| Popis: |
In this paper, we aim to use stochastic modeling approaches in order to build a model for an anaerobic digestion process. We consider a two-species and two-substrate process which is usually modeled in the deterministic context using the Anaerobic Model AM2. This model features four states representing, respectively, the concentrations of the substrate, the acidogenic bacteria, the volatile fatty acids, and the methanogenic bacteria. We propose here to build a stochastic version of this model by using three types of models: the pure jump Markov process, the Poisson model, and the Gaussian model. The pure jump Markov process is the most detailed one, it is hence valid at a microscopic size, i.e., for small-size bacteria populations, whereas the two others, which are two discrete-time approximations of the first model, are valid for the mesoscopic and macroscopic scales, which means, for medium-size and large-size bacteria populations. We also present the diffusion model which is the continuous version of the Gaussian approximation and is valid for mesoscopic and macroscopic scales. The validity domain is justified in the paper and a brief comparison between these models and with respect to the deterministic AM2 model is discussed and presented by simulation. |
