What is runaway reaction relief?

Runaway reaction relief is the emergency venting of a reactor when an exothermic reaction becomes uncontrolled, requiring properly sized relief devices to prevent vessel rupture.

What is the DIERS methodology?

DIERS (Design Institute for Emergency Relief Systems) provides methods for sizing emergency relief systems that account for two-phase vapor-liquid flow during runaway reactions.

What standard covers reaction relief vent sizing?

API 520 Part II provides guidance on emergency relief system design for reactors, including two-phase venting calculations.

Runaway Reaction Relief Fundamentals

1. Overview & Runaway Scenarios

Runaway reactions occur when exothermic reactions lose temperature control, causing self-accelerating temperature rise that can lead to overpressure, vessel rupture, and catastrophic release. Emergency relief systems provide the final layer of protection.

Figure 1: Adiabatic runaway reaction temperature and pressure profile showing onset, TMRad, and maximum rate.

Batch reactors

Polymerization, nitration

Exothermic batch processes in pharmaceutical and specialty chemical production.

Semi-batch reactors

Slow addition reactions

Reagent accumulation leads to runaway if cooling fails during addition.

Continuous reactors

CSTR, tubular

Cooling loss or flow upsets cause temperature excursions.

Decomposition

Peroxides, nitro compounds

Thermally unstable materials decompose above critical temperature.

Common Runaway Scenarios

Scenario	Initiating Event	Consequence	Protection
Cooling failure	Loss of cooling water, jacket failure, agitator failure	Temperature rises, reaction rate increases exponentially	Emergency cooling, quench addition, relief vent
Reagent addition error	Entire charge added at once instead of slow addition	Accumulated reactant releases heat rapidly	Interlock feed rate, relief vent
Contamination	Wrong material charged, catalyst overdose	Unexpected reaction or accelerated kinetics	QC procedures, relief vent
Thermal decomposition	Storage temperature exceeds stability limit	Self-heating runaway (organic peroxides, azo compounds)	Temperature monitoring, refrigeration, relief vent
Pressure buildup	Blocked vent, vapor-liquid equilibrium shift	Elevated pressure increases boiling point, suppresses boiling cooling	Pressure relief, rupture disk + vent

Layers of Protection (LOPA)

Emergency relief is the last layer of protection after process controls fail:

Process design: Minimize inventory of hazardous materials, use inherently safer chemistry
Basic process control: Temperature control loop, jacket cooling, reflux condenser
Alarm and operator response: High-temperature alarm, manual intervention (increase cooling, stop feed)
Safety instrumented system (SIS): High-high temperature trip to close feed, open emergency cooling, dump to catch tank
Emergency relief (PSV or rupture disk): Vent excess vapor/liquid to containment system when pressure exceeds set point

Why runaway relief is challenging: Unlike simple overpressure (blocked outlet, external fire), runaway reactions involve coupled thermal-hydraulic phenomena: heat generation increases with temperature (Arrhenius kinetics), vapor generation can be tempered (vapor-only) or gassy (two-phase), and relief changes system pressure affecting boiling point. DIERS (Design Institute for Emergency Relief Systems) developed systematic methodology to address these complexities.

2. Adiabatic Calorimetry Testing

Adiabatic calorimetry measures heat release rate (dT/dt) and pressure rise rate (dP/dt) during runaway reactions under near-adiabatic conditions. This data is essential for DIERS vent sizing.

Cross-section schematic of VSP2 adiabatic calorimeter showing 3000 psi rated containment vessel 12 inches diameter by 18 inches tall, thin-wall spherical test cell with phi factor 1.05-1.08 containing 100-120 mL sample, band heaters on vessel wall, guard heaters above and below test cell for adiabatic control, sample thermocouple, pressure transducer, pressure equalization port, magnetic stirrer with external drive, fill/vent lines with safety rupture disk, operating range 25-400°C and 0-3000 psi — Figure 2: VSP2 adiabatic calorimeter cross-section showing test cell, containment vessel, and instrumentation.

