4.2.1 Chemical Quantities

When evaluating the magnitude of matter from a chemical point of view, the unit used is the mole or kilomole. A mole is defined as that amount of substance containing 6.0223 × 10²³ molecules or atoms. This number is termed Avogadro's number or Avogadro's constant.

4.2.2 Chemical Reactions

At the most fundamental level, chemical reactions are the result of the migration of electrons and protons.

Chemical reactions describe, on a molecular scale, the combination of simple substances to form new ones and also the breakdown of complex substances into more simple ones.

In chemical reactions, substances are represented by their chemical symbols, with coefficients indicating the number of moles of substance present. For example:

In the above equation, one mole of hydrogen (H₂) combines with 0.5 moles of oxygen (O₂) to form one mole of water.

Note that coefficients having a value of 1 are omitted by convention.

The substances initially present in a reaction are termed the reactants. The substances resulting from a reaction are termed the products.

4.2.3 Physical Quantities

On a more macroscopic or everyday scale, the unit of mass is the kilogram.

There are many applications where a conversion between these two units, kilograms and kilomoles, is required and this is facilitated by a substance property called the molar mass (M, kg/kmol).

The approximate elemental molar masses of primary interest in this chapter are shown in Table 4.1.

The molar mass of molecules, or the molecular mass, can be found by simple accountancy. If a molecule contains i different elements, then the resulting molar mass can be calculated by summing the product of the number of atoms of each element with their attendant molar mass:

(4.1)

The mean molar mass of a mixture () can be found with knowledge of component molar fractions.

The molar fraction () is simply the ratio of the number of moles (n_i) of the component of interest (i) to the total number of moles in the mixture (n_tot), i.e.:

(4.2)

If a mixture contains i different components, then the resulting molar mass of the mixture can be calculated by summing the product of each component molar mass (M_i) with its attendant molar fraction (%) and dividing by a hundred; thus:

(4.3)

The relationship between the number of kilomoles of a substance (n), its mass (m, kg) and molar mass (M, kg/kmol) is given by:

(4.4)

This relationship is extremely useful, as it provides for a conversion from chemical to physical units.

4.3.1 Combustion Equations

Typically, in a combustion process we have:

When the fuel is a hydrocarbon, for example, methane (CH₄), ethane (C₂H₆), octane (C₈H₁₈) then:

• For the carbon 
• For the hydrogen 

For combustion of a hydrocarbon fuel with air, a balanced equation can be obtained by using the method outlined previously, with both reactions being considered simultaneously.

Combustion reactions usually take place with ambient air that consists of 21% O₂ and 79% N₂ by volume. So every mole of oxygen brings with it (79/21) 3.76 moles of N₂. This must be accounted for when balancing combustion equations.

Commonly, N₂ is assumed not to undergo any chemical change in simple combustion analysis. In reality, oxides of nitrogen are formed if the temperature is high enough.

Again, in simple analyses, the effects of other atmospheric components present in small concentrations, such as inert gases, water vapour etc., are ignored.

If the products of combustion comprise CO₂, H₂O, N₂, as above (and perhaps O₂, as will be shown later) then we have complete combustion.

Incomplete or partial combustion is associated with insufficient air supply or poor mixing and results in products that may contain H₂, CO, C, OH and N₂.

Any hydrogen or carbon in the products must be regarded as wasted fuel, as it could potentially be reacted with oxygen to release its energy.

4.4.1 Oxidizer Provision

The minimum amount of air that supplies sufficient O₂ for complete combustion in the previous examples is termed the 100% theoretical or stoichiometric (perfectly chemically proportioned) quantity of air.

The term air–fuel ratio (A/F) is defined as the ratio of the mass of air to the mass of fuel in a combustion process, i.e.

(4.5)

Due to imperfect mixing between fuel and air, it is common practice to supply an amount of air in excess of the stoichiometric amount to achieve complete combustion.

To describe this amount, the terms % excess air and % stoichiometric air (or % theoretical air) are in common usage.

The % excess air is commonly quoted in terms of the air–fuel ratio, thus:

(4.6)

and

(4.7)

where n = number of moles of air present.

Note that if excess air is employed, the unused oxygen and its attendant nitrogen will appear in the products. This must be accounted for when carrying out mass and energy balances.

Another term used to describe the state of the fuel–air mixture is the equivalence ratio (φ), defined thus:

(4.8)

• indicates a (fuel) rich mixture.
• indicates stoichiometric proportions.
• indicates a (fuel) lean mixture.

