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Data-driven dynamic risk analysis of offshore drilling operations
Journal of Petroleum Science and Engineering 165 (2018) 444–452
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Data-driven dynamic risk analysis of offshore drilling operations Sunday A. Adedigba, Olalere Oloruntobi, Faisal Khan *, Stephen Butt Centre for Risk, Integrity and Safety Engineering (C-RISE), Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John's, NL A1B 3X5, Canada
A R T I C L E I N F O
A B S T R A C T
Keywords: Dynamic failure probability Risk analysis Blowouts Drilling Bayesian tree augmented naive Bayes (TAN)
A data-driven dynamic risk analysis methodology is proposed here. The methodology is applied to offshore drilling operations. Modern drilling rigs are highly instrumented to monitor real time operational data. This provides sufficient data for time dependent risk analysis of drilling operations. The probabilistic relationships (structure) among the primary operational (drilling) parameters are modelled using the Bayesian Tree Augmented Naïve Bayes (TAN) algorithm. The developed model is used to predict time dependent probability of kick, and is continuously updated based on the current state of the key drilling parameters. The real-time probability of kick is used to model blowout risk as a function of time. The dynamic risk profile generated from the model is useful in operational decision making to prevent accidents and enhance the safety of drilling operations. The proposed dynamic risk methodology is tested and verified using actual drilling operational data.
1. Introduction The complexity and sophistication of the current process systems have greatly improved their productivity. However, this advancement in modern process systems presents a significant risk of failure along with their versatility and productivity (Yu et al., 2015; Adedigba et al., 2017a). Risk analysis is defined as “the process of characterizing, managing and informing others about the existence, nature, magnitude, prevalence, contributing factors and uncertainties of the potential losses” (Modarres, 2006). The static nature of conventional quantitative risk assessment (QRA) methods has limited their application in modelling and predicting risk variations during the operation of process systems (Yang et al., 2015). However, dynamic risk analysis provides a framework that captures risk variation during the operation. Khan et al. (2016) defined dynamic risk assessment “as a method that updates estimated risk of a deteriorating process according to the performance of the control system, safety barriers, inspection and maintenance activities, the human factors and procedure”. Various methods have been applied for executing a dynamic risk analysis of process systems. Detailed information about these methods can be found in (Al-shanini et al., 2014; Aven, 2016; Durga Rao et al., 2009; Kalantarnia et al., 2010; Khakzad et al., 2012; Khan and Abbasi, 1998; Khan et al., 2016; Paltrinieri et al., 2013; Adedigba et al., 2016a,b). An accident model offers thorough information about how and why process accidents occur and is a very important tool for implementing process risk assessment. Different types of process accident models have
been developed over the years. (Attwood et al., 2006; Adedigba et al., 2016a,b; Qureshi, 2007; Rathnayaka et al., 2010). However, most of these models do not take into consideration the dependency of the process variables and these process monitoring data are not used in these models. Offshore drilling, and in particular deep water drilling operations, is associated with high risk and a high cost of operation. One of most devastating accidents with severe consequences in the offshore oil and gas industry is a blowout, such as the Macondo blowout accident. Accident records have revealed that the majority of offshore blowouts have occurred during the drilling phase (Xue et al., 2013). A blowout is an unrestrained flow of gas and oil (hydrocarbons) to the environment (Khakzad et al., 2013). Many blowout accidents have occurred in offshore drilling operations around the globe. The most recent and most devastating environmental disaster in U.S history is the Macondo blowout of 20 April 2010. This accident was caused by a series of technical factors (Rathnayaka et al., 2013). Safety management of offshore drilling operations demands continuous monitoring of the safety performance and safety indicators of the system. Safety indicators provide information about the level of safety in a system to decision makers so the decision makers can activate safety systems whenever the level of safety in the system is below the acceptable range (Skogdalen et al., 2011). Most of the approaches adopted in risk analysis of offshore drilling operations are analytical methods (Khakzad et al., 2013; Kujath et al., 2010; Skogdalen et al.,
* Corresponding author. E-mail address: fi[email protected] (F. Khan). https://doi.org/10.1016/j.petrol.2018.02.049 Received 6 November 2017; Received in revised form 16 February 2018; Accepted 20 February 2018 Available online 23 February 2018 0920-4105/© 2018 Elsevier B.V. All rights reserved.
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Journal of Petroleum Science and Engineering 165 (2018) 444–452
Fig. 1. The flowchart for the proposed methodology.
(FP). Also, management and organizational error are adequately accounted for in the model. This paper is organised as follows. Section 2 discusses monitoring, prevention and control of well blowout. Section 3 presents the data driven dynamic risk analysis methodology. Section 4 provides the testing and verification of the proposed data driven risk assessment methodology with actual well specific data. The results and discussion are presented in section 5. Finally, the conclusion is given in Section 6.
2011; Xue et al., 2013). However, analytical techniques do not take into consideration the probabilistic dependencies (structure) among well specific data. The primary objective of the study is to develop a data-driven dynamic model for dynamic risk assessment. The developed model is demonstrated on an offshore drilling operation using the probabilistic relationships (structure) among actual industrial well-specific data such as bottom hole pressure (BHP), pore pressure (PP) and fracture pressure 445
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Fig. 2. BN structure constructed from well specific data.
Table 1 Failure probability of prevention barriers and control (Rathnayaka et al., 2013). Prevention barrier
Failure probability
Well control barrier (WCB) Influx mitigation barrier (IMB) Ignition prevention barrier (IPB) Escalation prevention barrier (EPB) Emergency management (EMB) Management and organization barrier (M &OB)
0.0713 0.0643 0.1377 0.1110 0.1088 0.1207
Table 2 The likelihood of kick from well specific data and time dependent probability of kick based on TAN BN model.
2. Monitoring, prevention, and control of blowouts The inflow of formation fluid (oil, gas water or mixture) into the wellbore is referred to as kick; the associated fluid is termed kick fluid (Azar and Samuel, 2007). During a drilling operation, the drilling mud is used as the well's primary safety barrier to ensure that the wellbore's bottom hole pressure (BHP) is higher than the pore pressure (PP) and at the same time less than fracture pressure (Fp). This relationship among these vital drilling parameters must be maintained to prevent the formation fluids from flowing into the wellbore and to ensure the formation is not fractured (Khakzad et al., 2013). Mathematically, this condition can be expressed as: Pp < BHP < F P
(1)
However, kick will occur whenever the differential pressure ΔP is negative. Mathematically ΔP can be expressed as: ΔP ¼ BHP PP
(2)
Depending on the algebraic value of ΔP, one of these conditions may result (Azar and Samuel, 2007). ΔP > 0; over balance condition no kick:
(3)
ΔP ¼ 0; balance condition no kick:
(4)
ΔP < 0; underbalance condition kick:
(5)
Time (hr)
The likelihood of kick from well specific data (CDF)
Time dependent probability of kick based on TAN BN model structure
0 5.25 6.25 7.25 11.75 14.5 46.3 53.3 73.05 75.8 77.3 77.55 149.3 161.05 167.05 185.05 188.05 224.8 233.05 257.05 281.05 287.05 305.05 310.3 397.8 400.05 405.55 433.55 434.05 438.3 439.8 440.55 442.05 458.05 466.05
3.1381E-02 3.1381E-02 3.1381E-02 3.1381E-02 2.6739E-02 3.1297E-02 3.1297E-02 4.8249E-02 4.1518E-02 5.7900E-02 5.7900E-02 8.4136E-02 8.4136E-02 8.4136E-02 1.3326E-01 1.1772E-01 1.3604E-01 1.3604E-01 1.3604E-01 1.3604E-01 1.4156E-01 1.4431E-01 1.2217E-01 1.0863E-01 1.0863E-01 6.8576E-01 6.8576E-01 1.0863E-01 1.5769E-01 1.5769E-01 1.4917E-01 1.4917E-01 1.3326E-01 1.3326E-01 1.3326E-01
1.1208E-03 1.1208E-03 1.1208E-03 1.1208E-03 9.5496E-04 1.1178E-03 1.1178E-03 1.7232E-03 1.4828E-03 2.0679E-03 2.0679E-03 3.0049E-03 3.0049E-03 3.0049E-03 4.7593E-03 4.2043E-03 4.8586E-03 4.8586E-03 4.8586E-03 4.8586E-03 5.0557E-03 5.1539E-03 4.3632E-03 3.8796E-03 3.8796E-03 2.4491E-02 2.4491E-02 3.8796E-03 5.6318E-03 5.6318E-03 5.3275E-03 5.3275E-03 4.7593E-03 4.7593E-03 4.7593E-03
2.1. Blowout
3. Data-driven dynamic risk analysis methodology
Usually, a kick propagates to a blowout due to either failure of secondary barriers or as a result of non-detection of the kick, which prevents the activation of kick preventing barriers.
