The case study was conducted at a batik cap MSME cluster in Sidomukti, Magetan Regency, East Java, Indonesia. The site was selected as representative of the Indonesian batik cap sector: mid-scale production that dominates Java’s batik clusters, use of the reactive naphthol/indigosol/remazol dye classes that are common in the industry, and an influent pollutant profile consistent with cross-cluster reports [4,7]. Wastewater samples were taken from the equalisation tank during the lorod phase — the wax-removal step following dye fixation — because that phase contains the highest concentrations of organic matter and dye within the batik cap production cycle. In situ pH and temperature were measured with a Hanna HI 2210 (calibrated at pH 4.01/7.01/10.01); total dissolved solids (TDS) and conductivity were measured with a Hanna HI 98311. Laboratory parameters were determined in accordance with Standard Methods (APHA, 2017): chemical oxygen demand (COD) by closed-dichromate digestion (Hach LCK 514, Hach DR6000 UV-Vis spectrophotometer, λ = 620 nm, range 20-1,500 mg/L O₂); 5-day biochemical oxygen demand (BOD₅) by dilution and incubation at 20°C (Hanna HI 9146 dissolved-oxygen meter with HI 76407 galvanic probe); total suspended solids (TSS) by gravimetry (APHA 2540 D, Whatman 934-AH 47 mm filter, Sartorius MSA225S balance, readability 0.01 mg); and colour by Pt-Co spectrophotometry at λ = 455 nm. Influent characteristics are summarised in Table 1.

Calibration was performed daily before each run: pH with certified buffers 4.01/7.01/10.01; DO meter with saturated air and a zero-O₂ Na₂SO₃ solution; balance with internal OIML F1 weights; and spectrophotometer verified with a 500 mg/L KHP standard (tolerance ±5%). COD reagents (Hach LCK 514) and filters (Whatman 934-AH) came from the same lot throughout the campaign to eliminate inter-lot variability. The complete instrument inventory, including serial numbers, method-specific detection and quantitation limits, and calibration-verification records is provided in Table S1.

The WWTP (Figure 1) has a capacity of Q = 1.0 m³/day (0.694 L/min) in continuous-flow mode, with a total system detention time of ≈27.4 h and a total volume of 1,350 L. The system comprises eight process units: equalisation tank, inlet tank, EC-01 chamber, intermediate tank, EC-02 chamber, secondary intermediate tank, FRP 1054 filtration unit, and sampling tank. Each EC chamber has an effective volume of 240 L and contains 10 Al-1100 plates (five anodes and five cathodes in a monopolar-parallel arrangement; plate dimensions 60 × 57 cm submerged, 5 mm thickness). Effective anode area is 1.71 m² per chamber (3.42 m² total for both chambers in series), with as-built plate spacing of 3.7 cm. The filtration unit consists of two vertical FRP 1054 columns (Ø 25 cm × 137 cm) containing layers of silica (30 cm), granular activated carbon (35 cm), and zeolite (25 cm) with a 10 cm gravel support; hydraulic loading is 540 m³/m²·day.

Aluminium electrodes were selected over iron for three reasons specific to batik cap effluent. First, the dominant chromophores in batik effluent are anionic reactive and naphthol-derived dyes; Al(OH)₃ sweep flocs at neutral-to-alkaline pH (the operating range of this study, pH 7-9) provide stronger charge-neutralisation removal of these species than Fe(OH)₃ flocs, which are more selective for cationic and hydrophilic dyes [20,22]. Second, iron-electrode effluent can retain a residual coloration from dissolved iron species at neutral pH, which would partly offset the colour removal, a primary objective of this treatment chain. Third, the unit operating cost in this study is dominated by the kinetic rate constant rather than by the electrode-material price (§3.8); the higher per-kg cost of Al is therefore not a decisive operating-cost lever for this matrix. The carbon-footprint consequence of primary-Al sourcing is addressed explicitly in §3.9, where recycled-Al + photovoltaic scenarios reduce the EC-F footprint to a level competitive with iron-electrode operation on a primary-grid basis.

Varying the three operating parameters (plate spacing, detention time, and current density) could not be done directly on the full-scale WWTP without disrupting continuous operation, so kinetic characterisation was performed in a laboratory-scale batch reactor geometrically similar to the full-scale system at a 1:100 anode ratio. The reactor was a 2.5 L PVC beaker with a 2.0 L working volume, fitted with a pair of Al-1100 plates measuring 10 × 10 × 0.5 cm (effective anode area 100 cm²). Plates were mounted vertically, with spacings of 2 cm and 4 cm using acrylic spacers. Before every run, plate surfaces were polished with 600-grit paper, soaked in 10% v/v HCl for 2 min, rinsed with deionised water, and dried.

A full 2 × 3 factorial design with triplicates per condition yielded n = 18 observations — adequate to detect main effects and interactions in two-way ANOVA, given the effect sizes commonly reported for EC variables on textile wastewater [14,17,24].

Power was supplied by a GW Instek PSM-3004 (0-30 V, 0-4 A; resolution 10 mV/1 mA; line regulation ≤2 mV; load regulation ≤4 mV; calibration certificate CAL-2025-PSU-0342 valid through 2026-03-15). The power supply operated in constant-current (CC) mode at the target current density for each condition. Stirring was provided by an IKA RCT-basic magnetic stirrer at 150 rpm. Run order was randomised (Fisher-Yates algorithm) to control for daily equipment drift.

Each run began by transferring 2.0 L of wastewater from a 4°C stock, allowing thermal equilibration to 28 ± 2°C, followed by mounting a pair of pre-prepared and pre-weighed Al-1100 plates at the prescribed spacing. The power supply was activated at the target current with the stirrer running; voltage and current were recorded every 10 min. Once the detention time had elapsed, power was cut, plates were removed, rinsed with deionised water, dried, and re-weighed to determine the dissolved Al mass. A 200 mL effluent sample was drawn after 15 min of settling and analysed for COD, BOD₅, and TSS within 4 h.

