Characterization and Pseudo-Components

Why characterization is needed

A petroleum plus fraction such as C7+ or C20+ represents material unresolved by detailed compositional analysis. It is not a single chemical compound. Characterization replaces that aggregate with a discrete distribution and then with a manageable set of pseudo-components for an equation of state.

The operations answer different questions:

1. splitting estimates a single-carbon-number-like distribution;
2. property characterization assigns density and EoS properties;
3. lumping combines contiguous cuts while preserving selected moments; and
4. fluid-model construction combines the pseudo-components with defined light components and interaction parameters.

Whitson and Brulé develop the shifted-gamma workflow in chapter 5 of Phase Behavior. Pedersen, Christensen, and Shaikh develop logarithmic splitting, property correlations, and lumping in chapter 5 (book DOI).

Moment constraints

For a plus fraction with total mole fraction \(z_+\), mean molar mass \(\overline{M}_+\), and discrete cuts \(N\),

\[ \sum_N z_N=z_+, \qquad \frac{\sum_N z_NM_N}{z_+}=\overline{M}_+. \]

A density assignment should also preserve the supplied bulk density under the chosen volume-mixing convention:

\[ \rho_+ = \frac{\sum_N z_NM_N} {\sum_N z_NM_N/\rho_N}. \]

These are conservation constraints, not model validation. Different distribution families can satisfy the same moments while giving different phase behavior.

Implemented split families

pedersen_logarithmic_split constructs a finite molar distribution while matching the specified plus-fraction mole and molar-mass balances. pedersen_density_split assigns a logarithmic carbon-number density trend and matches the specified bulk density.

whitson_gamma_split discretizes a shifted gamma distribution. Its final requested bin includes the remaining infinite tail, so truncating the nominal carbon-number labels does not discard the tail mass.

pedersen_cubic_properties then maps molar mass and density to EoS-specific critical temperature, critical pressure, and acentric factor. The SRK and PR coefficient sets are distinct; they must not be swapped.

Lumping

equal_weight_lump forms contiguous pseudo-components with approximately equal mass. It preserves total moles and mass, uses ideal-volume mixing for density, and can carry additional mass-weighted characterized properties.

A lumping scheme is part of the model definition. Changing boundaries changes critical properties, binary interactions, and phase behavior even if total plus-fraction mass is unchanged.

Runnable characterization example

"""Split, characterize, and lump a petroleum plus fraction."""

import torch

from torch_flash import (
    equal_weight_lump,
    pedersen_cubic_properties,
    pedersen_density_split,
    pedersen_logarithmic_split,
)

# SI units: the C20+ fraction has z+=0.00833 and M+=0.377 kg/mol.
split = pedersen_logarithmic_split(
    plus_mole_fraction=0.00833,
    plus_molar_mass=torch.tensor(0.377, dtype=torch.float64),
    first_carbon_number=20,
    max_carbon_number=80,
)
with_density = pedersen_density_split(
    split,
    plus_density=873.0,  # kg/m^3
    anchor_density=841.0,
    anchor_carbon_number=19,
)
pr_properties = pedersen_cubic_properties(with_density, "PR")
cuts = equal_weight_lump(
    with_density,
    groups=3,
    properties={
        "critical_temperature": pr_properties.critical_temperature,
        "critical_pressure": pr_properties.critical_pressure,
        "acentric_factor": pr_properties.acentric_factor,
    },
)

print("pseudo-component names =", cuts.names)
print("mole fractions =", cuts.mole_fractions)
print("molar masses [kg/mol] =", cuts.molar_masses)
print("densities [kg/m^3] =", cuts.densities)
torch.testing.assert_close(cuts.mole_fractions.sum(), split.total_mole_fraction)

The example uses only SI units:

• molar mass in kg/mol;
• density in kg/m3;
• critical temperature in K; and
• critical pressure in Pa.

The resulting LumpedDistribution contains pseudo-component names, carbon number bounds, mole fractions, molar masses, densities, and the supplied characterized properties. It is immutable scientific input for subsequent model construction.

Scientific and numerical cautions

• Prefer measured extended compositions when available; a correlation should not replace resolved measurements.
• Record the plus-fraction definition, measured moments, split family, truncation/tail convention, density anchor, EoS property correlation, and lump boundaries.
• Refit or validate binary interactions after changing characterization.
• Preserve mole, mass, and chosen volume moments numerically.
• Diagnose sensitivity to the number and placement of lumps.
• Label pseudo-components by their actual construction; do not present them as pure compounds.
• A fit to the same PVT data used to characterize the heavy end is calibration, not independent validation.