4.4.2 Combustion Product Analyses

Sampling and analysis of product gases is commonly employed to determine the state of fuel–air combustion mixtures.

Analyzers are usually dry‐gas based, i.e. the water vapour is removed before exposure to the analyzer's sensors. However, the balancing technique detailed above is still applicable providing that the water is reinstated into the product side of the combustion equation.

4.4.3 Fuel mixtures

The above discussion is limited to the combustion of a pure fuel, i.e. one comprising only a single species of hydrocarbon. In reality, some fuels can be complex mixtures, for example, natural gas is a mixture of methane, ethane and heavier hydrocarbons as well as some nitrogen and carbon dioxide. Coal and biomass‐sourced fuels can be even more complex. Nevertheless, the combustion equation‐balancing technique can still be applied to first approximation.

4.6.1 Steady‐flow Systems (SFEE) [Applicable to Boilers, Furnaces]

Applying the first law of thermodynamics to a combustion control volume and neglecting any potential or kinetic energy changes, the steady flow chemical reaction can be written as:

(4.10)

This form requires knowledge of the molar flow rates through the volume.

However, it is more common in combustion studies to express this relationship in per mole of fuel terms and to divide the above equation through by the molar flow rate of fuel. (Note that the LHS terms lose their ‘dot’ notation as a consequence.)

Assuming zero work exchange (and zero heat input), this becomes:

(4.11)

If the process is isothermal, the sensible enthalpy terms disappear and this further reduces to:

(4.12)

4.6.2 Closed Systems (NFEE) [Applicable to Engines]

Again, neglecting any kinetic or potential energy changes:

(4.13)

Internal energy tables are available, but to avoid using another property, advantage may be taken of the enthalpy/internal energy/flow work relationship, thus:

(4.14)

4.6.3 Flame Temperature

The adiabatic flame temperature is the ideal maximum temperature of the resulting combustion flame assuming no work, heat loss or changes in kinetic and potential energy, and is calculated from knowledge of the fuel energy content and the heat capacities of the combustion products.

For a constant‐pressure process, such as a gas turbine combustor or the burner of a furnace, these conditions reduce the first law of thermodynamics to:

(4.16)

For a constant‐volume process, such as part of a theoretical engine cycle, the first law becomes:

(4.15)

Since the temperature of the products is unknown at the outset, adiabatic flame temperature calculation involves an iterative process, as follows:

• Perform a balance for the combustion equation accounting for any prevailing conditions, for example, excess air etc.
• Guess a temperature for the products.
• Using enthalpy tables, perform a reactant–product energy balance at the estimated temperature.

For example, in the case of a constant‐pressure process:

If then the guess is correct.

In the absence of equality, guess a new product temperature using the magnitude and sign of the result of the previous guess as a guide. Re‐attempt a balance.

If still unlucky, interpolate over a small interval, say 200 K, to solve for a reactant–product balance and the resulting adiabatic flame temperature.

(As an alternative, plot the results on an enthalpy–temperature basis and read off.)

Actual flame temperatures are always less than this theoretical value due to heat loss from the flame by convection/radiation and unwanted dissociation (reverse chemical reactions) of the combustion products that consume energy.

4.7.1 Nitrogen and Sulphur

Elemental nitrogen is a relatively inert and harmless non‐metal. It was first identified as an element in 1772 by British chemist Daniel Rutherford. It has a relative atomic mass of approximately 14 and boils at −196 °C, so at normal temperature and pressure it is a gas.

Air in the lower atmosphere comprises approximately 79% nitrogen by volume and 76% by mass. Nitrogen makes up about 48% of all dissolved oceanic gas.

In combination with other elements, it is essential for life and it is to be found in many bio‐compounds, including DNA. It can be fixed directly from the air by some soil bacteria. When converted into nitrates it can be made available to plants.

It is not truly inert, as, under the right conditions, it will react with hydrogen, oxygen and some metals.

Nitrogen reacts with hydrogen to form ammonia (NH₃). Its compounds are essential in the manufacture of many products including fertilizer and explosives.

It is also used in processes requiring an operating environment with a low reactivity, and in its liquid form it is used as a coolant.

Elemental sulphur is a bright yellow non‐metal that can exist in three forms – as a powder, in crystalline form or as a soft solid. It was known to the ancient Greeks and Egyptians. French scientists Louis‐Josef Gay‐Lussac and Louis‐Jacques Thénard first identified it as an element in 1809.

It has a relative atomic mass of approximately 32. It melts at 115 °C and boils at 445 °C.

