Running a stack test

source testingisokinetic samplingemission rate calculationoxygen correctionstack sampling

Running a stack test: exit velocity, the isokinetic sampling rate, ppm to mass units, correction to reference oxygen, and the emission rate.

Stack Exit Velocity

v_s = \frac{4 Q_v}{\pi d^2}

The speed exhaust leaves a round stack, from the volumetric flow and the inside diameter. Every plume-rise calculation starts here, and so does the check against stack-tip downwash.

Isokinetic Sampling Rate

Q_n = v_s A_n

The flow a sampling train must draw so that gas enters the nozzle at exactly the stack velocity. Get this wrong and the particulate result is biased in a direction you can predict from the sign of the error.

ppm to mg/m³ Conversion

C = \frac{ppm \cdot M}{24.45}

Converts a gas concentration by volume into one by mass, using the molar volume of an ideal gas at 25 °C and 101.325 kPa. The bridge between an analyser that reads in ppm and a limit written in mg/m³.

Excess Air from Flue Gas Oxygen

EA = \frac{O_2}{20.9 - O_2}

How much air beyond stoichiometric is passing through a burner, read straight off the oxygen in the flue gas. The single most useful number a combustion analyser gives you, because everything about efficiency follows from it.

Emission Correction to Reference Oxygen

C_{corr} = C_{meas} \, \frac{20.9 - O_{2,ref}}{20.9 - O_{2,meas}}

Restates a measured stack concentration at the reference oxygen a limit is written at, so that adding dilution air can no longer make an emission look cleaner than it is. The US EPA convention, built on 20.9 % oxygen in ambient air.

Emission Rate from Stack Concentration

E = C \, Q_v

The mass of pollutant leaving a stack per unit time, from the measured concentration and the volumetric flow. This is the number a permit limit is written against and the source strength every dispersion model asks for.

Particulate Collection Efficiency

\eta = \frac{C_{in} - C_{out}}{C_{in}}

The fraction of the dust entering a control device that does not leave it, from inlet and outlet loadings. The number on every baghouse, cyclone and precipitator datasheet, and the one most often quoted with too many nines.

How they fit together

A stack test turns an instrument reading into a number on a compliance report, and every step between the two is a chance to be honestly wrong. Stack exit velocity comes first because the sampling depends on it: volumetric flow over the stack's internal area. Isokinetic sampling rate is the reason it matters. Draw sample gas slower than the stack is moving and the streamlines spread around your nozzle while heavy particles carry straight into it, and you over-report particulate; draw faster and light particles are pulled in while heavy ones are missed, and you under-report. Isokinetic means matching the two velocities so the sample is representative, and regulatory methods generally require the ratio to fall within 90 to 110%. Outside that window the run is void, not merely uncertain — which is why this calculation is done at the port before anything is measured, and repeated when conditions drift.

The middle three put the reading in reportable form. ppm to mg/m³ is a units conversion that hinges on molar mass, so it needs the pollutant named — the same 100 ppm is 143 mg/m³ of SO₂ and 205 mg/m³ of NO₂, and quoting a converted figure without saying which compound and at what temperature and pressure basis is meaningless. Correction to reference oxygen is the step outsiders find strangest and it exists to close an obvious loophole: dilution air lowers a measured concentration without removing a single gram of pollutant, so limits are written at a reference O₂ — commonly 3% for oil and gas boilers, 6% for solid fuel, 11% for incinerators — and everything is normalised to it. Excess air from flue gas oxygen is the same measurement read as combustion information rather than as a correction, and it is worth running alongside, because a high excess air figure explains both a comfortably low uncorrected reading and a poor thermal efficiency at the same time.

Emission rate from concentration is the answer the permit is written in: concentration times volumetric flow, giving mass per hour. Use the corrected concentration and the flow on the same basis — mixing a dry corrected concentration with a wet actual flow is the mistake that survives review because both numbers are individually right. Particulate collection efficiency sits at the end as the control device's own report card, inlet against outlet loading, and it is worth reading in the awkward direction: the difference between 99% and 99.9% sounds trivial and is a tenfold change in what leaves the stack. Efficiency is the wrong scale for judging an outcome. Emission rate is the right one.