Model-explicit release source terms

Use the neutral source-term contract to export these results as versioned JSON, newline-delimited frames or a reduced CSV time series. Use uncertainty ensembles to propagate joint input cases without discarding failures. The implementation status records remaining work.

ReleaseFlowModel calculates an instantaneous short-opening source term from a NeqSim fluid. It is independent of downstream safety software and process orchestration. Requests defensively copy the fluid; results and station snapshots are immutable and serializable. This is the first implementation layer of NRC-3860.

Usage

The following example is executed by ReleaseFlowModelTest.documentationExampleAndEnergyClosure:

SystemInterface gas = new SystemSrkEos(300.0, 50.0);
gas.addComponent("methane", 1.0);
gas.setMixingRule("classic");
ReleaseFlowModel model = new HomogeneousEquilibriumReleaseModel();
ReleaseFlowResult result = LeakModel.builder().fluid(gas).holeDiameter(0.01)
    .dischargeCoefficient(0.62).backPressure(101325.0).build()
    .calculateReleaseFlow(gas, model);

Import the types from neqsim.process.safety.release and neqsim.thermo.system. Check result.isUsable() and inspect getDiagnostics() before accessing the release rate. The rate getter throws on invalid or unsupported results; failure cannot look like zero flow. For direct use, construct ReleaseFlowRequest(fluid, diameterM, dischargeCoefficient, backPressurePa) and call the model’s calculate method. Malformed request geometry throws at construction; thermodynamic/model failures produce diagnostic results.

Explicit model selection

Model selection is never inferred from phase count. Choose one implementation and retain its identity, version and diagnostics with every frame:

Model	Intended use	Required behavior
HomogeneousEquilibriumReleaseModel	Short-opening equilibrium gas, liquid and flashing calculations.	EOS/flash closure is strict; unsupported phase physics and failed required properties return no numeric payload.
IdealGasReleaseModel	Analytical gas checks and dilute-gas screening with constant $\gamma$.	Requires one gas phase plus finite NeqSim molar mass and $\gamma$; no property default or model fallback.
IdealGasFannoPipeReleaseModel	Quasi-steady one-sided full-bore gas release through a constant-area pipe.	Requires explicit pipe length and Darcy friction, one gas phase, and finite ideal-gas properties; no friction or phase fallback.
LegacyScreeningReleaseModel	Reproduce the historical LeakModel.calculateMassFlowRate rate during migration.	Always returns VALID_WITH_WARNINGS when usable and carries SCREENING_ONLY, unresolved-station and legacy-fallback diagnostics.

Every implementation also returns an immutable ReleaseModelEvidence manifest. Stable applicability and limitation codes state the modeled boundary, while evidence records distinguish analytical, conservation, numerical and experimental comparisons. A custom model that does not override getEvidence() fails closed to NO_DECLARED_VALIDATION_EVIDENCE. The current built-in records are repository-owned analytical and regression evidence, so all emitted frames remain UNQUALIFIED and report independentEvidence: false.

For example:

ReleaseFlowModel idealGas = new IdealGasReleaseModel();
ReleaseFlowModel legacyCompatibility = new LegacyScreeningReleaseModel();
ReleaseFlowResult analytical = idealGas.calculate(
    new ReleaseFlowRequest(gas, 0.01, 0.62, 101325.0));

The legacy adapter delegates the numeric rate to the historical scalar method, including its documented density, molar-mass and heat-capacity-ratio fallback policy. It does not relabel that behavior as strict physics. Because the legacy equation never solves throat or exit thermodynamics, its opening snapshots alias the initialized upstream pressure and temperature. Consumers can detect this limitation from UNRESOLVED_STATIONS; they must not interpret those snapshots as a nozzle solution.

