Thermal Conductivity Models

This guide documents the thermal conductivity calculation methods available in NeqSim for gas, liquid, and multiphase systems.

Table of Contents

• Overview
• Available Models
  • PFCT (Pedersen)
  • Chung Method
  • Polynomial Correlation
  • CO₂ Reference
• Model Selection Guide
• Usage Examples

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Overview

Thermal conductivity ($\lambda$ or $k$) describes a material’s ability to conduct heat. It is essential for:

• Heat exchanger design
• Pipeline heat loss calculations
• Thermal simulation of process equipment

Units:

• Default output: W/(m·K) (Watts per meter-Kelvin)

Setting a conductivity model:

fluid.initPhysicalProperties();
fluid.getPhase("gas").getPhysicalProperties().setConductivityModel("Chung");
fluid.getPhase("oil").getPhysicalProperties().setConductivityModel("PFCT");

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Available Models

PFCT (Pedersen)

The Pedersen Corresponding States method uses methane as a reference fluid with molecular weight corrections.

Class: PFCTConductivityMethodMod86

Principle: Uses corresponding states with methane as reference:

\[\lambda_{mix} = \lambda_{ref}(T_0, P_0) \cdot \frac{\alpha_{mix}}{\alpha_0}\]

where:

• $\lambda_{ref}$ is methane thermal conductivity at corresponding conditions
• $T_0, P_0$ are the corresponding temperature and pressure
• $\alpha$ are molecular weight correction factors

Corresponding state mapping: \(T_0 = T \cdot \frac{T_{c,ref}}{T_{c,mix}} \cdot \frac{\alpha_0}{\alpha_{mix}}\)

\[P_0 = P \cdot \frac{P_{c,ref}}{P_{c,mix}} \cdot \frac{\alpha_0}{\alpha_{mix}}\]

Applicable phases: Gas, Oil

Best for:

• Petroleum mixtures
• Wide pressure-temperature ranges
• Systems with characterized fractions

Usage:

fluid.getPhase("oil").getPhysicalProperties().setConductivityModel("PFCT");

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Chung Method

The Chung method (1988) is a corresponding states correlation based on kinetic theory.

Class: ChungConductivityMethod

Equation (dilute gas): \(\lambda_0 = \frac{7.452 \eta_0 \Psi}{M}\)

where:

• $\eta_0$ is the dilute gas viscosity
• $\Psi$ is a correction factor
• $M$ is molar mass

The correction factor accounts for:

• Polyatomic structure
• Polar effects
• Association

Dense fluid correction: \(\lambda = \lambda_0 \cdot G_2(T^*, \rho^*) + B_1 q B_2\)

where $G_2$ and $B$ terms account for density effects.

Applicable phases: Primarily gas phase

Best for:

• Gas-phase calculations
• Polar gases
• As baseline correlation

Usage:

fluid.getPhase("gas").getPhysicalProperties().setConductivityModel("Chung");

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Polynomial Correlation

Uses component-specific polynomial coefficients from the database.

Class: Conductivity (in liquid package)

Equation: \(\lambda = A + BT + CT^2\)

where A, B, C are component-specific parameters.

Database columns: LIQUIDCONDUCTIVITY1, LIQUIDCONDUCTIVITY2, LIQUIDCONDUCTIVITY3

Mixing rule: \(\lambda_{mix} = \sum_i x_i \lambda_i\)

Applicable phases: Liquid

Best for:

• Pure components with available parameters
• Simple liquid mixtures

Usage:

fluid.getPhase("oil").getPhysicalProperties().setConductivityModel("polynom");

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CO₂ Reference

High-accuracy thermal conductivity for CO₂ based on the Vesovic et al. correlation.

Class: CO2ConductivityMethod

Coverage:

• Temperature: 200-1500 K
• Pressure: Up to 300 MPa
• All phases (gas, liquid, supercritical)

Best for:

• Pure CO₂ systems
• CCS applications
• Reference calculations

Usage:

fluid.getPhase("gas").getPhysicalProperties().setConductivityModel("CO2Model");

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Model Selection Guide

Application	Recommended Model	Notes
Petroleum mixtures	PFCT	Corresponding states with MW correction
Gas processing	Chung	Good for gases
Simple liquid mixtures	polynom	Uses database parameters
Pure CO₂	CO2Model	High accuracy
Wide P-T range	PFCT	Robust extrapolation
Polar systems	Chung	Includes polar corrections

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Usage Examples

Basic Conductivity Calculation

import neqsim.thermo.system.SystemSrkEos;
import neqsim.thermodynamicoperations.ThermodynamicOperations;

