Pool Fire

1. Introduction and Physical Phenomenon#

1.1 Pool Fire#

The Pool Fire model simulates the steady-state combustion of a flammable liquid that has spilled onto a flat surface and ignited. The model computes:

• Maximum pool diameter based on spill type
• Mass burning rate per unit area (burning rate)
• Flame geometry (height, wind-induced tilt angle)
• Thermal radiation intensity at any given distance
• Human effects (1st/2nd degree burns, fatalities) via Probit functions
• Domino effects on neighboring vessels using Cozzani correlations
• Expected fatalities by integrating thermal radiation with population density

1.2 Industrial Context#

1.3 Scope of This Model#

This model calculates:

1. Pool diameter and geometry based on source type (continuous, massive, circularDike, rectangularDike)
2. Burning rate using Burgess-Strasser, Mudan, or tabulated methods
3. Flame height via Thomas or Pritchard-Binding correlations
4. Surface Emissive Power (SEP) accounting for soot shielding in large hydrocarbon fires
5. Thermal radiation at any distance — Point Source or Solid Plume (tilted cylinder) model
6. Distance to a specified radiation threshold (inverse problem via Newton-Raphson)
7. Thermal dose and probit-based probability of 1st/2nd degree burns and fatalities
8. Domino effect time-to-failure for neighboring vessels (Cozzani correlations)
9. Population fatalities using concentric annular ring integration

2. Calculation Sequence#

flowchart TD
  A["Input Data<br/>(fuel, source type, weather)"] --> B["Chemical Properties<br/>YAWS: ΔHvap, cP, ρL at Tamb & Tb"]
  B --> C["Burning Rate<br/>ṁ'' = f(ΔHc, ΔHvap, cP, ρL)"]
  C --> D["Pool Diameter<br/>D = f(sourceType, Q or V)"]
  D --> E["Flame Geometry<br/>u*, H(Thomas|Pritchard), θ, SEP"]
  E --> F["For each distance x:<br/>F_view, τ_atm, q(x)"]
  F --> G["Forward problem<br/>q(x)"]
  F --> H["Inverse problem<br/>x(q_target) — Newton-Raphson"]
  G --> I["Thermal Dose<br/>D_dose = t_exp · (q×10³)^(4/3)"]
  H --> I
  I --> J["Probit Analysis<br/>(Burns 1°/2°, Fatalities TNO/CCPS, Domino)"]
  J --> K["Fatality Calculation<br/>(Concentric Rings + FatalityUtils)"]

  style A fill:#e1f5fe
  style K fill:#c8e6c9
  style F fill:#fff3e0

1. Chemical Properties — Retrieve fuel properties from YAWS database at $T_{amb}$: heat of vaporization $\Delta H_{vap}$, liquid heat capacity $c_P$, and liquid density $\rho_L$.

2. Burning Rate — Compute $\dot{m}''$ [kg/(m²·s)] using Burgess-Strasser, Mudan, or tabulated value (gasoline).

3. Pool Diameter — Determine maximum pool diameter $D$ based on source type: continuous spill, massive release, circular dike, or rectangular dike.

4. Flame Geometry — Compute dimensionless wind speed $u^*$, flame height $H$ (Thomas or Pritchard-Binding), tilt angle $\theta$, and Surface Emissive Power (SEP).

5. Thermal Radiation — Compute radiation $q(x)$ [kW/m²] at target distances using Point Source or Solid Plume (tilted cylinder) view factor model.

6. Probit Analysis — Convert thermal dose into probability of 1st/2nd degree burns, fatalities (TNO or CCPS), and domino effects (Cozzani).

7. Fatality Estimation — Integrate fatality probability over concentric annular rings to estimate total casualties.

2.1 Release tab: containment and inventory#

The Release tab describes the pool source with two decisions, in that order, because the first one fixes the area and the second only completes it:

1. Containment — Unconfined, Rectangular bund (length × width) or Circular bund (diameter). With a bund, the pool area is the bund area; without one, the area has to come from the inventory.

2. Inventory — Without a bund it is required: Released quantity (mass or volume) or Continuous feed. With a bund it is optional: Bund area only, Released quantity or Continuous feed. Options are named after the data you have, not the phenomenon, because with a full bund the radiation does not change with them.

