# Jet Fire
Source: https://tekrisk.com/en/docs/risk-models/jet-fire
Technical documentation for the Jet Fire consequence model — Solid Plume (Chamberlain) and Point Source (CCPS) methodologies for thermal radiation analysis
## 1. Introduction and General Description
A **jet fire** is a turbulent diffusion flame that results from the combustion of a pressurized gas or volatile liquid released continuously through an orifice or pipe failure. Unlike pool fires, jet fires are characterized by high momentum discharge, directional flame geometry, and intense localized thermal radiation.
### 1.1 Implemented Models
TekRisk PRO implements two complementary methodologies for jet fire consequence analysis:
**Approach:** Surface emitter
**Geometry:** Frustum-shaped flame with view factor
**Use Case:** Detailed near-field analysis with flame geometry
**Approach:** Point emitter
**Geometry:** Single radiant point at flame midpoint
**Use Case:** Simplified far-field analysis, conservative estimates
### 1.2 Source Types
- **`knownFlow`** — Mass flow rate is directly specified by the user (kg/s). Used when flow measurement data is available.
- **`gasLeakFromOrifice`** — Mass flow rate is calculated from vessel conditions (internal pressure, temperature, orifice diameter) using isentropic discharge equations.
---
## 2. Calculation Sequence
The algorithm follows 15 sequential stages:
**Input Processing & Unit Conversion** — Convert user inputs to SI units; compute atmospheric pressure and air density at altitude.
**Gas Properties (Cp polynomial, gamma)** — Evaluate heat capacity polynomial and compute specific heat ratio.
**Flow Regime (sonic vs subsonic)** — Determine whether the discharge is choked or unchoked via critical pressure ratio.
**Mass Flow Rate (vessel discharge)** — Calculate mass flow from orifice conditions using Kakosimos discharge equations.
**Exit Conditions (P, T, Mach, u, rho)** — Compute pressure, temperature, Mach number, velocity, and density at the jet exit.
**Equivalent Diameter (Ds)** — Calculate the effective source diameter for flame length correlations.
**Flame Length (Newton-Raphson / CCPS)** — Solve for flame length using the Chamberlain implicit equation or CCPS correlation.
**Flame Geometry (Solid Plume only)** — Compute tilt angle, lift-off, frustum dimensions, base and top widths.
**Surface Emissive Power (SEP)** — Calculate radiated fraction and surface emissive power from flame area and heat of combustion.
**Atmospheric Transmissivity (Wayne/CCPS)** — Evaluate atmospheric absorption using the Wayne humidity correlation.
**Thermal Radiation at Distance** — Compute incident radiation at a given distance using view factor (Solid Plume) or point source formula.
**Distance to Given Radiation (inverse Newton-Raphson)** — Find the distance at which a specified radiation level occurs.
**Probit Analysis (burns & fatality)** — Convert thermal dose to burn probabilities and fatality using probit functions.
**Domino Effect — TTF (Cozzani)** — Estimate time-to-failure for nearby vessels under thermal radiation loading.
**Fatality Estimation (concentric ring integration)** — Integrate fatality probability over concentric rings to estimate total casualties.
