Uncertainty analysis of Phast's atmospheric dispersion model for two industrial use cases

Uncertainty analysis ofPhast’s atmospheric dispersion model

for two industrial use cases

Nishant Pandya, Nadine Gabas & Eric Marsden

Loss Prevention 2013, Firenze

Context

. Postdoctoral work of Nishant Pandya• Toulouse Chemical Engineering laboratory (CNRS)• Foundation for an Industrial Safety Culture• industrial partners including DNV Software

. Simulation of atmospheric dispersion of gas releases• complex physical phenomena• often dimensioning scenarios for land-use planning

. Phast is widely used to analyze these release scenarios• modeling involves a large number of variables and parameters• variables and parameters affected by uncertainty

. Political pressure to improve characterization of uncertainty inmodelling results

• new French legislation on land-use planning around Seveso-typeinstallations

2 / 18 Loss Prevention 2013

Study objectives

. Uncertainty analysis of Phast version 6.7• leak source term• outdoor dispersion model

. Analyze 10–30 minute continuous releases of four materials• two toxic (ammonia, nitric oxide)• two flammable (methane, propane)

. Examine the impact of representative variations of physical variables& internal model parameters

• uncertainty propagation

. Two different use-cases:• accident-investigation• risk-prevention


Uncertainty analysis

choice of submodel

Phast

numerical resolutionparameters

input variables

sub-modelparameters

uncertainty analysis

sensitivity analysis

[Pandya et al 2011]

outputsikp

v∏∂=

Max number of iterations,of timesteps, etc.

Jet model, wind speed profile, etc.

Weather: - wind speed- stability class- atmospheric temp.Source term:- orifice diameter- release angle- roughness

Jet dilution params, passive transition params(rupas), etc.



. Study the effect on model outputs ofvariability or uncertainty affectingmodel inputs

. Histograms

. Quantified using the coefficient ofvariation

• CV =σ

µ




. Histograms


• CV =σ

µ

concentrationat 1000 m




. Histograms


• CV =σ

µ

concentrationat 1000 m

CV = 10%CV = 125%


Analysis strategy

Compare output variability for two industrial use-cases:. accident-investigation:

• user models a historical accident, for which he has some(uncertain) information on release conditions & weatherconditions

• wishes to assess the level of confidence given these “irreducible”input uncertainties

• input uncertainties: defined with help from expert Phast users

. risk-prevention:• risk assessment for regulatory purposes / process design• modeling guidelines impose stereotypical assumptions on releaseconditions to increase homogeneity of risk assessments across aregulatory domain

• assess confidence in model outputs given uncertainty oninternal Phast parameters

• input uncertainties: gaussian distribution with ±10% variabilityaround default value


Analysis strategy









Analysis strategy








releasecond

itions

uncertainty

mod

elun

certainty


Analysis strategy








releasecond

itions

uncertainty

mod

elun

certainty


Method1 Select products and storage conditions

2 Select relevant Phast parameters andtheir distributions

3 Decide on relevant outputs

4 Execute Phast multiple times andanalyze distribution of outputs

. NO

. NH3

. methane

. propane






Done with help fromexpert Phast users, to berepresentative of industrialuse cases

bounds allowedby Phast






12

C500: concentration at 500 m

C1k: concentration at 1 km

C2k: concentration at 2 km

Downwind distance (m)











No comparison with experimentalresults

More than a million Phast executionsover duration of project!


Scenario tree: risk-prevention use-case

. Fine-grained scenario-based approach facilitates interpretation of results

. 4 “bifurcation parameters”: release duration, release rate, weatherconditions, release angle→ 16 scenarios

θ 0°

10 min. duration 30 min. duration

continuous release

low release rate high release rate

θ 90°

neutralweather

stableweather

θ 0° θ 90°

Sc 3 Sc 4

θ 0° θ 90°

Sc 5

θ 0° θ 90°

Sc 6 Sc 7 Sc 8

θ 0° θ 90°

Sc 9

θ 0° θ 90°

Sc 10 Sc 11 Sc 12

θ 0° θ 90°

Sc 13

θ 0° θ 90°

Sc 14 Sc 15 Sc 16Sc 1 Sc 2

high release ratelow release rate

neutralweather

neutralweather

neutralweather

stableweather

stableweather

stableweather

“Low” and “high” release rates selected to be product-appropriate8 / 18 Loss Prevention 2013

Parameters: risk-prevention use-case

Parameter Default value

Distribution µ(mean) σ(std dev.)

α1 (jet entrainment parameter) 0.17 normal 0.17 0.0085

α2 (cross-wind entrainment parameter) 0.35 normal 0.35 0.0175

CDa (drag coefficient of plume in air) 0 exponential λ = 69.2

γ (dense cloud side entrainment parameter) 0 exponential λ = 34.6

CE (cross-wind spreading parameter) 1.15 normal 1.15 0.0575

epas (near-field passive entrainment parameter) 1 normal 1 0.05

rupas

(max cloud/ambient velocity parameter) 0.1 normal 0.1 0.005

rropas

(max cloud/ambient density parameter) 0.015 normal 0.015 0.00075

rEpas

(max non-passive entrainment fract° param.) 0.3 normal 0.3 0.015

Ri*pas

(max Richardson number) 15 normal 15 0.75

rtrpas

(distance for phasing in passive entrainment) 2 normal 2 0.1

Ri (Richardson number for lift-off criterion) -20 normal -20 1

rquasi (quasi-instantaneous parameter) 0.8 normal 0.8 0.04

Ripool (Richardson for passive transition above pool) 0.015 normal 0.015 0.00075

Entpool (pool vaporisation entrainment parameter) 1.5 normal 1.5 0.075

tavtox (s) (averaging time for toxic release) - uniform

For 10 min release: [540 – 660] For 30 min release: [1620 – 1980]


