 For cogeneration installations, the useful product can be mechanical energy, electrical energy and heat Credit: Emerson Process Management

Exhaust gas temperature and quantity can be indicators of process efficiency. In part three of a series of articles, Dr Jacob Klimstra explains how the in the exhaust gas affects the system efficiency of combustion installations.

Designers and users of combustion installations such as cogeneration systems, engines and boilers are always interested in the fuel efficiency of their installations. A good utilisation of the fuel energy often yields an economic optimum, and generally results in minimum emissions per unit of useful product.

For cogeneration installations, the useful product can be mechanical energy, electrical energy and heat such as hot air, hot water or steam. One can state that a low temperature of the exhaust gas normally means that the utilisation of the fuel, or in other words the fuel efficiency, is high. However, most fuel-consuming systems also have parasitic losses, such as radiation to the surroundings, auxiliary equipment such as pumps and ventilators as well as incomplete combustion. Here we will ignore the parasitic losses and concentrate on the usefulness of the exhaust gas temperature and quantity as indicators of the process efficiency. Figure 1. Representation of a fuel-using process having a useful product such as electricity and heat as well as losses via the exhaust gas and parasitic loads.

## Energy stored in fuels

The amount of energy stored in a fuel is generally called the calorific value of the fuel. This calorific value can be expressed in energy per unit of mass such as MJ/kg or in energy per unit of volume, such as MJ/m3. The calorific value of a fuel depends not only on its composition, but also on the definition of the boundary conditions of the combustion process. Currently, an initial temperature of 15°C is used internationally, while the calorific value is defined as the amount of energy released when the combustion end products have been cooled back to this initial temperature. The cubic metre, when the calorific value is expressed in MJ/m3, is generally normalised at a pressure of 101.325 kPa and a temperature of 288.15 K (=15°C). One distinguishes between the upper/higher/superior calorific value Hs and the lower/inferior calorific value Hi. In case of Hs, the water vapour in the combustion end products has also been condensed to the initial process temperature and has thereby released the heat required for vapourisation. All fuels containing hydrogen (H) will produce water vapour (H2O) during the combustion process. In general terms:

HC+O2 →H2O+ CO2

Table 1 gives the calorific value of a number of fuels expressed per kg and m3. In practice, the values in the literature for coal and lignite are always given as higher heating values. Apart from large district heating systems in combination with coal-fired central power plants, most cogeneration installations are fuelled by natural gas or biogas. We will therefore now concentrate on gaseous fuels. A fuel can only release its energy via oxidation, and the required oxygen is generally supplied to the fuel by means of ambient air. Standard ‘wet’ ambient air with 50% humidity at 20°C has an oxygen concentration of almost 21% oxygen (O2). The rest is primarily nitrogen (N2). For a precise determination of an energy balance, one has to take into account the actual relative humidity of the air used for the combustion process. Air at a temperature of 20°C and a relative humidity of 50% contains 1.15% of water. Figure 2 illustrates how the water content of ambient air depends on the temperature and the humidity. It is amazing to see that the water content in air can reach 7% in hot and humid climates. Since the volumetric oxygen content of the air decreases with increasing water content, more air is required for a complete oxidation of a fuel in case of a high water content in the air. Figure 2. The volume percentage of water vapour in ambient air increases rapidly with air temperature for a given relative humidity.

## Stoichiometric air requirement of gaseous fuels

The minimum amount of air required for complete combustion of a fuel is called the stoichiometric air requirement. This requirement is very much dependent on the composition of the fuel. Combustion of one m3 of propane requires about 2.5 times more air than combustion of one m3 of methane. Figure 3 shows the stoichiometric air requirement for a range of gaseous fuels. In this case, air is again considered to have 50% humidity at 20°C. We can see from Table 1 that the calorific value of one m3 of propane is about 2.5 times higher than that of methane. Figure 3 reveals that the stoichiometric air requirement of propane is also about a factor of 2.5 higher than that of methane. Figure 3. The stoichiometric air requirement heavily depends on the fuel.

Apparently, combustion of hydrocarbons requires a close-to-constant amount of air per unit of energy released. This means that the energy content of a stoichiometric mixture of fuel gas and air only slightly depends on the composition of the fuel. This even applies for hydrogen, which has a lower calorific value of only 10.22 MJ/m3 and a stoichiometric air requirement of only 2.41 m3/m3, resulting in an energy content of a stoichiometric mixture of 3.00 MJ/m3. Figure 4 compares the energy content for a number of common gaseous fuels. It clearly shows that the energy content of the stoichiometric mixtures do not differ very much from each other. This is important to know when analysing the fuel efficiency of combustion installations. If there were large differences in the energy content of stoichiometric mixtures depending on the fuel, this would result in differences in mass flow through the fuel-using device. If the exhaust temperature of the device is higher than the intake temperature, which is quite common in most installations, a higher mass flow means that the losses are higher for the same temperature difference. Figure 4. The energy content of stoichiometric mixtures of fuel gas and air does not depend very much on the fuel

