Journal of Petroleum Science and Engineering 201 (2021) 108407
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering
journal homepage: http://www.elsevier.com/locate/petrol
PERT based emergency disposal technique for fracture failure of deepwater
drilling riser
Yuanjiang Chang a, *, Yajie Jiang a, Changshuai Zhang a, Anti Xue a, Bin Chen b, Weiguo Zhang b,
Liangbin Xu c, Xiuquan Liu a, Yongguo Dai d
a
Centre for Offshore Engineering and Safety Technology (COEST), China University of Petroleum (East China), Qingdao, China
Shenzhen Branch of China National Offshore Oil Corporation, Shenzhen, China
Research Institute of China National Offshore Oil Corporation, Beijing, China
d
Jiangsu Shuguang Oil Tools Co.,Ltd, Taizhou, China
b
c
A R T I C L E I N F O
A B S T R A C T
Keywords:
Emergency disposal
PERT
Deepwater drilling riser
Fracture failure
Completion probability
Deepwater drilling risers are the crucial connections of subsea wellhead and floating drilling platform, and its
fracture failure would lead to disastrous consequences. However, few efforts have been devoted to studying the
way to efficiently and safely conduct the operation of emergency disposal for drilling riser fracture accident
rescue. In this paper, program evaluation and review technique (PERT) was employed to quantitatively design
the emergency disposal operation procedure of deepwater drilling riser fracture failure. The PERT model of
emergency control operation for riser fracture accident were developed respectively to reflect the sequential
logical relationships of each emergency disposal operation activity. Subsequently, the time parameters of
operation activity for the PERT model were calculated according to the working time of each operation activity
and expected completion time of the whole operation. Finally, the critical path and total duration of the
emergency control operation for riser fracture accident were determined respectively, and some relevant opti­
mization measures drawn from the results were presented to further ensure the completion of emergency
disposal of riser fracture accident on schedule during drilling operations.
1. Introduction
The deepwater drilling riser system is an important device for con­
necting floating drilling platform with the subsea wellhead, and the
fracture failure of the drilling riser is still one of the most dangerous and
costly accidents in the offshore oil industry, as shown in Fig. 1 (Holand
and Skalle, 2001; Per, 2014; Xu et al., 2013; Chang et al., 2018). The
primary functions of the drilling riser system include isolating seawater,
circulating drilling fluid, supporting the choke and kill (C/K) lines,
guiding the drilling tools, and compensating for the heave motion of the
drilling platform (Liu et al., 2013). However, the drilling riser system is
subjected to many complex dynamic loads, which significantly affect the
safety of the drilling riser and may lead to the severe drilling riser
fracture accident. On May 21, 2003, a drilling riser fracture occurred
when the drillship Discoverer Enterprise started pulling the drill string
from the bottom of the well hole in a BP development well in 6015 ft of
water in the Gulf of Mexico, as shown in Fig. 2 (Kirton et al., 2004). The
drilling riser fracture accident had an extremely serious impact on the
safety of marine drilling operations, which caused the grave losses to the
lives and property, and subsequent accident disposal also took a long
time and caused long downtime (Chang et al., 2019a; Kofiani et al.,
2011).
Currently, many scholars have conducted analysis of mechanical
behavior, safe operation, dynamic response of deepwater drilling risers
(Khakzad et al., 2013; Mao et al., 2019; Meng et al., 2018a, 2020). Be­
sides, risk analysis regarding the deepwater drilling risers have also been
performed (Nie et al., 2019). In the case of broken riser failure or in
extreme weather, the riser must be quickly disconnected from below the
LMRP to avoid damage to the riser or well structure (Lang et al., 2009).
Emergency disposal technology is an important tool to take corre­
sponding emergency measures and develop disposal strategies to com­
plete the emergency disposal project as soon as possible (Wei et al.,
2015). In recent years, many studies have contributed to emergency
disposal technology (Bruce et al., 2002; Wei, 2017; Qu and Hu, 2013).
Norrington et al. (2008) established Bayesian network model to solve
the reliability problem of maritime emergency force dispatching and
* Corresponding author.
