A New Thiele’s Modulus for the Monod Biofilm Model
FANG Yuanxiang 1,and GOVIND Rakesh 2 1National Risk Management and Research Laboratory,U.S.Environmental Protection Agency,26 W.Martin Lu- ther King Dr.Cincinnati,OH45268,USA2 Department of Chemical and Materials Engineering,University of Cincinnati,Cincinnati,OH45221,USA
A new Thiele’s modulus,φ F,was developed to provide a gradual transition between zero and the first order of kinetics,and to accurately calculate the mass transfer flux and the effectiveness factor for the Monod biofilm.Values of the effectiveness factor,calculated using the new Thiele’s modulus,were compared with those obtained from numerical solutions and from other published moduli and empirical formulae.The comparison indi- cated that the new Thiele’s modulus was the best modulus for the Monod biofilm model.In addition,another Thiele’s modulus,φ G,was developed for a Monod biofilm,covered with an external water layer.The overall effec- tiveness factor can also be calculated by using both moduliφ F andφ G.The criteria that were proposed for identifica- tion were based on the values ofφ F andφ G,the limiting processes for biomass growth,and substrate conversion. Developed fromφ F,a new parameterψwas related uniquely to such features as the depth and shallowness of the generalized substrate concentration profiles inside a Monod biofilm.Criteria were developed to identify the types of concentration distribution inside a Monod biofilm.These methods were used to estimate the substrate flux and the concentration distribution of the biofilms defined in the first benchmark problem(BM1),by a task group of the In- ternational Water Association on Biofilm Modeling.
【CateGory Index】： TQ018