## The real air-to-fuel ratio lambda

Most reciprocating engines and gas turbines using gaseous fuels do not run on a stoichiometric mixture. The combustion temperatures of stoichiometric mixtures are quite high, resulting in exponentially high NOx emissions and more thermal stress on the machine components. The air-to-fuel ratio of fuel-air mixtures is often expressed in the lambda value λ. A stoichiometric mixture has by definition a lambda value of 1. Having 50% more air in the mixture means that the lambda value is 1.5. Modern gas-fuelled reciprocating engines run at an air-to-fuel ratio λ between 1.8 and 2.2. Gas turbines generally have an air to fuel ratio λ exceeding 3. It will be clear that a higher λ value automatically means a higher mass flow per unit of fuel energy through the fuel-consuming device. As an example, for methane as a fuel, a stoichiometric mixture of fuel gas and air for 1 m3 of fuel gas has a volume of 1 + 9.765 = 10.765 m3. For λ = 2, we have twice as much air, meaning a total volume of 1 + 9.765 + 9.765 = 20.53 m3 for the same amount of fuel energy. Roughly speaking, for a given exhaust temperature this results in almost twice as much exhaust loss compared with that of a stoichiometric mixture. The benefits of a higher λ value are, however, generally higher than the negative consequences of a higher medium flow. Figure 5: The energy content of a fuel-air mixture decreases with increasing air-to-fuel ratio λ

## Sinsible heat content

A gaseous medium, such as air or fuel gas, contains a certain amount of heat depending on its temperature. We call this the . The specific heat of air cp is about 1 kJ/kgK. With that information, we can calculate the amount of heat E required to heat one m3 of air from 15 °C to 85°C. The density of air at 15°C is about 1.23 kg/m3.

E = m • cp • (Tstart – Tend) = 1.23 • 1 • (85–15) = 86.1 kJ/m3

The specific heat cp of methane is 2.26 kJ/kgK, while the density of a standard m3 of methane (101.325 kPa, 15°C) equals 0.68 kg/m3. Therefore, the per standard m3 of methane is about 1.54 kJ/m3K, which is slightly higher than the 1.23 kJ/m3K for standard air. For a combustible mixture with an air-to-fuel ratio of 2 and higher, the specific heat of the mixture is almost completely determined by the cp value of air, since the fuel gas fraction in the mixture is quite small.

The actual specific heat cp of gaseous media depends to some extent on the actual temperature: the cp value tends to increase with temperature. However, for the temperature levels present in the intake and exhaust systems of most cogeneration units we can ignore this fact here. In case a very accurate heat balance of an installation has to be determined, the actual cp values must be used. These can be found in engineering tables, nowadays also on the internet.

We can now approximate the loss in in the exhaust of an installation. For a standard starting temperature of 15°C, and a presumed cp value of 1.25 kJ/m3K for the air/fuel gas mixture as well as for the exhaust gas, an exhaust gas temperature of 115°C (a difference of 100 K) gives an exhaust loss in of: Eloss = 1 + λ · 9.765) · 1.25 · 100 kJ per m3 of methane. For λ = 1, this is 1346 kJ/m3, and since the lower calorific value of methane is 34.02 MJ/m3, the loss with the exhaust flow equals 1.346/34.02 · 100% = 4% in this example.

Figure 6 shows that the losses in with the exhaust flow are rather limited in the case of low exhaust temperatures, say below 75°C. Many cogeneration installations that supply heat for space heating and district heating operate at such low exhaust temperature levels. Naturally, the losses are higher for a higher air-to-fuel ratio λ. In the case of exhaust temperatures exceeding 100°C, as is the case with only steam production, the losses in become very relevant, especially for the higher lambda values. Figure 6. The loss in with the exhaust flow depends substantially on the air-to-fuel ratio λ of the combustible mixture for a given exhaust temperature (data for methane as a fuel, initial temperature 15oC)

It should be mentioned again that the values given in figures in figures 3, 4, 5 and 6 all apply for standard air with a relative humidity of 50% at 20°C. For air with higher moisture content, as is the case in hot and humid areas, the stoichiometric air requirement is higher than for standard air. In that case, corrections for the mixture composition can be made with the data in Figure 2. It is the oxygen in the air that is needed for oxidising/burning the fuel and humid air contains relatively more moisture than standard air. When more air is required, the loss in increases proportionally with the increased exhaust flow for a fixed temperature difference. Fortunately, in hot and humid areas the initial temperature is also higher, which decreases the loss in for a given exhaust temperature. Exhaust gas temperature and quantity can be indicators of process efficiency Credit: MWM/Caterpillar

## Summary

In summary, this article explains how an approximation can be found for the energy that escapes a combustion installation via the exhaust gas. Important factors in this determination are the temperature difference between intake and exhaust as well as the air-to-fuel ratio λ with respect to a stoichiometric mixture. These two quantities are relatively easy to measure. The end result for system efficiency is generally much more accurate when these two quantities are used, compared with using elaborate measurements of hot water or steam production. This article has, however, not yet discussed the effect of the so-called latent heat in the exhaust gases on the efficiency. The latent heat is the energy that is released when the water vapour in the exhaust gas condenses. This will be the subject of a future article.

Dr Jacob Klimstra is Managing Editor of COSPP