Combustion and Reacting Systems

Introduction and Context

Combustion is a chemical reaction in which a fuel reacts with an oxidizer and releases energy, usually as heat and high-temperature products. It is central to gas turbines, steam power plants, reciprocating engines, industrial furnaces, boilers, rockets, and many waste-treatment systems. Although combustion is a chemical process, engineering analysis usually combines chemistry with the first law of thermodynamics, conservation of mass, gas properties, heat transfer, fluid mechanics, and environmental regulations.

A combustion calculation may be required to determine the theoretical air requirement, composition of exhaust gases, fuel consumption, heating value, flame temperature, or pollutant formation. The accuracy of the result depends strongly on the chosen assumptions. Common simplifying assumptions include steady operation, complete combustion, ideal-gas behavior, negligible kinetic and potential-energy changes, and uniform reactant or product temperatures. These assumptions are useful for preliminary design but must be reconsidered for detailed equipment analysis.

Learning Objectives

After studying this chapter, you should be able to:

1. Balance combustion reactions and determine stoichiometric air requirements.
2. Analyze complete and incomplete combustion using molar and mass bases.
3. Calculate excess-air ratio, equivalence ratio, fuel composition, and flue-gas composition.
4. Use standard enthalpies of formation to evaluate reaction enthalpy and heating value.
5. Distinguish higher and lower heating values.
6. Estimate adiabatic flame temperature using energy balances.
7. Explain chemical equilibrium, dissociation, and their effects on flame calculations.
8. Identify major combustion emissions and evaluate practical decarbonization measures.

1. Chemical Representation of Combustion

A combustion equation must satisfy conservation of each chemical element. For a general hydrocarbon fuel C_xH_y, complete combustion with oxygen is

The coefficient x + y/4 is the stoichiometric oxygen requirement per mole of fuel. If the fuel contains oxygen, as in C_xH_yO_z, the equation becomes

For a fuel containing sulfur, nitrogen, or other elements, the products must include their likely oxidation products. For example, sulfur may form SO₂, while fuel-bound nitrogen may form N₂, NO, or NO₂, depending on conditions.

Air is commonly modeled as 21 mol% oxygen and 79 mol% nitrogen. Thus,

The factor 3.76 is the molar ratio of nitrogen to oxygen in dry air. A stoichiometric reaction for a hydrocarbon is therefore

This representation neglects argon and trace gases. For high-accuracy work, the complete dry-air composition should be used.

Example 1: Stoichiometric combustion of methane

For methane, x = 1 and y = 4. The balanced equation is

With air:

Thus, one mole of methane requires 2 mol of oxygen and 9.52 mol of theoretical air. The products contain 1 mol of carbon dioxide, 2 mol of water, and 7.52 mol of nitrogen when water remains in the vapor phase.

2. Stoichiometric Air, Excess Air, and Equivalence Ratio

Theoretical or stoichiometric air is the exact amount required for complete oxidation of the fuel. In practical combustion equipment, air is often supplied in excess to reduce carbon monoxide and unburned hydrocarbons. The excess-air ratio is

where λ is dimensionless. The percentage excess air is

For example, 20% excess air means λ = 1.20. The equivalence ratio is the reciprocal:

A mixture is stoichiometric when ϕ = 1, fuel-lean when ϕ < 1, and fuel-rich when ϕ > 1. These definitions assume that fuel and air ratios are expressed on compatible mass or molar bases.

For complete combustion of methane with excess air λ,

This equation assumes complete conversion of carbon to CO₂, hydrogen to H₂O, and no nitrogen oxides.

Worked Example 2: Methane with 25% excess air

For 1 kmol of methane, λ = 1.25. The air supplied is

The product equation is

The wet products total

The dry products exclude water:

The dry carbon-dioxide mole fraction is therefore

or approximately 9.17% by volume. The oxygen concentration is 4.59% dry by volume, and nitrogen is 86.24% dry by volume.

3. Fuel and Flue-Gas Calculations

Combustion analysis may be performed on a molar basis, mass basis, or volumetric basis. For gases at the same temperature and pressure, mole fractions equal volume fractions. Mass fractions do not equal mole fractions because molecular masses differ.

The molecular mass of a mixture is

where y_i is the mole fraction and M_i is the molecular mass of species i. The mass fraction is

A dry flue-gas analysis excludes water vapor. This distinction is essential when comparing a measurement with a calculated composition. Oxygen analyzers and many emissions regulations report concentrations on a dry basis, sometimes corrected to a specified oxygen concentration.

