Stack Test Fallout: When a Passing Average Isn't Compliance
A chemical plant's permit caps NOx at 0.020 lb/MMBtu, determined by the arithmetic average of three 1-hour EPA Method 7E runs conducted at or above 90% of the maximum operating rate. The 2024 test ran at 94%, 97%, and 99% of rated capacity. Results: Run 1 = 0.017, Run 2 = 0.021, Run 3 = 0.023 lb/MMBtu. During Run 2 the continuous opacity monitor logged a 6-minute average of 22%; the permit limit is 20% opacity on a 6-minute average. After the test, the lab reported that the Run 3 pre- and post-test analyzer responses to the calibration gas drifted by 5.0% (analyzer reading high), against the method's 2% calibration-drift criterion. The plant manager proposes to certify compliance, citing the three-run average and 'rounding to two decimals.'
1. Compute the three-run average as reported. Does it exceed the permit limit? Evaluate the manager's rounding argument.
Read the worked answer
Average as reported
$$\bar{x} = \frac{0.017 + 0.021 + 0.023}{3} = \frac{0.061}{3} = 0.02033\ \text{lb/MMBtu}$$
Against a limit of 0.0200, that is an exceedance of 0.00033 lb/MMBtu, or about 1.7% above the limit. Run 3 alone (0.023) is 15% above the limit, and Run 2 (0.021) is 5% above.
The rounding argument
Rounding 0.02033 to the three decimals of the limit gives 0.020, which the manager reads as equality. That is not a defensible compliance position:
- Compliance is judged by comparing the measured value to the standard at the precision of the measurement, not by rounding the measurement down onto the standard. Rounding a result into the limit would let any source exceed by up to half a unit in the last decimal and still 'pass.'
- If the limit is read as two significant figures (0.020), the result 0.0203 rounds to 0.020 as well - but the very fact that the answer flips depending on rounding convention means the test does not establish compliance.
- The margin (1.7%) is well inside normal stack-test uncertainty, so the honest reading is a marginal result that cannot support an unqualified compliance certification even before the QC failure is considered.
Bottom line: the test as reported shows an exceedance of the numerical limit, and the rounding argument should be rejected. The decisive issue, however, is the invalid Run 3.
2. Given the 5.0% calibration drift in Run 3, recompute the average assuming the drift is a proportional bias, and decide whether the test can be used to certify compliance. What must be reported?
Read the worked answer
Bias correction
An analyzer reading 5.0% high means the true value is the reading divided by 1.05:
$$C_3^{corr} = \frac{0.023}{1.05} = 0.02190\ \text{lb/MMBtu}$$
$$\bar{x}^{corr} = \frac{0.017 + 0.021 + 0.02190}{3} = 0.01997\ \text{lb/MMBtu}$$
The corrected average is 0.01997 - only 0.15% below the limit. That is numerically 'passing' and practically meaningless: it is inside the noise of the method, and it rests on an assumed uniform proportional bias that the drift data do not establish (drift could be a zero offset, not a span error).
Can the test certify compliance? No.
The 5.0% drift exceeds the method's 2% acceptance criterion, so Run 3 fails QC and the three-run average is not a valid reference-method result. The choices are:
- Invalidate the test and retest within the timeframe the permitting authority directs (commonly 30 days after notification), at the required operating load.
- Report the failed test as a deviation in the monitoring report.
Do not certify compliance, and do not substitute the corrected number for a valid run.
Separate and independent: the 22% six-minute opacity average in Run 2 is an exceedance of the 20% limit that the NOx analyzer drift cannot explain or cure. Opacity and NOx are different pollutants measured by different systems. The opacity excursion must be reported as a deviation regardless of how the NOx retest turns out, and it points to a combustion/particulate problem worth investigating.
3. The plant wants to report the opacity excursion as 'not a violation' because it lasted only six minutes and coincided with soot blowing. Evaluate that position and list what belongs in the deviation report.
Read the worked answer
Evaluate the position
- The limit is written on a 6-minute average. A 6-minute average of 22% is the exceedance; duration is not a defense, it is the averaging basis.
- Soot blowing is a planned, recurring, controllable activity, not a malfunction or an upset. Planned operations do not qualify for an affirmative defense, and the plant is expected to schedule and sequence soot blowing so that the limit is met.
- The one legitimate question is whether the permit itself contains a soot-blowing provision (some permits allow a short opacity allowance during soot blowing, or require a specific soot-blowing procedure). That must be checked against the permit's terms and conditions - not assumed.
- Absent such a provision, this is a deviation and should be reported as one. Contesting its status in the report rather than disclosing it converts a minor excursion into a credibility and enforcement problem.
Contents of the deviation report
- Date, start and end times, and duration of the excursion.
- The measured value, the limit, and the averaging period (22% vs 20%, 6-minute average) - magnitude and duration, not just a narrative.
- Probable cause (soot blowing on the economizer, which unit, what soot-blowing sequence was used).
- Corrective action taken and preventive measures (revised soot-blowing sequence, load adjustment, revised operating procedure, retraining).
- Statement of whether the excursion affected the NOx test or other limits.
- Certification signature and the name/title of the responsible official.
Also determine whether the permit requires prompt (often 2–5 day) notice for deviations exceeding a defined excursion threshold, in addition to the semiannual monitoring report - the two obligations are separate.