Viscosity Models

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

Table of Contents

• Overview
• Available Models
  • LBC (Lohrenz-Bray-Clark)
  • Friction Theory
  • PFCT (Pedersen)
  • Chung Method
  • Polynomial Correlation
  • Reference Fluid Methods
• Model Selection Guide
• Tuning Parameters
• Usage Examples

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Overview

Viscosity describes a fluid’s resistance to flow. NeqSim provides several viscosity models suitable for different applications:

Units:

• Default output: Pa·s (Pascal-seconds)
• Alternative: cP (centipoise), where 1 cP = 0.001 Pa·s

Setting a viscosity model:

fluid.initPhysicalProperties();
fluid.getPhase("gas").getPhysicalProperties().setViscosityModel("friction theory");
fluid.getPhase("oil").getPhysicalProperties().setViscosityModel("LBC");

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Available Models

LBC (Lohrenz-Bray-Clark)

The Lohrenz-Bray-Clark (1964) method is widely used in reservoir simulation. It combines a dilute gas correlation with a dense fluid polynomial correction.

Class: LBCViscosityMethod

Equation: \(\eta = \eta^* + \frac{(\eta_r - 0.0001)^4}{\xi}\)

where:

• $\eta^*$ is the dilute gas viscosity
• $\eta_r$ is a function of reduced density
• $\xi$ is the inverse viscosity parameter

The dense fluid contribution uses a polynomial: \(\eta_r = a_0 + a_1\rho_r + a_2\rho_r^2 + a_3\rho_r^3 + a_4\rho_r^4\)

Default parameters: {0.10230, 0.023364, 0.058533, -0.040758, 0.0093324}

Applicable phases: Gas, Oil

Best for:

• Reservoir simulation
• Light to medium oils
• Systems where tuning to lab data is available

Usage:

fluid.getPhase("oil").getPhysicalProperties().setViscosityModel("LBC");

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Friction Theory

The Quiñones-Cisneros and Firoozabadi (2000) friction theory relates viscosity to the repulsive and attractive pressure contributions from the equation of state.

Class: FrictionTheoryViscosityMethod

Equation: \(\eta = \eta_0 + \kappa_a P_a + \kappa_{aa} P_a^2 + \kappa_r P_r + \kappa_{rr} P_r^2\)

where:

• $\eta_0$ is the dilute gas viscosity (Chung correlation)
• $P_a$ is the attractive pressure from EoS
• $P_r$ is the repulsive pressure from EoS
• $\kappa$ are friction coefficients (EoS-dependent)

Applicable phases: Gas, Oil (any EoS-based phase)

Best for:

• Wide pressure/temperature ranges
• Near-critical conditions
• When using SRK or PR EoS

Automatic EoS detection: The method automatically selects SRK or PR constants based on the phase type.

Usage:

fluid.getPhase("oil").getPhysicalProperties().setViscosityModel("friction theory");

Custom constants (for other EoS):

FrictionTheoryViscosityMethod viscModel = 
    (FrictionTheoryViscosityMethod) fluid.getPhase("oil")
        .getPhysicalProperties().getViscosityModel();

// Set custom friction theory constants
viscModel.setFrictionTheoryConstants(kapac, kaprc, kaprrc, kapa, kapr, kaprr);

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PFCT (Pedersen)

The Pedersen Friction Corresponding States Theory uses methane as a reference fluid with shape factors for mixture calculations.

Classes:

• PFCTViscosityMethodMod86 - Standard Pedersen method (1987)
• PFCTViscosityMethodHeavyOil - Extended for heavy oils

Equation: \(\eta_{mix} = \eta_{ref} \cdot \frac{f_\eta \cdot \alpha_{mix}}{\alpha_0}\)

where:

• $\eta_{ref}$ is the reference fluid (methane) viscosity
• $f_\eta$ is the shape factor ratio
• $\alpha$ are molecular weight correction factors

Applicable phases: Gas, Oil

Best for:

• Petroleum mixtures with characterized fractions
• Heavy oil systems (use "PFCT-Heavy-Oil")
• Wide-range predictions

Usage:

// Standard Pedersen
fluid.getPhase("oil").getPhysicalProperties().setViscosityModel("PFCT");

// Heavy oil variant
fluid.getPhase("oil").getPhysicalProperties().setViscosityModel("PFCT-Heavy-Oil");

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Chung Method

The Chung method (1984, 1988) is a corresponding states method for dilute gas and dense fluid viscosity.

Class: ChungViscosityMethod

Equation (dilute gas): \(\eta_0 = \frac{40.785 F_c \sqrt{M T}}{\Omega_v V_c^{2/3}}\)

where:

• $F_c$ is the correction factor for polar/associating fluids
• $\Omega_v$ is the collision integral
• $V_c$ is critical volume
• $M$ is molar mass

Applicable phases: Primarily gas phase

Best for:

• Dilute gas mixtures
• Polar gases
• As baseline for other methods

Usage:

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

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Polynomial Correlation

Uses component-specific polynomial coefficients from the database.

Class: Viscosity (liquid), GasViscosity (gas)

Equation: \(\ln(\eta) = A + \frac{B}{T} + C\ln(T) + DT\)

where A, B, C, D are component-specific parameters from COMP database.

