# Wobbe number

The Wobbe number, or Wobbe index, is a description of a fuel gas (or mixture of gases), used in deciding whether that gas can be substituted for another in a particular burner. For example, can propane be used in a kitchen range made to burn natural gas? The Wobbe Index is sometimes called the Interchangeability Factor.¹ Symbol, WN or WI.²

The Wobbe number is named for the Italian engineer Goffredo Wobbe, who in 1926 published a paper³ defining a measure of fuel gas “quality”, with the idea that fuels of the same quality would be interchangeable.

The heat obtained when a gas is burned is directly proportional to that gas's heating value. Gases have different heating values; burning a molecule of butane will yield about ten times more heat than burning a molecule of hydrogen. Heating values are expressed as the amount of heat from burning a defined quantity of a gas (for example, a cubic foot) at a defined pressure and temperature. Pressure and temperature are important because they affect how many molecules are in that cubic foot. As a practical matter, gas workers had found that substituting one gas for another with the same heating value may not work. The substitute often did not provide the same amount of heat, either too much or too little. This was the problem Wobbe addressed.

The amount of heat provided by a burner depends on the gas's heating value, but it also depends, obviously, on the amount of gas burned. A butane lighter doesn't provide much heat, because although the butane has a high heating value, it is fed to the flame through a teeny-tiny tube. To create the measure of interchangeability that he sought, Wobbe needed a way to use the properties of a gas to predict how much of it could reach a flame.

On a gas kitchen range, the gas is fed to the flame through small holes in the burners. Small holes are found in burners in all sorts of uses. Wobbe got the idea that how a gas behaved when forced through a small hole could suggest the rate at which that gas could be supplied to a flame. The denser the gas, the slower the rate at which it flows through a small hole. However, the relationship between the flow rate and density is not a linear one, it is exponential. If the flow rate is graphed against density, the result is a curve, not a straight line. Wobbe found that using the square root of the density provided a better description of the flow rate than density. Or, to put it all more precisely, if a fuel gas is fed through a fixed hole at a fixed pressure, the relative mass flow rate of the gas is approximately inversely proportional to the square root of the gas's specific gravity (its density relative to air).

The measure Wobbe created is a ratio. It has two parts. One is the heating value of the gas, representing the potential heat produced by combustion. The second is the square root of the specific gravity, representing the supply of gas. The ratio of part one to part two is the Wobbe Index.

In concept, the Wobbe index takes into account not only the volumetric energy value of the gas, but also the rate at which molecules of that gas will be delivered through the burner. The usefulness of the Wobbe number is that in a burner where gases pass through a hole of a fixed size, gases and gas mixtures that have the same Wobbe number will deliver roughly the same amount of heat.

In the United States, the heating value is measured in Btu per standard cubic foot (scf).

Differing definitions of an scf exist, but for fuel gases in the U.S., a standard cubic foot is 1 cubic foot of gas at 60°F (15.6°C) and 14.73 pounds per square inch absolute. In Canada, a pressure of 101.6 kilopascals is specified. It is important to list the temperature and pressure being used as standard, since many standards are used worldwide.

Notice that the scf (and the normal cubic meter Nm³ and standard cubic meter Sm3 described below) are not units of volume. Because they specify temperature and pressure, for any particular gas they are a measure of quantity of matter. As a result, converting standard cubic feet to normal cubic meters is not the same as converting cubic feet to cubic metres (0.0283168) since the standard temperature and pressure used can be different.

In the rest of the world, the heating value is measured in

The expression Nm³ or Nm3 stands for Normal cubic meter (nothing to do with newtons) A Normal cubic meter is a cubic meter of gas at a temperature of 0°C at 101.325 kilopascals absolute (DIN 1343). A standard cubic meter has the same pressure, but a temperaure of 15deg;C (ISO 13443:1996). (In Canada, for example, a normal cubic meter is a cubic meter at at 15°C at 101.325 kPaA.)

Which set of units is being used is usually obvious from the great difference in the values. For example, using SI units the Wobbe number for methane is 50.7. Pure methane has a Wobbe number of 1363; natural gas as piped to homes in the United States typically has a Wobbe number between 1310 and 1390.

Fuel High heating value
MJ/Sm3
MJ/Nm3 btu/scf
hydrogen 45.5   1220
methane 49.9 53.28 1339
ethane 63.6 68.19 1708
ethylene   63.82
natural gas 46-52 53.72 1235-1396
propane 74.8 81.07 2008
propylene   77.04
n-butane 84.4 92.32 2266
iso-butane   91.96
propylene   77.04
pentane 92.5   2482
butylene-1   88.46
LPG   86.64
acetylene 57.0   1531
carbon monoxide
LNG 52.8   1417

The Wobbe number is sometimes said to be dimensionless, but it is not, as a glance at the fraction shows. The denominator is dimensionless. The numerator, however, has the same dimensions as heating value, and divided by one, retains those dimensions. Nonetheless a Wobbe number is often given without units, because:
a) People tend to confuse the Wobbe number with heating value. Showing the units encourages such confusion.
b) The only use of the Wobbe number of a gas is to see if it is bigger or smaller than the Wobbe numbers of other gases, calculated in the same way. In this comparison, the units used in the original measurements are irrelevant.

The Wobbe number is sometimes given as a pair of numbers, the first based on the high heating value of the gas, and the second on its low heating value. The high heating value includes the heat recovered by condensing the products of combustion, for example, in a condensing home furnace. The low heating value does not include the energy lost with the products of combustion, for example, in an oven in a kitchen range.

1. NGC+ Interchangeability Work Group.
White Paper on Natural Gas Interchangeability and Non-Combustion End Use. February 28, 2005, page 7.

2. International Gas Union and BP.
Guidebook to Gas Interchangeability and Gas Quality. 2011.
symbol, page 146.

3. Goffredo Wobbe.
La definizione della qualità del gas.
L'industria del gas e degli acquedotti, vol 15, no. 11, Rome, 30 November 1926.
Pages 165-172.

ASTM D 1945 (American Gas Association Bulletin No. 36)

Alternatives to the Wobbe number include the Weaver [email protected] and the AGA Bulletin 36 index.

@. Elmer R. Weaver.
Research Paper 2193
Formulas and Graphs for Representing the Interchangeability of Fuel Gases.
Journal of Research of the National Bureau of Standards, Vol. 46, No. 3, March 1951.

## examples of use

Sweden gets much of its fuel gas from the Netherlands. It is also very interested in encouraging local production of biogas. The Swedish biogas has a much lower Wobbe number than the Dutch natural gas, and so propane is added to the biogas to increase its Wobbe number to approximate that of the Dutch gas.

T. Q. Frandsen, L. Rodhe, A. Baky, M. Edström, I. Sipilä, ??, K., S.L. Petersen, K. Tybirk.
Best Available Technologies for Pig Manure Biogas Plants in the Baltic Sea Region.
Stockholm: Baltic Sea 2020, 2011.

## Modified Wobbe Number

General Electric, a major manufacturer of gas turbines, used a modified Wobbe number in recommending fuels for its turbines. In addition to heating value and density, it took into account temperature. The specific gravity is multiplied by the temperature, before taking the square root. The lower heating value is used, temperature is in kelvin.

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