The flowchart for the proposed methodology is given in Fig. 1. This methodology is explained using a drilling operation as an example. 446
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Fig. 3. Revised event tree for the proposed methodology (Rathnayaka et al., 2013).
3.1. Hazard identification and analysis
3.2. Failure probability assessment of safety barriers
This step involves identification of all the possible hazards and events that could initiate an undesired event. In this phase, many hazard identification techniques can be applied, as reviewed by Khan et al. (1998). Accident scenarios also need to be generated; this provides the opportunity of identifying all the relevant safety barriers required to place along potential accident's path to prevent or reduce the advancement of the accident process, because the failure of prevention or safety barriers results in an accident (Rathnayaka et al., 2011). Hazard identification and analysis of an offshore drilling operation is carried out to generate an accident scenario and identify necessary safety barriers to be put in place to avert or prevent a blowout.
Fault tree analysis is a widely used tool for estimating or predicting the reliability of highly complex systems. In fault tree analysis, a deductive graphical model is used to detect the potential causes of undesired events (Adedigba et al., 2016a,b). The construction of a fault tree starts by determining the undesired top event in the fault tree. Thereafter, all other combinations of the undesired top events likely to take place are deductively modelled downwards till the root cause or primary events that instigate the occurrence of the top event are detected. The most widely used logics in fault tree analysis are OR logic and AND logic. The occurrence probability of an undesired top event is computed based on the reliability data of basic or primary events. Analysis using the fault tree can be accomplished in various ways: qualitatively, quantitatively and, for some cases, a combination of both 447
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Table 3 The occurrence probability of end state consequence. Time (hr.)
Safe
Kick
Blowout
Fire & explosion
Catastrophic
0 5.25 6.25 7.25 11.75 14.5 46.3 53.3 73.05 75.8 77.3 77.55 149.3 161.05 167.05 185.05 188.05 224.8 233.05 257.05 281.05 287.05 305.05 310.3 397.8 400.05 405.55 433.55 434.05 438.3 439.8 440.55 442.05 458.05 466.05
1.0409E-03 1.0409E-03 1.0409E-03 1.0409E-03 8.8688E-04 1.0381E-03 1.0381E-03 1.6003E-03 1.3771E-03 1.9204E-03 1.9204E-03 2.7906E-03 2.7906E-03 2.7906E-03 4.4199E-03 3.9045E-03 4.5122E-03 4.5122E-03 4.5122E-03 4.5122E-03 4.6952E-03 4.7865E-03 4.0521E-03 3.6030E-03 3.6030E-03 2.2745E-02 2.2745E-02 3.6030E-03 5.2302E-03 5.2302E-03 4.9476E-03 4.9476E-03 4.4199E-03 4.4199E-03 4.4199E-03
7.4772E-05 7.4772E-05 7.4772E-05 7.4772E-05 6.3711E-05 7.4571E-05 7.4571E-05 1.1496E-04 9.8925E-05 1.3796E-04 1.3796E-04 2.0047E-04 2.0047E-04 2.0047E-04 3.1752E-04 2.8049E-04 3.2414E-04 3.2414E-04 3.2414E-04 3.2414E-04 3.3729E-04 3.4385E-04 2.9109E-04 2.5883E-04 2.5883E-04 1.6340E-03 1.6340E-03 2.5883E-04 3.7573E-04 3.7573E-04 3.5543E-04 3.5543E-04 3.1752E-04 3.1752E-04 3.1752E-04
4.9838E-06 4.9838E-06 4.9838E-06 4.9838E-06 4.2465E-06 4.9704E-06 4.9704E-06 7.6626E-06 6.5936E-06 9.1953E-06 9.1953E-06 1.3362E-05 1.3362E-05 1.3362E-05 2.1163E-05 1.8696E-05 2.1605E-05 2.1605E-05 2.1605E-05 2.1605E-05 2.2482E-05 2.2918E-05 1.9402E-05 1.7252E-05 1.7252E-05 1.0891E-04 1.0891E-04 1.7252E-05 2.5043E-05 2.5043E-05 2.3690E-05 2.3690E-05 2.1163E-05 2.1163E-05 2.1163E-05
1.3746E-07 1.3746E-07 1.3746E-07 1.3746E-07 1.1713E-07 1.3709E-07 1.3709E-07 2.1135E-07 1.8187E-07 2.5363E-07 2.5363E-07 3.6855E-07 3.6855E-07 3.6855E-07 5.8374E-07 5.1566E-07 5.9591E-07 5.9591E-07 5.9591E-07 5.9591E-07 6.2009E-07 6.3214E-07 5.3516E-07 4.7585E-07 4.7585E-07 3.0039E-06 3.0039E-06 4.7585E-07 6.9075E-07 6.9075E-07 6.5343E-07 6.5343E-07 5.8374E-07 5.8374E-07 5.8374E-07
1.6993E-08 1.6993E-08 1.6993E-08 1.6993E-08 1.4479E-08 1.6947E-08 1.6947E-08 2.6126E-08 2.2482E-08 3.1352E-08 3.1352E-08 4.5559E-08 4.5559E-08 4.5559E-08 7.2159E-08 6.3744E-08 7.3665E-08 7.3665E-08 7.3665E-08 7.3665E-08 7.6654E-08 7.8143E-08 6.6154E-08 5.8822E-08 5.8822E-08 3.7133E-07 3.7133E-07 5.8822E-08 8.5388E-08 8.5388E-08 8.0774E-08 8.0774E-08 7.2159E-08 7.2159E-08 7.2159E-08
compute the standard deviation of mean pressure for each depth interval. This value is adapted considering the standard expected variation. The value is confirmed through expert opinions obtained using the structural Delphi method (Clayton, 1997). The opinion is given equal weight and subsequently aggregated. The cumulative distribution function (CDF) for each depth is estimated from equation (6). Here, t is the mud pressure for each depth, μ is the mean pressure for each depth and σ is the standard deviation for each step.
(Adedigba et al. 2016a,b; Khakzad et al., 2011). The safety barriers that are placed along the accident path to prevent or avert a blowout at an offshore drilling facility are systematically analysed using a fault tree to predict the occurrence probability of the undesired top events for each safety barrier. 3.3. Collecting actual well specific data for analysis In this phase, actual well specific data are collected and analysed for the purpose of learning the probabilistic relationships (structure) that exist among the data. Well specific data collected are displayed in the appendix. Due to the propriety issue, the source of this data is not disclosed by the authors. Linking this data to any source or organization is prohibited.
