Gas analysers and gas chromatography

Why it matters

Combustion control needs flue-gas oxygen and CO; emission permits require continuous SO₂, NOx and CO₂ monitoring; refineries and petrochemical plants run on composition measured by on-line gas chromatographs; and safety systems watch for flammable and toxic gases. Each analyser exploits one physical or chemical property of a particular gas, and a gas chromatograph separates a mixture so that one detector can measure every component in turn. Knowing which principle suits which gas is a core instrumentation skill.

Key ideas

Single-component gas analysers (property-based).

• Non-dispersive infrared (NDIR): heteroatomic molecules (CO, CO₂, CH₄, SO₂, NO) absorb infrared at characteristic wavelengths. A sample cell between an IR source and a detector (often with a reference cell and optical filter or gas-filled detector) measures absorption, which follows the Beer–Lambert law. Symmetric diatomic gases (O₂, N₂, H₂) do not absorb IR. Water vapour and CO₂ cross-sensitivity must be handled.
• Paramagnetic oxygen analysers: O₂ is strongly paramagnetic (attracted into a magnetic field) while most other gases are weakly diamagnetic. In the magnetodynamic (dumbbell) type, a nitrogen-filled glass dumbbell in a non-uniform field is pushed out of the field by O₂; the restoring current needed to hold it still is proportional to O₂ partial pressure. Thermomagnetic (magnetic wind) types are cheaper but affected by gas thermal conductivity. NO and NO₂ are also paramagnetic and interfere.
• Zirconia oxygen probes: yttria-stabilised zirconia above about 600 °C conducts oxide ions. With air on one side and flue gas on the other, a Nernst emf develops that depends on the logarithm of the O₂ partial-pressure ratio. Mounted in situ in flues for combustion control; combustibles burn on the hot cell and make it read low.
• Electrochemical cells: O₂ and toxic gases (CO, H₂S, Cl₂) react at an electrode; current is proportional to concentration. Cheap, portable, but limited life.
• Thermal conductivity analysers: compare the conductivity of the sample with a reference in a heated-filament bridge; ideal for H₂ (or He) in a binary background, since H₂ conducts heat about seven times better than air.
• Other emission analysers: chemiluminescence for NOx (NO + O₃), UV fluorescence for SO₂, flame ionisation (FID) for total hydrocarbons.
• Sampling systems (probe, filter, heated line, cooler or dilution, pump) often decide reliability more than the analyser itself; analysis can be on a wet or dry basis, which must be stated.

Gas chromatography (GC).

• A small, fixed sample volume is injected (by a sample valve on-line) into a carrier gas (helium, hydrogen, nitrogen or argon) that flows through a column held in a temperature-controlled oven.
• The column contains a stationary phase (packed solid or liquid film on the wall of a capillary). Components spend different fractions of time dissolved or adsorbed in the stationary phase, so they emerge (elute) at different retention times t_R.
• Detectors: TCD (universal, non-destructive, moderate sensitivity, responds to any gas whose conductivity differs from the carrier), FID (hydrocarbons, very sensitive, destructive, needs H₂ and air), ECD (halogenated compounds), FPD (sulphur and phosphorus), and mass spectrometer (identification).
• Identification by retention time on a calibrated column; quantification by peak area with response factors from a calibration gas.
• Performance: the retention factor k = (t_R − t_M)/t_M, where t_M is the dead time of an unretained gas; selectivity α = k₂/k₁; efficiency as the number of theoretical plates N, or plate height H = L/N; resolution R_s. R_s ≥ 1.5 gives baseline separation. Raising oven temperature shortens analysis but reduces retention and may merge peaks; temperature programming balances the two.
• On-line process GCs use backflush and multiple columns to give a full analysis every few minutes, which makes them slow compared with property analysers.