---
## 3. Principal Equations
### 3.1 Input Processing and Unit Conversion
**Atmospheric pressure at altitude:**
$$P_a = 101325 \times (1 - 2.5577 \times 10^{-5} \times h)^{5.25588}$$
| Variable | Description | Unit |
|----------|-------------|------|
| $P_a$ | Atmospheric pressure at altitude | Pa |
| $h$ | Altitude above sea level | m |
*Reference: Standard barometric formula (ISO 2533)*
**Air density at altitude:**
$$\rho_{air} = \frac{P_a}{R_d \times T_a}$$
| Variable | Description | Unit |
|----------|-------------|------|
| $\rho_{air}$ | Air density | kg/m³ |
| $R_d$ | Specific gas constant for dry air (287.05) | J/(kg·K) |
| $T_a$ | Ambient temperature | K |
### 3.2 Gas Properties
**Heat capacity polynomial (Cp):**
$$C_{p,mol} = a + bT + cT^2 + dT^3 + eT^4$$
| Variable | Description | Unit |
|----------|-------------|------|
| $C_{p,mol}$ | Molar heat capacity at constant pressure | J/(mol·K) |
| $a$–$e$ | Polynomial coefficients (cpga through cpge) | various |
| $T$ | Internal gas temperature | K |
**Specific heat capacities and gamma:**
$$C_p = \frac{C_{p,mol}}{MW} \times 1000$$
$$C_v = C_p - \frac{R}{MW} \times 1000$$
$$\gamma = \frac{C_p}{C_v}$$
| Variable | Description | Unit |
|----------|-------------|------|
| $C_p$ | Specific heat at constant pressure | J/(kg·K) |
| $C_v$ | Specific heat at constant volume | J/(kg·K) |
| $R$ | Universal gas constant (8.31451) | J/(mol·K) |
| $MW$ | Molecular weight | kg/mol |
| $\gamma$ | Heat capacity ratio (must be > 1.0) | dimensionless |
$\gamma \leq 1.0$ indicates a non-gaseous substance and raises an error. This model supports **gas-phase releases only**.
### 3.3 Flow Regime Determination
**Critical pressure ratio (sonic threshold):**
$$\frac{P_0}{P_a} \leq \left(\frac{\gamma + 1}{2}\right)^{\gamma / (\gamma - 1)}$$
If the pressure ratio is less than or equal to the critical value, the flow is **subsonic** (unchoked). Otherwise, the flow is **sonic/supersonic** (choked).
*Reference: Kakosimos, Eq. B2.14, p. 36*
### 3.4 Mass Flow Rate from Vessel Discharge
**General discharge equation (Kakosimos B2.13):**
$$\dot{m} = C_d \times A \times P_0 \times K \times \sqrt{\frac{MW}{\gamma \times R \times T_0}}$$
| Variable | Description | Unit |
|----------|-------------|------|
| $\dot{m}$ | Mass flow rate | kg/s |
| $C_d$ | Discharge coefficient | dimensionless |
| $A$ | Orifice area ($\pi d^2 / 4$) | m² |
| $P_0$ | Internal pressure | Pa |
| $T_0$ | Internal temperature | K |
**Factor K for sonic flow (Kakosimos B2.14):**
$$K = \gamma \times \left(\frac{2}{\gamma + 1}\right)^{(\gamma + 1) / (2(\gamma - 1))}$$
**Factor K for subsonic flow (Kakosimos B2.15):**
$$K = \sqrt{\frac{2\gamma^2}{\gamma - 1} \times \left(\frac{P_a}{P_0}\right)^{2/\gamma} \times \left(1 - \left(\frac{P_a}{P_0}\right)^{(\gamma-1)/\gamma}\right)}$$
*Reference: Kakosimos, K.E., "Complex Hazardous Activities", Eqs. B2.13–B2.15, p. 36*
### 3.5 Exit Conditions
**Exit pressure for known flow (adiabatic, Kakosimos C2.55):**
$$P_{exit} = P_0 \times \left(\frac{2}{1 + \gamma}\right)^{\gamma / (\gamma - 1)}$$
**Exit pressure for orifice discharge (Kakosimos C2.52):**
$$P_{exit} = \frac{4\dot{m}}{\pi d^2} \times \sqrt{\frac{R \times T_o}{\gamma \times MW}}$$
where $T_o = 2T_0 / (1 + \gamma)$ (Kakosimos C2.54)
**Exit temperature (adiabatic, Kakosimos C2.56):**
$$T_j = T_0 \times \left(\frac{P_a}{P_0}\right)^{(\gamma - 1) / \gamma}$$
**Mach number at exit (sonic flow):**
$$M_j = \sqrt{\frac{(\gamma + 1)(P_{exit}/P_a)^{(\gamma-1)/\gamma} - 2}{\gamma - 1}}$$
