Flash Fire

Technical documentation for the Flash Fire (SLAB) consequence model — dense gas atmospheric dispersion, concentration field, flammability zones, and LFL/UFL distance estimation

1. Introduction and Physical Phenomenon

1.1 Flash Fire and SLAB

A Flash Fire occurs when a flammable gas cloud disperses in the atmosphere, reaches a flammable concentration (between LFL and UFL), and ignites without producing significant overpressure. The result is a rapidly propagating flame that sweeps through the cloud, causing lethal burns in the engulfed zone.

The SLAB (Simulating Large Atmospheric Body) engine is a direct JavaScript translation of the original Fortran code developed by Donald L. Ermak at Lawrence Livermore National Laboratory (1990). It preserves the physics, constants, and subroutine structure of the original model.

SLAB predicts the spatio-temporal evolution of a dense gas cloud along 61 downwind grid points, computing:

Substance concentration (mass fraction and volume fraction)
Cloud geometry (height, crosswind half-width, alongwind half-width)
Mixture temperature and density
Downwind, crosswind, and vertical velocities

1.2 Industrial Context

Dense gas behavior

SLAB was designed for gases denser than air (cryogenic LNG, LPG, chlorine). Dense gas clouds hug the ground and spread laterally under gravity, creating large flammable zones at low wind speeds.

Evaporating Pool (idspl=1)

Ground-level spill evaporating at steady state — LNG, LPG, or cryogenic liquid spills

Horizontal Jet (idspl=2)

Pressurized horizontal release at height $h_s > 0$ — pipeline or vessel failures

Vertical Jet (idspl=3)

Pressurized vertical release with plume rise — pressure relief vents, blowouts

Instantaneous (idspl=4)

Total mass released at once; transient puff mode — catastrophic vessel rupture

1.3 Scope of This Model

Results are used to determine:

Distance to LFL (Lower Flammable Limit) — inner boundary of flash fire zone
Distance to 50% LFL — precautionary planning distance
Distance to UFL (Upper Flammable Limit) — outer boundary of over-rich zone
IDLH, ERPG, and AEGL toxic thresholds (when applicable)
Cloud geometry (height, width) at each downwind distance
GeoJSON isopleths for GIS visualization

2. Calculation Sequence

Cargando diagrama...

Chemical Property Mapping — mapChemicalToSlabInput() retrieves gas/liquid heat capacities, liquid density, and heat of vaporization from the YAWS database, converting units for the SLAB engine.

Validation — Zod schema validates types and ranges; coherence checks ensure qs > 0 for continuous sources (idspl 1–3) and qtis > 0 for instantaneous release (idspl=4).

Initialization — Computes the Monin-Obukhov wind profile, estimates the mixing layer height $h_{mx}$ , and sets initial cloud state variables for the chosen source type.

Integration Loop — Advances the 11-ODE system along 61 grid points from $x=0$ to xffm using 4th-order Runge-Kutta, calling slope(), solve(), eval(), thermo(), and entran() at each step.

Concentration Field — Computes the crosswind concentration profile at 6 lateral positions, cloud duration $t_{cld}$ , and effective dispersion width incorporating wind meander.

Post-processing — Identifies LFL/UFL concentration zones by linear interpolation, computes cloud mass per isopleth, and generates GeoJSON polygons for visualization.

3. Input Parameters

Parameter	Symbol	Unit	Source
`wms`	$M_s$	kg/kmol	Chemical DB (`mw`)
`cps`	$c_{p,s}$	J/(kg·K)	YAWS gas polynomial
`tbp`	$T_{bp}$	K	Chemical DB (`boilingPoint`)
`dhe`	$\Delta H_{vap}$	J/kg	Chemical DB (`hvaptb`)
`cpsl`	$c_{p,sl}$	J/(kg·K)	YAWS liquid polynomial
`rhosl`	$\rho_{sl}$	kg/m³	YAWS density correlation
`cmed0`	$c_{med,0}$	—	Initial liquid mass fraction (0 = all vapor)
`spb`, `spc`	—	K	Clausius-Clapeyron constants

4. Chemical Properties — YAWS Mapping

Before running the SLAB engine, mapChemicalToSlabInput() computes thermodynamic properties from YAWS regression coefficients.

4.1 Ideal Gas Heat Capacity

c_{p,gas}(T) = \frac{c_{pga} + c_{pgb} T + c_{pgc} T^2 + c_{pgd} T^3 + c_{pge} T^4}{M_w} \times 10^3 \quad [\text{J/(kg·K)}]

Evaluated at $T = T_{bp}$ . Code: slabHelpers.ts → calculateGasHeatCapacity().

5. Wind Profile — Monin-Obukhov Similarity Theory

SLAB models the vertical wind speed profile using Monin-Obukhov Similarity Theory within the atmospheric surface layer:

u(z) = \frac{u_*}{\kappa} \left[\ln\!\left(\frac{z}{z_0}\right) - \Psi_M\!\left(\frac{z}{L}\right)\right]

Symbol	Description
$u_*$	Friction velocity [m/s]
$\kappa = 0.41$	von Kármán constant
$z_0$	Surface roughness length [m]
$L$	Monin-Obukhov length [m]; $\Lambda = 1/L$ = `ala`
$\Psi_M$	Momentum stability correction function

\Psi_M = 2\ln\!\left(\frac{1+\phi_M^{-1}}{2}\right) + \ln\!\left(\frac{1+\phi_M^{-2}}{2}\right) - 2\arctan(\phi_M^{-1}) + \frac{\pi}{2}

Code: slab-js/utils/uafn.js (function uafn). Reference: Ermak (1990), §2.1; Monin & Obukhov (1954).

