safety-relief-valve

name	safety-relief-valve
description	Safety and relief valve design — ASME Section VIII UG-125 to UG-140, API 520/521/526, required relieving capacity (vapor/liquid/fire case), orifice area calculation, back pressure effects (superimposed/built-up), balanced bellows vs. conventional vs. pilot-operated, set pressure, accumulation and overpressure, blowdown, inlet pressure drop, reaction forces, and PRV sizing for two-phase flow.
metadata	{"priority":7,"promptSignals":{"phrases":["safety relief valve","pressure relief valve","PRV sizing","API 520","relief valve","rupture disk"],"minScore":3}}

Safety and Relief Valve Design — Complete Skill

Regulatory Framework

ASME and API Standards

ASME Boiler and Pressure Vessel Code Section VIII Div. 1: UG-125: Protection against overpressure — every pressure vessel must have relief device UG-126: Safety and relief valves — spring-loaded; lift ≥ at set pressure UG-127: Rupture disks — non-reclosing; used alone or in combination with PRV UG-134: Set pressure ≤ MAWP (maximum allowable working pressure) UG-125(c): Accumulation limits — 10% or 3 psi (whichever greater) for single PRV; 16% for fire case

API 520 Part I: Sizing and Selection of Pressure-Relieving Devices API 520 Part II: Installation of Pressure-Relieving Devices API 521: Pressure-Relieving and Depressuring Systems (relief scenarios) API 526: Flanged Steel Pressure-Relief Valves (standard orifice sizes and dimensions)

Relief Scenarios (API 521)

Common Overpressure Scenarios

Blocked outlet: most common; full process flow must be relieved Q_relief = pump curve intersect with MAWP; for centrifugal pump: Q = rated flow × 1.0–1.1

Fire case (API 521 Section 5.15): Q_vapor = F × A_wetted^0.82 / λ [API 521 Eq. 3; F = environment factor; A_wetted [ft²]; λ = latent heat [BTU/lb]] F = 1.0 for bare vessel; F = 0.3 for sprinkler insulated; F = 0.075 for fireproofed + drainage Alternative: Q = C₁ × F × A_wetted^0.82 × (T_s)^0.5 for specific liquid and temperature

Cooling water failure: flash vapor from process side if water suddenly stops Power failure: loss of agitation, pumps, compressors — evaluate consequences

External fire heat input: Q_fire [BTU/hr] = 21,000 × F × A_wetted^0.82 (API 521 Equation 1; SI: Q [W] = 43,200 × F × A_wetted^0.82 [m²])

Two-phase relief scenario: Homogeneous equilibrium model (HEM) or Omega method (Leung); most conservative Use DIERS (Design Institute for Emergency Relief Systems) methodology

Orifice Area Sizing

Vapor / Gas (API 520 Part I)

Sonic (choked) flow — steam and gas: A = W / (C × K_d × P₁ × K_b × K_c) × √(T × Z / M) [in²; API 520 Eq. 1] [W = flow [lb/hr]; C = gas constant function of γ; K_d = effective discharge coefficient; P₁ = relieving pressure [psia]; K_b = back pressure correction; K_c = combination factor (rupture disk upstream = 0.9); T = temperature [°R]; Z = compressibility; M = molecular weight]

C constant (function of γ): C = 520 × √(γ × (2/(γ+1))^((γ+1)/(γ-1))) [API 520 Eq. 2] For γ = 1.4 (air, diatomic): C = 315; for γ = 1.0: C = 295; for γ = 1.3 (steam): C = 312

Effective discharge coefficient K_d: API 526 standard orifice (certified): K_d = 0.975 (gas); K_d = 0.65 (liquid) For preliminary sizing: K_d = 0.85 (conservative, both phases)

Back pressure correction K_b: For conventional spring-loaded PRV: K_b = 1.0 when P_back < 10% P_set (negligible back pressure) K_b from API 520 Figure 32 when 10% < P_back/P_set < 50% When P_back > 50% P_set: use pilot-operated or balanced bellows valve

Example — gas relief: W = 10,000 lb/hr steam; P₁ = 100 psia; T = 400°F (860°R); γ = 1.3; M = 18; K_d = 0.975; K_b = 1.0; K_c = 1.0 C = 312; Z = 0.99 (steam at these conditions) A = 10,000 / (312 × 0.975 × 100 × 1.0 × 1.0) × √(860 × 0.99/18) = 0.329 × 6.90 = 2.27 in² Select API 526 orifice letter J (2.853 in²) → next size up from 2.27 in²

Liquid Relief (API 520)

Liquid relief area: A = Q / (38.0 × K_d × K_w × K_c × K_v) × √(G / (P₁ - P₂)) [in²; Q [gpm]; G = specific gravity] [K_w = back pressure correction for liquid (balanced bellows effect); K_v = viscosity correction]

Viscosity correction K_v: K_v = 1.0 for μ ≤ 100 SSU (water-like liquids); iterate using Reynolds number: Re_P = 2800 × G × Q / (μ × A^0.5) [first assume K_v = 1.0; then correct] K_v from API 520 Figure 29 vs. Re_P

PRV Types and Selection

Conventional Spring-Loaded PRV

Design: Spring holds disc closed at set pressure; opens when P > P_set Blowdown: closes at P_reseat = P_set × (1 - blowdown%); typical blowdown = 7–10%

