# Fire Ball
Source: https://tekrisk.com/en/docs/risk-models/fire-ball

Technical documentation for the BLEVE-FireBall consequence model — thermal radiation, probit analysis, domino effects, and fatality estimation

## 1. Introduction and Physical Phenomenon

### 1.1 BLEVE and FireBall

A **BLEVE** (Boiling Liquid Expanding Vapor Explosion) occurs when a pressurized vessel containing a liquid at a temperature above its atmospheric boiling point fails catastrophically. The sudden depressurization causes instantaneous flash vaporization of a significant fraction of the liquid, generating a rapid two-phase release. If the substance is flammable and an ignition source is present, the resulting combustion produces a characteristic **fireball**.

The fireball is a luminous, approximately spherical mass of burning vapor/aerosol that rises due to buoyancy. It produces intense thermal radiation over a short duration (typically seconds to tens of seconds), capable of causing:

- **Burns** (first and second degree) to exposed persons
- **Fatalities** from lethal thermal dose
- **Domino effects** through failure of nearby equipment and vessels

### 1.2 Industrial Context

<Callout type="warn" title="High-severity scenario">
BLEVE/fireball events are among the most severe accident outcomes in industrial QRA. Historical incidents such as **San Juan Ixhuatepec** (Mexico, 1984) and the **Feyzin refinery explosion** (France, 1966) demonstrate their catastrophic potential.
</Callout>

<Cards>
  <Card title="LPG Storage & Transport">
    Propane and butane terminals, tank farms
  </Card>
  <Card title="Petroleum Refineries">
    Pressurized hydrocarbon vessels and process units
  </Card>
  <Card title="Chemical Plants">
    Flammable liquid storage under pressure
  </Card>
  <Card title="Rail & Road Transport">
    Tank cars and road tankers carrying pressurized flammable liquids
  </Card>
</Cards>

### 1.3 Scope of This Model

This model calculates:

1. Fireball geometry (diameter, height, duration)
2. Thermal radiation intensity at any distance
3. Distance to a specified radiation threshold (inverse problem)
4. Thermal dose and probit-based probability of burns/fatalities
5. Domino effect probability for nearby equipment (Cozzani method)
6. Population fatalities using concentric ring analysis

---

## 2. Calculation Sequence

<Mermaid>
{`flowchart TD
    A["Input Data<br/>(mass, Hc, fs, weather)"] --> B["Geometry Calculations<br/>Dmax, t_fb, H_fb"]
    B --> C["Combustion Parameters<br/>m'', SEP_max"]
    C --> D["For each distance x:<br/>X_surface, tau_atm, F_view, q"]
    D --> E["Forward: q(x)"]
    D --> F["Inverse: x(q_target)<br/>Newton-Raphson"]
    E --> G["Thermal Dose<br/>D = t * q^(4/3)"]
    F --> G
    G --> H["Probit Analysis<br/>Burns / Deaths"]
    G --> I["Domino Effect<br/>TTF - Cozzani"]
    H --> J["Fatality Calculation<br/>(Concentric Rings)"]
    I --> J

    style A fill:#e1f5fe
    style J fill:#c8e6c9
    style D fill:#fff3e0`}
</Mermaid>

The BLEVE-FireBall calculation follows these stages:

<Steps>
  <Step>
    **Geometry Calculations** — Compute maximum diameter ($D_{max}$), fireball duration ($t_{fb}$), and center height ($H_{fb}$) from the released fuel mass.
  </Step>
  <Step>
    **Combustion Parameters** — Calculate mass burning rate ($\dot{m}''$) and Surface Emissive Power ($SEP_{max}$) from fuel properties.
  </Step>
  <Step>
    **Atmospheric & View Factor** — For each distance, compute surface distance ($X_{surface}$), atmospheric transmissivity ($\tau_{atm}$), and geometric view factor ($F_{view}$).
  </Step>
  <Step>
    **Thermal Radiation** — Calculate incident radiation using three available models (solid plume, point source, empirical).
  </Step>
  <Step>
    **Inverse Distance** — Solve for the distance at which radiation equals a target threshold using Newton-Raphson iteration.
  </Step>
  <Step>
    **Thermal Dose & Probit** — Compute thermal dose and convert to burn/fatality probabilities via probit functions.
  </Step>
  <Step>
    **Domino Effect** — Estimate time-to-failure for nearby vessels using Cozzani correlations.
  </Step>
  <Step>
    **Fatality Estimation** — Integrate fatality probability over concentric rings to estimate total casualties.
  </Step>
</Steps>

