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A method for predicting the long-term effects of ferric on methane production was developed in an anaerobic membrane bioreactor treating food processing wastewater to provide management tools for maximizing methane recovery using ferric based on a batch test. The results demonstrated the accuracy of the predictions for both batch and long-term continuous operations using a Bayesian network meta-analysis based on the Gompertz model. The prediction bias of methane production for batch and continuous operations was minimized, from 11~19% to less than 0.5%. A biochemical methane potential-based Bayesian network meta-analysis suggested a maximum 2.55% ± 0.42% enhancement for Fe2.25. An anaerobic membrane bioreactor improved the methane yield by 2.27% and loading rate by 4.57% for Fe2.25, operating in the sequenced batch mode. The method allowed for a predictable methane yield enhancement based on the biochemical methane potential. Ferric enhanced the biochemical methane potential in batch tests and the methane yield in a continuously operated reactor by a maximum of 8.20% and 7.61% for Fe2.25, respectively. Copper demonstrated a higher methane (18.91%) and sludge yield (17.22%) in batch but faded in the continuous operation (0.32% of methane yield). The enhancement was primarily due to changing the kinetic patterns for the last period, i.e., increasing the second methane production peak (k 71 ), bringing forward the second peak (λ 7 , λ 8 ), and prolonging the second period (k 62 ). The dual exponential function demonstrated a better fit in the last three stages (after the first peak), which implied that syntrophic methanogenesis with a ferric shuttle played a primary role in the last three methane production periods, in which long-term effects were sustained, as the Bayesian network meta-analysis predicted.

Prediction of the Long-Term Effect of Iron on Methane Yield in an Anaerobic Membrane Bioreactor Using Bayesian Network Meta-Analysis