Viscosity Models in NeqSim

NeqSim provides a comprehensive suite of methods for calculating fluid viscosity, ranging from standard empirical correlations to advanced corresponding states models and specialized pure-component equations. This document details the available models, their applications, and how to use them in simulations.

Overview

NeqSim viscosity models are organized into several categories:

Category Models Applicability
General Purpose LBC, PFCT, Friction Theory Hydrocarbon mixtures, reservoir fluids
Pure Component Muzny, MethaneModel, CO2Model, KTA Specialized high-accuracy correlations
Aqueous Systems Salt Water (Laliberté), polynom Brine and water solutions
Heavy Oils PFCT-Heavy-Oil Viscous crude oils, bitumen

Available Models

1. Lohrenz-Bray-Clark (LBC)

The LBC method is the industry-standard correlation for calculating viscosity of reservoir fluids. It combines a low-pressure gas viscosity term with a dense-fluid contribution based on reduced density.

2. Corresponding States Principle (CSP/PFCT)

The CSP method (referred to as PFCT in NeqSim) uses the Corresponding States Principle to relate mixture viscosity to a reference substance (typically Methane) at corresponding thermodynamic conditions.

3. Corresponding States Principle for Heavy Oil

A variant of the CSP model specifically tuned for heavy oil systems with additional terms to represent the viscous behavior of heavy fractions.

4. Friction Theory

The Friction Theory (f-theory) model links viscosity to the equation of state (EOS) by separating total viscosity into a dilute gas contribution and a residual friction contribution.

5. Chung Method (Gas Phase)

The Chung method is a corresponding states correlation for gas-phase viscosity based on the Chapman-Enskog kinetic theory with empirical corrections.

6. Lee-Gonzalez-Eakin Correlation

A simple empirical correlation for natural gas viscosity estimation.

Pure Component Models

7. Muzny Hydrogen Viscosity

High-accuracy correlation for pure hydrogen viscosity based on the work of Muzny et al. Includes dilute-gas, first-density, and higher-density contributions.

8. Muzny Modified Hydrogen Viscosity

Extended version of the Muzny correlation with additional correction terms for improved accuracy at specific conditions.

9. Methane Viscosity Model

Specialized correlation for pure methane viscosity using LBC as base with empirical correction terms.

10. CO2 Viscosity Model

Reference-quality correlation for pure carbon dioxide based on Laesecke et al. (JPCRD 2017).

11. KTA Helium Viscosity

Simple power-law correlation for pure helium viscosity.

12. KTA Modified Helium Viscosity

Extended KTA model with pressure-dependent corrections for improved high-pressure accuracy.

Aqueous System Models

13. Salt Water (Laliberté)

Viscosity correlation for aqueous salt solutions using the Laliberté (2007) model with erratum corrections.

14. Polynomial Liquid Viscosity

General liquid viscosity calculation using the Grunberg-Nissan mixing rule with pure-component correlations.

Usage in NeqSim

To use a specific viscosity model, you must set it on the PhysicalProperties object of a phase. This is typically done after creating the system but before performing calculations.

Java Example

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

public class ViscosityExample {
    public static void main(String[] args) {
        // 1. Create a system
        SystemInterface system = new SystemSrkEos(298.15, 100.0); // 298.15 K, 100 bar
        system.addComponent("methane", 0.5);
        system.addComponent("n-heptane", 0.5);
        
        // 2. Set mixing rule and initialize
        system.setMixingRule("classic");
        ThermodynamicOperations ops = new ThermodynamicOperations(system);
        ops.TPflash();

        // 3. Set Viscosity Model for a specific phase (e.g., oil/liquid)
        // Available options: "LBC", "PFCT", "PFCT-Heavy-Oil", "friction theory"
        
        // Example: Using LBC
        system.getPhase("oil").getPhysicalProperties().setViscosityModel("LBC");
        system.initProperties();
        double lbcViscosity = system.getPhase("oil").getViscosity();
        System.out.println("LBC Viscosity: " + lbcViscosity + " kg/(m*s)");