---

## 3. Principal Equations

### 3.1 Geometry: Diameter, Duration, Height

#### Maximum Fireball Diameter

$$
D_{max} = 5.8 \cdot M^{1/3} \tag{2.1}
$$

| Symbol | Description | Unit |
|--------|-------------|------|
| $D_{max}$ | Maximum fireball diameter | m |
| $M$ | Mass of flammable fuel released | kg |

*Reference: CCPS, Guidelines for Chemical Process QRA, 2nd ed., Eq. 2.2.32, p. 207*

<Callout type="info" title="Alternative correlation">
The TNO Yellow Book (CPR 14E) provides: $D_{max} = 2 \times 3.24 \cdot M^{0.325}$ (Eq. 6.119), but is not used as the primary method.
</Callout>

The **initial diameter at ground level** accounts for the expansion phase before lift-off:

$$
D_{ground} = 1.3 \cdot D_{max} \tag{2.2}
$$

#### Fireball Duration

The duration depends on whether the fireball is momentum-dominated or buoyancy-dominated:

$$
t_{fb} = \begin{cases} 0.45 \cdot M^{1/3} & \text{if } M < 30{,}000 \text{ kg} \\ 2.6 \cdot M^{1/6} & \text{if } M \geq 30{,}000 \text{ kg} \end{cases} \tag{2.3/2.4}
$$

| Symbol | Description | Unit |
|--------|-------------|------|
| $t_{fb}$ | Fireball duration | s |
| $M$ | Mass of flammable fuel | kg |

*Reference: CCPS, Guidelines for Chemical Process QRA, 2nd ed., pp. 207-208*

#### Fireball Center Height

$$
H_{fb} = 0.75 \cdot D_{max} \tag{2.5}
$$

*Reference: CCPS, Guidelines for Chemical Process QRA, 2nd ed., p. 211*

<Callout type="info" title="Height factor">
Kakosimos proposes $H_{fb} = 1.0 \cdot D_{max}$, placing the fireball higher. The CCPS factor of 0.75 is used by default — a more conservative (closer to ground) assumption that yields higher radiation at ground-level receptors.
</Callout>

### 3.2 Combustion: Burning Rate and SEP

#### Burning Rate

$$\dot{m}'' = \frac{M}{\pi \cdot D_{max}^{2} \cdot t_{fb}}$$

| Symbol | Description | Unit |
|--------|-------------|------|
| $\dot{m}''$ | Burning rate | kg/(m$^2$ s) |
| $M$ | Fuel mass | kg |
| $D_{max}$ | Maximum diameter | m |
| $t_{fb}$ | Fireball duration | s |

*Reference: Kakosimos, Safety in Chemical Engineering, p. 102*

#### Surface Emissive Power (SEP)

$$SEP_{max} = f_s \cdot \dot{m}'' \cdot \Delta H_c$$

| Symbol | Description | Unit |
|--------|-------------|------|
| $SEP_{max}$ | Maximum surface emissive power | kW/m$^2$ |
| $f_s$ | Radiation fraction | dimensionless (0.2–0.4) |
| $\dot{m}''$ | Burning rate | kg/(m$^2$ s) |
| $\Delta H_c$ | Heat of combustion | kJ/kg |

*Reference: TNO Yellow Book (CPR 14E) and Kakosimos p. 102*

### 3.3 Atmospheric Transmissivity

**Surface distance** from the fireball to the ground-level receptor at horizontal distance $x$:

$$X_{surface} = \sqrt{H_{fb}^{2} + x^{2}} - \frac{D_{max}}{2}$$

**Partial vapor pressure of water:**

$$
p_a = 1013.25 \cdot RH \cdot \exp\left(14.4114 - \frac{5328}{T_a}\right) \tag{2.8}
$$

| Symbol | Description | Unit |
|--------|-------------|------|
| $p_a$ | Partial pressure of water vapor | Pa |
| $RH$ | Relative humidity | % (0–100) |
| $T_a$ | Ambient temperature | K |

