# Mathematical modeling of acetoclastic methanogenesis in two-phase biogas-plants

Ivo Muha*, Johannes Schneider, Gabriel Wittum

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

## Abstract

In this chapter the mathematical modeling of acetoclastic methanogenesis in the second stage, i.e., the anaerobic filter, of a two-phase biogas reactor is investigated. In 2002 a very general model for anaerobic digestion (the ADM1) was published by Batstone et al. (2002). The ADM1 covers all four phases of the anaerobic digestion process (hydrolysis, acidogenesis, acetogenesis and methanogenesis). To get a further understanding of biogas-plants, the process liquid flow within the different reactor parts needs to be considered as well. The main focus of this work is to couple hydraulic patterns of process liquid flow with microbiological processes within one mathematical model. For modeling process liquid flow, the second stage of the biogas reactor is considered to be a porous medium, of which the matrix consists of plastic tower packing and the immobilized microorganisms growing on them. In order to couple flow and microbiological processes the biogas reactor needs to be spatially discretized, meaning that the biogas reactor is approximated by a computational grid consisting of triangles or quadrangles in 2D or prisms in 3D. Typically, in each grid point all variables (concentrations, pressure, etc.) are computed. Furthermore, a new inhibition factor is introduced in order to account for the limited number of plastic tower packing within the reactor. This factor decreases the uptake and growth of microorganisms if the plastic tower packing are being overpopulated. In this chapter the mathematical model is validated by means of experimental data. Furthermore, the following computational results from the derived model are investigated: effectiveness of the anaerobic filter and distribution of anaerobic digestion phases to reactor parts. Finally, it is shown that including process liquid flow within a mathematical model is necessary in order to obtain a reasonable model.

Original language English (US) Methanogenesis Biochemistry, Ecological Functions, Natural and Engineered Environments Nova Science Publishers, Inc. 79-112 34 9781633215979 9781633215672 Published - Jul 1 2014