Bayesian-LOPA Methodology Development for LNG Industry [PDF]

using a conjugate gamma prior distribution such as OREDA (Offshore Reliability Data) and Poisson likelihood distribution. If there is no prior information, Jeffreys noninformative prior may be used. The LNG plant failure database was used as plant specific information. The PFDs (Probability of Failure on Demand) of IPLs.

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OUTLINE OF RESEARCH Bayesian-LOPA Methodology Development for LNG Industry Geun Woong Yun, Texas A&M University

In order to meet the fast growing LNG (Liquefied Natural Gas) demand, many LNG importation terminals are operating currently. Thus, it is important to estimate the potential risks in LNG terminals with LOPA (Layer of Protection Analysis) which can provide quantified results with less time and efforts than other methods. For LOPA application, failure data are essential to compute risk frequencies. However, the failure data from the LNG industry are very sparse and have statistically shake grounds. Therefore, Bayesian estimation, which can update the generic data with plant specific data, was used to compensate for its weaknesses. Based on Bayesian estimation, the frequencies of initiating events were obtained using a conjugate gamma prior distribution such as OREDA (Offshore Reliability Data) and Poisson likelihood distribution. If there is no prior information, Jeffreys noninformative prior may be used. The LNG plant failure database was used as plant specific information. The PFDs (Probability of Failure on Demand) of IPLs (Independent Protection Layers) were estimated with the conjugate beta prior such as EIReDA (European Industry Reliability Data Bank) and binomial distribution. In some cases, EIReDA did not provide failure data, so the newly developed Frequency-PFD conversion method was used instead. By the combination of Bayesian estimation and LOPA procedures, the Bayesian-LOPA methodology was developed and was applied to an LNG terminal. The found risk values were compared to the tolerable risk criteria to make risk decisions and compared to each other to make a risk ranking. The BayesianLOPA methodology can be used in other industries. Furthermore, it can be used with other frequency assessment methods such as Fault Tree Analysis (FTA) and Event Tree Analysis (ETA) to strengthen their results.

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LNG (Liquefied Natural Gas) is one of the fastest growing energy sources in the U.S. to fulfill the increasing energy demands and diversify the energy portfolio. In order to meet the LNG demand, many LNG facilities including LNG importation terminals are operating currently. Moreover, there are many proposed projects for LNG terminals to fill the gap between supply and demand of LNG in North America. Therefore, it is important to control and estimate the potential risks in LNG terminals to ensure their safety and reliability.

Figure 1. Description of an LNG importation terminal (www.kogas.co.kr)

One of the most cost effective ways to estimate the risk is LOPA (Layer of Protection Analysis) because it can provide quantified risk results with less time and efforts than other methods. Thus, LOPA was applied in this research. For LOPA application, failure data are essential to compute risk frequencies (see Figure 2). However, the failure data from the industry are very sparse and have statistically shaky grounds due to insufficient population of sample data and relatively short-term operational history. Bayesian estimation is identified as one of the better methods to use to compensate for the weaknesses found in the LNG industry’s failure data. It can update the generic data with plant specific data. In other words, the data updated by Bayesian logic can reflect both long-term based historical experiences and plant specific

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conditions. Thus, in this research, the new Bayesian-LOPA methodology was developed as shown in Figure 3, and it was applied to an LNG importation terminal to estimate the potential risks.

IPL1

IPL2

IPL3

Consequence occurs

SUCCESS Initiating event

Estimated frequency fi

SUCCESS

Undesired but tolerable outcome SUCCESS

FAILURE

PFD1 =p1 f 1 = f i * p1

FAILURE

PFD2 = p2 f2 = fi * p1 * p2

Note Impact event

Safe outcome

LOPA path FAILURE

PFD3 = p3

Undesired but tolerable outcome Consequences exceed criteria f3 = fi * p1 * p2 * p3

