A novel methodology for forecasting gas supply reliability of natural gas pipeline systems

Abstract

In this paper, a novel systematic and integrated methodology to assess gas supply reliability is proposed based on the Monte Carlo method, statistical analysis, mathematical-probabilistic analysis, and hydraulic simulation. The method proposed has two stages. In the first stage, typical scenarios are determined. In the second stage, hydraulic simulation is conducted to calculate the flow rate in each typical scenario. The result of the gas pipeline system calculated is the average gas supply reliability in each typical scenario. To verify the feasibility, the method proposed is applied for a real natural gas pipelines network system. The comparison of the results calculated and the actual gas supply reliability based on the filed data in the evaluation period suggests the assessment results of the method proposed agree well with the filed data. Besides, the effect of different components on gas supply reliability is investigated, and the most critical component is identified. For example, the 48th unit is the most critical component for the SH terminal station, while the 119th typical scenario results in the most severe consequence which causes the loss of 175.61×10⁴ m³ gas when the 119th scenario happens. This paper provides a set of scientific and reasonable gas supply reliability indexes which can evaluate the gas supply reliability from two dimensions of quantity and time.

Keywords

natural gas pipeline system / gas supply reliability / evaluation index / Monte Carlo method / hydraulic simulation

Introduction

Natural gas belongs to the main energy resources essential for industry and public [¹,²]. The consequence of loss of gas supply could be catastrophic [³,⁴]. Therefore, gas supply reliability is a crucial issue of high concern. The aim of this paper is to present a common scientific methodology for the evaluation of gas supply reliability. Gas supply reliability means the ability that the gas pipelines system can supply continuous and adequate amount of gas to users [⁵]. Different from the structural integrity of the natural gas pipelines system, the scope of the gas supply reliability is the satisfaction of natural gas user’s demand rather than the safety of installed equipment or the total system [⁶–⁸].

To evaluate the gas supply reliability, two major difficulties should be overcome:

The first difficulty involves the establishment of a scientific, reasonable, and appropriate evaluation index system. At present, the reliability evaluation index of natural gas pipeline system has not yet been widely recognized [⁹,¹⁰]. In the classical reliability theory, the reliability of the unit and system is always measured by these reliability evaluation indexes, such as reliability, maintainability, and availability [¹¹]. Moreover, the failure rate, mean time between failure (MTBF), and mean time to repair (MTTR) are also employed [¹²]. However, it is hard for the aforementioned indexes to reflect the security of the gas supply and the definition of the gas supply reliability reasonably. For example, based on the classical reliability theory [¹³], if all units are in the normal operating states, the system can be considered to be in the normal operating state, but this does not mean that the system can safeguard the sufficient amount of natural gas demand. The reason for this is that the gas supply reliability is determined by both the operating status of the system, the hydraulic characteristics of the system, and the user’s gas demand [¹⁴,¹⁵].

The network system gas pipelines is similar to the power system and water supply system in terms of topological structure [¹⁶]. Compared to the natural gas pipeline system, the power system and the water distribution system are more detailed and comprehensive in the study of supply reliability. In the power system, Heuberger et al. [¹⁷] proposed a series of quantitative indicators, such as the interruption frequency index, the interruption duration, and the unavailability to evaluate the supply reliability. In the water distribution system, the supply reliability was proposed to reflect the ability to deliver water to individual consumers in the quantity and quality required [¹⁸]. Reliability indexes, such as time averaged value of the ratio of the available flow to the required flow [¹⁹], the fraction of delivered volume, the fraction of delivered demand, and the fraction of the delivered quality [²⁰], are calculated to measure the supply reliability of the water distribution system.

However, there exist differences between the gas pipelines system, the power system, and the water supply system. First, the transport medium in the power system is propagated at the speed of light, which is different from the gas pipeline system where the gas supply speed is much lower than the speed of light. Second, gas is compressible and a large amount of natural gas is stored in the pipelines, which is also referred to as line pack. The existence of a line pack is one of the most significant differences between the natural gas transmission pipeline system and other energy supply systems [⁷]. Finally, the path redundancy of the natural gas pipelines network is less than that of the water and power supply system.

For the natural gas pipeline system, a reliable gas supply means that enough amount of gas is supplied to the users in the whole period and the amount of gas supplied to the user can meet the demand in each moment. Therefore, two core criteria for a reliable gas supply are the adequate amount of gas and the in-time supply of gas to users. In this paper, a set of index which can fully cover these two criteria are be introduced (Section 2).