Calorimetry Instruments

Instrument	Sample	φ-Factor	Primary Use
ARC	5-10 mL	1.05-1.20	Screening, TMRad determination
VSP2	100-130 mL	1.04-1.08	DIERS vent sizing, system classification
RSST	10 mL	~1.2	Quick screening, gas generation rate
Phi-TEC II	50-100 mL	1.02-1.05	Low φ tests, accurate T-P data

Phi-Factor (φ) Correction

Thermal Inertia Correction: φ = (m_sample × Cp_sample + m_bomb × Cp_bomb) / (m_sample × Cp_sample) Where: φ = Phi-factor (dimensionless, φ ≥ 1.0) m_sample = Mass of reactant sample Cp_sample = Heat capacity of sample m_bomb = Mass of test cell (stainless steel) Cp_bomb = Heat capacity of test cell For adiabatic conditions, φ = 1.0 (no thermal inertia). For VSP2 with 130 mL cell, typical φ = 1.05-1.08. Temperature Correction: dT/dt (φ=1) = φ × dT/dt (measured) T_final (φ=1) = T_initial + φ × (T_final,measured - T_initial) Higher φ means measured temperature rise is lower than true adiabatic case. Corrected data represents full-scale reactor behavior.

Key Parameters from Calorimetry

1. Self-Heat Rate (dT/dt)

dT/dt = Heat generation rate / (m × Cp) (°C/min or K/min) Arrhenius behavior: dT/dt = A × exp(-E/RT) Where: A = Pre-exponential factor E = Activation energy (J/mol) R = Gas constant (8.314 J/mol·K) T = Absolute temperature (K) Typical criteria: dT/dt < 0.1 K/min → Reaction under control dT/dt > 1 K/min → Potential runaway dT/dt > 10 K/min → Severe runaway, rapid pressure rise

2. Time to Maximum Rate (TMRad)

TMRad (Time to Maximum Rate under adiabatic conditions): TMRad = (T_final - T_initial) / (dT/dt)_max At temperature T, time to reach maximum rate: TMRad(T) ≈ integral from T to T_max of dT/(dT/dt) Safety criterion: TMRad > 24 hours at maximum storage/process temperature → Acceptable TMRad < 8 hours → Requires risk mitigation (lower temp, smaller batches, cooling) Example: T_process = 80°C, TMRad(80°C) = 12 hours If cooling fails, 12 hours available before runaway reaches maximum rate. Sufficient time for operator intervention or SIS to trip process.

3. Pressure Rise Rate (dP/dt)

Pressure Generation Rate: dP/dt = (dT/dt) × (∂P/∂T)_V + (dn_gas/dt) × (RT/V) Where: (∂P/∂T)_V = Vapor pressure slope (from Antoine equation) dn_gas/dt = Molar gas generation rate (for gas-producing reactions) V = Vapor space volume Typical values: Tempered system: dP/dt < 10 psi/min (vapor pressure rise only) Gassy system: dP/dt = 50-500 psi/min (rapid gas evolution) High dP/dt requires two-phase relief → larger vent area.

Vapor-Liquid Equilibrium During Relief

As relief vent opens and pressure decreases, boiling point drops. Heat release vaporizes liquid:

Tempered (all-vapor): Vapor generation rate low, liquid remains subcooled, vapor flashes to vent
Hybrid: Moderate vapor rate, liquid surface boils, vapor disengages and vents (possible two-phase)
Gassy (two-phase): High vapor rate, bulk boiling throughout liquid, two-phase foam/churn vents

Calorimetry best practices: Test at actual process composition and concentration. Use heat-wait-search mode to detect low-temperature onset. Run multiple tests at different fill levels (50%, 70%, 90%) to characterize vapor disengagement. Report φ-corrected data for DIERS calculations.