For an unknown hydrocarbon C_xH_y, complete combustion gives a carbon-to-carbon-dioxide relationship. If the dry product composition and oxygen concentration are known, elemental balances can be used to infer excess air or fuel composition. In real systems, carbon monoxide, unburned hydrocarbons, sulfur oxides, and nitrogen oxides must also be included.

Incomplete combustion

Incomplete combustion occurs when mixing, residence time, temperature, or oxygen availability is inadequate. Important products include CO, unburned fuel, soot, and partially oxidized hydrocarbons. A simplified rich-combustion equation may contain both carbon monoxide and carbon dioxide:

The coefficients must be determined using carbon, hydrogen, and oxygen balances. The equation alone does not predict how carbon partitions between CO and CO₂; that requires kinetic or equilibrium information.

4. Enthalpy of Formation and Reaction Energy

The enthalpy of formation, h_f^°, is the enthalpy change for forming one mole of a substance from its elements in their reference states at a specified temperature, commonly 298.15 K. By convention, the standard enthalpy of formation of an element in its reference state is zero.

The standard reaction enthalpy is calculated by Hess’s law:

Here, n_p and n_r are product and reactant stoichiometric coefficients. A negative value indicates an exothermic reaction.

The equation is applicable when all formation enthalpies refer to the same reference temperature, pressure convention, and physical phase. The phase of water is particularly important. Liquid water is used for the higher heating value, whereas water vapor is used for the lower heating value.

For a general control volume with negligible kinetic and potential-energy changes, the steady-flow energy balance is

where Q̇ is heat transfer to the control volume, Ẇ is work delivered by it, and ṅ is molar flow rate. For a reacting mixture, species enthalpy is represented as

The second term is sensible enthalpy relative to the reference temperature.

Heating values

The higher heating value (HHV) assumes that product water is condensed to liquid, recovering its latent heat. The lower heating value (LHV) assumes that product water remains vapor and therefore excludes condensation energy. Consequently,

The difference depends on the amount of water formed from hydrogen and the moisture already present in the fuel. Boiler efficiency and engine efficiency must be reported with the heating-value basis identified; otherwise comparisons can be misleading.

Worked Example 3: Methane reaction enthalpy

At 25 °C, approximate standard formation enthalpies are:

For liquid water products,

Thus, the HHV is approximately 890.3 MJ/kmol, or, dividing by the molecular mass of methane (16.04 kg/kmol), approximately 55.5 MJ/kg. Using water vapor instead gives the LHV:

which is approximately −802.3 MJ/kmol, or 50.0 MJ/kg. Differences from tabulated values arise from rounding and reference data.

5. Adiabatic Flame Temperature

The adiabatic flame temperature is the temperature attained by combustion when there is no heat transfer to the surroundings. For a steady, adiabatic combustor with negligible changes in kinetic and potential energy and no shaft work,

Using formation and sensible enthalpies,

The temperature T_ad is normally found iteratively because specific heats depend on temperature. A constant-specific-heat estimate is useful for hand calculations but may be inaccurate at flame temperatures.

Adiabatic flame temperature increases with fuel heating value and reactant preheating, and generally decreases with excess air, humidity, dilution, or exhaust-gas recirculation. At high temperatures, dissociation of CO₂, H₂O, and O₂ absorbs energy and lowers the actual equilibrium temperature.

Approximate calculation

If reactants enter at 298 K, products are assumed to have constant mean specific heats, and dissociation is neglected, an approximate balance is

where c̄_p is the mean molar heat capacity of each product over the temperature range. This is only an estimate because the heat capacities are not truly constant and because chemical equilibrium may alter the product composition.

A rigorous procedure is:

1. Write the balanced reaction and specify the reactant temperature.
2. Calculate reactant enthalpy using formation and sensible terms.
3. Guess a product temperature.
4. Calculate product enthalpy using temperature-dependent property data.
5. Adjust the temperature until the energy residual is acceptably small.
6. Include dissociation and equilibrium if the temperature is sufficiently high.

6. Chemical Equilibrium and Dissociation

Combustion products do not necessarily remain in their ideal complete-combustion forms. At high temperature, reversible reactions such as

and

become important. The equilibrium constant for a reaction is related to the standard Gibbs-energy change:

where K_p is the pressure-based equilibrium constant, ∆G° is standard Gibbs-energy change, R̄ is the universal gas constant, and T is absolute temperature. For ideal gases, the reaction quotient is constructed from partial pressures divided by the standard pressure.

