Fuzzy fault tree analysis of hydraulic fracturing flowback water storage failure

Journal Pre-proof Fuzzy fault tree analysis of hydraulic fracturing flowback water storage failure Guangji Hu, Hieuchi Phan, Rachid Ouache, Himani Gandhi, Kasun Hewage, Rehan Sadiq PII:

S1875-5100(19)30291-4

DOI:

https://doi.org/10.1016/j.jngse.2019.103039

Reference:

JNGSE 103039

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 2 April 2019 Revised Date:

11 October 2019

Accepted Date: 18 October 2019

Please cite this article as: Hu, G., Phan, H., Ouache, R., Gandhi, H., Hewage, K., Sadiq, R., Fuzzy fault tree analysis of hydraulic fracturing flowback water storage failure, Journal of Natural Gas Science & Engineering, https://doi.org/10.1016/j.jngse.2019.103039. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier B.V. All rights reserved.

Fuzzy fault tree analysis of hydraulic fracturing flowback water storage failure Guangji Hu a, Hieuchi Phan b, Rachid Ouache a, Himani Gandhi a, Kasun Hewage a, Rehan Sadiq a,* a

School of Engineering, University of British Columbia, Okanagan Campus, Kelowna, BC V1V 1V7, Canada;

b

Department of Civil Engineering, Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John's, NL A1B 3X5, Canada

*Corresponding Author: Dr. Rehan Sadiq, Professor School of Engineering, University of British Columbia, Okanagan 3333 University Way, Kelowna, British Columbia, Canada V1V 1V7 Tel: 1-(250) 807-9013; E-mail: [email protected]

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Abstract: Unintended release of flowback water as a result of above-ground walled storage system (AGWSS) failure was studied using a fuzzy fault tree analysis (FFTA). A fault tree comprising 45 basic events was constructed, and knowledge gathered through expert elicitation was used to estimate the occurrence possibilities of basic events. Fuzzy logic was introduced to reduce the epistemic uncertainties in expert judgments. Consistency analysis and grey pairwise comparison techniques were used to weight the judgments from different experts. The result of a case study shows that the failure probability of AGWSS was estimated to be 5.75E-04, indicating a relatively low level of failure possibility comparing to other systems used for oil and gas production. Importance analysis of basic events indicates that loss of containment integrity, water loading accidents, and external catastrophes are critical causes responsible for AGWSS failure. The developed FFTA methodology can be used by the unconventional gas industry for mitigation of flowback water spill risk. Keywords: flowback water; above-ground walled storage system; fuzzy fault tree analysis; unintended release; hydraulic fracturing; unconventional gas production

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List of Acronyms: AGWSS: above-ground walled storage system AP: aggregated occurrence probability of basic events BE: basic event CP: crisp probability CPS: crisp possibility score FFTA: fuzzy fault tree analysis MCS: minimum cut set TFTA: traditional fault tree analysis

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1. Introduction Unconventional gas production has been rapidly increasing in Canada over the past decades (NEB, 2017). The rapid growth of unconventional gas production is mainly ascribed to the combined use of horizontal drilling and hydraulic fracturing, which allows for economic extraction of natural gas from low-permeability gas-bearing formations (Gallegos and Varela, 2014). In hydraulic fracturing, millions of gallons of fracturing fluid is injected under high pressure to initiate fractures in subterranean geological formations (Ziemkiewicz et al., 2014). The injected fracturing fluid returns to the surface as a result of released pressure, which is known as flowback water. Flowback water needs proper treatment to reduce the content of harmful substances and minimize adverse environmental impacts from its disposal. Many studies have reported that flowback waters contain high concentrations of salts, metals, harmful organic compounds, and naturally occurring radioactive materials (Zolfaghari et al., 2016; He et al., 2017; Luek and Gonsior, 2017). Moreover, various chemicals with adverse environmental and human health effects (e.g., acute aquatic toxicity, carcinogenicity) are used in fracturing fluids, resulting in increased public concerns over the health risk posed by potential flowback water spills (Hu et al., 2018). Recovered flowback water is commonly stored in onsite storage systems, such as in-ground containment ponds, storage tanks, and above-ground walled storage systems (AGWSS) before transportation and treatment (Becklumb, 2015; Lutz et al., 2013). Unintended release of untreated flowback water as a result of storage failure can potentially cause soil and groundwater contaminations. In fact, the majority of reported flowback water spill accidents were related to transportation and storage (Gandhi et al.,

