1. Overview & Requirements
Blowdown (depressurization) systems rapidly reduce pressure in vessels and pipelines during emergencies such as fire, overpressure, or equipment failure. Accurate blowdown time calculations are critical for safety system design and regulatory compliance.
Fire case
15-minute target
Depressurize before fire weakens vessel, typically to 50% MAWP or 600 psig.
Emergency shutdown
Controlled depressure
Orderly reduction to safe pressure for maintenance or repair.
Runaway reaction
Process safety
Rapid venting to prevent overpressure from exothermic reactions.
Pipeline isolation
Block valve closure
Blowdown isolated sections for safe entry and repair work.
Design Objectives and Criteria
- API 521 fire case: Depressurize to 50% of design pressure or 690 kPa gauge (100 psig), whichever is lower, within 15 minutes
- Alternative criteria: Depressurize to pressure where vessel can withstand fire exposure without rupture
- Personnel safety: Minimize exposure time to hazardous pressure and temperature conditions
- Environmental protection: Controlled venting through flare or scrubber system
- Equipment protection: Avoid excessive cooling that causes brittle fracture (minimum design metal temperature)
Key Variables Affecting Blowdown Time
| Parameter | Effect on Blowdown Time | Design Consideration |
|---|---|---|
| Vessel volume | Larger volume longer time | Include piping, connected equipment |
| Initial pressure | Higher P longer time | Use maximum operating pressure |
| Valve size | Larger valve shorter time | Balance cost vs. depressure rate |
| Gas composition | Molecular weight affects flow | Use actual gas properties |
| Heat input (fire) | Heat slows depressurization | API 521 provides heat input rates |
| Two-phase flow | Liquid reduces vent rate | Use two-phase flow correlations |
Safety critical: Blowdown systems are safety-critical. Undersizing the blowdown valve can result in vessel rupture during fire exposure. Always include conservative margins and verify with rigorous simulation for large vessels or complex systems.
2. Thermodynamic Theory
Blowdown is a transient process involving changing pressure, temperature, and density. Understanding the thermodynamics is essential for accurate time predictions.
Adiabatic Expansion
Ideal Gas Adiabatic Expansion:
P × V^³ = constant
T / T = (P / P)^((³-1)/³)
Where:
³ = Specific heat ratio (Cp/Cv) H 1.3 for natural gas
P = Absolute pressure
T = Absolute temperature
V = Volume
Temperature drop during blowdown:
T = T × [1 - (P/P)^((³-1)/³)]
Example:
T = 520°R (60°F), P = 1000 psia, P = 100 psia, ³ = 1.3
T = 520 × (100/1000)^(0.3/1.3) = 520 × 0.736 = 383°R (-77°F)
Temperature drops 137°F during depressurization!
Mass Balance and Flow Rate
Conservation of Mass:
dm/dt = -W
Where:
m = Mass in vessel (lb)
t = Time (s)
W = Mass flow rate out (lb/s)
For ideal gas:
m = (P × V) / (Z × R × T)
Therefore:
d/dt [(P × V) / (Z × R × T)] = -W
If V, Z, R are constant and assuming adiabatic (T varies with P):
dP/dt = -(W × Z × R × T) / V
Choked Flow Through Orifice
When pressure ratio P/P exceeds critical value, flow becomes choked (sonic velocity at orifice):
Critical Pressure Ratio:
(P/P)_critical = [2/(³+1)]^(³/(³-1))
For ³ = 1.3 (natural gas): (P/P)_crit = 0.546
For ³ = 1.4 (air): (P/P)_crit = 0.528
If P/P < critical ratio, flow is choked.