Frequency

Figure 2. Description of LOPA methodology Based on Bayesian estimation, the frequencies of initiating events were obtained using a conjugate gamma distribution as the prior information and Poisson distribution as the likelihood function. OREDA (Offshore Reliability Data) database was used as a prior distribution because it was produced from a gamma distribution (see Figure 4). If there is no prior information, Jeffreys noninformative prior may be used. The LNG plant failure database was used as plant specific likelihood information. The PFDs (Probability of Failure on Demand) of IPLs (Independent Protection Layers) were estimated with the conjugate beta prior distribution and binomial likelihood distribution. EIReDA (European Industry Reliability Data Bank) database was used as prior

iv

information because it provided the failure data made from beta distribution. In some cases EIReDA did not provide failure data, so the newly developed Frequency-PFD conversion method was used instead. By the combination of Bayesian estimation and LOPA procedures, the Bayesian-LOPA methodology was developed. The method was applied to an LNG importation terminal. For seven incident scenarios, it produced valid risk values. The posterior values of every initiating event or IPLs are located between prior and likelihood values. This means that the posterior values are valid and wellupdated. The found risk values were compared to the tolerable risk criteria given by CCPS (Center for the Chemical Process Safety) to make risk decisions. Finally, the estimated risk values of seven incident scenarios were compared to each other to make a risk ranking in view of probabilistic risk analysis which considers only failure frequency without considering consequence analysis. In conclusion, as the good safety records of LNG industries speak, in this research, it can be generally concluded that the LNG terminal has good safety protections to prevent dangerous events (see Figure 5). The newly developed BayesianLOPA methodology as one of the risk assessment methods really does work well in an LNG importation terminal and it can be applied in other industries including refineries, petrochemicals, nuclear plants, and aerospace industries. Moreover, it can be used with other frequency analysis methods such as Fault Tree Analysis (FTA) and Event Tree Analysis (ETA).

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Process information

Process Flow Diagram, P&ID, Process Data

Process Hazard Analysis (PHA)

HAZOP

Estimate Consequence & Severity

Category approach

Develop Scenarios

From PHA results Scenario : Initiating event + Consequence

Identify Initiating Event Frequency

Generic Data & Plant Specific Data Bayesian Engine

IPL : Independence, Effectiveness, Auditability

Identify Related IPLs & Estimating PFDs of IPLs

PFD of IPLs : Generic, plant specific data J

f i = f i × ∏ PFD c

Estimate Scenario Frequency

I

j =1

f i = f i × PFD c

I

i1

i j

× PFD

i2

× .... × PFD

Risk Ranking, Make Risk Decisions

Risk Ranking Compare with tolerable risk criteria

Recommendations for Safety Enhancement

Add IPLs or safety measures

Figure 3. The flow diagram of this research

iJ

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Frequency of initiating event with informative prior

Likelihood function (probability)

Prior distribution (frequency)

Poisson distribution

Gamma distribution f (λ ) =

α prior

f (λ ) =

μ2

β α α −1 −λβ λ e Γ(α )

Pr( X = x ) =

OREDA

LNG facility failure data x : No. of failures t : time to failure

μ2 V σ2 = = 2 , γ prior = = μ μ V σ

OREDA −1 α

(γ ) α −1 −λ (γ −1 ) λ e Γ(α )

e − λt ( λ t ) x x!

Bayesian Engine

β = γ −1

Posterior distribution (frequency) Gamma distribution ( x +α prior ) −1 − λ ( t + β prior )

f post ∝ λ

e

, α post = x + α prior , β post = t + β prior = t + 1 / γ prior

Mean of Posterior frequency μ post =

x + α prior α post x + α prior = = β post t + β prior t + 1 / γ prior

90% Bayes credible interval λ0.05 = χ 2 0.05 (2α post ) / 2β post , λ0.95 = χ 2 0.95 ( 2α post ) / 2β post

Figure 4. The schematic diagram of Bayesian estimation for initiating events

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Comparison of scenario risk 1.00E+00 1.00E-01

Prior

Likelihood

Posterior

1.00E-02 1.00E-03 1.00E-04 frequency (/year)

1.08E-05

6.01E-05 3.03E-05

1.00E-05

1.00E-07 1.00E-08

2.90E-06

scenario 2

2.80E-07

scenario 3

1.35E-07

9.87E-08

1.48E-07

2.45E-08

scenario 1

3.16E-07

2.60E-06 1.00E-06

1.37E-05

1.43E-09

1.00E-09

scenario 4

1.88E-09

scenario 5 scenario 6 scenario 7

1.08E-09

1.00E-10 4.43E-11

6.86E-11

1.00E-11 4.54E-11

1.00E-12 1.00E-13 1.00E-14

5.50E-14 1.48E-14

Figure 5. The risk value graphs of seven incident scenarios from an LNG terminal

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