The second difficulty is the calculation method for gas supply reliability indexes. Gas supply reliability is determined by the operating status of the system, the hydraulic characteristics of the system, and the user’s gas demand [²¹,²²]. Therefore, it is necessary to employ hydraulic simulation under various operating conditions when calculating the gas supply reliability [⁸,¹⁴] to consider the hydraulic characteristics of the natural gas pipeline system. However, most existing methods ignore the hydraulic characteristics of the gas pipeline system when calculating the gas supply reliability. For example, the maximum flow algorithm was employed in Refs. [⁹,²³,²⁴] and the linear programming model was used in Refs. [²⁵–²⁷] to calculate the flow rate when assessing the gas supply reliability. In Refs. [²⁸,²⁹], the Monte Carlo based approaches were proposed to assess the ability of European natural gas pipeline network to meet the market demand under different demand and operating conditions. Moreover, in order to calculate the flow rate, the relationship between flow and pressure of the water supply system and the steady hydraulic simulation of the natural gas pipeline system was utilized in Ref. [³⁰] and Ref. [¹⁶], respectively. In addition, ecological network analysis (ENA) was adopted in Refs. [³¹,³²] to simulate the natural gas supply system in China, and thus the gas supply security was evaluated. Unfortunately, the aforementioned methods are not suitable for the natural gas pipeline system because the hydraulic characteristics of the gas pipeline system, especially the effect of the line pack caused by the compressibility of natural gas, are not considered. Actually, the existence of a line pack is one of the most significant differences between the natural gas pipeline system and other energy supply systems [³³,³⁴]. Ignoring the effect of the line pack will lead to a significant underestimation of the gas supply reliability.

To evaluate the gas supply reliability, two processes should be employed: the calculation of the probability of each operating situation and the using of hydraulic simulation for each operating situation, in which, the key problem actually lies in the first process. The difficulty is that there are a large variety of operating situations. The research conducted in Refs. [²³,³⁵,³⁶] showed that the solutions to such problem mainly included the analytical method and simulation method. The commonly used analytic methods consist of the state enumeration method, the probability graph method, the minimum cut set method, and so on. These methods are not appropriate for the large system because of the massive and complex calculations. The simulation method, especially the Monte Carlo sampling method, is therefore widely used to solve this problem [³⁷–⁴⁰]. In addition, each operating situation which corresponds to a gas supply flow rate can be computed by hydraulic simulation [³³,⁴¹]. Moreover, the reduction of the calculation time as much as possible while ensuring the accuracy of calculation is also a problem that needs to be solved in the evaluation of gas supply reliability [⁴²–⁴⁶].

The aim of this paper is to propose an integrated and systematic methodology to assess gas supply reliability, in which the two major difficulties mentioned above can be overcome. This methodology should not only evaluate the gas supply reliability in the past, but also forecast the gas supply reliability in the future. Moreover, a real natural gas pipeline network is applied to confirm the applicability of the approach proposed, and a comparison of the calculated results and the actual gas supply reliability based on the filed data in the evaluation period is presented. Furthermore, the effect of different components on gas supply reliability is investigated, and the key of the components is identified.

Indexes of gas supply reliability

As mentioned above, establishing a set of scientific, objective, and systemic gas supply reliability index is of great significance for the research on gas supply reliability [⁴⁷–⁵¹]. Two main factors including abundance and continuity can contribute to a reliable gas supply task. The abundance condition means that sufficient amount of gas from the gas network system can be supplied to meet the user’s demand in the evaluation period while the continuity condition means that the user’s demand can be met in each moment in the evaluation period.

In this paper, a set of gas supply reliability index is proposed, which can be divided into the abundance index and continuity index. Figure 1 shows the framework of the gas supply reliability indexes. The abundance index is the consumer satisfaction index (CSI) which can evaluate the degree of consumer’s satisfaction in gas amount, while the supplied continuity index includes the loss of enough gas amount (LEGA), the loss of enough gas frequency (LEGF), and the loss of enough gas duration (LEGD).

CSI

CSI aims at assessing the degree that the gas pipelines system meets the user’s demand in terms of the gas amount, which can be calculated as

(1){{\displaystyle \mathrm{C}\mathrm{S}\mathrm{I}}}_j={\displaystyle \frac{{{\displaystyle \mathrm{S}\mathrm{u}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{y}}}_j}{{{\displaystyle \mathrm{D}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{d}}}_j}},

where CSI_j represents the satisfaction degree of user j in the period, Demand_j is the gas demand needed by the jth (jnd, jst) user, Supply_j is the gas amount supplied to the jth (jnd, jst) user in the period.

In more detail, the gas amount supplied is defined as

(2){{\displaystyle \mathrm{S}\mathrm{u}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{y}}}_j={\displaystyle {\sum }_{i=\mathrm{1}}^N{{\displaystyle P}}_i}·{{\displaystyle Q}}_{j-i},

where P_i is the probability that the gas pipeline system in the ith (ind, ist) scenario in the period (It is supposed that there are N scenarios in the network system.); P_i can be obtained by statistical analysis, which will be described in Section 3; The P_i and N in the following index expressions have the same meaning; Q_j-i is the gas amount that gas pipelines system transports to the jth (jnd, jst) user in the ith(ind, ist) scenario in the period; and CSI is a macro-indicator that can just measure the gross amount between supply and demand.