E-mail address: changyj@upc.edu.cn (Y. Chang).
https://doi.org/10.1016/j.petrol.2021.108407
Received 1 December 2020; Received in revised form 11 January 2021; Accepted 12 January 2021
Available online 23 January 2021
0920-4105/© 2021 Elsevier B.V. All rights reserved.
Y. Chang et al.
Journal of Petroleum Science and Engineering 201 (2021) 108407
achieved good simulation results. Pang et al. (2017) analyzed the rela­
tionship between maritime emergency rescue forces and assessment
indicators, and built a rescue force assessment model, which effectively
improved the efficiency of maritime rescue. Meng et al. (2012) pre­
sented the principle, working process, applicable conditions, design
ideas and maturity of each deep water blowout emergency technology,
as well as the research focus of each emergency technology. Wang et al.
(2019) established the multi-objective optimization model of actual
arrival supplies and time under the conditions of insufficient supply and
sufficient supply to maximize the use of time and reduce supplies. Li
et al. (2019) analyzed the dispatch procedure of the emergency supplies
and proposed a joint dispatch model for offshore oil spill accidents.
However, studies for emergency disposal for drilling riser fracture ac­
cident rescue can be found sporadically in literatures.
PERT is a widely used method for measuring and controlling activity
progress in project. As a result of the attributes of PERT that it can deal
with the uncertainty of the operation activity time in the process of
project, some issues like project environment, the uncertain time of the
activities in the process of project implementation and uncertain factors
of the project itself can be solved (Fazar, 1959). Thus, PERT is gradually
applied to the calculation of project completion time, offshore engi­
neering construction, marine emergency rescue (Bates and Griffis, 2012;
Per, 2014). Li et al. (2019) combined with the PERT and job safety
analysis, presented a risk assessment system for deepwater drilling
operation. Wu et al. (2015) proposed the project duration risk evalua­
tion method based on PERT under the influence of multi-factors, and
analyzed the independent impact and portfolio impact of risk factors on
the project duration. Meng et al. (2019) used PERT to quantitatively
design the operation procedure of capping stack in Deepwater Horizon
blowout accident, ensuring that the whole operation was completed as
scheduled. Meng et al. (2018b) applied PERT to study the design of the
operation process and the mechanical model of working scenarios of the
LMRP cap system.
The risk analysis of riser failure in deepwater drilling has been
published (Chang et al., 2019b), which developed a model to identify
the hazards that may cause drilling riser fracture and to calculate dy­
namic failure probabilities of drilling riser fracture and failure proba­
bilities of consequences. The purpose of this paper is to make a further
study on the previous content, that is, the analysis of emergency disposal
after the accident. It is aimed at developing a PERT model for emergency
disposal of deepwater drilling riser fracture accident, which can be used
to quantitatively design the emergency disposal operation procedure
and determine the crucial path and total duration for emergency
disposal of drilling riser fracture accident. On this basis, optimization
measures were put forward to ensure that each process is completed as
soon as possible within the required time, to improve the completion
probability of accident emergency disposal, and to formulate the
optimal emergency plan.
The rest of the paper is structured as follows: Section 2 briefly
introduced PERT technique. In Section 3, the emergency disposal
methodology framework for fracture accident of drilling riser is pro­
posed. The PERT model of emergency control operation for riser fracture
accident and completion probability of accident emergency control
operation within time limit are presented in Section 4. Finally, the
present work is summarized in Section 5.
Fig. 1. Deepwater drilling riser system.
2. Program evaluation and review technique
2.1. PERT modeling process
The process of PERT network modeling is to decompose the project
into several more detailed operation activities, and design the network
according to the sequence of operation logic of each operation activity to
form the PERT network diagram. Then the time parameters of relevant
operation activities are calculated to determine the crucial path and
total duration of the operation based on the determined PERT network
Fig. 2. Drilling riser after fracture.
2
Y. Chang et al.
Journal of Petroleum Science and Engineering 201 (2021) 108407
model. Finally, by coordinating the time, human power and material
resources consumption of the relevant operation activities on the crucial
path, the operation time is shortened as much as possible to ensure that
the entire project is completed on schedule. The operation flow chart of
PERT is shown in Fig. 3.
2.2. PERT model basics
Fig. 4. Example of PERT network.