Both decisions are stored in a single field (sourceType) with eight values; the table summarises what each combination fixes in the stationary model (Yellow Book and ALOHA presets, and any preset with a fed bund):

Resulting pool. Below the two selectors, TekRisk shows live the effective area, the equivalent diameter and the duration the engine will use, together with the reason for the area (bund area, bund filled, inventory < bund, volume / depth, feed = combustion equilibrium or legacy sizing). It comes from the same code as the calculation, so what you read is what will be computed; if the engine cannot size the pool with the current data (for example, a feed with no equilibrium inside the bund), it says so instead of showing a number.

Rules and limits.

• A bund assumes full retention: overtopping is not simulated. Filling is only followed for a continuous feed with a release duration (section 2.2).
• A rectangular bund is approximated by an equal-area circle; solid-flame models require length/width ≤ 2.
• ALOHA-based radiation requires an equivalent diameter ≤ 200 m.
• The Conservative screening and Point source presets without a bund keep the engine's legacy sizing from quantity or feed (section 5); with a fed bund, screening uses the stationary model in this table and point source does not support it (the panel leaves only Bund area only).

2.2 Continuous release duration#

A continuous feed with no other data gives an equilibrium pool and no duration: the fire lasts as long as the release, which is not a property of the model. The optional Release duration field (time until isolation or until the vessel empties) settles both with the Yellow Book (CPR 14E, §6.5.5):

• Transient pool. With a constant feed the pool grows towards equilibrium as $A(t) = A_{eq}\,(1 - e^{-\tau})$, with $\tau = \dot m''\,t/(\rho_L\,\delta)$ (Eq. 6.82 with $\beta' = 0$). If the release is short the pool does not reach equilibrium and radiation uses the diameter reached.
• Fire duration. When the release stops, the remaining $\delta$ layer burns: $t = t_{rel} + \rho_L\,\delta/\dot m''$ (Eq. 6.87). With a bund, if the pool fills it before the release stops, it burns with the bund area and the duration follows from the mass balance (no overtopping).
• Depth. With a duration, the panel asks for the surface type (Table 3.1) as for a released quantity. With the Point source preset only the duration is added; the legacy diameter does not change.

The duration feeds the short-fire notice and the solid-ignition criterion (600 s); it does not cap the exposure time of the dose.

2.3 Leak flow calculator#

The Calculate flow button, next to the flow field, opens a Yellow Book outflow calculator for non-boiling liquids (CPR 14E, ch. 2 §2.5.4). Describe the vessel and the opening; the scale drawing and the result update as you type.

What is applied. The flow falls as the vessel drains, so you choose which one to apply: the initial flow (the maximum, giving the largest pool), the mean flow (mass released over the duration) or the flow at an instant t. The flow, converted to the field unit, and the release duration are applied to the scenario; the calculation runs when you save or calculate.

Calculation. Draining is integrated with Gauss–Legendre quadrature over the level, more accurate than the book's explicit time step, and the released mass comes exactly from the geometry. Viscosity (pipe only) comes from the substance; without it a fully rough regime is assumed, which gives the maximum flow.

Validation. It reproduces the book's worked examples: §2.6.4.1 (hole, 58.44 kg/s at 500 s and Table 2.8), §2.6.4.2 (100 m pipe, 22.33 kg/s; the book does not publish the viscosity) and the §6.6.4 drain ($t_{rel}$ = 5064 s).

Limits. Non-boiling liquids only: pressurised liquefied gases (two-phase outflow, §2.5.3) are out of scope, and the calculator warns when the substance boils at ambient temperature. The pad pressure is assumed constant.

2.4 Pipeline leak flow#

When the source is a pipeline (line or polyline), Calculate flow opens a dedicated calculator: there is no vessel or level, and the flow depends on pumping, the pressure along the line, the elevations and the isolation.

Basis. The Yellow Book has no model for liquid pipelines: it deems it "not relevant" (§2.4.4) and lists pipeline leak and rupture among the models not available (Diagram 2.6). It gives two rules (§2.3.5.4): for a rupture, the pump flow with less friction over the shorter length up to the break; for a small hole, the flow at the initial pipeline pressure at that point; and it refers to the equations of §2.5.4.2. The source term follows the Purple Book (CPR 18E) and the two-phase structure of 49 CFR 194.105.

