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

San Sebastian - 12/September/2007

Marco N. Carcassi.Gennaro M. Cerchiara.

University of Pisa

Dipartimento di Ingegneria Meccanica Nucleare e della Produzione – DIMNP

ICHS - 2007

International Conference on Hydrogen SafetyS. Sebastian - Spain

September 11 - 13 . 2007

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 (1/2):

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.

Structure of the work (2/2):

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

SYSTEM DEFINITION.

1) layout, components, control systems, operators etc., from a technical and operational point of view;

2) the characterisation of the site in which the system is placed (meteorology, demography, infrastructure presence, interfaces with other systems etc);

3) information about management and maintenance procedures.

System definition.

Uncertainty/Imprecision sources are identifiable in:

1) Vagueness associated with data and relative system information. Important in the case of systems in planning phase.

2) The uncertainty modelling the studied system. For complex systems a “simplification” of the truth can bring to important types of uncertainty.

3) Particular critical analysis of the redundant systems.

Analysis of the uncertainty sources.

Aleatory Uncertainty Epistemic Uncertainty

The type of uncertainty which results from the fact that a system can behave in random ways following a probabilistic law, also known as:

The type of uncertainty from the lack of knowledge about a system and is a property of the analysts performing the analysis, also known as:

– Type A (or Type I) uncertainty; – Type B (or Type II) uncertainty;

– Objective uncertainty; – Subjective uncertainty;

– Irreducible uncertainty; – Reducible uncertainty;

– Stochastic uncertainty; – State of Knowledge uncertainty;

– Variability. – Ignorance.

Representation of uncertainty

1) Imprecisely specified distributions;2) Scarcely known or even unknown dependencies;3) Non-negligible measurement U(p);4) Non-detects or other censoring in measurements;5) Small sample size;6) Inconsistency in the quality of input data;7) Model Uncertainty U(p);8) Non-stationarity and non-constant distributions.

General main uncertainty sources.

Cumulative Probability according to the kind of Uncertainty.

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);

Theory of Evidence Definitions.

Ignorance ( Ac ) = 1 – [Bel ( Ac ) + Bel (Āc)]

Ignorance ( Ac ) = [ Pl ( Ac ) + Pl (Āc)] – 1

Bel (Anc) = Pl (Anc) = Pr (Anc)

[ Pr ( Anc ) + Pr (Ānc)] = 1

Bel (Ac) Pr (Ac) Pl (Ac)

Bel ( Ac ) = 1 – [ Pl (Āc)]

Pl ( Ac ) = 1 – [Bel (Āc)]

Graphical representation of the complex event Ac Ignorance (Anc = not complex event).

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.

Structure of the work (2/2):

1) not uniform gas distribution in the environment; 2) volume geometry; 3) position of the ignition point;4) possible presence of multiple ignitions; 5) possible presence of mechanisms accelerating the flame;6) flame turbulence and the instability.

Qualitative Evolution of the pressure in a vented deflagration (the figure is not in scale).

In the guide the stoichiometric deflagrations are studied

absence of turbulence

stoichiometric tests are substantially too much conservative for gas, like hydrogen, hypothesis inapplicable for structures with low resistance (civil use)

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

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 the area of venting is not immediately available for the outflow of gases but it is characterized from its own inertia and from the position.

NFPA68 limits

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.

Structure of the work (2/2):

Simplified CVE Schema.

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

Variability of Pstat in increasing order.

The overpressure PMAX

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

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.

Structure of the work (2/2):

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.

TESTCODE

Av(m2)

Pstat(mbar)

H2%(%vol)

PMAX

experimental

(mbar)

PMAX

Neural Network(mbar)

Error(mbar)

Error%

CR07 0,35 20 13 151 146,66 -4,34 -3%

CR09 0,35 20 11,2 143 143,88 0,88 1%

CR28 0,7 20 11,7 92 90,48 -1,52 -2%

CR29 0,7 18 11,7 155 133,13 -21,57 -14%

CR31 0,7 21 11,7 98 77,12 -20,48 -21%

… … … … … … … …

Main Parameters for the vented deflagrations

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

Simplified NN schema.

Schema of the general Fuzzy Model (a) for vented deflagrations and preliminarily model (b) .

IF H2 is H2-LOW AND Av is Av-SMALL AND Pstat is Pstat-SMALL THEN PMAX is PMAX-LOW .

Fuzzy model general characteristics

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.

Fuzzy model Results

INPUT OUTPUT

Pstat = 60 mbar; PMAX ≡ [107 - 122]

mbarH2 = 11%vol;

U(PMAX) = 15 mbarAv = 1 m2;

University of Pisa

Dipartimento di Ingegneria Meccanica Nucleare e della Produzione – DIMNP

San Sebastian - 12/September/2007

THANK YOU

ICHS

International Conference on Hydrogen SafetyS. Sebastian - Spain

September 11 - 13 . 2007

Marco N. Carcassi.Gennaro M. Cerchiara.