Relief Valve Sizing

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Relief Valve Sizing Theory

Purpose of Relief Valves

Pressure Relief Valves (PRVs) are critical safety devices that protect pressure vessels, piping, and equipment from overpressure conditions. They automatically open to relieve excess pressure and close when normal conditions are restored.

Gas/Vapor Sizing (API 520)

A = W × √(T × Z) / (C × Kd × P₁ × Kb × Kc × √M)

A = Required orifice area (in²)

W = Mass flow rate (lb/hr)

T = Relieving temperature (°R = °F + 460)

Z = Compressibility factor

C = Coefficient from gas properties = 520√(k(2/(k+1))^((k+1)/(k-1)))

Kd = Discharge coefficient (typically 0.975)

P₁ = Relieving pressure (psia)

Kb = Back pressure correction factor

Kc = Combination correction factor (1.0 without rupture disk)

M = Molecular weight

Liquid Sizing (API 520)

A = Q × √G / (38 × Kd × Kw × Kc × Kv × √ΔP)

Q = Volumetric flow rate (GPM)

G = Specific gravity (relative to water)

Kd = Discharge coefficient (typically 0.65)

Kw = Back pressure correction factor

Kv = Viscosity correction factor

ΔP = Differential pressure (P₁ - P₂) in psi

Steam Sizing (API 520)

A = W / (51.5 × Kd × P₁ × Ksh × Kb × Kc)

W = Steam flow rate (lb/hr)

Ksh = Superheat correction factor

Critical vs. Subcritical Flow

For gases, the flow becomes critical (choked) when the downstream pressure drops below the critical pressure ratio. At this point, the flow velocity reaches sonic conditions and further pressure reduction does not increase flow.

Critical Pressure Ratio: Pc/P1 = (2/(k+1))^(k/(k-1))

API 526 Standard Orifice Sizes

API 526 defines standard orifice sizes designated by letters D through T. Selecting a standard orifice simplifies procurement and ensures interchangeability.

D: 0.110 in²
E: 0.196 in²
F: 0.307 in²
G: 0.503 in²
H: 0.785 in²
J: 1.287 in²
K: 1.838 in²
L: 2.853 in²

Overpressure Allowances

  • 10% - Standard overpressure for non-fire cases
  • 16% - Multiple relief devices (first valve)
  • 21% - Fire case scenarios
  • 3% - Accumulation for unfired pressure vessels per ASME

References

  • API 520 Part I - Sizing and Selection
  • API 520 Part II - Installation
  • API 521 - Pressure-relieving and Depressuring Systems
  • API 526 - Flanged Steel Pressure Relief Valves
  • ASME Section VIII - Pressure Vessels
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