Leak position. The calculation applies one flow to the whole route, so you pick the point: by distance from the pump ($x = 0$), by dragging it on the profile, with Worst case (it scans the pipeline and places the leak where the most mass escapes within the cap, with the elevation profile fixed) or with Pick on the map: the dialog hides without losing what you entered, you mark the leak on the route by clicking, dragging the marker or with the slider, and on accept the dialog returns with the position. The map shows which end is the pump and lets you reverse the direction if the route was drawn from the destination. The pipeline length is always the length of the drawn route; edit the route to change it.

What is applied. As for the vessel: the initial flow (sustained while the pump runs), the mean flow (mass released over duration) or the flow at an instant t, with the release duration.

Assumptions and warnings. Yellow Book initial-pressure rule at the leak, without iterating the pressure drop (a warning appears when the leak exceeds 5 % of the nominal flow; below 1 % it is probably not detected). The discharge pressure is taken as constant, so the hydraulic limit is an upper bound. The line vents through the break (no vacuum hold-up); if the pressure falls below the vapour pressure somewhere, a slack-line warning appears. Manual elevations at three points, piecewise linear. Neither the Yellow Book nor the Purple Book gives a worked example for liquid pipelines: the tests use closed-form drainage solutions and the mass balance.

3. Chemical Properties (YAWS Correlations)#

All fuel properties are retrieved from the YAWS chemical database evaluated at ambient temperature $T_{amb}$ (Kelvin).

4. Burning Rate — burningRate()#

The burning rate $\dot{m}''$ [kg/(m²·s)] is the mass of fuel consumed per unit area per unit time. It governs fire intensity and pool diameter.

5. Pool Diameter — poolDiameter()#

6. Time Calculations#

7. Dimensionless Wind Speed — ux()#

The physical minimum $u^* = 1.0$ corresponds to the no-wind condition. Dry air density uses ISA 1976 altitude correction:

Reference: ISA 1976. Code: PoolFire.js, lines 414–430.

8. Flame Height — alturaFlama()#

9. Surface Emissive Power (SEP) — SEP()#

The SEP [kW/m²] is the radiant power emitted per unit area of the flame surface.

10. Flame Tilt Angle — anguloFlama()#

Wind tilts the flame from the vertical. The angle $\theta$ [rad] is computed from the Froude and Reynolds numbers:

For $u_w \leq 0$, $\theta = 0$ (vertical flame). Kinematic viscosity $\nu$ [m²/s] is obtained from an empirical polynomial in $T_{amb}$ [K].

Code: PoolFire.js, lines 523–542.

11. View Factor — viewFactor(x)#

12. Atmospheric Transmissivity — ta(x)#

Atmospheric humidity attenuates thermal radiation. Transmissivity $\tau$ uses Wayne's correlation (cited in CCPS):

The partial pressure of water vapor $P_w$ [Pa]:

where $HR$ is relative humidity [%] and $T = T_{amb}$ [K]. Code: PoolFire.js, lines 620–638.

13. Thermal Radiation — qTermAtX(x)#

14. Distance to a Given Radiation Level — xTerm(q_target)#

Given a target radiation level $q_{target}$ [kW/m²], the distance $x$ [m] is found via Newton-Raphson. For the Point Source model:

Convergence tolerance: 0.01 m. Code: PoolFire.js, lines 681–737.

15. Thermal Dose — dose(x)#

The factor $10^3$ converts $q$ from kW/m² to W/m². Code: PoolFire.js, line 758.

16. Effects — Probit Functions#

Probit functions transform the thermal dose into damage probability via the standard normal distribution.

17. Time to Failure for Vessels (Domino Effect) — Cozzani Correlations#

18. Fatality Calculation — fatalidades()#

The method numerically integrates the probability of death over concentric annular rings:

For polygon receivers (zones with known population), FatalityUtils.js uses a 10 m grid to distribute the population within the polygon and excludes that area from the uniform density calculation.

Code: PoolFire.js, lines 818–860; delegated to FatalityUtils.js.

19. Model Limitations#

Wind direction in individual and societal risk#

Consequences (zones, receivers) are computed for a single wind bearing, the one of the selected weather scenario. Individual risk and the F-N curve do not take that bearing as certain: in the Weather tab the scenario chooses between the site wind rose (the radiation field is rotated to every sector and weighted by its probability) and the CCPS simplified method (Eq. 4.4.4) (disk of radius $R$ with factor $\theta_{eq}/360$ over the downwind profile). See the individual risk contours documentation. The point-source preset, scenarios without a bearing (circular envelope) and line sources are not directional.

