Wastewater-to-algae math breaks new ground

Circular wastewater management took a step toward simplicity this month with the release of a compact mathematical tool that tells engineers exactly how microalgae will behave inside effluent from anaerobic digesters. The new “ADBA” model abandons the sprawling parameter sets that have hampered earlier algae–bacteria simulators, instead capturing the essential chemistry and biology of the process in just eight state variables and 25 kinetic constants.

Unlike predecessors that assumed algae rely solely on carbon dioxide, ADBA recognises mixotrophy—the ability of many Chlorella strains to gulp both CO₂ and organic carbon depending on the hour of the day. A piece-wise function switches the metabolic mode at sunrise and sunset, while multiplicative Monod terms account for limitation by ammonium, dissolved oxygen and light. Haldane inhibition is added for high ammonia, and a novel “interaction exponent” damps algal growth when bacterial biomass rises, mimicking predatory stress observed in previous co-cultures.

The team trained the model on 8-day bench experiments that mixed the indigenous alga Chlorella vulgaris CA1 with its own bacterial community in sterilised, diluted and raw effluent from a campus dairy digester. Cultures received 1 % CO₂-enriched air, 6 g L⁻¹ glucose and 100 µmol m⁻² s⁻¹ illumination on a 16:8 h cycle. Dry-weight calibration curves, absorbance spectra and chemical oxygen demand measurements supplied 1.2 million data points; Monte-Carlo screening delivered the best parameter set with root-mean-square error below 20 %.

Validation against independent sterilised runs showed Theil inequality coefficients of 0.06–0.08, confirming that the model could extrapolate to systems free of bacterial competition. Once satisfied, the researchers used ADBA to probe scale-up constraints. Raising incident light from 325 to 1 000 µmol m⁻² s⁻¹ almost offset the productivity loss caused by 1 absorbance unit of turbidity, but going brighter delivered diminishing returns. Keeping ammonium in the 100–1 000 mg-N L⁻¹ band and organic carbon near 5 000–10 000 mg L⁻¹ lifted heterotrophic-specific growth rates above 2 d⁻¹, a figure competitive with mineral-media trials.

Because anaerobic digestate is strongly buffered, pH drift was minor; yet the simulations underscored the hidden penalty of suspended solids left after centrifugal pre-treatment. Every 0.1 AU of residual turbidity trimmed peak productivity by roughly 40 mg L⁻¹ d⁻¹, enough to erode annual biomass revenue if ponds are not polished beforehand. Designers could therefore justify low-cost lamella settlers or micro-screens that push clarity below the 0.5 AU threshold rather than investing in expensive cross-flow membranes.

The lean parameter set means ADBA can run on common spreadsheet platforms or programmable logic controllers, giving farm-scale operators a real-time predictor for feeding rates, harvest timing and aeration schedules. Developers of next-generation algae bioreactors say the advance arrives just as carbon-credit markets and fertiliser-price volatility make on-site nutrient recovery attractive. With further validation for seasonal temperature swings, the developers expect the model to accelerate deployment of covered high-rate ponds that turn dairy waste into animal feed or biogas while meeting upcoming discharge limits for nitrogen and phosphorus.