Optimal biogas production in a model for anaerobic digestion

Abstract

We investigate a model for anaerobic digestion, a process used to produce biogas. The model, introduced in Weedermann et al. (J Biol Dyn 7:59–85, 2013), consists of differential equations describing the interactions of microbial populations involved in three main stages of anaerobic digestion: acidogenesis, acetogenesis, and methanogenesis. We show that this model predicts that an increased yield in biogas can be achieved in regions where operating parameters push the system into a bistable state. In some regions of bistability, biogas production occurs at only one of the steady states while in others both steady states result in biogas production with one state being more productive than the other. We demonstrate which operating parameters and state variables have the most significant impact on system performance. Surprisingly, the optimal biogas production does not always occur at a steady state where all classes of microorganisms coexist.

Appendix

1.1 Parameter values used for simulations

All of the bifurcation diagrams and numerical simulations in this paper were completed for the two different sets of parameter values given in Tables 5 and 6. Both sets were derived from the ADM1 model, [1]. The first set corresponds to standard values listed in [1] for mesophilic high rate digesters. The second set corresponds to an ADM1-based simulation of a specific installation described in [30]. In [1], all concentrations are given in units of ${\text {kg COD m}}^{-3}$, which is equivalent to ${\text {g COD/L}}$.

Table 5 Derivation of parameter values called ADM1(1) in this paper from standard values given in [1] for high rate digesters under mesophilic conditions

Table 6 Parameter values based on Wett et al. [30] were derived similarly to those in Table 5

The growth of bacteria $X_{{\text {substrate}}}$ in [1] is generally given by expressions of the form

$$\begin{aligned} g(\alpha ) = Y_{\alpha } k_{m,\alpha } \frac{\alpha }{K_S + \alpha }X_{\alpha }\cdot ({\text {possible Inhibition}}). \end{aligned}$$

In our model, $Y_{\alpha } k_{m,\alpha } = m_{\alpha }$ with $\alpha , \beta \in \{S, V, A, H\}$, see also Table 4. Following the derivation of system (2) in our model, $c_{\alpha } = Y_{\alpha }$ in relationship to the corresponding bacteria group $\alpha$, and $\gamma _{\alpha , \beta }$ corresponds to

$$\begin{aligned} \gamma _{\alpha , \beta } = \frac{1-Y_{\alpha }}{Y_{\alpha }} f_{\beta , \alpha } \end{aligned}$$

in ADM1.

The microbial death rates were set to $d_s = d_v = d_a = d_h = 0.02$.