relief-valve

name	relief-valve
description	Pressure relief valve sizing — API 520/521, required relief area (vapor/liquid/two-phase), overpressure scenarios, set pressure, back-pressure correction (K_b), balanced bellows, PRV vs. rupture disk.
metadata	{"priority":7,"promptSignals":{"phrases":["relief valve","pressure relief valve","PRV sizing","API 520","API 521","overpressure protection","safety relief valve"],"minScore":3}}

Pressure Relief Valve Sizing — Complete Skill

Standards

API 520 Part I: sizing; calculation of required relief area API 520 Part II: installation; inlet/outlet piping, balanced bellows, pilot-operated API 521: pressure-relieving and depressuring systems; overpressure scenario analysis ASME VIII Div. 1 Appendix 11: mandatory appendix; PRV design and marking ASME PTC 25: testing and performance

PRV Terminology

Set pressure (P_set): pressure at which PRV starts to open [barg] Maximum allowable working pressure (MAWP): highest pressure at design temperature Accumulation: pressure above MAWP during relief; typically 10% MAWP Overpressure: pressure above set pressure during relief; typically 10% P_set for fire, 10% for others Back pressure: pressure at PRV outlet; affects flow capacity Blowdown: difference between set and reseat pressure; typically 7–10% of set pressure

MAWP relationship: P_set ≤ MAWP (or ≤ 1.03 × MAWP for multiple valves with one primary + one supplemental) P_set for fire case: ≤ 1.10 × MAWP (single valve)

Overpressure Scenarios (API 521)

1. Blocked outlet — control valve failure closed; most common governing case
2. Fire (pool fire / jet fire) — heat input to vessel from external fire
3. Utility failure — cooling water or power loss; controlled equipment fails unsafe
4. Tube failure (heat exchangers) — high-pressure side ruptures into low-pressure side
5. Thermal expansion — blocked liquid expands due to heat; small thermal relief valve
6. Runaway reaction — exothermic; rate exceeds cooling capacity
7. Vapor depressurization — rapid blowdown from adjacent vessel/system
8. Reflux failure — distillation tower flooding on loss of reflux

Relief scenario selection: most onerous (largest relief area required) governs PRV size

Required Relief Area — Vapor/Gas (API 520)

For critical flow (P_back/P_1 < P_critical): A = W / (C × K_d × P_1 × K_b × K_c) × √(TZ/M)

A = required area [in²] W = required flow rate [lb/hr] C = gas constant function = 520 × √(γ × (2/(γ+1))^((γ+1)/(γ-1))) [515–550 for most gases] K_d = discharge coefficient (0.975 for vapor PRV; 0.65 for rupture disk) P_1 = relieving pressure = P_set × (1 + accumulation fraction) + 14.7 [psia] K_b = back-pressure correction factor K_c = combination correction (1.0 without rupture disk; 0.9 with rupture disk) T = relieving temperature [°R = °F + 460] Z = compressibility factor; M = molecular weight [lb/lbmol]

C constant: C = 520 √(γ × (2/(γ+1))^((γ+1)/(γ-1))) For γ = 1.4: C = 356; γ = 1.3: C = 349; γ = 1.2: C = 340; γ = 1.0: C = 315

SI equivalent (metric): A [cm²] = W[kg/hr] / (0.2883 × C_metric × K_d × P_1[kPa,abs] × K_b × K_c) × √(TZ/M)

Required Relief Area — Liquid (API 520)

Liquid relief (incompressible): A = Q / (38 × K_d × K_w × K_c × K_v) × √(G / (P_1 - P_2))

Q = flow rate [US gpm] K_w = back-pressure correction for balanced bellows (= 1.0 for conventional PRV) K_v = viscosity correction (1.0 if Re > 20,000; from chart otherwise) G = specific gravity (water = 1.0) P_1, P_2 = inlet, outlet pressure [psia]