Formulas

I = I₀·e^(−a·c·l) (Beer–Lambert; absorbance A = log₁₀(I₀/I))

E = (R·T/(4·F))·ln(p_O₂,ref / p_O₂,sample) (zirconia cell)

k = (t_R − t_M)/t_M, α = k₂/k₁

N = 16·(t_R/W_b)² = 5.54·(t_R/W_½)², H = L/N

R_s = 2·(t_R2 − t_R1)/(W_b1 + W_b2)

1 % = 10 000 ppm (by volume)

Symbols: I, I₀ = transmitted and incident intensity; a = absorption coefficient; c = concentration; l = optical path length; E = cell emf (V); R = 8.314 J/(mol·K); T = cell temperature (K); F = 96 485 C/mol; p_O₂ = oxygen partial pressure (or volume fraction at equal total pressure); t_R = retention time; t_M = dead time; W_b = peak width at baseline; W_½ = width at half height (all in the same time unit); N = plate number; H = plate height (m); L = column length (m); R_s = resolution.

Worked examples

Example 1 (standard): zirconia oxygen probe. Given: cell at 700 °C (973.15 K); reference air 20.9 % O₂; flue gas 2.0 % O₂ (same total pressure).

1. R·T/(4·F) = 8.314 × 973.15/(4 × 96 485) = 0.020 96 V.
2. ln(20.9/2.0) = ln 10.45 = 2.347.
3. E = 0.020 96 × 2.347 = 0.0492 V.
4. Answer: E ≈ 49 mV. Because the output is logarithmic, the probe is most sensitive at low O₂, which suits combustion control (typically 1–4 % O₂).

Example 2 (GATE level): GC resolution and efficiency. Given: 30 m capillary column; unretained-gas dead time t_M = 1.0 min; component A: t_R = 5.2 min, W_b = 0.4 min; component B: t_R = 7.8 min, W_b = 0.6 min.

1. k_A = (5.2 − 1.0)/1.0 = 4.2; k_B = (7.8 − 1.0)/1.0 = 6.8.
2. α = 6.8/4.2 = 1.62.
3. N (from B) = 16 × (7.8/0.6)² = 16 × 169 = 2704 plates (A gives the same, 16 × 13² = 2704).
4. H = 30/2704 = 0.0111 m = 11.1 mm.
5. R_s = 2 × (7.8 − 5.2)/(0.4 + 0.6) = 5.2/1.0 = 5.2.
6. Answer: k = 4.2 and 6.8, α ≈ 1.62, N ≈ 2700, H ≈ 11 mm, R_s = 5.2 (far more than the 1.5 needed, so the analysis could be speeded up). A plate height of 11 mm is poor for a capillary column, which usually achieves well under 1 mm.

Example 3 (NDIR, Beer–Lambert). A CO₂ cell transmits 80 % of the IR at 1000 ppm. At 2500 ppm in the same cell, I/I₀ = 0.80^(2500/1000) = 0.80^2.5 = 0.572. The non-linear (exponential) response is linearised in the analyser electronics.

Common mistakes

• Expecting NDIR to measure O₂, N₂ or H₂ (they do not absorb IR).
• Forgetting that a zirconia cell's output is logarithmic and that combustibles make it read low.
• Using a paramagnetic analyser in gas with high NO without correction.
• Confusing retention time with the dead time, or using peak height instead of area for quantification.
• Mixing time units for t_R and W in the plate and resolution formulas.
• Ignoring the sample system: condensation, leaks and adsorption cause most analyser errors.
• Reporting concentration without stating wet or dry basis.

For GATE IN

Expect conceptual questions matching gases to analysers (O₂: paramagnetic or zirconia; CO/CO₂: NDIR; H₂: thermal conductivity; hydrocarbons: FID) and on GC components and detectors. Numericals use Beer–Lambert absorption, the zirconia Nernst equation, ppm–per cent conversion, and GC plate number, retention factor and resolution. Practise the logarithm forms carefully.

Quick check

1. Why does O₂ not absorb infrared?
2. Convert 0.04 % to ppm.
3. Which GC detector is universal and non-destructive?
4. Two peaks: t_R = 4.0 and 5.0 min, W_b = 0.5 and 0.5 min. What is R_s?
5. What does a paramagnetic analyser exploit?

Answers: 1. It is a symmetric diatomic molecule with no changing dipole moment, so it has no IR absorption bands. 2. 400 ppm. 3. The thermal conductivity detector. 4. 2 × 1.0/1.0 = 2.0. 5. The strong attraction of O₂ into a magnetic field.