## 1 Introduction
Goal of the transition from fossil to renewable energies is the decarbonization of the energy sector, which aims to address the question of the environmental impact of biogas plants, i.e., their carbon footprint (e.g., [15]). Renewable energy production is often much more decentralized than fossil energy production. Biogas production is widely applied in rural areas. This also poses new questions, such as:  
* What is the carbon footprint of biogas-based energy products? * What feedstock mixture is most sustainable and are there regional limitations? * How can biogas plants be included in regional energy systems? Such regional aspects of substrate availability and energy-related infrastructure are commonly modeled with geoinformation systems (GIS; e.g., [16]). The integration of biogas plants in energy systems thus links water or agricultural economies with the energy economy. This requires information transfer between the different sectors. Figure 1 shows possible system boundaries for different views on biogas plants from energy systems to microbiological processes in the AD process. This paper aims to bridge the gap between different academic fields and their respective research approaches for a beneficial integration of biogas plants in future renewable energy systems by comparing model approaches and their level of detail in anaerobic digestion literature with energy system literature. Earlier reviews on biogas modeling mainly provide an overview of research within their discipline. For example, a review from 1991 summarizes temperature and inhibitor depending microbial kinetic modeling approaches of the anaerobic treatment processes of complex organic materials [17]. Reference [18] shows modeling approaches of the AD process in the literature with respect to different kinetic approaches and generates an overview of software tools which calculate a biogas production rate based on substrate properties (2014). Reference [19] gives an overview of simplified AD process models(artificial neural networks, Fuzzy-logic, linear and non-linear regression models), as well as computational fluid dynamics modeling approaches of a digester (2012). The review in [20] summarizes existing AD process models and their modeling and kinetic parameters (2011). From an energy system point of view, reviews either regard energy system modeling in general (e.g., [21]) or greenhouse gas emissions based on biogas production [22; 23; 24; 25; 26; 27]. In comparison, this publication aims at a cross-disciplinary view of modeling methods with respect to biogas production. It thus presents a systematic review and classification of existing modeling approaches of biogas production within the different academic fields of energy systems, regional potentials, greenhouse gas emissions, and biogas processes. It focuses on an analysis of methodical concepts and modeling depths of physical and biological processes within literature with different views on the biogas production process. A systematic overview of different modeling approaches can be the basis for future cross-disciplinary views on biogas plants in energy systems by including the dynamic time-dependent behavior of the biogas process. The focus lies on biogas plant modeling within energy system studies and models of biogas production. Although computational fluid dynamics modeling is described in literature, e.g., to verify hydraulic retention times of anaerobic digesters [28] or to study hydraulic dynamics of the peripheral piping system [29], fluid flow modeling is not regarded within this paper. Furthermore, this paper does not claim to be a complete overview of every published modeling paper.