FðtÞ ¼ φ
tμ
σ
(6)
3.6. Structure learning of Bayesian network using states of well specific data
3.4. Deriving probability distribution (for well specific data) Bayesian networks are directed acyclic graphs usually used for reasoning under uncertainty. The BN is used to model the probabilistic relationship and interdependencies among parent and child nodes. The graphical part of the BN shows the structure of the problem under consideration and demonstrates the causal influences among the parent nodes and child nodes. The probabilistic relationships and interdependencies among the variables are represented using the conditional probability table (CTP) (Onisko et al., 2001). A BN possesses a strong capability to model complex systems and subsequently reduces parametric uncertainty by integrating new information whenever available. Therefore, BNs provide a unique opportunity to perform probability updating. The two main techniques to build or construct Bayesian networks are the knowledge driven technique and the data driven technique. The knowledge driven technique uses expert opinion and experience to draw the structure and conditional probability table of the BN. Principally,
A suitable probability distribution is derived from the well specific data, given in the appendix. The detailed methodology for obtaining probability distribution from given data is not presented here. The well specific data (presented in the appendix) is fitted to different distributions using a least square minimization approach. The fitted distributions are compared and selected using the Kolmogorov Smirnov test. In the present case, normal distribution is identified to be most appropriate. 3.5. Estimating the likelihood of unwanted kick situations The likelihood of kick is estimated from the well specific data, given in the appendix. The procedure for estimating the likelihood of kick is as follows: The mean pressure, which is the average of pore pressure and fracture pressure at each depth, is computed. For instance, at the depth of 3950 ft the mean pressure is 2271.3 psi. The covariance of 0.1 is used to 448
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procedure for using the TAN algorithm to learn the underlying BN structure and parameters of the structure (conditional probabilities) from data are given by (Adedigba et al., 2017b). This information is not presented here, to prevent replication. The objective of building a BN model from well specific data is to predict the time dependent probability of kick based on the probabilistic relationship among these variables. 3.7. Computing probability of kick using BN structure of well specific data The likelihoods of kick predicted from the well data using normal distribution are fed into the BN model structure shown in Fig. 2 to predict the time dependent probability of kick based on probabilistic dependencies that exist among well specific data. Detailed information on how to predict probability from BN model structure is presented by (Adedigba et al., 2017b, 2018). 3.8. Analysis of potential scenarios and computing end state probability of consequence at time (t) Analysis of the potential scenarios is carried out with event tree analysis. The event tree is an inductive logical technique that is widely used to denote incident scenarios. It begins with a particular accident instigating event and ends with every potential consequence of accident instigating events, usually called “end state consequences” of the event tree (Adedigba et al., 2016a,b). The event tree consists of two unique branches: the success and failure branch. These branches are used to predict the probability of success or failure of the safety barriers in the event tree and at the same time display the probable progression sequence of the accident instigating event to various potential consequences (Nývlt and Rausand, 2012; Adedigba et al., 2017b). The time dependent probabilities of kick predicted from the BN model developed from well specific data are used as an input to the event to quantify or estimate the occurrence probability of end state consequences. The probability of end state consequences in the event tree P (Ck) is computed by equation (7) (Ferdous et al., 2011). PðCK Þ ¼ λ x
n Y
Pi
(7)
i¼1
where λ is the probability of kick estimated from the BN model, n the number of safety barriers, and Pi is the failure probability of the safety barrier. 4. Case study: offshore drilling operations The case study considered in this work is an offshore well. Offshore facilities have a few dynamic process variables. The dependency among these variables must be maintained throughout the drilling operation; otherwise, deviation from normal dependency among the drilling parameters can significantly affect the risk of the drilling operation. Due to the propriety issue, detailed information about this offshore well is not made public. The actual well specific data is presented in the appendix. The procedure stated in section 3 is applied to this particular well.
Fig. 4. Real time risk profile end state consequences.
building a BN model involves two main steps: determining the structure of the network and determining the conditional probabilities for each node in the BN. Quite recently, researchers have developed techniques of learning the underlying BN structure and parameters of the structure (conditional probabilities) from data (Constantinou et al., 2016; Jensen and Nielsen, 2007; Adedigba et al., 2017b). These techniques are classified into two main categories: constraint based approaches and Bayesian based approaches (Jensen and Nielsen, 2007). The Tree Augmented Naïve Bayes (TAN) algorithm is a good example of a Bayesian based approach. The TAN algorithm is very coherent and has a very good performance compared to Naïve Bayes. Detailed information and the
5. Results and discussion For the purpose of clarity, the top-hole section (2200 hole section) has been excluded from the well specific data analysis. This section consists of primarily continental sands, with no hydrocarbon bearing intervals and no blowout preventers (BOPs - well control equipment) in place when the section was drilled. Therefore, no well control incident is expected in this section. The time zero represents the start of drilling the 1700 hole section. The time interval covers drilling, circulation, tripping, running casing, cementing and well suspension, as presented in the appendix. 449
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with time in the course of operation is used to model the probabilistic relationships among them, using the Bayesian TAN algorithm. The underlying dependency network structure and conditional probabilities are derived from well specific data. The developed model is tested on well specific data to detect faults early and predict the likelihood of kick. The occurrence probability of kick is predicted considering the time variant behaviour of the parameters and their dependent relationships. The likelihood of kick is subsequently used to compute the system failure risk if the safety barriers fail on demand. Six safety barriers are considered along the accident path after the occurrence probability of kick has been predicted. These barriers prevent or mitigate potential damage to the drilling crew, drilling rig and associated marine life. The system failure risk is updated as drilling proceeds and new well specific data are observed. Based on the test case, it is observed that this model has a strong capability of predicting risk as a function of time, which is a key function for drilling operations and evolving sub-surface conditions. The proposed data-driven risk assessment methodology for an offshore drilling operation has the following distinct features:
In the proposed risk assessment methodology for an offshore drilling operation, all possible accident scenarios are modelled using safety barrier based analysis and this provides the base to perform quantitative risk analysis. The serial cause-consequences relationships are depicted with fault tree and event tree analysis. The identified safety barriers in the developed model are methodically analysed using the fault tree. The identified safety barriers are the “well control barrier (WCB), influx mitigation barrier (IMB), ignition prevention barrier (IPB), escalation prevention barrier (EPB), emergency management barrier (EMB), and finally management and organizational barrier (M &OB)” These safety barriers have been identified as the main barriers needed to be placed in the accident's path for an offshore drilling operation (Rathnayaka et al., 2013). A detailed description of these barriers, associated fault trees and reliability data are given by (Rathnayaka et al., 2013). Table 1 shows the failure probability of the safety barriers. A Bayesian TAN algorithm is used to generate BN structure and parameters of the structure using the well specific data presented in the appendix. The BN model constructed from the well data shows an exact and precise representation of the probabilistic relationship existing among various variables in the well specific data. The comprehensive procedure for using the Bayesian TAN algorithm to construct BN model structure is clearly presented by (Adedigba et al., 2017b). Following the procedure, the BN model structure of Fig. 2 is constructed from actual well specific data, presented in the appendix. The likelihoods of kick predicted from the well data using normal distribution, given by Table 2, are fed into the BN model structure of Fig. 2 to predict the time dependent occurrence probability of kick, based on probabilistic dependencies that exist among well specific data. Table 2 also shows the time dependent occurrence probability of kick using the BN structure. The time dependent probabilities of kick are fed as inputs to the model event tree of Fig. 3. The time dependent probabilities of kick can be used to activate automatic well control whenever the time dependent probability of kick surpasses the acceptable range. Five different end consequences are given consideration in the model event tree of Fig. 3. The time dependent system failure risk predicted from the event tree is shown in Table 3. Very valuable information can be derived from the system failure risk profile generated from the application of the proposed methodology to an offshore drilling operation. Fig. 4 shows the real-time risk profile of end state consequences. Fig. 4a shows that the probability of a blowout event is below 4E-05 between 0 and 396 h of drilling operation for this particular well. However, there is a significant increase in the probability of blowout at 400hr of drilling operation. This probably indicates a shift in balance among the main operational drilling parameters (underbalance condition). However, timely counter responses and activation of well control systems by the operators significantly decreased the probability of blowout. This explanation is applicable to both Fig. 4b and c. Application of the proposed methodology provides a real time warning about any shift in balance of the drilling parameters. This creates awareness of impending dangers for the operators and timely activation of well control equipment if the deviation does not abate over time. The system failure risk profile can serve as a guide and an early warning for safety critical operational decision making before the progression of kick devastatingly affects the safety of drilling crew, drilling and the environment.
