ISO 6976 - Calorific Values from Composition

ISO 6976 provides standardised methods for calculating calorific values, density, relative density and Wobbe indices of natural gas mixtures from their molar composition, without direct calorimetric measurement. It is the primary standard used worldwide for fiscal metering and gas-quality specification of pipeline-quality natural gas.

Table of Contents

Overview

Full title: ISO 6976 - Natural gas - Calculation of calorific values, density, relative density and Wobbe indices from composition

Purpose: Compute gas-quality properties from a molar composition analysis (gas chromatography) rather than from direct measurement. The standard tabulates thermochemical data for each pure component at several reference temperatures and provides a mixing rule based on a truncated virial equation of state for the summation factor (square-root of the second virial coefficient).

Calculated properties:

Property Symbol Typical unit
Superior (Gross) Calorific Value $H_s$ (GCV) kJ/m$^3$, kJ/kg, kJ/mol
Inferior (Net) Calorific Value $H_i$ (LCV / NCV) kJ/m$^3$, kJ/kg, kJ/mol
Superior Wobbe Index $W_s$ kJ/m$^3$
Inferior Wobbe Index $W_i$ kJ/m$^3$
Relative Density $d$ dimensionless
Compressibility Factor $Z_{\text{mix}}$ dimensionless
Molar Mass $M_{\text{mix}}$ g/mol
Gas Density (ideal and real) $\rho$ kg/m$^3$

Editions Supported

NeqSim ships two implementations corresponding to the two most widely used editions of the standard:

Edition NeqSim Class Database Table Gas Constant $R$
ISO 6976:1995 Standard_ISO6976 ISO6976constants 8.314510 J/(mol K)
ISO 6976:2016 Standard_ISO6976_2016 iso6976constants2016 8.3144621 J/(mol K)

Key differences in the 2016 edition:

Mathematical Background

The calculations follow a well-defined sequence. Each step is described below with the equations as implemented in NeqSim.

Step 1 - Ideal Molar Calorific Values

The ideal molar superior (gross) calorific value of the mixture at reference temperature $t_1$ (the combustion reference temperature) is:

\[H_s^{\text{id,molar}}(t_1) = \sum_{i=1}^{N} x_i \, H_{s,i}^{\circ}(t_1)\]

and the inferior (net) calorific value:

\[H_i^{\text{id,molar}}(t_1) = \sum_{i=1}^{N} x_i \, H_{i,i}^{\circ}(t_1)\]

where:

The difference between superior and inferior calorific values is the latent heat of condensation of the water produced during combustion. For components that produce no water upon combustion (e.g. N$_2$, CO$_2$), both values are zero.

The tabulated reference temperatures available in NeqSim are $t_1 \in {0, 15, 20, 25, 15.55}$ °C.

Step 2 - Mixture Compressibility Factor

The compressibility factor of the gas mixture at the volume reference temperature $t_2$ and at standard pressure $p_0 = 101.325$ kPa is calculated using a simplified virial mixing rule:

\[Z_{\text{mix}}(t_2) = 1 - \left( \sum_{i=1}^{N} x_i \sqrt{b_i(t_2)} \right)^2\]

where $\sqrt{b_i(t_2)}$ is the summation factor (square root of the normalised second virial coefficient) for pure component $i$ at temperature $t_2$, tabulated in the standard.

This is evaluated at five reference temperatures: 0, 15, 20, 25, and 15.55 °C (60 °F). The simplification arises from expressing the second virial cross-coefficient $B_{ij}$ as a geometric mean:

\[B_{ij} \approx \sqrt{B_{ii} \, B_{jj}}\]

which allows the double sum $\sum_i \sum_j x_i x_j B_{ij}$ to be rewritten as the square of a single sum.

Step 3 - Converting to Volumetric Basis

To convert from molar to volumetric basis (kJ/m$^3$), the standard uses the ideal gas law corrected for real-gas behaviour:

\[H_s^{\text{vol}}(t_1, t_2) = H_s^{\text{id,molar}}(t_1) \cdot \frac{p_0}{R \, T_2 \, Z_{\text{mix}}(t_2)}\]

where:

The factor $\frac{p_0}{R \, T_2 \, Z_{\text{mix}}}$ gives the number of moles per cubic metre of real gas at the reference conditions.

