Journal of Natural Gas Science and Engineering
Journal of Natural Gas Science and Engineering
Journal of Natural Gas Science and Engineering
a r t i c l e i n f o a b s t r a c t
Article history: Leakage from natural gas pipelines causes severe economic loss and significantly affects social security
Received 8 January 2015 considering the gas' combustibility and the difficulties in detecting leakage. This study proposes a
Received in revised form comprehensive risk evaluation method by combining a risk matrix with a bow-tie model. First, a bow-tie
20 April 2015
model is built, considering the risk factors that may lead to an accident using a fault tree; the conse-
Accepted 21 April 2015
Available online
quences of unwanted events are then described in an event tree. Second, a fuzzy method is used to
calculate the failure probabilities. Third, the severity of an accident is evaluated through an index system
that includes personal casualties, economic losses and environmental disruptions. Finally, a risk matrix
Keywords:
Bow-tie model
consisting of a probability ranking criterion and a consequence ranking criterion is proposed to reach an
Risk matrix integrated quantitative conclusion of a bow-tie model. A case study of an underwater pipeline carrying
Fuzzy method natural gas has been investigated to validate the utility of the proposed method.
Natural gas pipeline © 2015 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jngse.2015.04.029
1875-5100/© 2015 Elsevier B.V. All rights reserved.
L. Lu et al. / Journal of Natural Gas Science and Engineering 25 (2015) 124e133 125
bow-tie model is an innovative approach and a good combination in Fig. 1 and consists of a risk analysis and a consequence assess-
of QRA and ACA and is thus widely used in safety analysis (Ferdous ment in terms of a building fault tree and an event tree, respec-
et al., 2013) and risk management (Chevreau et al., 2006). However, tively. In the risk analysis, a fuzzy method is applied to convert a
one of the limitations in the existing implementation of the bow-tie natural linguistic expression into a failure probability. In the
model is a lack of quantitative conclusions; many researchers have consequence assessment, an index system is introduced to further
investigated the construction of bow-tie models but not their assess the consequence in terms of environmental cost, personal
quantification. injury and economic loss. In the end, to reach a comprehensive
To achieve a quantitative conclusion from a bow-tie model, a conclusion, the risk matrix method is applied to combine the re-
quantitative risk matrix that includes ranking probability criteria sults of the risk analysis and the consequence assessment.
and consequence severity criteria is proposed in this study to
quantify the probability and consequence of a given accident. The 2.1. Construction of a bow-tie model
purpose of this study is to develop a comprehensive approach to
identify the risk factors and evaluate the severity of the conse- A bow-tie model is widely applied in risk analyses, including
quences of an unexpected event. The procedure of the proposed probability calculations (Khakzad et al., 2013), human error risk
approach is presented in Section 2. This procedure includes four analysis (Deacon et al., 2010, 2013), dynamic risk analysis (Khakzad
steps: the construction of the bow-tie model, the fuzzy probability et al., 2012), etc. A bow-tie model is comprised of a fault tree, which
calculation, the consequence analysis of an accident and a risk represents the risk factors of a failure, and an event tree, which
matrix analysis. In Section 3, an application of the proposed represents the consequences of a failure. Both the fault tree and the
approach is presented for the risk analysis and consequence event tree are effective graphical methods and are widely used in
assessment of an underwater pipeline. Section 4 then presents the safety analyses of complex systems; this makes a bow-tie model to
conclusions of the study. have significant potential in this field. Fig. 2 shows the basic
structure of a bow-tie model. X, E and T are the primary, interme-
2. Procedures diate and top events of the fault tree, respectively, and I and C stand
for the ignition (or safety barrier) and the accident consequence in
The procedure of the proposed risk evaluation method is shown an event tree, respectively.
8
Fig. 2. Basic structure of a bow-tie model.
> x 0:1
>
> 0:1 < x 0:25
>
>
< 0:15
2.2. Calculation of a fuzzy probability fL ðxÞ ¼ 0:4 x (4)
>
> 0:25 < x 0:4
>
> 0:15
>
:
To evaluate the failure probability of the top event in a fault tree, 0 otherwise
the probabilities of the primary events must be known in advance.
