Sensitivity and Bifurcation Analysis of a DAE Model for a Microbial Electrolysis Cell
Abstract
Microbial electrolysis cells (MECs) are a promising new technology for producing hydrogen cheaply, efficiently, and sustainably. However, to scale up this technology, we need a better understanding of the processes in the devices. In this effort, we present a differentialalgebraic equation (DAE) model of a microbial electrolysis cell with an algebraic constraint on current. We then perform sensitivity and bifurcation analysis for the DAE system. The model can be applied either to batchcycle MECs or to continuousflow MECs. We conduct differentialalgebraic sensitivity analysis after fitting simulations to current density data for a batchcycle MEC. The sensitivity analysis suggests which parameters have the greatest influence on the current density at particular times during the experiment. In particular, growth and consumption parameters for exoelectrogenic bacteria have a strong effect prior to the peak current density. An alternative strategy to maximizing peak current density is maintaining a long term stable equilibrium with nonzero current density in a continuousflow MEC. We characterize the minimum dilution rate required for a stable nonzero current equilibrium and demonstrate transcritical bifurcations in the dilution rate parameter that exchange stability between several curves of equilibria. Specifically, increasing the dilution rate transitions the system through three regimes where the stable equilibrium exhibits (i) competitive exclusion by methanogens, (ii) coexistence, and (iii) competitive exclusion by exolectrogens. Positive long term current production is only feasible in the final two regimes. These results suggest how to modify system parameters to increase peak current density in a batchcycle MEC or to increase the long term current density equilibrium value in a continuousflow MEC.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.06326
 Bibcode:
 2018arXiv180206326D
 Keywords:

 Mathematics  Dynamical Systems;
 Quantitative Biology  Other Quantitative Biology;
 37N25;
 92C40