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    Tools · Fluids & Thermodynamics

    VLE Parameter Regression

    Fit binary NRTL interaction parameters to measured vapor–liquid equilibrium data, ready to use in VLE / Flash.

    Updated October 1, 2026

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    VLE Parameter Regression fits binary NRTL interaction parameters to your measured vapor–liquid equilibrium data, so VLE / Flash can calculate with fitted parameters instead of tabulated or missing ones. Its params table is VLE / Flash's binary_params input, so the two chain directly in a workflow. It runs on CPU.

    How it works

    The model is the same as VLE / Flash's: an NRTL liquid with τᵢⱼ = aᵢⱼ + bᵢⱼ/T and a single symmetric α, plus a Peng–Robinson or SRK vapor. Feeding the fitted parameters back into VLE / Flash reproduces the fit.

    • What's fitted. Any of a12, a21, b12, b21, and alpha. The default fits b12 and b21 with α fixed at 0.3. Parameters you don't fit stay at initial_guess (0 by default) or alpha.
    • Objective. Bounded least squares on bubble-point residuals: temperature for isobaric data or pressure for isothermal data (residual_basis: auto decides), plus y₁ where the row has it.
    • Bounds. aᵢⱼ between −100 and 100, bᵢⱼ between −20,000 and 20,000 K, and α between 0.001 and 1.
    • Uncertainty. Asymptotic standard errors at the solution, or none when there are too few points.

    Warnings flag failed points, missing y₁, a solver that didn't converge, and poor fits (RMSE above 5 K or 10 % of P), which usually mean wrong units or the wrong components.

    Inputs

    • components: exactly two, by name or smiles, with optional tc_k, pc_pa, and omega.
    • data: up to 200 rows of temperature_k, pressure_pa, x1, and optional y1, with at least one more row than the number of fitted parameters (and at least 3). Units are in the column names; convert other units first, or run the data through the VLE Thermodynamic Consistency Checker, which converts them and emits this exact table.
    • eos, residual_basis, fit_parameters, alpha, and initial_guess.

    Outputs

    FileContents
    params.csvOne row per direction: component_i, component_j, tau_a, tau_b, alpha (VLE / Flash's binary_params)
    params.jsonThe fitted parameters as NRTL matrices, fit statistics, solver status, and warnings
    residuals.csvMeasured and calculated values and residuals per point, with ok or failed
    result.jsonA summary: basis, parameters, standard errors, and RMSE

    Not covered

    • Liquid–liquid equilibrium, ternary or larger systems, and UNIFAC group parameters.
    • Cubic-equation-of-state kᵢⱼ: VLE / Flash builds its vapor from critical properties alone, so a fitted kᵢⱼ wouldn't change its results.

    VLE Thermodynamic Consistency Checker, VLE / Flash, and Group-Contribution Properties for critical properties.

    Run it from the API

    Submit with Submit a job and the job_type below. Price it first with Estimate job reservation cost: submitting reserves that amount from your wallet, and the charge settles at the actual runtime.

    VLE Parameter Regression vle-regress

    Job type
    vle-regress
    Hardware
    cpu (default)
    Typical runtime
    5 min on CPU

    Payload

    Payload fields
    FieldTypeDescription
    componentsrequiredtableValue
    datarequiredtableValue
    eosstring

    One of: "peng-robinson", "srk"

    residual_basisstring

    One of: "auto", "temperature", "pressure"

    fit_parameters[]string[]

    One of: "a12", "a21", "b12", "b21", "alpha"Limits: min items 1, max items 5

    alphanumber

    Limits: > 0, ≤ 1

    initial_guessobject
    initial_guess.a12number
    initial_guess.a21number
    initial_guess.b12number
    initial_guess.b21number

    Example

    from cognichem_client import CogniChem

client = CogniChem.from_env()  # reads COGNICHEM_API_KEY
payload = {
    "components": [
        {
            "name": "ethanol",
            "tc_k": 513.9,
            "pc_pa": 6148000,
            "omega": 0.645,
        },
        {
            "name": "water",
            "tc_k": 647.1,
            "pc_pa": 22064000,
            "omega": 0.344,
        },
    ],
    "eos": "peng-robinson",
    "residual_basis": "temperature",
    "fit_parameters": ["b12", "b21"],
    "alpha": 0.2937,
    "data": [
        {
            "temperature_k": 363.615,
            "pressure_pa": 101325,
            "x1": 0.05,
            "y1": 0.31983,
        },
        {
            "temperature_k": 359.325,
            "pressure_pa": 101325,
            "x1": 0.1,
            "y1": 0.44341,
        },
        {
            "temperature_k": 355.668,
            "pressure_pa": 101325,
            "x1": 0.2,
            "y1": 0.54359,
        },
        {
            "temperature_k": 354.109,
            "pressure_pa": 101325,
            "x1": 0.3,
            "y1": 0.59014,
        },
        {
            "temperature_k": 353.14,
            "pressure_pa": 101325,
            "x1": 0.4,
            "y1": 0.62517,
        },
        "… 6 more",
    ],
}

estimate = client.jobs.estimate(job_type="vle-regress", payload=payload, resource="cpu")
print(f"Reserves ${estimate.cost:.2f}")

job = client.jobs.submit(
    job_name="my-vle-regress-run",
    job_type="vle-regress",
    payload=payload,
    resource="cpu",
)
status = client.jobs.wait(job.process_id)
if status.status == "completed":
    client.jobs.result(job.process_id, save_path=".")

    Sample data from the job catalog; long values are shortened here. Each job_name must be unique among your jobs.

    Workflow inputs

    • Table (list) · optionalCSV, JSON
    • Table (list) · optionalCSV, JSON

    Workflow outputs

    • ArchiveZIP
    • TableCSV
    • TableCSV