Choked Mass Flow Rate:
W = C × A × P × (³ / (Z × R × T)) × [2/(³+1)]^((³+1)/(2(³-1)))
Where:
W = Mass flow rate (lb/s)
C = Discharge coefficient (typically 0.6-0.85)
A = Orifice area (in²)
P = Upstream pressure (psia)
Z = Compressibility factor
R = Gas constant (10.73 psia·ft³/(lbmol·°R))
T = Upstream temperature (°R)
³ = Specific heat ratio
Simplified for choked flow:
W = 0.525 × C × A × P / (Z × T × MW)
Where MW = molecular weight (lb/lbmol)
Non-Choked (Subcritical) Flow
Subcritical Flow (P/P > 0.546):
W = C × Y × A × (2 × Á × P)
Where:
Y = Expansion factor (function of P/P and ³)
Á = Gas density at inlet (lb/ft³)
P = P - P (psi)
Expansion factor:
Y = [(³/(³-1)) × (P/P)^(2/³) × (1 - (P/P)^((³-1)/³)) / (1 - P/P)]
As vessel depressurizes, flow transitions from choked to non-choked when
P_vessel/P_atmospheric falls below critical ratio.
Important transition: Blowdown typically starts in choked flow (high pressure ratio) and transitions to non-choked flow as vessel pressure decreases. The flow rate drops significantly after transition, so most of the depressurization time occurs in the non-choked regime.
3. API 521 Methods
API Standard 521 "Pressure-Relieving and Depressuring Systems" provides methods for calculating blowdown time and sizing depressuring systems for fire cases.
API 521 Fire Case Blowdown
Fire Heat Input (API 521 Section 4.4.8):
Q = 21,000 × F × A^0.82
Where:
Q = Heat absorbed (Btu/hr)
F = Environment factor
= 1.0 for vessels with insulation or buried
= 1.0 for bare steel with water spray/deluge
= 1.0 for vessels > 25 ft above grade
A = Wetted surface area exposed to fire (ft²)
Wetted area (vertical vessel):
A = À × D × L_w
Where:
D = Vessel diameter (ft)
L_w = Wetted height (liquid level, ft)
For horizontal vessel:
A = (complex geometry; use actual wetted area)
Simplified Blowdown Time Estimate
Isothermal Blowdown (Conservative Estimate):
t = (V / (C × A)) × (MW / (Z × R × T)) × ln(P/P)
Where:
t = Time (seconds)
V = Vessel volume (ft³)
C = Discharge coefficient (0.6-0.8)
A = Valve orifice area (in²)
MW = Molecular weight
Z = Compressibility factor (average)
R = 10.73 psia·ft³/(lbmol·°R)
T = Temperature (°R, assume constant)
P = Initial pressure (psia)
P = Final pressure (psia)
Example:
V = 1000 ft³
C = 0.7
A = 3 in² (2" valve)
MW = 19 (natural gas)
Z = 0.9
T = 540°R (80°F)
P = 1000 psia
P = 100 psia
t = (1000 / (0.7 × 3)) × (19 / (0.9 × 10.73 × 540)) × ln(1000/100)
t = 476 × (19 / 5213) × 2.303
t = 476 × 0.0603 × 2.303
t = 661 seconds = 11 minutes
This is conservative; actual time slightly longer due to adiabatic cooling.
Rigorous Adiabatic Blowdown
For more accurate results, integrate the differential equations numerically:
Step-by-Step Integration Method:
1. Initialize: Set t = 0, P = P, T = T
2. At each time step t:
a) Calculate mass flow rate W from current P and T
b) Calculate mass discharged: m = W × t
c) Update vessel mass: m_new = m_old - m
d) Calculate new pressure from ideal gas law:
P_new = m_new × Z × R × T / V
e) Calculate new temperature from adiabatic relation:
T_new = T_old × (P_new / P_old)^((³-1)/³)
f) Add heat input if fire case: Q × t
g) Increment time: t = t + t
3. Repeat until P d P (target pressure)
This method accounts for:
- Adiabatic cooling (temperature drop)
- Choked to non-choked flow transition
- Fire heat input (if applicable)
- Real gas effects (Z-factor variation)
API 521 Fire Case Criteria
| Vessel Type | Target Pressure | Target Time | Notes |
|---|---|---|---|
| Gas storage vessels | 50% of MAWP or 690 kPa (100 psig) | 15 minutes | Whichever is lower |
| Liquid-filled vessels | Pressure at which liquid vaporization stops | Variable | Depends on heat input rate |
| Two-phase vessels | Pressure where liquid can be drained | 15 minutes typical | Consider liquid inventory |
| Pipeline sections | Near atmospheric | Varies by length | Coordinate with isolation valves |
Fire exposure time: API 521's 15-minute criterion is based on the time it takes for a steel vessel to heat up and lose strength under fire conditions. This assumes fire fighting efforts begin promptly. For remote locations or where fire response is delayed, consider more conservative design (e.g., 10 minutes or faster depressurization).