**Exit velocity (Kakosimos C2.50):**
$$u_j = M_j \times \sqrt{\frac{\gamma \times R \times T_j}{MW}}$$
**Exit density (ideal gas):**
$$\rho_j = \frac{P_{exit} \times MW}{R \times T_j}$$
*References: Kakosimos, Eqs. C2.50, C2.52, C2.54–C2.56, pp. 108–109; TNO Yellow Book, Eqs. 6.33, 6.36*
### 3.6 Equivalent Diameter
**For known mass flow (Kakosimos C2.59):**
$$D_s = \sqrt{\frac{4\dot{m}}{\pi \times \rho_{air} \times u_j}}$$
**For orifice discharge (Kakosimos C2.60):**
$$D_s = d \times \sqrt{\frac{\rho_j}{\rho_{air}}}$$
| Variable | Description | Unit |
|----------|-------------|------|
| $D_s$ | Equivalent diameter | m |
| $d$ | Orifice diameter | m |
*Reference: Kakosimos, Eqs. C2.59–C2.60, p. 110*
### 3.7 Flame Length
The flame length is computed by solving a non-linear equation for the dimensionless parameter $Y$ using Newton-Raphson iteration:
$$C_a Y^{5/3} + C_b Y^{2/3} - C_c = 0$$
where:
$$C_a = 0.024 \times \left(\frac{g \times D_s}{u_j^2}\right)^{1/3}$$
$$C_b = 0.2$$
$$C_c = \left(\frac{2.85}{W}\right)^{2/3}$$
$$W = \frac{MW}{15.816 \times MW + 0.0395}$$
**Newton-Raphson iteration:**
$$Y_{n+1} = Y_n - \frac{C_a Y_n^{5/3} + C_b Y_n^{2/3} - C_c}{(5C_a Y_n + 2C_b) / (3Y_n^{1/3})}$$
Convergence tolerance: 0.01
**Still-air flame length:**
$$L_{Bo} = Y \times D_s$$
**Wind-corrected flame length:**
$$L_f = L_{Bo} \times (0.51 \exp(-0.4 u_w) + 0.49) \times (1 - 0.00607(\theta - 90))$$
| Variable | Description | Unit |
|----------|-------------|------|
| $W$ | Stoichiometric mass fraction in air mixture | dimensionless |
| $Y$ | Dimensionless flame length parameter | dimensionless |
| $L_{Bo}$ | Still-air flame length | m |
| $L_f$ | Wind-corrected flame length | m |
| $u_w$ | Wind speed | m/s |
| $\theta$ | Hole axis angle relative to wind | degrees |
| $g$ | Gravitational acceleration (9.80665) | m/s² |
*Reference: TNO Yellow Book (CPR 14E, 3rd Ed.), pp. 6.97–6.101, Eqs. 6.30–6.56; Chamberlain (1987)*
For the Point Source model with orifice discharge, the flame length is calculated using the CCPS equation:
$$L_f = d \times \frac{15}{W} \times \sqrt{\frac{MW_{air}}{MW}}$$
where $MW_{air} = 0.029$ kg/mol.
For known flow with Point Source, the flame length is not required (set to 1.0 m as placeholder) since the radiant intensity is calculated directly from the mass flow rate.
*Reference: CCPS, "Guidelines for CPQRA", 2nd Ed., Eq. 2.2.64*
### 3.8 Flame Geometry (Solid Plume Only)
**Flame tilt angle (Kakosimos C2.68):**
$$R_1 = u_w / u_j$$
Richardson number:
$$Ri = L_{Bo} \times \left(\frac{g}{D_s^2 \times u_j^2}\right)^{1/3}$$
For $R_1 \leq 0.05$:
$$\alpha = (\theta - 90)(1 - e^{-25.6 R_1}) + \frac{8000 R_1}{Ri}$$
For $R_1 > 0.05$:
$$\alpha = (\theta - 90)(1 - e^{-25.6 R_1}) + \frac{134 + 1726\sqrt{R_1 - 0.026}}{Ri}$$
*Reference: Kakosimos, Eq. C2.68, p. 111; TNO Yellow Book*
**Lift-off distance:**
For zero wind: $b = 0.2 \times L_f$
For flame angle > 175 deg: $b = 0.015 \times L_f$
Otherwise (Chamberlain):
$$K_{lo} = 0.187 \exp(-20 R_1) + 0.015$$
$$b = L_f \times \frac{\sin(K_{lo} \times \alpha)}{\sin(\alpha)}$$
*Reference: TNO Yellow Book, Eq. 6.49, p. 6.57; Chamberlain (1987)*
**Frustum length:**
$$R_L = \sqrt{L_f^2 - b^2 \sin^2(\alpha)} - b \cos(\alpha)$$
**Base width (Chamberlain):**
$$C = 1000 \exp(-100 R_1) + 0.8$$
$$Ri_{Ds} = D_s \times \left(\frac{g}{u_j^2 \times D_s^2}\right)^{1/3}$$
$$W_1 = D_s \times (13.5 e^{-6R_1} + 1.5) \times \left(1 - e^{-70 Ri_{Ds}^{CR_1}} \left(1 - \frac{1}{15}\sqrt{\rho_r}\right)\right)$$
where $\rho_r = T_j MW_{air} / (T_a MW)$ is the relative density.
