1. Overview & Applications
Pressure Safety Valve (PSV) headers collect relieved fluids from multiple relief valves and route them to safe disposal (flare, vent stack, or catch tank). Proper header design ensures backpressure remains within allowable limits for all credible relief scenarios.
[IMAGE 1: PSV Header System Schematic]
Isometric view of typical PSV header arrangement showing multiple PSVs, branch connections, main header, knockout drum, and flare tip.
Gas plants
Low-pressure headers
Multiple process vessels relieve to common LP flare header (typically < 50 psig).
Refineries
Segregated systems
Separate headers for low/high pressure, clean/sour service, vapor/liquid relief.
Compressor stations
High-pressure headers
Station relief headers handle full-bore rupture disks and thermal relief valves.
Offshore platforms
Compact routing
Space-constrained headers require careful optimization for pressure drop.
Key Design Criteria
- Backpressure limit: Built-up backpressure must not exceed PSV capacity correction limits (10% conventional, 30-50% balanced bellows)
- Relief scenario: Size for credible simultaneous relief cases (fire case often governs)
- Pressure drop: Minimize ΔP through proper sizing, minimize fittings, avoid liquid slugs
- Vapor-liquid separation: Knockout drums upstream of flare to remove entrained liquids
- Layout considerations: Slope for drainage, support for thermal expansion, isolation for maintenance
Why header design matters: Undersized headers cause excessive backpressure, reducing PSV capacity below required relief rate → potential overpressure. Oversized headers waste capital. Proper design balances safety, cost, and future expansion needs.
Design Standards
| Standard | Scope | Key Requirements |
|---|---|---|
| API 521 | Pressure-relieving and depressuring systems | Relief scenarios, sizing methods, backpressure limits, flare system design |
| ASME Section VIII Div 1 | Pressure vessel code | PSV selection, nameplate capacity, overpressure limits (10% / 16% / 21%) |
| API 520 Part I | Sizing, selection, and installation of PSVs | Gas/vapor, liquid, two-phase relief sizing equations |
| API 520 Part II | Sizing for fire and runaway reaction | Fire exposure area, runaway reaction methods (DIERS) |
| ASME B31.3 | Process piping code | Header pipe wall thickness, material selection, support spacing |
2. API 521 Design Methodology
API 521 provides comprehensive guidance for designing pressure relief systems including relief valve sizing, header piping, knockout drums, and flare systems.
Relief Scenarios
API 521 Section 4 defines credible overpressure scenarios to consider:
| Scenario | Description | Typical Relief Rate |
|---|---|---|
| Fire exposure (pool fire) | Vessel exposed to external fire, liquid vaporizes | Q = 21,000 × F × A^0.82 (Btu/hr), A = wetted surface area (ft²) |
| Blocked outlet | Downstream valve closed, continued feed to vessel | Maximum feed rate (pump/compressor capacity) |
| Utility failure (cooling loss) | Cooling water failure, condenser ineffective | Heat duty that must be relieved as vapor |
| Runaway reaction | Exothermic reaction loses temperature control | DIERS method or adiabatic calorimetry (VSP2, RSST) |
| Tube rupture (heat exchanger) | High-pressure side leaks into low-pressure side | Orifice flow from HP to LP (limited by tube ID) |
| Thermal expansion | Liquid-full vessel heated (solar, jacket, ambient) | Volume expansion rate = β × V × dT/dt |
| Reflux failure (distillation) | Loss of overhead condenser, column pressure rises | Reboiler duty converted to vapor |
Fire Case Sizing (API 521 Section 4.4.12)
Fire Exposure Heat Input:
Q = 21,000 × F × A^0.82 (Btu/hr)
Where:
Q = Total heat input from fire
F = Environment factor
F = 1.0 for bare steel or insulated with damaged insulation
F = 0.3 for insulation in good condition (≥ 2 in thickness)
A = Total wetted surface area exposed to fire (ft²)
Wetted Surface Area (vertical vessel):
A = π D L_w
Where:
D = Vessel diameter (ft)
L_w = Wetted height (ft) = liquid level during fire
For horizontal vessel:
Use equations in API 521 Figure 15 based on liquid level
Relief Rate (gas/vapor):
W = Q / (λ × K_d) (lb/hr)
Where:
λ = Latent heat of vaporization at relief pressure (Btu/lb)
K_d = 1.0 for unstable fluids (light hydrocarbons)
K_d = 0.5 for stable fluids (may credit depressuring)
Example:
Propane storage sphere, D = 30 ft, 50% full
Wetted area A = π × 30 × 15 = 1414 ft²
F = 1.0 (bare steel)
Q = 21,000 × 1.0 × 1414^0.82 = 9.1 MMBtu/hr
Propane at 150 psig relief: λ = 125 Btu/lb
W = 9,100,000 / 125 = 72,800 lb/hr relief rate
Simultaneous Relief Scenarios
For facilities with multiple vessels, determine credible combinations of simultaneous relief:
- Single equipment failure: One PSV relieves at nameplate capacity, all others closed (most common basis)
- Fire scenario: All vessels within fire exposure zone relieve simultaneously (pool fire or jet fire diameter)
- Common cause failure: Utility failure (cooling water, electric power) affects multiple units
- Domino effect: Relief from one vessel triggers relief in downstream vessels (rare, conservative)
Credible vs incredible scenarios: API 521 does not require sizing for "incredible" scenarios like simultaneous failure of multiple independent systems. Use engineering judgment and company standards to define credible cases. Fire case often governs for gas plants and tank farms.