At equilibrium, the reaction quotient equals K_p. Equilibrium composition is obtained simultaneously from elemental balances, equilibrium relations, and any specified pressure or temperature condition.

Dissociation is favored by high temperature and low pressure. It reduces the concentration of fully oxidized products and absorbs energy, so an equilibrium adiabatic flame temperature is lower than a frozen-composition estimate. In a frozen calculation, composition is assumed to stop changing after the reaction zone. In an equilibrium calculation, composition adjusts to the final temperature and pressure.

Chemical equilibrium does not mean that every combustion device reaches equilibrium. Real combustors have finite residence times and mixing limitations. Equilibrium calculations provide a thermodynamic limit, whereas kinetic models are needed to predict finite-rate behavior.

7. Pollutants and Emissions

The principal combustion-related emissions are carbon dioxide, carbon monoxide, nitrogen oxides, sulfur oxides, particulate matter, unburned hydrocarbons, and aldehydes. Their formation mechanisms differ.

Carbon dioxide

CO₂ is the principal carbon-oxidation product under complete combustion. Its formation is approximately proportional to the carbon entering with the fuel. Reducing CO₂ requires reducing fossil carbon use, improving efficiency, using low-carbon fuels, capturing carbon, or removing carbon dioxide from the atmosphere through durable methods.

Carbon monoxide and hydrocarbons

CO and unburned hydrocarbons result from incomplete oxidation. They are promoted by low temperature, poor mixing, inadequate residence time, quenching near cold walls, and locally fuel-rich zones. More excess air can reduce these emissions, but excessive air lowers flame temperature and may reduce efficiency.

Nitrogen oxides

Thermal NO_x forms rapidly at high temperatures through reactions involving atmospheric nitrogen and oxygen. Prompt NO_x forms in fuel-rich flame zones through hydrocarbon-radical chemistry. Fuel NO_x originates from nitrogen compounds in the fuel. Strategies for reducing NO_x include staged combustion, lean premixed operation, flue-gas recirculation, water or steam injection, low-temperature combustion, and selective catalytic or noncatalytic reduction.

Sulfur oxides and particulates

Sulfur in fuel is oxidized mainly to SO₂, with some SO₃. Low-sulfur fuel, fuel desulfurization, and flue-gas desulfurization are common controls. Particulate matter includes soot, ash, sulfates, and condensed hydrocarbons. Soot formation is associated with locally fuel-rich regions and insufficient oxidation time.

Environmental compliance requires measured emissions, defined reference oxygen or carbon-dioxide conditions, averaging periods, and legally specified units. A technically correct calculation can still be unsuitable for regulatory reporting if the basis is wrong.

8. Decarbonization of Combustion Systems

Decarbonization should be evaluated over the complete energy system rather than by fuel label alone. Important options include:

• Efficiency improvement: Better heat recovery, insulation, combustion control, and maintenance reduce fuel use and emissions.
• Electrification: Heat pumps, electric furnaces, resistance heating, and electric drives can eliminate on-site combustion when supplied by low-carbon electricity.
• Renewable fuels: Biogas, biomethane, renewable hydrogen, and sustainable liquid fuels may reduce lifecycle emissions, but feedstock, leakage, land use, and production energy must be assessed.
• Carbon capture and storage: Post-combustion, pre-combustion, and oxy-fuel systems can reduce point-source carbon dioxide but require energy, equipment, transport, storage verification, and leakage management.
• Hybrid systems: Electrification combined with thermal storage or renewable fuels can address variable demand.

Hydrogen combustion produces no carbon dioxide from the fuel itself, but it can generate substantial thermal NO_x because flame temperature and oxygen chemistry are important. Hydrogen also has different flame speed, ignition behavior, leakage characteristics, and materials requirements. Therefore, replacing natural gas with hydrogen is not a simple one-for-one substitution.

Lifecycle assessment should include fuel production, processing, transport, infrastructure, direct emissions, indirect electricity emissions, and end-of-life effects. Professional decisions should also consider safety, affordability, reliability, resource availability, and environmental justice.

9. Applied Case: Excess Air and Emissions in a Natural-Gas Boiler

Background

Consider an industrial boiler burning methane at a rate of 100 kmol/h. The boiler operates with 20% excess air. Assume complete combustion, dry air containing 21% oxygen and 79% nitrogen, and no formation of nitrogen oxides or sulfur compounds.