// Create and flash fluid
SystemInterface fluid = new SystemSrkEos(350.0, 50.0);
fluid.addComponent("methane", 0.85);
fluid.addComponent("ethane", 0.10);
fluid.addComponent("propane", 0.05);
fluid.setMixingRule("classic");

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.TPflash();

// Initialize physical properties
fluid.initPhysicalProperties();

// Get thermal conductivity
double gasConductivity = fluid.getPhase("gas").getThermalConductivity("W/mK");
System.out.println("Gas thermal conductivity: " + gasConductivity + " W/(m·K)");

Comparing Conductivity Models

String[] models = {"PFCT", "Chung"};

for (String model : models) {
    SystemInterface fluid = createFluid();
    ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
    ops.TPflash();
    fluid.initPhysicalProperties();
    
    fluid.getPhase("gas").getPhysicalProperties().setConductivityModel(model);
    fluid.initPhysicalProperties();
    
    double k = fluid.getPhase("gas").getThermalConductivity("W/mK");
    System.out.println(model + ": " + k + " W/(m·K)");
}

Conductivity vs Pressure

SystemInterface baseFluid = new SystemSrkEos(350.0, 10.0);
baseFluid.addComponent("methane", 1.0);
baseFluid.setMixingRule("classic");

double[] pressures = {10, 50, 100, 150, 200};  // bar

for (double P : pressures) {
    SystemInterface fluid = baseFluid.clone();
    fluid.setPressure(P, "bar");
    
    ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
    ops.TPflash();
    fluid.initPhysicalProperties();
    
    double k = fluid.getPhase(0).getThermalConductivity("W/mK");
    System.out.println("P=" + P + " bar: " + k + " W/(m·K)");
}

Two-Phase System

SystemInterface fluid = new SystemSrkEos(280.0, 30.0);
fluid.addComponent("methane", 0.5);
fluid.addComponent("n-pentane", 0.5);
fluid.setMixingRule("classic");
fluid.setMultiPhaseCheck(true);

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.TPflash();
fluid.initPhysicalProperties();

if (fluid.hasPhaseType("gas")) {
    System.out.println("Gas k: " + 
        fluid.getPhase("gas").getThermalConductivity("W/mK") + " W/(m·K)");
}
if (fluid.hasPhaseType("oil")) {
    System.out.println("Oil k: " + 
        fluid.getPhase("oil").getThermalConductivity("W/mK") + " W/(m·K)");
}

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Physical Background

Kinetic Theory (Dilute Gas)

For dilute gases, thermal conductivity is related to viscosity through:

\[\lambda = \frac{f \cdot \eta \cdot C_v}{M}\]

where:

• $f$ is the Eucken factor (typically 1.32 for monoatomic, 1.77 for polyatomic)
• $\eta$ is dynamic viscosity
• $C_v$ is heat capacity at constant volume
• $M$ is molar mass

Mixing Rules

For mixtures, thermal conductivity is typically calculated using:

Mass fraction weighting: \(\lambda_{mix} = \sum_i w_i \lambda_i\)

Molar weighting with interaction: \(\lambda_{mix} = \sum_i \sum_j \frac{x_i x_j \lambda_{ij}}{\sum_k x_k \phi_{ik}}\)

where $\lambda_{ij}$ is a combining rule and $\phi_{ik}$ is an interaction factor.

Pressure Effects

Thermal conductivity increases with pressure, particularly in dense fluids:

• At low pressures: $\lambda \approx \lambda_0(T)$
• At high pressures: $\lambda = \lambda_0 + \Delta\lambda(\rho)$

The PFCT method accounts for this through corresponding states mapping to reference fluid behavior.

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Temperature and Pressure Dependence

Gases

• Conductivity increases with temperature (~$T^{0.8}$)
• Weak pressure dependence at low-moderate pressures
• Significant increase at high pressures (dense gas)

Liquids

• Conductivity typically decreases with temperature
• Slight increase with pressure
• Water is an exception (increases with T up to ~130°C)

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References

1. Pedersen, K.S., et al. (1989). Thermal Conductivity of Crude Oils. Chem. Eng. Sci.
2. Chung, T.H., et al. (1988). Generalized Multiparameter Correlation. I&EC Res.
3. Vesovic, V., et al. (1990). The Transport Properties of Carbon Dioxide. J. Phys. Chem. Ref. Data.
4. Poling, B.E., et al. (2001). The Properties of Gases and Liquids, 5th Ed.