GERG-2008 and EOS-CG Equations of State

NeqSim exposes implementations of the GERG-2008 and EOS-CG equations of state, which are model families explicit in Helmholtz free energy. The published formulations target natural-gas and CCS (Carbon Capture and Storage) property calculations.

The current SystemGERG2008Eos and SystemEOSCGEos implementations do not advertise analytical composition, pressure, or temperature fugacity derivatives. Positive finite results from the examples below prove API execution and model selection only; they do not establish custody-transfer accuracy, published-range reproduction, or fitness for a particular engineering decision. Validate the selected mixture and operating envelope against controlled reference data before use.

1. Mathematical Framework

Both GERG-2008 and EOS-CG share the same fundamental mathematical structure. They are fundamental equations of state explicit in the dimensionless Helmholtz free energy $\alpha$.

The dimensionless Helmholtz energy $\alpha$ is separated into an ideal gas part $\alpha^0$ and a residual part $\alpha^r$:

\[\alpha(\delta, \tau, \bar{x}) = \frac{a(\rho, T, \bar{x})}{RT} = \alpha^0(\delta, \tau, \bar{x}) + \alpha^r(\delta, \tau, \bar{x})\]

Where:

$\delta = \rho / \rho_r$ is the reduced density.
$\tau = T_r / T$ is the inverse reduced temperature.
$\bar{x}$ is the vector of mole fractions.

Ideal Gas Contribution ($\alpha^0$)

The ideal gas part is determined from the ideal gas heat capacity of the mixture components:

\[\alpha^0(\delta, \tau, \bar{x}) = \sum_{i=1}^{N} x_i \left[ \alpha_{0i}^0(\delta, \tau) + \ln x_i \right]\]

Residual Contribution ($\alpha^r$)

The residual part accounts for intermolecular forces and real fluid behavior. It is typically expressed as a sum of polynomial and exponential terms fitted to high-accuracy experimental data:

\[\alpha^r(\delta, \tau, \bar{x}) = \sum_{i=1}^{N} x_i \alpha_{0i}^r(\delta, \tau) + \sum_{i=1}^{N-1} \sum_{j=i+1}^{N} x_i x_j F_{ij} \alpha_{ij}^r(\delta, \tau)\]

Published reference-EOS formulations can represent density, speed of sound, and heat capacity more directly than cubic equations of state such as SRK or PR. Accuracy from the NeqSim implementation remains mixture-, property-, and state-dependent and requires application-specific validation.

2. GERG-2008

Full Name: GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures. Authors: O. Kunz and W. Wagner (Ruhr-Universität Bochum). Standard: ISO 20765-2.

Application

GERG-2008 is the standard reference equation for natural gas transport, processing, and custody transfer. It covers 21 components typical of natural gas.

Supported Components (21)

Methane, Nitrogen, Carbon Dioxide, Ethane, Propane, Butanes, Pentanes, Hexane, Heptane, Octane, Nonane, Decane, Hydrogen, Oxygen, Carbon Monoxide, Water, Helium, Argon.

Usage in NeqSim

To use GERG-2008 in NeqSim, use the SystemGERG2008Eos class.

import org.apache.logging.log4j.LogManager;
import org.apache.logging.log4j.Logger;
import neqsim.thermo.system.SystemGERG2008Eos;
import neqsim.thermo.system.SystemInterface;
import neqsim.thermodynamicoperations.ThermodynamicOperations;

public final class GergExample {
  private static final Logger logger = LogManager.getLogger(GergExample.class);

  private GergExample() {}

  public static void main(String[] args) {
    SystemInterface fluid = new SystemGERG2008Eos(298.15, 10.0); // K, bara
    fluid.addComponent("methane", 0.9);
    fluid.addComponent("ethane", 0.1);
    fluid.createDatabase(true);
    fluid.setMixingRule("classic");

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

    double density = fluid.getPhase(0).getDensity_GERG2008();
    double[] properties = fluid.getPhase(0).getProperties_GERG2008();
    assert Double.isFinite(density) && density > 0.0 : "GERG density must be finite and positive";
    assert properties != null && properties.length > 0 : "GERG property vector must be populated";

    logger.info("GERG-2008 density: {} kg/m3", density);
  }
}

3. GERG-2008-H2 (Hydrogen Enhanced)

Full Name: Extension of the equation of state for natural gases GERG-2008 with improved hydrogen parameters. Authors: R. Beckmüller, M. Thol, I. Sampson, E.W. Lemmon, R. Span (Ruhr-Universität Bochum, NIST).

