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Quantifying Uncertainty in Vented Deflagrations of Air-Hydrogen Mixtures

This paper discusses the quantification of uncertainty in the peak pressure value in vented deflagrations of air-hydrogen mixtures. It explores different sources of uncertainty and introduces fuzzy techniques to quantify the risk uncertainty. The advantages and limitations of NFPA68 and critical aspects of its venting systems are also discussed.

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Quantifying Uncertainty in Vented Deflagrations of Air-Hydrogen Mixtures

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  1. Quantification of the Uncertainty of the Peak Pressure Value in the vented Deflagrations of Air-Hydrogen mixtures. University of Pisa Dipartimento di Ingegneria Meccanica Nucleare e della Produzione – DIMNP ICHS - 2007 International Conference on Hydrogen Safety S. Sebastian - Spain September 11 - 13 . 2007 Marco N. Carcassi. Gennaro M. Cerchiara. San Sebastian - 12/September/2007

  2. Structure of the work (1/2): Risk Analysis fundamentals;a) Uncertainty sources in the quantitative risk analysis; b) Analysis of the uncertainty sources; c) Introduction to the representation of uncertainty. d) Belief and Plausibility as quantifiers of Uncertainty.

  3. Structure of the work (2/2): Application of Fuzzy Techniques to quantify the Risk Uncertainty. – The Problem of Gas Vented Explosions –a) Advantages and limits of NFPA68: Critical aspects of NFPA68 venting systems. b) Main Uncertainty Sources – CVE experimental activity; c) The predictive neural network and the fuzzy system quantifying the uncertainty.

  4. Uncertainty sources in the quantitativerisk analysis: The risk analysis structure.

  5. SYSTEM DEFINITION. • 1) layout, components, control systems, operators etc., from a technical and operational point of view; • the characterisation of the site in which the system is placed (meteorology, demography, infrastructure presence, interfaces with other systems etc); • information about management and maintenance procedures.

  6. Analysis of the uncertainty sources. • System definition. • Uncertainty/Imprecision sources are identifiable in: • Vagueness associated with data and relative system information. Important in the case of systems in planning phase. • The uncertainty modelling the studied system. For complex systems a “simplification” of the truth can bring to important types of uncertainty. • Particular critical analysis of the redundant systems.

  7. Representation of uncertainty

  8. General main uncertainty sources. Cumulative Probability according to the kind of Uncertainty. • Imprecisely specified distributions; • Scarcely known or even unknown dependencies; • Non-negligible measurement U(p); • Non-detects or other censoring in measurements; • Small sample size; • Inconsistency in the quality of input data; • Model Uncertainty U(p); • Non-stationarity and non-constant distributions.

  9. Theory of Evidence Definitions. Evidence = All what is known (also not completely) of a phenomenon. ___________ Plausibility = what is not in contrast (induction) with the evidence of the phenomenon. Belief = all what is possible to deduce from the body of evidence to the phenomenon. Possibility = Function of Plausibility defined on a nested sequence through the Basic Probability Assignments (BPA); Necessity = Function of Plausibility defined on a nested sequence through the Basic Probability Assignments (BPA);

  10. Bel ( Ac ) = 1 – [ Pl (Āc)] Pl ( Ac ) = 1 – [Bel (Āc)] Graphical representation of the complex event Ac Ignorance (Anc = not complex event). Ignorance ( Ac ) = 1 – [Bel ( Ac ) + Bel (Āc)] Ignorance ( Ac ) = [ Pl ( Ac ) + Pl (Āc)] – 1 Bel (Ac)  Pr (Ac)  Pl (Ac) Bel (Anc) = Pl (Anc) = Pr (Anc) [ Pr ( Anc ) + Pr (Ānc)] = 1

  11. Structure of the work (2/2): Application of Fuzzy Techniques to quantify the Risk Uncertainty. – The Problem of Gas Vented Explosions –a) Advantages and limits of NFPA68: Critical aspects of NFPA68 venting systems. b) Main Uncertainty Sources – CVE experimental activity; c) The predictive neural network and the fuzzy system quantifying the uncertainty.

  12. Qualitative Evolution of the pressure in a vented deflagration (the figure is not in scale). • not uniform gas distribution in the environment; • volume geometry; • position of the ignition point; • possible presence of multiple ignitions; • possible presence of mechanisms accelerating the flame; • flame turbulence and the instability.

  13. NFPA68 limits In the guide the stoichiometric deflagrations are studied stoichiometric tests are substantially too much conservative for gas, like hydrogen, hypothesis inapplicable forstructures with low resistance (civil use) absence of turbulence the guide in "3-4-3 Inertia of Vent Closure" only prescribes its applicability for closings of the vent with a weight for unit surface smaller then 2.5 lb/ft2 (12,2 kg/m2) emphasizing as thearea of venting is not immediately available for the outflow of gases but it is characterized from its own inertia and from the position. The gases which have a laminar burning rate more then 59.8 cm/sec (for H2 , 3.45 m/s) are not considered into the guide

  14. Structure of the work (2/2): Application of Fuzzy Techniques to quantify the Risk Uncertainty. – The Problem of Gas Vented Explosions –a) Advantages and limits of NFPA68: Critical aspects of NFPA68 venting systems. b) Main Uncertainty Sources – CVE experimental activity; c) The predictive neural network and the fuzzy system quantifying the uncertainty.

  15. Simplified CVE Schema.

  16. (a) Inlet system scheme; (b) pipeline schema of sampling and the exhausts.

  17. Variability of Pstat in increasing order. The overpressure PMAX versus Pstat for high concentration of H2 (from 10% to 12,5%).

  18. Structure of the work (2/2): Application of Fuzzy Techniques to quantify the Risk Uncertainty. – The Problem of Gas Vented Explosions –a) Advantages and limits of NFPA68: Critical aspects of NFPA68 venting systems. b) Main Uncertainty Sources – CVE experimental activity;c) The predictive neural network and the fuzzy system quantifying the uncertainty.

  19. Main Parameters for the vented deflagrations • H2 Concentration inside the CVE volume, H2% [6%vol – 14%vol]; • vent Area , Av [0.35 m2 – 2.5 m2]; • Peak Pressure vent rupture, Pstat range [20 mbar - 80 mbar]; • Max Peak Pressure with venting, PMAX range [5 mbar – 250 mbar]. Partial data set from experimental deflagrations.

  20. Simplified NN schema. The correlation between the experimental data and the NN predicted data.

  21. Fuzzy model general characteristics Schema of the general Fuzzy Model (a) for vented deflagrations and preliminarily model (b) . IFH2 is H2-LOWANDAv is Av-SMALLANDPstat is Pstat-SMALLTHENPMAX is PMAX-LOW .

  22. Fuzzy model Results MFs → Mamdani (triangular); AND method → min; OR method → max; Implication → min; Aggregation → max; Defuzzification → centroid. Results with Pstat = 60 mbar. Results with Pstat = 60 mbar H2 = 11%vol.

  23. THANK YOU University of Pisa Dipartimento di Ingegneria Meccanica Nucleare e della Produzione – DIMNP ICHS International Conference on Hydrogen Safety S. Sebastian - Spain September 11 - 13 . 2007 Marco N. Carcassi. Gennaro M. Cerchiara. San Sebastian - 12/September/2007

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