It is a simpler, repeatable, and prediction method to construct a real time failure risk profile of a drilling operation. The model is context specific; for example, the time dependent likelihood of kick during the drilling operation is estimated using a model having specific surface and sub-surface conditions. The real-time blow-out risk is estimated considering both elements: i) the likelihood of kick and ii) failure of safety barriers on demand. Both elements are time and operational condition dependent, which is captured in the model. This study has demonstrated the usefulness of using the Bayesian TAN algorithm to model the BN structure and parameters of well specific data for the purpose of risk assessment of drilling operations. The proposed methodology provides an efficient approach for predicting a dynamic system risk profile of a drilling operation. The time dependent risk profile generated from this methodology can be used by operators to activate safety measures any time the risk predicted exceeds the acceptable level. To effectively implement this methodology, adequate process monitoring data are needed. The methodology proposed is tested using actual well specific drilling data. The developed model is widely applicable, and valid for dynamic risk assessment of both onshore and offshore operations irrespective of differing field properties. This present work could be further improved by: i) evaluating the performance of the proposed model compared with other existing traditional approaches, ii) comparing the predictions of a constraint based approach and a Bayesian based approach and iii) analysing and visually representing the results of the developed model for quick decision making during drilling operations. Disclaimer This data is actual well data used only for educational purposes. Use of this data in any form is prohibited. To protect the propriety and the confidentiality of the data, the source of this data is not disclosed. The authors take no responsibility of the linking or similarity of this data to any source, person or organization.
6. Conclusion Acknowledgements This study presents a data driven risk assessment methodology for an offshore drilling operation. The proposed model makes use of well specific data. Offshore drilling facilities have many dynamic operational parameters. The variability of these operational parameters
The authors thankfully acknowledge the financial support provided by the Natural Science and Engineering Council of Canada and the Canada Research Chair (CRC) Program.
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Appendix A deviated gas exploratory well drilled to a total depth of 14,582 feet-measured depth (ft-MD) is considered as the case study. The well configuration consists of: (1) Piled 30 inch conductor pipe to 303 ft-MD, (2) Drilled 2200 hole to 3837 ft-MD, (3) Ran 18 5/8 inch casing to 3817 ft-MD, (4) Cemented 18 5/8 inch casing (5) Wellhead installation (6) Drilled 17 inch hole to 9420 ft-MD (7) Ran 13 3/8 inch casing to 9404 ft-MD (8) Cemented 13 3/8 inch casing (9) Carried out leak off test (10) Drilled 12 1/4 inch hole to total depth at 14,582 ft-MD and (11) Well suspension. Actual well data Activities
Time (hr)
Depth (ft-MD)
Depth (ft-TVD)
Pore Pressure (psi)
Bottom Hole Pressure (psi)
Fracture Pressure (psi)
Start Drilling Circulation Circulation Drilling Drilling Tripping Drilling Drilling Drilling Circulation Drilling Fishing Drilling Drilling Drilling Drilling Tripping Drilling Drilling Drilling Drilling Drilling Drilling Casing Running Cementing Cementing Well head Installation Drilling Leak Off Test Drilling Circulation Drilling Drilling Drilling Drilling Drilling Circulation Drilling Circulation Drilling Tripping Drilling Circulation Wiper Trip Mud Displacement Drilling Circulation Drilling Circulation Drilling Drilling Circulation Drilling Circulation Drilling Drilling Drilling Drilling Circulation Drilling Well Suspension
0 5.25 6.25 7.25 11.75 14.5 46.3 53.3 73.05 75.8 77.3 77.55 149.3 161.05 167.05 185.05 188.05 224.8 233.05 257.05 281.05 287.05 305.05 310.3 397.8 400.05 405.55 433.55 434.05 438.3 439.8 440.55 442.05 458.05 466.05 469.8 481.55 482.05 482.8 484.05 485.8 486.05 487.05 511.05 511.8 523.8 526.3 526.8 527.05 528.3 530.05 533.3 533.8 535.3 535.55 549.8 554.05 578.05 582.8 583.3 584.05 720.05
3837.0 3950.0 3950.0 3950.0 4338.0 4488.0 4488.0 4964.0 6104.0 6233.0 6233.0 6237.0 6237.0 6313.0 6356.0 6621.0 6648.0 6648.0 6867.0 7710.0 8427.0 8663.0 9204.0 9420.0 9420.0 9420.0 9420.0 9420.0 9440.0 9440.0 9484.0 9484.0 9579.0 10443.0 10905.0 11155.0 11800.0 11800.0 11834.0 11834.0 11942.0 11942.0 11970.0 11970.0 11970.0 11970.0 12123.0 12123.0 12141.0 12141.0 12137.0 12427.0 12427.0 12522.0 12522.0 13300.0 13470.0 14418.0 14572.0 14572.0 14582.0 14582
3837.0 3950.0 3950.0 3950.0 4337.8 4487.8 4487.8 4963.8 6103.8 6232.8 6232.8 6236.8 6236.8 6307.6 6346.8 6619.3 6646.2 6646.2 6863.1 7693.3 8384.9 8611.1 9128.2 9333.1 9333.1 9333.1 9333.1 9333.1 9283.9 9283.9 9325.7 9325.7 9415.9 10235.8 10674.9 10912.0 11524.0 11524.0 11556.2 11556.2 11661.9 11661.9 11688.9 11688.9 11688.9 11688.9 11837.1 11837.1 11854.2 11854.2 11850.4 12125.6 12125.6 12215.7 12215.7 12955.3 13116.5 14016.1 14162.3 14162.3 14171.8 14171.8
1803.4 1856.5 1856.5 1856.5 2038.8 2109.3 2109.3 2333.0 2868.8 2929.4 2929.4 2931.3 2931.3 2964.6 2983.0 3111.1 3123.7 3123.7 3225.7 3615.9 3940.9 4047.2 4290.3 4386.6 4386.6 4386.6 4386.6 4386.6 4363.4 4363.4 4383.1 4383.1 4425.5 4810.8 5017.2 5128.6 3572.4 3572.4 3582.4 3582.4 3615.2 5481.1 5493.8 5493.8 5493.8 5493.8 8286.0 8286.0 8179.4 8179.4 8176.8 8366.7 8366.7 8428.8 8428.8 9198.3 9312.7 9951.4 10055.2 10055.2 10062.0 10061.978
1795.7 1848.6 1848.6 1848.6 2030.1 2118.2 2118.2 2400.5 2951.8 3072.8 3072.8 3145.8 3145.8 3181.6 3300.3 3442.0 3490.6 3490.6 3604.5 4040.5 4491.0 4656.9 4960.3 5072.5 5072.5 6066.5 6066.5 5072.5 5199.0 5199.0 5222.4 5222.4 5272.9 5732.0 5977.9 6110.7 6453.4 6453.4 6550.1 6550.1 6610.0 6610.0 6625.3 6625.3 8532.9 8532.9 8641.1 8641.1 8653.6 8653.6 8650.8 8851.7 8851.7 8917.5 8917.5 9457.4 9575.0 10231.8 10383.8 10383.8 10390.8 10390.76376
2609.2 2686.0 2686.0 2686.0 2993.1 3096.6 3096.6 3425.0 4272.7 4363.0 4363.0 4365.8 4365.8 4415.3 4442.8 4699.7 4718.8 4718.8 4872.8 5462.2 6121.0 6372.2 6937.4 7186.5 7186.5 7186.5 7186.5 7186.5 7195.0 7195.0 7274.0 7274.0 7438.6 8086.3 8433.2 8729.6 8758.2 8758.2 8782.7 8782.7 8863.0 9562.8 9584.9 9584.9 9584.9 9584.9 10416.6 10416.6 10431.7 10431.7 10428.4 10670.5 10670.5 10749.8 10749.8 11659.8 11804.9 12614.5 12746.1 12746.1 12754.6 12754.62
451
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Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Data-driven dynamic risk analysis of offshore drilling operations Sunday A. Adedigba, Olalere Oloruntobi, Faisal Khan *, Stephen Butt Centre for Risk, Integrity and Safety Engineering (C-RISE), Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John's, NL A1B 3X5, Canada
A R T I C L E I N F O
A B S T R A C T
Keywords: Dynamic failure probability Risk analysis Blowouts Drilling Bayesian tree augmented naive Bayes (TAN)
A data-driven dynamic risk analysis methodology is proposed here. The methodology is applied to offshore drilling operations. Modern drilling rigs are highly instrumented to monitor real time operational data. This provides sufficient data for time dependent risk analysis of drilling operations. The probabilistic relationships (structure) among the primary operational (drilling) parameters are modelled using the Bayesian Tree Augmented Naïve Bayes (TAN) algorithm. The developed model is used to predict time dependent probability of kick, and is continuously updated based on the current state of the key drilling parameters. The real-time probability of kick is used to model blowout risk as a function of time. The dynamic risk profile generated from the model is useful in operational decision making to prevent accidents and enhance the safety of drilling operations. The proposed dynamic risk methodology is tested and verified using actual drilling operational data.