Because it is difficult to obtain detailed statistical probability data of 8
> x 0:3
>
> 0:3 < x 0:5
primary events, a fuzzy method that consists of 3 steps is proposed >
>
< 0:2
as shown below:
fM ðxÞ ¼ 0:7 x (5)
>
> 0:5 < x 0:7
>
> 0:2
Step 1: Collect a natural linguistic expression of a risk factor >
:
status. 0 otherwise
Step 2: Convert the natural linguistic expression to a fuzzy
8
number. > x 0:6
>
> 0:6 < x 0:75
Step 3: Convert the fuzzy number to a failure probability. >
>
< 0:15
fH ðxÞ ¼ 0:9 x (6)
Further explanations of the above steps are described below. >
> 0:75 < x 0:9
>
> 0:15
In step 1, the likelihood of occurrence of a primary event is >
:
0 otherwise
described in a natural linguistic expression by experienced experts
from different fields (e.g., operation, maintenance, management, 8
installation and design). This likelihood of occurrence can be > x 0:8
>
> 0:8 < x 0:9
categorized into five levels: Very Low (VL), Low(L), Medium(M), < 0:1
fVH ðxÞ ¼ 0:9 < x 1 (7)
High(H) and Very High(VH). Considering the different opinions >
> 1
given by experts, a multi-expert scoring method is frequently rec- >
:
0 otherwise
ommended. The weights of the experts are defined based on their
capabilities, and their capabilities are often evaluated by an analytic The corresponding fuzzy numbers are defined as follows:
hierarchy process (AHP).
In step 2, a numerical approximation approach is proposed to fVL ¼ ½0; 0; 0:1; 0:2; fL ¼ ½0:1; 0:25; 0:4; fM ¼ ½0:3; 0:5; 0:7;
convert the linguistic expression to a corresponding fuzzy number fH ¼ ½0:6; 0:75; 0:9; fVH ¼ ½0:8; 0:9; 1; 1:
(Chen et al., 1992). Fuzzy numbers can be expressed by fuzzy
membership functions. Triangular and trapezoidal fuzzy member- In fuzzy environments, the basic operations of fuzzy numbers
ship functions are generally preferred in fuzzy theory. The trian- such as their addition, subtraction, multiplication and division are
gular fuzzy number is defined as A ¼ (a,b,c), and its membership generally implemented through l-cut. For the given l 2 [0,1], the
function is shown in Eq. (1). Similarly, the trapezoidal fuzzy number l-cut for the fuzzy numbers A and B can be described as:
is defined as A ¼ (a,b,c,d), and its membership function is shown in h i
Eq. (2): Al ¼ fx; x2R; fA lg ¼ al1 ; bl1
8 h i
>
> 0 x>a Bl ¼ fx; x2R; fB lg ¼ al2 ; bl2
>
>
>
> xa
>
<b a a<x b
f ðxÞ ¼ (1)
>
> cx
>
> b<x<c
>
> c b
>
:
0 x>c
8
>
> 0 x>a
>
>
>
> x a
>
> a<x b
>b a
>
<
f ðxÞ ¼ 1 b<x<c (2)
>
>
>
> d x
>
> c<x<d
>
> d c
>
>
:
0 x>d Fig. 3. Membership functions.
L. Lu et al. / Journal of Natural Gas Science and Engineering 25 (2015) 124e133 127
Thus, the corresponding l-cuts of the fuzzy numbers are defined minimizing sets, respectively, and are defined as:
as:
x 0x1
l fmax ðxÞ ¼ (12)
fVL ¼ ½0; 0:2 0:1l; fLl ¼ ½0:15l þ 0:1; 0:4 0:15l; 0 otherwise
l
fM ¼ ½0:2l þ 0:3; 0:7 0:2l; fHl ¼ ½0:15l þ 0:6; 0:9 0:15l;
1x 0x1
l fmin ðxÞ ¼ (13)
fVH ¼ ½0:1l þ 0:8; 1 0 otherwise
Table 1
Factors to be considered in a consequence assessment.
Table 2
Total loss calculation for an event tree.
Personal casualty Economic loss Environmental disruption Personal casualty Economic loss Environmental disruption
1 P1 S1 C1 E1 P 1 S1 P1 C1 P1 E1
2 P2 S2 C2 E2 P 2 S2 P2 C2 P2 E2
3 P3 S3 C3 E3 P 3 S3 P3 C3 P3 E3
Table 3
2 2 risk matrix.
associated consequence with the risk in the 5 5 matrix can be level V is “very high risk”, which predicts on-going leakage and
categorized into 5 levels, as shown in Fig. 4. Level I is “very low indicates that a maintenance project must be implemented as soon
risk”, which indicates that no measurement should be taken; level as possible.