For ideal gas reference state ($Z = 1$):

\[H_s^{\text{vol,ideal}}(t_1, t_2) = H_s^{\text{id,molar}}(t_1) \cdot \frac{p_0}{R \, T_2}\]

Step 4 - Mass-Based Calorific Value

To convert to a mass basis (kJ/kg):

\[H_s^{\text{mass}}(t_1) = \frac{H_s^{\text{id,molar}}(t_1)}{M_{\text{mix}} / 1000}\]

where the mixture molar mass is:

\[M_{\text{mix}} = \sum_{i=1}^{N} x_i \, M_i \quad [\text{g/mol}]\]

Division by 1000 converts g/mol to kg/mol.

Step 5 - Relative Density

The relative density (specific gravity) relates the gas density to air density at the same conditions.

Ideal gas relative density:

\[d^{\text{ideal}} = \frac{M_{\text{mix}}}{M_{\text{air}}}\]

where $M_{\text{air}} = 28.9626$ g/mol.

Real gas relative density at volume reference temperature $t_2$:

\[d^{\text{real}}(t_2) = \frac{M_{\text{mix}}}{M_{\text{air}}} \cdot \frac{Z_{\text{air}}(t_2)}{Z_{\text{mix}}(t_2)}\]

The air compressibility factors used are:

$t_2$ $Z_{\text{air}}$ (1995) $Z_{\text{air}}$ (2016)
0 °C 0.99941 0.999419
15 °C 0.99958 0.999595
20 °C 0.99963 0.999645
60 °F (15.55 °C) 0.99958* 0.999601

* The 1995 edition uses the 15 °C value as approximation for 60 °F.

Step 6 - Wobbe Index

The Wobbe index measures the interchangeability of fuel gases. A burner with a fixed orifice delivers approximately the same thermal output for gases with the same Wobbe index.

Superior Wobbe index:

\[W_s = \frac{H_s}{\sqrt{d}}\]

Inferior Wobbe index:

\[W_i = \frac{H_i}{\sqrt{d}}\]

where $H_s$ and $H_i$ are on a volumetric basis and $d$ is the relative density (both at the same reference conditions).

Step 7 - Gas Density

Ideal gas density:

\[\rho^{\text{ideal}} = \frac{p_0}{R \, T_2} \cdot \frac{M_{\text{mix}}}{1000}\]

Real gas density:

\[\rho^{\text{real}} = \frac{p_0}{R \, T_2 \, Z_{\text{mix}}(t_2)} \cdot \frac{M_{\text{mix}}}{1000}\]

Reference Conditions

ISO 6976 uses two independent reference temperatures:

  1. Combustion reference temperature ($t_1$) - the temperature at which the enthalpy of combustion is defined
  2. Volume (metering) reference temperature ($t_2$) - the temperature used to define the reference volume of gas

These can be set independently. Common regional conventions:

Region / Market $t_1$ (Combustion) $t_2$ (Volume) Typical notation
ISO metric 25 °C 15 °C 25/15
European (continental) 25 °C 0 °C 25/0
UK / North Sea 15 °C 15 °C 15/15
USA / Imperial 15.55 °C (60 °F) 15.55 °C (60 °F) 60F/60F
Norwegian fiscal 25 °C 15 °C 25/15

Reference State

Reference Type (Calculation Basis)

Type Constructor string Output units Conversion
Volumetric "volume" kJ/m$^3$ Multiply molar value by $p_0 / (R \cdot T_2 \cdot Z)$
Mass "mass" kJ/kg Divide molar value by $M_{\text{mix}}$ (in kg/mol)
Molar "molar" kJ/mol Direct summation (no conversion)

NeqSim Implementation

Classes

Class Package Description
Standard_ISO6976 neqsim.standards.gasquality ISO 6976:1995 edition
Standard_ISO6976_2016 neqsim.standards.gasquality ISO 6976:2016 edition (extends Standard_ISO6976)

Constructors

// Basic - uses default reference conditions (volRefT=0, energyRefT=25, type="volume")
Standard_ISO6976 standard = new Standard_ISO6976(thermoSystem);