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2018). According to hydraulic fracturing flowback water spill data from 2006 to 2011 in the United States, roughly 46% of spills and 75% of the spilled volumes were linked to storage failure (Gandhi et al., 2018; US EPA, 2015). In British Columbia, Canada, recovered flowback water is commonly stored in AGWSSs on hydraulic fracturing sites (BC OGC, 2015). Therefore, it is important to measure the possibility of AGWSS failure and identify critical failure modes for informed flowback water spill risk management. Fault tree analysis is a widely applied systematic approach to conduct qualitative and quantitative analyses of safety and reliability of a system. This approach uses a tree-like hierarchical structure to describe logical relationships between the faults of a system and their causes (Kabir, 2017). Fault tree analysis starts with a system failure (i.e., a top event) and works backward from the top of the tree towards the bottom causes (i.e., basic events) (Kabir, 2017). The qualitative analysis can be carried out by identifying critical failure modes leading to the occurrence of the top event, while the quantitative analysis involves calculating the occurrence probabilities of failure modes and the top event (Ruijters and Stoelinga, 2015). This approach enables risk assessors to envision the entire system and each level of possible undesired events that potentially lead to the failure of the whole system. Traditional fault tree analysis (TFTA) requires the assignment of exact occurrence probabilities of basic events (BE) to estimate the top event occurrence probability. However, the precise occurrence probabilities of different events are often rarely known in real-world risk management due to a lack of sufficient statistical data and uncertainties in the available data (Shi et al., 2014; Lavasani et al., 2015). To address the issue of insufficient data, expert elicitation is often carried out to generate reasonable estimations

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on the occurrence possibilities of BEs. However, this process is inherently associated with subjectivity and imprecision, such as vagueness and ambiguities in risk perceptions by different risk assessors (Rajakarunakaran et al., 2015). Fuzzy logic has been incorporated with TFTA as it is capable of handling inexact information and vagueness of human thoughts (Ferdous et al., 2011). Fuzzy logic uses a strict mathematical framework in which vague conceptual information can be quantitatively studied. The combined use of fuzzy logic and fault tree analysis, known as fuzzy fault tree analysis (FFTA), has been widely used to estimate system failures in different industries, such as fire and explosion accidents of crude oil tanks (Shi et al., 2014; Wang et al., 2013), toxic chemical leaking accidents (Lavasani et al., 2015), oil leakage in subsea production systems (Cheliyan and Bhattacharyya, 2018), and drinking water system failure (Sadiq et al., 2008). However, limited studies have investigated the failure of flowback water storage system. There is a significant knowledge gap in flowback water spill prevention during its storage. The present work attempts to assess the probability of unintended flowback water release resulting from AGWSS failure for the first time. A fault tree of AGWSS failure was constructed and the BEs were developed based on consultation with experts from the industry and regulatory organization. The fuzzy occurrence possibilities of BEs were estimated through expert elicitation, and grey pairwise comparison technique was used to facilitate the aggregation of experts’ judgments. The assessment results from FFTA and TFTA were also compared. The developed FFTA methodology for AGWSS failure assessment could provide the unconventional gas industry with useful information for flowback water spill risk mitigation.

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2. Fault Tree of AGWSS Failure 2.1. Construction of Fault Tree In British Columbia, recovered flowback water is often stored in AGWSSs on the hydraulic fracturing site for a few months. As Fig. 1 shows, an AGWSS mainly consists of an open short cylindrical storage tank and an excavated berm enclosing the storage tank. The excavated berm, designed for containment, is used as the secondary spill prevention component of an AGWSS. The storage tank is composed of structurally insulated walls clamped with water-proof liners. The liners are commonly made from high-density polyethylene or other synthetic materials. A water discharging system comprising pipelines, valves, and pumps is used to load flowback water into/out of the storage tank. A typical AGWSS can hold up to millions of gallons of flowback water.

=========================== PLEASE INSERT FIG. 1 HERE ===========================

A fault tree was constructed for the analysis of AGWSS failure. As shown in Fig. 2, the top event of the fault tree is defined as unintended release of flowback water due to AGWSS failure. The top event can be broken down into two conditional intermediate events, including “failure of storage tank” and “failure of containment”. Unintended release of flowback water happens only if both of the intermediate events occur, and thus an AND gate is used to connect the two intermediate events. The intermediate event “failure of storage tank” will occur as a result of the occurrence of any one of the four

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sub-events, including “flowback water overflow”, “tank leaks or ruptures”, “external catastrophe”, and “spill during water loading”. Thus, these sub-events were connected by an OR gate. The downward branching of the fault tree stopped until all branches were terminated by BEs. All BEs were considered independent of each other. It should be noted that the fault tree was constructed based on experts’ knowledge, and it can be modified to suit assessors’ specific needs and different system configurations.