Problem

Determine the air flow rate, dry flue-gas flow rate, and dry carbon-dioxide concentration. Then interpret the effect of reducing excess air.

Analysis and solution

For methane, the stoichiometric oxygen requirement is 2 kmol per kmol fuel. The stoichiometric air requirement is

At 20% excess air, λ = 1.20, so the actual air flow is

The combustion equation is

For 100 kmol/h methane, the dry products are:

• CO₂: 100 kmol/h
• O₂: 40 kmol/h
• N₂: 902.4 kmol/h

Therefore,

The dry carbon-dioxide concentration is

or 9.59% by volume. The boiler operator might reduce excess air to improve efficiency, but the adjustment must be controlled. Too little air can cause carbon monoxide, soot, unstable flames, and unsafe operation. The appropriate target requires burner design, fuel composition, load, oxygen measurement, carbon-monoxide monitoring, and regulatory limits.

Outcome and learning points

The case demonstrates that excess air increases exhaust flow and sensible heat loss while lowering carbon-dioxide concentration on a dry volume basis. It does not reduce the carbon entering the boiler per unit of fuel. Emissions should therefore be compared both as concentration and as mass per unit energy or useful output.

10. Best Practices, Limitations, and Professional Judgment

A sound combustion analysis should:

1. State the fuel composition and whether it is measured on a mass or molar basis.
2. Identify the air composition and humidity assumption.
3. Specify wet or dry product analysis.
4. State whether combustion is complete, incomplete, frozen, or at equilibrium.
5. Identify the reference temperature, phase of water, and heating-value basis.
6. Check elemental balances and units.
7. Compare calculated oxygen and carbon dioxide with measurements.
8. Account for uncertainty in fuel composition, analyzer calibration, leakage, and operating load.
9. Distinguish thermodynamic potential from actual kinetic performance.
10. Include safety controls for flame failure, explosive mixtures, pressure, toxic gases, and backfire.

Computer tools can evaluate temperature-dependent properties, equilibrium composition, burner networks, and emissions. However, software does not replace formulation of the reaction, selection of a valid thermodynamic model, or engineering judgment. Artificial-intelligence tools may assist with data screening, fault detection, and combustion optimization, but their outputs require traceable data, validation, cybersecurity controls, and human approval for safety-critical decisions.

Chapter Summary

Combustion analysis begins with conservation of atoms and a correctly balanced reaction. Stoichiometric air is the theoretical air needed for complete oxidation, while excess-air ratio and equivalence ratio describe actual mixture conditions. Molar, mass, wet, and dry bases must not be confused.

Reaction enthalpy is obtained from standard enthalpies of formation. The higher heating value condenses product water, whereas the lower heating value leaves it as vapor. Adiabatic flame temperature follows from a reacting-system energy balance and generally requires iteration with temperature-dependent specific heats. At high temperatures, dissociation and chemical equilibrium alter product composition and reduce flame temperature.

Combustion produces useful energy but can also generate carbon dioxide, carbon monoxide, nitrogen oxides, sulfur oxides, particulates, and unburned hydrocarbons. Emission control involves fuel selection, combustion management, after-treatment, and accurate measurement. Decarbonization options include efficiency, electrification, renewable fuels, carbon capture, and hybrid systems. Their technical, economic, environmental, and safety implications must be evaluated together.

Key Terms

Stoichiometric combustion: Combustion using the exact theoretical oxidizer required for complete reaction.

Theoretical air: Air required for stoichiometric complete combustion.

Excess air: Air supplied above the theoretical requirement.

Excess-air ratio: Actual air divided by stoichiometric air.

Equivalence ratio: Actual fuel-to-air ratio divided by the stoichiometric fuel-to-air ratio.

Complete combustion: Ideal oxidation of carbon to carbon dioxide and hydrogen to water.

Incomplete combustion: Combustion producing carbon monoxide, soot, or unburned fuel.

Flue gas: Gaseous products leaving a combustion device.

Wet basis: Composition including water vapor.

Dry basis: Composition after excluding water vapor.

Enthalpy of formation: Enthalpy change associated with forming a compound from reference-state elements.

Reaction enthalpy: Enthalpy change for a chemical reaction at specified conditions.

Higher heating value: Fuel energy based on condensation of product water.

Lower heating value: Fuel energy based on product water remaining as vapor.