3. DIERS Methodology

DIERS (Design Institute for Emergency Relief Systems) developed a rigorous methodology for sizing relief vents for runaway reactions, published in AIChE DIERS Project Manual (1992).

System Classification

Systems are classified based on vapor-liquid behavior during relief:

Type	Behavior	Ψ	Sizing Method
Tempered	Vapor-only venting, liquid subcooled	→ 0	API 520 vapor (smallest vent)
Hybrid	Vapor disengages from boiling liquid	0.1-0.9	DIERS hybrid model
Gassy	Bulk two-phase flow, churn-turbulent	→ 1	HEM (largest vent)

Two-Phase Parameter (Ψ)

Dimensionless Vapor Generation Parameter: Ψ = (V_vapor / V_total) / (Q_gen / Q_removal) Where: V_vapor = Vapor space volume V_total = Total vessel volume Q_gen = Vapor generation rate from reaction heat Q_removal = Vapor removal rate through vent Simplified form: Ψ = (ρ_L / ρ_V) × (u_slip / u_mix) Where: u_slip = Vapor-liquid slip velocity (ft/s) u_mix = Two-phase mixture velocity (ft/s) Interpretation: Ψ = 0 → Vapor disengages instantly, vapor-only relief (tempered) Ψ = 1 → No slip, homogeneous two-phase flow (gassy) 0 < Ψ < 1 → Partial disengagement (hybrid) In practice: Low-viscosity solvents (water, methanol): Ψ = 0.1-0.5 (hybrid) High-viscosity liquids (polymers, heavy oils): Ψ = 0.8-1.0 (gassy) Foaming systems: Ψ → 1.0 (gassy, conservative)

DIERS Vent Sizing Equation

Required Vent Area (DIERS): A = (m_0 / G) × √(Cp × dT/dt × φ / ΔH_v) Where: A = Vent area (in²) m_0 = Initial liquid mass in reactor (lb) G = Two-phase mass flux (lb/s·in²) Cp = Liquid heat capacity (Btu/lb·°F) dT/dt = Self-heat rate at relief pressure (°F/s) φ = Phi-factor from calorimetry ΔH_v = Effective latent heat (Btu/lb) Two-Phase Mass Flux (G): For tempered system (Ψ → 0): G = √(2 g_c ρ_V ΔP) (vapor flow) For gassy system (Ψ = 1): G = √(2 g_c ρ_L ΔP / (1 + L)) (HEM) Where: L = v_fg / v_f × (Cp ΔT_sub / ΔH_v) (quality parameter) v_fg = Specific volume change on vaporization v_f = Liquid specific volume ΔT_sub = Subcooling For hybrid system: Interpolate between tempered and gassy using Ψ.

Leung Omega Method (Simplified DIERS)

Leung developed a simplified correlation for DIERS vent sizing:

Leung Omega Method: A = (Q_s / C) × √(ω / P_s) Where: Q_s = Volumetric flow rate at relief (ft³/s) C = Discharge coefficient (0.6-0.7 for rupture disk, 0.3-0.5 for PSV) ω = Homogeneous two-phase flow parameter P_s = Relief set pressure (psia) ω = f(reduced pressure P_r, quality χ) For low-quality two-phase flow (χ < 0.1): ω ≈ 1 + χ × (ρ_L/ρ_V - 1) This method is widely used in commercial software (SuperChems, RELIEF).

DIERS key insight: Two-phase venting is governed by liquid density, not vapor density. Even though vapor is flowing, the high liquid content in churn-turbulent flow means the effective density is close to liquid density → much lower velocity through vent → larger vent area required (often 5-10× larger than vapor-only case).

4. Two-Phase Flow Venting

Two-phase venting occurs when vapor generation rate is so high that liquid and vapor discharge together through the relief vent. Proper characterization and sizing prevents vessel overpressure.