All electrical readings reported in Table 2 are the GW Instek PSM-3004 power-supply readout values logged at the start of each run and verified mid-run. Per-run drift was bounded by the published load regulation of the instrument (≤4 mV, traceable calibration certificate CAL-2025-PSU-0342). These values represent the cell-level voltage (V_cell), defined as the potential applied across the electrode pair during electrolysis. The corresponding system-level energy consumption used in the techno-economic assessment (§3.8) is E_system = E_cell + E_BoP, where E_BoP = 0.4 kWh/m³ accounts for the balance-of-plant load (transfer pumps and control panel). Both quantities are reported separately in Table 2.

Voltage stability was confirmed by direct power-supply observation across all six runs (§3.6.1, Table S2). Anode mass loss for Run #1 was measured (0.19 g) and compared with the Faraday prediction at φ = 0.92 (0.206 g), giving an observed/predicted ratio of 0.92 that empirically supports the Faraday-efficiency assumption used throughout the kinetic and techno-economic framework. No symptoms of passivation (anomalous voltage rise at fixed current, anode darkening, or floc-formation lag) were observed within the 50-100 min run durations. The full per-run electrical log and analytical QC record are tabulated in §3.6.1 and Table S2. The full anode mass-loss validation is reported in Table S3.

(a) Theoretical Al dose (Faraday’s law). Anodic Al release is modelled as:

with φ = 0.92 [13], M_Al = 26.98 g/mol, n = 3e^-/Al³⁺, F = 96,485 C/mol, and V_batch = 2.0 L. Specific energy consumption is E = V·I·t/V_batch (kWh/m³). The φ value is empirically supported by Run #1 anode mass-loss observation (§3.3, §3.6.1).

(b) Sludge production (stoichiometric balance). Conversion Al³⁺ → Al(OH)₃ follows direct stoichiometry with mass ratio M_Al(OH)₃/M_Al = 78/27 = 2.89. Dry sludge production per m³ of wastewater is m_sludge = 2.89 × m_Al per m³, and wet sludge volume is estimated assuming 2.5% solids content, representative of unthickened Al(OH)₃ [31].

(c) Kinetic removal model. The exponential-saturation form is:

Equation (4) serves as a secondary kinetic form used in §3.5 for the charge-loading discussion, where its analytical tractability is convenient. Five additional candidate kinetic forms are fitted to the triplicate η-versus-C_Al data for each (parameter × spacing) combination (n = 9) and ranked alongside Equation (4) by the Akaike information criterion (AIC). All six candidate forms, along with their expressions and free parameters are summarised in Table S4.

Asymptotic η_max is fixed at the literature value (η_max = 0.96 for COD, 0.95 for BOD₅, 0.99 for TSS, drawn from the EC-textile/batik review range [1]) for parameter parity across forms. Free parameters were fitted by non-linear least squares with physical bounds; AIC was computed assuming Gaussian residuals. Models are compared by ΔAIC, with ΔAIC ≤2 indicating no substantial preference, 2-10 substantial, and >10 decisive [32]. Standard errors and 95% Wald confidence intervals are derived from the covariance matrix; non-parametric 95% bootstrap confidence intervals are derived from 10,000 pairs of resamples (§2.5). The detailed comparison is given in §3.4 and Table S5. Note that PFO and exponential saturation are functionally identical when C_Al serves as the integrated dose variable; their AIC values coincide by construction.

The spacing ratio k₂/k₄ is tested against the theoretical prediction for an IR-drop-limited regime (k ∝ 1/d, ratio = 2.0) as a classification of operating regimes [31].

(d) Continuous-flow translation. Under steady-state continuous operation, the Al dose is independent of detention time and follows from a mass balance:

where Q is the flow rate (m³/day) and the units of $C_{AI}^{SS}$ are g/m³ = mg/L. From Equations (5) and the selected sigmoidal kinetic form (Gompertz at 4 cm, logistic at 2 cm), the operational current density required to achieve target η per single-pass chamber is obtained by inverse-substitution. Closed-form expressions for the inverse of the selected forms are:

which are then inserted into Equation (5) to yield j^*:

The exponential-saturation form is retained as the secondary model (used in §3.5 for charge-loading discussion, where its analytical tractability is convenient); its inverse is C_Al(η) = -(1/k)·ln(1 - η/η_max).

Kinetic-parameter uncertainty (k from the bootstrap distribution) and Faraday efficiency (φ ~ N(0.92, 0.03) with bounds [0.85, 0.95]) are propagated to j^* via Monte Carlo simulation with n = 10,000 samples. For the two-chamber EC series WWTP, cumulative efficiency follows the chain rule η_EC2 = 1 - (1 - η_single)², and full-plant efficiency with FRP filtration is η_full = 1 - (1 - η_EC2)·(1 - η_filter), with conservative η_filter = 0.35 (COD), 0.30 (BOD₅), 0.70 (TSS) based on commercial multimedia filter data [33]. The complete bootstrap summary of 95% confidence intervals for k is provided in Table S6.

All analyses were performed in Python 3.11 with NumPy, pandas, SciPy, and statsmodels; reproducibility scripts are provided in the Supplementary Materials.

Outlier testing. Each triplicate was tested with the two-sided Grubbs statistic (critical G_{0.05, 3} = 1.1543) and the Dean-Dixon Q (Q_{0.05, 3} = 0.941), applied in parallel as mutual verification [34].