Application

GERG-2008-H2 is an extension of GERG-2008 with improved hydrogen binary interaction parameters. This extension is particularly important for:

Hydrogen-rich natural gas blends (power-to-gas applications)
Hydrogen transport in existing natural gas pipelines
CO₂-H₂ mixtures in CCS with hydrogen

Key Improvements

The GERG-2008-H2 model includes:

Updated binary reducing parameters for hydrogen with methane, nitrogen, CO₂, and other hydrocarbons
New departure function for N₂-H₂ (Model 8)
New departure function for CO₂-H₂ (Model 9)
Extended validation range for hydrogen-containing mixtures

Expected Differences from GERG-2008

Binary System	Typical Density Difference
CH₄-H₂	~0.1-0.25%
N₂-H₂	~0.05-0.5%
CO₂-H₂	~1-1.5% (largest)
C₂H₆-H₂	~0.5-0.8%

Differences increase with:

Higher hydrogen content
Higher pressure
Lower temperature

Usage in NeqSim

The GERG-2008-H2 model is available through SystemGERG2008Eos by enabling the hydrogen-enhanced mode:

import org.apache.logging.log4j.LogManager;
import org.apache.logging.log4j.Logger;
import neqsim.thermo.system.SystemGERG2008Eos;
import neqsim.thermo.util.gerg.GERG2008Type;
import neqsim.thermodynamicoperations.ThermodynamicOperations;

public final class Gerg2008H2Example {
  private static final Logger logger = LogManager.getLogger(Gerg2008H2Example.class);

  private Gerg2008H2Example() {}

  public static void main(String[] args) {
    SystemGERG2008Eos fluid = new SystemGERG2008Eos(300.0, 50.0); // K, bara
    fluid.addComponent("methane", 0.7);
    fluid.addComponent("hydrogen", 0.3);
    fluid.useHydrogenEnhancedModel();

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

    double density = fluid.getPhase(0).getDensity("kg/m3");
    assert Double.isFinite(density) && density > 0.0 : "H2-mixture density must be finite and positive";
    assert fluid.getGergModelType() == GERG2008Type.HYDROGEN_ENHANCED;
    assert fluid.isUsingHydrogenEnhancedModel();
    assert "GERG2008-H2-EOS".equals(fluid.getModelName());

    logger.info("GERG-2008-H2 density: {} kg/m3; model: {}", density, fluid.getModelName());
  }
}

API Methods

Method	Description
`useHydrogenEnhancedModel()`	Enable GERG-2008-H2 model
`setGergModelType(GERG2008Type.STANDARD)`	Use standard GERG-2008
`setGergModelType(GERG2008Type.HYDROGEN_ENHANCED)`	Use GERG-2008-H2
`getGergModelType()`	Get current model type
`isUsingHydrogenEnhancedModel()`	Check if H2 model is active

4. GERG-2008-NH3 (Ammonia Extended)

Full Name: Extension of the GERG-2008 equation of state with ammonia as a 22nd component. Authors: T. Neumann, M. Thol, E.W. Lemmon, R. Span (Ruhr-Universität Bochum, NIST); ammonia pure-fluid equation by K. Gao, J. Wu, E.W. Lemmon (NIST, Xi’an Jiaotong Univ.).