The PERT model is a network which uses directed lines with arrows
to connect the operation activities based on the sequence relationship of
operation activities. Fig. 4 shows an example of the PERT network
model.
PERT network chart is comprised of vertices (i.e., numbered circles,
also called events) and edges (i.e., solid and dotted arrows). The
numbered circles represent milestones (i.e., starting/finishing of activ­
ities). The solid arrows imply activities with corresponding estimated
durations. The dashed arrows indicate dummy activities. They serve as
pre-conditions to pointing milestones. For example, “2” and “3” in cir­
cles stand for the starting and finishing of activity “B”. “B 3” indicates
that the estimated duration of activity “B” is 3 h. The dashed arrow
between the numbered circles “3” and “5” represents that the activity
“F” can only start after the completion of the activities “B” and “E”. A
route starting at the numbered circles “1” and ending at “8” is called
path, and the path with the longest total operation time is called the
crucial path of the PERT network chart, and the activities on the crucial
path are called the crucial activity.
{
{
tE (1) = 0 {
}
tE (j) = max tE (i) + t(i,j) (j = 2, …, n)
(1)
tL ((n)
) = tE (n)
( ( )
} (
)
i = n − 1, …, 1
tL i = min tL j − t(i,j)
(2)
Where tE(1) and tE(n) represent the earliest start time of the total start
event and total finish event, respectively. tL(n) represents the latest
finish time of the total finish event and t(i,j) implies the activity duration
time.
(2) Time parameters of activity: Each activity in the PERT network
has six time parameters:
2.3. The time parameters calculation of PERT model
In PERT, several characteristic variables are defined to clarify the
logical relationships and estimated time of sub-activities (Frederick and
Gerald, 2006; Meng et al., 2018b; Winston and Goldberg, 2004):
(1) Time parameters of event: Each event in the PERT network has
two time parameters: the earliest start time and the latest finish
time of the event, which can be expressed as: tE(j) and tL(i).
tES (i, j) = tE (i)
(3)
tEF (i, j) = tE (i) + t(i,j)
tEF (i, j) = tES (i, j) + t(i,j)
(4)
tLF (i, j) = tL (j)
(5)
tLS (i, j) = tL (i) − t(i,j)
tLS (i, j) = tLF (i, j) − t(i,j)
(6)
Fig. 3. The operation flow chart of PERT.
3
Y. Chang et al.
Journal of Petroleum Science and Engineering 201 (2021) 108407
R(i, j) = tLS (i, j) − tES (i, j)
R(i, j) = tLF (i, j) − tEF (i, j)
(7)
r(i, j) = tE (j) − tES (i, j) − t(i,j)
r(i, j) = tE (j) − tEF (i, j)
(8)
where k is the last activity, Tk is the total project time, which follows the
Gaussian distribution. Tc(k) is the expectation of the earliest finish time
for the last activity. σ2Tc(k) is the variance of the total activity completion
time.
3. Proposed emergency disposal framework for drilling riser
fracture accident
where tES(i,j) and tEF(i,j) stand for the earliest activity start and finish
time, respectively, tLF(i,j) and tLS(i,j) represent the latest allowable ac­
tivity finish and start time, respectively, R(i,j) indicates the total activity
slack, which measures the excess time available to complete a project, r
(i,j) represents the activity free slack, with positive values indicating that
the task is ahead of schedule, negative values implying that the activity
is behind the schedule and with zero values revealing that the activity is
on time.
Based on the expected and variance time of activities, the probability
of the project for meeting the scheduled date (i.e., the deadline) can be
obtained. They are defined as (Meng et al., 2018b, 2019; Winston and
Goldberg, 2004):
Tij =
a + 4b + c
6
(9)
σ 2i,j =
(c − a)2
6
(10)
Since time is a key factor during the emergency rescue process, it is
helpful to quantitatively design the emergency response procedure.
Considering the continuity of accident evolution process of fracture
failure and the necessity of emergency disposal of accident, the proposed
methodology framework shown in Fig. 5 involved the following five
main steps.
1) Collecting necessary information. In this step, the necessary infor­
mation of the deepwater drilling riser fracture accident is collected,
including data information at all stages, empirical knowledge from
research paper and the tacit knowledge from domain experts, which
should have been collected first in order to provide a basis for
emergency response.