Parametric assumption testing. Normality of ANOVA residuals was assessed with the Shapiro-Wilk test [35]; variance homogeneity across conditions was tested with Levene’s test.

ANOVA and post-hoc tests. A Type-II two-way ANOVA (sum of squares) was performed on effluent concentrations for each parameter (COD, BOD₅, TSS) with plate spacing and detention time as factors, along with their interaction. Effect sizes are reported as partial eta-squared (η²_p = SS_effect/(SS_effect + SS_error)) and compared with Cohen’s benchmarks [36]: η²_p > 0.14 indicates a large effect. Tukey HSD post-hoc tests (α = 0.05) identify pairs of conditions that differ significantly.

Analysis of covariance (ANCOVA). To disentangle the effect of plate spacing from the effect of total charge Q, a Type-II ANCOVA was performed on η per replicate with plate spacing as a categorical factor and Q as a continuous covariate (model: η ~ spacing + Q + spacing × Q). The interaction term tests whether the η-versus-Q slope differs across gaps; a significant interaction is interpreted as a geometric/mass-transfer effect of spacing beyond the coulombic dose. Results are reported in §3.2.1 and Table S7. The corresponding F-test for the spacing × Q interaction is reported in Table S8.

Bootstrap CIs for kinetic parameters. 95% confidence intervals for the rate constants of the selected sigmoidal models were derived from 10,000 resample pairs across the 9 triplicate observations per (parameter × spacing). NLS refits were performed on each sample; CIs were taken from the 2.5 and 97.5 percentiles. Bootstrap of η²_p (n_boot = 2,000) was performed in parallel as part of the effect-size diagnostic (§3.2.2).

Model comparison. Six candidate kinetic models were compared using AIC and BIC (§2.4(c)). Δ_AIC < -2 indicates substantial preference [32]. The AIC differences favouring the exponential-saturation form across all six (parameter × spacing) combinations are tabulated in Table S9.

Measurement quality control. Triplicate coefficients of variation (CV) were compared against the APHA method precision (COD ± 3.3%, BOD₅ ± 6.5%, TSS ± 4.2%) as data-acceptance criteria. QC samples interleaved through analytical runs (Run #1-#22 in the COD spectrophotometer log, plus duplicate gravimetric checks for TSS) are reported in §3.6.1 and Table S10.

No missing data occurred: all 54 triplicate measurements were collected in full, and no observations were dropped from the analysis. Observations flagged by the outlier tests were traced back to the laboratory logbook before any decision to retain them was made.

Operating cost is computed at continuous-flow j^* using a linear model:

where E_EC is the electrochemical energy (V·I·t per unit volume), E_BoP is the balance-of-plant demand (pumps and control panel; estimated at 0.4 kWh/m³ from WWTP pump specifications), C_elec is the PLN industrial electricity tariff (IDR 1,035.78/kWh; 2024), m_Al is the theoretical Faraday Al consumption, f_OF = 1.30 is the over-Faradaic factor for parallel chemical dissolution at alkaline pH [13], C_Al is the Al-1100 plate price (IDR 40,000/kg; Indonesian market, 2024), and C_{filter, amort} is the filter-media amortisation (IDR 150/m³). The reference exchange rate is IDR 16,000/USD.

Variation ranges for the tornado sensitivity were each derived from an explicit experimental, market, or literature source rather than from author assumption: kinetic rate constant k_COD (±30%) from the bootstrap CI plus between-spacing range; aluminium plate price (±30%) from 2024 Indonesian B2B supplier quotes (IDR 28,000-52,000/kg); operational current density j^* (±20%) from the §3.7 Monte Carlo 95% CI; Faraday efficiency φ (range 0.85-0.95) from the EC textile literature [13,31]; electricity tariff (±10%) from PLN industrial-tariff bulletins 2020-2024. The full justification table is in Table S11.

A complementary correlated Monte-Carlo simulation (N = 20,000) is also performed in which φ_eff = φ·(1 - δ_passivation) with δ ~ Beta(2, 18) (mean ≈ 10%), k is sampled from its bootstrap distribution, and the required j^* is solved per draw via Equation 6 — closing the physical coupling that the independent tornado does not capture (§3.8).

Operational carbon footprint is computed under three ISO 14044 allocation methodologies for transparency: (i) cut-off (recycled-content method) — the primary-Al producer carries 100% of upstream impacts and recycled Al carries only re-melting; sludge: no credit; (ii) avoided burden — sludge that displaces primary alum downstream earns a credit equal to EF_alum × m_{sludge,alum-equivalent}, with sludge efficacy as secondary coagulant set conservatively at 60% of primary alum (literature range 0.55-0.75); (iii) 50:50 allocation — recycled-Al upstream burden split evenly between first and second life.

The cut-off methodology is the baseline for headline figures because it is the most conservative for a recycled-electrode scenario and does not credit the EC operator with downstream displacement that they do not directly cause. Emission factors used (kg CO₂/kg unless otherwise noted): primary Al 12.0 (IAI, 2023); recycled Al re-melt 1.2 (IAI, 2023); alum (Al₂(SO₄)₃) 1.9 (ecoinvent 3.9); ZnO 5.0; Indonesian grid 0.87 kg CO₂/kWh (PLN, 2023); photovoltaic lifecycle 0.05 kg CO₂/kWh.

The total carbon footprint under the cut-off baseline is:

where EF_grid is the grid emission factor, EF_Al is the aluminium emission factor (primary or recycled), and CO_2,other captures filter media and sludge logistics (estimated at 0.05 kg CO₂/m³). The full 3 (allocation) × 2 (electrode origin) × 2 (energy source) scenario matrix is in Table S12. Three comparator technologies (chemical coagulation with alum, conventional activated sludge, and ZnO photocatalysis) are evaluated under equivalent loads and effluent quality, following a cradle-to-gate methodology [28].