Application

GERG-2008-NH3 extends GERG-2008 to include ammonia (NH₃) as a fully integrated 22nd component. This is essential for:

Ammonia-based hydrogen energy carriers (green ammonia)
Ammonia co-firing in gas turbines
Ammonia refrigeration loops in LNG plants
CO₂-NH₃ mixtures in industrial processes

Key Features

Feature	Detail
Pure-fluid EOS	Full 20-term Gao et al. (2020) equation: 8 power + 10 Gaussian + 2 GaoB terms
Critical properties	$T_c = 405.56$ K, $\rho_c = 13.696$ mol/L (Gao et al.)
Ideal gas	Planck-Einstein terms with $v = [2.224, 3.148, 0.9579]$ and $\theta = [1646, 3965, 7231]$ K
Binary interactions	Reducing parameters and GBS departure functions for NH₃ with CH₄, N₂, CO₂, H₂O, H₂, and other GERG components (Neumann et al. 2020)
Published formulation	Gao and Neumann reference data cover ammonia-containing states; NeqSim results require application-specific validation

Usage in NeqSim

The GERG-2008-NH3 model is available through SystemGERG2008Eos by enabling the ammonia-extended mode:

import org.apache.logging.log4j.LogManager;
import org.apache.logging.log4j.Logger;
import neqsim.thermo.system.SystemGERG2008Eos;
import neqsim.thermo.util.gerg.GERG2008Type;
import neqsim.thermodynamicoperations.ThermodynamicOperations;

public final class Gerg2008NH3Example {
  private static final Logger logger = LogManager.getLogger(Gerg2008NH3Example.class);

  private Gerg2008NH3Example() {}

  public static void main(String[] args) {
    SystemGERG2008Eos fluid = new SystemGERG2008Eos(400.0, 50.0); // K, bara
    fluid.addComponent("nitrogen", 0.02);
    fluid.addComponent("methane", 0.80);
    fluid.addComponent("ammonia", 0.18);
    fluid.useAmmoniaExtendedModel();

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

    double density = fluid.getPhase(0).getDensity("kg/m3");
    assert Double.isFinite(density) && density > 0.0 : "NH3-mixture density must be finite and positive";
    assert fluid.getGergModelType() == GERG2008Type.AMMONIA_EXTENDED;
    assert fluid.isUsingAmmoniaExtendedModel();
    assert "GERG2008-NH3-EOS".equals(fluid.getModelName());

    logger.info("GERG-2008-NH3 density: {} kg/m3; model: {}", density, fluid.getModelName());
  }
}

API Methods

Method	Description
`useAmmoniaExtendedModel()`	Enable GERG-2008-NH3 model
`setGergModelType(GERG2008Type.AMMONIA_EXTENDED)`	Enable GERG-2008-NH3 model (enum form)
`isUsingAmmoniaExtendedModel()`	Check if NH3 model is active
`getModelName()`	Returns `"GERG2008-NH3-EOS"` when NH3 model is active

5. EOS-CG

Full Name: EOS-CG-2021: a Helmholtz energy equation of state for CCS mixtures. Authors: Tobias Neumann, Stefan Herrig, Ian Bell, Robin Beckmüller, Eric W. Lemmon, Monika Thol, and Roland Span.

Application

EOS-CG is an extension of the GERG framework designed for Carbon Capture and Storage (CCS) and combustion gas applications. It includes additional components found in CO2-rich transport streams and impurities relevant to CCS.

EOS-CG-2021 component coverage

The EOS-CG-2021 publication defines a 16-component CCS model: CO₂, water, N₂, O₂, Ar, CO, H₂, CH₄, H₂S, SO₂, monoethanolamine (MEA), diethanolamine (DEA), HCl, Cl₂, NH₃, and methyl diethanolamine (MDEA). NeqSim keeps the GERG-style hydrocarbon slots for compatibility while refreshing the EOS-CG reducing-parameter table and adding MDEA as an EOS-CG component.

Recent updates refreshed the EOS-CG component tables with the EOS-CG-2021 gas constant, MDEA pure-fluid parameters, and binary reducing parameters, improving consistency with the current CCS-mixture model.

