-Constraint(Eq.(15)).Therefore,this section studies the fluctuations ofRin L-Constraint,fluctuations ofqmaxin C-Constraint,and the simultaneous changes of the two on the layout results.

Fig.5.Optimized layout of the pipeline network.

6.2.1.Impact analysis of L-Constraint

Since the platform has a radius constraintR,we have considered the influence of the four different radii of 300 m,500 m,700 m,and 1000 m on the overall layout, ignoring the capacity constraints.Other constraints remain unchanged.When discussing radius constraints,the platform cost is a fixed value of¥925.06×104.The pipeline network layout is shown in Fig.6.By comparing the four layout structure diagrams (Fig.6 (a)-(d)) with different radius constraints,it can be seen that the center station is established on 8#, indicating that the change of the gathering radius cannot affect its location.As the radius constraint increases from 300 m to 1000 m, the number of platforms has a downward trend, and the number of wellheads connected to each platform is increasing.The corresponding total investment of the pipeline network is shown in Table 7.With the increase of the radius constraint, the overall investment cost is decreasing, in which the total investment cost under the condition ofR=1000 m is about¥1.2326×108less than that under the condition ofR=300 m.It should be noted that the number of platforms established is the same when the radii areR= 700 m andR= 1000 m respectively.However, except for the positions established on the 8#,16#and 31#wells,the positions of the other 3 platforms are different.In addition, the connection mode in wells, platforms and the center station are different,resulting in an investment ofR=700 m more than an investment ofR= 1000 m by ¥5.6 × 105.Furthermore, we tested that when the radius constraint reached 1100 m (Fig.6 (e)), the center station is established on 16 #, and 4 platforms are established on 6#, 16#,27#,31#separately.Total investment cost is¥2.4906×108.At this time,increasing the radius of gathering and transportation will not affect the layout of the pipeline network and investment costs(referred to as the boundary radius),but the node flow of platform 3 reaches to 247.5×104m3/d,which is close to half volume of the total gas.

6.2.2.Impact analysis of C-Constraint

The processing capacity of the platform is not infinitely increased, and different platforms have different platform investment costs.In order to test the influence of capacity constraints on the layout structure of the oil and gas pipeline network,the radius constraints are ignored, and other constraints are unchanged.In this paper,four sets of data are set for the platform’s capacityqmax:30×104m3/d,60×104m3/d,100×104m3/d and 150×104m3/d,regardless of radius constraints.The optimized network layouts of these four groups are shown in Fig.7, and their corresponding platform prices and total pipeline network investment are shownin Table 8.From the overall layout perspective, the capacity constraints have a great impact on the structure of the pipeline network.The four layouts represent the layout structure under different capacity constraints.The center stations is set up on 1#in the first three cases.When the capacity limit isqmax= 150 × 104m3/d, the center station is located at 4#.Whenqmax= 30 × 104m3/d, 36 platforms are established on 1# to 36#,and then the platform is connected to the center station with a star structure.In this case, the total investment cost is very high (¥5.126×108).This is because the gas production volume in each well is 16.5 × 104m3/d and the capacity constraint of the platform is small.Therefore,each platform can only connect one well,forming a pipeline network layout where the platform is established at each well.As the platform’s capacity constraints increase,the number of wells to which the platform can connect increases while the number of platforms decreases.At the same time, it can be seen that when the number of platforms is relatively large, such asqmax=60×104m3/d,the platforms are located closer to the center station.This is because the gas gathering pipeline is more expensive than the gas production pipeline, so there is such a layout structure that the wellhead is far from the platform.The total investment cost also decreases as the capacity constraint increases,where the total investment with capacity constraint ofqmax= 30 × 104m3/d is ¥2.5844 × 108more than the capacity constraint withqmax=150×104m3/d.In addition,in order to meet capacity constraints,some wells are connected to a platform that is far away from them, and unreasonable situations of pipeline crossing occurred (Fig.7 (d)).

Table 6 Optimized hydraulic results during gas injection and gas withdrawl process.

Table 7 Total investment cost under different radius constraints.

Table 8 Platform price and pipeline network investment under different capacities.

6.2.3.Effect analyis of L-Constraint and C-Constraint

Fig.6.Network layout under different R constraints: (a)300 m; (b)500 m; (c)700 m; (d)1000 m; (e)1100 m

The previous section discussed the impact of L-Constraint and CConstraint single constraints on the layout of the pipeline network,but this double constraint often occurs in practical applications of pipeline networks.Therefore,20 groups of calculation examples are tested, including 16 examples composed of radius constraints(300 m, 500 m, 700 m, 1000 m) and capacity constraints(30×104m3/d,60×104m3/d,100×104m3/d and 150×104m3/d).In addition, pipeline network investment under the boundary radius are also calculated under 4 capacity constraints.The impact of double constraints on the total investment,PIP investment,GDP investment,PF investment,and PF number of the pipeline network is shown in Fig.8.From the total investment in Fig.8(a),except for 30×104m3/d,on the whole,total investment gradually decreases with the increase of the radiusR.WhenRis greater than the critical radius,the total investment no longer changes.For PIP investment(Fig.8 (b)), it gradually increases asRincreases, but the effect ofqmaxon PIP investment is not significant.For the GDP investment(Fig.8(c)),it gradually decreases asRincreases.For the investment and number of PFs(Fig.8(d)and(e)),asRgrows,the number of PFs decreases and the PF investment decreases.WhenRexceeds 700 m,the number of PF basically remains stable.At this time,the layout of the pipeline network is mainly affected byqmax.