*Reference: Chamberlain (1987); ALOHA Technical Documentation, p. 75; Kakosimos Eq. C2.73*
**Top width:**
$$W_2 = L_f \times (0.18 e^{-1.5 R_1} + 0.31) \times (1 - 0.47 e^{-25 R_1})$$
*Reference: Chamberlain (1987)*
**Flame surface area (frustum):**
$$A_1 = \sqrt{R_L^2 + \left(\frac{W_2 - W_1}{2}\right)^2}$$
$$A_{flame} = \frac{\pi}{4}(W_1^2 + W_2^2) + \frac{\pi}{2}(W_1 + W_2) A_1$$
### 3.9 Surface Emissive Power (SEP)
**Molecular weight correction factor (ALOHA):**
| MW range | $C_{mw}$ |
|----------|------|
| $MW \leq 21$ | 1.0 |
| $21 < MW \leq 60$ | $\sqrt{MW / 21}$ |
| $MW > 60$ | 1.69 |
*Reference: ALOHA Technical Documentation, NOAA/EPA, p. 72*
**Radiated fraction (Chamberlain 1987):**
$$F_s = 0.21 \times C_{mw} \times \exp(-0.00323 \times u_j) + 0.11$$
**Surface Emissive Power:**
$$SEP = F_s \times \frac{\dot{m}}{A_{flame}} \times \Delta H_c$$
| Variable | Description | Unit |
|----------|-------------|------|
| $F_s$ | Fraction of heat radiated | dimensionless |
| $SEP$ | Surface emissive power ($SEP_{act} = SEP_{max}$, no soot correction) | kW/m² |
| $\Delta H_c$ | Heat of combustion | kJ/kg |
No soot correction is applied ($SEP_{act} = SEP_{max}$). This is conservative for sooty flames.
*Reference: Chamberlain, G.A. (1987), Chem. Eng. Res. Des., 65; ALOHA Technical Documentation, p. 72*
### 3.10 Atmospheric Transmissivity
**Wayne model (CCPS Eqs. 2.2.42–2.2.43):**
Partial vapor pressure of water:
$$p_w = 1013.25 \times RH \times \exp(14.4114 - 5328 / T_a)$$
Atmospheric transmissivity:
$$\tau = 2.02 \times (p_w \times x)^{-0.09}$$
| Variable | Description | Unit |
|----------|-------------|------|
| $\tau$ | Atmospheric transmissivity | dimensionless |
| $p_w$ | Partial pressure of water vapor | Pa |
| $RH$ | Relative humidity (as fraction 0–1) | dimensionless |
| $x$ | Distance from flame surface | m |
*Reference: CCPS, "Guidelines for CPQRA", 2nd Ed., Eqs. 2.2.42–2.2.43, p. 209*
### 3.11 Thermal Radiation at Distance
$$q(x) = SEP \times F_{view}(x) \times \tau(x)$$
The **view factor** $F_{view}$ is calculated from horizontal and vertical components using the tilted cylinder method:
$$F_{view} = \sqrt{F_v^2 + F_h^2}$$
where $F_v$ and $F_h$ are computed from geometric parameters (frustum length $R_L$, equivalent radius $R$, distance $X$, tilt angle) using analytical expressions involving arctangent functions. The full view factor formulation follows the TNO Yellow Book tilted cylinder methodology.