Overpressure Allowances (ASME Section VIII)
Allowable Overpressure:
Single PSV installation:
P_relief ≤ MAWP × 1.10 (10% overpressure, operating case)
P_relief ≤ MAWP × 1.16 (16% overpressure, fire case)
Multiple PSV installation:
First valve: P_set ≤ MAWP
Second valve: P_set ≤ MAWP × 1.05
Accumulation: P_max ≤ MAWP × 1.16 (operating), 1.21 (fire)
Where:
MAWP = Maximum Allowable Working Pressure (design pressure)
P_set = PSV set pressure (psig)
P_relief = Actual vessel pressure during relief
For unfired vessels, 10% accumulation is standard for operating cases.
For fire exposure, 16% or 21% accumulation is allowed (20% most common).
3. Pressure Drop Calculations
Pressure drop in relief headers reduces PSV capacity. Accurate calculation ensures backpressure remains within allowable limits.
[IMAGE 3: Pressure Drop Components in Header]
Diagram showing pressure profile along header with contributions from friction (pipe segments), fittings (elbows, tees), and acceleration effects.
Gas/Vapor Pressure Drop (Darcy-Weisbach)
Frictional Pressure Drop (incompressible approximation):
ΔP = f × (L/D) × (ρ V² / 2g_c)
Where:
f = Darcy friction factor (dimensionless)
L = Pipe length (ft)
D = Pipe inside diameter (ft)
ρ = Gas density at flowing conditions (lb/ft³)
V = Gas velocity (ft/s)
g_c = Gravitational constant = 32.2 lbm·ft/lbf·s²
For Mach number Ma < 0.3, incompressible approximation is valid.
Friction Factor (turbulent flow):
1/√f = -2.0 log₁₀(ε/(3.7D) + 2.51/(Re√f)) (Colebrook equation)
Or use Swamee-Jain explicit approximation:
f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re^0.9)]²
Where:
ε = Pipe roughness (ft), typically 0.00015 ft for carbon steel
Re = Reynolds number = ρ V D / μ
μ = Dynamic viscosity (lb/ft·s)
Velocity Calculation:
V = W / (ρ × A)
Where:
W = Mass flow rate (lb/s)
A = Pipe cross-sectional area = π D² / 4 (ft²)
Pressure Drop in Fittings
Fittings (elbows, tees, valves) cause additional pressure drop expressed as equivalent length or resistance coefficient:
Equivalent Length Method:
ΔP_total = f × (L_pipe + Σ L_e) / D × (ρ V² / 2g_c)
Where:
L_e = Equivalent length of fitting (ft)
Typical L/D ratios (equivalent length / diameter):
90° elbow (standard radius): L/D = 30
90° elbow (long radius): L/D = 16
45° elbow: L/D = 15
Tee (flow through run): L/D = 20
Tee (flow through branch): L/D = 60
Gate valve (fully open): L/D = 8
Globe valve (fully open): L/D = 340
Resistance Coefficient Method:
ΔP_fitting = K × (ρ V² / 2g_c)
Where K = resistance coefficient (dimensionless)
90° elbow: K = 0.9 (standard), 0.6 (long radius)
Tee (branch): K = 1.8
Sudden contraction (d/D = 0.5): K = 0.38
Sudden expansion (d/D = 0.5): K = 0.56
Total pressure drop:
ΔP_total = (f L/D + Σ K) × (ρ V² / 2g_c)
Compressible Flow Pressure Drop
For high pressure drop (ΔP/P > 10%) or high velocity (Ma > 0.3), use compressible flow equations:
Isothermal Compressible Flow (Crane TP-410, API 521 App. B):
P₁² - P₂² = (f × L / D + Σ K) × G² × Z × R × T / (MW × g_c × 144)
Where:
P₁ = Inlet pressure (psia)
P₂ = Outlet pressure (psia)
G = Mass flux = W / A (lb/ft²·s)
Z = Compressibility factor (dimensionless)
R = 10.73 psia·ft³/(lbmol·°R) [equivalent to 1545 ft·lbf/(lbmol·°R) ÷ 144 in²/ft²]
T = Gas temperature (°R)
MW = Molecular weight (lb/lbmol)
g_c = 32.174 lbm·ft/(lbf·s²)
The factor of 144 converts ft² to in² so the result is in psia². Solve for P₂ given P₁, or iterate if both are unknown.