Its natural occurrence is closely associated with volcanic activity and some fossil fuel reserves. It is malodorous and hazardous to health when in combination with hydrogen or when burnt.

Again, it is important in biochemistry as a component of some amino acids.

Its compounds are commonly used in bleaches and preservatives and are used in the production of sulphuric acid (H₂SO₄), which is a component that underpins a myriad of manufacturing processes.

4.7.2 Formation of Nitrogen Oxides (NO_x)

The reduction (i.e. the addition of hydrogen) of nitrogen produces ammonia (NH₃):

Oxidation of nitrogen produces, progressively, nitric oxide (NO) then nitrogen dioxide (NO₂).

In short:

At high levels of concentration, NO₂ is a lung irritant, causing inflammation of the airways and bronchitis‐like symptoms. The World Health Organization's time‐based concentration limits for exposure to the gas (2016) are:

NO_x in combination with hydrocarbon compounds (HC) also plays a part in the formation of low‐level ozone (O₃) which, again, is a lung irritant.

There are three main combustion‐sourced mechanisms of NO_x formation:

• Thermal NO_x formed by the combination of nitrogen and oxygen in high‐temperature (>1800 K) combustion systems over a range of equivalence ratios. The commonly used model of thermal NO_x formation is called the (extended) Zeldovich mechanism.

  This assumes that O radicals attack N₂ molecules, thus:

  

  The resulting N radicals can form NO by the following reaction:

  

  Nitrogen can also combine with hydroxyl radicals (OH), thus:

  

  Its formation is slow compared to the attendant fuel–oxygen combustion reactions and so its generation is generally limited to the exhaust gas environment.

• Prompt NO_x from reaction of fuel‐derived radicals with N₂, ultimately leading to NO. The commonly used model of NO_x formation, in this case, is called the Fenimore mechanism and is more prevalent in fuel‐rich mixtures. As suggested by its denomination, its formation is faster than thermal NO_x reactions and its generation can take place in the flame zone environment.

  The mechanism assumes the presence of hydrocarbon radicals (CH, C, H) to initiate the process and generate nitrogen (N), thus:

  
  

  Alternative routes to NO_x generation are possible.

  One of the most commonly quoted paths utilizing hydrogen cyanide (HCN) is:

  
  
  
  
• N₂O intermediate NO_x is generated in combustion systems with equivalence ratios of less than 1, i.e. fuel‐lean mixtures, and requires the presence of an unchanged, facilitating chemical species (M) and hydrogen and oxygen radicals, thus:
  
  
  

  N₂O and prompt NO_x are only weakly dependent on temperature.

4.7.3 NO_x Control

Two approaches to NO_x control are possible: combustion process modification or post flame/exhaust gas treatment.

4.7.3.2 Post‐flame Treatment

Most post‐flame treatments either add a reducing agent to the combustion gas stream to take oxygen away from NO or pass the NO_x over a catalyst.

For power plants and large furnaces, ammonia (or urea) is commonly added as a reducing agent.

and

Note the above reducing reactions are only effective at temperatures of between 850 and 1000 °C. Above 1000 °C the following reaction may occur, increasing NO formation:

Below 850 °C the conversion to N₂ and water vapour is unacceptably slow.

NO_x reductions of 60–80% are possible.

In a modern car engine, post‐flame treatment is carried out using a catalytic converter:

However, control over the NO/CO ratio is important for good conversion.

4.7.4 Formation of Sulphur Oxides (SO_x)

Oxides of sulphur are air pollutants.

Elemental sulphur will react with oxygen in the air to produce sulphur dioxide (SO₂):

The rate of the reaction increases with increasing temperature.

Sulphur dioxide (SO₂) is an air pollutant causing irritation and inflammation to the respiratory tract and eyes at high levels of concentration. The World Health Organization's time‐based concentration limits for exposure to the gas (2016) are:

• 20 µg/m³ – 24‐hour mean
• 500 µg/m³ – 10‐minute mean.

Sulphur in contact with hydrogen can be reduced to hydrogen sulphide (H₂S), also regarded as an air pollutant.

4.7.5 SO_x Control

Two fuel‐related sources of sulphur emissions will be considered here.

4.7.5.1 Flue Gas Sulphur Compounds from Fossil‐fuel Consumption

Sulphur is commonly found in coal and oil, so SO₂ in low (<0.5%) concentrations will be a minor component of their combustion gases. The total volume of the emission on a global scale is, however, very large.

Scrubbing systems for this problem are called flue gas desulphurization (FGD) units.

For this application, three possible removal arrangements are commonly in use: gas bubblers, spray chambers and packed chambers.

