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A Catalytic Effectiveness Factor for a Microbial Electrolysis Cell Biofilm Model

The aim of this work is to propose a methodology to obtain an effectiveness factor for biofilm in a microbial electrolysis cell (MEC) system and use it to reduce a partial differential equation (PDE) biofilm MEC model to an ordinary differential equation (ODE) MEC model. The biofilm mass balances of the different species are considered. In addition, it is considered that all the involved microorganisms are attached to the anodic biological film. Three effectiveness factors are obtained from partial differential equations describing the spatial distributions of potential and substrate in the biofilm. Then, a model reduction is carried out using the global mass balances of the different species in the system. The reduced model with three uncertain but bounded effectiveness factors is evaluated numerically and analyzed in the sense of stability and parametric sensibility to demonstrate its applicability. The reduced ODE model is compared with a validated model taken from the literature, and the results are in good agreement. The biofilm effectiveness factor in MEC systems can be extended to the reduction of PDE models to obtain ODE models that are commonly used in optimization and control problems.