**Atmospheric transmissivity:**

$$
\tau_{atm} = 2.02 \cdot (p_a \cdot X_{surface})^{-0.09} \tag{2.7}
$$

*Reference: CCPS, Guidelines for Chemical Process QRA, 2nd ed., Eqs. 2.2.42–2.2.43, p. 209*

<Callout type="info" title="Zero humidity guard">
If relative humidity is zero, it is replaced by 0.001 to avoid division by zero in the transmissivity calculation.
</Callout>

### 3.4 View Factors (4 Methods)

The view factor $F_{view}$ represents the geometric fraction of the fireball's radiation that reaches the receptor.

<Tabs items={["CCPS (Primary)", "Yellow Book / Kakosimos", "ALOHA (EPA/NOAA)", "Casal"]}>
  <Tab value="CCPS (Primary)">
    $$F_{view} = \frac{x \cdot (D_{max}/2)^{2}}{\left(x^{2} + H_{fb}^{2}\right)^{3/2}}$$

    This is the view factor used in the solid plume radiation model (`qTerm0`).

    *Reference: CCPS, Guidelines for Chemical Process QRA, 2nd ed., Eq. 2.2.47, p. 209*
  </Tab>
  <Tab value="Yellow Book / Kakosimos">
    $$F_{view} = \left(\frac{D_{max}/2}{X_{center}}\right)^{2}$$

    where $X_{center} = \sqrt{H_{fb}^{2} + x^{2}}$ is the distance from the **center** of the fireball to the receptor.

    *Reference: Kakosimos, Safety in Chemical Engineering, p. 103, Eq. C2.44*
  </Tab>
  <Tab value="ALOHA (EPA/NOAA)">
    $$F_{view} = \frac{x \cdot (D_{max}/2)^{2}}{\left(x^{2} + (D_{max}/2)^{2}\right)^{3/2}}$$

    *Reference: EPA/NOAA, ALOHA Technical Documentation, p. 68*
  </Tab>
  <Tab value="Casal">
    $$F_{view} = \frac{r^{2}}{4 \cdot (r + d)^{2}}$$

    where $r = D_{max}/2$ (fireball radius) and $d = X_{center} - r$ (surface-to-receptor distance).

    *Reference: Casal, J., Evaluation of the Effects and Consequences of Major Accidents in Industrial Plants, p. 137, Eq. 3.102*
  </Tab>
</Tabs>

### 3.5 Thermal Radiation Models (3 Equations)

Each model calculates the incident heat flux $q$ (kW/m$^2$) at a ground-level receptor located at horizontal distance $x$ from the fireball center projection.

<Tabs items={["qTerm1 — Point Source (PRIMARY)", "qTerm0 — Solid Plume", "qTerm2 — Empirical"]}>
  <Tab value="qTerm1 — Point Source (PRIMARY)">
$$
q_1(x) = \frac{2.2 \cdot \tau_{atm}(x) \cdot f_s \cdot \Delta H_c \cdot M^{2/3}}{4\pi \cdot X_{center}^{2}} \tag{2.6}
$$

    where $X_{center} = \sqrt{H_{fb}^{2} + x^{2}}$.

    | Symbol | Description | Unit |
    |--------|-------------|------|
    | $q_1$ | Thermal radiation at receptor | kW/m$^2$ |
    | $\tau_{atm}$ | Atmospheric transmissivity | dimensionless |
    | $f_s$ | Radiation fraction | dimensionless |
    | $\Delta H_c$ | Heat of combustion | kJ/kg |
    | $M$ | Fuel mass | kg |
    | $X_{center}$ | Center-to-receptor distance | m |

    The constant 2.2 is an empirical correction factor derived from experimental data. This is the **primary radiation model** used for all downstream calculations (dose, probit, fatalities, inverse distance).