1. Introduction The complexity and sophistication of the current process systems have greatly improved their productivity. However, this advancement in modern process systems presents a significant risk of failure along with their versatility and productivity (Yu et al., 2015; Adedigba et al., 2017a). Risk analysis is defined as “the process of characterizing, managing and informing others about the existence, nature, magnitude, prevalence, contributing factors and uncertainties of the potential losses” (Modarres, 2006). The static nature of conventional quantitative risk assessment (QRA) methods has limited their application in modelling and predicting risk variations during the operation of process systems (Yang et al., 2015). However, dynamic risk analysis provides a framework that captures risk variation during the operation. Khan et al. (2016) defined dynamic risk assessment “as a method that updates estimated risk of a deteriorating process according to the performance of the control system, safety barriers, inspection and maintenance activities, the human factors and procedure”. Various methods have been applied for executing a dynamic risk analysis of process systems. Detailed information about these methods can be found in (Al-shanini et al., 2014; Aven, 2016; Durga Rao et al., 2009; Kalantarnia et al., 2010; Khakzad et al., 2012; Khan and Abbasi, 1998; Khan et al., 2016; Paltrinieri et al., 2013; Adedigba et al., 2016a,b). An accident model offers thorough information about how and why process accidents occur and is a very important tool for implementing process risk assessment. Different types of process accident models have
been developed over the years. (Attwood et al., 2006; Adedigba et al., 2016a,b; Qureshi, 2007; Rathnayaka et al., 2010). However, most of these models do not take into consideration the dependency of the process variables and these process monitoring data are not used in these models. Offshore drilling, and in particular deep water drilling operations, is associated with high risk and a high cost of operation. One of most devastating accidents with severe consequences in the offshore oil and gas industry is a blowout, such as the Macondo blowout accident. Accident records have revealed that the majority of offshore blowouts have occurred during the drilling phase (Xue et al., 2013). A blowout is an unrestrained flow of gas and oil (hydrocarbons) to the environment (Khakzad et al., 2013). Many blowout accidents have occurred in offshore drilling operations around the globe. The most recent and most devastating environmental disaster in U.S history is the Macondo blowout of 20 April 2010. This accident was caused by a series of technical factors (Rathnayaka et al., 2013). Safety management of offshore drilling operations demands continuous monitoring of the safety performance and safety indicators of the system. Safety indicators provide information about the level of safety in a system to decision makers so the decision makers can activate safety systems whenever the level of safety in the system is below the acceptable range (Skogdalen et al., 2011). Most of the approaches adopted in risk analysis of offshore drilling operations are analytical methods (Khakzad et al., 2013; Kujath et al., 2010; Skogdalen et al.,
* Corresponding author. E-mail address: fi[email protected] (F. Khan). https://doi.org/10.1016/j.petrol.2018.02.049 Received 6 November 2017; Received in revised form 16 February 2018; Accepted 20 February 2018 Available online 23 February 2018 0920-4105/© 2018 Elsevier B.V. All rights reserved.
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Fig. 1. The flowchart for the proposed methodology.
(FP). Also, management and organizational error are adequately accounted for in the model. This paper is organised as follows. Section 2 discusses monitoring, prevention and control of well blowout. Section 3 presents the data driven dynamic risk analysis methodology. Section 4 provides the testing and verification of the proposed data driven risk assessment methodology with actual well specific data. The results and discussion are presented in section 5. Finally, the conclusion is given in Section 6.
2011; Xue et al., 2013). However, analytical techniques do not take into consideration the probabilistic dependencies (structure) among well specific data. The primary objective of the study is to develop a data-driven dynamic model for dynamic risk assessment. The developed model is demonstrated on an offshore drilling operation using the probabilistic relationships (structure) among actual industrial well-specific data such as bottom hole pressure (BHP), pore pressure (PP) and fracture pressure 445
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Fig. 2. BN structure constructed from well specific data.
Table 1 Failure probability of prevention barriers and control (Rathnayaka et al., 2013). Prevention barrier
Failure probability
Well control barrier (WCB) Influx mitigation barrier (IMB) Ignition prevention barrier (IPB) Escalation prevention barrier (EPB) Emergency management (EMB) Management and organization barrier (M &OB)
0.0713 0.0643 0.1377 0.1110 0.1088 0.1207
Table 2 The likelihood of kick from well specific data and time dependent probability of kick based on TAN BN model.
2. Monitoring, prevention, and control of blowouts The inflow of formation fluid (oil, gas water or mixture) into the wellbore is referred to as kick; the associated fluid is termed kick fluid (Azar and Samuel, 2007). During a drilling operation, the drilling mud is used as the well's primary safety barrier to ensure that the wellbore's bottom hole pressure (BHP) is higher than the pore pressure (PP) and at the same time less than fracture pressure (Fp). This relationship among these vital drilling parameters must be maintained to prevent the formation fluids from flowing into the wellbore and to ensure the formation is not fractured (Khakzad et al., 2013). Mathematically, this condition can be expressed as: Pp < BHP < F P
(1)
However, kick will occur whenever the differential pressure ΔP is negative. Mathematically ΔP can be expressed as: ΔP ¼ BHP PP
(2)
Depending on the algebraic value of ΔP, one of these conditions may result (Azar and Samuel, 2007). ΔP > 0; over balance condition no kick:
(3)
ΔP ¼ 0; balance condition no kick:
(4)
ΔP < 0; underbalance condition kick:
(5)
Time (hr)
The likelihood of kick from well specific data (CDF)
Time dependent probability of kick based on TAN BN model structure
0 5.25 6.25 7.25 11.75 14.5 46.3 53.3 73.05 75.8 77.3 77.55 149.3 161.05 167.05 185.05 188.05 224.8 233.05 257.05 281.05 287.05 305.05 310.3 397.8 400.05 405.55 433.55 434.05 438.3 439.8 440.55 442.05 458.05 466.05
3.1381E-02 3.1381E-02 3.1381E-02 3.1381E-02 2.6739E-02 3.1297E-02 3.1297E-02 4.8249E-02 4.1518E-02 5.7900E-02 5.7900E-02 8.4136E-02 8.4136E-02 8.4136E-02 1.3326E-01 1.1772E-01 1.3604E-01 1.3604E-01 1.3604E-01 1.3604E-01 1.4156E-01 1.4431E-01 1.2217E-01 1.0863E-01 1.0863E-01 6.8576E-01 6.8576E-01 1.0863E-01 1.5769E-01 1.5769E-01 1.4917E-01 1.4917E-01 1.3326E-01 1.3326E-01 1.3326E-01
1.1208E-03 1.1208E-03 1.1208E-03 1.1208E-03 9.5496E-04 1.1178E-03 1.1178E-03 1.7232E-03 1.4828E-03 2.0679E-03 2.0679E-03 3.0049E-03 3.0049E-03 3.0049E-03 4.7593E-03 4.2043E-03 4.8586E-03 4.8586E-03 4.8586E-03 4.8586E-03 5.0557E-03 5.1539E-03 4.3632E-03 3.8796E-03 3.8796E-03 2.4491E-02 2.4491E-02 3.8796E-03 5.6318E-03 5.6318E-03 5.3275E-03 5.3275E-03 4.7593E-03 4.7593E-03 4.7593E-03
2.1. Blowout
3. Data-driven dynamic risk analysis methodology
Usually, a kick propagates to a blowout due to either failure of secondary barriers or as a result of non-detection of the kick, which prevents the activation of kick preventing barriers.
