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Methods and validation
How each calculator works, what it leaves out, and how we check that it gives the right numbers.
Parity with the originals
Each calculator began as a standalone tool, and each engine here is a port of it. We run the original on hundreds of generated cases (its own examples, every option, edge cases and random inputs), and the engine must reproduce every result and error message: within 10⁻¹² relative, or within a recorded, looser tolerance where the original's numerical methods amplify rounding. The cases are generated from the original, never edited by hand.
Validation, regression and versions
Where we have published reference data, the engine is checked against it, and any case where the model is known to deviate is kept with its reason. Every fault that is fixed gets a case so that it cannot come back. Every result records the engine and data versions that made it, and a change to an engine needs new cases, a new version and an engineer's sign-off.
Calculations run only on our servers: the calculation code never reaches your browser.
| Calculator | Engine | Parity cases | Validation cases |
|---|---|---|---|
| ThermoWorks | engine 1.0.0 · data 1.0.0 | 882 | 21 |
| LineWorks | engine 1.0.0 · data 1.0.0+components-1.0.0 | 617 | none yet |
| GasWorks | engine 1.0.0 · data 1.0.0+components-1.0.0 | 884 | none yet |
| PhaseWorks | engine 1.0.0 · data 1.0.0 | 820 | none yet |
| DIERS | engine 1.0.0 · data 1.0.0 | 836 | none yet |
| GridWorks | engine 1.1.0 · data 1.0.0+components-1.0.0 | 315 | none yet |
| BatchReactorWorks | engine 1.1.0 · data 1.0.0 | 345 | none yet |
PHYSICAL PROPERTIES
ThermoWorks
Builds a fluid mixture from a catalogue of 34 components and calculates its phase split and its thermodynamic and transport properties at a given temperature and pressure, or a pure fluid at saturation with a given vapour quality.
Methods
- Phase split: K-values from a vapour-pressure correlation (a Wilson-type expression above the critical temperature) and a Rachford–Rice flash
- Vapour: the Peng–Robinson equation of state without binary interaction parameters; Wilke's mixing rule for viscosity
- Liquid: additive specific volumes from DIPPR-style densities (Peng–Robinson where a correlation is missing), logarithmic viscosity mixing and mole-weighted surface tension
- Bubble and dew temperatures: screening estimates from the same K-values, between 40 and 1000 K
Limits
- No activity coefficients, binary interaction parameters or solids
- Not calculated: thermal conductivity, liquid heat capacity and enthalpy
- γ is estimated as Cp/(Cp − R/Z), not a real-gas acoustic derivative
- Results outside a correlation's source range are extrapolated, and listed for review
How it is checked
- Parity with the original
- The engine is a port of the original standalone calculator, and reproduces it on 882 generated cases: every quantity within 10⁻¹² relative.
- Validation against reference data
- Saturation properties at 1.01325 bar against NIST reference data. 13 cases, 4 of them documented limits of the model.
Single-phase densities and viscosities against NIST reference data. 8 cases.
LIQUID HYDRAULICS
LineWorks
Calculates the pressure loss along a line: straight pipe, a reducer or expander to a second bore, fittings, up to two valves by their flow coefficient, an orifice, extra resistance and a change of elevation.
Methods
- Crane's Technical Paper 410 throughout
- Darcy friction factor: laminar flow up to a Reynolds number of 2100, Colebrook–White (in Serghides' form) above it; transitional flow is flagged
- Fittings as resistance coefficients from Crane's table; valves from their Cv; reducers, expanders and square-edged orifices from Crane's expressions
- A two-phase stream is treated as homogeneous, without slip
Limits
- Properties are constant along the line
- Homogeneous two-phase flow only: no slip or flow regime
- A loss above 10 % of the inlet pressure is flagged
How it is checked
- Parity with the original
- The engine is a port of the original standalone calculator, and reproduces it on 617 generated cases: every quantity within 10⁻¹² relative.
- Validation against reference data
- No published reference cases yet.
- The original's own checks
- Gives the saved workbook's velocity, Reynolds number, friction factor and pressure loss for its starting line.
GAS HYDRAULICS
GasWorks
Calculates compressible gas flow along a line: the inlet pressure a known outlet pressure needs, or the outlet pressure a known inlet pressure gives, with the density, velocity and Mach number at each end.