II is “low risk”, which indicates that the pipeline can be run regu- The quantitative and qualitative ranking criteria and their cor-
larly with increased monitoring and maintenance; level III is responding regarding failure probabilities are shown in Table 4. In
“medium risk”, which indicates that a detailed analysis and coun- Table 5, the ranking criteria of the consequences are expressed in
termeasures should be performed to reduce the risk of the situa- terms of economic loss (Hong et al., 2007).
tion; level IV is “high risk”, which indicates that a maintenance
project should be launched in the near future to avoid an accident;
3. Risk evaluation of an underwater pipeline
Table 4
Ranking criterion of failure probability.
Table 5
Ranking criterion of consequence severity. P1 ¼ 0.7 if m0 > 100 kg/s. For allocating the ignition probability, only
No. Amount of loss (thousand $) Level
the net flow rates to the atmosphere must be considered.
Fig. 5. Field conditions of the pipeline before being submerged and after being submerged.
130 L. Lu et al. / Journal of Natural Gas Science and Engineering 25 (2015) 124e133
Table 6
Description of the primary events.
No. Description
Given these left and right scores, the fuzzy possibility score of
the fuzzy number was calculated based on Eq. (9):
FM ¼ 0:3095
Finally, the fuzzy failure probability was calculated based on Eq.
(14) and Eq. (15):
Table 7
Introduction of the experts consulted in this case study.
Table 8
Probabilities of primary events.
this result is 2.44 102. Based on the information in Table 4, the and combusts easily. Therefore, a comprehensive risk evaluation
risk level of these pipelines is Level 5, which implies that leakage is method that helps to define and reduce the risk level of a pipeline is
likely occurring in these pipelines. necessary. Thus, this study establishes a comprehensive risk eval-
uation framework by combining a bow-tie model with a risk matrix
3.3. Consequence of leakage to define the risk level of a pipeline for pipeline management.
The bow-tie model is a quantitative model in this study that is
To assess the consequence of the pipeline leakage, an evaluation composed of an integrated quantitative methodology of risk anal-
index system is recommended in Section 2.3. The historical acci- ysis and a quantification consequence assessment system. The
dent record is also a good reference for this system. One puncture quantitative methodology of risk analysis provides a quantification
accident occurred in 2011 due to a scratch during construction; the of risk probabilities using a fuzzy method that converts natural
corresponding primary event is X14-1 in the fault tree. This event linguistic expressions into failure probabilities. The quantification
resulted in a leakage hole with a diameter of less than 1 mm. Due to of the possible consequences is determined by an index system
the small size of the leakage hole and the relatively quick detection, with three different categories: personal casualties, economic los-
this accident did not lead to a severe poisoning or combustion and ses and environmental damage. A quantitative conclusion of the
explosion event. However, the total loss of this accident exceeded bow-tie model is reached based on the above procedures; a risk
$48,000, including $16,000of maintenance costs and more tha- matrix that includes ranking probability and consequence severity
n$32,000of environmental disputation costs. Experts from the criteria is also proposed to define the risk level of system.
pipeline management reached an agreement that the total loss This study proposes a comprehensive risk evaluation framework
should be set between $16,000 and $160,000, which corresponds that can be applied in natural gas pipeline. A case study of a natural
with Level Medium in Table 3. gas underwater pipeline in CNPC is investigated in detail. The case
study showed that the combination of the bow-tie model and the
4. Results risk matrix creates an effective method for the comprehensive risk
evaluation. This method can help pipeline management compre-
As discussed above, the failure probability of the event investi- hensively identify risk factors and to assess their consequences.
gated is Level 5, and its consequence level is medium. Therefore, it Through the proposed integrated safety analysis method, risks of
can be concluded that the risk level is high based on the 2 2 risk pipeline use can be reduced.
matrix, and level IV based on the 5 5 risk matrix. The result of the
safety evaluation is that the pipeline is a high risk, and thus, a Acknowledgment
maintenance project should be implemented and completed as
soon as possible to avoid or mitigate a serious leakage accident This study was supported by the National Science and Tech-
from occurring. nology Major Project of China (Grant No. 2011ZX05055).
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