The flowchart for the proposed methodology is given in Fig. 1. This methodology is explained using a drilling operation as an example. 446
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Fig. 3. Revised event tree for the proposed methodology (Rathnayaka et al., 2013).
3.1. Hazard identification and analysis
3.2. Failure probability assessment of safety barriers
This step involves identification of all the possible hazards and events that could initiate an undesired event. In this phase, many hazard identification techniques can be applied, as reviewed by Khan et al. (1998). Accident scenarios also need to be generated; this provides the opportunity of identifying all the relevant safety barriers required to place along potential accident's path to prevent or reduce the advancement of the accident process, because the failure of prevention or safety barriers results in an accident (Rathnayaka et al., 2011). Hazard identification and analysis of an offshore drilling operation is carried out to generate an accident scenario and identify necessary safety barriers to be put in place to avert or prevent a blowout.
Fault tree analysis is a widely used tool for estimating or predicting the reliability of highly complex systems. In fault tree analysis, a deductive graphical model is used to detect the potential causes of undesired events (Adedigba et al., 2016a,b). The construction of a fault tree starts by determining the undesired top event in the fault tree. Thereafter, all other combinations of the undesired top events likely to take place are deductively modelled downwards till the root cause or primary events that instigate the occurrence of the top event are detected. The most widely used logics in fault tree analysis are OR logic and AND logic. The occurrence probability of an undesired top event is computed based on the reliability data of basic or primary events. Analysis using the fault tree can be accomplished in various ways: qualitatively, quantitatively and, for some cases, a combination of both 447
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Table 3 The occurrence probability of end state consequence. Time (hr.)
Safe
Kick
Blowout
Fire & explosion
Catastrophic
0 5.25 6.25 7.25 11.75 14.5 46.3 53.3 73.05 75.8 77.3 77.55 149.3 161.05 167.05 185.05 188.05 224.8 233.05 257.05 281.05 287.05 305.05 310.3 397.8 400.05 405.55 433.55 434.05 438.3 439.8 440.55 442.05 458.05 466.05
1.0409E-03 1.0409E-03 1.0409E-03 1.0409E-03 8.8688E-04 1.0381E-03 1.0381E-03 1.6003E-03 1.3771E-03 1.9204E-03 1.9204E-03 2.7906E-03 2.7906E-03 2.7906E-03 4.4199E-03 3.9045E-03 4.5122E-03 4.5122E-03 4.5122E-03 4.5122E-03 4.6952E-03 4.7865E-03 4.0521E-03 3.6030E-03 3.6030E-03 2.2745E-02 2.2745E-02 3.6030E-03 5.2302E-03 5.2302E-03 4.9476E-03 4.9476E-03 4.4199E-03 4.4199E-03 4.4199E-03
7.4772E-05 7.4772E-05 7.4772E-05 7.4772E-05 6.3711E-05 7.4571E-05 7.4571E-05 1.1496E-04 9.8925E-05 1.3796E-04 1.3796E-04 2.0047E-04 2.0047E-04 2.0047E-04 3.1752E-04 2.8049E-04 3.2414E-04 3.2414E-04 3.2414E-04 3.2414E-04 3.3729E-04 3.4385E-04 2.9109E-04 2.5883E-04 2.5883E-04 1.6340E-03 1.6340E-03 2.5883E-04 3.7573E-04 3.7573E-04 3.5543E-04 3.5543E-04 3.1752E-04 3.1752E-04 3.1752E-04
4.9838E-06 4.9838E-06 4.9838E-06 4.9838E-06 4.2465E-06 4.9704E-06 4.9704E-06 7.6626E-06 6.5936E-06 9.1953E-06 9.1953E-06 1.3362E-05 1.3362E-05 1.3362E-05 2.1163E-05 1.8696E-05 2.1605E-05 2.1605E-05 2.1605E-05 2.1605E-05 2.2482E-05 2.2918E-05 1.9402E-05 1.7252E-05 1.7252E-05 1.0891E-04 1.0891E-04 1.7252E-05 2.5043E-05 2.5043E-05 2.3690E-05 2.3690E-05 2.1163E-05 2.1163E-05 2.1163E-05
1.3746E-07 1.3746E-07 1.3746E-07 1.3746E-07 1.1713E-07 1.3709E-07 1.3709E-07 2.1135E-07 1.8187E-07 2.5363E-07 2.5363E-07 3.6855E-07 3.6855E-07 3.6855E-07 5.8374E-07 5.1566E-07 5.9591E-07 5.9591E-07 5.9591E-07 5.9591E-07 6.2009E-07 6.3214E-07 5.3516E-07 4.7585E-07 4.7585E-07 3.0039E-06 3.0039E-06 4.7585E-07 6.9075E-07 6.9075E-07 6.5343E-07 6.5343E-07 5.8374E-07 5.8374E-07 5.8374E-07
1.6993E-08 1.6993E-08 1.6993E-08 1.6993E-08 1.4479E-08 1.6947E-08 1.6947E-08 2.6126E-08 2.2482E-08 3.1352E-08 3.1352E-08 4.5559E-08 4.5559E-08 4.5559E-08 7.2159E-08 6.3744E-08 7.3665E-08 7.3665E-08 7.3665E-08 7.3665E-08 7.6654E-08 7.8143E-08 6.6154E-08 5.8822E-08 5.8822E-08 3.7133E-07 3.7133E-07 5.8822E-08 8.5388E-08 8.5388E-08 8.0774E-08 8.0774E-08 7.2159E-08 7.2159E-08 7.2159E-08
compute the standard deviation of mean pressure for each depth interval. This value is adapted considering the standard expected variation. The value is confirmed through expert opinions obtained using the structural Delphi method (Clayton, 1997). The opinion is given equal weight and subsequently aggregated. The cumulative distribution function (CDF) for each depth is estimated from equation (6). Here, t is the mud pressure for each depth, μ is the mean pressure for each depth and σ is the standard deviation for each step.
(Adedigba et al. 2016a,b; Khakzad et al., 2011). The safety barriers that are placed along the accident path to prevent or avert a blowout at an offshore drilling facility are systematically analysed using a fault tree to predict the occurrence probability of the undesired top events for each safety barrier. 3.3. Collecting actual well specific data for analysis In this phase, actual well specific data are collected and analysed for the purpose of learning the probabilistic relationships (structure) that exist among the data. Well specific data collected are displayed in the appendix. Due to the propriety issue, the source of this data is not disclosed by the authors. Linking this data to any source or organization is prohibited.