Therefore, it can be seen that the CSI is a dimensionless number between 0 and 1. The closer the calculation result of CSI to 1, the higher the degree that the gas network system can satisfy user’s demand in the evaluation period. This paper shows that temperature is the most obvious factor affecting the user’s demand. The long evaluation period will result in inaccurate gas supply reliability forecasting due to the inaccurate of user’s demand forecasting result.

Continuity indexes

It is far from enough to describe the gas supply reliability degree with CSI along. The satisfaction of the total quantity in the period cannot guarantee that the user’s demand can be satisfied in every single moment. Hence, continuity indexes, which are modified from the reliability indexes of electric power utilities, are used to reflect the gas supply reliability. The calculation result of these indexes can be used to guide the formulation of emergency measures for administrators of network system if gas supply shortage happens. Continuity indexes include LEGA, LEGF, and LEGD.

LEGA means the loss gas amount for users in the evaluation period. The expression of LEGA is described as

(3){{\displaystyle A}}_j={\displaystyle {\sum }_{i=\mathrm{1}}^N{{\displaystyle P}}_j}\ast {{\displaystyle LQ}}_{ij},

where A_j is the sufficient gas amount for user j in the evaluation period, m³/h; LQ_ij means the sufficient gas amount for jth (jnd, jst) user in the ith (ind, ist) scenario, m³/h; and LEGF stands for the frequency that gas supply shortages happen in the evaluation period.

(4){{\displaystyle F}}_j={\displaystyle {\sum }_{i=\mathrm{1}}^N{{\displaystyle P}}_i}\ast {{\displaystyle LD}}_{ij},

where F_j is the frequency that the gas shortages happen in jth(jnd, jst) user in the evaluation period; and LD_ij, the number of gas supply interruption to jth (jnd, jst) user in the ith (ind, ist) scenario.

LEGD refers to the time when the gas supply is insufficient to the user in the evaluation period.

(5){{\displaystyle D}}_j={\displaystyle {\sum }_{i=\mathrm{1}}^N{{\displaystyle P}}_i}\ast {{\displaystyle LT}}_{ij},

where D_j is the time the gas shortages happen in jth(jnd, jst) user in the evaluation period; and LD_ij, the number of gas supply interruption to jth(jnd, jst) user in the ith(ind,ist) scenario.

The three factors mentioned above constitute the continuous indexes of gas supply reliability. Moreover, each user in the network has a corresponding user satisfaction degree index. It is not reasonable to use a general index to describe the gas supply reliability of the whole gas pipelines network system. As a matter of fact, it is difficult for a comprehensive index to reflect the satisfaction for all the users in the network. Each user has different importance in the large natural gas pipelines system. Therefore, when gas supply shortage occurs, it is necessary to sacrifice some less important users to ensure the demand of more important user, which is common in the country where the government is in charge of production, transportation, and sale of natural gas.

Calculation of gas supply reliability indexes

The framework of the methodology of the gas supply reliability evaluation is shown in Fig. 2. The evaluation process includes the determination of the typical scenarios of the pipeline system and the calculation of the probability of each typical scenario; the calculation of the gas amount supplied to each user in each typical scenario; and the evaluation of the gas supply reliability using the proposed indexes.

In this paper, typical scenario is the operation scenario with a high probability, which includes the normal scenario and failure scenario.

Determination of the typical scenarios and their probabilities

Natural gas pipeline network system is a repairable, complicated, and large system, in which the operating states of the components are uncertainty. Hence, the Monte Carlo method is adopted for the calculation of the probability of each operation scenario and determination of the typical scenarios.

For the ith(ind, ist) Monte Carlo sample, a set of random number x_i is generated as x_i = (Num_i, FE_i, FT_i, RT_i), where Num_i which represents the number of the failed units in the ith(ind,ist) sample, is a nonnegative integer. FE_i represents the failed unit in the ith(ind,ist) sample. If the sample is in a normal operation scenario, the FE_i is a null set. FT_i and RT_i represent the failure time and maintenance time of units associated with FE_i, respectively.

If the number of Num_i equals 0, it means that there are no failed units in the system within the evaluation period in the ith(ind, ist) sample. Then the following three elements, FE_i, FT_i, and RT_i, in the x_i are null set. If the number of Num_i equals m (m is a positive integer), it means that there are m failed units within the evaluation period in the ith(ind, ist) sample. Therefore, FE_i = (f₁,f₂,…,f_m) represents the serial number of the failed units. Similarly, FT_i = (ft₁ ,ft₂,…,ft_m) and RT_i = (rt₁,rt₂,…,rt_m) represent the failure time and maintenance time corresponding to the failed units in the set of FE_i, respectively. Moreover, if the number of the occurrences of a certain type of operation scenario is M when the number of the Monte Carlo sample is N (a number large enough), the probability of this scenario equals M/N.