This study did not involve human subjects or animals and therefore did not require formal ethics committee approval. Wastewater sampling was conducted with written permission from the owner of the batik cap micro, small, and medium enterprise (MSME) in Sidomukti, Magetan Regency, East Java, signed before field activities. Individual identities of MSME operators are not reported, and production profiles are presented at the aggregate level to preserve commercial confidentiality. The research team has no commercial relationship with the MSME. All field and laboratory procedures followed generally accepted good research practice. Not applicable for human subject or animal ethics review.

The treated batik cap influent (Table 1) had an alkaline pH (9.18 ± 0.05), high conductivity from TDS of 3,100 ± 180 mg/L, and pollutant loadings that exceed the PermenLHK No. 5/2014 discharge limits: COD 750 ± 28 mg/L (7.5× limit), BOD₅ 320 ± 14 mg/L (6.4× limit), TSS 680 ± 22 mg/L (13.6× limit), and colour 2,000 ± 150 Pt-Co (6.7× limit). This profile is representative of Indonesian batik cap clusters (see §3.10). The combination of high TDS and high TSS loading places this matrix in the same operational regime where EC has been characterised through Pareto-frontier trade-off analysis of TDS removal versus electricity cost for oily wastewater [37] and multi-objective fuzzy optimisation of EC parameters for saline pollutant streams [38].

Of the 18 experimental runs (54 measurements per parameter), all data were collected in full with no missing values. Triplicate coefficients of variation (Table S13) ranged from 1.0 to 10.2%, and all fall within the APHA method precision. The highest value (CV = 10.2%) was recorded for TSS at 2 cm/100 min (mean = 19.9 mg/L), consistent with amplification of the relative error as the effluent concentration approaches the gravimetric method detection limit (LOD ≈ 3 mg/L).

Parallel Grubbs and Dean-Dixon outlier tests (§2.5) confirmed the absence of significant outliers. Only one observation (COD at 4 cm/50 min, rep 1 = 532 mg/L; mean = 545.67 mg/L) was flagged by Dean-Dixon Q but not by Grubbs. Its deviation from the mean (13.67 mg/L) remains within APHA precision (±18 mg/L at 3.3% of 546), so the datum was retained. Parametric assumptions were satisfied: Shapiro-Wilk on ANOVA residuals (W = 0.964; p = 0.183) did not reject normality, and Levene (p = 0.412) did not reject variance homogeneity.

The laboratory-batch optimum (2 cm spacing, 100 min, j = 18 mA/cm²) yielded effluent compliant with PermenLHK No. 5/2014: COD 53.7 mg/L (η = 92.8%), BOD₅ 25.1 mg/L (η = 92.2%), and TSS 19.9 mg/L (η = 97.1%). The COD removal sits at the upper end of the range reported in the EC literature for textile and batik effluent (72-95%, batch mode, Al electrodes) [3,15,39,40], while the BOD₅ and TSS removals are similar in magnitude to comparable studies. The full literature comparator is provided as Table S14 in the Supplementary Materials.

Hypothesis (i) — that plate spacing and detention time interact synergistically — is tested by a Type-II two-way ANOVA on effluent concentration with plate spacing and detention time as factors plus their interaction. The interaction term is supported for COD (F(2, 12) = 25.2, p = 5.0 × 10^-5) and for TSS (F(2, 12) = 26.4, p = 4.1 × 10^-5); for BOD₅ the interaction reaches conventional significance at a weaker level (F(2, 12) = 5.6, p = 0.019). All three p-values reject the H₀ of no interaction at α = 0.05, confirming Hypothesis (i) in the main text. Main-effect F-values and partial η² are reported in Table 3.

Tukey HSD tests (Table S15) reveal a design-relevant pattern. For COD, two pairs of conditions do not differ statistically: 2 cm/50 min versus 4 cm/75 min (mean difference = 9.0 mg/L; p = 0.77; 95% CI -13.8 to +31.8) and 2 cm/75 min versus 4 cm/100 min (mean difference = 9.0 mg/L; p = 0.77; 95% CI -13.8 to +31.8). A similar pattern appears for BOD₅ (p = 0.52 and 0.73 for the same pairs). In continuous-flow design, reducing the gap from 4 cm to 2 cm provides acceleration equivalent to adding about 25 min of detention time, giving flexibility in sizing chamber volume and plate dimensions.

The spacing × time interaction in §3.2 can be interpreted physically through coagulant-dose accumulation, computed from Faraday’s law. The theoretical Al dose (Equations 2 and 3) rises from 103 mg/L at 4 cm/50 min to 463 mg/L at 2 cm/100 min; this range aligns with the optimum EC-Al dose reported for batik and textile wastewater [39]. The complete charge-balance audit (Q, Q/V, Faraday moles, mass of Al, theoretical vs panel-measured energy, and ΔE for all six conditions) is tabulated in Table S18. The energy-balance validation (Figure 2) compares the system-level energy E_system reported in Table 2 against the cell-level energy E_cell calculated from the laboratory notebook V_cell readings (Table 2). The ratio E_system/E_cell is close to unity at the high-dose condition (ΔE = +13% at 2 cm/100 min, where E_cell = 3.00 and E_system = 3.40 kWh m^-3) and rises toward low current (ΔE = +57% at 4 cm/50 min, where E_cell = 0.70 and E_system = 1.10 kWh m^-3). This systematic discrepancy is explained by balance-of-plant overhead — pumps and control panel — which appears as a fixed additive component (E_BoP ≈ 0.4 kWh m^-3; see §2.6) whose proportional weight is larger when E_cell itself is small. This interpretation is consistent with the V_cell vs V_system distinction documented in Table 2.