Choked Flow Limit:
Maximum velocity = sonic velocity at throat
V_max = √(k g_c R T / MW)
For ideal gas, k = Cp/Cv ≈ 1.3 for natural gas
If calculated velocity exceeds sonic velocity, flow is choked.
Pressure drop is limited by choked flow condition.
Example: Header Pressure Drop Calculation
Given:
Header: 8" Sch 40 (ID = 7.981 in = 0.665 ft)
Flow rate: 50,000 lb/hr = 13.89 lb/s natural gas
Gas properties: MW = 19, T = 100°F = 560°R, μ = 0.011 cP = 7.4×10⁻⁶ lb/ft·s
Header pressure: P₁ = 100 psia (medium-pressure PSV header)
Layout: 200 ft straight pipe + 4 elbows (90° LR) + 1 tee (branch)
Step 1: Calculate gas density
Z = 0.98
ρ = P MW / (Z R T) = 100 × 19 / (0.98 × 10.73 × 560) = 0.323 lb/ft³
Step 2: Calculate velocity
A = π × 0.665² / 4 = 0.347 ft²
V = W / (ρ A) = 13.89 / (0.323 × 0.347) = 124 ft/s
Check Mach number:
a = √(k g_c R T / MW) = √(1.3 × 32.2 × 1545 × 560 / 19) = 1381 ft/s
Ma = V / a = 124 / 1381 = 0.09 (subsonic, incompressible approximation valid)
Step 3: Calculate friction factor
Re = ρ V D / μ = 0.323 × 124 × 0.665 / (7.4×10⁻⁶) = 3.6×10⁶
ε/D = 0.00015 / 0.665 = 0.00023
f = 0.25 / [log₁₀(0.00023/3.7 + 5.74/(3.6×10⁶)^0.9)]² = 0.014
Step 4: Calculate total resistance
L_e = 4 × 16D + 1 × 60D = 124D = 124 × 0.665 = 82.5 ft
L_total = 200 + 82.5 = 282.5 ft
Step 5: Calculate pressure drop (isothermal)
G = W / A = 13.89 / 0.347 = 40.0 lb/ft²·s
P₁² - P₂² = (f L/D) × G² × Z × R × T / (MW × g_c × 144)
= (0.014 × 282.5/0.665) × (1600 × 0.98 × 10.73 × 560) / (19 × 32.2 × 144)
= 5.95 × 9,422,000 / 88,100
= 636 psia²
P₂² = 10,000 - 636 = 9,364
P₂ = 96.8 psia
ΔP = 100 - 96.8 = 3.2 psi (3.2% of inlet pressure)
This is acceptable for most applications (< 10% backpressure).
Design Guidelines for Low Pressure Drop
- Limit velocity: Keep Ma < 0.5 (typically V < 0.5 × sonic velocity) to minimize pressure drop and noise
- Minimize fittings: Use long-radius elbows, avoid globe valves, minimize tees on branch flow
- Avoid flow restrictions: No orifices, strainers, or small-bore piping in relief header
- Size conservatively: Add 10-20% margin to calculated header diameter for future tie-ins
- Slope for drainage: 1/8 to 1/4 in/ft slope toward low point drain to remove condensate
4. Backpressure Limits & PSV Types
Backpressure in the discharge piping affects PSV capacity and operational stability. Different PSV types tolerate different backpressure levels.
