Composition analysers and transmitters

Why it matters

Product quality is defined by composition, not by temperature or pressure, so the most valuable loops in a plant (distillation purity, reactor conversion, flue-gas oxygen, effluent pH) end at an analyser. Analysers are also the slowest, least reliable and most expensive instruments on the plant, and their delays shape how tightly a composition loop can be tuned.

Key ideas

Direct and inferential measurement. A composition can be measured directly by an on-line analyser, or inferred from easier measurements (for example a tray temperature in a distillation column at known pressure, or density/refractive index of a binary mixture). Inferential measurements are fast but drift when the third components or the pressure change.

Common on-line analysers.

• Gas chromatograph (GC): a sample is injected into a carrier gas and separated in a column by differences in partitioning with the stationary phase; components elute at characteristic retention times and are detected by a thermal-conductivity (TCD) or flame-ionisation (FID) detector. Peak area is proportional to amount after calibration. It is a sampled (discontinuous) analyser with a cycle time of minutes.
• Infrared (IR/NDIR) and UV analysers: molecules absorb at characteristic wavelengths; the absorbance follows the Beer–Lambert law. NDIR is standard for CO, CO₂ and hydrocarbons.
• Oxygen analysers: paramagnetic (O₂ is strongly attracted by a magnetic field) and zirconia cells (a solid electrolyte at high temperature produces an emf depending on the ratio of O₂ partial pressures, Nernst equation), used for combustion control.
• Thermal-conductivity analysers for binary gases such as H₂ in N₂.
• Electrochemical: pH (glass electrode, Nernst slope about 59.16 mV per pH unit at 25 °C), ORP, conductivity, dissolved oxygen.
• Physical-property analysers: density, refractive index, viscosity, boiling point and flash point for products.
• Mass spectrometer: ionises the sample and sorts ions by mass-to-charge ratio; fast and multi-component but costly.

Sample conditioning. Most analysers need a sample withdrawn through a probe and a transport line, then filtered, pressure-reduced, cooled or vaporised, and returned or vented. The transport line adds a pure dead time equal to line volume divided by sample flow, often the largest delay in the loop. Fast-loop (bypass) sampling keeps this short.

Analyser dead time. A sampled analyser with cycle time T reports a result at the end of each cycle and holds it until the next. The information is therefore between T and 2T old, so the analyser behaves roughly like a dead time of about 1.5 T plus the sample transport delay. Dead time limits achievable controller gain (see controller tuning).

Transmitters. A transmitter converts the primary element's signal into a standard signal: 4–20 mA, 20–100 kPa pneumatic, or digital (HART superimposed on 4–20 mA, Foundation Fieldbus, Profibus). Key settings are zero (the value at 4 mA) and span (the range covered). Smart transmitters allow remote re-ranging, diagnostics and temperature compensation. Elevated or suppressed zero is used, for example, in level transmitters with wet legs.

Calibration. Analysers drift, so they are checked against certified calibration gases or standard solutions, usually at zero and one span point. A two-point calibration fixes both the offset and the slope of a linear response.

Formulas

A = −log₁₀(I/I₀) = ε·b·c

• Beer–Lambert law: A absorbance (dimensionless), I/I₀ transmittance, ε molar absorptivity (m²/mol), b path length (m), c concentration (mol/m³). Valid for dilute samples and monochromatic light.

c = c_std·(A / A_std)

• One-point calibration in the linear (Beer–Lambert) range with the same cell.

x = LRV + (I − 4)·(URV − LRV)/16

• Value x from a 4–20 mA signal I (mA) for a linear transmitter.

θ_line = V_line / Q_sample = (π·d²/4)·L / Q_sample

• Transport dead time (s): d tube inside diameter (m), L length (m), Q_sample sample flow (m³/s).

θ_analyser ≈ θ_line + 1.5·T_cycle

• Approximate effective dead time of a sampled analyser with cycle time T_cycle (s).

E = s·(7 − pH), s = 2.303·R·T/F ≈ 0.1984·T mV per pH

• Ideal glass electrode with isopotential point at pH 7: E in mV, T in K, R = 8.314 J/(mol·K), F = 96 485 C/mol. s = 59.16 mV/pH at 298.15 K.

Worked examples

Example 1 (standard): IR absorbance. An IR analyser cell gives an absorbance of 0.30 with a standard containing 2.0 mol/m³ of CO₂. A process sample in the same cell transmits 40 % of the incident beam. Find the CO₂ concentration.

1. A = −log₁₀(I/I₀) = −log₁₀(0.40) = 0.398.
2. Beer–Lambert, same ε and b: c = c_std·(A/A_std) = 2.0·(0.398/0.30).
3. c = 2.65 mol/m³.

c ≈ 2.65 mol/m³

Example 2 (GATE level): dead time of a GC composition loop. A GC analysing a distillate has a cycle time of 4 min. The sample travels through 30 m of tubing of 6 mm inside diameter at 1.0 L/min. Estimate the effective dead time contributed by the measurement.

1. Line volume: V = (π·d²/4)·L = (π·0.006²/4)·30 = 8.48 × 10⁻⁴ m³.
2. Sample flow: Q = 1.0 L/min = 1.0 × 10⁻³/60 = 1.667 × 10⁻⁵ m³/s.
3. Transport delay: θ_line = V/Q = 8.48 × 10⁻⁴ / 1.667 × 10⁻⁵ = 50.9 s.
4. Sampling delay: 1.5·T_cycle = 1.5·240 = 360 s.
5. θ ≈ 50.9 + 360 = 410.9 s.

θ ≈ 411 s (about 6.8 min). The analyser, not the column, may set the loop speed; a tray-temperature inner loop or a faster analyser is the usual remedy.

Example 3 (short): pH at temperature. At 60 °C (333.15 K) the electrode slope is s = 0.1984·333.15 = 66.1 mV/pH. A reading of E = +120 mV gives pH = 7 − 120/66.1 = 5.18. Using the 25 °C slope would give 7 − 120/59.16 = 4.97, which is why pH transmitters carry automatic temperature compensation.

Common mistakes

• Treating a GC like a continuous instrument and ignoring its cycle time and sample-line delay in the loop.
• Using percentage transmittance directly in place of absorbance; Beer–Lambert is linear in A = −log₁₀(I/I₀), not in I/I₀.
• Forgetting that a tray temperature is a composition proxy only at constant pressure.
• Mixing up zero and span when re-ranging a transmitter; changing the zero shifts the whole range, changing the span changes the slope.
• Applying the 25 °C pH slope at other temperatures.

For GATE CH

This topic mostly appears as conceptual questions: which analyser for which species (paramagnetic for O₂, NDIR for CO₂, GC for multicomponent hydrocarbons), what a transmitter does, and the 4–20 mA conversion. Its main numerical link is dead time: transport and sampling delays enter transfer functions as e^(−θs) and reduce the stability margin, which GATE tests through Bode and tuning questions.

Quick check

1. Why is a gas chromatograph called a discontinuous analyser?
2. A 4–20 mA O₂ transmitter ranged 0–5 % reads 14.4 mA. What is the O₂ content?
3. Doubling the sample flow in a transport line changes the transport delay by what factor?
4. Which property of oxygen does a paramagnetic analyser use?

Answers: 1. It analyses one injected sample per cycle and holds the result until the next cycle. 2. 3.25 % O₂. 3. It halves the delay. 4. Its strong attraction into a magnetic field (paramagnetism).