Four-panel diagram showing two-phase flow regimes in vertical relief vent pipes: Bubbly flow (α<0.3) with discrete bubbles and low vapor velocity using HEM sizing; Churn-turbulent (0.3<α<0.7) with chaotic mixing and unstable slugs using HEM conservative sizing; Annular (0.7<α<0.95) with liquid film on wall and vapor core using separated flow model; Mist flow (α>0.95) with vapor continuous and droplet entrainment using API 520 vapor sizing; void fraction scale from 0 to 1.0 — Figure 4: Two-phase flow regimes in vertical relief piping with void fraction ranges and sizing methods.

Flow Regimes During Venting

Regime	Description	Void Fraction (α)	Vent Sizing
Bubbly flow	Discrete bubbles in continuous liquid	α < 0.3	HEM (homogeneous)
Churn-turbulent flow	Chaotic mixing, large unstable bubbles	0.3 < α < 0.7	HEM (conservative)
Annular flow	Liquid film on walls, vapor core	α > 0.7	Separated flow models
Mist flow	Liquid droplets in vapor	α > 0.95	API 520 vapor with entrainment

Homogeneous Equilibrium Model (HEM)

HEM Assumptions: 1. Vapor and liquid travel at same velocity (no slip) 2. Thermodynamic equilibrium at all points 3. Isentropic expansion through vent Critical Flow (Choked): G_crit = √(ρ_m × (dP/dv)_s) Where: G_crit = Critical mass flux (lb/s·ft²) ρ_m = Mixture density = ρ_L (1-α) + ρ_V α α = Void fraction (vapor volume fraction) (dP/dv)_s = Slope of isentrope on P-v diagram For two-phase mixture: (dP/dv)_s ≈ -P / [(1-χ)v_f + χ v_g] Where χ = vapor mass fraction (quality) Required Vent Area: A = W / (C × G_crit) Where: W = Required mass relief rate (lb/s) C = Discharge coefficient (0.6-0.7 rupture disk, 0.3-0.5 PSV) G_crit = Critical mass flux from above Typical result: Two-phase venting requires 3-10× larger area than vapor-only.

Vapor Disengagement (Hybrid Systems)

In hybrid systems, some vapor separates from liquid and vents as vapor-only flow. Disengagement reduces required vent area compared to fully gassy (HEM) case.

Tall/slender vessels: Vapor disengages more easily → lower Ψ → smaller vent (approach tempered)
Short/squat vessels: Less disengagement height → higher Ψ → larger vent (approach gassy)
Low fill level (< 50%): Large vapor space allows disengagement → lower Ψ
High fill level (> 80%): Small vapor space, foam reaches vent quickly → higher Ψ → larger vent
High viscosity: Slow bubble rise → poor disengagement → Ψ → 1
Antifoam additives: Reduce foam stability, improve disengagement → lower Ψ (verify in testing)

Vent System Components for Two-Phase Relief

1. Rupture Disk vs PSV

Rupture disk: Preferred for two-phase, full-bore opening, no chatter, higher C (0.6-0.7), one-time use
Balanced bellows PSV: Reusable, may chatter in two-phase service, lower C (0.3-0.5), requires larger orifice
Combination: Rupture disk upstream of PSV protects PSV from corrosive/fouling fluids

2. Quench/Catch Tank

Catch Tank Sizing: V_tank = V_reactor × f_discharge + V_freeboard Where: V_reactor = Reactor liquid volume f_discharge = Fraction discharged during relief (0.5-0.9 typical) V_freeboard = Vapor space to prevent tank overfill (20-30% of total volume) Example: 2000-gal reactor, 80% full → 1600 gal liquid Assume 70% discharges during relief → 1120 gal Freeboard 25% → total catch tank volume = 1120 / 0.75 = 1500 gal minimum Catch tank must withstand: - Thermal shock from hot discharge (200-300°F liquid) - Pressure rise from vapor generation (size vent on catch tank) - Corrosive/reactive chemicals (material selection)