Scenario tree: accident-investigation use-case

. Examine influence of uncertainty in “physical” parameters ofscenario

. Similar to risk-prevention, but bifurcation parameters also uncertain

duration: [5-15] min duration: [25-35] min

continuous release

orifice diameter[20-60] mm


θ [0-30]° θ [60-90]°



neutralweather

stableweather

Sc 103 Sc 104 Sc 105 Sc 106 Sc 107 Sc 108 Sc 109 Sc 110 Sc 111 Sc 112 Sc 113 Sc 114 Sc 115 Sc 116Sc 101 Sc 102

neutralweather

neutralweather

neutralweather

stableweather

stableweather

stableweather

θ [0-30]° θ [0-30]° θ [0-30]°θ [60-90]° θ [60-90]° θ [60-90]° θ [0-30]° θ [0-30]° θ [0-30]°θ [0-30]°θ [60-90]° θ [60-90]° θ [60-90]° θ [60-90]°


Parameters: accident-investigation use-case

Parameter Nomenclature / Unit Distribution Range of variation

Tst Storage temperature / K triangular NH3: [263.15 – 283.15] centered at 273.15 K

NO, CH4, C3H8: [273.15-293.15] centered at 283.1K

Lh Liquid height / m uniform [12.75 - 17.25]

Ta Atmospheric temperature / K triangular [282.65 - 287.65] centered at 285.15 K

Pa Atmospheric pressure / Pa uniform [0.99·105 - 1.035·105]

Ha Relative atmospheric humidity / - triangular [0.55 - 0.85] centered at 0.7

DO Orifice diameter / m triangular Value 1: [0.02 - 0.06] centered at 0.04 Value 2: [0.16 - 0.20] centered at 0.18

Durmax Maximum release duration / s uniform Value 1: [300 - 900] Value 2: [1500 - 2100]

angle Release angle / degree uniform Value 1: [0 - 30] Value 2: [60 - 90]

SC Stability Class / - discrete Neutral: [10 % C/D, 80 % D, 10 % E]

Stable: [10 % E, 80 % F, 10 % G]

ua Wind speed / m·s-1 uniform Neutral: [4 - 6] Stable: [1.5 - 3]

Sflux Solar radiation flux / W·m-2 triangular Neutral: [250 - 1000] centered at 500

Stable: [0 - 500] centered at 250

ZR Release height above ground/ m uniform [1 - 10]

Z0 Surface roughness length / m triangular [0.5 - 1.5] centered at 1 m


Other modeling assumptions

. Continuous discharges from a storage tank (“leak” module of Phast)

. Cloud is assumed to progress in an open field (no impingement)

. Study downwind concentrations:• from 50 m to 200 m for flammable releases• from 500 m to 2 km for toxic releases

. Reference height for outputs:• 1.5 m for toxic releases• center of cloud for flammable releases

. Core averaging time set to averaging time for all simulations


Three types of results

1 Scenario-specific uncertainty information fordecision-makers

2 Comparing uncertainty for two industrial use-cases

3 Identify release conditions which lead to the highest levelof uncertainty


Use-case uncertainty comparisonm

ean

CV

(%)

NO-RP

NH3-RP

NO-AI

NH3-AI

CH4-RP

C3H8-

RP

CH4-AI

C3H8-A

I

C200C100C50C500

C1kC2k

As expected, level of uncertainty always higher for “accident-investigation”than for “risk-prevention” use-cases


Use-case uncertainty comparisonm

ean

CV

(%)

NO-RP

NH3-RP

NO-AI

NH3-AI

CH4-RP

C3H8-

RP

CH4-AI

C3H8-A

I

C200C100C50C500

C1kC2k

As expected, level of uncertainty always higher for “accident-investigation”than for “risk-prevention” use-cases


Release conditions leading to highestuncertainty

Risk-prevention use-case

Highest CV for vertical NO releases in stable weather conditions, with highrelease rates


Release conditions leading to highestuncertainty

Risk-prevention use-case

Highest CV for vertical NO releases in stable weather conditions, with highrelease rates


Conclusions


Conclusions

. For the 4 materials studied, model uncertainty is significantly lowerthan uncertainty resulting from variation in source term and weatherconditions

. We have identified the release conditions which lead to the highestlevel of model uncertainty (material-dependent)

. Quantitative information on level of uncertainty in consequenceestimations:

• helps risk analysts understand the degree of confidence they can placein modeling results

• when comparing risk reduction measures, tells whether investmentranking is robust, given modeling uncertainties

• when modeling results inform land-use planning, provides informationwhich can help arbitrate between different strategies

. All modeling results presented to decision-makers should ideallyinclude information on level of uncertainty


Thanks for your attention!

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Uncertainty analysis of Phast's atmospheric dispersion model for two industrial use cases