The CO2/SO2 mixture example and numerical validation boundary document the initialization-order repair for issue #3702. With that repair, the 95 mol% CO2 / 5 mol% SO2 flash at 298.15 K and 50 bara converges to gas and liquid; the earlier density-root limitation applies to versions without this repair. The linked example checks each phase’s pressure and the component inventories.

For pure-component EOS-CG volume–energy flashes, the saturation-volume stability check requires distinct, physically ordered roots: vapor molar volume must exceed liquid molar volume. Inverted or coalesced numerical roots cannot establish a stable single phase. The solver attempts a saturation-line solution and throws IllegalStateException if neither route meets the volume and energy specifications. EOS-CG refreshes temperature-dependent Helmholtz terms for every temperature change, including the small steps used near saturation. Reusing cached terms across successive sub-1e-7 K changes can otherwise make properties depend on the iteration history. The reference-EOS liquid-density root is refined to a pressure residual of max(1e-9 kPa, 1e-11 * abs(pressure in kPa)), so density roundoff does not dominate saturation-line volume closure. The VU solver retains its 1e-8 relative volume and energy acceptance tolerances.

Usage in NeqSim

To use EOS-CG in NeqSim, use the SystemEOSCGEos class. This introductory example uses pure CO2 gas at 298.15 K and 10 bara, also covered by the repository’s CO2 density regression. Mixture flashes require separate convergence and accuracy validation for the intended composition and operating range.

The previously shown 95 mol% CO2 / 5 mol% SO2 flash at 298.15 K and 50 bara fails density-root convergence in the current implementation. The reproducible limitation is tracked in issue #3702.

import org.apache.logging.log4j.LogManager;
import org.apache.logging.log4j.Logger;
import neqsim.thermo.system.SystemEOSCGEos;
import neqsim.thermo.system.SystemInterface;
import neqsim.thermodynamicoperations.ThermodynamicOperations;

public final class EosCgExample {
  private static final Logger logger = LogManager.getLogger(EosCgExample.class);

  private EosCgExample() {}

  public static void main(String[] args) {
    SystemInterface fluid = new SystemEOSCGEos(298.15, 10.0); // K, bara
    fluid.addComponent("CO2", 1.0);
    fluid.createDatabase(true);

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

    double density = fluid.getPhase(0).getDensity_EOSCG();
    assert Double.isFinite(density) && density > 0.0 : "EOS-CG density must be finite and positive";

    logger.info("EOS-CG density: {} kg/m3", density);
  }
}

6. Literature References

GERG-2008: Kunz, O., & Wagner, W. (2012). The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures: An Expansion of GERG-2004. Journal of Chemical & Engineering Data, 57(11), 3032–3091.
GERG-2008-H2: Beckmüller, R., Thol, M., Sampson, I., Lemmon, E.W., & Span, R. (2022). Extension of the equation of state for natural gases GERG-2008 with improved hydrogen parameters. Fluid Phase Equilibria, 557, 113411.
EOS-CG: Gernert, J., & Span, R. (2016). EOS-CG: A Helmholtz energy equation of state for combustion gases and CCS mixtures. The Journal of Chemical Thermodynamics, 93, 274–293.
EOS-CG-2021: Neumann, T., Herrig, S., Bell, I.H., Beckmüller, R., Lemmon, E.W., Thol, M., & Span, R. (2023). EOS-CG-2021: A Mixture Model for the Calculation of Thermodynamic Properties of CCS Mixtures. International Journal of Thermophysics, 44, 178.
MDEA Pure-Fluid EOS: Neumann, T., Baumhögger, E., Span, R., Vrabec, J., & Thol, M. (2022). Thermodynamic Properties of Methyl Diethanolamine. International Journal of Thermophysics, 43, 10.
GERG-2008-NH3: Neumann, T., Thol, M., Lemmon, E.W., & Span, R. (2020). Extension of the equation of state for natural gases (GERG-2008) with ammonia. Molecular Physics, 118(21–22), e1769856.
NH3 Pure-Fluid EOS: Gao, K., Wu, J., & Lemmon, E.W. (2020). A Helmholtz Energy Equation of State for Ammonia. International Journal of Thermophysics, 41, 68.