    *Reference: CCPS, Guidelines for Chemical Process QRA, 2nd ed., Eq. 2.2.41, p. 208*
  </Tab>
  <Tab value="qTerm0 — Solid Plume">
    $$q_0(x) = SEP_{max} \cdot F_{view,CCPS}(x) \cdot \tau_{atm}(x)$$

    This is the **solid flame** model that treats the fireball as a solid sphere with uniform surface emission.

    *Reference: CCPS, Guidelines for Chemical Process QRA, 2nd ed., Eq. 2.2.45, p. 209*
  </Tab>
  <Tab value="qTerm2 — Empirical">
    $$q_2(x) = \frac{828 \cdot M^{0.771}}{X_{center}^{2}}$$

    A simplified empirical correlation that does not require radiation fraction or atmospheric transmissivity inputs. Provides results that closely match ALOHA output for validation purposes.

    *Reference: CCPS, Guidelines for Chemical Process QRA, 2nd ed., Eq. 2.2.44, p. 209*
  </Tab>
</Tabs>

### 3.6 Inverse Calculation (Newton-Raphson)

To find the distance $x$ at which thermal radiation equals a target value $q_{target}$, the model solves:

$$f(x) = q_1(x) - q_{target} = 0$$

using the **Newton-Raphson iterative method**.

| Parameter | Value |
|-----------|-------|
| Initial guess | $x_0 = D_{max}/2$ (fireball radius) |
| Solver | `newton-raphson-method` npm package |
| Unit conversion | $1 \text{ BTU/(s ft}^2) = 11.3565 \text{ kW/m}^2$ |

### 3.7 Thermal Dose

$$D = t_{fb} \cdot (q_1(x) \times 1000)^{4/3}$$

| Symbol | Description | Unit |
|--------|-------------|------|
| $D$ | Thermal dose | W$^{4/3}$ s m$^{-8/3}$ |
| $t_{fb}$ | Fireball duration | s |
| $q_1$ | Thermal radiation (converted from kW to W) | W/m$^2$ |

The exponent 4/3 accounts for the non-linear relationship between radiation intensity and skin damage.

*Reference: TNO Green Book (CPR 16E), Methods for the Determination of Possible Damage, Chapter 3*

### 3.8 Probit Analysis (Burns and Fatalities)

Probit functions transform a physical exposure parameter into a normally-distributed probability. The general probit equation is $Y = a + b \cdot \ln(V)$.

**Probit equations:**

| Effect | Equation | Reference |
|--------|----------|-----------|
| First degree burn | $Y = -39.83 + 3.0186 \cdot \ln(D)$ | TNO Green Book, Eq. 3.4, p. 20 |
| Second degree burn | $Y = -43.14 + 3.0186 \cdot \ln(D)$ | TNO Green Book, Eq. 3.7, p. 20 |
| Fatality (CCPS) | $Y = -14.9 + 2.56 \cdot \ln(D / 10{,}000)$ | CCPS, p. 269 |
| Fatality (TNO) | $Y = -36.38 + 2.56 \cdot \ln(D)$ | TNO Green Book, Eq. 3.5, p. 20 |

<Callout type="info">
FireBall uses CCPS methodology for probit deaths by default. Both CCPS and TNO equations are mathematically equivalent.
</Callout>

**Probit to probability conversion:**

$$P(\%) = f_k \cdot 50 \cdot \left[1 + \text{sgn}(Y - 5) \cdot \text{erf}\left(\frac{|Y - 5|}{\sqrt{2}}\right)\right]$$

| Symbol | Description | Value |
|--------|-------------|-------|
| $f_k$ | Protection factor | 1.0 (no protection) |
| $\text{erf}$ | Error function (Taylor series, 50 terms) | — |

**Bounds:** If $Y < 0$ → $P = 0\%$. If $Y > 8.09$ → $P = 100\%$.

### 3.9 Domino Effect (TTF — Cozzani)

The domino effect analysis estimates the probability that nearby equipment will fail under thermal radiation exposure.