Methods
- The workbook's isothermal compressible-flow relation, solved by bisection
- Friction, fittings and valves as in LineWorks (Crane's Technical Paper 410)
- Gas properties from ThermoWorks: Peng–Robinson compressibility, Wilke viscosity and ideal-gas heat capacity, constant along the line; the far end is checked again for liquid
Limits
- Isothermal flow with constant properties
- Valves and orifices as resistance only: no choking
- Refused at or above Mach 1; warned above Mach 0.7
- All-vapour streams only
How it is checked
- Parity with the original
- The engine is a port of the original standalone calculator, and reproduces it on 884 generated cases: every quantity within 10⁻¹² relative.
- Validation against reference data
- No published reference cases yet.
- The original's own checks
- Replays the workbook's saved steam case.
TWO-PHASE FLOW
PhaseWorks
Calculates the frictional pressure loss of a two-phase (or single-phase) stream in a horizontal line with fittings and valves, and places it on the Baker flow-regime map.
Methods
- Each phase taken to flow alone through the line, with friction and fittings from Crane's Technical Paper 410
- The two-phase loss from a Lockhart–Martinelli-type liquid multiplier (the workbook's fit)
- The flow regime from Baker's map (Oil and Gas Journal, 1954)
Limits
- Horizontal lines only: no elevation, acceleration or heat transfer
- No slip or holdup: the regime is a classification and does not change the loss
- Properties are constant along the line
How it is checked
- Parity with the original
- The engine is a port of the original standalone calculator, and reproduces it on 820 generated cases: every quantity within 10⁻¹² relative.
- Validation against reference data
- No published reference cases yet.
- The original's own checks
- Reproduces the workbook's saved case: the Baker point, gradient, loss and regime.
RELIEF-SYSTEM ANALYSIS
DIERS
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.
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)
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
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.
NETWORK DESIGN
GridWorks
Solves steady, single-phase pipe networks of liquid or gas: the pressure at every free node and the flow in every connection, with pumps, fans, compressors, valves, regulators, orifices, heat exchangers, choking, junction losses, heat transfer and mixing.
Methods
- Each connection integrated along its length: friction, elevation, acceleration and heat transfer
- Newton's method on the nodes' mass balances and the connections' pressures, with mixing at the nodes between solves
- Gas by Peng–Robinson (or ideal gas) with Wilke viscosity; liquids from ThermoWorks' correlations
- Choked flow in pipes and restrictions
Limits
- Steady state, single phase and Newtonian
- No water hammer, surge, two-phase flow or solids
- Steam from ThermoWorks' correlations, not IAPWS
- Up to 100 nodes and 150 connections; larger networks take longer to solve
How it is checked
- Parity with the original
- The engine is a port of the original standalone calculator, and reproduces it on 315 generated cases: every quantity within 10⁻¹² relative, except 11 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.
- The original's own checks
- The original's verification networks: Hagen–Poiseuille flow, balanced loop and compressed-air examples, a choked orifice and a nozzle's critical pressure ratio.
BATCH OPERATIONS
BatchReactorWorks
Simulates a stirred batch reactor over time: a thermal programme (heat, hold and cool through a jacket or coil, a utility loop and an external circuit) or a process recipe of up to 100 operations, from purging and filling through reflux, distillation and decanting to cooling and discharge.
Methods
- Batch-side heat transfer from impeller correlations; jacket, half-pipe and condensing-steam film coefficients; wall resistances in series
- Explicit midpoint time steps, with energy closure checked
- Vapour–liquid equilibrium by NRTL, and a liquid–liquid split for toluene and water
- Steam saturation from IAPWS SR1-86
Limits
- One well-mixed Newtonian liquid: no reaction kinetics, solids or gas dispersion
- The wall at batch temperature, and quasi-steady utility films
- Boiling as a screening heat input: no nucleate boiling or dryout
- Correlation constants are literature values, not fitted to your equipment
How it is checked
- Parity with the original
- The engine is a port of the original standalone calculator, and reproduces it on 345 generated cases: every quantity within 10⁻¹² relative, except 11 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.
- The original's own checks
- The original's numerical checks: IAPWS saturation, water's latent heat, a worked jacket example, energy closure and the integrator against an exact solution.