*Reference: Kakosimos, Eq. C2.84, p. 119; TNO Yellow Book*
$$q(x) = \tau(x) \times f_r \times \dot{m} \times \Delta H_c \times F_{view,ps}(x)$$
where:
$$F_{view,ps} = \frac{1}{4\pi X_h^2}$$
$$X_h = \sqrt{(h_{source} + L_f/2)^2 + x^2}$$
| Variable | Description | Unit |
|----------|-------------|------|
| $q(x)$ | Thermal radiation at distance $x$ | kW/m² |
| $f_r$ | Radiation fraction (user-specified) | dimensionless |
| $X_h$ | Distance from point source to receiver | m |
| $h_{source}$ | Height of leak above ground | m |
*Reference: CCPS, "Guidelines for CPQRA", 2nd Ed., Eq. 2.2.65, p. 239*
### 3.12 Distance to Given Radiation (Inverse Calculation)
The distance $x$ at which a specified thermal radiation $q^*$ is received is found by solving:
$$q(x) - q^* = 0$$
This is solved using the **Newton-Raphson method** (npm package `newton-raphson-method`), with the flame top width as the initial guess. A fallback iterative method with 0.1 m increments is also implemented.
### 3.13 Probit Analysis
**Thermal dose:**
$$D = t_{exp} \times (q \times 1000)^{4/3}$$
| Variable | Description | Unit |
|----------|-------------|------|
| $D$ | Thermal dose | $(W/m^2)^{4/3} \cdot s$ |
| $t_{exp}$ | Exposure time | s |
| $q$ | Thermal radiation (converted from kW to W) | W/m² |
**Probit equations:**
| Effect | Equation | Reference |
|--------|----------|-----------|
| First degree burn | $Pr = -39.83 + 3.0186 \ln(D)$ | TNO Green Book, Eq. 3.4, p. 20 |
| Second degree burn | $Pr = -43.14 + 3.0186 \ln(D)$ | TNO Green Book, Eq. 3.7, p. 20 |
| Fatality (CCPS) | $Pr = -14.9 + 2.56 \ln(D / 10000)$ | CCPS, p. 269 |
| Fatality (TNO) | $Pr = -36.38 + 2.56 \ln(D)$ | TNO Green Book, Eq. 3.5, p. 20 |
JetFire uses CCPS methodology for probit deaths by default.
**Probit to probability conversion:**
$$P(\%) = f_k \times 50 \times \left(1 + \text{sgn}(Pr - 5) \times \text{erf}\left(\frac{|Pr - 5|}{\sqrt{2}}\right)\right)$$
| Variable | Description | Value |
|----------|-------------|-------|
| $f_k$ | Protection factor (no protective clothing) | 1.0 |
| $Pr$ | Probit value | dimensionless |
| $\text{erf}$ | Error function (Taylor series, 50 terms) | dimensionless |
The protection factor $f_k = 1.0$ assumes no protective clothing. This is conservative for industrial workers who may wear flame-retardant clothing.
*References: TNO Green Book (CPR 16E), p. 20; CCPS, p. 269*
### 3.14 Domino Effect — Time to Fail (Cozzani)
**TTF correlations by vessel type:**
| Vessel Type | Equation | Reference |
|-------------|----------|-----------|
| Atmospheric | $TTF = \exp(-1.13 \ln(q) - 2.667 \times 10^{-5} V + 9.877)$ | Cozzani et al. |
| Pressurized | $TTF = \exp(-0.95 \ln(q) + 8.845 V^{0.032})$ | Cozzani et al. |
| Full engulfment | $TTF = \exp(-1.29 \ln(q) + 10.97 V^{0.026})$ | Cozzani et al. |
| Variable | Description | Unit |
|----------|-------------|------|
| $TTF$ | Time to fail | s |
| $q$ | Thermal radiation received | kW/m² |
| $V$ | Vessel volume | m³ |
**Full engulfment criterion:** Equipment is considered fully engulfed when its distance from the jet fire source is less than $1.1 \times L_f$ (10% safety margin).
