Calculators › DIERS
RELIEF-SYSTEM ANALYSIS
DIERS
Investigate relief scenarios, vessel behaviour and discharge capacity.
Screens the emergency relief of a closed vessel of one pure solvent heated until its bursting disc ruptures (by a set duty, a fire or excess steam): whether the discharge is two-phase, the peak temperature and pressure after rupture, and Leung's reference vent area.
Prices
| Runs | Price |
|---|---|
| Every run | 1 credit |
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A credit costs 8p to 10p, depending on the pack. Credits don't expire. Packs and prices
Inputs and results
You enter
- The solvent (26 to choose from) and its charge
- The vessel's geometry and fill
- The heat input: a duty, an external fire or excess steam
- The bursting disc (from a database, or entered) and the outlet pipe
You get
- Discharge screening: vapour only or two-phase, with void fractions
- The peak temperature and pressure after rupture, against the limit
- The disc's burst state and the heat input at rupture
- Leung's zero-overpressure reference area
Example: Predicted peak state
CompletedWater in a 1.69 m³ vertical vessel at 80 % fill, heated at 51.5 kW, with a bursting disc set at 1.72 bar gauge and a 108.2 mm bore outlet pipe 30 m long.
The starting case every new DIERS case opens on, run by the engine on our servers and stored (engine 1.0.0 · data 1.0.0). Nothing is calculated in your browser, here or in the calculator. Exports and the other tools of a run need an account.
Water • external heating · WATER
WITHIN REVIEW PRESSURE
The predicted peak is below or equal to the selected review pressure. This comparison applies only to the model and inputs shown; it is not a relief-system approval.
Coupling converged · temperature residual -0.000000025 K
Vessel discharge screening
TWO-PHASE DISCHARGE PREDICTED
WATER · All-vapour flow basis · Bubbly vessel regime
αAV > α₀: the legacy test predicts liquid swell sufficient for two-phase discharge.
| Inventory mass / rupture fill | 1,391.089 kg / 88.49287 % |
| Rupture pressure / temperature | 2.4 bara / 126.1326 °C |
| Liquid / vapour density | 928.673 kg/m³ / 1.3253 kg/m³ |
| Surface tension | 53.0561 mN/m |
| Latent heat | 2,123.32 kJ/kg |
| PR compressibility Z | 0.982692 |
| Cp/Cv basis | Automatic · Yaws + PR real-gas |
| Vapour γ / discharge Cd | 1.3386597 / 0.9 |
| Critical-flow factor F | 0.674157 |
| Critical vapour mass flux Gv | 380.2098 kg/(m²·s) |
| Free vent area | 9,194.845 mm² · Pipe bore area · full-bore assumption |
| Flow area Ax / rest height H₀ | 1.13664 m² / 1.46102 m |
| Geometry factor F′ | 4 |
| Heat duty / heated area | 51.5 kW / 5.3834 m² |
| Heat flux q″ | 9,566.445 W/m² |
| All-vapour velocity Uavf | 2.0887 m/s |
| Uniform-heating velocity Uuhi | 0.0165147 m/s |
| Flow function X · based on Uuhi | 0.00352364 |
| Stability parameters Kf / Kv | 0.10738 / 0.00405647 |
| Terminal-velocity coefficient K | 1.18 |
| Terminal velocity U# | 0.18148 m/s |
| ψavf / ψuhi | 11.5092 / 0.091 |
| Selected ψ / Co | 11.5092 / 1.5 |
| Margin αAV − α₀ | 0.5454 |
Vapour heat-capacity audit at rupture
| Yaws ideal-gas Cp° | 34.2986125 J/(mol·K) |
| PR Cp departure | 0.580509444 J/(mol·K) |
| PR Cv departure | 0.07110647 J/(mol·K) |
| Real-gas Cp | 34.879122 J/(mol·K) |
| Real-gas Cv | 26.0552564 J/(mol·K) |
| Real-gas Cp / Cv on mass basis | 1.9361156 kJ/(kg·K) / 1.446309 kJ/(kg·K) |
| Ideal-gas Cp°/Cv° | 1.31998209 |
| PR real-gas Cp/Cv | 1.33865971 |
| Cp source row / temperature range | 1489 / 100–1500 K |
Yaws: Cp° = A + BT + CT² + DT³ + ET⁴, J/(mol·K). PR: Cv = Cp° − R + Cv departure; Cp = Cv − T(∂P/∂T)v²/(∂P/∂v)T. The largest physical PR root is used. Cp/Cv is not the real-gas isentropic exponent. The legacy F(γ) mass-flux expression with this ratio remains an approximation. Liquid Cp in the two-phase energy balance is separate.
