ISO 20414 Test 19: incapacitation by toxic gases

What is tested

ISO 20414:2020, Test 19 (Table 22): an occupant stands still in gas, and the time at which its dose reaches FED = 1 must equal a hand calculation. The standard asks for the test to be repeated for each hazardous condition the model has; here that is done for CO, CO₂ and O₂. Four gas mixtures switch these terms on one at a time. A wrong unit (ppm against %), a missing species read as zero, a dropped CO₂ factor or a missing O₂ gate (case c would cross 13 s early, case d 3 s) each moves the crossing in at least one case.

Equation

The gas FED of Purser (SFPE Handbook, 4th ed., Sec. 2 Ch. 6), as coded in FDS 6.10.1’s FED function (Source/func.f90; Models › FED; the published law is on Fundamentals › Asphyxiant FED). C_CO is in ppm, C_CO₂ and C_O₂ are in volume percent, and rates are per minute. The CO coefficient is Purser’s light-work value, 3.317 × 10⁻⁵ × 25 L/min ÷ 30 % COHb = 2.764 × 10⁻⁵:

r_CO   = 2.764e-5 x (C_CO)^1.036
HV_CO2 = exp(0.1903 x C_CO2 + 2.0004) / 7.1    if C_CO2 > 0
HV_CO2 = 1                                     if C_CO2 = 0
r_O2   = 1 / exp[8.13 - 0.54 x (20.9 - C_O2)]  if C_O2 < 20 %, else 0
r      = r_CO x HV_CO2 + r_O2

HV_CO₂ = 1 at C_CO₂ = 0 is FDS’s convention, not Purser’s law: Purser’s expression gives exp(2.0004)/7.1 = 1.041 there, so FDS’s factor jumps at zero. Only case c tests that branch; in air with 0.04 % CO₂, HV_CO₂ = 1.049. With the optional gases the sum is r = (r_CO + r_CN + r_NOx + r_irr) × HV_CO₂ + r_O₂; they are zero here.

The gas is constant, so FED grows linearly, FED(t) = r t / 60, and reaches 1 at

Setup

• FDS: the ISO room, 10 × 10 × 3 m, no fire, no vents, one mesh with 0.5 m cells. At t = 0 a single &INIT fills it with one mixture per case. Gas slices at 1.6 m, which FDS places at 1.5 m. A FED device sits at (5, 5, 1.6) m, next to the occupant.

• Cases from the FDS+Evac guide’s own FED test (Korhonen 2021, §4.2 Component Testing, Fig. 8 “A FED test”); ISO gives no values. The guide compares the agent’s FED with a worksheet and with an FDS FED device “at the position of the agent”, as this page does:

  case	CO₂	CO	O₂	terms switched on
  a	2 %	0.1 %	15 %	CO, CO₂ factor, O₂
  b	0	0	12 %	O₂ only
  c	0	0.1 %	21 %	CO only
  d	3.43 %	0.1 %	21 %	CO and CO₂ factor

• Occupant: one, near the centre (spawn box 4.4–5.6 m; it lands at (4.78, 4.94) m), held in place by a pre-evacuation time drawn from [1.2 × 10⁷, 2 × 10⁷] s, the method ISO prescribes (> 10⁷ s).

• Runs: one per case, --incapacitation-mode deterministic (the default, given explicitly), so the occupant is incapacitated at FED = 1, not at a random threshold. The FED is updated every 1 s (--smoke-update-interval 1).

Expected

The concentrations are read from the FDS slices with fdsreader, independently of pyFDS-Evac. Every cell at every slice time holds the same value, and each species is within 2 × 10⁻⁵ of what the deck prescribes.

FDS’s device crosses up to 0.10 s earlier. FDS uses 2.7641667 × 10⁻⁵ for the CO coefficient, not 2.764 × 10⁻⁵. That speeds the CO term by 6.0 × 10⁻⁵, which accounts for the whole gap: after correcting for it, FDS and the hand calculation agree to 2 × 10⁻⁷ of t*.

Before #194, pyFDS-Evac applied Purser’s expression at zero CO₂ as well, HV_CO₂ = 1.041, which gave 1626 s for case c. It now follows FDS’s convention, HV_CO₂ = 1 without CO₂; FDS’s device gives 1692.7 s, as the hand calculation does.

Result

In every case the occupant’s FED is on the hand line to within 3 × 10⁻¹⁴, and it is incapacitated at the first FED update after t*.