3. Scrubber/Separator

If relieving to flare or atmosphere, install knockout drum to separate liquid from vapor:

Gravity separator: Size for Stokes settling velocity (V_term = d_p² × g × Δρ / 18μ)
Cyclone separator: Compact, high efficiency, 5-10 psi pressure drop
Mesh pad demister: Capture fine droplets (> 10 micron), low pressure drop (< 1 psi)

Two-phase venting system design: Use adiabatic calorimetry (VSP2, Phi-TEC) to measure dT/dt and dP/dt during runaway. Classify system as tempered/hybrid/gassy based on Ψ parameter. Size vent using DIERS or Leung omega method for two-phase flow. Install rupture disk (not PSV) for gassy systems. Route to catch tank or separator before flare.

5. Relief Vent Sizing Examples

Emergency relief system P&ID for batch reactor R-101 showing 1000 gal jacketed reactor with agitator, cooling water jacket, TAHH temperature alarm and trip, 6-inch INCONEL rupture disk RD-101 set at 50 psig burst, 8-inch relief header sloping 1/4 inch per foot, V-101 knockout drum 500 gal with mesh pad demister, P-101 liquid collection pump to catch tank or recovery, vapor routing to flare through liquid seal V-103, optional V-102 catch tank with flame arrester, design basis cooling failure plus runaway reaction at 25,000 lb/hr two-phase relief rate — Figure 5: Emergency relief system P&ID showing reactor, rupture disk, knockout drum, and flare routing.

Example 1: Tempered System (Vapor-Only)

Scenario: Batch reactor, exothermic polymerization with reflux condenser Runaway scenario: Loss of cooling water, reflux condenser fails Reactor: 2000 gal (7.57 m³), 70% fill, P_set = 50 psig Calorimetry Data (VSP2): dT/dt (at 50 psig) = 5 K/min = 0.083 K/s φ = 1.06 Cp = 2.5 kJ/kg·K = 0.60 Btu/lb·°F ΔH_vap = 400 kJ/kg = 172 Btu/lb Liquid density ρ_L = 900 kg/m³ = 56.2 lb/ft³ Vapor density ρ_V (at 50 psig, 180°C) = 3.5 kg/m³ = 0.22 lb/ft³ System classification: Ψ < 0.1 (low viscosity, tall vessel, good disengagement) → TEMPERED, use API 520 vapor relief Required Vapor Relief Rate: Heat generation rate: Q_gen = m × Cp × (dT/dt) × φ m = 7.57 m³ × 0.7 fill × 900 kg/m³ = 4780 kg Q_gen = 4780 × 2.5 × 0.083 × 1.06 = 1050 kW = 3.58 MMBtu/hr Vapor generation rate: W_vapor = Q_gen / ΔH_vap = 1050 / 400 = 2.63 kg/s = 20,900 lb/hr API 520 Vapor Orifice Sizing: A = W / (C × K_d × K_b × K_c × P × √(M/TZ)) (API 520 Equation 7) Assume: C = 315 (constant for US units, k ≈ 1.0) K_d = 0.975 (discharge coefficient, conventional PSV) K_b = 1.0 (backpressure correction, low backpressure) K_c = 1.0 (combination correction factor) P = 50 + 10% overpressure = 55 psig = 69.7 psia M = 50 (average molecular weight of vapors) T = 180°C = 453 K = 816°R Z = 0.96 A = 20,900 / (315 × 0.975 × 1.0 × 1.0 × 69.7 × √(50/(816×0.96))) A = 20,900 / (315 × 0.975 × 69.7 × 0.253) A = 20,900 / 5409 A = 3.86 in² Select standard orifice: N (4.34 in²) per API 526 Actual orifice: 2.5" diameter (A = 4.91 in²) provides 27% margin

Example 2: Gassy System (Two-Phase)