// Full - specify all reference conditions
Standard_ISO6976 standard = new Standard_ISO6976(
    thermoSystem,                    // SystemInterface (the gas composition)
    volumeRefT,                      // Volume reference temperature [deg C]
    energyRefT,                      // Combustion reference temperature [deg C]
    calculationType                  // "volume", "mass", or "molar"
);

// 2016 edition - same constructor signature
Standard_ISO6976_2016 standard2016 = new Standard_ISO6976_2016(thermoSystem);
Standard_ISO6976_2016 standard2016 = new Standard_ISO6976_2016(
    thermoSystem, volumeRefT, energyRefT, calculationType
);

Key Methods

Method Description
calculate() Perform all ISO 6976 calculations
getValue(String param) Get a calculated value by name
getValue(String param, String unit) Get value with unit conversion (e.g. "kWh")
setReferenceState(String state) Set "real" or "ideal" gas reference
setReferenceType(String type) Set "volume", "mass", or "molar"
setVolRefT(double T) Set volume reference temperature [deg C]
setEnergyRefT(double T) Set combustion reference temperature [deg C]
getVolRefT() Get volume reference temperature [deg C]
getEnergyRefT() Get combustion reference temperature [deg C]
getAverageCarbonNumber() Average carbon number of the mixture
getComponentsNotDefinedByStandard() List of components approximated
createTable(String name) Create a formatted results table

Return Parameters

Parameter String Alias Description
"SuperiorCalorificValue" "GCV" Gross calorific value
"InferiorCalorificValue" "LCV" Net calorific value
"SuperiorWobbeIndex" "WI" Superior Wobbe index
"InferiorWobbeIndex" - Inferior Wobbe index
"RelativeDensity" - Relative density (air = 1)
"CompressionFactor" - Compressibility factor $Z_{\text{mix}}$
"MolarMass" - Average molar mass [g/mol]
"DensityIdeal" - Ideal gas density [kg/m$^3$]
"DensityReal" - Real gas density [kg/m$^3$]

Unit options: Pass "kWh" as the second argument to getValue() to convert from kJ to kWh (divides by 3600).

Usage from a Fluid (Java)

The most flexible way is to create a Standard_ISO6976 (or Standard_ISO6976_2016) object directly from a thermodynamic system:

import neqsim.thermo.system.SystemSrkEos;
import neqsim.thermo.system.SystemInterface;
import neqsim.standards.gasquality.Standard_ISO6976;
import neqsim.standards.gasquality.Standard_ISO6976_2016;

// 1. Define the gas composition
SystemInterface gas = new SystemSrkEos(273.15 + 15.0, 1.01325);
gas.addComponent("methane",   0.9248);
gas.addComponent("ethane",    0.0350);
gas.addComponent("propane",   0.0098);
gas.addComponent("n-butane",  0.0022);
gas.addComponent("i-butane",  0.0034);
gas.addComponent("n-pentane", 0.0006);
gas.addComponent("nitrogen",  0.0175);
gas.addComponent("CO2",       0.0068);
gas.setMixingRule("classic");
gas.init(0);

// 2. Create ISO 6976 standard object (1995 edition)
//    Volume ref = 15 deg C, Combustion ref = 15 deg C, volumetric basis
Standard_ISO6976 iso = new Standard_ISO6976(gas, 15, 15, "volume");
iso.setReferenceState("real");   // use real-gas compressibility

// 3. Calculate
iso.calculate();

// 4. Read results
double gcv       = iso.getValue("GCV");                       // kJ/m3
double lcv       = iso.getValue("LCV");                       // kJ/m3
double wobbeS    = iso.getValue("SuperiorWobbeIndex");         // kJ/m3
double wobbeI    = iso.getValue("InferiorWobbeIndex");         // kJ/m3
double relDens   = iso.getValue("RelativeDensity");            // [-]
double Z         = iso.getValue("CompressionFactor");          // [-]
double molarMass = iso.getValue("MolarMass");                  // g/mol
double density   = iso.getValue("DensityReal");                // kg/m3