Pass criteria

1. Gas arrives unaltered. Each FDS slice equals the prescribed value to 10⁻⁴ (relative), and is exactly 0 where the deck has none. The deck writes mass fractions to 6 significant digits from molar masses given to 3 decimals; each rounding is below 2 × 10⁻⁵. The gas the occupant sampled (fed_history.csv) equals the slice to the same 10⁻⁴.
2. Dose. |FED − r t/60| ≤ 10⁻⁹ at every update: both sides are the same arithmetic on the same numbers, so only round-off may differ.
3. Crossing and stop. The first update with FED ≥ 1 and the incapacitation are the same row, and \(t^{*} \le t < t^{*} + \Delta t\) with Δt = 1 s, the FED update interval. ISO asks for the same time; the model can only report the first update after t*, so the offset lies in [0, Δt) and shrinks with --smoke-update-interval. The automated test allows 2 Δt.
4. FDS agrees with the hand calculation. After correcting for FDS’s CO coefficient, |t_FDS − t*| ≤ 10⁻⁶ t*. FDS writes the device with 8 significant digits, so interpolating the crossing is good to about 10⁻⁷.
5. The occupant stays put. Position unchanged and not evacuated: otherwise the exposure, and the comparison, would be meaningless.

Run it yourself

The FDS output (slices only, 256 kB) is committed in assets/iso_table22_coupled/fds/, and tests/test_iso_table22_coupled.py runs on it in CI. For the figures you also need FDS’s _devc.csv, which is in the project’s data folder (fds-evac-data/iso_table22_coupled/), or rerun FDS, about 40 s per case:

python assets/iso_table22_coupled/build_geometry.py   # writes decks and configs
for c in a b c d; do
  mkdir -p <out>/fds/$c && cp assets/iso_table22_coupled/iso_table22_$c.fds <out>/fds/$c/
  (cd <out>/fds/$c && fds iso_table22_$c.fds)
done

Then run pyFDS-Evac, about 40 s per case, and draw the figures:

for c in a b c d; do
  uv run python run.py --scenario assets/iso_table22_coupled/config_$c.json \
    --fds-dir <out>/fds/$c --seed 420 --incapacitation-mode deterministic \
    --smoke-update-interval 1 \
    --output-sqlite <out>/evac/$c/run.sqlite \
    --output-fed-history <out>/evac/$c/fed_history.csv \
    --vis-cache <out>/evac/$c/vis_cache.npz
done
uv run python scripts/verification/iso_test19_figures.py --data <out>

The script prints each check and stops at the first pass criterion that fails.

Limits

• CO, CO₂ and O₂ only. The optional gases (HCN, NOx, irritants), the HCN − NOx correction and HV_CO₂ on the non-CO terms are not run in this layout (#257). The convective heat dose is checked in Heat dose in a uniform room.
• A missing O₂ gate is caught, a misplaced one is not: any gate between 15 % and 21 % gives the same four times.
• One occupant per case and the deterministic threshold. The opt-in probabilistic threshold is checked on 100 agents in CO dose in a uniform room.
• A uniform, constant field cannot show whether the gas is sampled at the agent’s current position (#24) or at the right height; the height is checked in test_fed_slice_height.py.
• The automated test takes its expected values from pyFDS-Evac’s own FED functions and allows 2 s; only the figure script uses the independent hand calculation and FDS’s device (#249).
• The FED equations are the Purser forms FDS uses, not the SFPE 5th edition ones (#149).
• A second version of this test, assets/ISO-table22 in tests/test_fed.py, supplies the gas directly without FDS. It checks the dose accumulator only, for one mixture (CO 0.1 %, CO₂ 5 %, O₂ 12 %).

References

• ISO 20414:2020. Fire safety engineering — Verification and validation protocol for building fire evacuation models, Table 22 (Test 19).
• Korhonen, T. (2021). Fire Dynamics Simulator with Evacuation: FDS+Evac. Technical Reference and User’s Guide (FDS 6.7.6, Evac 2.6.0 draft), §4.2, Fig. 8. VTT Technical Research Centre of Finland. github.com/tkorhon1/FDS-Evac-Guide.
• Purser, D. A. (2008). Assessment of hazards to occupants from smoke, toxic gases, and heat. In SFPE Handbook of Fire Protection Engineering, 4th ed., Sec. 2, Ch. 6. NFPA.