#### Time to Failure (TTF)

**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. |

| Symbol | Description | Unit |
|--------|-------------|------|
| $TTF$ | Time to failure | s |
| $q$ | Incident thermal radiation | kW/m$^2$ |
| $V$ | Vessel volume | m$^3$ |

<Callout type="warn" title="Full engulfment criterion">
Equipment is considered fully engulfed when its distance from the fireball center is less than $1.1 \times D_{max}/2$ (10% safety margin accounting for thermal radiation gradients at the fireball boundary).
</Callout>

#### Domino Probit

$$Y_{domino} = 9.25 - 1.847 \cdot \ln\left(\frac{TTF}{60}\right)$$

TTF is divided by 60 to convert from seconds to minutes.

*Reference: Cozzani, V. et al., Journal of Hazardous Materials, p. 300*

#### Equipment Type Mapping

| Database Type | Cozzani Category |
|---------------|------------------|
| `atmospheric_tanks`, `storage_tanks` | Atmospheric |
| `pressurized_vessels`, `lpg_tanks`, `gas_cylinders` | Pressurized |
| `reactors`, `heat_exchangers`, `columns` | Pressurized |

### 3.10 Fatality Calculation (Concentric Rings)

Population fatalities are estimated by dividing the affected area into concentric rings centered on the fireball ground projection.

**Algorithm:**

1. For each ring $i$ at distance $r_i$ (increment = 5 m, max = 10 km):
   - Calculate thermal radiation: $q = q_1(r_i)$
   - Calculate thermal dose: $D = t_{fb} \times (q \times 1000)^{4/3}$
   - Calculate CCPS probit: $Y = -14.9 + 2.56 \times \ln(D / 10000)$
   - Convert probit to percentage: $P = \text{probitToPercent}(Y)$
   - If $P < 0.1\%$: **STOP** (negligible fatalities beyond this distance)
2. Ring area: $A_{ring} = \pi (r_{outer}^{2} - r_{inner}^{2})$
3. Fatalities per ring: $F_i = A_{ring} \times \rho_{pop} \times P_i / 100$
4. Total fatalities: $F_{total} = \sum F_i$

| Parameter | Default Value |
|-----------|---------------|
| Ring increment | 5 m |
| Maximum radius | 10 km |
| Minimum probability threshold | 0.1% |
| Rounding rule | If $F > 0.6$ → $\lceil F \rceil$; otherwise 0 |

**Population density conversion:**

| Input Unit | Conversion Factor to p/m$^2$ |
|------------|-------------------------------|
| p/m$^2$ | 1 |
| p/ha | $\div$ 10,000 |
| p/km$^2$ | $\div$ 1,000,000 |
| p/mi$^2$ | $\div$ 2,589,988 |

*Reference: CCPS, Guidelines for Chemical Process QRA, 2nd ed., p. 273; TNO Purple Book (CPR 18E)*

### 3.11 Polygon Receiver Exclusion

When polygon-type receivers (e.g., residential zones, industrial areas) are defined, the model avoids double-counting population:

1. Polygon receivers overlapping with analysis rings are identified using geographic intersection
2. For each ring, the polygon area is subtracted: $A_{effective} = A_{ring} - A_{excluded}$
3. Fatalities from polygon areas are calculated separately using distributed grid analysis with their own population counts

---

## 4. Justification of Selected Methods

<Accordions type="multiple">
  <Accordion title="Why qTerm1 (Point Source) as Primary Model">
    1. **Conservative yet realistic** — The empirical factor 2.2 provides results between the solid plume model (higher estimates) and the simple empirical correlation (qTerm2)
    2. **Physical basis** — The $1/(4\pi X^2)$ factor correctly represents isotropic radiation attenuation from a point at the fireball center
    3. **Atmospheric correction** — Includes $\tau_{atm}$ for atmospheric absorption, unlike the purely empirical qTerm2
    4. **Newton-Raphson compatibility** — Smooth, monotonically decreasing behavior provides excellent convergence for inverse distance calculations
    5. **Industry adoption** — Used by SCRI and widely accepted in QRA practice
  </Accordion>
  <Accordion title="Why CCPS for Probit Fatalities">
    The CCPS probit equation ($Y = -14.9 + 2.56 \ln(D/10000)$) is mathematically equivalent to the TNO equation ($Y = -36.38 + 2.56 \ln(D)$). The CCPS version is preferred for:

