Modelling Biogas Production Kinetics of Various Heavy Metals Exposed Anaerobic Fermentation Process Using Sigmoidal Growth Functions

  • Yonglan TianEmail author
  • Kun Yang
  • Lei Zheng
  • Xiaoxi Han
  • Yanli Xu
  • Ying Li
  • Shusen Li
  • Xiang Xu
  • Huayong Zhang
  • Lei Zhao
Original Paper


The kinetic evaluation of the biogas potential from heavy metal stressed anaerobic fermentation process was performed using modified sigmoidal bacterial growth curve equations (modified Gompertz and Logistic) in order to investigate their suitability to describe the degradation patterns associated with varied heavy metal species and concentration. The anaerobic co-fermentation experiments were performed at mesophilic conditions with mixed cow dung and Phragmites straw as feedstocks. The results show that appropriate concentration of heavy metals brought forward the biogas peaks, shorten the lag-phase (λ) and promoted the efficiency of co-fermentation. In this way, the cumulative biogas yields expressed the one-phase process and fitted the sigmoidal bacterial growth curve equations better. Both the modified Gompertz model and Logistic model were able to represent the experimental data in the presence of heavy metals as shown by the no significant different correlation coefficients (R2). However, the discrepancies between the experimental and fitting results of the modified Gompertz model were smaller than the Logistic model which suggested that the earlier was more suitable for describing the degradation patterns under heavy metal stress. The results of this research are expected to provide theoretical guidance for studying the impact of heavy metals and modelling research of anaerobic fermentation process.

Graphic abstract


Anaerobic fermentation Kinetic study Modified gompertz model Logistic model Heavy metal Lag-phase 



Maximum cumulative biogas yields


Maximum methane production rate


Lag phase time


Correlation coefficients


Total solids



This work was funded by the Major Science and Technology Program for Water Pollution Control and Treatment [2017ZX07101003]; and the Fundamental Research Funds for the Central Universities [2018MS051].

Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Supplementary material

12649_2019_810_MOESM1_ESM.docx (150 kb)
Supplementary file1 (DOCX 149 kb)


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Research Center for Engineering Ecology and Nonlinear ScienceNorth China Electric Power UniversityBeijingChina
  2. 2.College of Resources and Environmental SciencesChina Agricultural UniversityBeijingChina

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