Food and beverage factories discharge some of the most nutrient-rich wastewater of any industry. Chemical oxygen demand in tequila processing effluent can reach 132,120 milligrams per liter, total nitrogen in poultry slaughterhouse wastewater can climb to 1,900 milligrams per liter, and total phosphorus in cheese processing effluents can hit 2,800 milligrams per liter. A new open-access review in Bioresources and Bioprocessing argues that the missing ingredient for turning these polluting streams into resources is not a new organism or reactor, but mathematics: kinetic models that describe how the microalga Chlorella grows, removes pollutants, and accumulates valuable compounds, and that can carry laboratory results reliably to industrial scale.
The review, authored by Vera Lavelli and Zhi Zhou and published on 14 October 2026, synthesizes the mathematical models that have been applied to Chlorella cultivation in food-industry effluents. These include sigmoidal growth models such as the modified Gompertz, logistic, and Verhulst equations, substrate-dependent models like Monod and Andrews, light-dependent photobioreactor models of the Huisman type, and Lotka–Volterra equations for microbial interactions in co-cultures. The authors compile kinetic parameters from published studies into a common framework intended to support consistent projections from laboratory experiments to industrial systems, and to feed future techno-economic analysis and life-cycle assessment. They also propose a decision tree to guide researchers in choosing the right model for a given effluent and process goal.
Chlorella species are attractive candidates for what researchers call phycoremediation because they assimilate carbon, nitrogen, and phosphorus while producing biomass that can be valorized as food ingredients, animal feed, biofertilizers, biofuels, or pigments. The genus grows quickly, tolerates harsh conditions, and has an established safety record as a food ingredient source. Conventional biological wastewater treatment, by contrast, is robust but generates large amounts of waste sludge without enabling resource recovery. Yet the review is blunt about the current state of the field: existing algal studies remain predominantly at the laboratory scale, and their competitive advantages have not been demonstrated for full-scale implementation.
The sigmoidal models occupy a central place in the review because they capture the full arc of a batch culture rather than a single number. The Gompertz and logistic equations estimate three biologically meaningful parameters: the lag time during which cells adapt to the substrate, the maximum specific growth rate during exponential phase, and the asymptotic biomass concentration reached when nutrients run out or inhibitory compounds accumulate. This matters because many studies on food-processing wastewaters never model the growth curve at all, instead calculating a specific growth rate from initial and final biomass values as if the culture stayed in exponential growth throughout. The authors argue that analyzing the full profile is essential both for understanding the physiology of the culture and for predicting optimal hydraulic retention times in continuous systems.
The lag phase emerges as a recurring theme. Effluents from tortilla processing showed longer lag phases and lower growth rates than synthetic media, and lag phases reaching up to 14.2 days have been reported in slaughterhouse wastewater. In anaerobically digested swine wastewater, a double Gompertz equation successfully captured biphasic growth, revealing sequential substrate use in which readily assimilable compounds were consumed first and more recalcitrant nutrients later. The models have also proven informative during scale-up attempts. For digested gelatin wastewater, comparable maximum specific growth rates of 0.343 per day were reported when moving from laboratory cultures to a bubble-column photobioreactor, but the lag phase lengthened to 1.77 days, attributed to less efficient mixing and mass transfer in the pneumatic agitation system. The review flags this as a critical limitation: models developed at small scales may not account for the hydrodynamic and mass-transfer constraints of larger systems.
Reported growth rates span a striking range. Under simple exponential assumptions at laboratory scale, specific growth rates for Chlorella on food-industry effluents typically fell between 0.115 and 0.18 per day, corresponding to optimal retention times of 11 to 17 days, with substrate complexity playing a dominant role. Under optimized synthetic conditions, Chlorella sorokiniana reached up to 0.61 per day. At the industrial extreme, Chlorella vulgaris grown on corn molasses in fed-batch mode achieved 1.0 per day, and outdoor cultivation of Chlorella pyrenoidosa on soybean effluents fluctuated from 0.73 per day in spring to 1.59 per day in summer. The authors treat these values, spanning 0.115 to 1.59 per day, as a baseline for future efficiency improvements, provided the lag-phase limitation can be overcome through cultivation strategies or chemical and enzymatic pretreatments.