=========================== PLEASE INSERT FIG. 2 HERE ===========================

2.2. Evaluation of Fault Tree Both qualitative and quantitative analyses were carried out to evaluate the constructed fault tree. The qualitative analysis aims to find out the minimal cut sets (MCSs) that lead to the occurrence of the top event. A cut set is a combination of BEs that can cause the top event. MCS is the minimal combination of BEs, which if all occur will result in the occurrence of the top event. Based on BEs and logic gates in the fault tree, the equation of MCSs identified responsible for AGWSS failure is shown as T = MCS1 + MCS2 + L MCS N = ∑ X i X 22 X 44 + ∑∑ X i X j X 33 + ∑∑ X i X k X 24 i

i

j

i

(1)

k

+∑∑ X i X l X 20 + ∑∑ X i X m + ∑∑ X i X q + ∑ X p i

l

i

m

i

q

p

8

where i ∈ (1, 2, 3, 4, 8, 9, 10); j ∈ (36, 37, 38, 42, 43, 45); k ∈ (23, 25); l ∈ (21, 22); m ∈ (5, 6, 7, 19, 25, 26, 27, 28, 29, 30, 31, 32, 39, 40, 41); q ∈ (11, 12, 13, 14); p ∈ (15,

16, 17, 18); X represents a BE; and N is the total number of MCSs. The quantitative analysis aims to measure the occurrence probability of the top event and the major faults causing AGWSS failure. The quantitative analysis requires the occurrence probability of each BE in a fault tree. The occurrence probabilities of BEs are propagated upward through the fault tree using the Boolean relationships. As a result, the occurrence probabilities of MCSs can be determined and used to calculate the occurrence probability of the top event (PT): k

k

PT = 1 − ∑ ∏ (1 − Pi ) + ∑ r =1 X i ∈Cr

∏

r ≥1 X i ∈( Cr UCs )

k

(1 − Pi ) −L − (−1)( k −1) ∏ (1 − Pi )

(2)

X i ∈Cr

where Cr is a MCS, r and s (r ≤ s) are the ordinal numbers of MCSs, (1-Pi) denotes the non-occurrence probability of the MCS containing BE Xi, Xi ∈ Cr denotes the ith BE within MCS Cr, and Xi ∈ (Cr U Cs) is the ith BE that belongs to Cr or Cs. In real-world system failure analyses, the precise probabilities of BEs are often unavailable due to insufficient data; in fact, some BEs in a fault tree may not have any quantitative data at all. Thus, it is difficult to generate an accurate probability value for each BE. As a solution to the lack of real-world statistical data, safety engineers and risk assessors often estimate event failure possibilities through an expert elicitation process with the help of probability rating scales and linguistic variables. Nevertheless, this approach is inherently associated with epistemic uncertainties, such as vagueness and ambiguity of human thoughts, which could lead to inaccurate failure estimations (Kabir, 2017). Therefore, it is desirable to use fuzzy logic-based techniques to handle the uncertainties caused by imprecise information and vagueness of subjective estimation. 9

In this study, possibility is defined as a qualitative characteristic indicating the likelihood of occurrence of an event, whereas probability is a numerical value reflective of that likelihood. Thus, a qualitative linguistic judgment from experts such as “the chance that an event will occur is high” can be labeled as the occurrence possibility of the event. FFTA is used to quantify numerical probabilities of system failure and the occurrence of failure modes based on the occurrence possibilities of basic events obtained from expert elicitation. 3. Fuzzy Fault Tree Analysis 3.1. Fuzzification of BE Occurrence Probability scales have been widely used for rating the occurrence of failure modes in different system reliability assessments. As Table 1 outlines, a probability rating scale was used to describe the occurrence possibilities of failure modes and BEs (Liu et al., 2013). The linguistic description of occurrence possibility, also known as a linguistic variable, can be converted to a fuzzy number using fuzzy membership functions. A brief introduction of fuzzy numbers and membership functions related to this study is provided in the supplementary file.

=========================== PLEASE INSERT TABLE 1 HERE ===========================

As shown in Fig. 3, the linguistic description of BE occurrence possibility was mapped into fuzzy membership functions representing “very low” (VL), “low” (L),

