This study pointed out the performance of a full-scale internal circulation (IC) bioreactor (140 m³) inoculated with anaerobic granular sludge for the treatment of dairy wastewater for 91 days. The average COD removal was 80% and the average biogas was 69.8 m³ per influent COD/L per day. Then the anaerobic digestion of cheese whey (CW) at a pH 5–6 was examined at a laboratory level as a strategy to reduce the requirement for alkalinity. First, anaerobic granular sludge from IC bioreactor (pH 7–7.5), was exposed to pH 5–6 while utilizing acetic acid for 7 months. This laboratory adapted anaerobic granular sludge when fed with CW showed 30% higher methane generation under batch conditions compared to non-acclimatized granular sludge under the same conditions (pH 5–6). Higher percentage of hydrogenotrophic methanogens (mostly Methanolinea) and increase of Clostridium at the anaerobic granular sludge exposed to pH 5–6 compared to initial granular sludge was found. Propionic acid was the reaction limiting step for granular sludge under pH 5–6. Anaerobic digestion at moderately low pH required 68% less NaOH (50 %v/v) per m³ of CW however it can theoretically produce 53% less kWh per day compared to digestion at neutral pH.