In this paper, the homogeneous Poisson process (HPP) is used to simulate the failure events of the unit in the pipeline system. Let N(t) be the number of failed units within the time interval (0,t), (S₁,S₂,…,S_n) is a sequence of the failure moment, and T_i(i =1,2,…) is the time interval between S_i–1 and S_i. A counting process ({N(t), t≥0}) can be treated as a HPP when it satisfies

① N(0)=0;

② [N(t₁) – N(0)], [N(t₂) – N(t₁)],…, [N(t_k) – N(t_k–1)] are all independent random variables with 0<t₁<…<t_k, (k= 2,3,…);

③ The interval time of all failures is independent of each other and follows the exponential distribution of parameter l:

(6)\mathrm{Pr}[N(t+s)-N(s)=n]={\displaystyle \frac{{(\lambda t)}^n}{n!}}{\mathrm{e}}^{-\lambda t},n=\mathrm{0},\mathrm{1},\mathrm{2}\dots

,

(7)\mathrm{Pr}[N(\mathrm{\Delta }t)=\mathrm{1}]=\lambda \mathrm{\Delta }t+o(\mathrm{\Delta }t),

(8)\mathrm{Pr}[N(\mathrm{\Delta }t)\ge \mathrm{2}]=o(\mathrm{\Delta }t).

Hence, it can be concluded that it might not happen that a scenario has two or more failed units at the same time.

It is easy to deduce the main features of the HPP based on the above definitions:

①In HPP, l is a constant and represents the failure rate of gas pipelines system.

②The number of system failure in the time interval (t, t+v] follows the Poisson distribution with parameter lt:

(9)\mathrm{Pr}[N(t+v)-N(t)=n]={\displaystyle \frac{{(\lambda v)}^n}{n!}}{\mathrm{e}}^{-\lambda v},t\ge \mathrm{0},v>\mathrm{0.}

③The mean number of failed units in the interval (t, t+v] is

(10)W(t+v)-W(t)=\mathrm{E}[N(t+v)-N(t)]=\lambda v.

④{{\displaystyle S}}_n={\displaystyle {\sum }_{i=\mathrm{1}}^n{{\displaystyle T}}_i} obeys the Gamma distribution of parameter (n,l), whose probability density function is

(11){{\displaystyle f}}_{{{\displaystyle S}}_n}(t)={\displaystyle \frac{\lambda }{(n-\mathrm{1})!}}{(\lambda t)}^{n-\mathrm{1}}{\mathrm{e}}^{-\lambda t},t\ge \mathrm{0.}

Therefore, the probability that N(t) = n can be calculated by the total probability formula, if {{\displaystyle S}}_n\le t\le {{\displaystyle S}}_{n+\mathrm{1}} and {{\displaystyle T}}_{n+\mathrm{1}}={{\displaystyle S}}_{n+\mathrm{1}}-{{\displaystyle S}}_n :

(12)

Suppose that there is a HPP with failure rate in the interval time (0,t₀], the distribution of failure time T₁ is:

(13)\begin{array}{l}\mathrm{Pr}P[{{\displaystyle T}}_{\mathrm{1}}\ge t|N({{\displaystyle t}}_{\mathrm{0}})=\mathrm{1}]={\displaystyle \frac{\mathrm{Pr}[{{\displaystyle T}}_{\mathrm{1}}\le t\cap N({{\displaystyle t}}_{\mathrm{0}})=\mathrm{1}]}{\mathrm{Pr}[N({{\displaystyle t}}_{\mathrm{0}})=\mathrm{1}]}}=\\ {\displaystyle \frac{\mathrm{Pr}(\mathrm{one}\mathrm{}\mathrm{failure}\mathrm{}\mathrm{event}\mathrm{}\mathrm{happensin}\mathrm{}\mathrm{(0,t]}\cap \mathrm{no}\mathrm{}\mathrm{failure}\mathrm{}\mathrm{events}\mathrm{}\mathrm{happenin}\mathrm{}\mathit{(t,}{{\displaystyle t}}_{\mathrm{0}}])}{\mathrm{Pr}[N({{\displaystyle t}}_{\mathrm{0}})=\mathrm{1}]}}={\displaystyle \frac{\mathrm{Pr}[N(t)=\mathrm{1}]\ast \mathrm{Pr}[N({{\displaystyle t}}_{\mathrm{0}})-N(t)=\mathrm{0}]}{\mathrm{Pr}[N({{\displaystyle t}}_{\mathrm{0}})=\mathrm{1}]}}=\\ {\displaystyle \frac{\lambda t{\mathrm{e}}^{-\lambda t}{\mathrm{e}}^{-\lambda ({{\displaystyle t}}_{\mathrm{0}}-t)}}{\lambda {{\displaystyle t}}_{\mathrm{0}}{\mathrm{e}}^{-\lambda {{\displaystyle t}}_{\mathrm{0}}}}}={\displaystyle \frac{t}{{{\displaystyle t}}_{\mathrm{0}}}}\end{array}

where 0<t ≤t₀.

