In this work a simulator for the estimation of effectiveness factors in heterogeneous enzymatic reactions is developed to be used as virtual laboratory for the students.

Theoretical background:
Many of the biochemical reactions catalyzed by enzymes are carried out with enzymes immobilized in solid supports. These processes have a number of advantages over those with enzymes in solution. Thus, the biocatalyst can be easily separated from the reaction products, which allows its reuse with the consequent reduction of costs and the obtaining of products of higher purity.

The solid supports used are usually porous, as this significantly increases the surface area where the enzyme is immobilized. In these cases, the internal diffusional resistances of the substrates and/or products play an important role, since profiles of radial concentrations appear in the particle, which it is necessary to know in order to estimate the real rate of the reaction. The effectiveness factor is the quotient between this real rate and that which would exist in the absence of internal diffusional limitations, indicating its value, quantitatively, the importance of these limitations. For the design of the reactors where these reactions take place, the calculation of the effectiveness factor is essential.

The diffusion-reaction differential equations that are obtained for particles with different geometries only have an analytical solution for kinetics of order zero and one. In this work, a mathematical model is presented to calculate the profiles of dimensionless concentrations of substrate and product in spherical particles and the effectiveness factor, for a Michaelis-Menten kinetics with competitive inhibition per product. To do this, a series of dimensionless variables and modules are defined that allow the diffusion-reaction equations to be transformed into their corresponding dimensionless equations and then, with a change of variable, to obtain a single differential equation of which the initial values of the variables are known. This equation can be solved numerically by the finite difference method, then obtaining the value of the efficiency factor.

Simulator as Virtual laboratory:
The calculation algorithm has been coded in the Visual Basic language for Applications, whose Editor is integrated into the Excel Spreadsheet. The simulation results are shown in the form of generalized curves, both of the concentration profiles in the particles and of the effectiveness factors, for a wide range of the modules used, thus covering most of the experimental situations that may arise, acting as a Virtual Laboratory.

This simulator can be used in subjects of two Degrees of the University of Murcia: "Biochemical Engineering", of the Degree in Chemical Engineering, and "Engineering of Biochemical Reactions. Bioreactors", of the Degree in Biotechnology.

From an educational perspective, it is interesting for students to solve the model equations using numerical calculations and to transfer the calculation algorithm to the programming language. The simulator is available in the Virtual Classroom so they can autonoumosly study the influence of the different variables involved in dimensionless modules on internal diffusional limitations and discuss these results. This tool can be used for distance learning and is also an example of flipped class where the students can do all the simulation cases by themselves and explain the results to their partners.

Keywords: Simulator, technology, virtual laboratory, virtual learning.