5.1 Pasquill-Gifford Stability Classes

PG Class	`stab`	$\Lambda = 1/L$ [1/m]	Condition
A	1	−0.10 to −0.05	Very unstable
B	2	−0.05 to −0.02	Unstable
C	3	−0.02 to −0.005	Slightly unstable
D	4	≈ 0	Neutral
E	5	+0.005 to +0.02	Slightly stable
F	6	+0.02 to +0.10	Stable

6. Conservation Equations (11-ODE System)

The engine solves 11 ordinary differential equations along the downwind direction $x$ . The most important equations are:

7. Velocities and Cloud Height — `eval()`

At each step, eval() iteratively solves (max. 11 iterations, tolerance $\Delta u/u < 0.001$ ) the coupled system:

Cloud height (from mass conservation):

h = \frac{r}{\rho \cdot u \cdot b_b}

Downwind velocity (cubic equation, Ermak 1990 §3.2):

u^3 - u_0 \, u^2 + u_{g}^3 = 0

solved analytically using the trigonometric form of Cardano's formula.

Boundary layer mean velocity (Simpson's rule integration):

\bar{u}_a \approx \frac{u_1 + 4u_{1/2} + u_2}{6}

Code: slab-js/core/eval.js.

8. Entrainment Rates — `entran()`

Entrainment is the primary cloud dilution mechanism — the process by which ambient air mixes into the cloud and reduces concentration.

8.1 Vertical Entrainment Velocity

w = \frac{u_{ref}}{u_a(h_{tp})} \cdot \alpha_e \cdot \kappa \cdot u_* \cdot \left(\frac{f_{pr}}{\phi_m(h_{tp})} + \frac{f_{pr,b}}{\phi_m(h_b)}\right)

Symbol	Value	Description
$\alpha_e$	1.50	Entrainment coefficient
$\kappa$	0.41	von Kármán constant
$f_{pr}$	$1 - h_{tp}/h_{mx}$	Profile factor (vanishes at mixing layer top)

Code: entran.js, lines 251–272.

c(x, y, z) = c_{max}(x, z) \cdot F_c\!\left(\frac{y}{b_{bc}}\right)

with uniform distribution for $|y| \leq b_{bc}$ and Gaussian decay outside.

11. Numerical Integration — Runge-Kutta 4

The 11-ODE system is integrated along $x$ using the 4th-order Runge-Kutta method:

y_{n+1} = y_n + \frac{\Delta x}{6}(k_1 + 2k_2 + 2k_3 + k_4)

The integration step $\Delta x$ is automatically adjusted by the ncalc sub-step multiplier. The output grid has 61 points distributed logarithmically from $x = 0$ to xffm.

Code: slab-js/core/rungeKutta.js.

12. Post-processing and Outputs

12.1 Flammability and Hazard Zones

Zone	Concentration	Criterion
LFL	`lel` % vol	Lower Flammable Limit — inner flash fire boundary
50% LFL	`0.5 × lel` %	Precautionary planning zone
UFL	`uel` % vol	Upper Flammable Limit — over-rich zone boundary

Distances are obtained by linear interpolation on the 61-point output grid.

Code: slabAction.ts, function findDistanceForConcentration().

Flash Fire

1. Introduction and Physical Phenomenon

1.1 Flash Fire and SLAB

1.2 Industrial Context

Evaporating Pool (idspl=1)

Horizontal Jet (idspl=2)

Vertical Jet (idspl=3)

Instantaneous (idspl=4)

1.3 Scope of This Model

2. Calculation Sequence

3. Input Parameters

4. Chemical Properties — YAWS Mapping

4.1 Ideal Gas Heat Capacity

5. Wind Profile — Monin-Obukhov Similarity Theory

5.1 Pasquill-Gifford Stability Classes

6. Conservation Equations (11-ODE System)

7. Velocities and Cloud Height — `eval()`

8. Entrainment Rates — `entran()`

8.1 Vertical Entrainment Velocity

9. Thermodynamics — `thermo()`

10. Concentration Field

10.1 Crosswind Concentration Profile

11. Numerical Integration — Runge-Kutta 4

12. Post-processing and Outputs

12.1 Flammability and Hazard Zones

13. Physical Constants

14. Model Limitations

15. Bibliographic References

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Flash Fire

Evaporating Pool (idspl=1)

Horizontal Jet (idspl=2)

Vertical Jet (idspl=3)

Instantaneous (idspl=4)

Mass Conservation — f[1]

Lateral Spreading — Half-width bb — f[2]

Crosswind Momentum (Gravitational Spreading) — f[4]

Vertical Momentum — Center Height zc — f[7], f[8]

Energy Conservation (Temperature Flux) — f[5]

Energy Balance — Initial Temperature Estimate

Vapor-Liquid Equilibrium (Clausius-Clapeyron)

Newton-Raphson Temperature Iteration

Cloud Density

View model constants

Flat, homogeneous terrain

Constant, unidirectional wind

Single cloud simulation

Dense gas assumption

No reactive chemistry

Surface boundary layer validity

61-point spatial resolution

Clausius-Clapeyron parameters

Fixed empirical constants

Near-source uncertainty

View complete reference list

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