  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 differential-algebraic 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 batch-cycle MECs or to continuous-flow MECs. We
conduct differential-algebraic sensitivity analysis after fitting simulations
to current density data for a batch-cycle 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 non-zero current density in a
continuous-flow 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 batch-cycle MEC or to increase
the long term current density equilibrium value in a continuous-flow MEC.