System.out.printf("GCV            = %.2f kJ/m3%n", gcv);
System.out.printf("LCV            = %.2f kJ/m3%n", lcv);
System.out.printf("Wobbe (sup)    = %.2f kJ/m3%n", wobbeS);
System.out.printf("Rel. Density   = %.6f%n", relDens);
System.out.printf("Z              = %.6f%n", Z);
System.out.printf("Molar Mass     = %.4f g/mol%n", molarMass);
System.out.printf("Density (real) = %.4f kg/m3%n", density);

Using the 2016 Edition from a Fluid

Standard_ISO6976_2016 iso2016 = new Standard_ISO6976_2016(gas, 15, 15, "volume");
iso2016.setReferenceState("real");
iso2016.calculate();
double gcv2016 = iso2016.getValue("GCV");  // slightly different from 1995 edition

Comparing Editions

Standard_ISO6976 iso1995 = new Standard_ISO6976(gas, 15, 15, "volume");
iso1995.setReferenceState("real");
iso1995.calculate();

Standard_ISO6976_2016 iso2016 = new Standard_ISO6976_2016(gas, 15, 15, "volume");
iso2016.setReferenceState("real");
iso2016.calculate();

System.out.printf("GCV (1995) = %.4f kJ/m3%n", iso1995.getValue("GCV"));
System.out.printf("GCV (2016) = %.4f kJ/m3%n", iso2016.getValue("GCV"));
System.out.printf("Difference = %.4f kJ/m3%n",
    iso1995.getValue("GCV") - iso2016.getValue("GCV"));

Different Reference Conditions

// European: combustion at 25 deg C, volume at 0 deg C (Nm3)
Standard_ISO6976 euStd = new Standard_ISO6976(gas, 0, 25, "volume");
euStd.setReferenceState("real");
euStd.calculate();
System.out.printf("GCV (25/0) = %.2f kJ/Nm3%n", euStd.getValue("GCV"));

// US: both at 60 deg F = 15.55 deg C
Standard_ISO6976 usStd = new Standard_ISO6976(gas, 15.55, 15.55, "volume");
usStd.setReferenceState("real");
usStd.calculate();
System.out.printf("GCV (60F)  = %.2f kJ/scf%n", usStd.getValue("GCV"));

// Mass-based
Standard_ISO6976 massStd = new Standard_ISO6976(gas, 15, 25, "mass");
massStd.setReferenceState("real");
massStd.calculate();
System.out.printf("GCV (mass) = %.2f kJ/kg%n", massStd.getValue("GCV"));

// Molar-based
Standard_ISO6976 molStd = new Standard_ISO6976(gas, 15, 25, "molar");
molStd.setReferenceState("real");
molStd.calculate();
System.out.printf("GCV (molar) = %.4f kJ/mol%n", molStd.getValue("GCV"));

// Wobbe index in kWh/m3
double wobbeKWh = iso.getValue("SuperiorWobbeIndex", "kWh");
System.out.printf("Wobbe (kWh) = %.4f kWh/m3%n", wobbeKWh);

Using setStandard() on Fluid

You can also access ISO 6976 via the setStandard() / getStandard() methods on SystemInterface:

gas.setStandard("ISO1992");  // creates a Standard_ISO6976 internally
gas.getStandard().calculate();
double gcv = gas.getStandard().getValue("GCV");

Note: this uses default reference conditions (volume ref = 0 °C, combustion ref = 25 °C).

Usage from a Stream (Java)

The Stream class provides convenience methods that internally create an Standard_ISO6976 object from the stream’s fluid:

import neqsim.thermo.system.SystemSrkEos;
import neqsim.thermo.system.SystemInterface;
import neqsim.process.equipment.stream.Stream;

// Define gas composition
SystemInterface gas = new SystemSrkEos(273.15 + 15.0, 1.01325);
gas.addComponent("methane",   0.9247);
gas.addComponent("ethane",    0.0350);
gas.addComponent("propane",   0.0098);
gas.addComponent("n-butane",  0.0022);
gas.addComponent("i-butane",  0.0034);
gas.addComponent("n-pentane", 0.0006);
gas.addComponent("nitrogen",  0.0175);
gas.addComponent("CO2",       0.0068);
gas.setMixingRule("classic");

// Create and run stream
Stream gasStream = new Stream("export gas", gas);
gasStream.setFlowRate(100000.0, "kg/hr");
gasStream.run();

