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Steady-state analysis of the Anaerobic Digestion Model No. 1 (ADM1)

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Abstract

The steady-state behavior of the Anaerobic Digestion Model No. 1 (ADM1) with respect to dilution rate and substrate concentration is analyzed in this study. Thereby, up to ten coexisting steady-state solutions are observed under the same operating conditions. The parameter region of a methane producing operation is limited regarding high dilution rates as well as low or high substrate concentrations. The underlying mechanisms causing those limits are investigated in detail, and the common core is identified, namely a positive feedback loop between growth of acetate degraders and acetate itself. The difference lies in the activation mechanisms of this feedback loop, which differs in the three investigated cases.

The comparison of the present results with literature studies of simpler two-step models reveals qualitative differences regarding the substrate concentration. Therefore, an alternative simplified model is suggested, which shows qualitatively the same bifurcation behavior as the ADM1 considering variation of the substrate concentration.

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Acknowledgements

This work was funded by the Federal State of Saxony-Anhalt under the grant Green-FC (6003398800).

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Authors and Affiliations

  1. Process Systems Engineering, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Astrid Bornhöft & Kai Sundmacher

  2. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany

    Richard Hanke-Rauschenbach & Kai Sundmacher

Authors
  1. Astrid Bornhöft
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  2. Richard Hanke-Rauschenbach
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  3. Kai Sundmacher
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Corresponding author

Correspondence to Richard Hanke-Rauschenbach.

Appendix: Monod type model

Appendix: Monod type model

A simple biochemical model for a one-step reaction in a CSTR can be described as follows:

(22)
(23)

S is the substrate concentration and X the concentration of the microbial biomass. D is the dilution rate, Y the yield coefficient, and μ the specific growth rate, which is given by a Monod kinetic as follows:

(24)

μ max is the maximal growth rate and k S the saturation constant.

The steady-states of this model can be derived analytically and are given by

(25)
(26)

The first steady-state (Eq. (25)) is the desired one, since in the second one (Eq. (26)) no microbial biomass is present and the substrate is not converted. From the equations, for the first steady-state it can be seen that the substrate concentration S depends only on the dilution rate and the kinetic parameters, but not on the inlet concentration S in. If the inlet concentration is changed, only the concentration of the microbial biomass X is influenced.

Another aspect that becomes clear at this simple model, is the region of validity of the first steady-state (Eq. (25)). Since the concentrations should be positive, for a given dilution rate, the inlet concentration has to be larger than the corresponding substrate concentration.

(27)

This fact can be seen from a biochemical point of view, also. If the inlet concentration of the substrate is too low, the maintenance metabolism of the microbial biomass is not sufficiently supplied with nutrients.

Furthermore, the dilution rate has to be chosen beneath a certain limit, such that \(S_{\mathrm {ss,1}}\) is larger than zero.

(28)

The second steady-state (Eq. (26)) is valid for the whole parameter region, but it is obviously not desired.

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Bornhöft, A., Hanke-Rauschenbach, R. & Sundmacher, K. Steady-state analysis of the Anaerobic Digestion Model No. 1 (ADM1). Nonlinear Dyn 73, 535–549 (2013). https://doi.org/10.1007/s11071-013-0807-x

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