Carlo Simulations. Brian Freeman, PE, PMP, QEP 1 Dec Copyright 2011 IES. 6 th Kuwait ASSE Conference

Transcription

1 Quantifying HSE Risks Using Monte Carlo Simulations Brian Freeman, PE, PMP, QEP 1 Dec 211

2 Agenda Communicating Risks Probability Distributions Assigning i Risk ik Monte Carlo Analysis Risk Quantification

3 Communicating Risks High versus Low Red versus Green What is acceptable?

4 Risk is a probability HSE risks are usually measured as a statistic 1 in 1 15% chance Real world is not exact variability exists in all dt data Statistics are inputs to Probability Density Functions (PDFs)

5 Discrete PDFs Individual occurrences Used to predict likelihood of events

6 Continuous PDFs Describes real time activities and measurements

7 Choosing a PDF Selecting Discrete vs. Continuous Does it happen with ihwhole units (1,2, 3, ) or decimal units (2.14, Selecting Mean and Variance Use real data if available Selecting Tails Finite or infinite tails? Weighting/Skewing Does a particular range seem more likely? Rule of Thumb: Ifindo doubt, use a Triangle orpert continuous o distributiontion

8 Using PDFs.% Likelihood 2 times a year % 5.%.15 Use Poisson s.1 Distribution Each Event costs on -1 average $2,5 Use Triangle Distributionib i Range $5 $3, Values x 1^ g(,, ) 5 3,113.% 95.% 5.% 5 1, 1,5 2, 2,5 3, 3,5 4,

9 Monte Carlo Analysis Randomly assigns values against the PDF to determine the probability bili The more iterations the more accurate to the distribution Va alues x 1^ ,79.% 95.% 5.%.% 94.1% 5.9% 5 1, 1,5 2, 2,5 3, 3,5 4 es x 1^ ,11.% 95.% 5.%.% 94.9% 5.1% 1 Iterations 1, Iterations Valu , 1,5 2, 2,5 3, 3,5 4

10 Combining PDFs Likelihood (Discrete). 5..% 95.% 5.% , % 5.% Impact (Continuous) g(,, ) 5 3,113.% 95.% 5.% Values x 1^ Values x 1^-4 2, 4, 6, 8, 1, 12, 14, 16, 18, 2, , 1,5 2, 2,5 3, 3,5 4,

11 Confidence Intervals Shows percent of occurrence 95% Confidence 1, % % Values x 1^-4 75% Confidence 6,81 75.% 25.% , Values x 1^-4 2, 4, 6, 8, 1, 12, 14, 16, 2, 5% Confidence 3,631 5.% 5.% Values x 1^-4 2, 4, 6, 8, 1, 12, 14, 16, 18, 2,.5. What is good enough? 2, 4, 6, 8, 1, 12, 14, 16, 18, 2,

12 Environmental Example MW of Mixture (Gas) Component Mol% MW Component MW Methane e 53.4% Ethane 17.2% Propane 14.6% n Butane 5.3% H2 2.6% CO2 1.9% I Butane 1.7% n Pentane 1.7% i Pentane 1.6% % Total Mixture MW Assign variation to each component (PERT distribution)

13 Worst Case Mixture MW % 9.% 5.% Total Component MW / Component MW Minimumi Maximum Mean Std Dev.473 Values 1.1.

14 Sensitivity Analysis Methane / Mol% Propane / Mol% Ethane / Mol% n-butane / Mol% n-pentane / Mol% i-pentane / Mol% I-Butane / Mol% CO2 / Mol% H2 / Mol% g.116 pp Total Component MW / Component MW

15 Spill Kit Example Average 2 oil spills annually Each spill ranges from 1 liters to 5 liters Most tlikely l is 15lit liters How many spill kits do you need? Each kit can clean on average 11 liters Actual ranges from 2 11 liters Direct calculation: 272 spill kits

16 # of Spills Monte Carlo Method % 9.% 5.%.35.3 # of Spill Kits Needed % 5.%.25 Spill Kit Size of individual spill % 9.% 5.% Minimum 2. Maximum 86. Mean Std Dev Values kits needed to be 95% sure Worst case 86 kits!

17 Fatalities USOSHA: 3.5 fatalities per 1, FT workers p= % 9.% 5.% 95% chance that up to 7 people will be killed

18 Incidents to Fatalities Heinrich s Triangle.6 Incidents % 9.% 5.% Pert(25,3,8) Minimum 25. Maximum 8. Mean 375. Std Dev

19 Expected Incidents Before a Fatality 1, % 22.% , 1,5 5 2, 2,5 5 3, 3,5 5 4, If we have as few as 1, incidents we still have a 78% chance of 4 fatalities!

20 Fault Trees

21 The real potential for damage? 1 in 24,63 1 in 3,33

22 Summary Variance cannot be neglected The right PDF can model variance Monte Carlo analysis provides accurate confidence by Palisades Microsoft Excel add in

23 Questions?

24 Vacancy BBS Specialist Must speak English and Arabic Bachelor s Degree 88 years experience Oil & Gas Experience Kuwait residency preferred