Vessel Thermomechanical Safety

This page documents the vessel thermomechanical safety models in neqsim.process.safety.depressurization, neqsim.process.safety.rupture, and neqsim.process.util.heattransfer. They cover the transient pressure and temperature behavior of a pressurized vessel during emergency depressurization, fast filling, fire exposure, and cryogenic storage — the cases that govern relief device sizing, low-metal-temperature material selection, and wall rupture.

These models complement the steady-state blowdown / MDMT workflow in the neqsim-depressurization-mdmt skill and the relief and flare network classes. They resolve effects that a single-temperature lumped model misses: the gas–liquid temperature bifurcation in a fire, the conservatism of steady-state PSV sizing, the compression heating of a fast-filled cylinder, and the through-wall thermal lag of a composite wall.

Background and Validation

The models reproduce the headline application results of:

Andreasen, A. (2026). Thermomechanical safety analysis of pressurized equipment. Journal of Loss Prevention in the Process Industries, 103, 106088.

The committed JUnit regression tests assert the robust, model-independent findings of that study (trends, governing-limit flagging, conservatism direction) rather than brittle absolute values:

Case Application Validated finding
§4.1 Dynamic PSV sizing (fire case) Steady-state API 521 sizing is conservative; the dynamically required orifice is smaller (oversizing ratio > 1)
§4.2 Type IV hydrogen cylinder fast fill Compression heating raises the gas temperature; the liner upper-temperature limit governs a safe fill rate
§4.3 CO₂ storage boil-off Boil-off load falls sharply with insulation thickness; the effective heat-transfer coefficient is conduction-limited
§4.4 LPG vessel in a fire A bare vessel ruptures within minutes; passive fire protection keeps the wall stress below the derated strength

Standards

Non-Equilibrium (Two-Temperature) Blowdown

NonEquilibriumBlowdownModel carries two temperature zones — vapour and liquid — at a shared, vapour-controlled pressure. During depressurizing fire exposure the vapour space can superheat by several hundred kelvin while the boiling liquid stays pinned near its saturation temperature. This gas–liquid temperature bifurcation is the governing input for low-metal-temperature and wall-rupture assessments and is missed by single-temperature models.

import neqsim.thermo.system.SystemSrkEos;
import neqsim.thermo.system.SystemInterface;
import neqsim.process.safety.depressurization.NonEquilibriumBlowdownModel;
import neqsim.process.safety.depressurization.NonEquilibriumBlowdownModel.NemResult;

SystemInterface fluid = new SystemSrkEos(273.15 + 20.0, 50.0);
fluid.addComponent("methane", 0.40);
fluid.addComponent("propane", 0.30);
fluid.addComponent("n-butane", 0.30);
fluid.setMixingRule("classic");

NonEquilibriumBlowdownModel model =
    new NonEquilibriumBlowdownModel(fluid, 10.0, 0.025, 0.72, 1.0e5);
model.setFireExposure(0.9, 1100.0, 30.0, 25.0); // emissivity, flame T [K], h [W/m2K], area [m2]
model.setWall(8000.0, 470.0);                   // wall mass [kg], cp [J/kgK]
model.setLatentHeat(350000.0);
model.setTimeStep(1.0).setMaxTime(600.0).setStopPressure(1.5e5);

NemResult res = model.run();
double bifurcationK = res.maxTemperatureBifurcationK; // peak (T_gas - T_liquid)
double finalGasT = res.finalGasTemperatureK;
double finalLiqT = res.finalLiquidTemperatureK;

The vapour-controlled pressure is found with an EOS-consistent constant-volume flash each step; boil-off transfers moles from the liquid zone to the vapour zone; and the vapour discharges through a choked / subsonic orifice. This is a screening-grade non-equilibrium method (NEM): all flashes are guarded, so a transient property failure degrades a single step rather than aborting the run.

The NemResult exposes time-series lists (timeS, pressureBara, gasTemperatureK, liquidTemperatureK, wallTemperatureK, gasMassKg, liquidMassKg) and scalar summaries (initialPressureBara, finalGasTemperatureK, finalLiquidTemperatureK, maxTemperatureBifurcationK, flashFallbackCount).