4. Two-Phase Blowdown
When liquid is present during depressurization, two-phase flow significantly affects vent rate and blowdown time. Two-phase flow is more complex than single-phase gas flow and requires specialized correlations.
Two-Phase Flow Regimes
Homogeneous Equilibrium Model (HEM):
Assumes vapor and liquid are in thermal and mechanical equilibrium (same velocity).
W_two-phase = A × G
Where:
G = Mass flux (lb/s·ft²)
For critical (choked) two-phase flow:
G_critical = [(2 × Á_mixture × (h - h_throat))]
Where:
Á_mixture = Combined density of vapor + liquid
h = Inlet enthalpy (Btu/lb)
h_throat = Enthalpy at throat (Btu/lb)
Requires iterative solution or steam tables for properties.
Omega Method (API 521)
API 521 Omega Method for Two-Phase Relief:
W = C × A × (Á_inlet × P_critical) × É
Where:
É = Two-phase multiplier (function of liquid fraction and properties)
É = [1 + x × (v_g/v_f - 1)]
Where:
x = Quality (vapor mass fraction)
v_g = Specific volume of vapor (ft³/lb)
v_f = Specific volume of liquid (ft³/lb)
For all-liquid (x = 0): É = 1
For all-vapor (x = 1): É = (v_g/v_f) >> 1
Two-phase flow rate is between liquid and vapor rates.
Depressurization with Liquid Carryover
Vessels containing liquid undergo complex behavior during blowdown:
- Flash vaporization: As pressure drops, liquid flashes to vapor, absorbing latent heat and cooling remaining liquid
- Liquid swell: Vapor formation increases liquid level, potentially reaching vessel outlet
- Entrainment: High vapor velocity entrains liquid droplets, creating two-phase flow
- Vessel emptying: Eventually liquid drains out, and system transitions to single-phase vapor blowdown
Flashing Liquid Calculation
Flash Vaporization During Depressurization:
Energy balance:
m_total × h_initial = m_vapor × h_vapor + m_liquid × h_liquid
Mass balance:
m_total = m_vapor + m_liquid
Quality (vapor fraction):
x = m_vapor / m_total
For isenthalpic flash (h_initial = h_final):
x = (h_initial - h_f) / (h_fg)
Where:
h_f = Saturated liquid enthalpy at final pressure (Btu/lb)
h_fg = Latent heat of vaporization (Btu/lb)
Example:
Liquid propane at 100°F (h = 134 Btu/lb)
Flashes to 14.7 psia (60°F):
h_f = 103 Btu/lb, h_fg = 162 Btu/lb
x = (134 - 103) / 162 = 0.19 (19% vapor by mass)
Volume of vapor >> volume of liquid due to density difference!
Consequences of Two-Phase Flow
| Effect | Impact | Mitigation |
|---|---|---|
| Reduced flow rate | Longer blowdown time | Size valve for two-phase flow |
| Liquid slugging | Piping vibration, water hammer | Use slug catchers, properly support piping |
| Flare system liquid | Liquid carryover to flare | Install knockout drum upstream of flare |
| Hydrate formation | Blockage from cooling + water vapor | Insulate piping, inject methanol/glycol |
| Low temperature | Brittle fracture risk | Use low-temp materials, limit depressure rate |
Design practice: For vessels that may contain significant liquid during blowdown, use specialized software (Aspen HYSYS Dynamic, ProMax, etc.) to rigorously simulate the transient two-phase behavior. Simple hand calculations are inadequate for two-phase blowdown design.
5. Design Applications
Blowdown Valve Sizing Procedure
Step-by-Step Sizing Procedure:
1. Define scenario:
- Fire case or emergency shutdown?
