Relief Valve Sizing
Engineering fundamentals for overpressure protection
1. Relief Valve Principles
Relief valves are the last line of defense against overpressure. They must open automatically at set pressure and relieve enough flow to prevent pressure from exceeding allowable limits.
📊 Pressure Relief Valve Operation
Cross-section diagram of spring-loaded PRV showing: (1) Inlet nozzle connected to vessel, (2) Disc held closed by spring force, (3) Spring with adjusting screw for set pressure, (4) Outlet to flare/atmosphere. Show force balance: Spring force vs. Pressure × Area. Annotate set pressure, overpressure, blowdown, reseat pressure.
Key Terminology
| Term |
Definition |
| MAWP |
Maximum Allowable Working Pressure (vessel design pressure) |
| Set Pressure |
Pressure at which valve begins to open (≤ MAWP) |
| Overpressure |
Pressure above set pressure during relieving (typically 10%) |
| Relieving Pressure |
Set pressure + Overpressure (sizing basis) |
| Blowdown |
Pressure drop required to reseat (typically 7–10%) |
| Accumulation |
Maximum pressure above MAWP during relieving |
Allowable Accumulation (ASME VIII)
| Scenario |
Single Valve |
Multiple Valves |
| Non-fire case |
110% MAWP |
116% MAWP |
| Fire case |
121% MAWP |
121% MAWP |
Set pressure rule: For single relief valve, set pressure ≤ MAWP. For multiple valves, one valve set at MAWP, others can be set up to 105% MAWP.
2. API 520 Sizing Methods
Gas/Vapor Service (Critical Flow)
API 520 Equation (US Units):
A = W / (C × Kd × P1 × Kb × Kc × √(M/TZ))
Where:
A = Required orifice area (in²)
W = Mass flow rate (lb/hr)
C = Gas constant (varies with k)
Kd = Discharge coefficient (0.975 typical)
P1 = Relieving pressure, absolute (psia)
Kb = Backpressure correction factor
Kc = Combination correction (0.9 with rupture disc)
M = Molecular weight
T = Relieving temperature (°R)
Z = Compressibility factor
C Factor (Function of k)
| k (Cp/Cv) |
C |
Typical Gas |
| 1.0 |
315 |
— |
| 1.2 |
345 |
Natural gas (approx) |
| 1.3 |
356 |
Air, N₂ |
| 1.4 |
366 |
Air (ideal) |
| 1.6 |
382 |
— |
Liquid Service
API 520 Liquid Equation:
A = Q × √(G) / (38 × Kd × Kw × Kc × Kv × √(P1 - P2))
Where:
A = Required orifice area (in²)
Q = Flow rate (GPM)
G = Specific gravity (water = 1.0)
Kd = Discharge coefficient (0.65 typical for liquid)
Kw = Backpressure correction
Kv = Viscosity correction
P1 - P2 = Differential pressure (psi)
Example: Gas Relief Sizing
Given: 50,000 lb/hr natural gas, MAWP = 300 psig, T = 150°F, MW = 18, k = 1.25, Z = 0.9
Relieving: P1 = (300 + 14.7) × 1.10 = 346 psia, T = 150 + 460 = 610°R
C = 350 (interpolated for k=1.25)
A = 50,000 / (350 × 0.975 × 346 × 1.0 × 1.0 × √(18/(610×0.9)))
A = 50,000 / (350 × 0.975 × 346 × 0.181)
A = 2.34 in² → Select "L" orifice (2.853 in²)
3. Relief Scenarios
API 521 identifies contingencies that may require pressure relief. Evaluate each scenario; the governing case determines valve size.
Common Relief Scenarios
| Scenario |
Cause |
Typical Governing |
| Blocked outlet |
Closed valve, plugged line |
Often governing for pumped systems |
| Fire exposure |
External fire heating vessel |
Often governing for large liquid inventory |
| Tube rupture |
Heat exchanger tube failure |
High-pressure to low-pressure side |
| Control valve failure |
CV fails open |
Upstream of pressure-limiting equipment |
| Thermal expansion |
Liquid trapped, heated |
Thermal relief valves |
| Power failure |
Loss of cooling/reflux |
Distillation columns |
🔥 Fire Case Heat Input
Diagram showing horizontal vessel with fire underneath. Label wetted surface area A_ws (portion of vessel shell in contact with liquid inside, below liquid level, within fire zone height). Show fire zone typically extends 25 ft above grade. Include formula: Q = 21,000 × F × A_ws^0.82 (BTU/hr) with F = environmental factor.
Fire Case Sizing (API 521)
Heat input from fire:
Q = 21,000 × F × A0.82 (BTU/hr)
Relief rate (boiling liquid):
W = Q / λ (lb/hr)
Where:
A = Wetted surface area (ft²) within fire zone
F = Environmental factor (1.0 bare, 0.3 insulated)
λ = Latent heat of vaporization (BTU/lb)
Environmental factor F: 1.0 = bare vessel, 0.3 = insulated with drainage (water deluge gives 0.3), 0.15 = fireproofed concrete. Insulation credit requires certified fire-resistant insulation.
4. Orifice Selection
Standard orifice designations per API 526. Select next size larger than calculated area.
| Letter |
Area (in²) |
Typical Inlet × Outlet |
| D |
0.110 |
1" × 2" |
| E |
0.196 |
1" × 2" |
| F |
0.307 |
1.5" × 2.5" |
| G |
0.503 |
1.5" × 3" |
| H |
0.785 |
2" × 3" |
| J |
1.287 |
3" × 4" |
| K |
1.838 |
3" × 4" |
| L |
2.853 |
4" × 6" |
| M |
3.60 |
4" × 6" |
| N |
4.34 |
4" × 6" |
| P |
6.38 |
4" × 6" |
| Q |
11.05 |
6" × 8" |
| R |
16.0 |
6" × 10" |
| T |
26.0 |
8" × 10" |
⚠ Never undersize: Always select the next standard orifice larger than calculated. Verify rated capacity exceeds required relief rate at relieving conditions.
5. Installation Requirements
Inlet Piping
- Pressure drop: ≤3% of set pressure (API 520 Part II)
- Pipe size: ≥ valve inlet size, short and direct
- No valves: Between vessel and PRV (or use car-sealed-open)
Outlet Piping
- Backpressure: Built-up + superimposed ≤ 10% of set (conventional valve)
- Support: Support outlet piping independently of valve
- Drainage: Provide low-point drain for liquid accumulation
🔧 PRV Installation Detail
Isometric piping detail showing: Vessel nozzle → Short vertical riser → PRV (mounted upright) → Outlet elbow → Supported header to flare. Label key dimensions: inlet line ≥ PRV inlet size, outlet to reduce backpressure. Show car-sealed-open block valve if present. Include drain at low point and tell-tale vent.
References
- API 520 Part I – Sizing and Selection
- API 520 Part II – Installation
- API 521 – Pressure-relieving and Depressuring Systems
- API 526 – Flanged Steel PRVs
- API 527 – Seat Tightness of PRVs
- ASME Section VIII – Pressure Vessel Code