Anaerobic co-digestion of primary and secondary sewage sludge and Cladophora green algae was investigated under mesophilic temperature conditions. The design of experiment method and the optimal mixture design were used to systematically optimize the substrate composition ratios and elucidate the possible synergistic effects for an anaerobic digestion system. A reduced cubic model was created by Design-Expert software as a function of substrate composition ratios. The model was validated by ANOVA experimentally. Also, the substrate composition ratio's effects on variations in biogas production were studied. All linear impacts on changes in biogas production were significantly observed, and interactions between substrates in combined digestion had synergistic impacts on biogas production rate. The highest amount of biogas (235.17-296.03 ml/g VS) was obtained with ratios of equal to 70-60%, B equal to 0-17%, and C equal to 18-30%. Eventually, the model optimization was performed to predict the optimal conditions to achieve the maximum biogas production rate. It was seen that the predicted and actual values of produced biogas in favorable conditions with an error of about 1.3% are well consistent. The authors conclude that the optimal mixture design can be utilized to assess the optimal composition of substrates in an anaerobic digestion system