- Vessel volume and geometry
- Initial pressure and temperature
- Target final pressure
- Target depressurization time
2. Calculate heat input (if fire case):
- Use API 521 fire heat input formula
- Determine wetted surface area
3. Estimate required orifice area:
- Use isothermal equation for initial guess
- A_guess = (V / (C × t)) × (MW / (Z × R × T)) × ln(P/P)
4. Perform rigorous simulation:
- Time-step integration of adiabatic blowdown
- Include fire heat input
- Account for choked/non-choked transition
- Calculate final time
5. Iterate valve size:
- If t_calculated > t_target, increase valve size
- If t_calculated << t_target, consider smaller valve (cost)
6. Select standard valve size:
- Round up to next standard orifice size
- Verify with final calculation
7. Check minimum metal temperature:
- Calculate lowest temperature during blowdown
- Verify materials suitable for minimum temperature
Pipeline Blowdown
Depressurizing pipeline sections requires special considerations:
Pipeline Blowdown Time:
For long pipelines, cannot assume uniform pressure. Use wave equation or:
Simplified for short sections (L < 1 mile):
t = (V_pipeline / (C × A_valve)) × (MW / (Z × R × T)) × ln(P/P)
Where:
V_pipeline = À/4 × D² × L (volume of pipeline section)
For long pipelines (L > 1 mile):
- Pressure wave travels at speed of sound
- Use computational fluid dynamics (CFD) or pipeline simulation software
- Consider multiple blowdown points to reduce time
Typical blowdown rates:
- Small lines (< 6"): 5-10 minutes to near atmospheric
- Medium lines (12-24"): 15-30 minutes
- Large trunk lines (> 30"): May take hours without multiple vent points
Flare System Integration
Blowdown systems typically discharge to a flare system for safe combustion:
- Knockout drum sizing: Must handle liquid carryover and condensation from cooling gas
- Flare tip capacity: Verify flare can handle peak blowdown flow rate and heat release
- Radiation limits: Check thermal radiation to personnel and equipment during large blowdowns
- Backpressure: Flare header backpressure affects blowdown rate; include in calculations
- Noise: High-velocity gas creates noise; may require silencers for frequent blowdowns
Temperature During Blowdown
Minimum Temperature Calculation:
For adiabatic blowdown with no heat input:
T_min = T_initial × (P_final / P_initial)^((³-1)/³)
Example:
T_initial = 80°F = 540°R
P_initial = 1200 psia
P_final = 100 psia
³ = 1.3
T_min = 540 × (100/1200)^(0.3/1.3)
T_min = 540 × (0.0833)^0.231
T_min = 540 × 0.520
T_min = 281°R = -179°F
This extreme cooling can cause:
- Brittle fracture if materials not rated for low temp
- Hydrate formation if water vapor present
- Ice formation on external surfaces
Mitigation: Limit depressure rate, use insulation, select low-temp materials
Common Mistakes and Design Pitfalls
- Ignoring fire heat input: Fire significantly extends blowdown time; must include per API 521
- Undersizing for two-phase: Liquid carryover reduces vent rate; use two-phase correlations
- Not accounting for piping volume: Include volume of connected piping to vessel in total volume
- Using gauge pressure: All calculations require absolute pressure (psia, not psig)
- Assuming isothermal: Adiabatic cooling reduces temperature and density, affecting flow rate
- Neglecting backpressure: Flare system backpressure reduces blowdown rate
- Inadequate low-temp design: Specify materials and components suitable for minimum temperature
- Single vent point on long pipeline: Use multiple vent points to meet time requirements
Software Tools for Blowdown Analysis
- Aspen HYSYS Dynamic: Rigorous dynamic simulation of blowdown, including two-phase and fire heat input
- ProMax: Process simulation with transient blowdown module
- PIPESYS (Engineered Software): Pipeline transient hydraulics for blowdown analysis
- Excel/VBA: Time-stepping integration for simple single-phase gas blowdown
- Mathcad/MATLAB: Custom integration of differential equations for specific cases
Regulatory note: Many jurisdictions require emergency depressurization systems for vessels exposed to fire risk. Verify local codes and company standards for specific requirements. API 521 is widely adopted but not a legal codecheck applicable regulations (ASME, OSHA PSM, etc.).
Ready to use the calculator?
→ Launch Calculator