Félix Monteiro Pereira

Mathematical Modeling of Controlled-Release Systems of Herbicides Using Lignins as Matrices A Review

The herbicides applied in soils can be easily lost, owing to leaching, volatilization, and bio-and photodegradation. Controlled-release systemsusing polymeric matrices claim to solve these problems. The movement of the herbicides in the soilisalso an important phenomenon to be studied in order to evaluate the loss processes. The development of mathematical models is a relevantrequirement for simulation and optimization of such systems. This study reviews mathematical models as an initial step for modeling data obtained for controlled-release systems of herbicides (diuron, 2,4-dichlorophenoxyacetic acid, and ametryn) using sugarcane bagasse lignin as a polymeric matrix. The release kinetic studies were carried out using several acceptorsystems includinga water bath, soil, and soil-packed columns. Generally, these models take into account phenomena such as unsteady-state mass transfer by diffusion (Fickslaw) and convection, consumption by several processes, and partitioning processes, resulting in partial differential equations with respect to time and space variables.

Estimation of Solubility Effect on the Herbicide Controlled-Release Kinetics from Lignin-Based Formulations

Understanding the main phenomena involved in the controlled-release kinetics of herbicides in a water bath is a very important requisite for diffusive- parameter estimation, because, some mathematical models based on Ficks second law for diffusion have been developed to describe the controlled-release kinetic data. However, the validity of these models is restricted to the following assumptions: (1) the formulation is an isothermal slab; (2) the release occurs through the two faces of the slab; (3) the herbicide is dissolved in the water contained in the slab pores at a concentration less than the saturation concentration (cis); (4) the total sum of the individual volumes of the pores is epsilonAL (epsilon is the slab porosity, A is the slab area, and L is the slab thickness); and (5) the initial concentration of herbicide in the pores is M0/epsilonAL (M0 is the initial amount of herbicide in the matrix). The fourth assumption may be invalid for mathematical description of systems in which the herbicide concentration in the slab may be above the saturation concentration. If this were true, the final assumption would also be invalid, because the initial concentration of herbicide in the pores is cis in this case. This work presents a study of the solubility effect on the controlled-release kinetics of herbicides from lignin matrices.

Kinetic Modeling of 1‐G Ethanol Fermentations

The most recent rise in demand for bioethanol, due mainly to economic and environmental issues, has required highly productive and efficient processes. In this sense, mathematical models play an important role in the design, optimization, and control of bioreactors for ethanol production. Such bioreactors are generally modeled by a set of first-order ordinary differential equations, which are derived from mass and energy balances over bioreactors. Complementary equations have also been included to describe fermentation kinetics, based on Monod equation with additional terms accounting for inhibition effects linked to the substrate, products, and biomass. In this chapter, a reasonable number of unstructured kinetic models of 1-G ethanol fermentations have been compiled and reviewed. Segregated models, as regards the physiological state of the biomass (cell viability), have also been reviewed, and it was found that some of the analyzed kinetic models are also applied to the modeling of second-generation ethanol production processes.

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis–Menten kinetics and assessment of numerical methods

In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis–Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis–Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis–Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion–reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.