Quantification of the Uncertainty of the Peak Pressure Value in the vented Deflagrations of Air-Hydr...
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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

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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


Structure of the work (1/2): in the vented Deflagrations of Air-Hydrogen mixtures.

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.


Structure of the work (2/2): in the vented Deflagrations of Air-Hydrogen mixtures.

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.


Uncertainty sources in the quantitative in the vented Deflagrations of Air-Hydrogen mixtures.risk analysis: The risk analysis structure.


  • SYSTEM DEFINITION. in the vented Deflagrations of Air-Hydrogen mixtures.

  • 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.


Analysis of the uncertainty sources. in the vented Deflagrations of Air-Hydrogen mixtures.

  • 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.


Representation of uncertainty in the vented Deflagrations of Air-Hydrogen mixtures.


General main uncertainty sources. in the vented Deflagrations of Air-Hydrogen mixtures.

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.


Theory of Evidence Definitions. in the vented Deflagrations of Air-Hydrogen mixtures.

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);


Bel ( A in the vented Deflagrations of Air-Hydrogen mixtures.c ) = 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


Structure of the work (2/2): in the vented Deflagrations of Air-Hydrogen mixtures.

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.


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.


NFPA68 limits deflagration (the figure is not in scale).

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


Structure of the work (2/2): deflagration (the figure is not in scale).

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.


Simplified CVE Schema. deflagration (the figure is not in scale).



Variability of Pstat in increasing order. the exhausts.

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


Structure of the work (2/2): the exhausts.

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.


Main Parameters for the vented deflagrations the exhausts.

  • 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.


Simplified NN schema the exhausts..

The correlation between the experimental data and the NN predicted data.


Fuzzy model general characteristics the exhausts.

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 .


Fuzzy model Results the exhausts.

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.


Thank you

THANK YOU the exhausts.

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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