Differential Algebraic Equation Model for a Microbial Electrolysis Cell

By Karthika Cohen

Microbial electrolysis cells (MECs) produce hydrogen from renewable organic matter, such as wastewater. Requiring less energy input than water electrolysis and with greater efficiency than fermentative hydrogen production, the technology is very promising. 

The devices use a biofilm of bacteria, which oxidizes an organic substrate to generate current. Specifically, the biofilm holds the microorganisms in place while exoelectrogenic bacteria (so called because they transfer electrons extracellularly) oxidize a substrate. Electrons are thus transferred to the anode and an external circuit then generates current due to the potential difference between the anode and cathode. 

While MECs show promise, their performance remains low due to a variety of reasons. 

Fermenting microorganisms in MECs convert substrate, such as complex wastewater, into simpler compounds, which the exoelectrogens can consume. Several reasons can be attributed to the decreased efficiency of the cells. 

For instance, other microorganism types may sometimes be accidentally introduced into the organic material fed into the MEC, such as,methanogenic or methane-producing organisms which compete with exoelectrogens for substrate, reducing the latter’s growth. Some methanogens are also capable of consuming some of the hydrogen produced at the cathode. Exoelectrogens themselves can also consume hydrogen to accelerate current generation but this can also lead to the energy loss on the electrodes. Several processes also contribute to overpotentials of the electrodes, i.e., voltage losses or inefficiencies in the MEC.

A better understanding of such device processes is needed to scale up this technology and make it more efficient.

Microbial Electrolysis Cells are biological fuel cells that produce hydrogen.

Harry Dudley (University of Colorado Boulder) presented a model to that end at a minisymposium talk titled “Sensitivity and Bifurcation Analysis of a Differential Algebraic Equation Model for a Microbial Electrolysis Cell” at the SIAM Annual Meeting being held in Portland, Ore., this week. 

Dudley proposed a semi-explicit index one differential-algebraic equation (DAE) model of a microbial electrolysis cell with an algebraic constraint on current. 

Differential equations represent the substrate, microorganism, oxidized mediator concentrations, and current. Terms represent voltage losses, concentration losses related to the reduced mediator, and activation losses. Growth rates are modeled by multiplicative Monod kinetic equations.

The biofilm retention function models two phases of the biofilm growth, a growth phase and an equilibrium phase. With data from MEC current over time for various substrates, the researchers use an ordinary least squares fit to current density data. 

Looking at best fit concentrations allows one to increase the maximum current and study how each parameter affects current density at particular times. 

Dudley’s group considers a continuous-flow or batch-cycle MEC in which methanogens and exoelectrogens compete for a single substrate such as acetate. Fermenting and hydrogenotrophic microorganisms are not considered.

Sensitivity analysis performed by his team gave insight on temporal regions that show largest impact on productivity based on reactor adjustments. Bifurcation analysis demonstrated that dilution rates must be chosen carefully to ensure that the system approaches a stable equilibrium with positive current density.

Karthika Swamy Cohen is the managing editor ofSIAM News.