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“relatively low” (RL), “moderate” (M), “relatively high” (RH), “high” (H), and “very high” (VH) levels (Shi et al., 2014; Wang et al., 2013). It should be noted that defining the fuzzy membership functions is a subjective process, and using different fuzzy membership functions may lead to different fuzzy numbers based on the same ratings of BE occurrence possibility (Rajakarunakaran et al., 2015). Intelligent algorithms (e.g., genetic algorithm, neural networks) can be used to facilitate defining the fuzzy membership functions, depending on the size of available data. Therefore, the fuzzy membership functions defined in this study can be modified by different assessors to suit their preferences and case-specific data. The linguistic descriptions of BE occurrence possibility were obtained through expert elicitation (Lavasani et al., 2015). The failure probability rating scale (Table 1) was provided to experts to facilitate them in estimating the occurrence possibilities of BEs. Three experts were consulted in this study, including a safety engineer (E1) from a local unconventional gas production company; an academic researcher (E2) whose research focuses on water infrastructure failure risk assessment (e.g., water storage and transportation); and a governmental regulator (E3) specializing in oil and gas pipeline integrity and spill risk assessment. Particularly, the safety engineer has abundant handson experience in AGWSS installation and management. Thus, the experts’ judgments represent the best available, multi-perspective information regarding the failure of AGWSS components in the context of real-world flowback water management. The Delphi method was used repeatedly until a final judgment was made by each expert. After expert elicitation, an occurrence probability and the corresponding linguistic description, presented as a fuzzy number, were generated for each BE by each expert.

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=========================== PLEASE INSERT FIG. 3 HERE ===========================

3.2. Aggregation of Fuzzy Numbers Since expert knowledge is influenced by individual perspectives and experience, complete impartiality of expert judgment is difficult to achieve in expert elicitation. It is necessary to aggregate different experts’ judgments presented in fuzzy numbers to one fuzzy number reflective of an amalgamated occurrence possibility of a BE. In this study, a consistency aggregation method was used to obtain the amalgamated fuzzy numbers for BEs. The consistency aggregation begins with the calculation of the relative agreement degree (RA) of each expert’s judgment. The RA was calculated following steps used in Wang et al. (2013). Detailed calculation steps of RA were provided in the supplementary file. The resulting RA of the uth expert, denoted by RA(Eu), was used in combination with expert importance degree (IDu) to determine the integrated weight (wu) of this expert. As shown in Table 2, a scoring scale for determining the IDu of experts was commonly used in failure assessments of petrochemical engineering systems (Lavasani et al., 2015; Rajakarunakaran et al., 2015). The scoring scale consists of three criteria, including professional title (PT), experience (EXP), and education level (ED), and each criterion contains five sub-indices reflective of an expert’s professionalism. Based on the expert information listed in Table 2, the IDu was determined for each expert using the grey

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pairwise comparison method. The calculation steps were also included in the supplementary file. =========================== PLEASE INSERT TABLE 2 HERE ===========================

Based on IDu and RA(Eu), the integrated weight (wu) of the uth expert can be calculated: wu = ζ ⋅ IDu + (1 − ζ ) ⋅ RA( E u )

(3)

where ζ (0 ≤ ζ ≤ 1) is a relaxation factor; if ζ = 0, then the difference in professionalism between different experts is considered negligible; if ζ = 1, then experts’ professionalism has the most significant influence on the final judgment. It is the responsibility of assessors to assign an appropriate value to ζ . In this study, the value of ζ was set at 0.6. The resulting wu was used to aggregate experts’ judgments: M

p% i = ∑ wu ⊗ p% ui

(4)

u =1

where

p% i

is the aggregated fuzzy number of BE Xi; p% ui is the fuzzy number of BE Xi

estimated by the uth expert; M is the total number of experts, and wu is the integrated weight of the uth expert. The resulting p% i represents the amalgamated fuzzy occurrence possibility of BE Xi. The integrated weight (wu) were also used to aggregate the occurrence probabilities derived from expert elicitation to generate an aggregated occurrence probability (AP) for each BE.

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3.3. Estimation of Top Event Occurrence Probability The occurrence probability of the top event was calculated using FFTA and TFTA. The main steps of the two FTAs were outlined in Fig. 4. In FFTA, the aggregated fuzzy number of a BE was defuzzified to a crisp number (i.e., defuzzification), referred to as a crisp possibility score (CPS), and then the CPS was converted into a real-world crisp probability (CP) of occurrence (i.e., conversion). The steps of defuzzification and conversion are described in the following sections. The resultant CPs of BEs were used as inputs to the fault tree to generate an output as the real-world CP of the top event using Eq. (2). In TFTA, the APs were used as inputs to the fault tree to predict the CP of the top event using the same equation. =========================== PLEASE INSERT FIG. 4 HERE ===========================

The fuzzy occurrence possibility of a failure event needs to be defuzzified to a CPS to provide meaningful information for risk management. In this study, the centroid method was used for defuzzification as it is the most commonly used defuzzification approach in engineering applications of fuzzy logic (Yager, 1980). The defuzzification equation is presented as Eq. (5). An aggregated fuzzy number of a BE after defuzzification will generate a CPS indicating the occurrence possibility of the BE, where a higher value of CPS indicates a higher occurrence possibility.