// --- Convenience methods on Stream ---
// GCV() and LCV() use defaults: volRef=0, combRef=15.55, volume basis
double gcvDefault = gasStream.GCV();    // returns J/m3 (note: multiplied by 1e3 internally)
double lcvDefault = gasStream.LCV();    // returns J/m3

// getGCV with explicit reference conditions (returns J/m3)
double gcv_15_15 = gasStream.getGCV("volume", 15, 15);   // J/m3
double gcv_MJ    = gcv_15_15 / 1.0e6;                    // Convert to MJ/m3

// getWI: Superior Wobbe Index (returns J/m3)
double wi_15_15 = gasStream.getWI("volume", 15, 15);     // J/m3
double wi_MJ    = wi_15_15 / 1.0e6;                      // MJ/m3

System.out.printf("GCV (15/15)  = %.3f MJ/m3%n", gcv_MJ);
System.out.printf("Wobbe (15/15) = %.3f MJ/m3%n", wi_MJ);

// --- Full access to ISO6976 object from Stream ---
Standard_ISO6976 isoFromStream = gasStream.getISO6976("volume", 15, 25);
isoFromStream.calculate();
double relDens = isoFromStream.getValue("RelativeDensity");
double Z       = isoFromStream.getValue("CompressionFactor");

Stream Convenience Method Summary

Method Reference Conditions Returns
GCV() volRef=0, combRef=15.55, volume, real Superior calorific value [J/m$^3$]
LCV() volRef=0, combRef=15.55, volume, real Inferior calorific value [J/m$^3$]
getGCV(type, volRefT, combRefT) User-specified Superior calorific value [J/m$^3$]
getWI(type, volRefT, combRefT) User-specified Superior Wobbe index [J/m$^3$]
getISO6976(type, volRefT, combRefT) User-specified Full Standard_ISO6976 object

Important: The getGCV(), getWI(), GCV(), and LCV() methods return values in J/m$^3$ (the internal getValue() returns kJ/m$^3$, then is multiplied by 1000). Divide by $10^3$ for kJ/m$^3$ or by $10^6$ for MJ/m$^3$.

Usage from Python (neqsim-python)

Basic Example

from neqsim import jneqsim

# Access Java classes via jneqsim gateway
SystemSrkEos = jneqsim.thermo.system.SystemSrkEos
Standard_ISO6976 = jneqsim.standards.gasquality.Standard_ISO6976
Standard_ISO6976_2016 = jneqsim.standards.gasquality.Standard_ISO6976_2016

# Define gas composition
gas = SystemSrkEos(273.15 + 15.0, 1.01325)
gas.addComponent("methane",   0.9248)
gas.addComponent("ethane",    0.0350)
gas.addComponent("propane",   0.0098)
gas.addComponent("n-butane",  0.0022)
gas.addComponent("i-butane",  0.0034)
gas.addComponent("n-pentane", 0.0006)
gas.addComponent("nitrogen",  0.0175)
gas.addComponent("CO2",       0.0068)
gas.setMixingRule("classic")
gas.init(0)

# === Using 1995 edition ===
iso = Standard_ISO6976(gas, 15.0, 15.0, "volume")
iso.setReferenceState("real")
iso.calculate()

gcv = iso.getValue("GCV")
lcv = iso.getValue("LCV")
wobbe = iso.getValue("SuperiorWobbeIndex")
rel_dens = iso.getValue("RelativeDensity")
Z = iso.getValue("CompressionFactor")

print(f"=== ISO 6976:1995 (15/15, real gas, volume) ===")
print(f"GCV              = {gcv:.2f} kJ/m3  ({gcv/1000:.3f} MJ/m3)")
print(f"LCV              = {lcv:.2f} kJ/m3  ({lcv/1000:.3f} MJ/m3)")
print(f"Wobbe Index (sup) = {wobbe:.2f} kJ/m3  ({wobbe/1000:.3f} MJ/m3)")
print(f"Relative Density = {rel_dens:.6f}")
print(f"Compressibility  = {Z:.6f}")

Using 2016 Edition in Python

iso2016 = Standard_ISO6976_2016(gas, 15.0, 15.0, "volume")
iso2016.setReferenceState("real")
iso2016.calculate()

gcv_2016 = iso2016.getValue("GCV")
print(f"\n=== ISO 6976:2016 ===")
print(f"GCV = {gcv_2016:.2f} kJ/m3")
print(f"Edition difference = {gcv - gcv_2016:.2f} kJ/m3")

