The model of South et al. [South et al. (1995) Enzyme Microb Technol 17(9): 797-803] for simultaneous saccharification of fermentation of cellulosic biomass is extended and modified to accommodate intermittent feeding Of Substrate and enzyme, cascade reactor configurations, and to be more computationally efficient. A dynamic enzyme adsorption Model is found to be much more computationally efficient thin the equilibrium model used previously, thus increasing the feasibility of incorporating the kinetic model in a computational fluid dynamic framework in the future. For continuous or discretely fed reactors, it is necessary to use particle conversion in conversion-dependent hydrolysis rate laws rather than reactor conversion. Whereas reactor conversion decreases due to both reaction and exit of particles from the reactor, particle conversion decreases due to reaction only. Using the modified models, it is predicted that cellulose conversion increases with decreasing feeding frequency (feedings per residence time, f). A computationally efficient strategy for modeling cascade reactors involving a modified rate constant is shown to give equivalent results relative to an exhaustive approach considering the distribution of particles in each successive fermenter. Biotechnol. Bioeng. 2009;102: 59-65. (C) 2008 Wiley Periodicals, Inc.