Dynamic PSV Sizing (Fire Case)

DynamicPsvSizingStudy quantifies the conservatism of steady-state API 521 fire PSV sizing. A spring-loaded PSV on a gas system cycles (pops at the set pressure, reseats at the blowdown pressure), and a transient simulation that resolves this cycling typically shows a smaller orifice keeps the peak accumulated pressure within the allowable limit than the steady-state equation requires.

import neqsim.process.safety.depressurization.DynamicPsvSizingStudy;
import neqsim.process.safety.depressurization.DynamicPsvSizingStudy.SizingComparison;

// gas fluid with mixing rule already set, e.g. SystemSrkEos methane
DynamicPsvSizingStudy study =
    new DynamicPsvSizingStudy(gas, 1.0, 150000.0, 11.0e5, 0.21, 1.0e5);
// vesselVolume [m3], fireHeatInput [W], setPressure [Pa], overpressureFraction (0.21 fire), backPressure [Pa]
study.setBlowdownFraction(0.1).setDischargeCoefficient(0.975);

SizingComparison cmp = study.run();
double ratio = cmp.oversizingRatio;          // steady / dynamic required area (> 1 => conservative)
double steadyArea = cmp.steadyRequiredAreaM2;
double dynamicArea = cmp.dynamicRequiredAreaM2;
double peakP = cmp.peakDynamicPressurePa;

The dynamically required orifice area is found by bisection as the smallest area that keeps the peak vessel pressure at or below the allowable accumulated pressure, then compared against the steady-state API 521 area from ReliefValveSizing.calculateRequiredArea. The cycling dynamics use ideal-gas energy bookkeeping seeded from a single NeqSim flash for molar mass, heat-capacity ratio, and compressibility.

Fast Filling (Type IV Hydrogen Cylinders)

VesselFillingSimulator solves the coupled mass and energy balance for a vessel being charged with gas. Because enthalpy (not internal energy) crosses the boundary, the flow work of the incoming stream is captured automatically, which reproduces the gas-temperature rise during fast filling. Liner temperature limits relevant for Type III / Type IV composite hydrogen cylinders are checked against configurable minimum and maximum temperatures.

import neqsim.thermo.system.SystemSrkEos;
import neqsim.thermo.system.SystemInterface;
import neqsim.thermodynamicoperations.ThermodynamicOperations;
import neqsim.process.safety.depressurization.VesselFillingSimulator;
import neqsim.process.safety.depressurization.VesselFillingSimulator.VesselFillingResult;

SystemInterface h2 = new SystemSrkEos(273.15 + 10.0, 51.0); // residual gas at 51 bara
h2.addComponent("hydrogen", 1.0);
h2.setMixingRule("classic");
new ThermodynamicOperations(h2).TPflash();
h2.initProperties();

VesselFillingSimulator sim = new VesselFillingSimulator(h2, 0.06); // 60 L cylinder
sim.setInletConditions(283.15, 360.0, 0.015); // supply T [K], supply P [bara], mass flow [kg/s]
sim.setTargetPressure(351.0);                 // stop pressure [bara]
sim.setLinerTemperatureLimits(233.15, 338.15); // -40 C / +65 C liner limits
sim.setTimeStep(1.0).setMaxTime(4000.0);

VesselFillingResult res = sim.run();
double peakGasT = res.maxFluidTemperatureK;
boolean linerOk = res.linerLimitsMet;
boolean tooHot = res.linerOverTemperature;

The internal gas-to-wall film coefficient may be a fixed value (via setWall) or computed each step from the Woodfield mixed-convection charging correlation (via setWoodfieldHeatTransfer). The VesselFillingResult exposes time-series lists (time, pressureBara, temperatureK, massKg, wallTempK) and the scalar flags maxFluidTemperatureK, minFluidTemperatureK, maxPressureBara, linerOverTemperature, linerUnderTemperature, and linerLimitsMet.

Cryogenic Boil-Off

BoilOffCalculator is a steady-state heat-ingress model for insulated cryogenic or refrigerated vessels. The series thermal resistance of the outer film and the insulation layer gives an effective heat-transfer coefficient

\[h_{eff} = \left( \frac{1}{h_o} + \frac{t_{ins}}{k_{ins}} \right)^{-1}\]

from which the heat ingress $Q = h_{eff} A (T_{amb} - T_{fluid})$ and the latent-heat boil-off rate $\dot{m} = Q / L$ follow. Sweeping the insulation thickness reproduces the BoilFAST-style trade-off between insulation thickness and relief load.

import neqsim.process.util.heattransfer.BoilOffCalculator;

