Relief Device Calculations: Why They Matter and How DIERS Changed the Game

Relief devices are the last line of defense when pressure builds up in a vessel or pipeline and things start to go sideways. Whether it’s a runaway reaction, a blocked outlet, or fire exposure, you need a way to vent that pressure safely. But sizing these devices isn’t just about plugging numbers into a spreadsheet. It’s about understanding the physics of what’s happening inside the system—and that’s where DIERS comes in.

DIERS (Design Institute for Emergency Relief Systems) revolutionized how we think about emergency venting. Before DIERS, most relief systems were sized using vapor-only assumptions. That worked fine for simple systems, but it failed miserably for reactive or foamy ones. DIERS showed that two-phase flow—where gas and liquid vent together—can choke the vent line, reduce flow efficiency, and lead to catastrophic failure if not properly accounted for.

So let’s break it down. Why do we care? How do we calculate it? And what does DIERS actually tell us?

 

 

Example 1: Heated Water Tank Overflow

Let’s start simple. A vertical tank stores water for utility use. It’s equipped with a steam coil to prevent freezing. One day, the steam valve fails open, and the water starts heating up. As it approaches boiling, vapor forms and pushes liquid upward. The tank isn’t pressurized, but the liquid swell causes an overflow.

Specs:

• Tank volume: 10 m³
• Fill level: 90%
• Heating rate: 10 kW
• Specific heat: 4186 J/kg·K
• Vaporization heat: 2.26 MJ/kg

Step-by-step:

1. Temperature rise
   
2. Vapor generation
   
3. Liquid swell volume
   

Over an hour, that’s about 17 liters of overflow. Not dramatic, but enough to flood a containment area or trigger alarms. DIERS methodology helps quantify this and size the overflow pipe or catch basin.

 

Example 2: Styrene Polymerization Runaway

Now let’s turn up the heat. A batch reactor is polymerizing styrene. During a thermal runaway, the reaction accelerates, generating vapor and foam. The vessel needs to vent fast—but the fluid is foamy and behaves like a two-phase mixture.

Specs:

• Reactant mass: 9500 kg
• Specific heat: 2470 J/kg·K
• Self-heat rate: 0.493 K/s
• Heat of reaction: 3.1 × 10⁵ J/kg
• Relief pressure: 4.5 × 10⁵ Pa
• Temperature: 482.5 K
• Molecular weight: 106

 

 

DIERS sizing:

1. Mass flow rate
   
   
2. Vent area (homogeneous flow)
   

DIERS calculated: [ A_v = 0.0264 \text{ m}^2 ]

3. Two-phase correction
   

Without this correction, the vent would be undersized and the reactor could rupture. DIERS helps avoid that by modeling real flow behavior.

 

PSV Orifice Sizes and Nomenclature (API 526)

Once you’ve calculated the required vent area, you need to select a relief valve with a matching orifice. API 526 standardizes this using a letter-based system. Each letter corresponds to a specific effective discharge area.

Orifice Letter	Area (in²)	Area (mm²)
D	0.110	71
E	0.196	126
F	0.307	198
G	0.503	325
H	0.785	507
J	1.287	830
K	1.838	1186
L	2.853	1841
M	3.600	2323
N	4.920	3174
P	6.380	4116
Q	11.050	7129
R	16.000	10323
T	26.000	16774

These sizes are standardized across manufacturers, so a “J” orifice from one vendor will match another’s. API 526 also defines standard inlet and outlet flange sizes for each orifice, ensuring compatibility and minimizing pressure drop.

 

Inlet and Outlet Pressure Drop: The Silent Saboteur

Even with the right valve and orifice, your system can fail if the piping isn’t right. Excessive pressure drop in the inlet or outlet lines can cause serious problems.

Inlet Pressure Drop

• Limit: ≤ 3% of PSV set pressure (API 520, ASME VIII Appendix M)
• Why it matters: Too much inlet loss causes valve chatter, delayed opening, and reduced flow
• Formula:
  Include all losses from vessel nozzle to PSV inlet—entrance effects, elbows, reducers, and pipe friction.

 

Outlet Pressure Drop

• Limit:
• Conventional PSV: ≤ 10% of set pressure
• Bellows PSV: ≤ 30%
• Pilot-operated PSV: ≤ 50%
• Why it matters: High backpressure reduces valve lift and flow capacity
• Formula:
  

Exclude the exit pipe fitting if venting to atmosphere—it doesn’t contribute to backpressure.

 Consequences of High dP

• Valve chattering and vibration
• Premature reseating or failure to open
• Reduced relief capacity
• Risk of exceeding MAWP
• Regulatory non-compliance and fines

 

 

Reference Standards

• DIERS methodology – Two-phase flow and reactive system modeling
• API 520 Part I & II – Sizing and pressure drop limits
• API 526 – PSV orifice sizes and flange combinations
• ASME Section VIII – Relief system design rules
• Smith & Burgess on outlet pressure drop
• Eng-Tips discussion on inlet/outlet dP
• IoMosaic primer on inlet pressure loss

 

Final Takeaways

• Even simple systems like water tanks can overflow due to thermal input
• DIERS helps quantify liquid swell and vent sizing
• Reactive systems need two-phase modeling to avoid undersizing
• PSV orifice selection must match calculated relief area using API 526
• Inlet and outlet piping must be sized to avoid excessive pressure drop
• Chatter, backpressure, and poor flow can sabotage safety systems

 

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