20. Radiation Model Presets#

A radiation preset selects six methodological blocks at once — burning rate, flame geometry, emissive power, transmissivity, the density reference used in the dimensionless wind speed $u^*$, and the radiative fraction — stored together in RiskModel.poolFireRadiationConfig. A scenario with no saved configuration falls back to the legacy point_source preset, which reproduces the engine documented in sections 4–13 above unchanged.

20.1 Presets#

yellow_book implements the CPR 14E solid-plume procedure (Yellow Book, 2005, §6.5.4) with simplified transmissivity. conservative_screening retains historical screening, which is not equivalent to ALOHA. point_source retains the legacy engine. Extended-flame results predating version 2.0 require recalculation; their historical traces are not rewritten.

aloha_fixed_area retains its identifier but is displayed as ALOHA-based radiation. It uses NOAA OR&R 43 §§6.3.3 and 6.5 scalar correlations with equivalent diameter ≤ 200 m. The pool source is described in the Release tab by containment and inventory (see section 2.1): TekRisk calculates static area from V/δ, feed/combustion equilibrium or geometry, limited by containment, with full retention and no overtopping check. A feed without equilibrium inside the bund is rejected. Rectangles use an equal-area circle with aspect ratio ≤ 2. Pool growth and tank discharge are not modelled. TekRisk geometric integration, optical path and SEP cap are retained; numerical equivalence to the ALOHA executable is not claimed. Dose and risk are TekRisk extensions.

The burgess_aloha block does not apply the Babrauskas diameter factor, even with tabulated kβ. The cook block uses $\tau=1.389-0.135\log_{10}(p_w L_p)$ and $p_w=99.89\,RH\,\exp(21.66-5431.3/T_a)$, with RH as a fraction, temperature in K, pressure in Pa and optical path in m. τ is bounded to [0,1]; dry air or zero path gives τ = 1. Both blocks are also available in custom configurations.

All three presets — and any combination of advanced blocks — compute thermal dose, probit, fatalities and the fatality-probability field that feeds individual risk and the F-N curve: the incident flux is thermal radiation whatever the emissive-power method, so the dose follows from the same $q$ and the same exposure time. What changes across presets is not whether lethality exists but how conservative it is: with a fixed radiative fraction the flux is overestimated by design and the lethality derived from it inherits that overestimate, as the scenario panel, the calculation memory and the PDF report all state. Results saved before September 2026, when screening did not evaluate dose, stay out of individual risk with that reason until they are recalculated.

20.2 Advanced Blocks#

Each block can be overridden independently of the preset; a manual value requires a written justification.

• Burning rate ($\dot m''$): burgess (mass form $10^{-3}\cdot\Delta H_c/\Delta H^*$, see section 4.2 above, with the Babrauskas diameter factor applied when $k_\beta$ is known) · babrauskas (tabulated $\dot m''_\infty$ and $k_\beta$ per substance, Babrauskas 1983; falls back to burgess without the diameter factor when substance data is missing) · mudan (mass form without the diameter factor, matching the legacy engine's Mudan branch) · manual value.
• Flame geometry: point_source (legacy) · vertical_cylinder (Thomas or Pritchard, no tilt) · tilted · tilted_drag (Moorhouse drag, Eq. 6.18-2). Tilt is selected separately: Binding (Eq. 6.70) for Yellow Book or the AGA alternative.
• Surface emissive power (SEP): fixed_fraction (configured radiative fraction $f$) · fs_diameter ($F_s(D) = 0.35\cdot e^{-0.05D}$) · yb_soot (CPR 14E ch. 6: a cold-soot fraction $\zeta$ near 20 kW/m² blended with the luminous SEP) · mudan_ed (Mudan's empirical $E(D)$) · manual value.
• Atmospheric transmissivity: bagster_pitblado (Yellow Book Eq. 6.29, simplified approximation) · wayne (Wayne 1991 alternative) · cook (NOAA OR&R 43) · none ($\tau = 1$). The extended engine bounds the result to [0,1] and warns about extrapolation (see "Transmissivity validity range" below).