∫ x ⋅ µ dx CPS = ∫ µ dx x A%

x A%

(5)

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The obtained CPS needs to be translated into a CP because there is an inconsistency between the real-world probability and the possibility score. The inconsistency can be solved by the conversion function (Eqs. (6) and (7)) developed by Onisawa (1990), which is a popular method used to link the CPS and real-world probability of failure modes in the petrochemical industry (Lavasani et al., 2015; Shi et al., 2014; Wang et al., 2013). For the top event, the calculated CP equals PT.  1  ; CPS ≠ 0 CP = 10τ  0; CPS = 0

(6)

where 1

1 − CPS  3 τ =   × 2.301  CPS 

(7)

3.4. Importance Analysis of BEs and MCSs Importance analysis can identify the critical BEs and MCSs that contribute the most to the occurrence of the top event. Fussell-Vesely’s importance analysis (FV) was used to FV identify critical BEs and MCSs. The importance index ( I BE ) of BE Xi can be calculated:

N

FV I BE =

1 − ∏ (1 − PjX i ) j =1

Pt

(8)

where PjX is the occurrence probability (i.e., CP) of the jth MCS containing BE Xi, and Pt i

FV is the occurrence probability of the top event. The importance index ( I MCS ) of the jth MCS

can also be calculated: FV I MCS =

Pj Pt

(9)

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The resulting IFV is on a range from 0 to 1, where a higher value indicates a higher contribution to the occurrence of the top event. Risk assessors can identify the critical BEs/MCSs by ranking the IFV values from the highest to the lowest. The identified critical BEs/MCSs should be given priority in risk mitigation. 4. A Case Study The failure of a hypothetical AGWSS was assessed using the two FTAs. The hypothetical AGWSS has a storage capacity of 4500 m3 and it is located in Northeastern British Columbia, overlying the unconventional gas-rich Montney Formation. The operation time of the AGWSS is from April to early October in a year to avoid the harsh winter climate. The AGWSS is also operated under the normal climate conditions of the Montney Formation region for storage of 4500 m3 of flowback water generated from an ordinary fracturing operation. The historical climate data of the site can be found in the Canadian Climate Normals database for the city of Dawson Creek (Government of Canada, 2019). Considering unintended release of flowback water due to AGWSS failure as the top event, the constructed fault tree (Fig. 2) can be used to qualitatively and quantitatively assess the occurrence of the top event. The qualitative analysis indicates that 45 BEs are the basic causes, which form 221 MCSs that can lead to the occurrence of the top event. Based on the qualitative analysis results, the occurrence probability of the top event can be quantified. 4.1. Possibility of BE Occurrence The probabilities and linguistic judgments of BE occurrences were estimated by experts using the failure rating scale (Table 1) due to the lack of precise real-world data. The descriptions of BEs and the linguistic judgments of their occurrence possibilities are

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listed in Table 3. As can be seen, the strictness of judgments on the occurrence possibility of BEs made by E1 and E2 are generally similar as the majority (i.e., > 70%) of the judgments fall within “VL” level. It is interesting to note that E3 (i.e., the government regulator) made more conservative judgments as about 44% and 33% of BEs were estimated with “L” and “M” levels of occurrence possibility, respectively. The difference in judgments can be attributed to different perspectives, experience, and risk perceptions of the three experts. Thus, it is important to identify the RA degree of judgments on the same BE by different experts to generate an amalgamated result. The expert judgments were converted to fuzzy numbers according to the fuzzy membership functions shown in Fig. 3.

The fuzzy numbers were aggregated to one fuzzy number representing the

amalgamated fuzzy occurrence possibility of a BE. =========================== PLEASE INSERT TABLE 3 HERE ===========================

4.2. Top Event Occurrence Probability The top event occurrence probabilities predicted by using two different FTAs were compared. In FFTA, aggregated fuzzy numbers of BEs were defuzzified to CPSs, which were further converted into CPs. The resulting CPs were used as inputs to the fault tree and generated a CP of 5.75E-04 for the top event, and this probability value corresponds to a CPS of 0.263. When mapping the CPS into the fuzzy membership functions representing the linguistic descriptions of event occurrence possibility levels (Fig. 3), it can be found that the degrees of membership to “L” and “RL” possibility levels are 0.370 and 0.630, respectively, suggesting that the possibility of AGWSS failure can mainly be 17

