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Qwestrum Engineering360 · Chemical Engineering · Process Safety

Relief Valve Sizing

Relief-valve sizing first determines the worst-case relief load (from fire, blocked outlet, or runaway reaction) and then computes the orifice area from the API 520 equation, ensuring the set pressure does not exceed the vessel’s MAWP.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Set pressure ≤ MAWP; allowable accumulation ~10% (single relief), 21% (fire)
  • Two-phase relief needs the omega method or a homogeneous-equilibrium model
  • Back-pressure correction K_b accounts for relief-header pressure

Topic details

Introduction

This Crowl & Louvar topic sizes pressure-relief devices. You enumerate credible over-pressure scenarios, select the governing (largest) relief load, apply the API 520 orifice equation with discharge and back-pressure corrections, and confirm the set pressure and allowable accumulation stay within code limits.

Key relations & formulas

A=W(CKdP1KbKc)×TZMA = \frac{W}{(C K_{d} P_{1} K_{b} K_{c})} \times \sqrt{T \frac{Z}{M}}
(API 520 vapour, critical flow)

Formulas (Indian textbook notation)

  • W=requiredreliefmassflowrateW = required relief mass flow rate
P1=upstreamrelievingpressure;Kd≈0.975P_{1} = upstream relieving pressure; K_{d} \approx 0.975
(discharge coefficient)

Notation and sign conventions

Relation 1 —
A=W/A = W /
A=W(CKdP1KbKc)×TZMA = \frac{W}{(C K_{d} P_{1} K_{b} K_{c})} \times \sqrt{T \frac{Z}{M}}
(API 520 vapour, critical flow)
Write this relation with symbols exactly as in Crowl Louvar Safety — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
W=requiredreliefmassflowrateW = required relief mass flow rate

Formulas (Indian textbook notation)

  • W=requiredreliefmassflowrateW = required relief mass flow rate
Write this relation with symbols exactly as in Crowl Louvar Safety — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
P1=upstreamrelievingpressure;Kd≈0.975P_{1} = upstream relieving pressure; K_{d} \approx 0.975
P1=upstreamrelievingpressure;Kd≈0.975P_{1} = upstream relieving pressure; K_{d} \approx 0.975
(discharge coefficient)
Write this relation with symbols exactly as in Crowl Louvar Safety — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

A relief device is the last line of defence against vessel rupture, so scenario analysis comes first: fire exposure, a blocked outlet with a pump running, thermal expansion, or a runaway reaction each impose a relief load, and the device must handle the worst credible one. The API equation sizes the orifice for critical (choked) flow, where downstream conditions no longer affect the rate, corrected for the valve’s discharge coefficient and any back-pressure in the relief header. The set pressure must sit at or below the maximum allowable working pressure, with a code-defined accumulation margin above it during relief. Two-phase relief, common in runaway reactions, needs special methods because the mixture is denser and harder to vent.

Assumptions and validity limits

State assumptions explicitly before using any relation for relief valve sizing — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Process Safety viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Process Safety papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to relief valve sizing.
4. Use equation 1:
A=W/A = W /
.
5. Use equation 2:
W=requiredreliefmassflowrateW = required relief mass flow rate
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Relief Valve Sizing appears in oil, gas, and chemical plants. In Indian chemical curricula this topic is tested because it connects theory to HAZOP, relief, and risk assessment.
GATE and semester exams often combine relief valve sizing with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use relief valve sizing?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Students size for a non-governing scenario, forget that fire and non-fire cases allow different accumulation, and ignore back-pressure and two-phase effects. Setting the relief pressure above the MAWP is a fundamental code violation.

Quick revision checklist

Before attempting relief valve sizing problems, confirm you can:
1. Set pressure ≤ MAWP; allowable accumulation ~10% (single relief), 21% (fire)
2. Two-phase relief needs the omega method or a homogeneous-equilibrium model
3. Back-pressure correction K_b accounts for relief-header pressure
Revise the solved examples in Crowl Louvar Safety — Standard reference and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Governing relief scenario

Problem

A vessel could relieve 500 kg/h under blocked outlet, 1200 kg/h under fire, and 300 kg/h under thermal expansion. Which load sizes the valve?

Solution

The valve is sized for the largest credible load, 1200 kg/h (fire case), since it must protect against the worst credible over-pressure — smaller scenarios are then automatically covered.

Conceptual check — Relief Valve Sizing

Problem

In a Process Safety semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of relief valve sizing." What should a complete answer include?

Exams & GATE

Crowl & Louvar Ch. 10 — identify fire, blocked-outlet and runaway-reaction scenarios.

📖 Standard books (India)

  • Crowl Louvar Safety — Standard reference

    Read: Syllabus unit

    Referenced in Indian B.Tech syllabus

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