Viscosity correction (Re < 20,000): Calculate Re = 2.8 × Q × G / (μ × √A) [iterative; μ in cP] K_v from API 520 Figure 30

Required Relief Area — Fire Case (API 520 / API 521)

Heat input from pool fire (API 521 Table 5): Q_fire = C × F × A_wetted^0.82 [BTU/hr] F = environmental factor (F = 1.0 for bare vessel; F = 0.1 for adequate drainage + fire fighting) A_wetted = wetted surface area (up to 25 ft above grade for ground-level fire)

Two-phase fire relief: If liquid inside, relief is vapor (flashing) — use vapor equation with latent heat: W = Q_fire / H_v [lb/hr; H_v = latent heat at relieving conditions BTU/lb]

Back-Pressure Correction Factor K_b

Conventional PRV (spring-loaded)

Back pressure reduces effective relieving pressure 10% rule: if P_back < 10% P_set → K_b = 1.0 (negligible effect) For higher back pressure: K_b < 1.0 (from API 520 chart for critical flow)

Balanced Bellows PRV

Back-pressure effect on spring force eliminated by bellows K_b = 1.0 for back pressure up to rated limit of bellows (typically 40–50% P_set) Advantage: higher back pressure tolerance

Pilot-Operated PRV

Back pressure has no effect on set pressure (sensing line not affected) K_b = 1.0 for all back pressures < 100% P_set Advantage: can set close to MAWP; good for high back-pressure systems

PRV Types

Type	Advantages	Disadvantages
Conventional spring	Simple; low cost	Back pressure affects set; chattering risk
Balanced bellows	Tolerates back pressure; corrosion protection	Bellows can fail; cannot be in flammable gas without secondary containment
Pilot-operated	Very tight shutoff; large Cv available	Complex; potential for pilot fouling; slower response
Rupture disk	No leakage; simple; handles viscous	One-time use; uncertainty on burst pressure

Inlet and Outlet Piping (API 520 Part II)

Inlet pressure drop: ≤ 3% of set pressure (non-chattering requirement) ΔP_inlet = f × L/D × ρV² / 2 ≤ 0.03 × P_set Outlet (tailpipe) back pressure: must stay within K_b limits Size tailpipe for all concurrent relief scenarios discharging simultaneously

Reactive force on PRV during discharge: F = W × v_exit / g_c + (P_exit - P_atm) × A_exit [lbf] Must be considered for pipe flexibility and support design

Rupture Disk vs. PRV

Rupture disk alone: allowed for non-toxic, non-flammable services (ASME VIII, NB-18) PRV alone: standard; must have monthly/annual leak check Rupture disk upstream of PRV: prevents PRV seat corrosion; combination factor K_c = 0.9; NB mark required PRV upstream of rupture disk (backpressure isolation): permitted; must account for back pressure

PRV Selection Sizing Procedure

1. List all credible overpressure scenarios
2. Calculate required relief rate W or Q for each
3. Calculate required relief area A for each
4. Select largest A → governs PRV size
5. Select next standard API orifice area (D through T per API 526)
6. Check inlet ΔP ≤ 3% P_set
7. Check outlet K_b within PRV tolerance
8. Specify P_set, MAWP, temperature, connections, material, code stamp

Standard API 526 orifice designations (area in²): D = 0.110; E = 0.196; F = 0.307; G = 0.503; H = 0.785; J = 1.287; K = 1.838; L = 2.853; M = 3.60; N = 4.34; P = 6.38; Q = 11.05; R = 16.0; T = 26.0

Output

Provide: governing overpressure scenario, required relief flow W [lb/hr] or Q [gpm], required area A [in²], selected API orifice letter and actual area, set pressure P_set [barg], PRV type (conventional/balanced bellows/pilot), K_b and K_d used, inlet ΔP check [% of P_set], back-pressure limit [% of P_set], applicable standard (API 520/521, ASME VIII).