**Domino probit (Cozzani):**
$$Pr_{domino} = 9.25 - 1.847 \times \ln(TTF / 60)$$
*Reference: Cozzani, V. et al., "The assessment of risk caused by domino effect in quantitative area risk analysis", Journal of Hazardous Materials, p. 300*
### 3.15 Fatality Estimation
Fatalities are estimated using **concentric ring integration**:
1. The area around the source is divided into concentric rings of width $\Delta r = 5$ m
2. For each ring at distance $r_i$:
- Thermal radiation $q(r_i)$ is calculated
- Thermal dose $D_i = t_{exp} \times (q_i \times 1000)^{4/3}$ is computed
- Probit value is converted to fatality probability $P_i$
- Ring area: $A_i = \pi (r_{out}^2 - r_{in}^2)$ where $r_{in} = r_i - \Delta r/2$, $r_{out} = r_i + \Delta r/2$
- Fatalities in ring: $F_i = A_i \times \rho_{pop} \times P_i / 100$
3. Total fatalities: $F = \sum F_i$ for all rings where $P_i \geq 0.1\%$
4. If $F > 0.6$, result is $\lceil F \rceil$; otherwise result is 0
**Polygon receiver exclusion:** When polygon receivers are defined, their areas are subtracted from the concentric rings to avoid double-counting population (polygon populations are calculated separately with distributed spatial discretization).
| Parameter | Default Value |
|-----------|---------------|
| Ring increment | 5 m |
| Maximum radius | 10 km |
| Minimum probability threshold | 0.1% |
| TNO methodology | Used for ring-based fatalities |
*Reference: CCPS, "Guidelines for CPQRA", 2nd Ed., p. 273*
---
## 4. Justification of Methodology Selection
### 4.1 Chamberlain Frustum Model (Solid Plume)
The Chamberlain (1987) model was selected for the Solid Plume approach because:
- It provides a **validated frustum geometry** for the flame shape, allowing accurate near-field radiation calculations
- The model has been **extensively validated** against full-scale natural gas jet fire experiments
- It accounts for wind effects on flame tilt, lift-off, and width variation
- The view factor calculation captures the directional nature of radiation from an extended source
- It is the **standard model used by ALOHA** (NOAA/EPA) and recommended in the TNO Yellow Book
### 4.2 CCPS Point Source Model
The Point Source model was selected as an alternative because:
- It provides **conservative estimates** suitable for preliminary hazard assessment
- It requires fewer input parameters (no flame geometry needed for known flow)
- The model is **computationally simpler** and avoids view factor convergence issues
- It is recommended by CCPS for far-field radiation estimates where flame geometry is less critical
### 4.3 Newton-Raphson Method
Newton-Raphson iteration is used for two purposes:
1. **Flame length calculation** (solving the non-linear $Y$ equation) — Provides rapid convergence (typically 3–5 iterations) for the implicit Chamberlain equation
2. **Inverse distance calculation** — Finding the distance at which a given thermal radiation level occurs
The `newton-raphson-method` npm package is used for the inverse distance calculation, with the flame top width as the initial guess.
### 4.4 Dual Probit Methodologies
Two probit approaches are available:
- **TNO (default for ring-based fatalities):** Standard European methodology, widely used in QRA
- **CCPS (default for JetFire probit):** Standard American methodology, mathematically equivalent when properly normalized
### 4.5 Cozzani Domino Correlations
The Cozzani correlations are the only published empirical correlations specifically developed for estimating time-to-failure of industrial vessels under thermal radiation loading. They are supported by experimental data and distinguish between atmospheric and pressurized vessel behavior.
---
## 5. Model Limitations
1. **Gas phase only** — The model requires $\gamma > 1.0$ (ideal gas). Two-phase (gas-liquid) releases are not supported.
2. **Steady-state flow** — The release rate is assumed constant throughout the event duration. Transient vessel blowdown is not modeled.