The failure moment will equably distributed in the interval (0, t₀] when only one failure event happens. Therefore, in the interval (0, t₀], the failure probability in each equal length time interval is the same as that of the others. The expected time of failure is

(14)\mathrm{E}[{{\displaystyle T}}_{\mathrm{1}}|N({{\displaystyle t}}_{\mathrm{0}})=\mathrm{1}]={\displaystyle \frac{t}{{{\displaystyle t}}_{\mathrm{0}}}}.

The following assumptions are made in this paper:

① The failure in the system is caused by the failed unit;

② According to Eq. (8), the event that two or more units fail simultaneously is ignored;

③ Under the assumption of the short repair time and evaluation period, the same unit that failed twice or more in the evaluation is ignored;

④ The failure rate of the unit is assumed as 20 times/a; and

⑤ The repair time of the unit is assumed as logarithmic normal distribution, namely T~log normal (μ, τ²). The mean time to repair (MTTR) is{\mathrm{e}}^{\frac{\mu +{\tau }^{\mathrm{2}}}{\mathrm{2}}} .

According to Eq. (9), the probability of different numbers of failed units can be calculated. When the evaluation period is one month, the probability of the different numbers of failed units is presented in Table 1. Obviously, the total probability of all events is 1. It is assumed that R is the random number that is generated in the interval [0, 1] and obeys uniform distribution. If R is in interval [0, 0.8703), the number of failed units in the evaluation period is 0. If R is in interval [0.8703, 0.9912), in which 0.9912 equals 0.8703 plus 0.1209, the number of failed units is 2. Then, the probability of the other operation scenarios can be calculated, and the results are summarized in Table 1.

After determining the probability of different operation scenarios, the next step is to determine the failed units. Supposed that the failure rate of the ith(ind, ist) unit is λ_i, a random number uniformly distributed in the interval [\mathrm{0},{\displaystyle {\sum }_{i=\mathrm{1}}^n{{\displaystyle \lambda }}_i}] is generated. As shown in Fig. 3, if the number generated is in interval [λ_i–1, λ_i], it means that the failed unit is the ith (ind, ist) unit.

Hydraulic analysis based on typical scenarios

In addition, each operating situation corresponds to a gas supply flow rate which can be computed by hydraulic simulation. The commercial software Stoner Pipeline Simulator (SPS) is used to develop the thermal-hydraulic system model of the natural gas pipeline system. The fundamental equations of gas flow including continuity equation, equation of motion, energy equation, equation of state, enthalpy equation, and internal energy equation are considered in the software. The core of the hydraulic analysis is to determine the control models under various abnormal operating conditions. The principle of the control modes is to ensure that the amount of natural gas supplied to the users is maximum, and the control modes include the flow control stage and the pressure control stage. The schematic of the control models is depicted in Fig. 4.

In Fig. 4, Q and P are the flow rate and pressure of the natural gas supplied to the users, respectively; Q_r and P_r are the required flow rate and required pressure of the natural gas supplied to the users, respectively; P_min is the minimum required pressure of the natural gas supplied to the users; f_t and r_t are the failure time and maintenance time, respectively. According to Fig. 4, when system transits to the abnormal operating conditions, the flow rate of the natural gas supplied to the users, Q, is maintained equal to the required flow rate Q_r, and then the pressure P decreases from the required pressure P_r with time. This stage is called the flow control stage in which the pressure is needed to determine whether pressure P is greater than the minimum required pressure P_min. If P≤P_min, P is maintained equal to the required minimal pressure P_min, and the flow rate Q decreases from the required flow rate Q_r with time. This stage is called the pressure control stage. Therefore, the flow rate and pressure under each operating situation can be obtained once the failed unit, the failure time, and the maintenance time are determined.

Finally, the index of the gas supply reliability can be obtained by combining the above process.

Case study

Introduction to the natural gas pipelines network system

The gas supply reliability of a real natural gas pipeline system in China is assessed using the methodology proposed. This natural gas pipeline system consists of 1 primary line, 2 branch lines, and 1 connecting line. The layout of this gas pipeline system is illustrated in Fig. 5. The total length of the primary line is 2826 km, and the design capacity, design pressure, and pipe diameter are 17 billion m³ per year, 10 MPa, and 1016 mm, respectively.

In this case study, the evaluation period is 7 days. Based on the framework of the methodology shown in Fig. 2, the typical scenarios can be determined of and the hydraulic simulation can be implemented.

Determination of typical scenarios

As mentioned before, the typical scenarios of the case-study pipeline system are determined by determining the number of system failures in the evaluation period, determining the failed units, determining the failure time, and determining the maintenance time.

The network system is assumed to be in a stable period of operation, and the operation process is treated as a HPP process. According to the EGIG between 1970 to 2010, the failure rate of European pipelines was between 0.162 and 0.372 time per 1000 km per year. However, China still has defects in pipeline integrity management and equipment maintenance. Therefore, there is still a certain gap in unit safety performance between western countries and China. According to the information published from the General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China in 2014, the operation life of oil and gas pipeline is long, and more than 30% onshore pipelines have been in operation for more than 10 years. Therefore, the accident rate of China’s pipelines is approximately 4 times per 1000 km per year, which is higher than the average of western countries.

