Worked examples and reproduction

All cases in this chapter are synthetic. Some execute the T1 2.3 core directly; others are independent balances used to interpret inputs and outputs. Keeping them separate helps locate errors in the model, units or layout without conflating them.

Example 1: four turnovers do not mean 94% COD removal

Assume COD 500, BOD5 250, TSS 220, N 40 and P 8 mg/L; pH 7.2 and ammoniacal fraction 0.8. COD/BOD=2, so the matrix receives no penalty in this scenario. For one T1-16 at four turnovers without chemical options, the COD ceiling is 0.64 and exposure factor 0.9375.

r_COD = 0.64 * 0.9375 = 0.60
COD_out = 500 * (1-0.60) = 200 mg O2/L
r_BOD = 0.72 * 0.9375 = 0.675
BOD_out = 250 * (1-0.675) = 81.25 mg O2/L

These results are checked by executing frozen JavaScript. The 93.75% describes approach to the ceiling, not removal of all inlet concentration. Confusing them would materially overstate proposed capacity.

Example 2: one additional turnover

Within the same branch, five turnovers give A=0.96875, COD removal 62% and outlet 190 mg/L. Relative to four turnovers, additional exposure improves the outlet by ten mg/L. The energy cost does not fall merely because the benefit is smaller.

At declared power 1.925 kW and nominal flow 15 m3/h, each turnover costs P/q=0.128333 kWh/m3. Moving from four to five adds that energy to remove another 0.010 kg COD/m3: marginal consumption is 12.8333 kWh/kg. This does not contradict lower average consumption for the complete treatment; it answers a different question.

Example 3: operating hours and production

For 75 m3/day, a 15 m3/h unit operating 20 h/day provides c_d=15*20/75=4. Estimated energy is 1.925*20=38.5 kWh/day, or 0.513333 kWh/m3.

If production rises to 100 m3/day without changing equipment or hours, the index falls to three. Maintaining four would require 26.6667 hours from that unit within the same day, which is impossible. Capacity, storage strategy, period or configuration must change. More than 24 operating hours per day is not an acceptable operating schedule.

Example 4: three sizes at equal exposure

Using the core's declared powers and nominal flows, four turnovers require:

The difference follows from P/q without establishing equal chemistry across sizes. Performance comparison requires other exposures to be measured or maintained. External auxiliaries are not automatically included in declared power.

Example 5: attainable target and target beyond a branch

At fixed ceiling 0.64, reducing 500 to 250 mg/L requires 50% removal. Inversion gives c=-ln(1-0.5/0.64)/ln(2)=2.192645. The unit's indicative minimum-turnover rule may require more exposure than that mathematical solution. The mathematical target and operating-selection criterion are separate checks.

Reducing 500 to 125 mg/L requires 75%, above the fixed ceiling. There is no time solution within that branch. The complete engine contains bonuses and stages, so the actual configuration must be executed; the inverse calculation cannot be extended across rule changes. Another configuration predicting success is not experimental validation.

Example 6: equal concentration, different load

Two waters contain 500 mg COD/L. At 30 m3/day incoming load is 15 kg/day; at 300 m3/day it is 150 kg/day. Equal percentage removal requires ten times the removed load. With one unit's time and current unchanged, electrical dose per volume falls as production rises.

This explains why the same composition does not mean the same installation. Composition and quantity differ. It also explains why both treated flow and circulation must be reported: a 15 m3/h pump does not automatically produce 360 m3/day at the target quality.

Example 7: two interpretations of a second stage

From 500 mg/L, a first stage removing 60% leaves 200. A second removing 50% of that residual leaves 100: 80% overall. This is a correct balance under those efficiencies, not a T1 experimental prediction.

If instead a persistent residual of 180 mg/L is assumed, repeating the same mechanism cannot reach 100 under that hypothesis. The disagreement defines a useful test: determine whether the second stage acts on still-susceptible material or the first plateau was persistent. Solids separation and dose controls help interpret the result.

Example 8: signed net energy savings

For balance illustration alone, suppose aeration avoids 6000 kWh/year while added treatment uses 9000 and auxiliaries 500. Net savings are 6000-9000-500=-3500 kWh/year. Energy rises even if there is another benefit, such as achieving a quality target.

If later optimisation avoids 14000 kWh/year with unchanged added consumption, savings become 4500. The second figure cannot replace the first without supporting operating conditions. Neither is a measurement of a particular treatment plant.

Example 9: a censored result

With inlet 500 and outlet <20 mg/L, removal exceeds 96%; it is neither exactly 96% nor 100%. A simulator outlet of 19 is compatible with the censored measurement, but does not establish an error of only 1 mg/L. Actual concentrations of 2 or 18 would also be compatible.

Example 10: a known discontinuity

For the first scenario, executing 11.999 and 12 turnovers reveals the bonus change. COD removal jumps by approximately 6.40 percentage points. Physical testing on either side could investigate real continuity, but the software already explains the table's jump: a discrete condition changes branch.

This behaviour is retained as a regression test rather than a promotional result. If a future release smooths the transition, change the version, record the reason and repeat comparison cases.

Reproducing and submitting a comparison

The package contains captured code, parameters, public inputs and results. Local Node.js execution requires no AI API and sends no data to a server. reproduce.cjs checks the version and four-turnover COD/BOD outputs through three assertions. book_checks.cjs adds 33 specific checks of examples, conversions and numerical balances, identified in BOOK_CHECKS.json. It is not a universal unit or balance validator: the assertions establish computational consistency for those cases, not scientific validation.

For a comparison, retain input JSON, asset names and hashes, configuration and outputs. Then add measurements, provenance and experimental boundary. Do not change constants before calculating error on held-out results. This sequence separates reproduction, evaluation and model updating.

Opening the benchmark from this PDF

This PDF embeds T1_REPRO_2_1.zip as a file attachment. A viewer supporting attachments can extract it; some browser viewers do not expose that feature. The same ZIP is supplied separately within this edition's package. The benchmark needs no network or API and does not execute when the PDF opens. Reproduction requires an installed Node.js runtime and voluntary execution of the commands in its README.

The FILES_SHA256.json file identifies the benchmark contents. SHA-256 hashes of the captured core assets are:

t1_parametros.js
24f0d7e82a97efdc1c6310e35845e243225f2536ff9021d820fc10b8d970fc25
t1_motor_v2.js
5e306ae6953271efed422eccd9664b7a1d5c2353f6f552bb73e43556f888527d

Matching hashes establish identical bytes, not measured performance. The benchmark loads parameters then engine, without external T1_CONFIG. Website configuration changes must be recorded as differences; the frozen edition does not automatically follow the live site.