Back pressure limitation: Conventional PRV sensitive to back pressure — back pressure opposes spring force, reduces effective set P_set_effective = P_set_adjusted = P_set - P_back Only acceptable when P_back < 10% P_set (superimposed back pressure must be included in spring setting)

Applications: steam service; atmospheric discharge; low back pressure service

Balanced Bellows PRV

Design: Bellows isolates spring from process fluid; cancels effect of superimposed back pressure on set pressure Back pressure acts equally on both sides of disc → no net force change on set pressure Maximum built-up back pressure = 30–40% of set pressure for certified capacity

Applications: corrosive fluids; variable back pressure; refinery service; API 526 Type B

Pilot-Operated PRV (POPRV)

Design: Main valve held closed by system pressure (force area ratio > 1); pilot senses pressure → opens main Advantages: very tight shut-off; large capacity; low proportional band (opens fully at set + 2%) Can operate against very high back pressure (up to 100% of set for balanced pilot)

Applications: compressors; high-pressure gas; systems requiring very low leakage; large sizes (>6")

Set Pressure, Accumulation, and Overpressure

Terminology

MAWP: Maximum allowable working pressure — stamp on vessel Set pressure: Pressure at which PRV begins to open (or rupture disk bursts) Overpressure: Pressure above MAWP during relief; expressed as % MAWP Accumulation: Maximum pressure during relief = MAWP + allowable overpressure Blowdown: PRV closes at: P_reseat = P_set - blowdown (% of set)

Accumulation limits (ASME UG-125): Non-fire single PRV: +10% MAWP; Non-fire multiple PRVs: +16% MAWP Fire case: +21% MAWP (higher overpressure permitted for fire) For set pressure: P_set ≤ MAWP; supplemental PRV: P_set ≤ 1.05 × MAWP; fire PRV: ≤ 1.10 × MAWP

Relieving pressure P₁: P₁ = P_set × (1 + accumulation%) = MAWP × (1 + 0.10) for single non-fire PRV P₁ used in all API 520 sizing equations — not set pressure

Inlet Pressure Drop (3% Rule)

API 520 requirement: Inlet pressure drop (pipe from vessel to PRV inlet) ≤ 3% of set pressure Failure: PRV chattering (rapid opening/closing → disc damage); instability → seat damage

Check: ΔP_inlet = f × L/D × ρV²/2 [Darcy-Weisbach]; must be ≤ 0.03 × P_set Typical: maximize inlet pipe diameter; minimize length; avoid elbows close to inlet Minimum inlet pipe diameter: same as PRV inlet size (no reducers)

Discharge Pipe and Reaction Force

Reaction force at PRV outlet during relief: F_reaction = W × V_e / g_c + (P_e - P_atm) × A_e [lbf; F in piping direction] Simplified API 520: F = 129 × W × √(T/M) / (P₁ × K_d) [lbf; for initial estimate] Piping must be supported to take reaction force; thermal expansion and reaction loads combined

Common discharge arrangements: To atmosphere: open-ended stack; height and exit velocity for dispersion (API 521) To header/closed system: back pressure analysis required (pressure relief header sizing) Rupture disk + PRV combination: K_c = 0.9 applied; combination must not exceed set of PRV

Two-Phase Relief — Omega Method (DIERS)

Omega parameter: ω = (v₀/(v_fg0)²) × (dv_fg/dP)_0 × P₀/v₀ [dimensionless; characterizes phase change severity] Subcooled: ω → 0; Saturated (all-vapor): ω → ∞; Two-phase: intermediate ω

Leung Omega method sizing: G = P₀/v₀ × C_tph(ω, η) [mass flux [kg/m²s]; η = P_back/P₀; C_tph from charts] A = W / G [m²]

Flashing liquids (ω > 1): single-phase orifice area significantly underestimates; use DIERS

Standards and References

Standard	Scope
API 520 Part I	PRV sizing and selection
API 520 Part II	PRV installation requirements
API 521	Relief scenarios and pressure systems
API 526	Standard PRV flanged orifice dimensions
ASME Sec. VIII UG-125 to UG-140	Code requirements for pressure relief
API 2000	Venting of atmospheric and low-pressure tanks
DIERS Technology	Two-phase relief sizing methodology

Output

Provide: vessel description (MAWP [psig/barg]; design temperature; fluid/phase; contents), relief scenario (blocked outlet/fire case/other; basis per API 521; multiple scenarios analyzed), required capacity (W [lb/hr or kg/hr] or Q [gpm or m³/hr]; latent heat λ [BTU/lb]; specific gravity G), set pressure (P_set [psig]; P_relieving = P_set × 1.10 or 1.21 for fire [psig]; accumulation case used), orifice sizing (A_required [in²]; API 520 equation; C; K_d; K_b; K_c; back pressure [%] of set), selected PRV (API 526 orifice letter; actual area [in²]; type: conventional/balanced/pilot), back pressure check (superimposed [psi]; built-up [psi]; total < limit for valve type; balanced bellows if >10%), inlet ΔP check (calculated [psi] vs. 3% limit [psi]; pipe diameter recommendation), reaction force [lbf] (direction; piping support requirement), two-phase check (if applicable: ω; flashing liquid; area correction factor), and applicable standard (ASME UG-125; API 520 Part I equation; API 521 scenario credit).