described as “RL”. In comparison, the final CP of AGWSS failure determined by using TFTA is 2.36E-04, which is approximately half of the CP estimated by using FFTA. However, this probability still reflects a “RL” level of failure rate. According to the results from the two FTAs, it can be concluded that the failure rate of AGWSS is “RL”. In the petrochemical industry, FFTA has been widely used to predict the failure probabilities of various hazardous production processes/systems. For example, by using FFTA, the occurrence probabilities of undesired events such as fire and explosion of crude oil tank, unintended release of chlorine, de-ethanizing system failure, and liquified petroleum gas refueling leakage were predicted to be 4.51E-02, 0.80E-02, 3.02E-01, and 4.82E-02, respectively (Lavasani et al., 2015; Rajakarunakaran et al., 2015; Renjith et al., 2010; Wang et al., 2013). According to the failure rating scale shown in Table 1, these predicted probabilities reflect “M” to “VH” levels of system failure rate. The failure rate of AGWSS was estimated to be much lower than the above-mentioned system failures. 4.3. Importance Analysis of BEs and MCSs The purpose of importance analysis is to identify the most critical BEs and MCSs for resource allocation in spill prevention. As shown in Fig. 5a and b, BEs were ranked FV according to the I BE values determined by using the two FTAs. The I FV and CP values

were converted to − log( I FV ) and − log(CP) in Fig. 5, and thus a lower value indicates a higher importance/occurrence probability. As Fig. 5a shows, the ranking result from FFTA suggests that X3, X9, X10, X8, X6, X1, X2, X4, X5, and X30 are the top ten BEs that have the most significant contributions to AGWSS failure. Hence, these BEs need to be given extra attention during AGWSS installation and operation. Particularly, X6, X3,

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and X5 are critical BEs not only because of the high I FV values but also because of their relatively high CPs. It is interesting to note that seven of the top ten BEs (i.e., X3, X9, X10, X8, X1, X2, and X4) are linked to containment failure, such as chronic erosion, bulking, and use of improper construction materials in berms. As a secondary spill prevention component of AGWSS, the importance of containment is often overlooked. The results show that the containment of AGWSS plays an important role in preventing the accidental release of flowback water. In addition to containment failure, the rest critical BEs are relevant to flowback water loading and monitoring (i.e., X6 and X5), suggesting that flowback water transportation is another important aspect that needs attention during AGWSS operation. In comparison, TFTA identified that external catastrophes (Fig. 5b), such as strong wind (X17) and external fire and explosion (X18), are the most critical basic causes of AGWSS failure. Although FFTA and TFTA predicted the same “RL” level of failure rate for the top event, the importance rankings of BEs from the two approaches are different. The reason for the difference is that FFTA manipulated the uncertainties in BE occurrence estimations through the aggregation of fuzzy numbers, while TFTA only generated single-point estimations for BE occurrence probability. It is more reasonable to estimate BE occurrence possibilities by considering uncertainties as a result of the imprecision and vagueness of subjective judgment than a single-point estimation (Wang et al. 2013; Yadiz and Kabir, 2018). The importance analysis results from the two FTAs show that the loss of containment integrity, water loading failure, and external catastrophes are the important causes responsible for AGWSS failure.

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The top ten important MCSs identified by the two FTAs are presented in Fig. 5c and d, and the rankings of important MCSs are slightly different. As Fig. 5c shows, MCS X3X6 was identified as the most critical cut set by using FFTA, followed by X17 and X18, which represent two types of external catastrophe. The two catastrophe events were also confirmed as the most critical MCSs by using TFTA (Fig. 5d). Since an external catastrophe event can be the cause of both storage tank and containment failures, it was identified as an independent cut set capable of causing the failure of the entire AGWSS. In addition to external catastrophes, flowback water loading failure combined with the loss of containment integrity was diagnosed as an important AGWSS failure mode. This failure mode is represented by MCSs comprising a water loading failure event and a containment failure event, such as cut sets X3X6, X6X9, and X3X13. Therefore, the risk implication of MCS importance analysis is consistent with that of BE importance analysis.

=========================== PLEASE INSERT FIG. 5 HERE ===========================

5. Conclusions Unintended release of flowback water resulting from storage failure is one of the most concerning environmental risks that require the unconventional gas industry to implement risk measurement and safety planning against potential environmental contamination. In this study, an FFTA methodology was developed for analyzing

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AGWSS failure, and the results were compared with those from TFTA. A fault tree was constructed to model AGWSS failure by comprehensively considering all possible causes and their relationships. Expert elicitation was employed to obtain linguistic judgments on the occurrence possibility of BEs. Fuzzy logic was used to manipulate the ambiguities and vagueness in the linguistic variables. Consistency analysis and grey pairwise comparison techniques were also used to mitigate the influence of human subjectivity and improve the accuracy of failure analysis. The probability of AGWSS failure was quantified as 5.75E-04 by using FFTA. This probability indicates a relatively low failure possibility according to a widely accepted failure rating scale. The quantified failure probability is higher than the result (i.e., 2.36E04) generated from TFTA. The importance rankings of BEs and MCSs generated from the two FTAs are different due to different treatments on the estimations of BE occurrence possibility. However, both FTAs identified that containment, water loading, and external catastrophes are three critical aspects that should be given attention during AGWSS installation and operation. There are several limitations of this study; for example, the fuzzy membership functions and weighting parameters used in the aggregation of fuzzy numbers were defined subjectively and a relatively small set of qualitative data was used in the analysis of AGWSS failure. These limitations could result in uncertainties in the assessment results, which are difficult to address due to data constraints. However, the developed FFTA methodology, as a framework, can still be used by other assessors to provide useful information for mitigating the risk of flowback water spill and help the unconventional gas industry transit towards more environmentally responsible production.

