A New Thiele's Modulus for the Monod Biofilm Model

方元祥; GOVIND Rakesh

doi:10.1016/S1004-9541(08)60075-0

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A New Thiele's Modulus for the Monod Biofilm Model

Updated：2026-01-06

- A New Thiele's Modulus for the Monod Biofilm Model
- A New Thiele's Modulus for the Monod Biofilm Model
- 中国化学工程学报（英文版） 2008年16卷第2期页码：277-286
- Affiliations：
  
  1. National Risk Management and Research Laboratory, U.S.Environmental Protection Agency, 26 W.Martin Lu-ther King Dr., 68,Cincinnati,USA,OH452
  2. Department of Chemical and Materials Engineering, University of Cincinnati,, 21,Cincinnati,USA,OH452
- Author bio：
- Funds：
- DOI：10.1016/S1004-9541(08)60075-0
  中图分类号：
- 纸质出版：2008
- Accepted：
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方元祥, GOVIND Rakesh. A New Thiele's Modulus for the Monod Biofilm Model[J]. 中国化学工程学报（英文版）, 2008,16(2):277-286.

FANG Yuanxiang, GOVIND Rakesh. A New Thiele's Modulus for the Monod Biofilm Model[J]. , 2008, 16(2): 277-286.
方元祥, GOVIND Rakesh. A New Thiele's Modulus for the Monod Biofilm Model[J]. 中国化学工程学报（英文版）, 2008,16(2):277-286. DOI： 10.1016/S1004-9541(08)60075-0.

FANG Yuanxiang, GOVIND Rakesh. A New Thiele's Modulus for the Monod Biofilm Model[J]. , 2008, 16(2): 277-286. DOI： 10.1016/S1004-9541(08)60075-0.

摘要

Abstract

A new Thiele's modulus

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 indicated that the new Thiele's modulus was the best modulus for the Monod biofilm model.In addition

another Thiele's modulus

was developed for a Monod biofilm

covered with an external water layer.The overall effectiveness factor can also be calculated by using both moduli φ

and φ

.The criteria that were proposed for identification were based on the values of φ

andφ

the limiting processes for biomass growth

and substrate conversion. Developed from φ

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 International Water Association on Biofilm Modeling.

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