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UNCERTAINTIES AND ERRORS
OF QRA Laura Bruce, Ifiok Etukudo, Widya Siswanto, Ugoeze
Emmanuella Uzor and Shobha Venkataswamy.
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T YPES OF UNCERTAINTIES IN QRA
Parameter Uncertainty: When the values of the
parameters used in the models are not accurately
known. It might be stochastic or epistemic
uncertainty.
Model Uncertainty: Any model, conceptual or
mathematical, will inevitably be a simplification of
the reality it is designed to represent
Completeness Uncertainty: Originates from the
fact that not all contributions to risk are addressed
in QRA models.
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UNCERTAINTIES INTRODUCED AT THE
DIFFERENT STAGES OF QRA
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THE IDENTIFICATION STAGE
Produce a comprehensive list of possible initiating events
To identify priorities between them and make decisions on which of them are to be analysed further
Major uncertainty: Completeness.
Have all major hazards and/ or possible accident
scenarios been identified? Methods for structured identification (to facilitate
completeness): HAZOP, what-if analysis, FMEA, etc.
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THE IDENTIFICATION STAGE (CONT·D)
Example of accidents with their coverage in standard QRA methodologies.
Accident Mechanism Included in
Standards
QRA
Methodologies?
Models
Available?
Texas City
2005
K O drum
overflow,
spraying vent
N Y
Tosco Avon
1997
Hydrocracker
reactor
runaway
N Y
Buncefield2005
Overflow,
splashing flow,
UVCE
N Y
CAI, Danvers 2006
Confined VCE N Y (Adapted from Taylor, 2010)
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FREQUENCY ESTIM ATION
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FREQUENCY ESTIM ATION (CONT·D)
The two main methods of likelihood and frequency
estimation are:
Historical Data: Questions raised on accuracy and
applicability. Data may be inaccurate, incomplete or
inappropriate. Issue on parameter uncertainty.
E.g.: Leak frequency data for North Sea to elsewhere.
Fault and event tree analysis: Questions raised on
completeness, simplification and parameter uncertainty in the model.
E.g.: Omission of significant failure mechanisms can
lead to erroneous results.
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FREQUENCY ESTIM ATION (CONT:)
Major sources of uncertainty in frequency
estimation:
- failure frequency;
- leak frequency;- ignition probability; and
- explosion probability.
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CONSEQUENCE ESTIM ATION
The consequence estimation scheme involves
three steps:
y Accident scenario analysis Identification of initiating events.
Generation of accident scenarios for each initiating events.
Quantification of accident scenarios.
y Identification and classification of losses
y Estimation of losses
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CONSEQUENCE ESTIM ATION (CONT·D)
Conducted using physical and effect models.
y Physical models: flash fire, pool fire, BLEVEs,
etc.
y Effect models: explosion effects, heat radiation, toxic effects, etc.
Major uncertainty:
y Model uncertainty in physical and effect models
y Parameter uncertainty, such as leak size.
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CONSEQUENCE ESTIM ATION (CONT·D)
Scenario:
Piping connecting Separator A with Gas Compressor experience 30 mm leak (9 in piping with 110 m length).
Operating pressure is 30 bar and operating temperature
is 27o
C.
Model uncertainty and parameter uncertainty was identified in the consequence estimation.
Leak
Diameter
(mm)
Cd Full Analysis Spouge
Difference
(%)Leak
(kg/s)
Flame
length (m)
Leak
(kg/s)
Flame
length (m)
in flame
length
30 0.8 2.87 28.51 2.7 27.8 2.50%
25 0.8 1.99 24.55 1.875 23.94 2.50%
30 0.7 2.51 26.99 2.7 27.8 2.99%
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CONSEQUENCE ESTIM ATION (CONT·D)
With the same scenario, if SD V is used as
safeguard, the consequence estimation presented
below.Time (minutes) Leak (kg/s) Flame length (m)
0 2.87 28.51
5 3.25E-04 0.7
10 3.60E-08 0.02
Uncertainty relates to the assumption made on the condition of the safeguard, such as full closure (air-tight) condition of the valve, time response, etc.
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ESTIM ATION OF RISK
The final step in the QRA is to generate the
actual risk measure.
Risk is product of the probability of a certain
outcome with the consequence of that particular outcome.
Risk indices represented by:
y Individual Risk Per Annum (IRPA);
y Probable Loss of life (PLL);
y Temporary Refuge Impairment Frequency (TRIF);
and
y Societal Risk (F-N Curve).
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ESTIM ATION OF RISK (CONT·D)
Major uncertainty:
y Assumption and simplification made in order to
decrease the complexity of the analysis
Example: assumptions on distribution of ignition
sources, population distributions, etc.
y Relative importance of risk
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CONCLUSION
Identification of the contributors to the overall
uncertainty is important to improve the quality
of the QRA
Whenever necessary, increased investment indata collection or model development could
significantly reduce uncertainty.
However, uncertainty in inherent statistical
variability in failure rate data can not be
removed.
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REFERENCES
Abrahamsson, Marcus. Uncertainty in
Quantitative Risk Analysis ² Characterization
and Methods of Treatment. 2002.
Lees, Frank P. L
oss Preven
tion
in
the ProcessI ndustries, 3 rd Edition. 2004.
Taylor, J.R. Accuracy in Quantitative Risk
Assessment? 13th International Symposium on
Loss Prevention. 2010.
Borysiewicz, M.J, et. al. Quantitative Risk
Assessment (QRA).
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