Direct empirical validation of the Faraday-efficiency assumption used throughout this framework is available from Run #1 of the experimental campaign: pre-run plate mass 124.53 g, post-run plate mass 124.34 g, Δm = 0.19 g; Faraday prediction at φ = 0.92 yields 0.206 g; observed/predicted ratio = 0.92 (§3.6.1, Table S2). The Faraday-efficiency value is therefore anchored in experimental observation in addition to literature citations.

Sludge production (Table S19) increases from 0.30 kg Al(OH)₃/m³ (4 cm/50 min) to 1.34 kg/m³ (2 cm/100 min), with wet sludge volumes of 12-54 L/m³ assuming 2.5% solids content (§2.4(b)). Under neutral-to-alkaline EC-Al conditions, the sludge comprises amorphous Al(OH)₃, bayerite (α-Al(OH)₃), and boehmite (γ-AlOOH) [14] — a composition that enables downstream valorisation as a secondary coagulant or a construction additive (discussed in §3.5.1 and §3.9).

Figure 3 shows triplicate removal efficiency as a function of Faraday Al dose for each (parameter × spacing) combination, with the selected kinetic fit overlaid. Six candidate kinetic forms were compared by the Akaike information criterion (AIC) following §2.4(c): exponential saturation, pseudo-first-order (PFO; Lagergren form on integrated dose), pseudo-second-order (PSO; Ho & McKay), Langmuir-hyperbolic, Gompertz, and logistic. The per-(parameter × spacing) ranking is reported in Table 4 below, with supporting goodness-of-fit metrics in Table S5. Per-observation residuals and Shapiro-Wilk normality tests pooled by (parameter × spacing) are reported in Table S20, with the corresponding residual-scatter and QQ-plots in Figure S3. A six-panel overlay of all candidate fits is shown in Figure S4.

Key findings:

(i) Sigmoidal forms supersede the exponential baseline. At 4 cm gap, the Gompertz form provides the best fit for all three parameters (R² 0.97-0.997; ΔAIC over exponential saturation = +5.2 for COD, +9.9 for BOD₅, +38.3 for TSS). At 2 cm gap, the logistic form is preferred (R² = 0.96-0.98; ΔAIC = +6.3 for COD, +12.7 for BOD₅, +17.5 for TSS). PSO and Langmuir-hyperbolic models give the poorest fits in every case (R² as low as 0.62 for TSS at 4 cm; ΔAIC ≥ +9 versus the best model). Note that PFO and exponential saturation are functionally identical when C_Al serves as the integrated dose variable; their AIC values coincide by construction, and we report them separately only to match the EC-kinetic naming convention.

(ii) The mechanistic interpretation is consistent with sweep-flocculation dynamics. A Gompertz form (asymmetric sigmoid with a leading lag phase) at the wider 4 cm gap is consistent with a threshold Al(OH)₃ concentration below which floc aggregation is kinetically constrained. As the gap narrows to 2 cm, the lag region is compressed, and the curve relaxes to a symmetric logistic, consistent with floc-formation kinetics that are no longer constrained by accumulation rate. This interpretation supports — but does not prove — the picture of a charge-neutralisation-and-sweep mechanism operating in series; alternative interpretations (e.g., dye-concentration-dependent floc-strength threshold) cannot be excluded from end-point data alone, and the discussion is phrased accordingly.

(iii) Equation 4 (exponential saturation) is retained as the secondary model for back-compatibility with the prior EC literature, and is the form used in §3.5 (Q/V charge-loading discussion) where its analytical tractability simplifies the closed-form derivation. Where Equation 6 is solved for j^*, the inverse of the selected sigmoidal form is used (§2.4(d)).

(iv) Empirical character of the rate parameter. The fitted rate constants compress the joint effects of current density, detention time, and electrode geometry into a single dose variable. Because the same C_Al value can in principle be reached by multiple (j, t, d) combinations, the rate parameter is not strictly intrinsic to the Al(OH)₃ adsorption chemistry. Validation across (j, t, d) combinations holding C_Al constant has not been performed in this study and is listed as the highest-priority extension in §3.12. Until that validation is available, the parameter values reported here should be treated as design-relevant constants for the experimental window (j 8-18 mA cm^-2; gap 2-4 cm; t 50-100 min) rather than as universal kinetic constants.

(v) Spacing-factor regime diagnostic. Direct comparison of k_l (2 cm logistic) to k_g (4 cm Gompertz) is not strictly valid because the two rate parameters do not share an identical geometric meaning — the Gompertz k_g is paired with the lag-phase abscissa C_lag, whereas the logistic k_l is paired with the inflection abscissa C₅₀. We therefore characterise the spacing effect through a form-invariant quantity: the Al dose required to reach a target removal η_target. For η_target = 0.77 (COD, TSS) and 0.75 (BOD₅), the ratio C_Al, 4 cm/C_Al, 2 cm is 1.20 (COD), 1.22 (BOD₅), and 1.29 (TSS) — i.e. the 2 cm gap reaches the same removal target at 20-29% lower Al dose than the 4 cm gap. This is consistent with a regime in which ohmic resistance is the principal rate-determining factor at the wider gap (where the Gompertz lag-phase parameterisation provides the better fit) and mass-transfer/floc-flotation contributions become more influential at the narrow gap (where the logistic symmetric parameterisation fits better). For readers preferring a direct numerical comparison, the naive k_l/k_g ratios are 1.44 (COD), 1.47 (BOD₅), and 1.25 (TSS); these are reported for transparency but should not be interpreted as a pure spacing factor because of the cross-form pairing. Observed versus model-predicted efficiencies for all fitted conditions are compared in Figure 4.