In a simple bubbler, the waste gas is forced, under pressure, through a perforated pipe submerged in the scrubbing liquid. With small bubbles, good contact will result. However, large gas‐side pressure drops may occur in tall towers.

In a spray chamber, the gas flows up an open chamber through a shower of descending scrubbing liquid released from spray nozzles. Gas–liquid contact is inferior to a bubbler but lower pressure drops prevail.

A packed column bed (see Figure 4.1) is a modified spray chamber with the column interior filled with some kind of solid medium on which the liquid can form a thin film, giving a large surface area to facilitate mass transfer. The medium or bed can comprise engineered ceramic, plastic or metal shapes or even natural materials such as rocks/gravel. This type of arrangement provides the best mass transfer per unit pressure drop performance.

In this application, the SO₂ is ultimately converted to calcium sulphate (CaSO₄) by using limestone (CaCO₃) slurry as the liquid in a wet scrubber. This facilitates its capture and removal. The basic chemical reaction is:

A typical arrangement for calcium sulphate removal and scrubbing liquid reuse is shown in Figure 4.2. The principal components of the system are the scrubber, holding tank and settling chamber.

The liquid exiting the scrubber is transferred to a holding tank where finely ground limestone and oxygen are added.

The resulting slurry is recirculated from the holding tank to the scrubber liquid inlet.

A fraction of the holding tank recirculation is transferred to a settling chamber to facilitate solid removal.

The outflow of the settling chamber has its water content reduced by vacuum filtration and is then often mixed with dry flyash (particulate matter from the combustion process) for easier handling before going to landfill. The liquid fraction overflow of the settling chamber is returned to the holding tank.

Liquid circulation rates are very large in these types of scrubbers, with the slurry spending only a few seconds in the tower and up to ten minutes in the holding tank, where most of the reactions take place.

In modern plant, it is becoming less common for an FGD's output to end up in landfill. Many plants are able to sell their calcium sulphate waste on to the construction supply industry for the manufacture of gypsum‐based plasters.

Limestone scrubbers have associated with them many operational considerations. For example:

• Scrubbing cools the flue gas and so there is a requirement to reheat the cleaned flue gas to maintain plume buoyancy for later dispersal. Reheating is also required to raise the temperature to above the acid dew point, preventing any acid condensation and corrosion downstream of the scrubber.
• As indicated earlier, the basic removal of limestone reaction generates carbon dioxide.
• Solid deposition either via entrainment of slurry droplets in the exhaust system or plugging and scaling of FGD‐associated fluid flow systems, e.g. pumps, valves etc., is a problem.

This list is not exhaustive.

4.7.6 Acid Rain

The natural acidity of freshwater sources such as lakes, rivers and streams is dependent on several factors including rainfall as well as the local geology and ecosystem.

For example, as a result of a reaction with atmospheric carbon dioxide, carbonic acid (H₂CO₃) can be formed in naturally occurring rainwater.

Rainfall pH values of around 5.6 are possible.

The pH of freshwater can also be altered by the composition of run‐off and leachate entering its volume after passage through/over surrounding rocks and soils.

However, as a consequence of nitrogen and sulphur oxide reactions with atmospheric water, more extreme acid deposition, more commonly referred to as acid rain, can result.

In the presence of water vapour in the atmosphere, NO₂ can react to form nitric acid (HNO₃):

Oxidation of sulphur dioxide produces sulphur trioxide (SO₃):

Upon contact of SO₃ with atmospheric water, sulphuric acid (H₂SO₄) will be formed:

As a result of the above reactions, localized and trans‐national freshwater lake pH levels can be as low as 3.5 in some areas. The impact is exacerbated by the fact that some elemental metals become soluble at elevated pH values and so can be dissolved out of rocks and soils then washed into feeder streams and rivers, where they can affect the developmental biology of a number of species.

Sulphur‐based acid rain can be particularly damaging to buildings constructed from carbonate‐based materials that react with the pollutant, replacing the carbonates with less‐cohesive sulphate compounds (gypsum) that have a tendency to blacken and flake from the building surface.

The conversion process from air pollutant gas to water pollutant is not instantaneous and, in some cases, oxide gases can be carried by the prevailing wind far from their source before acid deposition occurs. For example, much of the historical acid deposition experienced in Scandinavian forests is thought to have originated in other, predominantly coal‐burning areas of northern Europe such as Germany and the UK. A similar set of circumstances prevails between the coal‐burning plants of the north‐eastern states of the USA and Canada.