Estimation of An Event Occurrence for LOPA Studies Randy Freeman S&PP Consulting Houston, TX 77041 713 408 0357 rafree@yahoo.com 1
Problem Your LOPA team members tell you that the initiating event of concern has never happened in the history of the process unit. No bad events in 20 years. What do you do? Ignore the event and move on It can never happen What else? 2
Available Methods to Handle Problem Assume event has happened once, M1 = 1/N Assume event has almost happened M2 = 1/2N Bayesian Results M3 = 1/3N M4 = 1/4N 3
Methods (cont) Poisson Arrivals of Failures At 90% limit M5 = 0.105/N = 1/10N At 10% limit M6 = 2.303/N 4
Methods (cont.) Chi Square Confidence Limit (95%) M7 = λ = χ α;2 / (2 n) = 5.991/(2 n) Chi Square Confidence Limit (50%) M8 = λ = χ α;2 / (2 n) = 1.3863/(2 n) 5
Methods (cont.) Binomial Distribution M9 = 1 [0.9] 1/n 6
Methods (cont.) Uniform Distribution Bayes Estimator M10 = 1/(N+2) 7
Methods (cont.) Hypothesis Test Normal distribution with 95% confidence M11 = ( n z + 2 α Zα = 1.6445 z 2 α ) 8
Methods (cont.) Explosive Initiation Test M12 = 1 [0.5] 1/N 9
1.00E+00 Best Guess Methods Legend Failure Rate, fail/yr. 1.00E-01 1.00E-02 M3 M1 M2 M3 M4 M8 M9 M10 1.00E-03 0 10 20 30 40 50 60 70 80 90 100 Nunber of Trials, N 10
1.00E+01 Confidence Limit Methods Failure Rate, fail/yr. 1.00E+00 1.00E-01 1.00E-02 M11 M12 M7 M6 Legend M5 M6 M7 M11 M12 M5 1.00E-03 0 10 20 30 40 50 60 70 80 90 100 Number of Trials, N 11
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Recommendations for Basic LOPA Determine if the event of concern is physically possible. If not physically possible, delete from LOPA analysis Make sure you have a minimum of 10 years of data. If not use values from LOPA book Use M1 = 1/N for events found to be physically possible 13
Recommendations for Beyond Basic LOPA Reviews Use estimators M3, M8 or M12. M3 (Rule of 1/3N) is easier to remember and calculate. 14
Example Case 1 Data No occurrences in three years What frequency should be assigned? Answer Since the history is less than 10 years, use the frequency presented in LOPA book. 15
Example Case 2 Data One occurrence in ten years What frequency should be assigned? Answer Methods presented in this paper do not apply when an event has occurred. Start with a frequency of 1/10 and review value in LOPA book. 16
Example Case 3 Data No occurrences in ten years What frequency should be assigned? Answer Determine if history is valid Start with a frequency of 1/10 If LOPA at greater than order of magnitude significance, use 1/30 17
Example Case 4 Data No occurrences in 30 years What frequency should be assigned? Answer Determine if history is valid Start with a frequency of 1/10 If LOPA at greater than order of magnitude significance, use 1/90 18
Example Case 5 Data No occurrences in 20 years What frequency should be assigned? Answer Determine if history is valid No history of pump overpressure of PRV PRV set P = 150 psig Pump Deadhead P = 100 psig Not credible scenario Delete from LOPA Study 19
Can it really happen? We pressurize a vessel to 130 psig. The MAWP is 100 psig. What happens????? Does the vessel blow up???? 20
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More Information Vessel in good condition per API 579 Fitness for Service Test Pressure = 1.5 * MAWP Test Pressure = 150 psig Piping is 2 inch schedule 40 with a catastrophic burst pressure of 7000 psig ANSI Class 150 Flanges with a MAOP of 285 psig at 100 F 22
ANSWER NOTHING HAPPENS! No rupture No weld tear No flange failure No release Nothing happens! Maybe an ASME code violation requiring an inspection for fitness for service 23
Lessons Learned Before starting detailed LOPA analysis verify that the scenario of interest can actually happen. Physics and Chemistry are powerful tools to sort out imaginary from real safety issues. 24
Conclusions There is no single correct answer Use an estimator that is consistent with the other assumptions in your LOPA study 25
Does the Audience Know of Another Estimator?? 26
More Details What to Do When Nothing Has Happened?, pp 204-211,Process Safety Progress, Vol. 30, No. 2, September 2011 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/prs.10463, 2011 27
QUESTIONS???? 28
Have a Merry Christmas! 29