Numerical Simulation

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Numerical simulation for reactive Pressure Safety Valve (PSV) design refers to the use of chemical reaction kinetics, the rates at which reactants convert to products—to predict how pressure and temperature will evolve during undesired conditions, a runaway reaction or thermal decomposition event. This modeling is crucial when designing relief systems (PSVs, rupture disks, or vent systems) for reactive systems, where pressure buildup is driven by chemical reactions, not just physical effects like vapor expansion.

Why Kinetic Modeling Matters?

In reactive systems, traditional PSV sizing methods (like those for vapor-liquid equilibrium) can be insufficient because:

The reaction rate determines how quickly pressure rises.
The energy release rate depends on the reaction kinetics and temperature sensitivity.
The composition of vented gases changes as the reaction progresses.
The worst-case scenario (runaway, decomposition, etc.) is governed by kinetics, not steady-state assumptions.

Therefore, kinetic modeling is used to simulate dynamic pressure and temperature profiles during an upset condition to determine:

When the PSV will open,
How fast the pressure will rise,
The total relief load (mass flow), and
Whether the PSV capacity is sufficient to prevent vessel rupture.

A kinetic model typically couples:

Reaction kinetics:
- Rate laws (e.g., first-order, nth-order, autocatalytic).
- Parameters from experiments (Arrhenius equation: ).
Energy balance:
- Heat generated by reaction ( ) vs. heat removed ( ).
Mass balance:
- Accumulation of gas/vapor and liquid volumes.
Thermodynamic properties:
- Heat capacity, vapor pressure, density, etc.
Relief system model:
- PSV set pressure, back pressure, discharge coefficients, and vent area.

These equations are solved numerically (often in tools like DIERS, Aspen Plus Dynamics, or custom MATLAB/Python codes) to simulate the runaway event.

References

Article: “Pressure relief sizing of reactive system using DIERS simplified methods and dynamic simulation method”

Authors: Surendra K. Singh, Richard Huh

Read here: https://doi.org/10.1016/j.jlp.2016.08.017

FAQ:

1. What are the applications of Kinetic modeling?

Reactive chemical processes (e.g., polymerizations, nitration, esterification).
Thermal decomposition reactions (e.g., peroxides, azides).
Battery venting and BESS safety (as reactions drive internal pressure).
DIERS (Design Institute for Emergency Relief Systems) relief studies.

2. What is the output of Kinetic modeling?

From these simulations, engineers determine:

Time to maximum rate: Time before runaway occurs.
Maximum pressure rise rate:
Peak pressure and temperature: Defines PSV set and design pressure.
Required vent area: Ensures safe pressure relief during the reaction.

3. How is DSC used in process safety or chemical reaction hazard analysis?

No. While it’s commonly used for batch and semi-batch reactors (due to higher runaway potential), it’s also applicable to continuous reactors, polymerization units, and thermal decomposition systems—anywhere reaction-driven pressure buildup can occur.

4. What are the industry standards or guidelines for reactive relief system design?

DIERS Guidelines (AIChE) – foundational framework for reactive vent sizing
API 520 / 521 – Relief system design and venting of reactive systems
CCPS Guidelines for Safe Handling of Reactive Chemicals – kinetic data and modeling practices

Numerical Simulation