5.2 Emergency Relief System Sizing & Two-Phase Flow (DIERS)

The DIERS Methodology & Historic Context

Prior to the mid-1970s, emergency relief vents on chemical reactors were sized assuming single-phase vapour or gas flow using standard aerodynamic equations (such as API RP 520). However, following major chemical disasters—most notably the Seveso disaster in 1976 in Italy, where a runaway reaction in a 2,4,5-trichlorophenol reactor released toxic dioxins into the atmosphere—the global chemical industry recognised that conventional relief sizing methods were dangerously non-conservative.

In 1976, the American Institute of Chemical Engineers (AIChE) formed the Design Institute for Emergency Relief Systems (DIERS), a consortium of 29 companies. DIERS research established that when a reactor overpressurises during a thermal runaway, rapid boiling and gas evolution cause foam formation and liquid swell, forcing a two-phase (liquid-vapour/gas) mixture through the relief vent.

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Characterisation of Reaction Systems (Vapour vs. Gassy vs. Hybrid)

DIERS classifies runaway reaction systems into three distinct categories based on their thermodynamic behavior during pressure relief:

                  +-----------------------------------+
                  |      DIERS System Types           |
                  +-----------------------------------+
                                    |
         +--------------------------+--------------------------+
         |                          |                          |
         v                          v                          v
  +--------------+           +--------------+           +--------------+
  |    Vapour    |           |    Gassy     |           |    Hybrid    |
  |  (Tempered)  |           | (Non-Tempered|           |  (Combined)  |
  +--------------+           +--------------+           +--------------+
  | Boiling moderates        | Gas evolution            | Both non-     |
  | temp; venting cools      | drives pressure;         | condensable   |
  | the vessel mass.         | temp continues rising.   | gas & boiling.|
  +--------------+           +--------------+           +--------------+

1. Vapour Systems (Tempered Systems)

In a vapour system, the reaction mass contains volatile solvents or reactants. As the temperature rises, the liquid reaches its boiling point at the relief set pressure.

• Tempering Effect: The latent heat of vaporisation ($\Delta H_{vap}$) removes thermal energy from the liquid bulk. Venting vapour extracts mass and heat, effectively arresting further temperature rise once the relief valve opens.
• Sizing Basis: Sized based on the latent heat of vaporization required to balance the peak volumetric heat generation rate at maximum allowable overpressure.

2. Gassy Systems (Non-Tempered Systems)

In a gassy system, the runaway reaction decomposes to generate non-condensable gases (e.g., $CO_2$, $N_2$, $O_2$) without significant liquid boiling or vaporisation (e.g., organic peroxide decomposition or acid-catalyzed nitration).

• No Latent Cooling: Because non-condensable gas generation does not remove latent heat, venting gas does not cool the liquid mass. The reaction temperature continues to rise even while the vessel is actively venting!
• Sizing Basis: Vent sizing must accommodate the maximum volumetric gas generation rate ($dV/dt$) at the peak reaction temperature.

3. Hybrid Systems (Combined Systems)

A hybrid system exhibits both non-condensable gas generation and boiling volatile liquid. Pressure generation is driven by both gas partial pressure and solvent vapour pressure. These systems require complex adiabatic calorimetry modeling (using ARC or Vent Sizing Package / VSP) to isolate gas evolution rates from vapour pressures.

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Two-Phase Flow Hydraulics & Vent Sizing Mechanics

When relief occurs under two-phase flow conditions, liquid droplets or foam are entrained in the expanding vapour stream. Because liquid density ($\rho_L$) is orders of magnitude higher than vapour density ($\rho_V$), two-phase mixtures exhibit significantly lower volumetric discharge rates per unit area than pure gas.

Foamy vs. Non-Foamy Hydrodynamics

• Foamy Systems: Minor concentrations of surfactants, polymers, or fine particulates stabilize bubbles, causing uniform volumetric expansion (homogeneous swell). The entire vessel content swells to fill the vapour space, forcing two-phase flow throughout the entire relief event.
• Non-Foamy Systems: Bubbles coalesce rapidly and rise through the liquid phase (churn-turbulent regime). If the freeboard vapour space above the liquid level is sufficiently large, disengagement occurs and venting transitions to single-phase vapour after an initial liquid prompt purge.

       Foamy Swell vs Non-Foamy Disengagement
       
       [ Foamy Regime ]            [ Non-Foamy Regime ]
      +----------------+          +----------------+
      | ~~~~~~~~~~~~~~ | -> Vent  |                | -> Vapour Vent
      | O o O o O o O  | (Two-    | - - - - - - - -| (Disengaged)
      | o O o O o O o  |  Phase)  | O  o   O   o   | 
      | O o O o O o O  |          |~~~~~~~~~~~~~~~~| Liquid level
      +----------------+          +----------------+

Vent Area Comparison

Because the mass flux ($G$, $kg/m^2\cdot s$) of a two-phase mixture is dramatically lower than that of pure vapour, a vent sized for two-phase flow requires an orifice surface area 200% to 1000% (2x to 10x) larger than a single-phase vent for the same reactor volume!

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Relief Device Technology: Bursting Discs vs. Safety Relief Valves

Primary emergency pressure relief is achieved using reclosing devices (Safety Relief Valves / SRVs) and non-reclosing devices (Bursting / Rupture Discs).

   Rupture Disc + Safety Valve Combination
              |
              v To Effluent Header / Flare
         +---------+
         |  SRV    |  Safety Relief Valve (Reclosing)
         +---------+
              |
              | <-- Tell-Tale Pressure Gauge & Bleed Valve
         +---------+
         |  DISC   |  Bursting Disc (Non-Reclosing, Zero Leakage)
         +---------+
              |
              v From Corrosive Reactor Vapour Space

Requirements for Combined Assemblies

When a rupture disc is installed upstream of a safety relief valve (to protect the valve from corrosive process fluids):

1. Tell-Tale Gauge / Excess Pressure Indicator: A pressure gauge, try-cock valve, or pressure transmitter MUST be installed in the interspace between the disc and valve seat.
2. Interspace Backpressure: Any leakage through the rupture disc creates backpressure in the interspace, increasing the effective burst pressure of the disc dollar-for-dollar and preventing the disc from opening at its design pressure!

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Downstream Containment & Effluent Handling Systems

Direct atmospheric discharge of hazardous two-phase relief streams is unacceptable under modern environmental and safety legislation (such as COMAH and DSEAR). Relief headers must route effluent to dedicated treatment systems:

1. Knock-Out Drums & Liquid-Vapour Separators: Gravity settling vessels designed to reduce vapour velocity below the terminal settling velocity of liquid droplets ($u_t$), separating liquid bulk from the gas stream.
2. Quench Tanks & Dump Vessels: Submerged dip-pipe vessel filled with cold water or neutralizing fluid to condense steam/vapour and chemically neutralize acid gases.
3. Scrubbers & Absorption Towers: Packed towers utilizing counter-current chemical reagents (e.g., sodium hydroxide solution for chlorine or acid gas absorption).
4. Flare Stacks & Thermal Oxidisers: High-elevation elevated flares with continuous pilot burners to combust flammable hydrocarbon gases safely.