Assuming the evaluation period is 7 days, the calculated results of the probability of system failure in the evaluation period are listed in Table 2.

As can be seen from Table 2 that the joint failure probabilities of three or more components are sufficiently rare. Therefore, it is reasonable to restrict the analysis to single component failures in the case study. Three types of failure scenarios are considered in the evaluation period, i.e., no component failure, single component failure, and joint failure of two components.

As mentioned above, the maintenance time is related to many uncertain factors, such as the personal factor. Therefore, the maintenance time of the failed units in the case study is assumed as the average maintenance time {\mathrm{e}}^{\frac{\mu +{\tau }^{\mathrm{2}}}{\mathrm{2}}} .

For this assessment, 1000 Monte Carlo trials are conducted to calculate the average gas supply reliability of the pipeline system in the case-study in the evaluation period. According to the 1000 Monte Carlo trials, 798 trails are the scenarios of no component failure, 184 trails are the scenario of single component failure, and 18 trails are the scenario of joint failure of two components. After determining the typical scenario of the tested pipeline system, hydraulic analysis is employed to calculate the flow rate in different scenarios.

Results and discussion

Based on the determination of the typical scenarios and the hydraulic simulation, the gas flow rate of each typical scenario and the evaluation indexes are calculated for each station, as listed in Table 3.

For comparison, the filed data in the evaluation period is collected to calculate the actual gas supply reliability, and the comparison results are listed in Table 4. As observed from Table 4, the assessment results obtained by using the methodology proposed agree well with the filed data. Moreover, the CSI indexes of all the users exceed 99%, which means that the gas supply reliability for each station in the main line is high. The reason for this can be attributed to the low failure rate and the short evaluation period.

The critical component for each station in the pipeline system can be identified, and the corresponding amount and the duration of the gas shortage are calculated. The pipelines or the combinations with high consequences have relative high criticalities, which brings a large gas deficiency.

Obviously, the SH terminal station (abbreviated as SH) is the most important station in the primary line. Its gas demand amount is large and the consequences of the loss of gas supply in SH could cause catastrophic failures. Figure 6 shows the gas supply reliability of SH terminal station when 127 different scenarios happen. The horizontal axis represents the serial number of different kinds of scenarios while the vertical axis represents different reliability indexes, including CSI, ALECF, ALEGA, and ALEGD. The 1st point is the calculation result of the intact scenario where there is no failed unit. The 2nd to 108th points show the calculation results of the scenarios where there is one failed component, and the 109th to 127th points reflect the calculation results of scenarios where there are two failed components.

According to Fig. 6, the 49th scenario is the most severe scenario for the 2nd to the 108th scenario, which means that the 48th unit is the most critical component for the SH terminal station. Moreover, the fact that there exist two failed components has a greater impact on the gas supply reliability than the fact that there exist a single failed component. Finally, the 119th typical scenario results in the most severe consequence, and the loss of enough gas when the 119th scenario happens is 175.61×10⁴ m³.

Conclusions and future work

In this paper, the abundance index and continuity index were proposed to evaluate the gas supply reliability from quantity and time, respectively. Besides, the calculation method for the reliability indexes was proposed considering both the hydraulic characteristics and the uncertainties of the operating state of natural gas pipeline network system. In the method proposed, the failure scenarios for natural gas pipelines network were sampled by the Monte Carlo method based on the counting process theory, and the hydraulic simulation based on SPS software was employed to calculate the flow rate in each scenario.

The method proposed for gas pipelines system analysis was applied in a simulation case study which made it possible to determine the effect of failure and sequential closure of failed element on the gas supply for the consumers. The calculation results can also determine the fatalness of each failed unit to the whole system. Moreover, the developed method demonstrates its applicability for the gas supply reliability assessment of a real gas pipelines system, and the assessment results of the developed methodology agree well with the filed data. Furthermore, the most critical component and scenarios in the tested system can be identified. For example, the 48th unit is the most critical component for the SH terminal station, and the 119th typical scenario results in the most severe consequence, because the loss of enough gas amount when the 119th scenario happens is 175.61×10⁴ m³.

Nevertheless, the methodology proposed still suffers from several limitations, whose major drawbacks are the long time of the simulation and the lack of convergence analysis. In the future, this methodology will be supplemented and improved, especially with respect to shortening the simulation time and performing convergence analysis.