    - **Consistency** with other CCPS equations used throughout the model
    - **Numerical stability** — the $D/10000$ scaling keeps the logarithm argument in a convenient range
  </Accordion>
  <Accordion title="Why Cozzani for Domino Effect">
    1. **Vessel-type specificity** — Separate correlations for atmospheric, pressurized, and full engulfment scenarios
    2. **Volume dependency** — Includes vessel volume, which significantly affects TTF
    3. **Widely validated** — Most cited empirical TTF models in process safety literature
    4. **Direct radiation input** — Uses $q$ (kW/m$^2$) directly available from the fireball calculation
  </Accordion>
  <Accordion title="Why Concentric Ring Analysis for Fatalities">
    1. **Captures decay gradient** — Ring method captures the radiation decrease with distance
    2. **Computationally efficient** — Typically &lt; 100 rings before reaching the 0.1% threshold
    3. **Standard practice** — Recommended by CCPS (p. 273) and TNO Purple Book (CPR 18E)
    4. **Extensible** — Polygon exclusion allows integration with specific population zones
  </Accordion>
</Accordions>

---

## 5. Model Limitations

<Accordions type="multiple">
  <Accordion title="Geometric Limitations">
    - **Spherical assumption** — The fireball is modeled as a perfect sphere; real fireballs are irregularly shaped and deform during rise
    - **Static geometry** — Uses maximum diameter, single height, and total duration; does not model the dynamic evolution (expansion → rise → burnout)
    - **No ground reflection** of thermal radiation
    - **Flat terrain assumed** — Topographic shielding is not modeled
  </Accordion>
  <Accordion title="Atmospheric Limitations">
    - **No wind effects** — Wind shear causing fireball tilt or drift is not modeled; the fireball is assumed to rise vertically
    - **Simplified transmissivity** — Empirical fit for standard conditions; extreme humidity, fog, dust, or smoke may not be accurately represented
    - **Humidity floor** — Minimum 0.1% enforced to avoid singularity; may slightly overestimate absorption in extremely dry conditions
    - **Uniform atmosphere** — Temperature and humidity gradients along the radiation path are not considered
  </Accordion>
  <Accordion title="Combustion Limitations">
    - **Constant radiation fraction** — $f_s$ is treated as user-supplied constant (0.2–0.4); in reality it varies with fuel type, fireball size, soot formation, and combustion efficiency
    - **Complete combustion assumed** — Ground-level pooling, incomplete mixing, and multi-phase effects reduce the effective mass in practice
    - **Single fuel** — Multi-component fuel mixtures are not explicitly handled
  </Accordion>
  <Accordion title="Population / Receptor Limitations">
    - **Uniform density** — Base fatality calculation assumes uniform population density in all directions (polygon exclusion partially addresses this)
    - **No sheltering** — Protection factor $f_k = 1.0$ assumes all persons are outdoors with no protection
    - **No evacuation** — Emergency response actions that could reduce exposure time are not modeled
    - **Static population** — Distribution is assumed fixed during the event
  </Accordion>
  <Accordion title="Domino Effect Limitations">
    - **Cozzani correlations only** — TTF equations exist only for atmospheric and pressurized vessels; other equipment types cannot be assessed
    - **Thermal radiation only** — Domino effects from overpressure or projectile impact are handled by the VCE model
    - **Steel vessels** — Correlations were derived for steel; other materials may have different failure characteristics
    - **No partial failure** — Only catastrophic failure (loss of containment) is considered
  </Accordion>
  <Accordion title="Numerical Limitations">
    - **Newton-Raphson convergence** — May fail for very low radiation thresholds (far field) or poor initial guesses
    - **Ring discretization** — 5 m increment introduces $\pm 2.5$ m error (negligible for most industrial scenarios)
    - **Probit extrapolation** — Values below 0 are clamped to 0%, above 8.09 are clamped to 100%
  </Accordion>
</Accordions>