2) Model development. The purpose of this stage is to develop a
definitive PERT model after an accident. It includes two aspects, i.e.
determination of logical relationship, and duration time. Consider
the logical relationships and duration of the related activities and
integrate them into a PERT network model according to the corre­
sponding rules.
3) Model analysis. Calculate the element parameters according to the
above model. The total activity slack and the activity free slack are
calculated by PERT model. According to the above calculation time
where Tij is the expected time of the activity (i, j), a is the optimistic time,
b is the most likely time, and c is the pessimistic time. It is assumed that
Tij = b, that is, a + c = 2b. σ 2i,jis the variance of time. The probability of a
project for meeting scheduled date Tdk is:
)
(
∫ Tdk ( ( )
)
Tdk − Tc (k)
N Tc k , σ2Tc(k) dt = Φ
(11)
P(Tk ≤ Tdk ) =
− ∞
σTc (k)
Fig. 5. Methodology framework for emergency disposal of drilling riser fracture accident.
4
Y. Chang et al.
Journal of Petroleum Science and Engineering 201 (2021) 108407
to determine the critical path, get the total project time. Based on the
relevant time parameters, the duration and variance of a process on
the critical path are calculated to obtain the total expectation and
variance of the emergency response and completion operation, and
finally the probability of completion of the corresponding operation
process within the specified time is calculated, which provide time
basis for the subsequent optimization scheme.
4) Propose the optimization to make the critical path complete on time
and improve the completion probability. The calculation results and
conclusions of the above steps can provide reference for the deter­
mination of the emergency plan, and on this basis, update the key
route, select the optimal scheme, shorten the construction period,
and improve the completion probability of accident emergency
control operation within time limit to reduce the severity and con­
sequences of riser fracture failure.
4. Case study
4.1. Analysis of emergency control operation of riser fracture accident
Fig. 7. Riser joint leans against the BOP adjacent to control lines.
This section takes the drilling riser fracture accident of the Drilling
ship Discoverer Enterprise in the Gulf of Mexico on May 21, 2003 as an
example and conducts PERT emergency control operation research on
riser rupture accident.
The drilling riser fracture accident scenario is shown as follows: On
May 21, 2003, a fracture accident of drilling riser occurred during the
drilling operation of dynamic positioning drilling ship at the water depth
of 1875m in the Gulf of Mexico. The riser rupture caused a powerful riser
recoil on the top tension provided by the tensioner system. The riser
recoil damaged the hull, equipment in the recoil path, and further
fractured the drilling riser. Subsequently, the remotely operated
Remotely Operated Vehicle (ROV) was deployed and it was found that
the drilling riser broke at an underwater depth of 975.36 m and was
suspended from the drilling ship. Then the second fracture was then
found at the 1860m ROV, which was located on the upper part of the
LMRP at the top of the BOP. Both the riser and drill pipe were broken.
Riser-joint number 1 was resting against the BOP close to the control
lines that operate the stack (Fig. 6) (Kirton et al., 2004).
In addition, about 580 m of risers were still connected and scattered
around the center of the well, either buried in mud or lying on the
seabed and on the wellhead of the abandoned development well, and the
risers also rested on the control line of the blowout preventer’s shut­
down stack, threatening wellhead safety at any time, as shown in Fig. 7
(Kirton et al., 2004). Besides, 275 m risers still stood vertically on the
seabed around the broken drill pipe. Drilling fluid spilled from multiple
locations and 2450 barrels of synthetic based drilling fluid was released.
The primary task after the accident is to carry out the emergency
control of riser fracture accident and to prevent it from developing in a
more unfavorable direction. Therefore, in order to efficiently and timely
complete the riser fracture accident emergency control operation target,
using the PERT analysis to determine a series of emergency control
operation process, through the reasonable process adjustment, resource
allocation, accident emergency control in the shortest possible time to
achieve, to control the development of accident control, and ensure the
accident loss minimized.