Screening uses the original workbook correlations at rupture. It does not calculate restricted disc-plus-pipe capacity or a vapour-only relief size. See Methods for equations and geometry assumptions.
Specified constant heat input
51.5 kW
This duty is held constant in the DIERS peak-pressure model. Fire uses the supplied legacy workbook basis; steam duty uses the rupture-state temperature.
Rupture & inventory
| Saturation temperature | 126.133 °C |
| Inventory basis | Conserved initial liquid charge |
| Entered liquid volume | 1,353.92 L |
| Charge reference density | 1,027.453 kg/m³ at 25 °C |
| Conserved inventory M₀ | 1,391.089 kg |
| Liquid fill at rupture | 88.49287 % |
| Liquid mass at rupture | 1,390.83 kg |
| Vapour mass quality at rupture | 0.01855 % |
| Vapour-space fraction at rupture | 11.51 % |
| No-overshoot flow W₀ | 15.0213 kg/s |
| Pipe capacity at rupture | 11.0527 kg/s |
Capacity at rupture is below the no-overshoot flow; the model predicts a temperature rise.
Outlet at peak
| Inlet pressure P₁ | 2.3918 bara |
| Exit pressure P₂ | 1.33671 bara |
| Back pressure | 1.01325 bara |
| Mass flux G | 1,203.51 kg/(m²·s) |
| Omega ω | 42.19 |
| Resistance N | 5.545 |
| Gravity parameter Fᵢ | 0.03024 |
Exit choking sets capacity. Expansion to back pressure occurs beyond the modeled pipe.
Property audit
| Property | At rupture | At peak | Unit |
|---|---|---|---|
| Temperature | 126.1326 | 126.1789 | °C |
| Liquid density | 928.6735 | 928.6246 | kg/m³ |
| Vapour density · PR | 1.325298 | 1.327048 | kg/m³ |
| Liquid heat capacity | 4.246075 | 4.246196 | kJ/(kg·K) |
| Latent heat · source correlation | 2,123.325 | 2,123.197 | kJ/kg |
| Specific volume difference | 0.7534705 | 0.7524754 | m³/kg |
WATER · permitted combined calculation range: 0.01 °C–341.624 °C. The vessel equation uses rupture properties; pipe calculations use peak properties with inlet mass quality fixed at its rupture value.
Property source records
ThermoMix_Physical_Property_Studio(1).html · workbook row references retained from the supplied file.
| Liquid density | Sheet2 row 1489 |
| Vapour pressure | Property Studio · Sheet7 row 1489 |
| Liquid heat capacity | Sheet9 row 1489 |
| Latent heat | Sheet11 row 1489 |
| PR critical constants | Sheet5 row 1489 |
Zero-overpressure reference
Leung equations 32 / 41. G ≈ 1,947.86 kg/(m²·s). Includes an assumed discharge coefficient of 0.90; excludes pipe losses. The coefficient is not a certified device value. It is a reference result, not a final selected bore.
Convergence & calculation sequence
| 1 · Saturation root | 126.13256 °C |
| 2 · Inventory mass quality | 0.000185536 |
| 3 · Nozzle critical ratio at peak | 0.92933652 |
| 4 · Pipe inlet / exit ratios | 0.99517375 / 0.55617247 |
| 5 · Pipe bisection iterations | 58 |
| 6 · Pipe integral residual | 1.776e-15 |
| 7 · Quadrature 256 / 512 panel difference | 2.521e-9 |
| 8 · Coupling evaluations | 30 |
| 9 · Peak temperature residual | -0.000000025 K |
Bracketed bisection; Simpson quadrature. Residuals test the numerical solution, not the physical assumptions.
Methods
- Properties from the workbook's correlations, with a Peng–Robinson vapour
- The workbook's vessel-swell screening (bubbly, churn-turbulent and droplet flow)
- The peak state from Leung's simplified vent-sizing equations (AIChE Journal, 1986)
- Outlet capacity by the omega method for flashing flow in nozzles and pipes (Leung, 1990; Leung and Epstein, 1990)
How every calculator is tested: Methods and validation.
Limits
- One pure solvent: no mixtures, runaway reactions or gassy systems
- No foaming correlations, subcooled feeds or time-resolved blowdown
- Constant-bore, horizontal or upward outlet pipes only
- An engineering development version: not certified device sizing or a relief-system approval
Results are screening estimates from the methods described. A competent engineer must check them before relying on them in design, safety or operating decisions.
How it is checked
- Parity with the original
- The engine is a port of the original standalone calculator, and reproduces it on 836 generated cases: every quantity within 10⁻¹² relative, except 21 groups of quantities with a recorded tolerance of its own, where the original's numerical methods amplify rounding (iterative solvers, finite differences, residuals near zero).
- Validation against reference data
- No published reference cases yet.