[IMAGE 2: PSV Types Cross-Section Comparison]
Side-by-side cross-sectional diagrams of conventional, balanced bellows, and pilot-operated PSVs showing internal components and backpressure effects.
Types of Backpressure
Superimposed Backpressure:
Pressure in discharge header when PSV is closed (static condition)
Caused by: Other PSVs discharging, header elevation, flare system pressure
Built-up Backpressure:
Additional pressure rise when this PSV opens and discharges
Caused by: Friction and momentum change in discharge piping
Total Backpressure:
P_back,total = P_superimposed + P_built-up
PSV capacity must be corrected for total backpressure.
PSV Type Selection Based on Backpressure
| PSV Type | Allowable Built-Up Backpressure | Applications | Cost |
|---|---|---|---|
| Conventional (spring-loaded) | ≤ 10% of set pressure (constant or variable) | Atmospheric discharge, low-pressure headers (< 15 psig) | Lowest cost |
| Balanced bellows | ≤ 30% of set pressure (variable) or ≤ 50% (constant) | Moderate-pressure headers, most common for gas plants | 15-25% higher than conventional |
| Pilot-operated | Up to 50% of set pressure (variable) or 80% (constant) | High backpressure applications, tight shutoff required | 40-60% higher than conventional |
| Rupture disk | Up to 90% of burst pressure (no spring to overcome) | High backpressure, corrosive service, one-time use | Low device cost, high replacement cost |
Capacity Correction for Backpressure
API 520 Backpressure Correction Factor (K_b):
For conventional PSVs:
K_b = 1.0 if P_back ≤ atmospheric (14.7 psia)
PSV must vent to atmosphere if P_back > 10% of P_set
For balanced bellows PSVs:
K_b = 1.0 - (P_back / P_set) / F_b
Where F_b is a vendor-specific factor (typically 2.0 to 3.3)
Example:
Set pressure: P_set = 100 psig = 114.7 psia
Backpressure: P_back = 35 psia (30.5% of set pressure)
Vendor factor: F_b = 3.0
K_b = 1.0 - (35 / 114.7) / 3.0 = 1.0 - 0.102 = 0.898
Effective capacity = Nameplate capacity × K_b
If nameplate W = 10,000 lb/hr, effective W = 10,000 × 0.898 = 8,980 lb/hr
Must verify: Required relief rate ≤ 8,980 lb/hr
If required rate is 9,500 lb/hr → PSV is undersized, use larger orifice or reduce backpressure
Superimposed Backpressure Sources
- Other PSVs discharging: Calculate pressure drop from other relief sources to this PSV's connection point
- Header static pressure: If header vents to flare tip elevated 100 ft, static pressure ≈ 4-5 psi (0.5 psi per 10 ft elevation for gas)
- Flare system pressure drop: Knockout drum, liquid seal, molecular seal, or flare tip restriction
- Blowdown/depressuring flow: If depressuring valves discharge to same header, add that flow to backpressure calculation
Backpressure calculation sequence: (1) Define relief scenario (which PSVs discharge simultaneously). (2) Calculate flow rate and pressure drop from each source to confluence points. (3) Sum flows in header and calculate cumulative pressure drop to flare. (4) Work backward to calculate backpressure at each PSV. (5) Verify backpressure < allowable limit for PSV type. (6) If exceeded, increase header size or change PSV type.
5. Multiple Relief Scenarios
Relief headers must accommodate all credible combinations of simultaneous PSV discharges. Proper scenario analysis ensures adequate capacity for worst-case conditions.
[IMAGE 4: Header Segment Flow Analysis]
Plan view schematic showing header segments with cumulative flow rates, branch connections from PSVs, and backpressure calculation points.