References

[1] Qiao W, Lu H, Zhou G, Azimi M, Yang Q, Tian W. A hybrid algorithm for carbon dioxide emissions forecasting based on improved lion swarm optimizer. Journal of Cleaner Production, 2020, 244: 118612

[2] Qiao W, Tian W, Tian Y, Yang Q, Wang Y, Zhang J. The forecasting of PM_2.5 using a hybrid model based on wavelet transform and an improved deep learning algorithm. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 142814–142825

[3] Flouri M, Karakosta C, Kladouchou C, Psarras J. How does a natural gas supply interruption affect the EU gas security? A Monte Carlo simulation. Renewable & Sustainable Energy Reviews, 2015, 44: 785–796

[4] Lochner S. Modeling the European natural gas market during the 2009 Russian–Ukrainian gas conflict: ex-post simulation and analysis. Journal of Natural Gas Science and Engineering, 2011, 3(1): 341–348

[5] Huang W. Reliability of large-scale natural gas pipeline network. Acta Petrolei Sinica, 2013, 34: 401–404

[6] Yuan Q, Li J, Liu H, Yu B, Sun D, Deng Y. Parametric regression of a multiparameter thixotropic model for waxy crude oil based on multiobjective strategy. Journal of Petroleum Science Engineering, 2019, 173: 287–297

[7] Yu W, Song S, Li Y, Min Y, Huang W, Wen K, Gong J. Gas supply reliability assessment of natural gas transmission pipeline systems. Energy, 2018, 162: 853–870

[8] Yuan Q, Liu H, Li J, Yu B, Wu C. Study on parametric regression of a complex thixotropic model for waxy crude oil. Energy & Fuels, 2018, 32: 5020–5032

[9] Su H, Zhang J, Zio E, Yang N, Li X, Zhang Z. An integrated systemic method for supply reliability assessment of natural gas pipeline networks. Applied Energy, 2018, 209: 489–501

[10] Rimkevicius S, Kaliatka A, Valincius M, Dundulis G, Janulionis R, Grybenas A, Zutautaite I. Development of approach for reliability assessment of pipeline network systems. Applied Energy, 2012, 94: 22–33

[11] Yu W, Zhang J, Wen K, Huang W, Min Y, Li Y, Yang X, Gong J. A novel methodology to update the reliability of the corroding natural gas pipeline by introducing the effects of failure data and corrective maintenance. International Journal of Pressure Vessels and Piping, 2019, 169: 48–56

[12] Kołowrocki K, Kwiatuszewska-Sarnecka B. Reliability and risk analysis of large systems with ageing components. Reliability Engineering & System Safety, 2008, 93(12): 1821–1829

[13] Zio E. Reliability engineering: old problems and new challenges. Reliability Engineering & System Safety, 2009, 94(2): 125–141

[14] Sukharev M, Karasevich A. Reliability models for gas supply systems. Automation and Remote Control, 2010, 71(7): 1415–1424

[15] Faertes D, Saker L, Heil L, Vieira F, Risi F, Domingues J, Alvarenga T, Mussel P, Carvalho E. Reliability modelling: petrobras 2010 integrated gas supply chain. In: 2010 8th International Pipeline Conference, Calgary, Alberta, Canada, 2010: 497–505

[16] Fan M, Gong J, Wu Y, Kong W. The gas supply reliability analysis of natural gas pipeline network based on simplified topological structure. Journal of Renewable and Sustainable Energy, 2017, 9(4): 045503

[17] Heuberger D, Wittenberg P, Moser A. Optimization of natural gas distribution networks considering the reliability of supply. In: PSIG Annual Meeting, Pipeline Simulation Interest Group, 2011

[18] Jensen H, Jerez D. A stochastic framework for reliability and sensitivity analysis of large scale water distribution networks. Reliability Engineering & System Safety, 2018, 176: 80–92

[19] Surendran S, Tanyimboh T, Tabesh M. Peaking demand factor-based reliability analysis of water distribution systems. Advances in Engineering Software, 2005, 36(11–12): 789–796

[20] Ostfeld A, Kogan D, Shamir U. Reliability simulation of water distribution systems – single and multiquality. Urban Water, 2002, 4(1): 53–61

[21] Qiao W, Yang Z, Kang Z, Pan Z. Short-term natural gas consumption prediction based on Volterra adaptive filter and improved whale optimization algorithm. Engineering Applications of Artificial Intelligence, 2020, 87: 103323

[22] Qiao W, Huang K, Azimi M, Han S. A novel hybrid prediction model for hourly gas consumption in supply side based on improved machine learning algorithms. IEEE Access: Practical Innovations, Open Solutions, 2019

[23] Yu W, Wen K, Li Y, Huang W, Gong J. A methodology to assess the gas supply capacity and gas supply reliability of a natural gas pipeline network system. In: 2018 12th International Pipeline Conference Calgary, Alberta, Canada, 2018

[24] Praks P, Kopustinskas V, Masera M. Probabilistic modelling of security of supply in gas networks and evaluation of new infrastructure. Reliability Engineering & System Safety, 2015, 144: 254–264

[25] Olanrewaju O, Chaudry M, Qadrdan M, Wu J, Jenkins N. Vulnerability assessment of the European natural gas supply. In: Proceedings of the Institution of Civil Engineers—Energy, 2015, 168: 5–15

[26] Vasconcelos C, Lourenço S, Gracias A, Cassiano D. Network flows modeling applied to the natural gas pipeline in Brazil. Journal of Natural Gas Science and Engineering, 2013, 14: 211–224