Representing performance as a function of specific charge loading Q/V (Coulomb per litre of wastewater; Figure 5) is common in the EC literature [31] because Q/V aggregates the effects of current and time. The data show that the curves for 4 cm and 2 cm spacings do not overlap at the same Q/V: a vertical separation of about 10-15% is observed for COD and BOD₅, and about 20% at Q/V 2,000-3,000 C/L for TSS — consistent with an interpretation involving floc-H₂ flotation that intensifies at a narrow gap. In other words, charge loading alone is not a sufficient single design variable; reactor geometry (gap) must be considered as an independent coordinate.

The vertical separation between 4 cm and 2 cm spacing series at fixed Q/V is consistent with — though not by itself proof of — a geometric/mass-transfer effect beyond the coulombic load. The ANCOVA in §3.2.1 (Table S7) directly tests this question and confirms the spacing main effect after Q is controlled. The full spacing-factor test of the observed k₂/k₄ ratios against the theoretical value of 2.0, with regime interpretation, is given in Table S21.

Specific Energy Demand (SED; Table 5) normalises energy consumption against the mass of pollutant removed, enabling comparison across wastewater matrices. At the laboratory optimum (2 cm, 100 min), SED_COD is 4.45 kWh/kg, SED_BOD5 is 10.51 kWh/kg, and SED_TSS is 4.70 kWh/kg. The relatively high SED_BOD5 value reflects a smaller concentration difference (ΔBOD₅) compared with ΔCOD and ΔTSS in this influent. SED_COD sits at the lower end of the EC textile literature range of 8-50 kWh/kg [2] because the batik cap influent carries a relatively high organic load, thereby making the denominator — mass of pollutant removed — is also large.

Figure S5 gives a 2 × 3 factorial heat-map as a direct per-condition view of efficiency; Figure S6 extends this to a second-order polynomial response surface (RSM) that interpolates the continuous design space. The RSM shows the steepest η gradient along the gap axis (confirming spacing as the dominant design variable), while the η-maximum ridge shifts from (4 cm, 100 min) to (2 cm, 75 min) — predicting that a 2 cm gap with 75 min detention is already sufficient for COD ≈80%, in line with the Tukey HSD result (the pair [2 cm, 75] ≈ [4 cm, 100]).

All continuous-flow performance numbers in this section are predictive. They are derived from the kinetic-Faraday framework calibrated on laboratory-batch data, propagated through a two-EC-in-series cumulative-efficiency rule and a literature-based filter-stage efficiency. They have not been validated against measurements from the 1 m³/day pilot plant. This predictive nature is the first item of §3.12 (Limitations). Numerical results below are intended as a design-window estimate suitable for cost-benefit and feasibility appraisal — not as performance guarantees.

For a continuous-flow WWTP with Q = 1.0 m³/day and total anode area of 3.42 m² (two chambers in series), Equation (5) predicts that if the batch current densities (8-18 mA/cm²) were applied directly, the steady-state C_Al dose would reach 1,014-2,281 mg/L per chamber (2,027-4,561 mg/L total). Such doses exceed the kinetic requirement by a factor of 4-10.

Propagating uncertainty through Equation (6) via Monte Carlo simulation (§2.4(d)), using the inverse of the logistic form (the preferred kinetic model at 2 cm gap; Table 4) and the fixed-η_max parameters listed there, yields the optimum operational current density and its 95% confidence interval (Figure 8; Table 6):

The 95% CI for j^* spans about ±12-15% around the median, providing an operational margin. To meet all three parameters simultaneously, the WWTP can be operated at j^* ≈ 1.4 mA/cm² (I_total ≈ 48 A for A = 3.42 m²). This is one order of magnitude below the batch current-density range. The recommended j^* in the present revision is ≈9% lower than the submitted version value of 1.5 mA/cm² (which was based on the exponential-saturation fit); the shift reflects the higher curvature of the logistic form at intermediate doses, which reaches η_target at slightly lower C_Al than the exponential-saturation form predicts.

Following the cautionary framing of §3.4(iv) on the empirical character of the rate parameter, the j^* recommended above should be understood as the operational current density that the design-relevant kinetic constants (fitted to this batik cap matrix and to the (j, t, d) window of the batch campaign) imply for full-scale operation. It is not a transferable kinetic constant. Applying this j^* directly to a different batik cluster — and especially to a different dye-class matrix — requires reparameterising of the kinetic model for the new wastewater, not direct transplantation of the present numerical value. The framework is transferable; the numerical j^* is not.

The 1:100 anode-area scale-up retains electrochemical similarity (current density, Faraday-derived Al dose) but not necessarily hydrodynamic similarity. The 2 L batch beaker is mechanically stirred at 150 rpm, giving turbulent mixing with negligible dead zones; the 240 L full-scale chambers operate under quiescent multi-plate continuous flow, where rising H₂ bubbles provide the dominant mixing intensity. Three deviations are therefore expected at scale-up: (i) some short-circuiting along the plate stack may reduce the effective residence-time distribution below the design value; (ii) mass-transfer-limited regions may emerge near static plate surfaces; (iii) the floc-flotation pathway will operate differently in the absence of mechanical agitation. Tracer-based residence-time-distribution measurement on the full-scale unit is the recommended verification step and is listed as the second priority in §3.12.

With single-pass efficiencies propagated through two EC chambers in series and FRP filtration, the projected full-plant effluent at j^* ≈ 1.4 mA/cm² is COD ≈ 60 mg/L, BOD₅ ≈ 30 mg/L, and TSS ≈ 28 mg/L — below the PermenLHK No. 5/2014 limits with a 40-44% margin. Figure 9 displays the projected cumulative efficiency at each stage — single-chamber batch, dual EC chambers in series, and full plant with FRP filtration — across all experimental conditions. The per-condition projection (single → 2-EC → 2-EC + FRP, with compliance checks for each parameter) is tabulated in Table S25.