7.Conclusion

In this paper, a mixed-integer nonlinear optimization model considering the injection and withdrawal characteristics of UNGS is established.The objective function considers the investment of the entire pipeline network and incorporates constraints such as affiliation, number of platforms, radius, capacity, flow/pressurebalance, node pressure, gas velocity, and discrete pipe diameter.Both platform and center staion are optimized in discrete space and built with wells.It can determine the optimal layout and diameters of pipelines of UNGS surface pipeline network that meets the constraints under the injection and production conditions,making the investment in the pipeline network the least.

Fig.7.Network layout under different qmax constraints: (a) 30 × 104 m3/d; (b) 60 × 104 m3/d; (c) 100 × 104 m3/d; (d) 150 × 104 m3/d.

Fig.8.Comparison of pipeline network investment under different constraints of L-Constraint and C-Constraint:(a)total investment;(b)PIP investment;(c)GDP investment;(d)PF investment; (e) PF number.

Through the design of the UNGS’s pipeline network,the optimal solution under given constraints can be determined, and the correctness of the model in this paper is verified.In addition, we present the pipeline network structure and pipe diameter results,as well as pipe flow, node pressure, and maximum/minimum flowrates during gas injection and gas withdrawal.

The optimal design of UNGS surface pipeline network is affected by many factors.This paper systematically explores the effects of LConstraint and C-Constraint on the pipeline network results under a single factor condition.The results show that within the range of variable fluctuations, the pipeline network structure has a greater impact.For example, the length of procesing radius increases and the investment decreases,but there is a critical limit.Exceeding this value will not affect the pipeline network structure.The capacity shows a similar pattern,but under a single factor condition,it may cause unreasonable layout, such as excessive flowrate of a single platform, wells connected to a distant platform, and pipeline crossing problems.Therefore,it is more reasonable to consider the two constraints.In addition, we have discussed the analysis of pipeline network optimization results under the dual factors of LConstraint and C-Constraint.The two have different degrees of impact on each part of the pipeline network, and the gathering radius constraint has a more significant impact on PIP investment.While the investment and number of platforms gradually decrease with the radius constraint increases.When it exceeds a certain constraint radius, the increase of the gathering radius constraint has no significant effect on it due to the capacity constraint.

The model established in this paper can obtain the optimal solution of the pipeline network under the given constraints,which is more advanced than the artificial design of the pipeline network structure.However, because some constraints are set from field experience or equipment parameter restrictions, these factors cannot be accurately given for the time being.This brings new challenges to the optimal design of the UNGS surface pipeline network.We will further study these factors as optimization variables in future research.

Declaration of competing interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgements

This work was part of the program “Study on the optimization method and architecture of oil and gas pipeline network design in discrete space and network space”,funded by the National Natural Science Foundation of China,grant number 51704253.The authors are grateful to all study participants.

Nomenclature

GDP gathering and distribution pipe

PIP production and injection pipe

PF platform

nthe number of wells

mthe number of platforms

ithe welli

jthe platformj

kthe central stationk

INthe injection process

Wthe withdrawal process

Cthe constant of the gas pressure drop equation

Rthe maximal allowable pipe length from well to platform

D the available diameter set

Δ the relative density

x,ythe coordinate of central station

aj,bjthe coordinate of platformj

xi,yithe coordinate of welli

fjthe platform cost

fkthe central station cost

fWPthe withdrawal and injection pipe investment

fPSthe gathering and distribution pipe investment

ffacilitythe facility investment

αjthe platform location decision variables, 0 or 1

βkthe central station location decision variables, 0 or 1

qmaxthe capacity of platform

Ai,jthe connection relationship between welliand platformj, 0 or 1

Di,jthe pipe diameter between welliand platformj

Dj,kthe pipe diameter between platformjand central stationk

Li,jthe pipe length from wellito platformj

Lj,kthe pipe length from platformjto central stationk

Ci,jthe pipe price between welliand platformj

Cj,kthe pipe price between platformjand central stationk

the pressure of welliin the injection process

the pressure of welliin the withdrawal process

the pressure of platformjin the injection process

the pressure of platformjin the withdrawal process

the pressure of central stationkin the injection process

the pressure of central stationkin the withdrawal process

the minimal allowable pressure in the injection process

the maximal allowable pressure in the injection process

the minimal allowable pressure in the withdrawal process

the maximal allowable pressure in the withdrawal process

the node volume flow of welliin the injection process

the node volume flow of welliin the withdrawal process

the node volume flow of platformjin the injection process

the node volume flow of platformjin the withdrawal process

the node volume flow of central stationkin the injection process

the node volume flow of central stationkin the withdrawal process

the volume flow between welliand platformjin the injection process

the volume flow between welliand platformjin the withdrawal process

the volume flow between platformjand central stationkin the injection process

the volume flow between platformjand central stationkin the withdrawal process

the gas temperature between welliand platformjin the injection process

the gas temperature between platformjand central stationkin the injection process

the gas temperature between welliand platformjin the withdrawal process

the gas temperature between platformjand central stationkin the withdrawal process

the compressibility factor between welliand platformjin the injection process

the compressibility factor between platformjand central stationkin the injection process

the compressibility factor between welliand platformjin the withdrawal process

the compressibility factor between platformjand central stationkin the withdrawal process

the pressure drop per length between welliand platformjin the injection process

the pressure drop per length between welliand platformjin the withdrawal process

the pressure drop per length between platformjand central stationkin the injection process

the pressure drop per length between platformjand central stationkin the withdrawal process

the minimal allowable pressure drop per length in the injection process

the maximal allowable pressure drop per length in the injection process

the minimal allowable pressure drop per length in the withdrawal process

the maximal allowable pressure drop per length in the withdrawal process

Statement of data availability

All data, models, and code generated or used during the study appear in the submitted article.