Note:

This calculator estimates the temperature history during homogeneous-vessel venting when there is a constant external heat input. It considers the effects of heat addition, vaporization, and the venting process. This is crucial for analyzing scenarios with external heating sources, such as fire exposure. This formula assumes homogeneous conditions within the vessel, meaning the temperature and composition are uniform throughout. Also, this formula assumes that the liquid is vaporizing. If there is no liquid left, then the formula is no longer valid.

Formula Explanation:

The formula calculates the temperature (T) at a given time (t) during venting, accounting for constant external heat input (QT), heat removal due to vaporization, and the venting dynamics. The logarithmic term, ln(tr / (tr - t)), accounts for the increasing rate of venting as the vessel empties.

Parameters:

• T (Temperature): The temperature at time t.
• Tr (Set Temperature): The initial or set temperature.
• QT (Constant External Heat Input): The constant rate of heat input from an external source. It is important to know the units of this value.
• G (Mass Flux): The mass flow rate per unit area, indicating how quickly the substance is being vented.
• A (Vent Area): The area of the vent.
• Cv (Specific Heat): The specific heat at constant volume.
• t (Time): The time elapsed since the start of venting.
• tr (Emptying Time): The time it takes to empty the vessel. The accuracy of the emptying time (tr) is crucial, as it directly affects the calculated temperature profile.
• V (Volume): The volume of the vessel.
• mo (Initial Mass): The initial mass of the substance.
• hfa (Latent Heat): The latent heat of vaporization. This is the amount of heat required to vaporize a unit mass of the liquid. It plays a key role in the cooling effect during venting.
• vfa (Specific Volume): The specific volume of the liquid.

Real-life Applications:

• Chemical Process Safety: Analyzing temperature rise during venting with external heating sources (e.g., fire exposure).
• Emergency Relief System Design: Designing relief systems for scenarios with external heating.
• Thermal Hazard Analysis: Assessing potential thermal hazards in processes where external heating is a factor.

Conclusion:

This calculation helps in understanding and mitigating thermal hazards during venting processes when external heating is present. Accurate input is crucial for reliable results and effective safety planning. Understanding the temperature history is vital for designing effective safety measures and preventing thermal runaway.