Chemical Reactor Engineering

Contois growth kinetics

Many processes associated with the food industries produce slurries or wastewaters. For instance, the production of slurries is a feature of large pig and poultry farms and other operations involving intensive animal production. Typically the wastewater (or slurry) contains appreciable amounts of biodegradable organic materials (pollutants); the concentration of these must be lowered prior to disposal. One way to do this is to pass the wastewater through a reactor containing biomass which grows through consumption of the pollutant. The cleaning-up of wastewaters imposes a financial burden upon the producer, although this is reduced if there is a return on the treated product. For example, fertilisers may be produced by the the processing of slurries from farms.

Although there exists detailed models for wastewater treatment kinetics, such as the IWA ASM model (Henze et al, 1987), a simple two-variable kinetic mode in which the degradation of a biodegradable organic material is given by the Contois growth model (Contois, 1959) has been found to fit a variety of experimental results. The Contois specific growth rate is given by
μ(X,S) = μmS

where μ is the specific growth rate, μm is the maximum specific growth rate, Kx is the Contois saturation constant, S is the substrate concentration and X is the cell mass concentration. A feature of the Contois growth model is that cell-mass growth rate depends upon the concentrations of both substrate and cellmass with growth being inhibited at high concentrations of the cellmass.

The Contois model has been used to model the aerobic degradation of waste water originating in the industrial treatment of black olives (Beltran-Heredia et al, 2000), the anaerobic treatment of dairy manure (Bhattacharya and Khai, 1987; Ghaly et al, 2000), the anaerobic digestion of ice-cream wastewater (Hu et al, 2000), the anaerobic treatment of textile wastewater (Isik and Sponza, 2005) and the aerobic biodegradation of solid municipal organic waste (Krzystek et al, 2001). Anaerobic conditions are favoured for the processing of waste materials with high levels of biodegradable organic pollutants as these can be removed with low investment and operational costs (Lettinga, 1995).

The Contois growth expression has been found to model the anaerobic reduction of sulphate by a sulphate-reducing bacteria (Moosa et al, 2002). This procedure has application in the cleaning of sulphate-containing industrial effluents and in the cleaning of acid mine drainage.

Simulation dynamics based upon Contois kinetics for the hydrolysis kinetics of swine waste, sewage sludge, cattle manure and cellulose have been found to fit experimental data (Vavilin et al, 1996). The Contois growth rate has also been used as a default growth-rate model in simulations of the cleaning of wastewater by microorganisms (Czeczot et al). The Contois growth model has been validated by comparing model predictions against experimental data (Beltran-Heredia et al, 2000; Bhattacharya and Khai, 1987; Ghaly et al, 2000; Hu et al, 2002; Isik and Sponza, 2005; Moosa et al, 2002; Vavilin et al, 1996). In (Bhattacharya and Khai, 1987; Hu et al, 2002; Isik and Sponza, 2005; Moosa et al, 2002) the Contois model was shown to be better suited to depict experimental results than other growth rate expressions.

Wastewater from the food industries contains a complex mixture of biodegradable organic materials, such as fresh and partially decomposed food scraps and crop-residues, that may be in suspension or dissolved. Lumping these into a single substrate species, and the variety of microorganisms existing in the biological reactor into a single microorganism, is a convenient mathematical approximation. Formally, the use of a model containing a single substrate and a single microorganism can be justified if the overall process kinetics are controlled by a process-rate limiting step . The work cited above suggests that in some cases this provides a reasonable approximation to an undoubtedly more complex process.

It has been suggested that when the Contois growth rate law accurately models experimental data that this indicates that the process is limited by the available surface area, causing mass-transfer limitations. When this interpretation is made, the specific growth rate is often written in the equivalent form
μ(X,S) = μmS/X
Thus as the population density of biomass increases there is an increasing obstruction to the substrate uptake and growth of any particular microbe. In the limit of large biomass concentration the Contois growth rate reduces to
μ(X,S) = μmS/X
indicating that the limiting factor is the surface area of the particulate substrate. Examples where the Contois model is interpreted as a surface limiting process include (Myint et al, 2006; Ruel et al, 2002; Vavilin et al, 1996).


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  2. S.C. Bhattacharya and P.Q. Khai. Kinetics of anaerobic cowdung digestion. Energy, 12(6):497--500, 1987.
  3. D.E. Contois. Kinetics of bacterial growth: Relationship between population density and specific growth rate of continuous cultures. Journal of General Microbiology, 21:40--50, 1959.
  4. J. Czeczot, M. Metzger, J.P. Babary, and M. Nihtilä. Filtering in adaptive control of distributed parameter bioreactors in the presence of noisy measurements. Simulation Practice and Theory, 8:39--56, 2000.
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  7. W.C. Hu, K. Thayanithy, and C.F. Forster. A kinetic study of the anaerobic digestion of ice-cream wastewater. Process Biochemistry, 37:965--971, 2002.
  8. M. Isik and D.T. Sponza. Substrate removal kinetics in an upflow anaerobic sludge blanket reactor decolorising simulated textile wastewater. Process Biochemistry, 40:1189--1198, 2005.
  9. L. Krzystek, S. Ledakowicz, H-J. Kahle, and K. Kaczorek. Degradation of household biowaste in reactors. Journal of Biotechnology, 92:103--112, 2001.
  10. G. Lettinga. Anaerobic-digestion and waste-water treatment systems. Antonie van Leeuwenhoek International Journal of General and Molecular Microbiology, 67(1):3--28, 1995.
  11. S. Moosa, M. Nemati, and S.T.L. Harrison. A kinetic study on anaerobic reduction of sulphate, Part I: Effect of sulphate concentration. Chemical Engineering Science, 57:2773--2780, 2002.
  12. M. Myint and N. Nirmalakhandan. Evaluation of first-order, second-order, and surface-limiting reactions in anaerobic hydrolysis of cattle manure. Environmental Engineering Science, 23(6):970--980, 2006.
  13. S.M. Ruel, Y. Comeau, P. Ginestet, and A. Héduit. Modeling acidogenic and sulfate-reducing processes for the determination of fermentable fractions in wastewater. Biotechnology and Bioengineering, 80(5):525--536, 2002.
  14. V.A. Vavilin, S.V. Rytov, and L. Ya Lokshina. A description of hydrolysis kinetics in anaerobic degradation of particulate organic matter. Bioresource Technology, 56:229--237, 1996.

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Page Created: 17th August 2007.
Last Updated: 5th January 2009.