Examples of transport properties are viscosities, thermal conductivities, diffusion coefficients and thermal diffusion coefficients. The viscosity is a key property for flow of fluids in pipes or reservoirs. The thermal conductivity determines the rate of heat transfer. Diffusion and thermal diffusion are slower ways to transport components, e.g. in a reservoir due to concentration or temperature gradients.

GAS MIXTURES: The most accurate methodology to calculate transport properties of gases is kinetic gas theory, which allows the viscosities, thermal conductivities, diffusion coefficients and thermal diffusion coefficients of most components to be calculated within a few percent of experimental data.
LIQUID MIXTURES: Extended corresponding state theory is arguably the most accurate methodology to calculate the transport properties of liquid-phase mixtures. The theory can predict transport properties nearly within the experimental accuracy.

Here, we will provide a description of the transport property models that will be available in TP-Cloud.

The SuperTRAPP Method

SuperTRAPP is the default method for calculating viscosities and thermal conductivities in TP-Cloud

Overview

SuperTRAPP is a semi-empirical extended corresponding states model developed at the US National Institute of Standards and Technology (NIST) in the SUPERTRAPP program for predicting viscosity and thermal conductivity of pure fluids and mixtures. ¹, ²

It modifies the original TRAPP (TRAnsport Property Program) model approach ³ by adding “shape factors” and enhancements to better match experimental data over wide conditions, especially for hydrocarbon fluids. The SuperTRAPP model is based on the work by Klein and McLinden ⁴, and relies on accurate pure fluid models for viscosity and thermal conductivity.

Core concept

SuperTRAPP splits each transport property (viscosity, $\eta$ , or thermal conductivity, $\lambda$ ) into three contributions:

A dilute (gas) contribution, computed from kinetic theory or reference correlations
A residual contribution, scaled from a reference fluid via corresponding-states and shape corrections
A critical enhancement contribution, accounting for the increased viscosity and thermal conductivity in the critical region

Thus:

\eta(T,\rho) = \eta_{\text{dilute}}(T) + \Delta \eta_{\text{res}}(T,\rho) + \eta_{\text{crit}}(T,\rho)

\lambda(T,\rho) = \lambda_{\text{dilute}}(T) + \Delta \lambda_{\text{res}}(T,\rho) + \lambda_{\text{crit}}(T,\rho)

The residual part is scaled using reference fluid properties, reduced variables, and empirical shape factors that reflect molecular structure. This scaling refers to the The Extended Corresponding States (ECS) Principle.

The Extended Corresponding States (ECS) Principle

The extended corresponding states (ECS) principle expresses the residual reduced Helmholtz free energy and compressibility factor of a real fluid in terms of a conformal (reference) fluid through scaling (or shape) factors ( $f_j$ ) and ( $h_j$ ).

a^{\text{res}} \left( T, \rho \right) = a^{\text{res}} \left( \frac{T}{f_j}, \rho h_j \right)

Z \left( T, \rho \right) = Z \left( \frac{T}{f_j}, \rho h_j \right)

where:

$a^{\text{res}}$ is the residual reduced Helmholtz free energy,
$Z$ is the compressibility factor,
$f_j$ is the temperature scaling factor, and
$h_j$ is the density scaling factor.

The Third Shape Factor

In addition to $f_j$ and $h_j$ , a third shape factor $\Psi_j$ is used to relate transport properties such as viscosity and thermal conductivity to those of the reference fluid:

\Psi_j = \frac{\rho^0}{\rho h_j}

Here:

$\rho^0$ is the density at which the reference fluid residual viscosity is determined.
$\rho$ is the density of the real fluid being modeled.

This formulation enables the prediction of transport properties of complex fluids by scaling data from a well-characterized reference fluid (often nitrogen or R134A). The ECS method forms the theoretical basis of SuperTRAPP.

Mixtures

In applying SuperTRAPP to mixtures, the model uses:

Conformal (reduced) mapping of temperature and density to match each component to a reference fluid
Mixing rules for the residual contributions and shape factors
Cross-terms or interaction corrections addressing nonidealities

Accuracy & Limitations

Typical deviation is about ±5 % for many pure fluids and mixtures, though performance degrades for mixtures with large molecular size disparities.
For natural gas, SuperTRAPP is within ~3–6 % deviation.
It is less reliable in extreme conditions (very high pressure, near critical) or for strongly associating fluids.

References

Chichester, J. C.; Huber, M. L. Documentation and Assessment of the Transport Property Model for Mixtures Implemented in NIST REFPROP (Version 8.0). NIST IR 6650. 2008. ↩
Huber, M. L.; Lemmon, E. W.; Bell, I. H.; McLinden, M. O. The NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids. Ind. Eng. Chem. Res., 61, 2022. ↩
Ely, J. F.; Hanley, H. J. M. A Computer Program for the Prediction of Viscosity and Thermal Conductivity in Hydrocarbon Mixtures. NBS Technical Note 1039, National Bureau of Standards, Washington, D.C. 1981. ↩
Klein, S. A.; McLinden, M. O. and Laesecke, A., An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures, Int. J. Refrig., 20, 1997. ↩

Transport properties