Adiabatic flame temperature: Temperature reached without heat transfer from the reacting system.

Chemical equilibrium: State in which forward and reverse reaction rates balance thermodynamically.

Dissociation: Breakdown of molecules into simpler species at high temperature.

Thermal NOx: Nitrogen oxides formed by high-temperature oxidation of atmospheric nitrogen.

Carbon capture and storage: Separation, transport, and long-term storage of carbon dioxide.

Lifecycle emissions: Emissions over fuel production, delivery, use, and disposal stages.

Review Questions

Short Answer Questions

1. What is the difference between stoichiometric air and excess air?
2. Define equivalence ratio and explain the meanings of ϕ < 1 and ϕ > 1.
3. Why are flue-gas compositions reported on both wet and dry bases?
4. Distinguish higher heating value from lower heating value.
5. Name three important mechanisms or sources of nitrogen oxides.

Long Answer Questions

1. Derive the complete-combustion equation for a general fuel C_xH_y using air modeled as O₂ + 3.76N₂.
2. Explain how standard enthalpies of formation are used to calculate the enthalpy of combustion, including the importance of the water phase.
3. Describe a rigorous iterative procedure for determining adiabatic flame temperature.
4. Explain how chemical equilibrium and dissociation affect high-temperature combustion calculations.
5. Compare efficiency improvement, electrification, renewable fuels, and carbon capture as decarbonization strategies.

Analytical / Application Questions

1. Propane C₃H₈ is burned with 30% excess air. Write the complete product equation and calculate the dry flue-gas composition.
2. A furnace analyzer reports 6% dry oxygen. Explain how this information can be used to estimate excess air, and identify assumptions that may make the estimate inaccurate.
3. A plant proposes replacing natural gas with hydrogen to reduce carbon dioxide. Evaluate the proposal considering emissions, flame behavior, safety, infrastructure, and lifecycle impacts.

Multiple Choice Questions with Answers

Question 1

For complete combustion of CH₄ with oxygen, how many moles of O₂ are required per mole of methane?

A. 1

B. 2

C. 3

D. 4

Correct Answer: B. 2

Question 2

An excess-air ratio of 1.25 corresponds to what percentage of excess air?

A. 20%

B. 25%

C. 75%

D. 125%

Correct Answer: B. 25%

Question 3

For a fuel-lean mixture, the equivalence ratio is:

A. Greater than 1

B. Equal to 1

C. Less than 1

D. Equal to zero in all cases

Correct Answer: C. Less than 1

Question 4

Which product is excluded from a dry flue-gas analysis?

A. Carbon dioxide

B. Nitrogen

C. Oxygen

D. Water vapor

Correct Answer: D. Water vapor

Question 5

The higher heating value is greater than the lower heating value primarily because it:

A. Uses more combustion air

B. Recovers condensation energy from product water

C. Includes nitrogen heating

D. Assumes incomplete combustion

Correct Answer: B. Recovers condensation energy from product water

Question 6

The standard reaction enthalpy is calculated as:

A. Reactant formation enthalpy minus product formation enthalpy

B. Product formation enthalpy minus reactant formation enthalpy

C. Product temperature divided by reactant temperature

D. Fuel mass divided by air mass

Correct Answer: B. Product formation enthalpy minus reactant formation enthalpy

Question 7

Increasing excess air in an otherwise complete combustion process generally causes the adiabatic flame temperature to:

A. Increase because nitrogen reacts

B. Decrease because more inert mass is heated

C. Remain exactly constant

D. Become equal to the fuel temperature

Correct Answer: B. Decrease because more inert mass is heated

Question 8

Dissociation at high flame temperature generally:

A. Releases energy and raises flame temperature

B. Consumes energy and lowers the equilibrium flame temperature

C. Eliminates nitrogen from air

D. Guarantees complete combustion

Correct Answer: B. Consumes energy and lowers the equilibrium flame temperature

Question 9

Which pollutant is especially associated with locally fuel-rich regions and insufficient oxidation?

A. Carbon monoxide

B. Oxygen

C. Argon

D. Water vapor

Correct Answer: A. Carbon monoxide

Question 10

Replacing fossil natural gas with hydrogen eliminates direct fuel-carbon dioxide formation but may increase concern about:

A. Thermal nitrogen oxides

B. Formation of sulfur from pure hydrogen

C. Carbon in the hydrogen molecule

D. Condensation of nitrogen as liquid fuel

Correct Answer: A. Thermal nitrogen oxides