In view of the occurrence of the deepwater drilling riser fracture
accident, the first time for emergency control should be lowered to ROV
to observe the fracture of the riser, and then the salvage vessels should
be mobilized to salvage the drilling riser string that may cause two
damage to the wellhead. Subsequently, because the underwater BOP has
been damaged, the automatic shut in function cannot be realized at this
time, in order to effectively control the underwater wellhead, it is
necessary to further cut the LMRP part to level the wellhead and prepare
for the installation of simple BOP group. The cutting operation is shown
in Figs. 8 and 9 (Kirton et al., 2004). Finally, the installation and
commissioning of the simple BOP group are completed, and the well
shut-in operation is completed to control the riser fracture accident
within the controllable range. Therefore, the emergency control opera­
tion of riser fracture accident mainly includes three main sub tasks:
Fig. 6. Top of the Lower Marine Riser Package (LMRP) after riser fracture.
Fig. 8. ROV circular saw cut away the riser auxiliary line.
5
Y. Chang et al.
Journal of Petroleum Science and Engineering 201 (2021) 108407
Table 1
Completion time and relations of emergency control operation.
Symbol
Name of the
activity
Preceding
activities
Duration/
h
Time can
be
shortened/
h
Increased
costs (ten
thousand
dollar/h)
A
Lower the
ROV and
observe the
riser fracture
Pull the bent
drillpipe
Reposition the
original
drilling vessel
away from the
primary drill
center
Mobilize
rescue drilling
vessel
Position
rescue drilling
vessel to
drilling center
Install
expansion
packer at the
fracture of
suspended
riser of
original
drilling vessel
Inject water
base mud into
the suspended
riser
Recovery of
suspended
riser
Lower circular
saw cutting
tool
Cut LMRP
upper riser
auxiliary line
Lower
diamond
cutting tool
Cut riser
above LMRP
Separate
LMRP from
original BOP
Retrieve
LMRP
Lower the
simple BOP
Stack
Lower the
accumulator
and control
system
Debug the
simple BOP
group on the
seabed
Install a
simple BOP
Stack
Determine
shut-in
strategy
Close the
simple BOP
Stack
–
9
4.5
6.5
A
12
6.5
7
B
5
3.5
7
–
15
2
9
C, D
6
2.5
7.5
C
11
2
7
F
4
2
9.5
G
10
2
9
E
8
1.5
7.5
I
2
–
–
I
8
1.5
8
J, K
5
0.5
7
L
2
–
–
M
48
8
10
E
15
3.5
7
E
12
2
7
O, P
5
1
5
M, Q
3
–
–
R
6
–
–
S
2
–
–
H
10
2
B
C
D
Fig. 9. Diamond wire saw used to cut riser.
E
recovery of fractured drilling riser, leveling of accident wellhead,
installation and closing of simple BOP, and then based on the specific
subtasks, the more detailed operation process is divided. According to
the accident report and marine emergency rescue experience, combined
with the emergency response situation of the accident, the operation
efficiency of the operators and the relevant equipment of the existing
offshore platform, the completion time and operation relationship of the
emergency control operation for the riser fracture accident can be ob­
tained, as shown in Table 1.
F
G
4.2. PERT chart for emergency control operation of riser fracture accident
H
4.2.1. PERT of emergency control operation
After the relationship between the emergency control operation
procedure and the operation procedure of the riser fracture accident is
determined, according to the drawing rules of the above PERT diagram
and the relationship between the emergency control operation proced­
ure and the operation procedure of the riser fracture accident in Table 1,
the PERT diagram of the emergency control operation of the riser frac­
ture accident can be drawn as shown in Fig. 10.
I
J
K
L
4.2.2. Operation time parameters
After the PERT diagram of emergency control operation of riser
fracture accident is determined, the parameters of emergency control
operation time of riser fracture accident can be calculated according to
the planned completion time of operation procedure given in Table 1
and the relevant formulas in Section 2.3.
Let tES(1,2) = tES(1,8) = 0. It is assumed that all work should be
finished within 96 h, namely, tLF(7,20) = tLF(14,20) = tLF(19,20) = 96.
The calculation process of the PERT network is shown in Table 2.
M
N
O
P
4.3. Emergency control operation design for fracture accident of drilling
riser
Q
4.3.1. Critical path of accident emergency control operations
Because the total time difference of the working procedures with
codes A, B, C, E, I, K, L, M and N is negative, and the route composed of
them takes the most time, the critical route for emergency control of
riser fracture accident is A-B-C-E-I-K-L-M-N, as shown in Fig. 11.
