A novel mathematical model was developed to estimate the volumetric nitrogen conversion rates of a high-rate Anammox UASB reactor based on the packing patterns of granular sludge. A series of relationships among granular packing density, sludge concentration, hydraulic retention time and volumetric conversion rate were constructed to correlate Anammox reactor performance with granular packing patterns. It was suggested that the Anammox granules packed as the equivalent simple cubic pattern in high-rate UASB reactor with packing density of 50-55%, which not only accommodated a high concentration of sludge inside the reactor, but also provided large pore volume, thus prolonging the actual substrate conversion time. Results also indicated that it was necessary to improve Anammox reactor performance by enhancing substrate loading when sludge concentration was higher than 37.8 gVSS/L. The established model was carefully calibrated and verified, and it well simulated the performance of granule-based high-rate Anammox UASB reactor. (C) 2013 Elsevier B.V. All rights reserved.