        // Example: Using PFCT
        system.getPhase("oil").getPhysicalProperties().setViscosityModel("PFCT");
        system.initProperties();
        double pfctViscosity = system.getPhase("oil").getViscosity();
        System.out.println("PFCT Viscosity: " + pfctViscosity + " kg/(m*s)");
        
        // Example: Using PFCT for Heavy Oil
        system.getPhase("oil").getPhysicalProperties().setViscosityModel("PFCT-Heavy-Oil");
        system.initProperties();
        double pfctHeavyViscosity = system.getPhase("oil").getViscosity();
        System.out.println("PFCT Heavy Oil Viscosity: " + pfctHeavyViscosity + " kg/(m*s)");

        // Example: Using Friction Theory
        system.getPhase("oil").getPhysicalProperties().setViscosityModel("friction theory");
        system.initProperties();
        double frictionViscosity = system.getPhase("oil").getViscosity();
        System.out.println("Friction Theory Viscosity: " + frictionViscosity + " kg/(m*s)");
    }
}

Tuning LBC dense-fluid parameters

The LBC implementation exposes the dense-fluid polynomial coefficients (“Whitson/Bray-Clark” $a_0 \dots a_4$ parameters) so you can tune the model against laboratory data. After selecting the "LBC" viscosity model, update the coefficients via setLbcParameters or setLbcParameter, then re-initialize properties to apply them:

system.getPhase(1).getPhysicalProperties().setViscosityModel("LBC");
system.initProperties();
double baseViscosity = system.getPhase(1).getViscosity();

double[] tunedCoefficients = new double[] {0.11, 0.030, 0.065, -0.045, 0.010};
system.getPhase(1).getPhysicalProperties().setLbcParameters(tunedCoefficients);
system.getPhase(1).getPhysicalProperties().setLbcParameter(2, 0.070); // tweak a single term
system.initProperties();
double tunedViscosity = system.getPhase(1).getViscosity();

System.out.println("Base viscosity:  " + baseViscosity);
System.out.println("Tuned viscosity: " + tunedViscosity);

Python Example (via JPype)

from neqsim.thermo import SystemSrkEos
from neqsim.thermodynamicoperations import ThermodynamicOperations

# 1. Create system
system = SystemSrkEos(298.15, 100.0)
system.addComponent("methane", 0.5)
system.addComponent("n-heptane", 0.5)
system.setMixingRule("classic")

# 2. Flash
ops = ThermodynamicOperations(system)
ops.TPflash()

# 3. Set Viscosity Model
# Note: Phase index 0 is usually gas, 1 is oil/liquid
system.getPhase(1).getPhysicalProperties().setViscosityModel("LBC")
system.initProperties()
print("LBC Viscosity:", system.getPhase(1).getViscosity(), "kg/(m*s)")

system.getPhase(1).getPhysicalProperties().setViscosityModel("PFCT")
system.initProperties()
print("PFCT Viscosity:", system.getPhase(1).getViscosity(), "kg/(m*s)")

system.getPhase(1).getPhysicalProperties().setViscosityModel("friction theory")
system.initProperties()
print("Friction Theory Viscosity:", system.getPhase(1).getViscosity(), "kg/(m*s)")

Mathematical Details

1. Lohrenz-Bray-Clark (LBC) Model

The LBC model calculates the viscosity of a fluid ($\eta$) as the sum of a low-pressure gas contribution ($\eta^*$) and a dense-fluid contribution ($\eta_{dense}$):

\[\eta = \eta^* + \frac{\eta_{dense}}{\xi_m}\]

where $\xi_m$ is the mixture viscosity parameter:

\[\xi_m = \frac{T_{cm}^{1/6}}{M_m^{1/2} P_{cm}^{2/3}}\]

The dense-fluid contribution is a function of the reduced density $\rho_r = \rho_m / \rho_{cm}$:

\[[(\eta - \eta^*) \xi_m + 10^{-4}]^{1/4} = a_0 + a_1 \rho_r + a_2 \rho_r^2 + a_3 \rho_r^3 + a_4 \rho_r^4\]

Mixing Rules:

2. Corresponding States Principle (CSP)

The CSP model uses the Corresponding States Principle to relate the viscosity of a mixture to that of a reference substance (typically Methane) at a corresponding state ($T_0, P_0$).