---

## 6. Input/Output Summary

### 6.1 Required Inputs

| Parameter | Description | Unit |
|-----------|-------------|------|
| `mass` | Flammable fuel mass | kg, lb, g, ton |
| `hckjkg` | Heat of combustion | kJ/kg |
| `radiationFraction` | Fraction of energy radiated ($f_s$) | 0.2–0.4 |
| `tempAmb` | Ambient temperature | C, F, K |
| `humidityRel` | Relative humidity | % (0–100) |
| `populationDensity` | Population density | p/m$^2$, p/ha, p/km$^2$, p/mi$^2$ |
| `thermalZones` | Risk zones with radiation thresholds | kW/m$^2$ |

### 6.2 Outputs

| Output | Description | Unit |
|--------|-------------|------|
| `diameterMax` | Maximum fireball diameter | m |
| `durationFireBallCombustion` | Fireball duration | s |
| `heigthFireBall` | Fireball center height | m |
| `burningRate` | Mass burning rate | kg/(m$^2$ s) |
| `SEPmax` | Maximum surface emissive power | kW/m$^2$ |
| `zones` | Array of risk zones with distances | m |
| `zones[i].dose` | Thermal dose at zone boundary | W$^{4/3}$ s m$^{-8/3}$ |
| `fatalidades` | Fatality calculation results | Object or 0 |
| `receiverEffects` | Effects on each receiver | Array |

### 6.3 Receiver Effect Categories

| Category | Effect | Probit Source |
|----------|--------|---------------|
| Thermal | 1st degree burn | TNO Eq. 3.4 |
| Thermal | 2nd degree burn | TNO Eq. 3.7 |
| Thermal | Fatality | CCPS p. 269 |
| Domino | Equipment failure | Cozzani p. 300 |

---

## 7. References

<Accordions type="single">
  <Accordion title="CCPS — Guidelines for Chemical Process QRA, 2nd Edition">
    Center for Chemical Process Safety, AIChE/Wiley, 2000. Diameter (Eq. 2.2.32, p. 207), Duration (pp. 207-208), Height (p. 211), Transmissivity (Eqs. 2.2.42-2.2.43, p. 209), View Factor (Eq. 2.2.47, p. 209), Radiation models (Eqs. 2.2.41, 2.2.44, 2.2.45, pp. 208-209), Probit fatalities (p. 269), Fatality rings (p. 273).
  </Accordion>
  <Accordion title="TNO Green Book (CPR 16E, 3rd Edition)">
    *Methods for the Determination of Possible Damage*. Committee for the Prevention of Disasters, 2005. Probit equations for 1st degree burns (Eq. 3.4, p. 20), 2nd degree burns (Eq. 3.7, p. 20), Deaths (Eq. 3.5, p. 20), Thermal dose exponent.
  </Accordion>
  <Accordion title="TNO Purple Book (CPR 18E)">
    *Methods for the Determination of Possible Damage*. Committee for the Prevention of Disasters, 1999. Fatality calculation methodology, concentric ring analysis.
  </Accordion>
  <Accordion title="TNO Yellow Book (CPR 14E, 3rd Edition)">
    *Methods for the Calculation of Physical Effects Due to Releases of Hazardous Materials*. Alternative diameter correlation (Eq. 6.119), View factor formulations.
  </Accordion>
  <Accordion title="Cozzani, V. et al.">
    "Escalation thresholds in the assessment of domino accidental events." *Journal of Hazardous Materials*, 129(1-3), 2006, pp. 1-21. TTF correlations (atmospheric, pressurized, full engulfment), Domino probit (p. 300).
  </Accordion>
  <Accordion title="Casal, J. (2008)">
    *Evaluation of the Effects and Consequences of Major Accidents in Industrial Plants*. Elsevier. View factor Casal (Eq. 3.102, p. 137), Radiation fraction discussion (p. 136).
  </Accordion>
  <Accordion title="EPA/NOAA — ALOHA Technical Documentation">
    U.S. EPA / NOAA, 2013. View factor ALOHA (p. 68).
  </Accordion>
  <Accordion title="Kakosimos, K.E.">
    *Safety in Chemical Engineering*. Burning rate (p. 102), View factor Kakosimos (p. 103, Eq. C2.44).
  </Accordion>
  <Accordion title="Lees, F.P. (2004)">
    *Loss Prevention in the Process Industries*. 3rd ed. Butterworth-Heinemann. General QRA methodology, fatality estimation.
  </Accordion>
</Accordions>