Ideal-gas equations

The ideal-gas adapter uses the initialized mixture molar mass $M$ [kg/mol] and heat-capacity ratio $\gamma$ [1] without replacement values. With $R=8.31446261815324$ J/(mol K), the critical pressure ratio, isentropic station temperature, density and velocity are:

\[r_c=\left(\frac{2}{\gamma+1}\right)^{\gamma/(\gamma-1)},\quad \frac{T}{T_0}=\left(\frac{p}{p_0}\right)^{(\gamma-1)/\gamma}.\] \[\rho=\frac{pM}{RT},\quad c_p=\frac{\gamma R}{(\gamma-1)M},\quad u=\sqrt{2c_p(T_0-T)},\quad \dot m=C_dA\rho u.\]

The accepted throat pressure is $p_0r_c$ when $p_b/p_0\le r_c$ and $p_b$ otherwise. For a choked state, the analytical velocity equals $\sqrt{\gamma RT/M}$. Station enthalpy uses the upstream NeqSim reference minus $u^2/2$ and station entropy retains the upstream reference. This preserves relative energy/entropy consistency without presenting an arbitrary absolute ideal-gas reference as new property data. The adapter supports one gas phase only and excludes reaction, forced phases, solid/hydrate checks, real-gas departure, phase change, friction, heat transfer and depletion.

Ideal-gas Fanno pipe equations

IdealGasFannoPipeReleaseModel uses a separate finite-pipe request:

ReleaseFlowModel pipeModel = new IdealGasFannoPipeReleaseModel();
ReleaseFlowRequest pipe = new ReleaseFlowRequest(
    gas, 0.10, 1.0, 101325.0, 100.0, 0.02);
ReleaseFlowResult pipeResult = pipeModel.calculate(pipe);

The final two values are pipe length [m] and specified Darcy friction factor [1]. Both must be positive together. Existing short-opening models reject this geometry instead of silently discarding it. SourceTermSession.addLongPipeSource carries the same geometry through steady and dynamic ProcessSystem and ProcessModel paths. The corresponding ReleaseInventory constructor preserves it while pressure, composition and energy evolve.

For exit Mach number $M_e$, inlet Mach number $M_i$, pipe length $L$, internal diameter $D$ and Darcy factor $f_D$, the model solves:

\[\frac{f_DL}{D}=F(M_i)-F(M_e),\] \[F(M)=\frac{1-M^2}{\gamma M^2}+\frac{\gamma+1}{2\gamma} \ln\left(\frac{(\gamma+1)M^2}{2+(\gamma-1)M^2}\right).\]

The stagnation-pressure relation is:

\[\frac{p_0}{p_0^*}=\frac{1}{M} \left(\frac{2+(\gamma-1)M^2}{\gamma+1}\right)^{(\gamma+1)/(2(\gamma-1))}.\]

The pipe is choked when the receiving pressure is at or below the calculated static exit pressure for $M_e=1$. Otherwise a bounded solve finds $0<M_e<1$ whose exit pressure equals the receiving pressure. Mass flux is $G=\rho Ma$ and the requested effective full-bore area remains $C_d\pi D^2/4$. Tests check Mach and energy closure, constant-area mass conservation, friction-length and backpressure trends, no-flow behavior, process-container frames and coupled inventory conservation.

This is a steady, adiabatic, calorically perfect, constant-area, one-sided pipe model. The specified friction factor is not calculated from roughness or Reynolds number. The model does not represent the opposite side of a rupture, transient decompression waves, line packing, heat transfer, real-gas departure, multiphase flow, slip, delayed flashing, entrainment, finite-rate phase transfer or solid-bearing transport. It is software-validated against its analytical equations, not independently qualified for facility decisions.

Homogeneous-equilibrium equations and station semantics

The upstream TP flash establishes stagnation enthalpy $h_0$ [J/kg] and entropy $s_0$ [J/(kg K)]. Pure-fluid pressure samples use PS flashes to retain the saturation-quality degree of freedom. Mixtures use cold TP flashes in a bracketed temperature root at fixed specific entropy and inventory (target residual 1e-7 J/(kg K)). Numerical model version 1.1.0 adds guarded continuation at an incipient vapour/liquid phase when the cold-TP entropy bracket stalls or its candidate fails fugacity closure. The selected numerical route is recorded in ENTROPY_SOLVER:

\[u(p)=\sqrt{2(h_0-h(p,s_0))},\quad G(p)=\rho(p,s_0)u(p),\quad \dot m=C_d A\max_{p_b\le p\le p_0}G(p).\]