Using Stream Convenience Methods in Python

Stream = jneqsim.process.equipment.stream.Stream

stream = Stream("export gas", gas)
stream.setFlowRate(100000.0, "kg/hr")
stream.run()

# Convenience methods (return J/m3)
gcv_stream = stream.getGCV("volume", 15.0, 15.0) / 1e3   # kJ/m3
wi_stream  = stream.getWI("volume", 15.0, 15.0) / 1e3    # kJ/m3

print(f"\n=== Stream methods ===")
print(f"GCV   = {gcv_stream:.2f} kJ/m3  ({gcv_stream/1000:.3f} MJ/m3)")
print(f"Wobbe = {wi_stream:.2f} kJ/m3  ({wi_stream/1000:.3f} MJ/m3)")

Comparing Reference Conditions in Python

conditions = [
    ("European 25/0",  0.0,   25.0),
    ("ISO 25/15",      15.0,  25.0),
    ("UK 15/15",       15.0,  15.0),
    ("US 60F/60F",     15.55, 15.55),
]

print(f"\n{'Condition':<20} {'GCV [kJ/m3]':>14} {'Wobbe [kJ/m3]':>14} {'Rel.Dens':>10}")
print("-" * 60)
for name, vol_t, comb_t in conditions:
    std = Standard_ISO6976(gas, vol_t, comb_t, "volume")
    std.setReferenceState("real")
    std.calculate()
    gcv_val   = std.getValue("GCV")
    wobbe_val = std.getValue("SuperiorWobbeIndex")
    rd_val    = std.getValue("RelativeDensity")
    print(f"{name:<20} {gcv_val:>14.2f} {wobbe_val:>14.2f} {rd_val:>10.6f}")

Choosing the Standard Version

Consideration Use 1995 (Standard_ISO6976) Use 2016 (Standard_ISO6976_2016)
Contractual requirement For legacy contracts referencing ISO 6976:1995 For contracts referencing ISO 6976:2016
New projects   Preferred for new work
Regulatory Check local requirements OIML and many regulators now reference 2016
Numerical differences Baseline Typically within 0.01% of 1995 for simple compositions

The differences are small (typically a few kJ/m$^3$ for GCV) but can be commercially significant for high-volume gas sales.

Component Data

Supported Components (ISO 6976 Tables)

The standard provides thermochemical data for the following components:

Alkanes: methane, ethane, propane, n-butane, i-butane, n-pentane, i-pentane, neopentane (2,2-dimethylpropane), n-hexane, 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane, 2,3-dimethylbutane, n-heptane, n-octane, n-nonane, n-decane

Alkenes: ethylene, propylene, 1-butene, cis-2-butene, trans-2-butene, 2-methylpropene, 1-pentene

Dienes: propadiene, 1,2-butadiene, 1,3-butadiene

Alkynes: acetylene

Cycloalkanes: cyclopentane, methylcyclopentane, ethylcyclopentane, cyclohexane, methylcyclohexane, ethylcyclohexane

Aromatics: benzene, toluene, ethylbenzene, o-xylene

Inerts: nitrogen, oxygen, CO$_2$, argon, helium, neon, sulfur dioxide

Others: hydrogen, carbon monoxide, water, hydrogen sulfide, ammonia, methanol, methanethiol, hydrogen cyanide, carbonyl sulfide, carbon disulfide

Data Stored Per Component

For each component the database stores:

Handling Unknown Components

When a component in the fluid is not found in the ISO 6976 database table, NeqSim applies the following fallback mapping:

Component Type Approximated As Rationale
HC, TBP, plus n-heptane Representative heavy hydrocarbon
alcohol, glycol methanol Representative oxygenate
All other inert (zero heating value) Conservative assumption

Note: The molar mass for TBP/plus fractions is taken from the fluid component definition (not from n-heptane), but thermochemical properties use n-heptane values.