Environmental factors receive their own modeling treatment. The Monod model describes growth as a function of a single limiting substrate, while the Andrews model adds an inhibition constant to capture declining growth at high substrate levels. Applied to gelatin wastewater, the Andrews model identified an optimal ammonium concentration of 37.59 milligrams per liter at pH 7.5, later validated in a bubbled photobioreactor, but the review stresses that such optima are substrate-specific and strongly pH-dependent, since pH governs the equilibrium between ammonium and the more toxic ammonia. Multifactorial polynomial models have identified optimal combinations of glucose and the phytohormone indole-3-acetic acid in hydroponic lettuce effluent, and optimal total nitrogen and phosphorus levels of 425 and 65 milligrams per liter for poultry-slaughterhouse effluent. Across studies, light intensity, typically ranging from 0 to 800 microeinsteins per square meter per second, emerged as the most influential growth factor, though growth is constrained above the saturation threshold.
One notable gap the review identifies concerns the Huisman model, which describes how light governs algal growth in continuous systems and defines a critical light intensity below which populations decline. Chlorella has a particularly low critical light intensity of 2.75 microeinsteins per square meter per second, far below the 6.49 required by Scenedesmus, meaning Chlorella is predicted to outcompete other algae under light-limited conditions. Despite this predictive power, the model has not been used in any of the Chlorella wastewater applications reported so far. The authors also call for standardizing how light is reported, noting that illuminance in lux, weighted to human eye sensitivity, cannot be converted to photosynthetic photon flux density without knowing the light spectrum, and that PPFD should be preferred for photosynthesis studies.
Pollutant removal and product formation each have their own kinetic literature, both incomplete. Removal efficiencies above 80 percent for chemical oxygen demand, total nitrogen, and total phosphorus were consistently reported, but the time-course of removal has been modeled in only a limited number of studies, using reformulated Monod models, zero-order or first-order kinetics, or multifactorial polynomials. Zero-order COD removal rates ranged from 10 milligrams per liter per day in cassava-processing wastewater to 89.9 in anaerobically digested swine wastewater, while continuous cultures of C. vulgaris in salmon aquaculture effluent achieved nitrate removal rates of 480 milligrams per liter per day. Affinity constants for nutrient removal varied so widely between dairy wastewater studies that the authors conclude the Monod approach cannot reliably capture general trends. On the product side, lipid contents of 6.3 to 30.7 percent, carbohydrate contents up to 40.19 percent, and protein contents up to 60 percent have been reported, but the accumulation of high-value compounds remains largely unexplored from a kinetic perspective, and it does not necessarily correlate with cell growth.
Looking toward implementation, the review projects laboratory and pilot performance against benchmark facilities. A two-stage heterotrophic process for C. vulgaris achieving 58 tons per year serves as one benchmark, which heterotrophic cultivation on corn molasses, at 22 grams per liter per day, approaches. A sunlight-driven tubular photobioreactor in the Netherlands producing 41 tons per year per hectare sets the second target, which projected scale-up of soybean-effluent cultivation could exceed while delivering roughly 55 percent protein. For phycoremediation, no large-scale plants currently operate, likely due to cost, but several lab-scale systems exceeded the removal rates of a Belgian benchmark photobioreactor. The authors also review emerging artificial intelligence and machine learning approaches, including a model that predicted high algal lipid productivity with 95.2 percent accuracy and identified exogenous iron and phosphorus, rather than nitrogen starvation, as key drivers of lipid production. Their proposed decision tree integrates all of these tools: fit sigmoidal models to characterize the effluent, apply factor-specific or multifactorial models to optimize conditions, evaluate bioremediation kinetics, and finally project performance against benchmarks, with computational fluid dynamics guiding bioreactor design before experimental validation. The consistent message is that modelling, not optimism, is the bridge from promising laboratory results to industrial reality.
Subject of Research: Kinetic modelling of Chlorella-based wastewater treatment and resource recovery in the food and beverage industry
Article Title: Kinetic modelling of Chlorella spp. wastewater treatment and resource recovery in the food industry
Article References: Lavelli, V., & Zhou, Z. (2026). Kinetic modelling of Chlorella spp. wastewater treatment and resource recovery in the food industry. Bioresources and Bioprocessing, 13(1), Article 150. https://doi.org/10.1186/s40643-026-01145-x
Image Credits: AI Generated
DOI: 10.1186/s40643-026-01145-x
Keywords: Chlorella, phycoremediation, kinetic modelling, wastewater treatment, food industry, Gompertz model, Monod model, Huisman model, resource recovery, machine learning, photobioreactor, scale-up
News Source: Gregory Coleman. (October 29, 2026). Kinetic Models Could Bridge the Gap Between Lab-Scale Algae Wastewater Treatment and Real Industry. Scienmag.
