In this work, a mathematical description of a Microbial Electrolysis Cell (MEC) is proposed, taking into account the global mass balances of the different species in the system and considering that all the involved microorganisms are attached to the anodic biological film. Three main biological reactions are introduced, which were obtained from the solution of partial differential equations describing the spatial distribution of potential and substrate in the biofilm. The simulation of the model was carried out using numerical methods, and the results are discussed.

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.

In this work, a classical linear control approach for the peroxide (H${}_2$O${}_2$) dosage in a photo-Fenton process is presented as a suitable solution for improving the efficiency in the treatment of recalcitrant organic compounds that cannot be degraded by classical wastewater treatment processes like anaerobic digestion. Experiments were carried out to degrade Lignin, Melanoidin, and Gallic acid, which are typical recalcitrant organic compounds present in some kinds of effluents such as vinasses from the Tequila and Cachaça industries. Experiments were carried in Open-Loop mode for obtaining the degradation model for the three compounds in the form of a Transfer Function, and in Closed-Loop mode for controlling the concentration of each compound. First-order Transfer Functions were obtained using the reaction curve method, and then, based on these models, the parameters of Proportional Integral controllers were calculated using the direct synthesis method. In the Closed-Loop experiments, the Total Organic Carbon removal was 39% for lignin, 7% for melanoidin, and 29% for Gallic acid, which were greater than those obtained in the Open-Loop experiments.