The sum of the working time on the critical path is duration. Its
duration is 103 h, which is more than the supposed 96 h, and the time of
the critical path needs to be shortened. It is recommended to fulfill the
emergency operation on time by mobilizing rescue drilling vessel,
pulling out the bent drill pipe, shortening the time of lowering drilling
riser cutting tool, and recovering LMRP.
R
S
T
U
8
(continued on next page)
6
Y. Chang et al.
Journal of Petroleum Science and Engineering 201 (2021) 108407
In addition, the emergency control operation design of riser fracture
accident will enter the field implementation stage after four steps: PERT
diagram drawing, time parameter calculation, critical route determi­
nation and operation completion probability calculation. Due to the
harsh marine operating environment and sudden accidents, emergency
control on-site operations often need to be adjusted in time according to
feedback. If there is a need to adjust the operation during the on-site
operation, it is necessary to re-adjust the design of the emergency con­
trol operation, otherwise the whole emergency control operation will be
completed in turn until the end of the accident emergency control
activity.
Table 1 (continued )
Symbol
Name of the
activity
Preceding
activities
Duration/
h
Time can
be
shortened/
h
Increased
costs (ten
thousand
dollar/h)
Salvage the
rest of the
riser string
scattered on
the sea bed
4.3.2. Probability of completion of accident emergency control operation
By using the PERT diagram to design the emergency control opera­
tion flow of the riser fracture accident, the critical path of the emergency
control operation flow of the accident is obtained, and then the timely
completion can be ensured by adjusting the duration of the operation
process on the critical path. Therefore, determining the completion
probability of emergency operations within the specified time limit is of
great value for emergency planning and rescue decision-making.
First of all, the expected duration Tii and variance σ 2i,j of a certain
process on a critical path are calculated according to Eqs. (9) and (10). In
order to simplify the calculation in the emergency control accident
environment, it is assumed that t(i,j) is equal to the most probable time b,
that is a+b = 2c. The expectation and variance of the completion time of
critical path operation for emergency control of riser fracture accident
are shown in Table 3. Then according to the total expectation and total
variance of the completion time of the critical route, combined with Eq.
(11), the completion probability of the emergency control operation of
the riser fracture accident within the specified time limit Tdk is
calculated.
The earliest realization time of the whole emergency control oper­
ation (item 20) Tc (20) is the sum of the expected completion time of the
critical path operation, which is equal to 103 h. When the prescribed
time limit is 85–120 h respectively, the completion probability of
emergency control operation of riser fracture accident in different
specified periods can be obtained by Eq. (11), as shown in Table 4 and
Fig. 12. With the increase of the prescribed time limit of the emergency
control operation, the probability of completion of the operation in­
creases, on the contrary, it decreases, and the growth rate is the highest
near the total duration of the critical path. The probability of completion
of emergency control operation of riser fracture accident should be
improved according to the suggestion of operation optimization, and the
duration of operation process should be reduced within a certain range
near the total length of critical path, which can reasonably reduce the
probability of completion of emergency control operation, so as to
improve the efficiency of emergency control.
Table 2
Computational table of PERT for emergency control operation.
Symbol
Activity
(i, j)
t (i,
j)
t ES
(i, j)
t EF
(i, j)
t LS
(i, j)
t LF
(i, j)
R (i,
j)
F (i,
j)
A
D
B
C
F
Dummy
activity
G
H
U
E
I
O
P
J
K
Dummy
activity
L
M
Dummy
activity
N
Dummy
activity
Q
R
S
T
(1,
(1,
(2,
(3,
(4,
(4,
2)
8)
3)
4)
5)
8)
9
15
12
5
11
0
0
0
9
21
26
26
9
15
21
26
37
26
− 7
4
2
14
61
19
2
19
14
19
72
19
− 7
4
− 7
− 7
35
− 7
0
11
0
0
0
0
(5, 6)
(6, 7)
(7, 20)
(8, 9)
(9, 10)
(9, 15)
(9, 16)
(10, 11)
(10, 12)
(11, 12)
4
10
10
6
8
15
12
2
8
0
37
41
51
26
32
32
32
40
40
42
41
51
61
32
40
47
44
42
48
42
72
76
86
19
25
65
68
39
33
41
76
86
96
25
33
80
80
41
41
41
35
35
35
− 7
− 7
33
36
− 1
− 7
− 1
0
0
35
0
0
0
3
0
0
6
(12, 13)
(13, 14)
(14, 17)
5
2
0
48
53
55
53
55
55
41
46
85
46
48
85
− 7
− 7
30
0
0
0
(14, 20)
(15, 16)
48
0
55
47
103
47
48
80
96
80
− 7
33
− 7
0
(16, 17)
(17, 18)
(18, 19)
(19, 20)
5
3
6
2
47
55
58
64
52
58
64
66
80
85
88
94
85
88
94
96
33
30
30
30
3
0
0
30
Fig. 10. PERT of emergency control operation in drilling riser fracture accident.