Block-by-block guide: what it is, when to use it and limitations#

The help buttons in the dialog open each block of this guide. When a calculation runs into a limitation, TekRisk flags it in Results and in the calculation memory.

Burning rate#

Burgess–Strasser (burgess). Mass form $\dot m'' = 10^{-3}\,\Delta H_c/\Delta H^*$ (section 4.2), with the Babrauskas diameter factor when $k_\beta$ is known. When: hydrocarbons without tabulated data. Limitations: a large-pool correlation; for small pools (under 1–2 m) it overestimates when there is no $k_\beta$.

Burgess (ALOHA, burgess_aloha). The same mass form without the diameter correction, as in ALOHA. When: comparing with ALOHA. Limitations: ignores the diameter effect even when $k_\beta$ exists; overestimates the rate for small pools.

Babrauskas (babrauskas). Tabulated $\dot m''_\infty$ and $k_\beta$ per substance (Babrauskas 1983), with $\dot m'' = \dot m''_\infty(1 - e^{-k_\beta D})$. When: default and recommended whenever the substance is in the table; it is the Yellow Book method. Limitations: without substance data it falls back to Burgess without the diameter factor (the results table says so); the data come from pools on land, not cryogenic gases on water.

Mudan (mudan). Mudan's (1984) mass form without a diameter factor. When: reproducing studies based on Mudan/SFPE. Limitations: the same as uncorrected Burgess.

Own value (user_value). A measured or reference rate. Requires a written justification and marks the scenario as custom.

Flame geometry#

Point source (point_source). Legacy engine: all radiation leaves a point at mid flame height (section 11.1). When: far field, quick screening. Limitations: valid only beyond 5 pool diameters from the flame centre (Yellow Book, §6.3.4.2); describes neither the near field nor the wind asymmetry; circular zones.

Vertical cylinder (vertical_cylinder). Cylindrical flame without tilt; height by Thomas (1963) or Pritchard–Binding (section 8). When: calm wind or when a symmetric envelope is wanted. Limitations: with real wind it underestimates the downwind flux and overestimates the upwind one.

Tilted cylinder (tilted). Cylinder tilted by the wind, with the AGA tilt (u*^−0.5) or Binding's (eq. 6.70, with Fr and Re). When: comparing with ALOHA (Thomas/AGA) or with classical studies. Limitations: the base stays circular: it does not capture the downwind elongation of the flame base.

Tilted with drag (tilted_drag). Yellow Book §6.5.4: elliptical base elongated downwind by Moorhouse drag ($D'$) and Binding tilt. When: default for risk analysis; the most complete geometry. Limitations: needs a wind direction to draw directional zones (without it, a circular envelope); the Fr and Re correlations come from hydrocarbon pools of 1 to 50 m; very elongated rectangular dikes (aspect ratio above 2) are not well represented by a cylinder.

Surface emissive power (SEP)#

Fixed radiant fraction (fixed_fraction). $E = f\,\dot m''\,\Delta H_c / (1 + 4L/D)$ with a configurable $f$ (0.30 in ALOHA, 0.35 in the screening). When: conservative screening and comparison with ALOHA. Limitations: does not discount soot, so for large heavy-hydrocarbon fires it overestimates the flux (and with it dose, probit and fatalities); TekRisk marks it as conservative.

Fs with diameter (fs_diameter). $F_s(D) = 0.35\,e^{-0.05D}$ (Mudan and Croce, SFPE): the fraction decreases with diameter because of smoke. When: large pools without soot data. Limitations: an empirical hydrocarbon correlation; it does not distinguish clean fuels (methanol, LNG) from very smoky ones.

Yellow Book with soot (yb_soot). $SEP_{max} = F_s\,\dot m''\,\Delta H_c/(1+4L/D)$ and $E = SEP_{max}(1-\zeta) + 20\,\zeta$, with the luminous $F_s$ per fuel (table 6.6) and soot fraction $\zeta$. When: default; the most faithful for smoky hydrocarbons. Limitations: $F_s$ and $\zeta$ are per-fuel data; when unknown, TekRisk uses defaults and writes them in the results table.

Mudan E(D) (mudan_ed). $E = 140\,e^{-0.12D} + 20\,(1 - e^{-0.12D})$ kW/m² (Mudan 1984). When: typical hydrocarbons without substance data. Limitations: depends only on diameter; unsuitable for clean fuels or very small pools.