Viscosity Mapping: \(\eta_{mix}(T, P) = \eta_{ref}(T_0, P_0) \cdot F_{\eta} \cdot \frac{\alpha_{mix}}{\alpha_{ref}}\)

where the scaling factor $F_{\eta}$ is: \(F_{\eta} = \left(\frac{T_{cm}}{T_{c,ref}}\right)^{-1/6} \left(\frac{P_{cm}}{P_{c,ref}}\right)^{2/3} \left(\frac{M_{mix}}{M_{ref}}\right)^{1/2}\)

Corresponding State ($T_0, P_0$): The reference substance is evaluated at: \(T_0 = T \cdot \frac{T_{c,ref}}{T_{cm}} \cdot \frac{\alpha_{ref}}{\alpha_{mix}}\) \(P_0 = P \cdot \frac{P_{c,ref}}{P_{cm}} \cdot \frac{\alpha_{ref}}{\alpha_{mix}}\)

The parameter $\alpha$ accounts for deviations from the simple CSP and is typically a function of reduced density and molecular weight.

3. Friction Theory (f-theory)

The Friction Theory model separates the total viscosity into a dilute gas term ($\eta_0$) and a friction term ($\eta_f$):

\[\eta = \eta_0 + \eta_f\]

The friction term is derived from mechanical friction concepts applied to the van der Waals repulsive and attractive pressure terms of the Equation of State (EOS):

\[\eta_f = \kappa_r P_r + \kappa_a P_a + \kappa_{rr} P_r^2\]

where:

This approach ensures that the viscosity model is consistent with the thermodynamic behavior predicted by the EOS, making it robust across a wide range of conditions, including high pressure and near-critical regions.

4. Muzny Hydrogen Viscosity Model

The Muzny correlation for pure hydrogen viscosity follows a multi-term structure:

\[\eta = \eta_0 + \eta_1 \rho + \Delta\eta(\rho_r, T_r)\]

where:

The dilute-gas term is:

\[\eta_0 = \frac{0.021357 \sqrt{MT}}{\sigma^2 S^*}\]

where $S^*$ is the reduced collision integral and $\sigma = 0.297$ nm is the Lennard-Jones size parameter.

5. CO2 Viscosity Model (Laesecke JPCRD 2017)

The CO2 viscosity correlation consists of dilute-gas and residual terms:

\[\eta = \eta_0(T) + \Delta\eta(\rho, T)\]

The dilute-gas term follows an empirical correlation, and the residual term is expressed as:

\[\Delta\eta = \eta_{t,L} \left[ c_1 T_r \rho_r^3 + \frac{\rho_r^2 + \rho_r^\gamma}{T_r - c_2} \right]\]

where $T_t = 216.592$ K is the triple point temperature and $\rho_{t,L} = 1178.53$ kg/m³ is the triple point liquid density.

6. Salt Water (Laliberté Model)

The Laliberté mixture rule for aqueous salt solutions:

\[\eta_m = \eta_w^{w_w} \prod_i \eta_i^{w_i}\]

where $\eta_w$ is pure-water viscosity and $\eta_i$ are solute viscosities:

\[\eta_i = \frac{\exp\left[\frac{\nu_1(1-w_w)^{\nu_2} + \nu_3}{\nu_4 t + 1}\right]}{\nu_5(1-w_w)^{\nu_6} + 1}\]

with $w_w$ = water mass fraction and $t$ = temperature in °C.