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Journal of Petroleum Science and Engineering 201 (2021) 108407
Fig. 11. Critical path of PERT for emergency control operation in drilling riser fracture accident.
4.4. Optimization of PERT network
Table 3
Expectation and variance of critical path operation completion time.
Symbol
Activity (i,
j)
Estimated duration
(a-b-c)/h
Expected
duration/h
Variance
A
B
C
Dummy
activity
E
I
K
L
M
N
(1, 2)
(2, 3)
(3, 4)
(4, 8)
6-9-12
7.5-12-16.5
3-5-7
0
9
12
5
0
1.0000
2.2500
0.4444
0
(8, 9)
(9, 10)
(10, 12)
(12, 13)
(13, 14)
(14, 20)
4.5-6-7.5
5.5-8-10.5
5.5-8-10.5
3-5-7
1.5-2-2.5
35-48-61
6
8
8
5
2
48
0.2500
0.6944
0.6944
0.4444
0.0278
18.7778
4.4.1. New critical path
The optimization of network plan refers to shortening the whole
construction period through some measures. Usually shortening the
construction period is to increase the cost, and the goal of optimization is
to minimize the increase in cost. The sum of the working time on the
critical path is the minimum time required to complete the whole
project. Therefore, the activities on the critical path play a key role in the
whole project.
The critical path of emergency control operation is C – D – E − F, as is
shown in Fig. 13. The activity with the minimum marginal cost is A
[6.5], and the duration of the project needs to be shortened:
Table 4
Completion probability of emergency control operation within time limit.
Time limit
Tdk/h
85
90
95
100
105
110
115
120
Completion probability P
0.0001
0.0039
0.0505
0.2709
0.6591
0.9236
0.9929
0.9997
Fig. 12. Completion probability of accident emergency control operation within time limit.
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Journal of Petroleum Science and Engineering 201 (2021) 108407
Fig. 13. New critical path of PERT.
⎧
⎫ ⎧
⎫
⎨ the duration needs to be shortened ⎬ ⎨ 7 ⎬
Δt = min the activity can shortened at most
= 4.5
⎩
⎭ ⎩
⎭
the new critical path
4.5
Table 6. With the increase of the prescribed time limit of the emergency
control operation, the probability of completion of the operation in­
creases, on the contrary, it decreases, and the growth rate is the highest
near the total duration of the critical path. The completion probability
before and after optimization is compared in Fig. 14. After the optimi­
zation of the operation process, the completion probability increases
correspondingly in each specified time limit, especially near the con­
struction period, and the completion probability is greatly improved.
In addition, the following measures can be taken to shorten the
construction period. Check whether the time of each activity is reason­
able, and if it is too long, consider shortening it. Further subdivide the
jobs on the critical path and adopt the method of multi-station or par­
allel operation. Allocate resources on non-critical paths to support op­
erations on critical paths. Redesign the workflow and change the PERT
network structure diagram. Due to the harsh marine operating envi­
ronment and sudden accidents, emergency control on-site operations
often need to be adjusted in time according to feedback.
= 4.5h
If activity time fail to meet the requirements of the construction
period, the adjustment should be continued.
After shortening activity A, the activity with the minimum marginal
cost is B [7]. And after adjusting the network diagram, D is the critical
activity on the new network diagram, as shown in Fig. 13, and the
duration of the project needs to be shortened:
⎧
⎫
⎨ 2.5 ⎬
Δt = min 6.5 = 2.5h
⎩
⎭
5
The cumulative cost:
4.5 × 6.5 + 6.5 × 7 = 0.7475 million dollars.