[27] Tran T, French S, Ashman R, Kent E. Impact of compressor failures on gas transmission network capability. Applied Mathematical Modelling, 2018, 55: 741–757

[28] Monforti F, Szikszai A. A Monte Carlo approach for assessing the adequacy of the European gas transmission system under supply crisis conditions. Energy Policy, 2010, 38(5): 2486–2498

[29] Szikszai A, Monforti F. GEMFLOW: a time dependent model to assess responses to natural gas supply crises. Energy Policy, 2011, 39(9): 5129–5136

[30] Liang G, Luo M, Zhang C, Pu H, Zheng Y. Analysis methods for hydraulic reliability of gas transmission pipeline networks. Natural Gas Industry, 2006, 26: 125–127

[31] Shaikh F, Ji Q, Fan Y. Evaluating China’s natural gas supply security based on ecological network analysis. Journal of Cleaner Production, 2016, 139: 1196–1206

[32] Su M, Zhang M, Lu W, Chang X, Chen B, Liu G, Hao Y, Zhang Y. ENA-based evaluation of energy supply security: comparison between the Chinese crude oil and natural gas supply systems. Renewable & Sustainable Energy Reviews, 2017, 72: 888–899

[33] Pambour K, Cakir Erdener B, Bolado-Lavin R, Dijkema G. SAInt—a novel quasi-dynamic model for assessing security of supply in coupled gas and electricity transmission networks. Applied Energy, 2017, 203: 829–857

[34] Yu W, Wen K, Min Y, He L, Huang W, Gong J. A methodology to quantify the gas supply capacity of natural gas transmission pipeline system using reliability theory. Reliability Engineering & System Safety, 2018, 175: 128–141

[35] Fu X, Zhang X. Failure probability estimation of gas supply using the central moment method in an integrated energy system. Applied Energy, 2018, 219: 1–10

[36] Fu X, Li G, Zhang X, Qiao Z. Failure probability estimation of the gas supply using a data-driven model in an integrated energy system. Applied Energy, 2018, 232: 704–714

[37] Zio E, Baraldi P, Patelli E. Assessment of the availability of an offshore installation by Monte Carlo simulation. International Journal of Pressure Vessels and Piping, 2006, 83(4): 312–320

[38] Zio E. The Monte Carlo Simulation Method for System Reliability and Risk Analysis. London: Springer, 2013

[39] Liu H, Lu Y, Zhang J. A comprehensive investigation of the viscoelasticity and time-dependent yielding transition of waxy crude oils. Journal of Rheology (New York, N.Y.), 2018, 62(2): 527–541

[40] Liu H, Zhang J, Lu Y. Yielding characterization of waxy gels by energy dissipation. Rheologica Acta, 2018, 57(6-7): 473–480

[41] Yu W, Gong J, Song S, Huang W, Li Y, Zhang J, Hong B, Zhang Y, Wen K, Duan X. Gas supply reliability analysis of a natural gas pipeline system considering the effects of underground gas storages. Applied Energy, 2019, 252: 113418

[42] Chaudry M, Wu J, Jenkins N. A sequential Monte Carlo model of the combined GB gas and electricity network. Energy Policy, 2013, 62: 473–483

[43] Qiao W, Huang K, Azimi M, Han S. A novel hybrid prediction model for hourly gas consumption in supply side based on improved whale optimization algorithm and relevance vector machine. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 88218–88230

[44] Qiao W, Yang Z. Modified dolphin swarm algorithm based on chaotic maps for solving high-dimensional function optimization problems. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 110472–110486

[45] Qiao W, Yang Z. An improved dolphin swarm algorithm based on Kernel Fuzzy C-means in the application of solving the optimal problems of large-scale function. IEEE Access: Practical Innovations, Open Solutions, 2020, 8: 2073–2089

[46] Qiao W, Yang Z. Solving large-scale function optimization problem by using a new metaheuristic algorithm based on quantum dolphin swarm algorithm. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 138972–138989

[47] Badea A C, Rocco S C M, Tarantola S, Bolado R. Composite indicators for security of energy supply using ordered weighted averaging. Reliability Engineering & System Safety, 2011, 96(6): 651–662

[48] Qiao W, Yang Z. Forecast the electricity price of US using a wavelet transform-based hybrid model. Energy, 2020, 193: 116704

[49] Zhou G, Moayedi H, Foong L. Teaching–learning-based metaheuri-stic scheme for modifying neural computing in appraising energy performance of building. Engineering with Computers, 2020, online, doi:10.1007/s00366-020-00981-5

[50] Qiao W, Bing F, Zhang Y. Differential scanning calorimetry and electrochemical tests for the analysis of delamination of 3PE coatings. International Journal of Electrochemical Science, 2019, 14: 7389–7400

[51] Cabalu H. Indicators of security of natural gas supply in Asia. Energy Policy, 2010, 38(1): 218–225

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