The activated sludge process is the most widely used biological wastewater treatment method for domestic and industrial wastewaters. One drawback of this process is the production of `sludge'. The expense for treating excess sludge accounts for 50-60% of the operating costs in a wastewater treatment plant. Traditional methods for disposing of excess sludge are increasingly regulated due to environmental concerns about the presence of potentially toxic elements in the sewage sludge. A promising method to reduce excess sludge production is to increase its biodegradability by disintegrating it within the bioreactor. We extend an earlier model by allowing the sludge disintegration reactions to occur at a finite rate. Furthermore, we include a more realistic model for the hydrolysis of particulate matter by allowing the rate of hydrolysis to saturate at high particulate concentrations. We analyze the steady-state operation of an activated sludge system incorporating a sludge disintegration unit to prevent excess sludge production. References A. Alharbi, M. I. Nelson, A. L. Worthy and H. Sidhu. Sludge formation in the activated sludge process with a sludge disintegration unit. In M. Nelson, T. Hamilton, M. Jennings and J. Bunder, Eds, Proceedings of the 11th Biennial Engineering Mathematics and Applications Conference, EMAC-2013, ANZIAM J. , 55:C348–C367, 2013. doi:10.21914/anziamj.v55i0.7803 P. S. Barker and P. L. Dold. Sludge production and oxygen demand in nutrient removal activated sludge systems. Water Sci. Technol. , 34(5–6):43–50, 1996. doi:10.1016/0273-1223(96)00627-0 A. Canales, A. Pareilleux, J. L. Rols, G. Goma and A. Huyard. Decreased sludge production strategy for domestic wastewater treatment. Water Sci. Technol. , 30(8):97–106, 1994. doi:10.1016/S0043-1354(03)00441-X C. P. Chu, W. C. Feng, B.-V. Chang, C. H. Chou, and D. J. Lee. Reduction of microbial density level in wastewater activated sludge via freezing and thawing. Water Res. , 33:3532–3535, 1999. doi:10.1645/0022-3395(2002)088[0718:EOFTEO]2.0.CO;2 E. Egemen, J. Corpening, and N. Nirmalakhandan. Evaluation of an ozonation system for reduced waste sludge generation. Water Sci. Technol. , 44(2–3):445–452, 2001. http://wst.iwaponline.com/content/44/2-3/445 M. Henze, C. P. L. Grady Jr, W. Gujer, G. V. R. Marais, and T. Matsuo. A general model for single-sludge wastewater treatment systems. Water Res. , 21(5):505–515, 1987. doi:10.1016/0043-1354(87)90058-3 M. I. Nelson and E. Balakrishnan. An analysis of an activated sludge process containing a sludge disintegration system. In F. Chan, D. Marinova, and R. S. Anderssen, Eds, 19th International Congress on Modelling and Simulation, MODSIM 2011, 331–337, 2011. http://www.mssanz.org.au/modsim2011/A3/nelson.pdf M. I. Nelson and T. C. L. Yue. A Mathematical Analysis of a Membrane Bioreactor Containing a Sludge Disintegration System . Chem. Eng. Commun. , 201(10):1384–1403, 2014. doi:10.1080/00986445.2013.809001 Y.-K. Oh, K.-R. Lee, K.-B. Ko, and I.-T. Yeom. Effects of chemical sludge disintegration on the performance of wastewater treatment by membrane bioreactor. Water Res. , 41:2665–2671, 2007. doi:10.1016/j.watres.2007.02.028 Z. Wang, L. Wang, B. Z. Wang, Y. F. Jiang, and S. Liu. Bench-scale study on zero excess activated sludge production process coupled with ozonation unit in membrane bioreactor. J. Environ. Sci. Heal. A , 43(11):1325–1332, 2008. doi:10.1080/10934520802177987 Y. Wei, R. T. Van Houten, A. R. Borger, D. H. Eikelboom, and Y. Fan. Minimization of excess sludge production for biological wastewater treatment. Water Res. , 37:4553–4467, 2003. doi:10.1016/S0043-1354(03)00441-X H. Yasui, K. Nakamura, S. Sakuma, M. Iwasaki, and Y. Sakai. A full-scale operation of a novel activated sludge process without excess sludge production. Water Sci. Technol. , 34(3–4):395–404, 1996. doi:10.1016/0273-1223(96)00604-X S.-H. Yoon. Important operational parameters of membrane bioreactor-sludge disintegration (MBR-SD) system for zero excess sludge production. Water Res. , 37:1921–1931, 2003. doi:10.1016/S0043-1354(02)00578-X S.-H. Yoon, H.-S. Kim, and S. Lee. Incorporation of ultrasonic cell disintegration into a membrane bioreactor for zero sludge production. Process Biochem. , 39(12):1923–1929, 2004. doi:10.1016/j.procbio.2003.09.023