Database columns: LIQVISC1, LIQVISC2, LIQVISC3, LIQVISC4

Applicable phases: Primarily liquid

Best for:

• Pure components with available parameters
• Simple mixtures with mixing rules

Usage:

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

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Reference Fluid Methods

Specialized high-accuracy methods for specific fluids:

Methane (Reference)

Class: MethaneViscosityMethod

• Uses Setzmann & Wagner reference equation
• High accuracy for pure methane
• Used as reference in PFCT calculations

CO₂

Class: CO2ViscosityMethod

• Fenghour et al. correlation
• Covers gas, liquid, and supercritical regions

Hydrogen

Classes: MuznyViscosityMethod, MuznyModViscosityMethod

• High-accuracy hydrogen viscosity
• Important for hydrogen energy applications

Usage:

fluid.getPhase("gas").getPhysicalProperties().setViscosityModel("MethaneModel");
fluid.getPhase("gas").getPhysicalProperties().setViscosityModel("CO2Model");
fluid.getPhase("gas").getPhysicalProperties().setViscosityModel("Muzny");

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Model Selection Guide

Application	Recommended Model	Notes
Reservoir simulation	LBC	Tunable, industry standard
Wide P-T range	Friction Theory	Good near critical
Heavy oils	PFCT-Heavy-Oil	Extended for high MW
Characterized crudes	PFCT	Works with pseudo-components
Gas processing	Chung	Good for gases
Pure CO₂	CO2Model	High accuracy
Pure H₂	Muzny	Reference accuracy
Aqueous systems	Salt Water	Water correlation

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Tuning Parameters

LBC Parameter Tuning

The LBC method is commonly tuned to match laboratory viscosity data:

// Get current parameters
LBCViscosityMethod lbc = (LBCViscosityMethod) 
    fluid.getPhase("oil").getPhysicalProperties().getViscosityModel();

// Set all 5 parameters
double[] params = {0.1023, 0.023364, 0.058533, -0.040758, 0.0093324};
fluid.getPhase("oil").getPhysicalProperties().setLbcParameters(params);

// Or tune individual parameters
fluid.getPhase("oil").getPhysicalProperties().setLbcParameter(0, 0.105);

Tuning procedure:

1. Measure viscosity at multiple P-T conditions
2. Run flash and calculate properties
3. Adjust parameters to minimize error
4. Validate at other conditions

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Usage Examples

Basic Viscosity Calculation

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

// Create and flash fluid
SystemInterface fluid = new SystemSrkEos(350.0, 150.0);
fluid.addComponent("methane", 0.70);
fluid.addComponent("ethane", 0.10);
fluid.addComponent("propane", 0.05);
fluid.addComponent("n-heptane", 0.10);
fluid.addComponent("n-decane", 0.05);
fluid.setMixingRule("classic");

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

// Initialize physical properties
fluid.initPhysicalProperties();

// Get viscosities
double gasVisc = fluid.getPhase("gas").getViscosity("cP");
double oilVisc = fluid.getPhase("oil").getViscosity("cP");

System.out.println("Gas viscosity: " + gasVisc + " cP");
System.out.println("Oil viscosity: " + oilVisc + " cP");

Comparing Viscosity Models

String[] models = {"LBC", "friction theory", "PFCT"};

for (String model : models) {
    SystemInterface fluid = createFluid();
    ops.TPflash();
    fluid.initPhysicalProperties();
    
    fluid.getPhase("oil").getPhysicalProperties().setViscosityModel(model);
    fluid.initPhysicalProperties();
    
    double visc = fluid.getPhase("oil").getViscosity("cP");
    System.out.println(model + ": " + visc + " cP");
}

Viscosity vs Temperature

SystemInterface baseFluid = createFluid();
baseFluid.initPhysicalProperties();

double[] temps = {300, 320, 340, 360, 380, 400};  // K

for (double T : temps) {
    SystemInterface fluid = baseFluid.clone();
    fluid.setTemperature(T, "K");
    
    ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
    ops.TPflash();
    fluid.initPhysicalProperties();
    
    double visc = fluid.getPhase("oil").getViscosity("cP");
    System.out.println("T=" + (T-273.15) + "°C: " + visc + " cP");
}

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Mathematical Details

Dilute Gas Viscosity (Chapman-Enskog)

For dilute gases, viscosity is calculated from kinetic theory:

\[\eta_0 = \frac{5}{16} \frac{\sqrt{\pi m k_B T}}{\pi \sigma^2 \Omega^{(2,2)*}}\]

where:

• $m$ is molecular mass
• $\sigma$ is Lennard-Jones diameter
• $\Omega^{(2,2)*}$ is the collision integral

Mixing Rules

Most models use molar fraction-weighted mixing:

\[\eta_{mix} = \exp\left(\sum_i x_i \ln \eta_i\right)\]

or the more rigorous:

\[\eta_{mix} = \frac{\sum_i x_i \sqrt{M_i} \eta_i}{\sum_i x_i \sqrt{M_i}}\]

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References

1. Lohrenz, J., Bray, B.G., Clark, C.R. (1964). Calculating Viscosities of Reservoir Fluids from Their Compositions. JPT.
2. Quiñones-Cisneros, S.E., Firoozabadi, A. (2000). One Parameter Friction Theory. AIChE J.
3. Pedersen, K.S., et al. (1987). Viscosity of Crude Oils. Chem. Eng. Sci.
4. Chung, T.H., et al. (1988). Generalized Multiparameter Correlation for Nonpolar and Polar Fluid Transport Properties. I&EC Res.