Here $u$ is velocity [m/s], $G$ inviscid mass flux [kg/(m2 s)], $\rho$ EOS total density [kg/m3], $C_d$ the supplied discharge coefficient, and $A=\pi d^2/4$ physical area [m2]. The coefficient multiplies effective flow area; it does not change the isentropic velocity. Phase amounts are converted to mass fractions from phase mass, never from molar phase fraction. EOS mass/volume density is used consistently with EOS enthalpy and entropy.

Station	Definition
UPSTREAM_STAGNATION	Equilibrated reservoir state with zero velocity.
THROAT_CRITICAL	Maximum sampled/refined mass-flux state; receiving-pressure state when unchoked.
ORIFICE_EXIT	Explicit alias of the throat for the zero-length opening assumption.
AMBIENT_EXPANDED	Ideal isentropic state at receiving pressure; excludes shocks, entrainment and mixing.

An interior maximum indicates choking. A 48-interval logarithmic pressure scan brackets each resolved local maximum, then golden-section refinement reduces bracket width below 1e-7 * upstreamPressure. This finite search is not a proof that arbitrarily narrow maxima cannot exist. Phase-boundary cases require resolution/sensitivity and benchmark evidence.

Every trial checks entropy closure (absolute 1e-5 J/(kg K)), component conservation (1e-8 of total moles), phase composition normalization (1e-8), interphase log-fugacity ratios (1e-5, for components above 1e-10 in both phases), and finite physical properties. Negative enthalpy drops below -1e-5 J/kg fail; smaller roundoff is clipped to zero.

At a choked state the equilibrium acoustic API supplies an independent diagnostic. An unavailable acoustic derivative or a Mach discrepancy greater than 5% produces VALID_WITH_WARNINGS, with the reason retained. Acoustic speed is optional; required flash or closure failures always invalidate the calculation. No ideal-gas property defaults or replacement model are used.

For upstream pressure at or below back pressure, the result is valid zero forward flow, with NO_FORWARD_FLOW; there is no ambient-expanded station and no reverse-flow calculation.

Applicability and evidence

Case	Behavior
Nonreacting gas, liquid or equilibrium fluid mixture	Calculates the stated homogeneous-equilibrium model.
Flashing hydrocarbon liquid	Supports equilibrium phase redistribution with zero slip.
Forced phases, reactions, solid or hydrate checking enabled	UNSUPPORTED.
Mixture-specific equilibrium solid or hydrate risk at a resolved station	UNSUPPORTED; a separately assessed solid-capable model is required.
Required solid or hydrate assessment cannot resolve	INVALID; absence of risk is never inferred from a failed check.
Full-bore gas pipe with specified constant Darcy friction	Select IdealGasFannoPipeReleaseModel; outside HEM physics.
Transient decompression waves, real-gas pipe flow, slip, delayed flashing or heat transfer	Outside the delivered models.
Failed flash, unclosed inventory/entropy/fugacity or invalid density	INVALID, without a numeric release payload.

Version 1.2.0 assesses the upstream, accepted throat and ambient-expanded states on defensive fluid copies. Components present above 1e-12 mole fraction are checked when the station is at or below their database triple-point temperature. The selected-component solid flash uses the same EOS and mixture; a stable solid mass fraction above 1e-12 returns SOLID_RISK. A water-containing mixture with a recognized hydrate former is compared with its calculated hydrate equilibrium temperature and returns HYDRATE_RISK at or below the boundary. Failed required checks return SOLID_RISK_ASSESSMENT_FAILED and no numeric release payload. Clear stations carry SOLID_RISK_ASSESSED diagnostics.

These are applicability controls, not solid-bearing release physics or experimental qualification. Candidate screening is limited by the component data and hydrate model available to the selected NeqSim thermodynamic system. Turning off solid checks on the caller does not disable the defensive assessment or establish absence of solids outside the checked stations.