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Acknowledgments The authors would like to thank the staff at the British Columbia Oil and Gas Commission (BCOGC) and Secure Energy Inc. for their technical support and willingness to provide the data for this study. The authors would also like to thank Dr. Ezzeddin Bakhtavar for his assistance.

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TABLES

Table 1 A probability rating scale for failure occurrence. Rating 1

Level and description

Extremely high: failure is almost inevitable 2 Very high (VH): failure is likely to occur 3 High (H): repeated failures 4 Relatively high (RH): failure rate is in between “Moderate” and “High” 5 Moderate (M): occasional failures 6 Relatively low (RL): failure rate is in between “Moderate” and “Low” 7 Low (L): a few failures in historical record 8 Very low (VL): failure is unlikely to occur 9 Extremely low: failure is nearly impossible a Not considered in this study.

Failure rate 1/2

Occurrence probability 5.00E-01

1/3

3.33E-01

(0.8, 0.9, 1.0, 1.0)

1/20 1/80

5.00E-02 1.25E-02

(0.7, 0.8, 0.9) (0.5, 0.6, 0.7, 0.8)

1/200 1/2000

5.00E-03 5.00E-04

(0.4, 0.5, 0.6) (0.2, 0.3, 0.4, 0.5)

1/15000

6.67E-05

(0.1, 0.2, 0.3)

1/150000

6.67E-06

(0, 0, 0.1, 0.2)

1/1500000

6.67E-07

Fuzzy number -a

-

Table 2 A scoring scale for expert importance degree measurement. Criteria Professional title (PT)

Experience (EXP)

Education level (EL)

Sub-indices Senior Intermediate Junior Technician Non-technical ≥ 30 years 20 to 29 years 10 to 19 years 5 to 9 years ≤ 5 years Ph.D. Master Bachelor High school < High school

Score 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1

E1

E2

E3
























Table 3 Fuzzy occurrence possibility of BEs causing AGWSS failure. No.

Description

X1

Burrows/holes created by animals and/or roots of plants voids Containment failure due to insufficient capacity Chronic erosion of berm caused by rain and wind Containment damage caused by traffic accident Operator fails to monitor flowback water level Rupture of flexible hoses connecting pipelines Loose connection between flexible hoses and pipelines Using improper construction materials in containment Berm failure due to bulking Berm failure due to construction at incorrect slope angles Fail to shutdown water loading Error in commissioning shutdown of water loading Inlet/outlet value fails to control flowback water Malfunction of pump to control flowback water Failure of AGWSS due to flooding Failure of AGWSS due to earthquake Failure of AGWSS due to strong wind Failure of AGWSS due to external fire/explosion accidents Failure of AGWSS due to wall plate corrosion Anti-corrosion coating fails to provide protection to hollow steel stand (HSS) HSS is constantly contacting water, increasing the corrosion rate Corrosive soils contact with AGWSS components Damages to wall plates caused by faulty installation Omission in inspecting/reporting/acting upon areas of poor workmanship Settlement of soils due to the heavy burden from AGWSS Rupture of wall plates due to defective wall materials Damages to wall plates caused by vehicle/fork lifter collisions Inadequate removal of debris and smoothening of ground Wall rupture due to tilting or displacement of AGWSS Failure of liner due to use of defective material Tear of liner by clamps due to improper clamping Loss of liner integrity due to aging effects Cracking of liner caused by acidic flowback water Lowered tensile resistance in the areas of scratch Damages to liner caused by the impact of installation equipment Induced stress because of high overburden pressure Wrinkles fold over under load and create weakened areas Liner is lifted off at concave areas, resulting in excessive stress Pipeline rupture caused by overloading Pipeline puncture due to use of defective building material Pipeline malfunction caused by improper installation Tensile stress due to pressure surge in pipeline Tensile stress due to external load on pipeline Pipeline corrosion due to loss of external protective coating Pipeline corrosion due to loss of internal protective coating

X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 *

AP-aggregated occurrence probability of basic event

Linguistic judgment E1 E2 E3 VL VL VL

Aggregated fuzzy number

AP*

(0.000, 0.000, 0.100, 0.200)

