Anaerobic digestion bacteria algae (ADBA): A mathematical model of mixotrophic algal growth with indigenous bacterial inhibition in anaerobic digestion effluent

• A kinetic model for algal mixotrophic growth in anaerobic digester effluent. • The interaction between algae and bacteria was analyzed using the model. • The dilution and sterilization of wastewater showed better algal growth. • The process was optimized with varying nutrients and operating conditions. A comprehensive kinetic model called anaerobic digestion bacteria algae (ADBA) was developed to describe and predict the complex algae-bacterial system in anaerobic digestion (AD) wastewater under mixotrophic growth conditions. The model was calibrated and validated using the experimental growth data from cultivating the algae ( Chlorella vulgaris CA1) with its indigenous bacteria in Blue Green 11 (BG-11) media and different combinations of sterilized, diluted, and raw AD effluent. Key parameters were obtained, including the distinct maximum growth rate of algae on CO 2 ( μ a , C O 2 , 1.23 per day) and organic carbon ( μ a , OC , 3.30 per day), the maximum growth rate of bacteria ( µ b , 1.20 per day), along with two noble parameters, i.e., the algae-bacteria interaction exponent ( n , 0.03) and the growth inhibition coefficient ( a e = 30 000 mg/L per AU) due to effluent turbidity. The model showed a good fit with an average R 2 = 0.90 in all cases adjusted with 25 kinetic parameters. This was the first model capable of predicting algal and bacterial growth in AD effluent with their competitive interactions, assuming shifting growth modes of algae on organic and inorganic carbon under light. It could also predict the removal rate of substrate and nutrients from effluent, light inhibition due to biomass shading and effluent turbidity, mass transfer rate of O 2 and CO 2 from gas phase to liquid phase, and pH-driven equilibrium between dissolved inorganic carbon components (CO 2 , HCO 3 – , and CO 3 2– ). Algal growth in the strongly buffered AD effluent resulted in odor removal, turbidity reduction, and the removal of ∼80% of total ammonium-nitrogen and 90% of organic carbon. In addition to process parameter prediction, this study offered a practical solution to wastewater treatment, air pollution, and nutrient recycling, ensuring a holistic and practical approach to ecological balance.