BoilOffCalculator calc = new BoilOffCalculator()
    .setSurfaceArea(150.0)             // m2
    .setOuterFilmCoefficient(10.0)     // W/(m2.K)
    .setInsulationConductivity(0.025)  // W/(m.K)
    .setAmbientTemperatureK(288.15)
    .setFluidTemperatureK(253.15)      // refrigerated CO2
    .setLatentHeat(320000.0);          // J/kg

double thinBoilOff = calc.boilOffRateKgPerH(0.05); // 5 cm insulation
double thickBoilOff = calc.boilOffRateKgPerH(0.30); // 30 cm insulation
double hEff = calc.effectiveHeatTransferCoefficient(0.30);
double qIngress = calc.heatIngressW(0.30);

For a conduction-limited wall the effective coefficient approaches $k_{ins}/t_{ins}$, so thicker insulation strongly reduces both the heat ingress and the boil-off relief load.

Composite-Wall Conduction

CompositeWallConduction is a one-dimensional transient heat-conduction solver for a multi-layer vessel wall (for example an inner polymer liner, a composite overwrap, and an outer steel shell). The non-uniform grid is integrated with the unconditionally stable Crank-Nicolson scheme and a Thomas-algorithm tridiagonal solve. The outer face receives a prescribed absorbed fire flux (Neumann boundary) and the inner face exchanges heat with the contained fluid through a convective film coefficient (Robin boundary).

Because the solver resolves the temperature gradient across the wall thickness, it captures the through-wall thermal lag that the lumped-capacitance model misses once the Biot number is no longer small. The static CompositeWallConduction.biotNumber(...) helper supports that screening: the lumped model is adequate for $Bi < 0.1$, and this distributed solver should be preferred above it. Wetted and unwetted zones of a partially filled vessel are represented by two independent instances driven with the same outer fire flux but different inner film coefficients and fluid temperatures.

Vessel Rupture in Fire / Blowdown

VesselRuptureAnalyzer tracks the von Mises wall stress against the temperature-derated allowable tensile strength of the material throughout a fire or blowdown transient. Rupture is predicted at the first crossover where the stress reaches the allowable strength; the crossover time is found by linear interpolation. The temperature derating is supplied by MaterialStrengthCurve.

import neqsim.process.safety.rupture.VesselRuptureAnalyzer;
import neqsim.process.safety.rupture.VesselRuptureAnalyzer.VesselRuptureResult;
import neqsim.process.safety.rupture.MaterialStrengthCurve;

MaterialStrengthCurve steel = MaterialStrengthCurve.carbonSteel("CS", 245.0e6, 415.0e6);
VesselRuptureAnalyzer analyzer = new VesselRuptureAnalyzer(0.5, 0.012, steel); // radius [m], thickness [m]

// transient history (e.g. from a fire model) — time [s], pressure [Pa], metal temperature [K]
double[] timeS = {0.0, 60.0, 120.0, 180.0, 240.0, 300.0};
double[] pressurePa = {18e5, 20e5, 22e5, 24e5, 25e5, 26e5};
double[] metalTempK = {300.0, 420.0, 540.0, 660.0, 780.0, 900.0};

VesselRuptureResult res = analyzer.analyze(timeS, pressurePa, metalTempK);
boolean ruptured = res.ruptured;
double ruptureTime = res.ruptureTimeS;       // NaN if no rupture
double minMargin = res.minMarginPa;          // closest approach to rupture

A bare vessel exposed to a full fire ramps quickly to wall temperatures where the derated strength falls below the hoop stress and ruptures within minutes. With passive fire protection (a much slower wall heat-up and lower peak pressure) the margin stays positive throughout and rupture is prevented — the §4.4 LPG validation case.

Choosing the Right Model

Question Model
Does the gas superheat while the liquid stays cold during a fire blowdown? NonEquilibriumBlowdownModel
Is the steady-state fire PSV oversized? DynamicPsvSizingStudy
How hot does a fast-filled H₂ cylinder get, and is the liner limit exceeded? VesselFillingSimulator
What relief / vent rate must a cryogenic vessel handle, and how much insulation? BoilOffCalculator
Does the through-wall thermal lag matter for a composite wall? CompositeWallConduction (check biotNumber)
Will the vessel wall rupture in a fire, and is PFP sufficient? VesselRuptureAnalyzer + MaterialStrengthCurve
What is the blocked-outlet overpressure with a relief device? BlockedOutletOverpressureAnalyzer

For steady-state blowdown sizing and the MDMT material check, use the neqsim-depressurization-mdmt skill.