6.67E-06

VL RL VL L M VL VL L VL VL VL VL L VL VL L VL

VL L VL L RL L VL VL VL VL VL L RL VL VL VL L

VL M VL M M L L M M L M M L VL VL L L

(0.000, 0.000, 0.100, 0.200) (0.238, 0.338, 0.373, 0.473) (0.000, 0.000, 0.100, 0.200) (0.204, 0.304, 0.304, 0.404) (0.338, 0.438, 0.469, 0.569) (0.065, 0.131, 0.165, 0.265) (0.035, 0.069, 0.135, 0.235) (0.173, 0.242, 0.273, 0.373) (0.138, 0.173, 0.238, 0.338) (0.035, 0.069, 0.135, 0.235) (0.138, 0.173, 0.238, 0.338) (0.169, 0.234, 0.269, 0.369) (0.131, 0.231, 0.262, 0.362) (0.000, 0.000, 0.100, 0.200) (0.000, 0.000, 0.100, 0.200) (0.069, 0.138, 0.169, 0.269) (0.065, 0.131, 0.165, 0.265)

6.67E-06 3.96E-04 6.67E-06 3.37E-04 7.40E-04 3.70E-05 1.96E-05 3.53E-04 2.64E-04 1.96E-05 2.64E-04 3.51E-04 6.40E-05 6.67E-06 6.67E-06 3.88E-05 3.70E-05

VL VL

VL VL

L M

(0.035, 0.069, 0.135, 0.235) (0.138, 0.173, 0.238, 0.338)

1.96E-05 2.64E-04

VL

VL

M

(0.138, 0.173, 0.238, 0.338)

2.64E-04

VL VL VL

VL VL L

L L L

(0.035, 0.069, 0.135, 0.235) (0.035, 0.069, 0.135, 0.235) (0.065, 0.131, 0.165, 0.265)

1.96E-05 1.96E-05 3.70E-05

VL VL VL

VL VL VL

M L VL

(0.138, 0.173, 0.238, 0.338) (0.035, 0.069, 0.135, 0.235) (0.000, 0.000, 0.100, 0.200)

2.64E-04 1.96E-05 6.67E-06

L VL M VL VL VL VL M

VL VL VL L VL VL VL RH

VL L L L L M L M

(0.035, 0.069, 0.135, 0.235) (0.035, 0.069, 0.135, 0.235) (0.173, 0.242, 0.273, 0.373) (0.065, 0.131, 0.165, 0.265) (0.035, 0.069, 0.135, 0.235) (0.138, 0.173, 0.238, 0.338) (0.035, 0.069, 0.135, 0.235) (0.431, 0.531, 0.562, 0.662)

1.97E-05 1.96E-05 3.54E-04 3.70E-05 1.96E-05 2.64E-04 1.96E-05 4.38E-03

VL VL L

VL VL VL

L L VL

(0.035, 0.069, 0.135, 0.235) (0.035, 0.069, 0.135, 0.235) (0.035, 0.069, 0.135, 0.235)

1.96E-05 1.96E-05 1.97E-05

VL VL

L VL

VL L

(0.031, 0.062, 0.131, 0.231) (0.035, 0.069, 0.135, 0.235)

1.79E-05 1.96E-05

VL VL VL VL

L L VL VL

L VL VL M

(0.065, 0.131, 0.165, 0.265) (0.031, 0.062, 0.131, 0.231) (0.000, 0.000, 0.100, 0.200) (0.138, 0.173, 0.238, 0.338)

3.70E-05 1.79E-05 6.67E-06 2.64E-04

VL

VL

M

(0.138, 0.173, 0.238, 0.338)

2.64E-04

FIGURES

Fig. 1. Schematic view of AGWSS for hydraulic fracturing flowback water.

Fig. 2. A fault tree of AGWSS failure.

Fig. 2. (Continued.)

Fig. 3. Fuzzy membership functions representing linguistic descriptions of event occurrence possibility.

Fig. 4. Flowchart of FFTA and TFTA of AGWSS failure.

Fig. 5. Importance analyses of BEs using (a) FFTA and (b) TFTA, and MCSs using (c) FFTA and (d) TFTA.

Highlights: •

The failure of flowback water storage system was assessed for the first time

•

The failure possibility of the storage system was identified to be relatively low

•

Containment and water loading failures and external catastrophe are the main causes

•

Secondary containment is an important component to reduce the system failure rate

Statement of Conflicts of Interest The authors of this publication declare that that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. All of the sources of support for the work described in this publication are acknowledged.

Dr. Guangji Hu on behalf of all the authors Oct 11, 2019