摘要
A new Thiele＇s modulus, φF, 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, φG, was developed for a Monod biofilm, covered with an external water layer. The overall effectiveness factor can also be calculated by using both moduli φF and φG. The criteria that were proposed for identifica- tion were based on the values of φF and φG, the limiting processes for biomass growth, and substrate conversion. Developed from φF, a new parameter ψ was 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 International Water Association on Biofilm Modeling.
新 Thiele 的模量， F，被开发提供在零之间的渐渐的转变和动力学的一级，并且精确地为 Monod 简历电影计算传质流动和有效性因素。有效性因素的价值，用新 Thiele 的模量计算，与从数字答案并且从另外的出版 moduli 和实验公式获得的那些相比。比较显示新 Thiele 的模量是为 Monod 简历电影模型的最好的模量。另外，另一 Thiele 是模量， G，为一部 Monod 简历电影被开发，用外部水层盖住。全面有效性因素能被使用 moduli F 和 G 也计算。被建议因为鉴定基于 F 和 G，为生物资源生长的限制进程，和底层变换的值的标准。从 F 发展了，新参数Ψ在一部 Monod 简历电影内与象深度和概括底层浓度剖视图的浅海角的如此的特征特别地有关。标准被开发在一部 Monod 简历电影内识别集中分发的类型。这些方法被用来估计底层流动和处于第一个基准问题(BM1 ) 定义的简历电影的集中分发，由 Biofilm 建模上的国际水协会的一个任务组。
