Formation of CO, HC, NOx and particulate matter

Why it matters

Emission norms limit carbon monoxide (CO), unburned hydrocarbons (HC), oxides of nitrogen (NOx) and particulate matter (PM), and each of them is born from a different physical mechanism inside the cylinder. If you know where a pollutant comes from, you can predict how air–fuel ratio, timing, load, compression ratio, EGR or injection pressure will move it, and why fixing one pollutant often worsens another (the classic NOx–PM trade-off in diesels). Calibration, aftertreatment and test engineers use this reasoning every day.

Key ideas

Equivalence ratio φ = (actual F/A)/(stoichiometric F/A); λ = 1/φ. φ > 1 is rich, φ < 1 is lean. SI engines run close to φ = 1; CI engines run overall lean (φ ≈ 0.2–0.8) but burn in locally rich zones.

Carbon monoxide (CO)

• Formed when there is not enough oxygen to complete C → CO₂. Dominant control variable is φ: CO rises steeply on the rich side and is very low on the lean side.
• Even at stoichiometric, some CO remains because CO₂ dissociates at flame temperatures and the CO oxidation reaction freezes as the gas cools on expansion.
• Important for SI engines (cold start, full-load enrichment); low for diesels, which have excess air.

Unburned hydrocarbons (HC)

• Mainly not "incomplete combustion of the bulk charge" but fuel that escapes the flame:
  • Crevice volumes (top-land gap above the first ring, head-gasket crevice, spark-plug threads) store unburned mixture during compression and release it during expansion: the largest source in SI engines.
  • Flame quenching at cold walls leaves a thin unburned layer.
  • Absorption of fuel vapour into the oil film and deposits, released later.
  • Misfire or partial burn (very lean or high EGR), and liquid fuel films during cold start.
  • Valve overlap short-circuiting in two-stroke engines (very high HC).
• In CI engines: over-lean mixture at the edge of the spray during the delay period, and fuel dribbling from the injector sac volume after the end of injection.

Oxides of nitrogen (NOx = NO + NO₂)

• In engines mostly NO (NO₂ is a minor share in SI engines and a larger share in diesels). Formed mainly by the thermal (extended Zeldovich) mechanism:
  • O + N₂ ⇌ NO + N
  • N + O₂ ⇌ NO + O
  • N + OH ⇌ NO + H
• The rate is extremely sensitive to temperature (strongly above roughly 1,800–2,000 K) and needs free oxygen atoms and residence time. NO forms in the hot burned gas behind the flame and freezes during expansion.
• So NOx peaks at slightly lean mixtures (φ ≈ 0.9–0.95), where temperature is still near its maximum and there is excess oxygen; it falls on the rich side (no oxygen) and on the very lean side (low temperature).
• Increases with spark or injection advance, compression ratio, load, intake temperature; falls with dilution (EGR, residual gas), retarded timing and charge cooling.
• Prompt NO (in the flame front) and fuel-bound nitrogen contribute little in automotive engines.

Particulate matter (PM)

• Mostly a diesel issue (also gasoline direct-injection engines). Collected on a filter at below 52 °C after dilution with air, so it includes soot (elemental carbon), adsorbed heavy hydrocarbons (the soluble organic fraction from fuel and lube oil), sulphates (from fuel sulphur) and ash.
• Soot forms in fuel-rich, hot zones of the spray (φ above about 2, temperatures roughly 1,000–2,800 K) by pyrolysis, formation of polycyclic aromatic species, nucleation, surface growth and agglomeration. Most of the soot formed is oxidised later in the cycle; what escapes oxidation is emitted.
• Black smoke rises sharply when the overall fuelling approaches the smoke limit (insufficient air), in turbo lag, or with poor atomisation.

The NOx–PM trade-off in diesels: high temperature and good oxygen availability burn soot but create NOx; retarding injection or adding EGR lowers NOx but raises PM. High injection pressure, better air motion and aftertreatment are the ways out.

Rough summary against φ (SI engine): CO rises sharply rich, HC has a minimum slightly lean and rises again with lean misfire, NOx peaks slightly lean. This is why a three-way catalyst (next topic) needs φ held at 1.

Formulas

φ = (F/A)_actual / (F/A)_stoich, λ = 1/φ

• F/A: fuel–air mass ratio (–). For iso-octane C₈H₁₈ the stoichiometric A/F is about 15.1; for petrol take about 14.6–14.7 from your data book.

