Source: https://guthlabs.ai/docs/instruments/compressibility-factor-z-estimator/

instrument / verified-clean

# Compressibility Factor (Z) Estimator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/compressibility-factor-z-estimator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/compressibility-factor-z-estimator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/compressibility-factor-z-estimator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/compressibility-factor-z-estimator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Thermodynamics, Fluids & Aero

**Tranche**: tranche-7

**Evidence ID**: t7-003

**Ledger rows**: 1

No ledger note is attached.

## Review findings

Core definitions are standard, but the instrument is not fully verifiable as specified. The exact correlation variant, authoritative critical-property table, chart values, interpolation scheme, valid domain, and corrected-output equations must be fixed. The honest label should state the validated pressure/temperature/domain range and should not imply ±5% accuracy near critical conditions or across all gases.

### Formula and scope findings

- Z=PV/(nRT) is the standard definition of compressibility factor.

- Pr=P/Pc and Tr=T/Tc are standard, provided P and Pc use the same pressure units and T and Tc are absolute temperatures.

- “Lee-Kesler/Pitzer correlation” is not a complete algorithm: the specification does not provide the Lee-Kesler equations, the Pitzer equations, the generalized-chart table, the reference-fluid convention, or the interpolation rule.

- The stated engine says bilinear interpolation, but no rectangular chart coordinates or interpolation behavior at table boundaries are specified.

- Corrected-volume and corrected-mole-number formulas are omitted. They should explicitly include V=ZnRT/P and n=PV/(ZRT).

- A single generalized correlation should be selected. Lee-Kesler and the low-pressure Pitzer virial correlation are not interchangeable, especially near the critical region or at elevated pressure.

### Unit assumptions

- P and Pc are absolute pressures in identical units; the worked vectors use Pa.

- T and Tc are absolute temperatures in kelvin, never degrees Celsius.

- R=8.314462618 J mol^-1 K^-1 is used, so P is in Pa and V is in m^3 mol^-1.

- Acentric factor omega is dimensionless.

- The chart fragments below use a dimensionless generalized Lee-Kesler-style representation Z=Z0(Pr,Tr)+omega*Z1(Pr,Tr); these fragments must be replaced or versioned against the actual production table before release.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not provide the Lee-Kesler/Pitzer coefficients, lookup-table values, interpolation grid, or pressure convention. Consequently, nontrivial numerical Z outputs and the two sides of the interpolation branch switch cannot be reproduced or independently verified. The estimator must also reject Pc=0 and handle P=0 volume correction explicitly.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "gas": "Methane",
    "P_Pa": 4599200,
    "T_K": 190.56,
    "Pc_Pa": 4599200,
    "Tc_K": 190.56,
    "omega": 0.01142
  },
  "expected_outputs": {
    "Pr": 1,
    "Tr": 1,
    "Z": 0.286,
    "molar_volume_m3_per_mol": 0.00009853
  },
  "reference_data": {
    "Pc_Pa": 4599200,
    "Tc_K": 190.56,
    "omega": 0.01142,
    "source_convention": "NIST Chemistry WebBook / widely tabulated standard methane critical properties",
    "Z0_at_Pr_1_Tr_1": 0.2957,
    "Z1_at_Pr_1_Tr_1": -0.85,
    "source_convention_chart": "Lee-Kesler generalized compressibility chart, standard textbook tabulation"
  },
  "working": "Pr=P/Pc=4,599,200/4,599,200=1.000000. Tr=T/Tc=190.56/190.56=1.000000. Z=Z0+omega*Z1=0.2957+(0.01142*-0.85)=0.2957-0.009707=0.285993, rounded to 0.286. V=ZRT/P=(0.286*8.314462618*190.56)/4,599,200. First, RT=8.314462618*190.56=1,584.404796 J/mol. Then ZRT=0.286*1,584.404796=453.539772 J/mol. Finally V=453.539772/4,599,200=0.00009861 m^3/mol, approximately 9.86e-5 m^3/mol."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche7/tranche7-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`