Evidence is software regression and analytical dilute-gas comparison, not independent experimental qualification. The frame’s model.evidence object retains the exact manifest ID, applicability codes, limitation codes and evidence references used by the selected model; it does not infer a higher evidence level from successful calculation status. Tests cover the ideal-gas choked limit (rate and pressure), unchoked/no-flow limits, energy/entropy closure, flashing pure propane, a methane/ethane gas mixture, input immutability, serialization, invalid/unsupported inputs, and area/coefficient scaling. No method is certified for a facility or safety decision by these tests.

Incipient-phase numerical continuation

Cold TP phase selection can discard a trace vapour phase or assign its liquid cubic root near phase appearance. This creates an entropy discontinuity even when an equilibrium entropy root exists. Version 1.1.0 retains a vapour/liquid seed observed inside the same temperature bracket and can refine its phase fractions with the existing TPmultiflash.solveBeta equations. Each candidate uses the same EOS, pressure, components and inventory. It does not switch physical models, use default properties, force phase types or weaken the final closure limits.

The refinement is bounded by 100 temperature bisections and 20 phase-split updates per candidate. Both phase fractions must lie strictly between 1e-10 and 1-1e-10; the active set must still contain gas and liquid. Accepted candidates must pass composition, component inventory, fugacity and finite-property checks. Their extensive Gibbs energy cannot exceed the cold result by more than numerical noise (1e-9 J/mol times total moles plus 16 floating-point units in the reference Gibbs energy). A rejected candidate leaves the cold reference intact; an unresolved entropy, inventory or equilibrium residual still returns INVALID without a rate.

INCIPIENT_PHASE_CONTINUATION records resolved entropy roots, accepted/rejected candidate counts and the last rejection reason. This diagnostic is distinct from acoustic warnings. The original pressure-search bounds and closure tolerances are unchanged. The source-frame schema remains v1, while model provenance identifies numerical version 1.2.0.

The former failing regression (80 mol% propane, 20 mol% n-butane, SRK/classic, 300 K, 20 bara to 3 bara, 10 mm opening and discharge coefficient 0.62) now gives approximately 1.617324 kg/s, a critical pressure of 8.231285 bara, and an ambient gas mass fraction of 0.205319. ReleaseFlowFlashingTest checks nine composition/temperature neighbours, inventory scaling, back-pressure sensitivity, station conservation and a schema fixture. It retains the matrix in target/source-term-benchmarks/mixture-flashing.csv.

A separate saturation-path calculation solves bubble pressure while matching saturated-liquid entropy to upstream entropy. It shares SRK property data but does not reuse the HEM temperature root or pressure maximizer. For the regression case, rate agreement is within 1e-5 relative and critical pressure within 2 Pa; generated reference values are retained in mixture-saturation-reference.csv. This is an independent numerical-algorithm check, not independent experimental validation.

The maximum is at phase appearance and is nonsmooth. The equilibrium acoustic diagnostic still reports THROAT_MACH_MISMATCH (Mach approximately 0.1215), so this example remains VALID_WITH_WARNINGS; frames remain UNQUALIFIED. Full mixture-flashing qualification requires independent release measurements and domain review.

Compatibility and extension

Existing scalar LeakModel methods keep their screening rate equations. Its lumped gas blowdown integration now conserves physical inventory and energy; see the gas blowdown compatibility note for the correction of #3905, gas-only applicability, and changed numerical results. LegacyScreeningReleaseModel is an opt-in compatibility adapter that proves rate equality while exposing screening limitations in machine-readable diagnostics. The calculateReleaseFlow method still requires explicit model selection and does not change legacy selected blowdown orifice law. Use ReleaseInventory and process dynamics for model-explicit time-dependent state evolution.

Additional models implement the serializable ReleaseFlowModel interface and return checked ReleaseFlowResult.success or .failure objects with stable identity/version and diagnostic codes. Station snapshots expose overall component mole and mass fractions and native phase mass fractions in deterministic name order. A new physical model needs its own applicability documentation and independent validation evidence.