Introduction & Context
Solvent flammability assessment is a critical safety procedure in process engineering, particularly for units handling volatile organic compounds like n-Hexane. In systems such as continuous desolventizers or extractors, the accumulation of solvent vapors can create an explosive atmosphere if the concentration exceeds the Lower Explosive Limit (LEL) or if oxygen levels remain above the Limiting Oxygen Concentration (LOC). This calculation methodology provides a rigorous framework for determining the required nitrogen inerting flow rates and purging durations necessary to maintain a safe operating environment, ensuring compliance with NFPA 69 standards.
Methodology & Formulas
The assessment follows a sequential approach, beginning with the determination of thermodynamic properties at the operating temperature, followed by mass transfer analysis and inert gas requirements.
1. Vapor Pressure and Density: The saturation vapor pressure is calculated using the Antoine equation, which is then used to determine the saturation vapor density:
\[ \log_{10}(P_{sat}) = A - \frac{B}{C + T} \]
\[ \rho_{vap,sat} = \frac{P_{sat} \cdot M_w}{R \cdot T} \]
2. LEL Correction: The LEL is adjusted for temperature using the modified Burgess-Wheeler law to account for the increased volatility at elevated process temperatures:
\[ LEL_{T} = LEL_{25} \cdot (1 - 0.000784 \cdot (T - 25)) \]
\[ y_{target} = 0.25 \cdot \left( \frac{LEL_{T}}{100} \right) \]
3. Evaporation and Inerting Requirements: The mass transfer of solvent from the wet meal surface is modeled to determine the source term, which dictates the required nitrogen sweep gas flow rate to maintain the target concentration:
\[ \dot{m}_{hex} = k_g \cdot A \cdot \rho_{vap,sat} \]
\[ \dot{n}_{hex} = \frac{\dot{m}_{hex}}{M_w} \]
\[ \dot{n}_{N_2} = \frac{\dot{n}_{hex}}{y_{target}} \]
\[ \dot{V}_{N_2} = \frac{\dot{n}_{N_2} \cdot R \cdot T}{P} \]
4. Purging Time: The time required to inert a vessel from an initial oxygen concentration to a safe target level is calculated using a CSTR model incorporating a mixing efficiency factor:
\[ t = \frac{V}{\eta \cdot Q} \cdot \ln\left( \frac{C_{initial}}{C_{target}} \right) \]
| Parameter |
Regime / Constraint |
Threshold |
| Antoine Equation |
Temperature Validity |
243.2 K ≤ T ≤ 342.7 K |
| Burgess-Wheeler |
Temperature Validity |
25 °C ≤ T ≤ 150 °C |
| Mixing Efficiency (η) |
Safety Bound |
0.1 ≤ η ≤ 0.5 |
| Flow Regime |
Laminar (Sherwood Correlation) |
Re < 5 × 105 |
Worked Example: Nitrogen Inerting for Hexane Extractor
A continuous desolventizer-toaster operates at 60 °C using n-hexane as solvent. To maintain safe conditions per NFPA 69, the vapor concentration must be kept below 25 % of the lower explosive limit (LEL) and the oxygen concentration below 60 % of the limiting oxygen concentration (LOC). Nitrogen is used as the inerting gas. The following calculation determines the required nitrogen dilution flow and the purging time needed to reduce the oxygen level from 21 % to the target 7.2 % (v/v).
Knowns:
- Operating temperature: \(T = 60\;^\circ\text{C}\) (333.15 K)
- Vapor space volume: \(V = 200.0\;\text{m}^3\)
- Wet meal surface area: \(A = 10.0\;\text{m}^2\)
- Mass transfer coefficient: \(k_g = 0.01\;\text{m/s}\)
- Initial oxygen concentration: \(C_{O_2,0} = 21.0\;\%\text{v/v}\)
- Target oxygen concentration: \(C_{O_2,\text{target}} = 7.2\;\%\text{v/v}\)
- Purge flow rate: \(Q = 5.0\;\text{m}^3/\text{s}\)
- Mixing efficiency: \(\eta = 0.3\)
- Molecular weight of hexane: \(M_w = 86.18\;\text{kg/kmol}\)
- Gas constant: \(R = 0.08206\;\text{m}^3\cdot\text{atm}/(\text{kmol}\cdot\text{K})\)
- LEL at 25 °C: \(\text{LEL}_{25} = 1.1\;\%\text{v/v}\)
- Atmospheric pressure: \(P_{\text{atm}} = 1.0\;\text{atm}\)
Step-by-Step Calculation:
- Vapor pressure and saturation density
Antoine equation: \(\log_{10}P_{\text{sat}}(\text{mmHg}) = 6.87632 - \frac{1171.17}{224.41 + T}\)
\(P_{\text{sat}} = 0.755\;\text{atm}\)
Saturation vapor density: \(\rho_{\text{vap,sat}} = \frac{P_{\text{sat}} M_w}{R T} = 2.38\;\text{kg/m}^3\)
- LEL correction and target concentration
Burgess-Wheeler: \(\text{LEL}_{60} = \text{LEL}_{25} \left[1 - 0.000784 (T - 25)\right] = 1.07\;\%\text{v/v}\)
Safe target (25 % LEL): \(y_{\text{target}} = 0.25 \times \frac{\text{LEL}_{60}}{100} = 0.00268\ \text{mol fraction}\)
- Evaporation source term
Mass flow: \(\dot{m}_{\text{hex}} = k_g A \rho_{\text{vap,sat}} = 0.01 \times 10.0 \times 2.38 = 0.238\;\text{kg/s}\)
Molar flow: \(\dot{n}_{\text{hex}} = \frac{\dot{m}_{\text{hex}}}{M_w} = 0.00276\;\text{kmol/s}\)
- Required nitrogen dilution
CSTR mass balance: \(\dot{n}_{\text{hex}} = y_{\text{target}} \dot{n}_{N_2}\)
\(\dot{n}_{N_2} = 1.03\;\text{kmol/s}\)
Volumetric flow: \(\dot{V}_{N_2} = \frac{\dot{n}_{N_2} R T}{P_{\text{atm}}} = 28.2\;\text{m}^3/\text{s}\)
- Purging time for initial inerting
CSTR purging: \(t = \frac{V}{\eta Q} \ln\left(\frac{C_{O_2,0}}{C_{O_2,\text{target}}}\right)\)
\(t = \frac{200.0}{0.3 \times 5.0} \ln\left(\frac{21.0}{7.2}\right) = 143\;\text{s}\)
Final Results:
- Required nitrogen volumetric flow rate: \(\dot{V}_{N_2} = 28.2\;\text{m}^3/\text{s}\)
- Purging time to reach safe oxygen level: \(t = 143\;\text{s}\) (approx. 2.38 minutes)