The operational current-density recommendation in §3.7 calls for an economic evaluation to assess the feasibility of MSME deployment. At the recommended j^* ≈ 1.4 mA/cm² (logistic-kinetics-based; Table 6), the total operating cost (Table 7) calculated with the linear model of §2.6 is IDR 21,392/m³, equivalent to USD 1.34/m³ at IDR 16,000/USD. For batik cap MSMEs with an effluent load of 1-3 m³/day, the total operating cost is IDR 21,000-64,000/day (USD 1.34-4.02/day). For context, the EC literature on textile and batik effluent reports operating costs spanning USD 0.50-4.93/m³ across batch and continuous configurations [3,15,16,17,18,39,40,42]; the base estimate derived here sits at the centre of this range. The recommended continuous-flow current density of ≈1.4 mA/cm² is one order of magnitude below the batch range (5-40 mA/cm²) and at the low end of the continuous-mode synthetic-effluent range (5-12 mA/cm²) reported for textile streams [17]. The full literature comparison is in Table S14.

The variation ranges used in the tornado sensitivity (Figure 10) are each anchored to an explicit experimental, market, or literature source (Table S11): kinetic rate constant k_COD (±30%) from the bootstrap CI plus between-spacing range; aluminium plate price (±30%) from 2024 Indonesian B2B supplier quotes (IDR 28 000-52 000 kg^-1); operational current density j^* (±20%) from the §3.7 Monte Carlo 95% CI; Faraday efficiency φ (range 0.85-0.95) from the EC textile literature; electricity tariff (±10%) from PLN industrial-tariff bulletins 2020-2024. The complete tornado inputs and outputs, along with the ranking of input impacts on cost, are tabulated in Table S26.

In rank order, the cost-variance contributors are: kinetic rate constant k_COD (40% of variance; ±30% range → ±32% cost effect), required operational current density j^* (30%, itself responsive to k), aluminium plate price (29%, ±30% market range → ±25% cost). Faraday efficiency, passivation, and electricity tariff together account for less than 2% of cost variance. The operational implication for MSME deployment is that operating-cost predictability rests on the accuracy of the kinetic constant for the local batik dye matrix, not on commodity-price volatility.

The independent-parameter tornado overstates the standalone influence of k. In practice, the operator (or a feedback controller) compensates for a low-k draw with a higher j, transferring sensitivity from one variable to another rather than amplifying it. To capture this physical coupling, a correlated Monte-Carlo simulation (N = 20,000) was performed in which φ_eff = φ·(1 - δ_passivation) with δ ~ Beta (2, 18) (mean ≈10%), k is sampled from its bootstrap distribution, and the required j is solved per draw via Equation 6. The result (Figure 11) gives a 95% CI for total cost of IDR 16,800-28,000/m³ (USD 1.05-1.75/m³) — narrower than the naive independent tornado would suggest. The cost distribution is approximately symmetric around the median (IDR 21,560/m³ = USD 1.35/m³), with the upper tail driven primarily by joint draws of low k and high Al price.

Sustained operation at TDS ≈ 3,100 mg/L over weeks to months is a recognised passivation risk for Al electrodes; published data on comparable high-conductivity matrices [30,41] indicate 5-15% φ_eff degradation per 100 hours of continuous operation without polarity reversal. The Beta (2, 18) passivation factor in the correlated MC brackets this range. Even at the 97.5th percentile of δ, the propagated 95% cost CI remains within USD 1.05-1.75/m³, indicating that passivation is not a dominant cost driver but is non-negligible for long-term operation planning.

Beyond the operating-cost analysis, environmental burden is assessed under three ISO 14044 end-of-life allocation methodologies for transparency: cut-off (recycled-content method; primary-Al producer carries 100% of upstream impacts, recycled-Al carries re-melt only), avoided burden (sludge that displaces primary alum downstream earns a credit equal to EF_alum × m_{sludge, alum-equivalent}), and 50:50 allocation (recycled-Al upstream burden split evenly between first and second life). The cut-off methodology is the baseline for headline figures because it is the most conservative for a recycled-electrode scenario and does not credit the EC operator with downstream displacement that they do not directly cause. The avoided-burden scenario is reported solely to bracket the upper plausibility of net-CO₂ benefit; it is not used as a basis for any sustainability claim.

Emission factors used (kg CO₂/kg unless noted): primary Al 12.0 (IAI 2023), recycled Al re-melt 1.2 (IAI 2023), alum (Al₂(SO₄)₃) 1.9 (ecoinvent 3.9), ZnO 5.0, Indonesian grid 0.87 kg CO₂/kWh (PLN 2023), photovoltaic lifecycle 0.05 kg CO₂/kWh.

Baseline result (primary Al + grid + cut-off): the EC-F WWTP operating at j^* produces 10.4 kg CO₂/m³ of treated effluent, of which 9.2 kg CO₂/m³ (89%) comes from primary-Al production.

Mitigation levers (Table S12 reports the full 3 × 2 × 2 scenario matrix):

(i) Recycled-Al electrodes alone (cut-off methodology, grid power) reduce the footprint to 2.05 kg CO₂/m³ — an 80% reduction. The electrode-origin lever is therefore one of the highest-leverage decisions in EC-F deployment.

(ii) Recycled-Al + photovoltaic power further reduces the footprint to 0.99 kg CO₂/m³, competitive with chemical coagulation (0.46 kg CO₂/m³) and conventional activated sludge (0.62 kg CO₂/m³), while delivering superior effluent quality.

