Scale-Up: Preserve Conditions, Explain Differences

The transfer question

Scaling the proprietary commercial Aguas SB T1 method means transferring an operation to another capacity while preserving what determines its response, or measuring how those determinants change. It does not mean multiplying volume while retaining a removal percentage. The comparison concerns a defined system: water, equipment, hydraulic regime, exposure, dose, separation and measurement boundary. Before asking whether a plant reproduces a pilot, the transferable outcome must be specified: outlet concentration, mass removed from water, specific consumption or stability over an operating campaign.

T1 2.3 remains frozen in this edition. Its rules provide sizing hypotheses, not a publicly calibrated scale-up correlation. A difference between prediction and observation may reflect poorly represented inputs, unequal conditions or an insufficient model structure. Immediately attributing it to size would obstruct investigation of these alternatives. Agreement does not prove physical similarity either: different mechanisms can produce the same final COD while leaving different amounts of solids, organic carbon or nitrogen.

Five similarities worth separating

Hydraulic similarity describes flow paths, mixing and residence-time distribution. It requires identification of feed, recirculation, working volume, pressure and connections. Matching the flow-to-volume ratio does not ensure the same exposure distribution when a dead zone or preferential bypass develops. Parallel branches allow independently measured flows to be added; in series, the same flow crosses several modules. Counting module contacts does not turn that series into a multiplied tank flow.

Exposure similarity concerns how much water circulates and for how long. For a constant-volume batch, c=Qr*t/Vb; with variable flow, c=integral((Qr(t)/Vb(t)) dt). The latter expression also requires volume changes to be recorded. Continuous operation additionally involves Qr/Qf and Vb/Qf. The configurator's daily ratio, c=sum(q_i*h_i)/Vd, uses daily treated volume; it does not itself establish a distribution of individual passes.

Dose similarity distinguishes electrical charge per volume, active reagent, metal supplied and oxygen transferred. Energy similarity adds total energy and its allocation to pumping, electrical conversion and auxiliaries. Finally, matrix similarity requires composition and physical state: waters with identical COD can differ in soluble fraction, particles, conductivity, alkalinity or oxidant demand. These five similarities form a checklist, not five numbers that must be maintained simultaneously at any cost.

Example 1: Equal exposure, different operation

Consider an entirely synthetic calculation. A pilot batch of Vb=0.5 m3, recirculated at Qr=3 m3/h for t=1 h, has c=6. Another batch of Vb=5 m3, recirculated at Qr=15 m3/h for t=2 h, also has c=6. The second receives the same relative recirculated volume but takes twice as long. Equality of specific electrical charge, temperature, aeration or electrode ageing cannot be inferred.

If both hypothetically operated at constant current I=10 A, electrical dose would be D=I*t_s/Vb: 72000 C/m3 in the pilot and 14400 C/m3 in the larger batch. These are invented design quantities illustrating a balance, not recommended conditions or T1 measurements. Matching c has left a fivefold difference in specific electrical charge. If outcomes differ, this design cannot attribute the difference exclusively to hydraulic scale.

A useful comparison would establish which quantity is held constant: c, electrical dose or energy. When all cannot be preserved, a second comparison should decouple the variables. This constraint is engineering information: it reveals which similarities the architecture prevents, instead of concealing that limitation within a single correction factor.

From mechanisms to defensible extrapolation

In cavitation, geometry and pressure fields affect local exposure; a vapour cavity is not an aspirated air bubble. Visible gas does not establish cavitation intensity. A primary study of vortex devices found scale-dependent degradation per pass within its tested geometry and compound. That finding justifies measuring response transfer, not imposing the same penalty on T1. Vortex scale-up study.

Multi-mechanism extrapolation requires recognition that each operation may have a different dominant variable. Electrocoagulation requires metal dose and fate; electrooxidation requires electrical conditions and mass transfer; aeration requires gas actually transferred; separation requires solids capture and evacuation. A design preserving total energy can redistribute it between operations. Equal energy therefore does not establish equivalent treatment either.

A practical strategy compares the complete architecture first and investigates discrepancies through partial controls afterwards. Disabling an operation can change pressure losses or mixing; the control must measure those changes. A perfect decomposition is not necessary for useful learning, but unresolved confounding must be declared. Experimentally observed pH and bubble effects are recorded as findings; they do not automatically modify constants or branches of the frozen engine.

Operational plateau and persistent residual

An observed plateau indicates that increasing exposure within the tested conditions barely changes the resolvable response. It does not by itself identify an untreatable fraction. It may reflect limitations in dose, transfer, separation or analytical resolution. Formulating a persistent-residual hypothesis requires asking whether the remainder retains its behaviour when conditions are renewed and its composition is measured.

In a stage approximation, r(c)=theta*(1-exp(-k*c)). Here theta is an operational amplitude and k is an exposure sensitivity. Interpreting theta as an immutable susceptible proportion assumes more than fitting a curve. Repeating fractional removal on the entire residual allows continued removal in the calculation; if a genuinely persistent mass exists, it must be explicitly preserved between stages. These hypotheses cannot be exchanged after the outcome becomes known.

Example 2: Three tests of a plateau

A proposed mini-protocol splits the same batch into three branches after reaching a plateau defined beforehand through analytical precision and a minimum relevant change. The first branch continues under the same conditions. The second introduces intermediate separation and continues operating. The third renews a limiting condition selected in advance, such as electrode condition, while keeping the other quantities recorded. Removed volumes and masses are accounted for.

If only the second branch improves, the evidence supports a separation-related limitation, not definitive proof of a unique mechanism. If the third recovers a response, the residual was not immutable under that intervention. If none changes, several explanations remain, including inadequate experimental sensitivity. Final interpretation should compare whole-water and soluble measurements, additional energy and generated residues. Removal from water and mineralization remain different outcomes.

Example 3: Comparing pilot and plant

The proposed transfer record starts with a characterized batch or feed window, without publicly identifying facilities. Each scale requires measurement of effective volume, flows, tracer behaviour where necessary, integrated energy, doses and separation conditions. Inlet and outlet samples must correspond appropriately to residence times. Responses are then compared in physical units before percentages or performance ratios are calculated.

A condition excluded from the initial interpretation should be reserved for testing an explicit prediction. For example, if a hypothesis attributes the discrepancy to electrical dose, it should predict which comparison ought to converge when that dose is matched, without anticipating an efficacy value. New agreement would support the explanation within the tested domain; a persistent discrepancy would require another similarity to be reconsidered.

Decisions without a universal penalty

A scale-up report should conclude with a domain, not a magic coefficient: represented matrices, operating ranges, preserved variables and observed limitations. A plant may perform better, equally or worse than a pilot for measurable reasons. Commercial decisions also require capacity, maintainability and final quality, not merely maximum removal per pass. The reproducibility bank allows verification of what T1 2.3 calculates; the proposed experimental comparison investigates when those calculations transfer. These tasks complement each other but cannot replace each other.