4.4.2. Probability of completion
The new critical path is obtained by adjusting the time of activities
on the longest path in the PERT network. The expected duration Ti and
variance σ2i,j of a certain process on the new critical path are calculated
according to Eqs. (9) and (10). The expectation and variance of the
completion time of new critical path operation for emergency control of
riser fracture accident are shown in Table 5. Then according to the total
expectation and total variance of the completion time of the critical
path, combined with Eq. (11), the new completion probability of the
emergency control operation of the riser fracture accident within the
specified time limit Tdk’ is calculated.
After path adjustment, the earliest realization time (item 20) is the
sum of the expected completion time of the critical path operation,
which is equal to 96 h. That is, the specified time. When the prescribed
time limit is 85–120 h respectively, the new completion probability in
different specified periods can be obtained by Eq. (11), as shown in
5. Summary and conclusions
Based on the plan review technology, a novel PERT network is
developed for emergency disposal technique for fracture failure of
deepwater drilling riser. According to the logical relationship and
duration of the process, the emergency disposal plan for the fracture
failure of drilling riser is figured out, and the PERT network diagram is
drawn to characterize the emergency disposal process of the accident.
Further, calculate the probability that the emergency disposal plan will
be completed within the specified time limit. It provides a reference for
time optimization measures and emergency treatment of fracture failure
accident of deepwater drilling riser.
The present study indicates that the proposed model could be effi­
ciently applied to emergency disposal for fracture failure of drilling
riser. It includes 21 sub-operation procedures, and the total duration of
the key route is 103 h. The network shows that A (Lower the ROV and
observe the riser fracture), B (Pull the bent drillpipe), C (Reposition the
original drilling vessel away from the primary drill center), E (Position
rescue drilling vessel to drilling center), I (Lower circular saw cutting
tool), K (Lower diamond cutting tool), L (Cut riser above LMRP), M
(Separate LMRP from original BOP) and N (Retrieve LMRP) are critical
activities for the emergency disposal plan. Meanwhile, the correspond­
ing completion probability of accident emergency disposal is calculated
when the construction period is 103 h and the prescribed time limit is
85–120 h, it can be found that the completion probability increases with
the increase of the specified time, and the growth rate of completion
probability is the largest near the total length of the critical path.
According to the network diagram, combined with the activity cost,
the duration of activities A, B, C is reduced, and the timescale is
Table 5
Expectation and variance of new critical path operation completion time.
Symbol
Activity(i,
j)
Estimated duration
(a-b-c)/h
Expected
duration/h
Variance
D
Dummy
activity
E
I
K
L
M
N
(1, 8)
(4, 8)
10-15-20
0
15
0
2.7778
0
(8, 9)
(9, 10)
(10, 12)
(12, 13)
(13, 14)
(14, 20)
4.5-6-7.5
5.5-8-10.5
5.5-8-10.5
3-5-7
1.5-2-2.5
35-48-61
6
8
8
5
2
48
0.2500
0.6944
0.6944
0.4444
0.0278
18.7778
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Journal of Petroleum Science and Engineering 201 (2021) 108407
Table 6
New Completion probability of emergency control operation.
Time limit
Tdk’/h
85
90
95
100
105
110
115
120
Completion probability P′
0.0119
0.1093
0.4168
0.7939
0.9678
0.9980
0.9999
0.9999
Fig. 14. Comparison of completion probability.
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CRediT author statement
Yuanjiang Chang: Conceptualization, Methodology, Writing – review
& editing; Yajie Jiang: Software, Writing – original draft; Changshuai
Zhang: Visualization, Data curation; Anti Xue: Investigation, Resources;
Bin Chen: Supervision, Data curation; Weiguo Zhang: Software, Vali­
dation; Liangbin Xu: Investigation, Resources; Xiuquan Liu: Project
administration; Yongguo Dai: Investigation, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgement
Authors gratefully acknowledge the financial support provided by
National Natural Science Foundation of China (52071337) and Key
Project of Natural Science Foundation of China (51890914).
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