3. **Ideal gas behavior** — Real gas effects (compressibility factor $Z \neq 1$) are not accounted for. This may introduce errors at very high pressures.
4. **Flat terrain, no obstacles** — The model assumes unobstructed propagation of thermal radiation. Buildings, terrain features, and shielding effects are not considered.
5. **No soot correction** — $SEP_{act} = SEP_{max}$. For heavy hydrocarbons with significant soot production, the actual emissive power may be lower than calculated. This makes the result conservative.
6. **Simplified transmissivity** — The Wayne model (CCPS 2.2.42) is a simplified correlation. More detailed models (e.g., LOWTRAN) may give different results at long distances or extreme humidity conditions.
7. **Protection factor $f_k = 1.0$** — No protective clothing is assumed. This is conservative for industrial workers who may wear flame-retardant clothing.
8. **Frustum approximation** — The actual flame shape is approximated as a truncated cone (frustum). Complex flame shapes due to crosswind, buoyancy effects, or turbulence are simplified.
9. **Point Source ignores geometry** — The Point Source model does not consider flame shape, making it less accurate in the near field but conservative overall.
10. **Newton-Raphson convergence** — The iterative solver may fail to converge for extreme parameter combinations. The fallback iterative method (0.1 m increments) is available but slower.
11. **Uniform population density** — The base fatality calculation assumes spatially uniform population density. This limitation is mitigated by polygon receiver support, which allows spatially distributed population modeling.
12. **Chamberlain validation** — The model was primarily validated against natural gas (methane) jet fire experiments. Application to other substances, particularly heavy hydrocarbons, should be treated with caution.
13. **Cozzani correlations** — The TTF correlations apply only to atmospheric and pressurized vessels. Other equipment types (reactors, heat exchangers, columns) are mapped to the closest available vessel type.
14. **Atmospheric effects** — Detailed atmospheric turbulence effects on flame geometry and radiation propagation are not modeled.
---
## 6. Range of Applicability
| Parameter | Typical Range | Notes |
|-----------|---------------|-------|
| Internal pressure | 1–200 atm | Higher pressures may violate ideal gas assumption |
| Orifice diameter | 1–500 mm | Very large diameters may produce non-jet behavior |
| Molecular weight | 2–150 g/mol | MW correction factor applied for SEP |
| Wind speed | 0–30 m/s | Model validated primarily for moderate winds |
| Gas temperature | > boiling point | Must be gas phase at release conditions |
| Heat capacity ratio | $\gamma > 1.0$ | Strictly gas-phase releases only |
| Hole angle | 0–180° | 90° = horizontal, relative to wind |
---
## 7. References
*Complex Hazardous Activities: Preventing and Managing Industrial Disasters*. Safety in Chemical Engineering. Equations B2.13–B2.15 (pp. 36), C2.50–C2.60 (pp. 108–110), C2.68 (p. 111), C2.73 (p. 112), C2.84 (p. 119).
*Methods for the Calculation of Physical Effects Due to Releases of Hazardous Materials*. Committee for the Prevention of Disasters, The Netherlands. Flame geometry pp. 6.97–6.101, Eqs. 6.30–6.56.
*Methods for the Determination of Possible Damage to People and Objects Resulting from Releases of Hazardous Materials*. Probit equations, p. 20, Eqs. 3.4, 3.5, 3.7.
Center for Chemical Process Safety, AIChE. Point source model Eqs. 2.2.64–2.2.65 (p. 239), transmissivity Eqs. 2.2.42–2.2.43 (p. 209), probit (p. 269), fatalities (p. 273).
"Developments in design methods for predicting thermal radiation from flares." *Chemical Engineering Research and Design*, 65, pp. 299–309. Frustum model, radiated fraction, flame geometry correlations.
NOAA/EPA. Molecular weight correction for radiated fraction (p. 72), Chamberlain implementation (p. 75).
"The assessment of risk caused by domino effect in quantitative area risk analysis." *Journal of Hazardous Materials*. TTF correlations for atmospheric/pressurized vessels (p. 300).
"An Analysis and Interpretation of Casualty Rates in Major Hazard Events." Referenced in overpressure probit calculations (FatalityUtils).