Relief Scenario Matrix
Develop a matrix of credible scenarios and calculate header loading for each:
| Scenario | PSVs Discharging | Total Flow (lb/hr) | Governing Header Section |
|---|---|---|---|
| Case 1: PSV-101 only | PSV-101 (vessel V-101 fire) | 50,000 | Branch A to main header |
| Case 2: PSV-201 only | PSV-201 (compressor high discharge) | 35,000 | Branch B to main header |
| Case 3: Pool fire (south area) | PSV-101, PSV-102, PSV-103 | 120,000 | Main header (sections A+B+C) |
| Case 4: Cooling water failure | PSV-201, PSV-202 (both compressors) | 70,000 | HP header to LP header |
| Case 5: Blowdown + relief | PSV-301 + depressuring valve XV-301 | 80,000 | Section to flare knockout drum |
Header Segment Analysis
Divide header into segments and track cumulative flow through each segment:
Segmented Pressure Drop Calculation:
For header with multiple branch connections:
Segment 1: PSV-A connection to PSV-B connection
Flow = W_A
ΔP₁ = f(W_A, D₁, L₁)
Segment 2: PSV-B connection to PSV-C connection
Flow = W_A + W_B
ΔP₂ = f(W_A + W_B, D₂, L₂)
Segment 3: PSV-C connection to flare
Flow = W_A + W_B + W_C
ΔP₃ = f(W_A + W_B + W_C, D₃, L₃)
Total pressure drop:
ΔP_total = ΔP₁ + ΔP₂ + ΔP₃
Backpressure at PSV-A:
P_back,A = P_flare + ΔP₁ + ΔP₂ + ΔP₃
Backpressure at PSV-B:
P_back,B = P_flare + ΔP₂ + ΔP₃
Backpressure at PSV-C:
P_back,C = P_flare + ΔP₃
Check each PSV for allowable backpressure limit.
Header Sizing Strategy
- Identify scenarios: List all credible single and multiple PSV discharge cases
- Calculate relief rates: For each scenario, determine mass flow rate from each PSV (API 520 sizing equations)
- Preliminary header sizing: Size each segment for maximum flow using velocity limit (e.g., Ma < 0.5 or V < 200 ft/s)
- Calculate pressure drop: For each scenario, calculate backpressure at each PSV using segmented analysis
- Check capacity: Verify PSV capacity (corrected for backpressure) exceeds required relief rate
- Iterate if needed: If backpressure exceeds limit, increase header diameter in critical segments
- Add margin: Upsize header by 10-20% or one pipe schedule for future tie-ins
Example: Gas Plant Flare Header
System:
- 3 process vessels with PSVs (set pressures 150, 200, 250 psig)
- LP flare header (design pressure 50 psig)
- Flare knockout drum at 15 psig
Fire Scenario (governing case):
PSV-101: 80,000 lb/hr at 150 psig set
PSV-102: 60,000 lb/hr at 200 psig set
PSV-103: 40,000 lb/hr at 250 psig set
Header Layout:
Segment A: PSV-101 to confluence (12" header, 150 ft)
Segment B: PSV-102 to confluence (10" header, 100 ft)
Segment C: PSV-103 to confluence (8" header, 80 ft)
Segment D: Confluence to flare KO drum (16" header, 300 ft)
Pressure Drop Calculations:
Segment A: W = 80,000 lb/hr, D = 12", L = 150 ft
→ ΔP_A = 0.8 psi
Segment B: W = 60,000 lb/hr, D = 10", L = 100 ft
→ ΔP_B = 0.9 psi
Segment C: W = 40,000 lb/hr, D = 8", L = 80 ft
→ ΔP_C = 0.7 psi
Segment D: W = 180,000 lb/hr, D = 16", L = 300 ft
→ ΔP_D = 1.5 psi
Flare KO drum pressure: 15 psig
Backpressure at Each PSV:
PSV-101: P_back = 15 + 0.8 + 1.5 = 17.3 psig (10.3% of 150+14.7 = 165 psia) → OK for balanced bellows
PSV-102: P_back = 15 + 0.9 + 1.5 = 17.4 psig (8.1% of 214.7 psia) → OK
PSV-103: P_back = 15 + 0.7 + 1.5 = 17.2 psig (6.5% of 264.7 psia) → OK
All PSVs have < 30% backpressure → Acceptable for balanced bellows valves
Common Design Mistakes
- Ignoring superimposed backpressure: Must include flare system pressure, not just header friction drop
- Using nameplate capacity without backpressure correction: PSV capacity decreases with backpressure (K_b factor)
- Undersizing branch connections: Branch piping from PSV to header can have higher velocity than main header
- Not accounting for future expansion: Adding PSVs later requires re-analysis of all scenarios
- Mixing incompatible fluids: Don't combine acid gas with sweet gas, or oxygen-rich with flammable streams
- Inadequate drainage: Liquid slugs in vapor header cause water hammer and backpressure spikes
Design for flexibility: Size header 10-20% larger than calculated minimum to accommodate future debottlenecks, process changes, or additional PSV tie-ins. This margin is cheaper to install during initial construction than to replace piping later. Document assumptions and limitations in design basis for future reference.
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