A simple microbial electrochemical cell model and dynamic analysis towards control design

A Catalytic Effectiveness Factor for a Microbial Electrolysis Cell Biofilm Model

“…The MEC model in (1)-( 12) predicts the noncoexistence of microbial species in biofilm, although an inert fraction remains at steady state. The coexistence of MEC microbial species has been discussed in [24].…”

“…Notice that only the equilibrium point ψ 01 exhibits stable behavior and has a physical meaning. It is said that the MEC system is operating in a desirable condition of noncoexistence of microorganisms in which only exoelectrogenic microorganisms degrade the substrate [24]. Equilibrium point ψ 02 exhibits stable behavior, but this point does not have physical meaning because this would imply a physically impossible negative value for the substrate at steady state.…”

“…where M total is the total mediator fraction per microorganism; M red is the reduced mediator fraction per exoelectrogenic microorganism; q max,e and q max,m are the maximum acetate consumption rates; µ max,e and µ max,m are the maximum growth rates; K S,e and K S,m are the saturation constants; and X max the maximum attainable biomass concentration. Table 7 summarizes the set of parameters used in the model in (23) and in the auxiliary functions (24). Notice that the biofilm in the model in ( 23) is limited by X max .…”

“…Other categories can be related to the complexity of the model, for instance, spatial dimension (1D, 2D, or 3D), time dependence, or steady state models. In this regard, most MEC models have been proposed as either ordinary differential equation (ODE) systems [21][22][23][24][25] or partial differential equation (PDE) systems [12,15,[26][27][28]. Generally, both model types also include algebraic equations (AE), resulting in ordinary differential algebraic equations (ODAE) and partial differential algebraic equations (PDAE).…”

“…The concentration of microorganisms in biofilm is mainly a function of growth kinetics. However, additional biofilm mass retention terms could be included, for instance: (i) constant parameter [22,24]; (ii) continuous AE [30]; and (iii) piecewise constant AE [30], where the maximum value is an upper-bounded constant related to the maximum mass retention (i.e., X max ).…”