AbstractThe sludge-water mixture in anaerobic reactors with confined sludge, such as the upflow anaerobic sludge blanket (UASB) with anaerobic sludge confined in a sludge bed and the internal reflux packed-bed anaerobic reactor with anaerobic sludge attached to a filler, can be mixed according to the designed hydraulic dynamic process. In this study, sludge-water mixing models of an UASB and an internal reflux packed-bed anaerobic reactor were established and validated using test models reported in the literature. The sludge-water mixing in the UASB consists of an advective diffusion unit and a water complete mixing output unit connected in series. The sludge-water mixing and reaction of the internal reflux packed-bed anaerobic reactor achieved that of a continuous stirred tank reactor (CSTR) in large-scale reflux transport mode with cycle time as the mixing time scale. The internal mixing pattern, complete mixing time, and the volume participating in complete mixing were obtained for the UASB test with hydraulic retention time (HRT)=5, 6, 8, and 10 h by model calculation to analyze the sludge-water mixing process. Its mixing achieved that of a CSTR under higher hydraulic load, and that of a series connected two-stage CSTR in advective diffusion mode under lower hydraulic load. The model analysis for the reported internal reflux packed-bed anaerobic reactor with HRT=72, 48, 24, 12, 6, and 0.25 days showed that there existed mixing time scales shorter than the minimum reflux cycle time adopted in the test, in which the transport of the reflux alone made the sludge-water mixing and reaction stably equivalent to that of a CSTR. Both test reactors achieved CSTR at a lower mixing intensity with a velocity of 0.40–0.80 m/h and complete mixing time scale of 1.0–1.9 h for the UASB and an available velocity of 5.0 m/h and complete mixing time scale of 0.15 h for the internal reflux packed-bed anaerobic reactor.