Quick Reference Table

Model Keyword Applicability Phase Multi-Component
"LBC" Hydrocarbons, reservoir fluids Gas/Liquid Yes
"PFCT" Light-medium hydrocarbons Gas/Liquid Yes
"PFCT-Heavy-Oil" Heavy oils, bitumen Liquid Yes
"friction theory" General fluids, EOS-consistent Gas/Liquid Yes
"polynom" Liquids with database parameters Liquid Yes
"Muzny" Pure hydrogen Gas/Liquid No
"Muzny_mod" Pure hydrogen (extended) Gas/Liquid No
"MethaneModel" Pure methane Gas/Liquid No
"CO2Model" Pure CO2 Gas/Liquid No
"KTA" Pure helium Gas No
"KTA_mod" Pure helium (extended) Gas No
"Salt Water" Brine, salt solutions Liquid Yes (aqueous)

Additional Examples

Using Pure Component Models

// Pure Hydrogen Viscosity
SystemInterface h2System = new SystemSrkEos(300.0, 50.0);
h2System.addComponent("hydrogen", 1.0);
h2System.setMixingRule("classic");
ThermodynamicOperations h2Ops = new ThermodynamicOperations(h2System);
h2Ops.TPflash();

h2System.getPhase(0).getPhysicalProperties().setViscosityModel("Muzny");
h2System.initProperties();
System.out.println("H2 Viscosity (Muzny): " + h2System.getPhase(0).getViscosity() + " Pa·s");

// Pure CO2 Viscosity
SystemInterface co2System = new SystemSrkEos(350.0, 100.0);
co2System.addComponent("CO2", 1.0);
co2System.setMixingRule("classic");
ThermodynamicOperations co2Ops = new ThermodynamicOperations(co2System);
co2Ops.TPflash();

co2System.getPhase(0).getPhysicalProperties().setViscosityModel("CO2Model");
co2System.initProperties();
System.out.println("CO2 Viscosity (Laesecke): " + co2System.getPhase(0).getViscosity() + " Pa·s");

Salt Water Viscosity

// Brine viscosity calculation
SystemInterface brine = new SystemSrkCPAstatoil(323.15, 10.0);
brine.addComponent("water", 0.95);
brine.addComponent("NaCl", 0.05);
brine.setMixingRule(10); // CPA mixing rule

ThermodynamicOperations brineOps = new ThermodynamicOperations(brine);
brineOps.TPflash();

// Set Laliberté salt water model
brine.getPhase("aqueous").getPhysicalProperties().setViscosityModel("Salt Water");
brine.initProperties();
System.out.println("Brine Viscosity: " + brine.getPhase("aqueous").getViscosity() + " Pa·s");

Troubleshooting

Common Issues

  1. “Model only supports PURE X” error: Pure-component models (Muzny, CO2Model, MethaneModel, KTA) only work with single-component systems. Use LBC or PFCT for mixtures.

  2. Unexpected viscosity values: Ensure initProperties() is called after setting the viscosity model and after any flash calculations.

  3. Phase selection: Use getPhase("oil"), getPhase("gas"), or getPhase("aqueous") to select the correct phase, or use phase index (0, 1, 2).

  4. Heavy oil predictions too low: Try "PFCT-Heavy-Oil" or tune LBC parameters using setLbcParameters().

References

  1. Lohrenz, J., Bray, B.G., and Clark, C.R., “Calculating Viscosities of Reservoir Fluids from Their Compositions”, JPT, 1964.
  2. Pedersen, K.S., and Fredenslund, A., “An Improved Corresponding States Model for the Prediction of Oil and Gas Viscosities”, Chemical Engineering Science, 1987.
  3. Quiñones-Cisneros, S.E., and Deiters, U.K., “Generalization of the Friction Theory for Viscosity Modeling”, J. Phys. Chem. B, 2006.
  4. Muzny, C.D., et al., “Correlation for the Viscosity of Normal Hydrogen”, J. Chem. Eng. Data, 2013.
  5. Laesecke, A., and Muzny, C.D., “Reference Correlation for the Viscosity of Carbon Dioxide”, JPCRD, 2017.
  6. Laliberté, M., “Model for Calculating the Viscosity of Aqueous Solutions”, Ind. Eng. Chem. Res., 2007.
  7. Lee, A.L., Gonzalez, M.H., and Eakin, B.E., “The Viscosity of Natural Gases”, SPE-1340-PA, 1966.
  8. Chung, T.H., et al., “Generalized Multiparameter Correlation for Nonpolar and Polar Fluid Transport Properties”, Ind. Eng. Chem. Res., 1988.