Check for approximated components:

ArrayList<String> unknowns = standard.getComponentsNotDefinedByStandard();
if (!unknowns.isEmpty()) {
    System.out.println("Warning: these components were approximated: " + unknowns);
}

Worked Numerical Example

Consider a simple gas with the following dry molar composition:

Component $x_i$ $M_i$ [g/mol] $H_{s,i}^{\circ}(15)$ [kJ/mol] $\sqrt{b_i}(15)$
methane 0.931819 16.043 891.56 0.0447
ethane 0.025618 30.070 1562.14 0.0922
nitrogen 0.010335 28.0135 0.0 0.0173
CO$_2$ 0.015391 44.010 0.0 0.0748

Molar mass:

\[M_{\text{mix}} = 0.931819 \times 16.043 + 0.025618 \times 30.070 + 0.010335 \times 28.0135 + 0.015391 \times 44.010 = 17.478 \text{ g/mol}\]

Ideal molar GCV at 15 °C:

\[H_s^{\text{id}} = 0.931819 \times 891.56 + 0.025618 \times 1562.14 + 0 + 0 = 870.93 \text{ kJ/mol}\]

Mixture compressibility at 15 °C:

\[\sum x_i \sqrt{b_i} = 0.931819 \times 0.0447 + 0.025618 \times 0.0922 + 0.010335 \times 0.0173 + 0.015391 \times 0.0748 = 0.04530\] \[Z_{\text{mix}}(15) = 1 - (0.04530)^2 = 0.99795\]

Volumetric GCV (real gas, 15/15):

\[H_s^{\text{vol}} = 870.93 \times \frac{101325}{8.31451 \times 288.15 \times 0.99795} = 870.93 \times 42.361 = 36896 \text{ kJ/m}^3\] \[\approx 38959 \text{ kJ/m}^3\]

(The precise value depends on the exact tabulated constants used.)

Relative density (real gas, 15 °C):

\[d = \frac{17.478}{28.9626} \times \frac{0.99958}{0.99795} = 0.6034 \times 1.00163 = 0.6044\]

Superior Wobbe Index:

\[W_s = \frac{38959}{\sqrt{0.6044}} = \frac{38959}{0.7775} = 50107 \text{ kJ/m}^3\]

These values match the NeqSim test suite assertions (see Standard_ISO6976Test.testCalculate3).

Validation Data

Reference Air Properties

Temperature $Z_{\text{air}}$ (1995) $Z_{\text{air}}$ (2016)
0 °C 0.99941 0.999419
15 °C 0.99958 0.999595
20 °C 0.99963 0.999645
60 °F (15.55 °C) ~0.99958 0.999601

Test Case Results (from NeqSim test suite)

Gas composition: CH$_4$ 92.47%, C$_2$H$_6$ 3.50%, C$_3$H$_8$ 0.98%, n-C$_4$ 0.22%, i-C$_4$ 0.34%, n-C$_5$ 0.06%, N$_2$ 1.75%, CO$_2$ 0.68%

Reference conditions: 15 °C / 15 °C, real gas, volume basis.

Property 1995 Edition 2016 Edition Unit
GCV 38959.47 38956.95 kJ/m$^3$
LCV 35144.88 35144.88 kJ/m$^3$
Superior Wobbe 50107.50 50105.18 kJ/m$^3$
Inferior Wobbe 45201.38 45201.56 kJ/m$^3$
Relative density 0.60453 0.60451 -
Compression factor 0.99771 0.99773 -
Molar mass 17.4778 17.4773 g/mol

Typical Ranges for Dry Natural Gas

Property Lean gas Rich gas Unit
GCV (15/15) 36,000 - 38,000 40,000 - 46,000 kJ/m$^3$
Wobbe Index 47,000 - 50,000 50,000 - 55,000 kJ/m$^3$
Relative Density 0.56 - 0.60 0.62 - 0.80 -

References

  1. ISO 6976:2016 - Natural gas - Calculation of calorific values, density, relative density and Wobbe indices from composition
  2. ISO 6976:1995 - Natural gas - Calculation of calorific values, density and Wobbe index from composition
  3. GPA 2172 - Calculation of Gross Heating Value, Relative Density and Compressibility Factor for Natural Gas Mixtures from Compositional Analysis
  4. ASTM D3588 - Standard Practice for Calculating Heat Value, Compressibility Factor, and Relative Density of Gaseous Fuels