Own value (user_value). A measured or reference SEP. Requires a written justification.

Black-body SEP cap#

No hydrocarbon flame radiates more than a black body at its temperature ($\sigma T^4 \approx 300$ kW/m² at 1500 K); measured SEPs range from about 20 kW/m² (large, very smoky pools) to about 150 kW/m² (small clean flames). The fixed radiative-fraction correlations (fixed_fraction, fs_diameter) have no upper bound and, without a diameter correction, return an $E$ that grows with the pool (up to 337 kW/m² for a 130 m pool), the opposite of physical behaviour. The yb_soot and mudan_ed methods do not approach the cap, and user_value is the analyst's own figure.

The Black-body SEP cap option, under Advanced parameters, only appears with fixed_fraction and fs_diameter. It is not a preset block: changing it does not turn the methodology into "Custom".

• On (default for the pool fire). $E$ is capped at 300 kW/m² and Results flags it (sep_capped_black_body). When: almost always; it keeps fixed-fraction screening from publishing an impossible emissive power for large pools.
• Off. $E$ is published as the correlation returns it and Results flags it when it exceeds 300 kW/m² (sep_above_black_body). When: only to reproduce literally another tool that does not cap (for example, an ALOHA calculation with a fixed radiative fraction) or to show the effect of the cap in a report.

The jet fire has the same option, but off by default: there the excess appears with heavy gases in short flames, and ALOHA does not cap it (see jet fire).

Atmospheric transmissivity#

Bagster–Pitblado (bagster_pitblado). Yellow Book eq. 6.29, $\tau = 2.02\,(p_w L_p)^{-0.09}$. When: default. Limitations: published only for $10^4 \le p_w L_p \le 10^5$ N/m (about 6 to 63 m at 25 °C and 50 % RH); outside the range it is capped at 1 or extrapolated, and TekRisk warns. Details and comparison table under "Transmissivity validity range" below.

Wayne (wayne). Wayne's (1991) correlation with CO₂ and water vapour. When: studies that cite it (CCPS). Limitations: valid from 10 to 1000 m; does not resolve the near field.

Cook (cook). $\tau = 1.389 - 0.135\,\log_{10}(p_w L_p)$ (NOAA OR&R 43). When: comparing with ALOHA and near field, where it does not exceed 1. Limitations: no published range; beyond about 60 m it matches eq. 6.29.

No attenuation (none). $\tau = 1$. When: conservative screening at any distance or when humidity is unknown. Limitations: overestimates the flux far from the flame (up to 30 % at 60 m in humid air).

20.3 Yellow Book v2 parameters and limits#

• Enter wind at 10 m. Air kinematic viscosity ν is optional; automatic mode uses Sutherland μ(T)/ρa.
• Tilt: $c=0.666 Fr^{0.333}Re^{0.117}$, $\sin\theta=2c/(\sqrt{1+4c^2}+1)$; $Fr=U^2/(gD)$ and $Re=UD/\nu$.
• $SEP_{max}=F_s\dot m''\Delta H_c/(1+4L/D)$; $E=SEP_{max}(1-\zeta)+20\zeta$. Luminous Fs is a fuel-dependent input (Table 6.6); 0.35 is an initial assumption. No exponential diameter attenuation precedes soot coverage. Different fuel Fs values do not count as mixed methodologies.
• Instantaneous spill: explicit final thickness δ (by surface type, Yellow Book Table 3.1, or a custom value), $D=\sqrt{4V/(\pi\delta)}$, duration $\rho_L\delta/\dot m''$. Mass input is conserved; volumetric inventory and feed are interpreted at pool temperature.
• Continuous spill: steady area balancing feed and combustion. No transient growth or tank-emptying calculation. For a hole leak the flow is $\dot V = C_d\,A_0\sqrt{2gh}$ with $C_d$ applied once (in the Yellow Book $v_0 = C_0\sqrt{2gh}$ already includes it and the flow is $A_0 v_0$).
• Rectangular bunds with aspect ratio greater than 2 are rejected: a flat radiator is required, not an equivalent cylinder.
• $\tau=2.02(p_w L_p)^{-0.09}$: published range $10^4\le p_wL_p\le10^5$ N/m. The detailed absorptivity method of Eq. 6.24 is not implemented here.
• The surface is an oblique elliptical body with uniform emission. View factors are integrated numerically, using solid angle near the surface without artificially imposing $q=E$ on exterior receivers.