C_xH_y + (a_st/φ)(O₂ + 3.76 N₂) → products, with a_st = x + y/4

• a_st: moles O₂ for stoichiometric combustion per mole fuel. For rich mixtures without H₂ in products, use carbon, hydrogen and oxygen balances to split C between CO₂ and CO.

EI_i = m_i / m_f = x_i · M_i · (n_products / n_fuel) / M_f

• EI_i: emission index of species i (g per kg fuel); x_i: mole fraction of i in the exhaust (–; 1 ppm = 10⁻⁶); M_i: molar mass (g/mol; NOx is reported as NO₂, 46 g/mol); n_products/n_fuel: moles of exhaust per mole of fuel; M_f: fuel molar mass (g/mol).

(specific emission, g/km) = EI × (fuel used per km, kg/km)

Mass of C in CO = m_CO × 12/28

• Converts CO mass to carbon mass (kg) before a carbon balance.

Worked examples

Example 1 (standard): CO from rich combustion. Given: iso-octane C₈H₁₈ burned with 90% of theoretical air; assume all H forms H₂O, no H₂ or O₂ in the products.

1. Stoichiometric oxygen: a_st = 8 + 18/4 = 12.5 mol O₂. Supplied: 0.9 × 12.5 = 11.25 mol O₂, with 11.25 × 3.76 = 42.3 mol N₂.
2. Products: a CO₂ + b CO + 9 H₂O + 42.3 N₂. Carbon: a + b = 8. Oxygen atoms: 2a + b + 9 = 22.5, so 2a + b = 13.5.
3. Solving: a = 5.5 mol CO₂, b = 2.5 mol CO.
4. Dry exhaust moles = 5.5 + 2.5 + 42.3 = 50.3; CO fraction = 2.5/50.3 = 4.97%.
5. Mass of CO per kg fuel = 2.5 × 28 / 114 = 0.614 kg. Answer: about 5.0% CO (dry, by volume), i.e. 0.614 kg CO per kg of fuel. A 10% rich mixture sends nearly a third of the fuel carbon out as CO.

Example 2 (GATE level): NOx in g/km from a ppm reading. Given: a car runs on iso-octane at stoichiometric; exhaust NO concentration is 1,000 ppm (wet). Fuel use 6.0 L/100 km, fuel density 740 kg/m³. Report NOx as NO₂.

1. Stoichiometric products per mole fuel: 8 CO₂ + 9 H₂O + 12.5 × 3.76 = 47 N₂, so n_products = 64 mol.
2. NO per mole fuel: x · n_products = 1000 × 10⁻⁶ × 64 = 0.064 mol.
3. Emission index: EI = 0.064 × 46 / 114 = 0.02583 kg/kg, i.e. 25.8 g NOx per kg fuel.
4. Fuel per km: 6.0 L/100 km = 0.06 L/km × 0.74 kg/L = 0.0444 kg/km.
5. NOx per km: 25.8 × 0.0444 = 1.15 g/km. Answer: about 1.15 g/km of NOx engine-out, many times the tailpipe limits, which is why a catalyst is mandatory.

Common mistakes

• Treating CO mass as carbon mass in a carbon balance; multiply by 12/28 first.
• Saying NOx is highest at the richest, hottest mixtures; it peaks slightly lean because it needs oxygen as well as temperature.
• Thinking HC comes mainly from bulk incomplete combustion; crevices, wall quenching and oil-film absorption dominate in SI engines.
• Saying rich mixtures cause knock; enrichment actually cools the charge and suppresses knock, at the cost of CO and HC.
• Forgetting to report NOx as NO₂ (46 g/mol) when converting ppm to mass.
• Confusing PM (filter mass, including adsorbed organics and sulphates) with soot alone or with smoke opacity.

For GATE ME

Expect stoichiometry: theoretical air, equivalence ratio, products of rich combustion, percentage of CO or CO₂ in dry exhaust, and conversion of ppm to mass or g/km. Conceptual questions ask which pollutant rises with which change (richer mixture, advanced timing, higher compression ratio, EGR) and about the Zeldovich mechanism and the NOx–PM trade-off. Practise atom balances quickly and carry molar masses carefully.

Quick check

1. Which pollutant falls when the mixture is made richer than stoichiometric?
2. Name the largest HC source in a port-injected SI engine.
3. Why does retarding injection timing lower NOx in a diesel?
4. 1.4 kg of CO contains how much carbon?

Answers: 1. NOx. 2. Crevice volumes (especially the top-land ring crevice). 3. Combustion happens later, after TDC, so peak temperatures are lower. 4. 0.6 kg.