Scenario: Batch reactor, nitration reaction with gas evolution (NO₂) Runaway scenario: Cooling failure + rapid decomposition Reactor: 1000 gal (3.79 m³), 80% fill, P_set = 30 psig Calorimetry Data (VSP2): dT/dt (at 30 psig) = 15 K/min = 0.25 K/s (rapid runaway) dP/dt = 120 psi/min = 2.0 psi/s (high gas generation) φ = 1.05 Cp = 3.0 kJ/kg·K ΔH_vap = 350 kJ/kg ρ_L = 1100 kg/m³ = 68.7 lb/ft³ μ = 50 cP (high viscosity, polymer solution) System classification: Ψ = 0.95 (high viscosity, high gas rate, foaming) → GASSY, use HEM two-phase model DIERS Vent Sizing: m_0 = 3.79 m³ × 0.8 × 1100 kg/m³ = 3330 kg = 7340 lb Self-heat rate: q = Cp × (dT/dt) × φ = 3000 × 0.25 × 1.05 = 788 J/kg·s = 0.34 Btu/lb·s Two-phase mass flux (HEM): G = √(2 × g_c × ρ_L × ΔP / (1 + L)) Assume L ≈ 0.1 (low quality, mostly liquid): ΔP = 10% overpressure = 0.1 × 30 = 3 psi = 432 lb/ft² G = √(2 × 32.2 × 68.7 × 432 / 1.1) G = √(1.95 × 10⁶) G = 1396 lb/s·ft² = 9.7 lb/s·in² Required vent area: A = (m_0 / G) × √(q / ΔH_v) ΔH_v = 350 kJ/kg = 150 Btu/lb A = (7340 / 9.7) × √(0.34 / 150) A = 756 × 0.048 A = 36.3 in² With discharge coefficient C = 0.65 (rupture disk): A_actual = 36.3 / 0.65 = 55.8 in² Select 8" rupture disk (A = 50.3 in²) or 9" (A = 63.6 in²) Use 9" disk for 15% margin Comparison: If sized as vapor-only (tempered), would get A ≈ 5-7 in² → 8-10× undersized! Two-phase relief requires much larger vent due to low mixture velocity.

Regulatory and Industry Standards

Standard	Scope	Key Requirements
API 520 Part I	PSV sizing (vapor, liquid, two-phase)	Vapor orifice sizing equations, backpressure limits
API 520 Part II	Runaway reaction relief	Refers to DIERS methodology, fire exposure, decomposition
DIERS Project Manual	Emergency relief for runaway reactions	VSP testing, tempered/gassy classification, vent sizing equations
NFPA 68	Explosion venting (dust/gas deflagrations)	Vent panel sizing for dust explosions, not runaway reactions
CCPS Guidelines	Chemical Process Safety (CCPS)	Inherently safer design, layers of protection analysis (LOPA)

Software Tools for Vent Sizing

SuperChems (DIERS-licensed): Complete DIERS methodology, tempered/hybrid/gassy sizing, VSP data import
Aspen HYSYS RELIEF: API 520 and DIERS methods integrated with process simulation
PRO/II SAFIRE: Safety analysis and relief sizing with rigorous thermodynamics
FauRe SAFIRE: Standalone DIERS tool with extensive thermodynamic database

Vent sizing workflow: (1) Perform adiabatic calorimetry testing (VSP2, ARC, RSST). (2) Classify system as tempered/hybrid/gassy based on Ψ parameter or observation. (3) For tempered, use API 520 vapor sizing. For hybrid/gassy, use DIERS or Leung omega method. (4) Apply 20-30% safety margin. (5) Verify with dynamic simulation if critical (high-risk scenarios). (6) Design containment system (catch tank, scrubber) sized for total discharge.

Runaway Reaction Relief: DIERS Engineering Fundamentals

Vapor-only relief

Two-phase relief

2-10× larger for 2-phase

Contents

Use this guide when you need to: