Condensing the water vapour in exhaust gases of combustion processes such as cogeneration installations releases useful heat and improves fuel efficiency. The amount of this so-called latent heat depends on the composition of the fuel, the air-to-fuel ratio and the exit temperature of the exhaust gas. In the fourth of a series of articles, Dr Jacob Klimstra explains these relationships and also highlights some side effects of condensation
Readers familiar with work in the kitchen can roughly estimate how much time it takes to get one litre of water to the point of boiling. Engineers can even calculate the time required to reach boiling.
A typical electric water cooker has a power capacity of around 2 kW. One litre of water has a mass of close to 1 kg. The specific heat of water is 4.186 kJ/(kg K). Increasing the temperature of 1 kg of water from 15°C to 100°C requires 1 ∙ 4.186 · (100–15) = 356 kJ.
For a cooker with a power capacity of 2 kW, it takes – in the idealised case – 356 kJ/ 2 kW = 178 seconds to reach the boiling point, equalling about three minutes. In reality, it takes a little more time, since during the heating process the cooker loses some heat to the surroundings. Well-insulated cookers perform best in this respect.
As soon as the water reaches its boiling point while the heat source is not switched off, steam will be produced. The water evaporates (vapour = damp, steam) and if one waits long enough, the cooker will run dry and will be damaged. Again, people familiar with cooking know that it takes quite some time before one litre of water has fully evaporated from the cooker. The reason is that changing the liquid into a gaseous state takes a considerable amount of energy. The evaporation heat of water is 2249 kJ/kg under standard atmospheric conditions. This is a factor of 2249/356 = 6.3 times more energy than is required to increase the water temperature from 15°C to 100°C. Consequently, it takes at least 1124 seconds, equalling almost 19 minutes, to fully evaporate the 1 kg of water in the cooker. Experts in steam-based power plants are fully aware of this behaviour. Producing steam takes a lot of energy.
Conversely, condensing the water vapour present in the exhaust gas of combustion installations releases quite a lot of energy. Unfortunately, gas turbines and gas engines cannot benefit directly from this condensation energy, since the temperatures at the exit of the heat to mechanical energy conversion processes are too high for condensation to occur. However, using the exhaust gas for heating applications offers possibilities for condensation. This is typical for cogeneration installations.
Modern domestic natural gas-based home heating systems also almost exclusively use condensation to recover most of the energy present in the fuel. This works best if the return temperature of the water is low, as is the case with under-floor heating.
The amount of water vapour in exhaust gas depends on the type of fuel. Complete combustion of one mol of methane (CH4) at standard conditions (absolute pressure 101.325 kPa, absolute temperature of 273.15 K) with oxygen (O2) produces two mol of water vapour: the molar mass of water vapour at standard conditions is 18.015 kg/kmol, while the molar mass of methane is 16.043 kg/kmol.
Therefore, complete combustion of 1 kg of methane releases 2 · 18.015/16.043 = 2.25 kg of water vapour. The density of methane is 0.717 kg/m3, again at standard conditions. Consequently, the combustion of one m3 of methane releases 0.717 · 2.25 = 1.61 kg of water vapour.
Complete combustion of one m3 of methane at standard conditions without condensation releases 35.88 MJ of energy if the starting temperature of the combustion process is 25°C and the combustion end products are cooled back to this starting temperature. However, if the combustion end products are really cooled down to 25°C, a large part of the water vapour in the exhaust flow will condense and release its vaporisation heat. With the condensation included, combustion of one m3 of methane releases 39.82 MJ of energy.
We call the amount of energy released without condensation the inferior, net, or lower calorific value Hi of the fuel, while when the condensation energy is included we talk about the gross, superior, upper or higher calorific value Hs. For methane, the Hs is a factor 1.11 higher than the Hi. For most natural gases, the Hs is about 10% higher than the Hi.
The heat present in the combustion end products without condensation is generally called the sensible heat. One can sort of sense the heat in the combustion end products based on the temperature. The heat resulting from condensation is called the latent heat. This heat is basically available, but it is only released by condensation.
Combustion of pure carbon (C) and carbon monoxide (CO) produces no water vapour at all. For fuels containing no hydrogen, the gross calorific value therefore equals the net calorific value. Table 1 compares the gross and net calorific values of a number of gaseous components.
|Table 1. Calorific values and densities of a number of fuels (conditions p = 101.325 kPa and T = 273.15 K for the volumes and 25°C for initial conditions of the combustion process|
The temperature at which the water vapour present in air or in any gas, such as exhaust gas, begins to turn from the gaseous state into the liquid state is generally called the dew point. This dew point depends on the concentration of the water vapour in the gaseous medium.
If methane is burned with so-called standard air, defined at a relative humidity of 50% at a temperature of 20°C, the air itself contains 1.15% of water. In a stoichiometric mixture of methane and standard air, the water content in the combustion end products, i.e., the exhaust gas, is 19.93% by volume. In a stoichiometric mixture, exactly enough air is present for complete combustion. If the combustion air had been completely dry, the volumetric water content in the exhaust gas would have been 18.34%. If the combustion end products are cooled, the dew point of the combustion process of methane with standard air is reached at a temperature of 59.6°C. At that temperature, the exhaust gas is saturated with water vapour. Cooling of the exhaust gas below 59.6°C will make that water vapour condense.
Figure 1 shows that, at a temperature of 45°C, half of the water present in the exhaust gas has already condensed. At a temperature of -10°C, no water vapour is present in the exhaust gas: all the water has condensed.
|Figure 1. The amount of water condensate per m3 natural gas from the exhaust gas of a stoichiometric mixture of methane and air, depending on the exhaust temperature|
In practice, an exhaust temperature of 25°C is the ultimate minimum that will be used for heating purposes. The natural gas industry currently tends to use 15°C as the reference temperature for the upper heating value Hs. This gives a slightly higher value for Hs, but the value is not realistic for most existing installations
Many combustion processes do not use stoichiometric mixtures of fuel gas and air. Modern reciprocating engines use lambda (λ) values between 1.8 and 2.2. Operating with such fuel-lean mixtures yields much lower process temperatures in the engines, resulting in better fuel efficiency and considerably lower NOx emissions. The power output can also be drastically increased with lean mixtures, since the knock tendency decreases with leaner mixtures. However, for leaner mixtures, the concentration of water vapour in the exhaust is lower, meaning that the temperature of the dew point is lower. Figure 2 compares the condensate flow of a lean mixture with 100% extra air (λ = 2.0) with that of a stoichiometric mixture (λ = 1.0). For λ = 2.0, the dew point lies at 47.5°C; at 35°C, half of the water content has condensed in this case. This is at a 10 K lower temperature than for a stoichiometric mixture. For λ = 3.0, which is a common value for gas turbines, the dew point lies at 40.8°C. Here, one has to cool the exhaust gas to 28°C in order to get half of the water contents to condense.
|Figure 2. The amount of condensed water per m3 of methane, depending on the air-to-fuel ratio λ and the exhaust temperature|
Interestingly, chilling the exhaust gas to below 0°C yields more water for the leaner mixtures. The reason is that more air is present in leaner mixtures, and air has its own humidity. One might argue that exhaust gases are normally never cooled below some 25°C. However, the latest developments are installations where heat pumps extract heat from the exhaust gas. The heat pumps lift the temperature of the heat to easily usable values of higher than, say, 70°C.
Figure 3 summarises the effect of the air-to-fuel ratio λ on the water dew point. Three curves are given, one for dry air, one for standard air and one for humid air with 100% relative humidity at 35°C. The latter condition can occur under tropical conditions.
|Figure 3. The water dew point of exhaust gas depends on the air-to-fuel ratio λ and the relative humidity of the air used for the combustion process|
Based on the information given above, we can now calculate the positive effect on fuel efficiency of reducing the exhaust temperature below the dew point. The major benefit is the release of the condensation heat of water vapour in the exhaust, although further cooling also results in a better utilisation of the sensible heat.
Figure 4 shows that, above an exhaust temperature of 25°C, leaner fuel-air mixtures have a lower process efficiency for the same exhaust temperature due to less condensation and a higher exhaust flow per unit of energy. In this diagram, the heat losses in the system due to radiation and convection have not been taken into account. The diagram represents the idealised efficiency of a boiler or the combined efficiency for a cogeneration installation including electricity and heat. For a real process, boiler losses, engine radiation, incomplete combustion and generator losses have to be taken into account. However, the diagram gives proper insight into the efficiency gains achieved by lowering the exhaust gas temperature. Especially when condensation takes place, substantial gains in efficiency can be reached. Cooling the exhaust gas from 60°C to 35°C results in a 9% efficiency gain for λ = 1.0, an 8% gain for λ = 2.0 and a 6% gain for λ = 3.0. If no condensation took place, all efficiency lines would reach 100% at 25°C. That 25°C is the reference point for starting the combustion process.
|Figure 4. The idealised combustion process efficiency based on the lower heating value Hi for three different air-to-fuel ratios λ|
The benefit of condensing the exhaust gas for fuel efficiency is apparent. Heat exchangers working with condensing exhaust gas, however, must be corrosion-resistant. The CO2 in the exhaust gas, together with some NOx and SO2, makes the water slightly acidic. Special stainless steel with a high fraction of Cr and Mo has to be used. At the same time, the exhaust and drain systems require a design where no water puddles remain in the system.
Engineers and system builders tend to design a layout with perfectly horizontal pipes and flat chimney bottoms. A design where the condensed water can easily flow out of the system helps to prevent corrosion. The fuel efficiency benefit of condensing systems is such that applying low exhaust temperatures as much as possible is recommended.
Dr Jacob Klimstra is Managing Editor of COSPP