FðtÞ ¼ φ
tμ
σ
(6)
3.6. Structure learning of Bayesian network using states of well specific data
3.4. Deriving probability distribution (for well specific data) Bayesian networks are directed acyclic graphs usually used for reasoning under uncertainty. The BN is used to model the probabilistic relationship and interdependencies among parent and child nodes. The graphical part of the BN shows the structure of the problem under consideration and demonstrates the causal influences among the parent nodes and child nodes. The probabilistic relationships and interdependencies among the variables are represented using the conditional probability table (CTP) (Onisko et al., 2001). A BN possesses a strong capability to model complex systems and subsequently reduces parametric uncertainty by integrating new information whenever available. Therefore, BNs provide a unique opportunity to perform probability updating. The two main techniques to build or construct Bayesian networks are the knowledge driven technique and the data driven technique. The knowledge driven technique uses expert opinion and experience to draw the structure and conditional probability table of the BN. Principally,
A suitable probability distribution is derived from the well specific data, given in the appendix. The detailed methodology for obtaining probability distribution from given data is not presented here. The well specific data (presented in the appendix) is fitted to different distributions using a least square minimization approach. The fitted distributions are compared and selected using the Kolmogorov Smirnov test. In the present case, normal distribution is identified to be most appropriate. 3.5. Estimating the likelihood of unwanted kick situations The likelihood of kick is estimated from the well specific data, given in the appendix. The procedure for estimating the likelihood of kick is as follows: The mean pressure, which is the average of pore pressure and fracture pressure at each depth, is computed. For instance, at the depth of 3950 ft the mean pressure is 2271.3 psi. The covariance of 0.1 is used to 448
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procedure for using the TAN algorithm to learn the underlying BN structure and parameters of the structure (conditional probabilities) from data are given by (Adedigba et al., 2017b). This information is not presented here, to prevent replication. The objective of building a BN model from well specific data is to predict the time dependent probability of kick based on the probabilistic relationship among these variables. 3.7. Computing probability of kick using BN structure of well specific data The likelihoods of kick predicted from the well data using normal distribution are fed into the BN model structure shown in Fig. 2 to predict the time dependent probability of kick based on probabilistic dependencies that exist among well specific data. Detailed information on how to predict probability from BN model structure is presented by (Adedigba et al., 2017b, 2018). 3.8. Analysis of potential scenarios and computing end state probability of consequence at time (t) Analysis of the potential scenarios is carried out with event tree analysis. The event tree is an inductive logical technique that is widely used to denote incident scenarios. It begins with a particular accident instigating event and ends with every potential consequence of accident instigating events, usually called “end state consequences” of the event tree (Adedigba et al., 2016a,b). The event tree consists of two unique branches: the success and failure branch. These branches are used to predict the probability of success or failure of the safety barriers in the event tree and at the same time display the probable progression sequence of the accident instigating event to various potential consequences (Nývlt and Rausand, 2012; Adedigba et al., 2017b). The time dependent probabilities of kick predicted from the BN model developed from well specific data are used as an input to the event to quantify or estimate the occurrence probability of end state consequences. The probability of end state consequences in the event tree P (Ck) is computed by equation (7) (Ferdous et al., 2011). PðCK Þ ¼ λ x
n Y
Pi
(7)
i¼1
where λ is the probability of kick estimated from the BN model, n the number of safety barriers, and Pi is the failure probability of the safety barrier. 4. Case study: offshore drilling operations The case study considered in this work is an offshore well. Offshore facilities have a few dynamic process variables. The dependency among these variables must be maintained throughout the drilling operation; otherwise, deviation from normal dependency among the drilling parameters can significantly affect the risk of the drilling operation. Due to the propriety issue, detailed information about this offshore well is not made public. The actual well specific data is presented in the appendix. The procedure stated in section 3 is applied to this particular well.
Fig. 4. Real time risk profile end state consequences.
building a BN model involves two main steps: determining the structure of the network and determining the conditional probabilities for each node in the BN. Quite recently, researchers have developed techniques of learning the underlying BN structure and parameters of the structure (conditional probabilities) from data (Constantinou et al., 2016; Jensen and Nielsen, 2007; Adedigba et al., 2017b). These techniques are classified into two main categories: constraint based approaches and Bayesian based approaches (Jensen and Nielsen, 2007). The Tree Augmented Naïve Bayes (TAN) algorithm is a good example of a Bayesian based approach. The TAN algorithm is very coherent and has a very good performance compared to Naïve Bayes. Detailed information and the
5. Results and discussion For the purpose of clarity, the top-hole section (2200 hole section) has been excluded from the well specific data analysis. This section consists of primarily continental sands, with no hydrocarbon bearing intervals and no blowout preventers (BOPs - well control equipment) in place when the section was drilled. Therefore, no well control incident is expected in this section. The time zero represents the start of drilling the 1700 hole section. The time interval covers drilling, circulation, tripping, running casing, cementing and well suspension, as presented in the appendix. 449
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with time in the course of operation is used to model the probabilistic relationships among them, using the Bayesian TAN algorithm. The underlying dependency network structure and conditional probabilities are derived from well specific data. The developed model is tested on well specific data to detect faults early and predict the likelihood of kick. The occurrence probability of kick is predicted considering the time variant behaviour of the parameters and their dependent relationships. The likelihood of kick is subsequently used to compute the system failure risk if the safety barriers fail on demand. Six safety barriers are considered along the accident path after the occurrence probability of kick has been predicted. These barriers prevent or mitigate potential damage to the drilling crew, drilling rig and associated marine life. The system failure risk is updated as drilling proceeds and new well specific data are observed. Based on the test case, it is observed that this model has a strong capability of predicting risk as a function of time, which is a key function for drilling operations and evolving sub-surface conditions. The proposed data-driven risk assessment methodology for an offshore drilling operation has the following distinct features:
In the proposed risk assessment methodology for an offshore drilling operation, all possible accident scenarios are modelled using safety barrier based analysis and this provides the base to perform quantitative risk analysis. The serial cause-consequences relationships are depicted with fault tree and event tree analysis. The identified safety barriers in the developed model are methodically analysed using the fault tree. The identified safety barriers are the “well control barrier (WCB), influx mitigation barrier (IMB), ignition prevention barrier (IPB), escalation prevention barrier (EPB), emergency management barrier (EMB), and finally management and organizational barrier (M &OB)” These safety barriers have been identified as the main barriers needed to be placed in the accident's path for an offshore drilling operation (Rathnayaka et al., 2013). A detailed description of these barriers, associated fault trees and reliability data are given by (Rathnayaka et al., 2013). Table 1 shows the failure probability of the safety barriers. A Bayesian TAN algorithm is used to generate BN structure and parameters of the structure using the well specific data presented in the appendix. The BN model constructed from the well data shows an exact and precise representation of the probabilistic relationship existing among various variables in the well specific data. The comprehensive procedure for using the Bayesian TAN algorithm to construct BN model structure is clearly presented by (Adedigba et al., 2017b). Following the procedure, the BN model structure of Fig. 2 is constructed from actual well specific data, presented in the appendix. The likelihoods of kick predicted from the well data using normal distribution, given by Table 2, are fed into the BN model structure of Fig. 2 to predict the time dependent occurrence probability of kick, based on probabilistic dependencies that exist among well specific data. Table 2 also shows the time dependent occurrence probability of kick using the BN structure. The time dependent probabilities of kick are fed as inputs to the model event tree of Fig. 3. The time dependent probabilities of kick can be used to activate automatic well control whenever the time dependent probability of kick surpasses the acceptable range. Five different end consequences are given consideration in the model event tree of Fig. 3. The time dependent system failure risk predicted from the event tree is shown in Table 3. Very valuable information can be derived from the system failure risk profile generated from the application of the proposed methodology to an offshore drilling operation. Fig. 4 shows the real-time risk profile of end state consequences. Fig. 4a shows that the probability of a blowout event is below 4E-05 between 0 and 396 h of drilling operation for this particular well. However, there is a significant increase in the probability of blowout at 400hr of drilling operation. This probably indicates a shift in balance among the main operational drilling parameters (underbalance condition). However, timely counter responses and activation of well control systems by the operators significantly decreased the probability of blowout. This explanation is applicable to both Fig. 4b and c. Application of the proposed methodology provides a real time warning about any shift in balance of the drilling parameters. This creates awareness of impending dangers for the operators and timely activation of well control equipment if the deviation does not abate over time. The system failure risk profile can serve as a guide and an early warning for safety critical operational decision making before the progression of kick devastatingly affects the safety of drilling crew, drilling and the environment.