With a wind direction available, the tilted geometries produce downwind/upwind/crosswind-oriented zone polygons instead of circles; without a wind direction the contour degrades to a circular envelope. The full intermediate chain per zone and receiver ($\dot m''$, $u^*$, $\theta$, $L$, $D'$, $E$, $\zeta$, $F_s$, $\tau$) is written to the calculation memory (MD/DOCX) from the result's radiationTrace; the PDF report publishes from that same trace the preset with its references, the scalar intermediates, the transmissivity of each zone and, per receiver, its view factor and transmissivity. A study with pool fires on different presets blocks individual and social risk with an explanatory alert, since the contours are not comparable across presets.

On a line source (a pipeline or duct route, RiskModel.coords of type LineString) the directional field is anchored per target: the effect on each receiver is evaluated in a local wind frame whose origin is the point of the route nearest to that receiver, so the published flux corresponds to the published perpendicular distance and the downwind/upwind asymmetry is preserved along the whole route. Two simplifications remain downstream and are stated in the scenario panel, the calculation memory and the PDF report: the map corridors are built as a symmetric buffer whose half-width is the downwind radius of each zone, an envelope that is conservative on the upwind side; and individual risk keeps the radial path (the azimuth-averaged fatality profile replicated along the discretised route), because the 2D fatality field is anchored in absolute grid coordinates and cannot be stamped at every point of the route.

Transmissivity validity range#

Eq. 6.29 (Bagster and Pitblado) is an empirical correlation published only for $10^4 \le p_w L_p \le 10^5$ N/m, where $L_p$ is the optical path from the flame surface to the receiver. In metres the range depends on humidity: with $p_w = 1584$ Pa (about 25 °C and 50 % relative humidity) it covers paths between $10^4/p_w = 6.3$ m and $10^5/p_w = 63.1$ m. A scenario with several zones usually leaves it at both ends: high-threshold zones and upwind radii lie a few metres from the flame, while low-threshold zones of large pools lie beyond 63 m.

Outside the range the power law is extrapolated:

• Below the range the curve keeps rising and exceeds 1 for $p_w L_p < 2{,}470$ N/m (about 1.6 m with this $p_w$); the engine bounds it to [0, 1], which is the physical limit (no path, no absorption). Between that point and the lower bound the deviation is a few percentage points in $\tau$.
• Above the range the curve decreases slowly and practically matches Cook (NOAA OR&R 43), so the extrapolation is reasonable.
• It does not depend on the view factor. The view factor is pure geometry and has no validity range; it only supplies the distance to the flame surface used as $L_p$. Changing the flame geometry does not remove the extrapolation.

TekRisk warns on screen and in the calculation memory when a published zone or receiver falls outside the range; the PDF report does not repeat the warning. To avoid extrapolation, choose none ($\tau = 1$, conservative at any distance) or cook, which has no equivalent published range, in the advanced blocks. Wayne (1991) does not solve it in the near field: its range is 10 to 1000 m.

20.4 Comparison with the Yellow Book worked examples#

The preset equations reproduce the CPR 14E examples §6.6.3 and §6.6.4 step by step (±0.5 %, apart from the book's rounding and typos). The final flux published by TekRisk is nevertheless higher than the example's: 100 m downwind, 6.34 versus 4.58 kW/m² (§6.6.3) and 2.78 versus 2.14 kW/m² (§6.6.4). This is not a calculation error: the examples simplify the method the book itself describes in §6.5.4, and TekRisk applies the full method.

The method text supports both choices. Steps 9 and 10 define $x$ as "a distance x, between the flame surface and the object", and step 12 asks to "use the calculated flame dimensions and the distance from the flame to the radiated object"; the example instead uses 100 m from the pool centre (its own text even says "50 m from the flame surface") and discards $D'$. With the example's convention (circular base $D$, $x$ from the centre and its $\tau$), the same TekRisk functions give 4.58 and 2.16 kW/m², so no equation is wrong.

The result is conservative downwind and the effect depends on where the receptor is. Receptor at 100 m, §6.6.3, in kW/m²:

The step-by-step breakdown and the checks that rule out an error (energy balance, view factor, optical path) are in Model validation.

21. Bibliographic References#