(iii) Adopting avoided-burden allocation (sludge → alum-equivalent credit) shifts the recycled-Al + PV scenario to a notionally negative footprint of -1.55 kg CO₂/m³. This is reported for transparency but not headlined; it requires that the sludge actually displaces primary alum in a downstream operation, which is operationally plausible but not guaranteed.

Practical feasibility of recycled-Al sourcing for MSMEs. Two operational risks must be managed. First, automotive-grade Al alloys (6063, 6061) contain 0.4-0.8% Mg, 0.2-0.6% Si, and trace Cu/Fe; co-dissolution at the EC anode would introduce Cu²⁺ (toxic at >1 mg/L for aquatic receiving bodies) and Si into the effluent. The mitigation is to source only commercial-purity Al-1050/Al-1100 (≥99.5% Al) scrap, verified by a handheld XRF spot check at the supplier (cost-effective at ≤USD 5 per sample). The Indonesian Ministry of Energy and Mineral Resources lists ~14 ISO-certified Al recyclers offering Al-1100 ingots from beverage-can scrap (KemenESDM 2023). Second, anodised or painted Al scrap can introduce F^- or organic coating residues; the standard acid-pickling pretreatment (10% v/v HCl, 5 min) already specified in §2.3 is sufficient mitigation.

Cross-technology comparison. Figure 12b benchmarks the EC-F footprint against three textile-wastewater treatment technologies under like-for-like effluent-quality targets: chemical coagulation (alum 150 mg/L) at 0.46 kg CO₂/m³, conventional activated sludge at 0.62 kg CO₂/m³, and UV/ZnO photocatalysis at 4.4 kg CO₂/m³. Under the baseline (primary Al + grid + cut-off), EC-F at 10.4 kg CO₂/m³ has the highest-footprint option of the four. Under recycled-Al + PV (still cut-off), EC-F at 0.99 kg CO₂/m³ moves into the same range as chemical coagulation, while retaining the discharge-compliant effluent quality (§3.7) that coagulation alone does not achieve. The decisive sustainability lever for EC-F is therefore the electrode origin and the power source, not the treatment technology choice in isolation. The full cross-technology breakdown — emission factors, energy and chemical inputs, and per-technology CO₂ components — is tabulated in Table S27. The complete allocation × electrode × energy scenario matrix is shown in Figure S9.

The Magetan influent profile (pH 9.2; COD 750 mg/L; BOD₅ 320 mg/L; TSS 680 mg/L; colour 2,000 Pt-Co; TDS 3,100 mg/L) is positioned within the published Indonesian and Malaysian batik wastewater range [43,44] in the Supplementary Materials (Table S28). Agreement on bulk parameters does not, however, demonstrate kinetic transferability — dye composition, conductivity, and trace-ion chemistry also modulate Al(OH)₃ floc behaviour, and the framework must be reparameterised rather than transplanted when applied to clusters whose dye class differs from the reactive-naphthol/indigosol/remazol matrix studied here. Multi-cluster kinetic validation is listed as a priority extension in §3.12.

Table 8 places this study in the context of the EC literature for textile and batik wastewater. The reported COD efficiency range for batch mode (72-95%) is comparable to the present result (92.8%); however, an explicit translation framework for translating batch kinetic parameters into continuous-flow current-density recommendations with propagated uncertainty is not available in the literature compared. The operating cost of USD 1.34/m³ sits in the middle of the literature range (USD 0.50-6.26/m³), while the recommended continuous-flow current density (≈1.4 mA/cm²) lies below the commonly reported range (5-40 mA/cm² for batch; 5-12 mA/cm² for continuous with synthetic effluent). The two non-textile comparators (coffee industry [27]; slaughterhouse effluent [22]) are retained in Table 8 only as order-of-magnitude operating-cost benchmarks for matrices of comparable organic load; their inclusion is not intended as a kinetic comparator, and we note that batik dye chemistry differs substantially from food-processing effluents.

Four limitations must be acknowledged.

First, all continuous-flow performance projections (§3.7) — including the headline 99.7% cumulative COD removal — are model-based and have not been validated with operating data from the 1 m³/day plant. Tracer residence-time-distribution measurement, intermediate-tank sampling between EC chambers, and a ≥1 month continuous-operation campaign at the recommended j^* are the highest-priority next steps.

Second, current density j is not independent of plate spacing and time under the batch factorial design (the power supply operates in constant-current mode); the fitted rate parameter is therefore not strictly intrinsic. Validation across (j, t, d) combinations that hold the Faraday Al dose C_Al constant — by varying j and t inversely at fixed gap — is the second priority and would settle the question of parameter intrinsicness.

Third, hydrodynamic similarity between the 2 L stirred batch reactor and the 240 L quiescent multi-plate chambers is not preserved. Mixing-regime deviations, dead zones, and floc-flotation behaviour are expected to differ at scale, and the predicted full-plant efficiency should be regarded as an upper bound until verified by tracer RTD measurement (§3.7).

Fourth, long-term stability was not tested in this batch study. Field studies on high-conductivity matrices [30,41] show that ohmic-loss-dominated electrode fouling and Al anode passivation can degrade Faraday efficiency over time. However, these can be mitigated by polarity-reversal strategies (30-60 min reversal intervals). Physical characterisation of Al(OH)₃ flocs (XRD/SEM/FTIR) was also outside the scope of this study.

Priority areas for further research include: (i) full-scale field validation at the predicted j^*; (ii) photovoltaic integration and exploration of recycled-Al electrodes to reduce the carbon footprint; (iii) valorisation of Al(OH)₃ sludge as a secondary coagulant or construction additive; (iv) multi-cluster validation across dye compositions (reactive naphthol versus indigosol); and (v) real-time pH/turbidity/colour sensor monitoring for automated j control [45].