It is a simpler, repeatable, and prediction method to construct a real time failure risk profile of a drilling operation. The model is context specific; for example, the time dependent likelihood of kick during the drilling operation is estimated using a model having specific surface and sub-surface conditions. The real-time blow-out risk is estimated considering both elements: i) the likelihood of kick and ii) failure of safety barriers on demand. Both elements are time and operational condition dependent, which is captured in the model. This study has demonstrated the usefulness of using the Bayesian TAN algorithm to model the BN structure and parameters of well specific data for the purpose of risk assessment of drilling operations. The proposed methodology provides an efficient approach for predicting a dynamic system risk profile of a drilling operation. The time dependent risk profile generated from this methodology can be used by operators to activate safety measures any time the risk predicted exceeds the acceptable level. To effectively implement this methodology, adequate process monitoring data are needed. The methodology proposed is tested using actual well specific drilling data. The developed model is widely applicable, and valid for dynamic risk assessment of both onshore and offshore operations irrespective of differing field properties. This present work could be further improved by: i) evaluating the performance of the proposed model compared with other existing traditional approaches, ii) comparing the predictions of a constraint based approach and a Bayesian based approach and iii) analysing and visually representing the results of the developed model for quick decision making during drilling operations. Disclaimer This data is actual well data used only for educational purposes. Use of this data in any form is prohibited. To protect the propriety and the confidentiality of the data, the source of this data is not disclosed. The authors take no responsibility of the linking or similarity of this data to any source, person or organization.
6. Conclusion Acknowledgements This study presents a data driven risk assessment methodology for an offshore drilling operation. The proposed model makes use of well specific data. Offshore drilling facilities have many dynamic operational parameters. The variability of these operational parameters
The authors thankfully acknowledge the financial support provided by the Natural Science and Engineering Council of Canada and the Canada Research Chair (CRC) Program.
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Appendix A deviated gas exploratory well drilled to a total depth of 14,582 feet-measured depth (ft-MD) is considered as the case study. The well configuration consists of: (1) Piled 30 inch conductor pipe to 303 ft-MD, (2) Drilled 2200 hole to 3837 ft-MD, (3) Ran 18 5/8 inch casing to 3817 ft-MD, (4) Cemented 18 5/8 inch casing (5) Wellhead installation (6) Drilled 17 inch hole to 9420 ft-MD (7) Ran 13 3/8 inch casing to 9404 ft-MD (8) Cemented 13 3/8 inch casing (9) Carried out leak off test (10) Drilled 12 1/4 inch hole to total depth at 14,582 ft-MD and (11) Well suspension. Actual well data Activities
Time (hr)
Depth (ft-MD)
Depth (ft-TVD)
Pore Pressure (psi)
Bottom Hole Pressure (psi)
Fracture Pressure (psi)
Start Drilling Circulation Circulation Drilling Drilling Tripping Drilling Drilling Drilling Circulation Drilling Fishing Drilling Drilling Drilling Drilling Tripping Drilling Drilling Drilling Drilling Drilling Drilling Casing Running Cementing Cementing Well head Installation Drilling Leak Off Test Drilling Circulation Drilling Drilling Drilling Drilling Drilling Circulation Drilling Circulation Drilling Tripping Drilling Circulation Wiper Trip Mud Displacement Drilling Circulation Drilling Circulation Drilling Drilling Circulation Drilling Circulation Drilling Drilling Drilling Drilling Circulation Drilling Well Suspension
0 5.25 6.25 7.25 11.75 14.5 46.3 53.3 73.05 75.8 77.3 77.55 149.3 161.05 167.05 185.05 188.05 224.8 233.05 257.05 281.05 287.05 305.05 310.3 397.8 400.05 405.55 433.55 434.05 438.3 439.8 440.55 442.05 458.05 466.05 469.8 481.55 482.05 482.8 484.05 485.8 486.05 487.05 511.05 511.8 523.8 526.3 526.8 527.05 528.3 530.05 533.3 533.8 535.3 535.55 549.8 554.05 578.05 582.8 583.3 584.05 720.05
3837.0 3950.0 3950.0 3950.0 4338.0 4488.0 4488.0 4964.0 6104.0 6233.0 6233.0 6237.0 6237.0 6313.0 6356.0 6621.0 6648.0 6648.0 6867.0 7710.0 8427.0 8663.0 9204.0 9420.0 9420.0 9420.0 9420.0 9420.0 9440.0 9440.0 9484.0 9484.0 9579.0 10443.0 10905.0 11155.0 11800.0 11800.0 11834.0 11834.0 11942.0 11942.0 11970.0 11970.0 11970.0 11970.0 12123.0 12123.0 12141.0 12141.0 12137.0 12427.0 12427.0 12522.0 12522.0 13300.0 13470.0 14418.0 14572.0 14572.0 14582.0 14582
3837.0 3950.0 3950.0 3950.0 4337.8 4487.8 4487.8 4963.8 6103.8 6232.8 6232.8 6236.8 6236.8 6307.6 6346.8 6619.3 6646.2 6646.2 6863.1 7693.3 8384.9 8611.1 9128.2 9333.1 9333.1 9333.1 9333.1 9333.1 9283.9 9283.9 9325.7 9325.7 9415.9 10235.8 10674.9 10912.0 11524.0 11524.0 11556.2 11556.2 11661.9 11661.9 11688.9 11688.9 11688.9 11688.9 11837.1 11837.1 11854.2 11854.2 11850.4 12125.6 12125.6 12215.7 12215.7 12955.3 13116.5 14016.1 14162.3 14162.3 14171.8 14171.8
1803.4 1856.5 1856.5 1856.5 2038.8 2109.3 2109.3 2333.0 2868.8 2929.4 2929.4 2931.3 2931.3 2964.6 2983.0 3111.1 3123.7 3123.7 3225.7 3615.9 3940.9 4047.2 4290.3 4386.6 4386.6 4386.6 4386.6 4386.6 4363.4 4363.4 4383.1 4383.1 4425.5 4810.8 5017.2 5128.6 3572.4 3572.4 3582.4 3582.4 3615.2 5481.1 5493.8 5493.8 5493.8 5493.8 8286.0 8286.0 8179.4 8179.4 8176.8 8366.7 8366.7 8428.8 8428.8 9198.3 9312.7 9951.4 10055.2 10055.2 10062.0 10061.978
1795.7 1848.6 1848.6 1848.6 2030.1 2118.2 2118.2 2400.5 2951.8 3072.8 3072.8 3145.8 3145.8 3181.6 3300.3 3442.0 3490.6 3490.6 3604.5 4040.5 4491.0 4656.9 4960.3 5072.5 5072.5 6066.5 6066.5 5072.5 5199.0 5199.0 5222.4 5222.4 5272.9 5732.0 5977.9 6110.7 6453.4 6453.4 6550.1 6550.1 6610.0 6610.0 6625.3 6625.3 8532.9 8532.9 8641.1 8641.1 8653.6 8653.6 8650.8 8851.7 8851.7 8917.5 8917.5 9457.4 9575.0 10231.8 10383.8 10383.8 10390.8 10390.76376
2609.2 2686.0 2686.0 2686.0 2993.1 3096.6 3096.6 3425.0 4272.7 4363.0 4363.0 4365.8 4365.8 4415.3 4442.8 4699.7 4718.8 4718.8 4872.8 5462.2 6121.0 6372.2 6937.4 7186.5 7186.5 7186.5 7186.5 7186.5 7195.0 7195.0 7274.0 7274.0 7438.6 8086.3 8433.2 8729.6 8758.2 8758.2 8782.7 8782.7 8863.0 9562.8 9584.9 9584.9 9584.9 9584.9 10416.6 10416.6 10431.7 10431.7 10428.4 10670.5 10670.5 10749.8 10749.8 11659.8 11804.9 12614.5 12746.1 12746.1 12754.6 12754.62
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